%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW310+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 : n028.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 18:07:06 EDT 2024 % Result : Theorem 188.18s 188.24s % Output : CNFRefutation 188.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWW310+1 : TPTP v8.2.0. Released v5.2.0. % 0.04/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Wed Jun 19 08:31:24 EDT 2024 % 0.13/0.34 % CPUTime : % 0.61/0.64 start to proof:theBenchmark % 187.86/188.10 %------------------------------------------- % 187.86/188.10 % File :CSE---1.7 % 187.86/188.10 % Problem :theBenchmark % 187.86/188.10 % Transform :cnf % 187.86/188.10 % Format :tptp:raw % 187.86/188.10 % Command :java -jar mcs_scs.jar %d %s % 187.86/188.10 % 187.86/188.10 % Result :Theorem 171.080000s % 187.86/188.10 % Output :CNFRefutation 171.080000s % 187.86/188.10 %------------------------------------------- % 187.86/188.10 %------------------------------------------------------------------------------ % 187.86/188.11 % File : SWW310+1 : TPTP v8.2.0. Released v5.2.0. % 187.86/188.11 % Domain : Software Verification % 187.86/188.11 % Problem : Hoare's Logic with Procedures 434937, 5000 axioms selected % 187.86/188.11 % Version : Especial. % 187.86/188.11 % English : % 187.86/188.11 % 187.86/188.11 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 187.86/188.11 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 187.86/188.11 % Source : [Bla11] % 187.86/188.11 % Names : hoare_434937.5000.p [Bla11] % 187.86/188.11 % 187.86/188.11 % Status : ContradictoryAxioms % 187.86/188.11 % Rating : 0.72 v8.2.0, 0.69 v8.1.0, 0.75 v7.4.0, 0.83 v7.3.0, 0.79 v7.1.0, 0.74 v7.0.0, 0.83 v6.4.0, 0.81 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 187.86/188.11 % Syntax : Number of formulae : 5229 (1699 unt; 0 def) % 187.86/188.11 % Number of atoms : 12675 (4461 equ) % 187.86/188.11 % Maximal formula atoms : 13 ( 2 avg) % 187.86/188.11 % Number of connectives : 8436 ( 990 ~; 148 |; 702 &) % 187.86/188.11 % ( 891 <=>;5705 =>; 0 <=; 0 <~>) % 187.86/188.11 % Maximal formula depth : 22 ( 6 avg) % 187.86/188.11 % Maximal term depth : 19 ( 2 avg) % 187.86/188.11 % Number of predicates : 150 ( 149 usr; 0 prp; 1-6 aty) % 187.86/188.11 % Number of functors : 395 ( 395 usr; 53 con; 0-7 aty) % 187.86/188.11 % Number of variables : 16677 (16523 !; 154 ?) % 187.86/188.11 % SPC : FOF_CAX_RFO_SEQ % 187.86/188.11 % 187.86/188.11 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 187.86/188.11 % 2011-03-01 11:39:22 % 187.86/188.11 %------------------------------------------------------------------------------ % 187.86/188.11 %----Relevant facts (4985) % 187.86/188.11 fof(fact_ext,axiom, % 187.86/188.11 ! [V_g_2,V_f_2] : % 187.86/188.11 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 187.86/188.11 => V_f_2 = V_g_2 ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_empty,axiom, % 187.86/188.11 ! [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))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 187.86/188.11 ! [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))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_triple_Oinject,axiom, % 187.86/188.11 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] : % 187.86/188.11 ( 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) % 187.86/188.11 <=> ( V_fun1_2 = V_fun1_H_2 % 187.86/188.11 & V_com_2 = V_com_H_2 % 187.86/188.11 & V_fun2_2 = V_fun2_H_2 ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_cut,axiom, % 187.86/188.11 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] : % 187.86/188.11 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 187.86/188.11 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2) % 187.86/188.11 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_hoare__derivs_Oinsert,axiom, % 187.86/188.11 ! [V_ts_2,V_t_2,V_Ga_2,T_b] : % 187.86/188.11 ( 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)))) % 187.86/188.11 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) % 187.86/188.11 => 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)) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_bot__fun__def,axiom, % 187.86/188.11 ! [V_x_2,T_c,T_b] : % 187.86/188.11 ( class_Orderings_Obot(T_b) % 187.86/188.11 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_triple_Orecs,axiom, % 187.86/188.11 ! [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) ). % 187.86/188.11 % 187.86/188.11 fof(fact_triple_Osimps_I2_J,axiom, % 187.86/188.11 ! [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) ). % 187.86/188.11 % 187.86/188.11 fof(fact_empty__not__insert,axiom, % 187.86/188.11 ! [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) ). % 187.86/188.11 % 187.86/188.11 fof(fact_insert__not__empty,axiom, % 187.86/188.11 ! [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)) ). % 187.86/188.11 % 187.86/188.11 fof(fact_doubleton__eq__iff,axiom, % 187.86/188.11 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.86/188.11 ( 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)))) % 187.86/188.11 <=> ( ( V_a_2 = V_ca_2 % 187.86/188.11 & V_ba_2 = V_d_2 ) % 187.86/188.11 | ( V_a_2 = V_d_2 % 187.86/188.11 & V_ba_2 = V_ca_2 ) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_singleton__inject,axiom, % 187.86/188.11 ! [V_ba_2,V_a_2,T_b] : % 187.86/188.11 ( 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))) % 187.86/188.11 => V_a_2 = V_ba_2 ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_bot__apply,axiom, % 187.86/188.11 ! [V_x_2,T_c,T_b] : % 187.86/188.11 ( class_Orderings_Obot(T_b) % 187.86/188.11 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_escape,axiom, % 187.86/188.11 ! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] : % 187.86/188.11 ( ! [B_Z,B_s] : % 187.86/188.11 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 187.86/188.11 => 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)))) ) % 187.86/188.11 => 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)))) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_hoare__derivs_OSkip,axiom, % 187.86/188.11 ! [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)))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 187.86/188.11 ! [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)))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_conseq2,axiom, % 187.86/188.11 ! [V_Q_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 187.86/188.11 ( 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)))) % 187.86/188.11 => ( ! [B_Z,B_s] : % 187.86/188.11 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 187.86/188.11 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 187.86/188.11 => 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)))) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_insert__code,axiom, % 187.86/188.11 ! [V_x_2,V_A_2,V_y_2,T_b] : % 187.86/188.11 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 187.86/188.11 <=> ( V_y_2 = V_x_2 % 187.86/188.11 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_insert__commute,axiom, % 187.86/188.11 ! [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)) ). % 187.86/188.11 % 187.86/188.11 fof(fact_insert__absorb2,axiom, % 187.86/188.11 ! [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) ). % 187.86/188.11 % 187.86/188.11 fof(fact_the__elem__eq,axiom, % 187.86/188.11 ! [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 ). % 187.86/188.11 % 187.86/188.11 fof(fact_conseq1,axiom, % 187.86/188.11 ! [V_Pa_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] : % 187.86/188.11 ( 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)))) % 187.86/188.11 => ( ! [B_Z,B_s] : % 187.86/188.11 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 187.86/188.11 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 187.86/188.11 => 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)))) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_Comp,axiom, % 187.86/188.11 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 187.86/188.11 ( 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)))) % 187.86/188.11 => ( 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)))) % 187.86/188.11 => 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)))) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_conseq12,axiom, % 187.86/188.11 ! [V_Q_2,V_Pa_2,V_Q_H_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] : % 187.86/188.11 ( 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)))) % 187.86/188.11 => ( ! [B_Z,B_s] : % 187.86/188.11 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 187.86/188.11 => ! [B_s_H] : % 187.86/188.11 ( ! [B_Z_H] : % 187.86/188.11 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s)) % 187.86/188.11 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) ) % 187.86/188.11 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) % 187.86/188.11 => 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)))) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 187.86/188.11 ! [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)))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_Ass,axiom, % 187.86/188.11 ! [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)))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_the__elem__def,axiom, % 187.86/188.11 ! [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))))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_Collect__conv__if,axiom, % 187.86/188.11 ! [T_b,V_a_2,V_Pa_2] : % 187.86/188.11 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 187.86/188.11 => 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))) ) % 187.86/188.11 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 187.86/188.11 => 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)) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_Collect__conv__if2,axiom, % 187.86/188.11 ! [T_b,V_a_2,V_Pa_2] : % 187.86/188.11 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 187.86/188.11 => 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))) ) % 187.86/188.11 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 187.86/188.11 => 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)) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_singleton__conv,axiom, % 187.86/188.11 ! [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))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_singleton__conv2,axiom, % 187.86/188.11 ! [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))) ). % 187.86/188.11 % 187.86/188.11 fof(fact_image__constant__conv,axiom, % 187.86/188.11 ! [V_ca_2,T_c,T_b,V_A_2] : % 187.86/188.11 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.86/188.11 => 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)) ) % 187.86/188.11 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.86/188.11 => 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))) ) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_Collect__def,axiom, % 187.86/188.11 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 187.86/188.11 % 187.86/188.11 fof(fact_image__image,axiom, % 187.86/188.11 ! [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) ). % 187.86/188.11 % 187.86/188.11 fof(fact_empty__is__image,axiom, % 187.86/188.11 ! [V_A_2,V_f_2,T_c,T_b] : % 187.86/188.11 ( 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) % 187.86/188.11 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_image__empty,axiom, % 187.86/188.11 ! [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)) ). % 187.86/188.11 % 187.86/188.11 fof(fact_image__is__empty,axiom, % 187.86/188.11 ! [V_A_2,V_f_2,T_b,T_c] : % 187.86/188.11 ( 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)) % 187.86/188.11 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_image__insert,axiom, % 187.86/188.11 ! [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)) ). % 187.86/188.11 % 187.86/188.11 fof(fact_empty__Collect__eq,axiom, % 187.86/188.11 ! [V_Pa_2,T_b] : % 187.86/188.11 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 187.86/188.11 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_Collect__empty__eq,axiom, % 187.86/188.11 ! [V_Pa_2,T_b] : % 187.86/188.11 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.86/188.11 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 187.86/188.11 % 187.86/188.11 fof(fact_empty__def,axiom, % 187.86/188.11 ! [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)) ). % 187.86/188.11 % 187.86/188.11 fof(fact_insert__Collect,axiom, % 187.86/188.11 ! [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)) ). % 187.86/188.11 % 187.86/188.11 fof(fact_com_Osimps_I13_J,axiom, % 187.86/188.11 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 187.86/188.11 % 187.86/188.11 fof(fact_com_Osimps_I12_J,axiom, % 187.86/188.11 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 187.86/188.11 % 187.86/188.11 fof(fact_com_Osimps_I9_J,axiom, % 187.86/188.11 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 187.86/188.11 % 187.86/188.11 fof(fact_com_Osimps_I8_J,axiom, % 187.86/188.11 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 187.86/188.11 % 187.86/188.11 fof(fact_com_Osimps_I25_J,axiom, % 187.86/188.11 ! [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) ). % 187.86/188.11 % 187.86/188.11 fof(fact_com_Osimps_I24_J,axiom, % 187.86/188.11 ! [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) ). % 187.86/188.11 % 187.86/188.11 fof(fact_the__eq__trivial,axiom, % 187.86/188.11 ! [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 ). % 187.86/188.11 % 187.86/188.11 fof(fact_the__sym__eq__trivial,axiom, % 187.86/188.11 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 187.86/188.11 % 187.86/188.11 fof(fact_image__ident,axiom, % 187.88/188.11 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 187.88/188.11 % 187.88/188.11 fof(fact_com_Osimps_I3_J,axiom, % 187.88/188.11 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 187.88/188.11 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 187.88/188.11 <=> ( V_com1_2 = V_com1_H_2 % 187.88/188.11 & V_com2_2 = V_com2_H_2 ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_com_Osimps_I1_J,axiom, % 187.88/188.11 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 187.88/188.11 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 187.88/188.11 <=> ( V_vname_2 = V_vname_H_2 % 187.88/188.11 & V_fun_2 = V_fun_H_2 ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_image__constant,axiom, % 187.88/188.11 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] : % 187.88/188.11 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.11 => 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))) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_equalityCE,axiom, % 187.88/188.11 ! [V_ca_2,T_b,V_B_2,V_A_2] : % 187.88/188.11 ( V_A_2 = V_B_2 % 187.88/188.11 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.11 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) % 187.88/188.11 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.11 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_emptyE,axiom, % 187.88/188.11 ! [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)))) ). % 187.88/188.11 % 187.88/188.11 fof(fact_insertCI,axiom, % 187.88/188.11 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 187.88/188.11 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 187.88/188.11 => V_a_2 = V_ba_2 ) % 187.88/188.11 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_insertE,axiom, % 187.88/188.11 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 187.88/188.11 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 187.88/188.11 => ( V_a_2 != V_ba_2 % 187.88/188.11 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_image__eqI,axiom, % 187.88/188.11 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_ba_2] : % 187.88/188.11 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 187.88/188.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 187.88/188.11 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_CollectI,axiom, % 187.88/188.11 ! [T_b,V_a_2,V_Pa_2] : % 187.88/188.11 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 187.88/188.11 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_eq__mem__trans,axiom, % 187.88/188.11 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 187.88/188.11 ( V_a_2 = V_ba_2 % 187.88/188.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 187.88/188.11 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_eqelem__imp__iff,axiom, % 187.88/188.11 ! [V_A_2,T_b,V_y_2,V_x_2] : % 187.88/188.11 ( V_x_2 = V_y_2 % 187.88/188.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.11 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_eqset__imp__iff,axiom, % 187.88/188.11 ! [V_x_2,T_b,V_B_2,V_A_2] : % 187.88/188.11 ( V_A_2 = V_B_2 % 187.88/188.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.11 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_mem__def,axiom, % 187.88/188.11 ! [V_A_2,V_x_2,T_b] : % 187.88/188.11 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.11 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_equals0D,axiom, % 187.88/188.11 ! [V_a_2,T_b,V_A_2] : % 187.88/188.11 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.11 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 187.88/188.11 % 187.88/188.11 fof(fact_empty__iff,axiom, % 187.88/188.11 ! [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)))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_ex__in__conv,axiom, % 187.88/188.12 ! [V_A_2,T_b] : % 187.88/188.12 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.12 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_all__not__in__conv,axiom, % 187.88/188.12 ! [V_A_2,T_b] : % 187.88/188.12 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.12 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__absorb,axiom, % 187.88/188.12 ! [V_A_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.12 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insertI2,axiom, % 187.88/188.12 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__ident,axiom, % 187.88/188.12 ! [V_B_2,V_A_2,V_x_2,T_b] : % 187.88/188.12 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 187.88/188.12 => ( 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) % 187.88/188.12 <=> V_A_2 = V_B_2 ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__iff,axiom, % 187.88/188.12 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 187.88/188.12 <=> ( V_a_2 = V_ba_2 % 187.88/188.12 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insertI1,axiom, % 187.88/188.12 ! [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))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_rev__image__eqI,axiom, % 187.88/188.12 ! [T_c,V_f_2,V_ba_2,V_A_2,V_x_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_imageI,axiom, % 187.88/188.12 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => 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))) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_image__iff,axiom, % 187.88/188.12 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 187.88/188.12 <=> ? [B_x] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.12 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_CollectE,axiom, % 187.88/188.12 ! [V_Pa_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.12 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_CollectD,axiom, % 187.88/188.12 ! [V_Pa_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.12 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_mem__Collect__eq,axiom, % 187.88/188.12 ! [V_Pa_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.12 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_Collect__mem__eq,axiom, % 187.88/188.12 ! [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 ). % 187.88/188.12 % 187.88/188.12 fof(fact_singletonE,axiom, % 187.88/188.12 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.12 ( 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))))) % 187.88/188.12 => V_ba_2 = V_a_2 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_singleton__iff,axiom, % 187.88/188.12 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.12 ( 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))))) % 187.88/188.12 <=> V_ba_2 = V_a_2 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__image,axiom, % 187.88/188.12 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => 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) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__compr__raw,axiom, % 187.88/188.12 ! [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))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__compr,axiom, % 187.88/188.12 ! [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))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_bot__empty__eq,axiom, % 187.88/188.12 ! [V_x_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 187.88/188.12 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_pred__equals__eq,axiom, % 187.88/188.12 ! [V_S_2,V_R_2,T_b] : % 187.88/188.12 ( 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) % 187.88/188.12 <=> V_R_2 = V_S_2 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_the__inv__into__def,axiom, % 187.88/188.12 ! [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))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_override__on__def,axiom, % 187.88/188.12 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 187.88/188.12 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.12 => 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) ) % 187.88/188.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.12 => 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) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_imageE,axiom, % 187.88/188.12 ! [V_A_2,V_f_2,T_c,V_ba_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 187.88/188.12 => ~ ! [B_x] : % 187.88/188.12 ( V_ba_2 = hAPP(V_f_2,B_x) % 187.88/188.12 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_eq__mem,axiom, % 187.88/188.12 ! [V_y_2,V_x_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 187.88/188.12 <=> V_x_2 = V_y_2 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_override__on__emptyset,axiom, % 187.88/188.12 ! [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 ). % 187.88/188.12 % 187.88/188.12 fof(fact_override__on__apply__notin,axiom, % 187.88/188.12 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 187.88/188.12 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.12 => 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) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_override__on__apply__in,axiom, % 187.88/188.12 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.12 => 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) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__singleton__eq,axiom, % 187.88/188.12 ! [V_ba_2,V_f_2,T_c,V_a_2,T_b] : % 187.88/188.12 ( 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)))))) % 187.88/188.12 <=> hAPP(V_f_2,V_a_2) = V_ba_2 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__Diff,axiom, % 187.88/188.12 ! [V_A_2,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.12 => 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 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_Diff__insert__absorb,axiom, % 187.88/188.12 ! [V_A_2,V_x_2,T_b] : % 187.88/188.12 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => 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 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_DiffI,axiom, % 187.88/188.12 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 187.88/188.12 => 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))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_DiffE,axiom, % 187.88/188.12 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.12 ( 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))) % 187.88/188.12 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimageI,axiom, % 187.88/188.12 ! [T_c,V_B_2,T_b,V_ba_2,V_a_2,V_f_2] : % 187.88/188.12 ( hAPP(V_f_2,V_a_2) = V_ba_2 % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__Diff,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_Diff__idemp,axiom, % 187.88/188.12 ! [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) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__code,axiom, % 187.88/188.12 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 187.88/188.12 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__ident,axiom, % 187.88/188.12 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 187.88/188.12 % 187.88/188.12 fof(fact_Diff__iff,axiom, % 187.88/188.12 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.12 ( 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))) % 187.88/188.12 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.12 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_DiffD1,axiom, % 187.88/188.12 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.12 ( 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))) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_DiffD2,axiom, % 187.88/188.12 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.12 ( 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))) % 187.88/188.12 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__eq,axiom, % 187.88/188.12 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 187.88/188.12 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimageD,axiom, % 187.88/188.12 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimageI2,axiom, % 187.88/188.12 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_empty__Diff,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_Diff__empty,axiom, % 187.88/188.12 ! [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 ). % 187.88/188.12 % 187.88/188.12 fof(fact_Diff__cancel,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__empty,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__Collect__eq,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__Diff1,axiom, % 187.88/188.12 ! [V_A_2,V_B_2,V_x_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 187.88/188.12 => 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) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__Diff__if,axiom, % 187.88/188.12 ! [V_A_2,V_B_2,V_x_2,T_b] : % 187.88/188.12 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 187.88/188.12 => 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) ) % 187.88/188.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 187.88/188.12 => 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)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_Diff__insert,axiom, % 187.88/188.12 ! [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)))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_Diff__insert2,axiom, % 187.88/188.12 ! [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) ). % 187.88/188.12 % 187.88/188.12 fof(fact_insert__Diff__single,axiom, % 187.88/188.12 ! [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) ). % 187.88/188.12 % 187.88/188.12 fof(fact_set__diff__eq,axiom, % 187.88/188.12 ! [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)))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__def,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__diff__def,axiom, % 187.88/188.12 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.12 ( class_Groups_Ominus(T_b) % 187.88/188.12 => 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)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_minus__apply,axiom, % 187.88/188.12 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.12 ( class_Groups_Ominus(T_b) % 187.88/188.12 => 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)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__image,axiom, % 187.88/188.12 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 187.88/188.12 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => 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)))))) ) % 187.88/188.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => 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) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 187.88/188.12 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => ( 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) % 187.88/188.12 => 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)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_inj__on__insert,axiom, % 187.88/188.12 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 187.88/188.12 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.12 & ~ 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))))))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_subset__insert__iff,axiom, % 187.88/188.12 ! [V_B_2,V_x_2,V_A_2,T_b] : % 187.88/188.12 ( 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))) % 187.88/188.12 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => 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)) ) % 187.88/188.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_diff__single__insert,axiom, % 187.88/188.12 ! [V_B_2,V_x_2,V_A_2,T_b] : % 187.88/188.12 ( 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)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.12 => 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))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimage__const,axiom, % 187.88/188.12 ! [T_c,V_A_2,V_ca_2,T_b] : % 187.88/188.12 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.12 => 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)) ) % 187.88/188.12 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.12 => 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)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_vimageE,axiom, % 187.88/188.12 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__left__comm__idem__remove,axiom, % 187.88/188.12 ! [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))))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_diff__eq__diff__eq,axiom, % 187.88/188.12 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.12 ( class_Groups_Oab__group__add(T_b) % 187.88/188.12 => ( 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) % 187.88/188.12 => ( V_a_2 = V_ba_2 % 187.88/188.12 <=> V_ca_2 = V_d_2 ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_order__refl,axiom, % 187.88/188.12 ! [V_x,T_a] : % 187.88/188.12 ( class_Orderings_Opreorder(T_a) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_equalityI,axiom, % 187.88/188.12 ! [V_B_2,V_A_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.12 => V_A_2 = V_B_2 ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_top1I,axiom, % 187.88/188.12 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__triv,axiom, % 187.88/188.12 ! [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 ). % 187.88/188.12 % 187.88/188.12 fof(fact_subsetD,axiom, % 187.88/188.12 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_UNIV__I,axiom, % 187.88/188.12 ! [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)))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_empty__subsetI,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_inj__on__empty,axiom, % 187.88/188.12 ! [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))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_predicate1D,axiom, % 187.88/188.12 ! [V_x_2,V_Q_2,V_Pa_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 187.88/188.12 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 187.88/188.12 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_rev__predicate1D,axiom, % 187.88/188.12 ! [V_Q_2,T_b,V_x_2,V_Pa_2] : % 187.88/188.12 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 187.88/188.12 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 187.88/188.12 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 187.88/188.12 => 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)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 187.88/188.12 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 187.88/188.12 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_linorder__le__cases,axiom, % 187.88/188.12 ! [V_y,V_x,T_a] : % 187.88/188.12 ( class_Orderings_Olinorder(T_a) % 187.88/188.12 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_le__funE,axiom, % 187.88/188.12 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 187.88/188.12 ( class_Orderings_Oord(T_c) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 187.88/188.12 => 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))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_equalityE,axiom, % 187.88/188.12 ! [T_b,V_B_2,V_A_2] : % 187.88/188.12 ( V_A_2 = V_B_2 % 187.88/188.12 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.12 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_xt1_I6_J,axiom, % 187.88/188.12 ! [V_z,V_x,V_y,T_a] : % 187.88/188.12 ( class_Orderings_Oorder(T_a) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_xt1_I5_J,axiom, % 187.88/188.12 ! [V_x,V_y,T_a] : % 187.88/188.12 ( class_Orderings_Oorder(T_a) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.12 => V_x = V_y ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_order__trans,axiom, % 187.88/188.12 ! [V_z,V_y,V_x,T_a] : % 187.88/188.12 ( class_Orderings_Opreorder(T_a) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_order__antisym,axiom, % 187.88/188.12 ! [V_y,V_x,T_a] : % 187.88/188.12 ( class_Orderings_Oorder(T_a) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.12 => V_x = V_y ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_xt1_I4_J,axiom, % 187.88/188.12 ! [V_c,V_a,V_b,T_a] : % 187.88/188.12 ( class_Orderings_Oorder(T_a) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.88/188.12 => ( V_b = V_c % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_ord__le__eq__trans,axiom, % 187.88/188.12 ! [V_c,V_b,V_a,T_a] : % 187.88/188.12 ( class_Orderings_Oord(T_a) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.12 => ( V_b = V_c % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_subset__trans,axiom, % 187.88/188.12 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_xt1_I3_J,axiom, % 187.88/188.12 ! [V_c,V_b,V_a,T_a] : % 187.88/188.12 ( class_Orderings_Oorder(T_a) % 187.88/188.12 => ( V_a = V_b % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_ord__eq__le__trans,axiom, % 187.88/188.12 ! [V_c,V_b,V_a,T_a] : % 187.88/188.12 ( class_Orderings_Oord(T_a) % 187.88/188.12 => ( V_a = V_b % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_order__antisym__conv,axiom, % 187.88/188.12 ! [V_x_2,V_y_2,T_b] : % 187.88/188.12 ( class_Orderings_Oorder(T_b) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.12 <=> V_x_2 = V_y_2 ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_le__funD,axiom, % 187.88/188.12 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 187.88/188.12 ( class_Orderings_Oord(T_c) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 187.88/188.12 => 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))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_order__eq__refl,axiom, % 187.88/188.12 ! [V_y,V_x,T_a] : % 187.88/188.12 ( class_Orderings_Opreorder(T_a) % 187.88/188.12 => ( V_x = V_y % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_equalityD2,axiom, % 187.88/188.12 ! [T_b,V_B_2,V_A_2] : % 187.88/188.12 ( V_A_2 = V_B_2 % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_equalityD1,axiom, % 187.88/188.12 ! [T_b,V_B_2,V_A_2] : % 187.88/188.12 ( V_A_2 = V_B_2 % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_order__eq__iff,axiom, % 187.88/188.12 ! [V_y_2,V_x_2,T_b] : % 187.88/188.12 ( class_Orderings_Oorder(T_b) % 187.88/188.12 => ( V_x_2 = V_y_2 % 187.88/188.12 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_set__eq__subset,axiom, % 187.88/188.12 ! [T_b,V_B_2,V_A_2] : % 187.88/188.12 ( V_A_2 = V_B_2 % 187.88/188.12 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_linorder__linear,axiom, % 187.88/188.12 ! [V_y,V_x,T_a] : % 187.88/188.12 ( class_Orderings_Olinorder(T_a) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.12 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_le__fun__def,axiom, % 187.88/188.12 ! [V_g_2,V_f_2,T_b,T_c] : % 187.88/188.12 ( class_Orderings_Oord(T_c) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 187.88/188.12 <=> ! [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))) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_top__apply,axiom, % 187.88/188.12 ! [V_x_2,T_c,T_b] : % 187.88/188.12 ( class_Orderings_Otop(T_b) % 187.88/188.12 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_subset__refl,axiom, % 187.88/188.12 ! [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)) ). % 187.88/188.12 % 187.88/188.12 fof(fact_top__greatest,axiom, % 187.88/188.12 ! [V_x,T_a] : % 187.88/188.12 ( class_Orderings_Otop(T_a) % 187.88/188.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_subset__UNIV,axiom, % 187.88/188.12 ! [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)))) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__idem,axiom, % 187.88/188.12 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 187.88/188.12 ( hAPP(V_f_2,V_x_2) = V_y_2 % 187.88/188.12 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_subset__inj__on,axiom, % 187.88/188.12 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 187.88/188.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.12 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_injD,axiom, % 187.88/188.12 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.12 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.88/188.12 => V_x_2 = V_y_2 ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_inj__eq,axiom, % 187.88/188.12 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.12 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.88/188.12 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_inj__fun,axiom, % 187.88/188.12 ! [T_d,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.12 => 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))) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__other,axiom, % 187.88/188.12 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 187.88/188.12 ( V_z_2 != V_x_2 % 187.88/188.12 => 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) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__twist,axiom, % 187.88/188.12 ! [V_d_2,V_ba_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] : % 187.88/188.12 ( V_a_2 != V_ca_2 % 187.88/188.12 => 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) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__apply,axiom, % 187.88/188.12 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 187.88/188.12 ( ( V_z_2 = V_x_2 % 187.88/188.12 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) % 187.88/188.12 & ( V_z_2 != V_x_2 % 187.88/188.12 => 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) ) ) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__same,axiom, % 187.88/188.12 ! [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 ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__upd,axiom, % 187.88/188.12 ! [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) ). % 187.88/188.12 % 187.88/188.12 fof(fact_fun__upd__idem__iff,axiom, % 187.88/188.12 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 187.88/188.12 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2 % 187.88/188.13 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__def,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 <=> ! [B_x] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.13 => ! [B_xa] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 187.88/188.13 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 187.88/188.13 => B_x = B_xa ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__image__subset__iff,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__image__eq__iff,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => ( 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) % 187.88/188.13 <=> V_A_2 = V_B_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__id2,axiom, % 187.88/188.13 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 187.88/188.13 % 187.88/188.13 fof(fact_diff__eq__diff__less__eq,axiom, % 187.88/188.13 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( 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) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__subsetI,axiom, % 187.88/188.13 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => ( 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))) % 187.88/188.13 => 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)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_the__inv__f__f,axiom, % 187.88/188.13 ! [V_x_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => 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 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fun__upd__def,axiom, % 187.88/188.13 ! [V_ba_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 187.88/188.13 ( ( V_x_2 = V_a_2 % 187.88/188.13 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_ba_2),V_x_2) = V_ba_2 ) % 187.88/188.13 & ( V_x_2 != V_a_2 % 187.88/188.13 => 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) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fun__left__comm__idem__insert,axiom, % 187.88/188.13 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__image__mem__iff,axiom, % 187.88/188.13 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_range__ex1__eq,axiom, % 187.88/188.13 ! [V_ba_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => ( 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))))) % 187.88/188.13 <=> ? [B_x] : % 187.88/188.13 ( V_ba_2 = hAPP(V_f_2,B_x) % 187.88/188.13 & ! [B_y] : % 187.88/188.13 ( V_ba_2 = hAPP(V_f_2,B_y) % 187.88/188.13 => B_y = B_x ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__image__set__diff,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.13 => 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)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__set__diff,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__contraD,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( V_x_2 != V_y_2 % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.88/188.13 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__iff,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.88/188.13 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.88/188.13 <=> V_x_2 = V_y_2 ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__onD,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.88/188.13 => V_x_2 = V_y_2 ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__vimage__image__eq,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => 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 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__fun__updI,axiom, % 187.88/188.13 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 187.88/188.13 => 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) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__diff,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__subsetD,axiom, % 187.88/188.13 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 187.88/188.13 ( 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)) % 187.88/188.13 => ( 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)) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 187.88/188.13 ! [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) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 187.88/188.13 ! [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) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__singleton,axiom, % 187.88/188.13 ! [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))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_set__mp,axiom, % 187.88/188.13 ! [V_x_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_set__rev__mp,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_x_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_in__mono,axiom, % 187.88/188.13 ! [V_x_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bot__least,axiom, % 187.88/188.13 ! [V_x,T_a] : % 187.88/188.13 ( class_Orderings_Obot(T_a) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__empty,axiom, % 187.88/188.13 ! [V_A_2,T_b] : % 187.88/188.13 ( 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)))) % 187.88/188.13 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_UNIV__not__empty,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_insert__mono,axiom, % 187.88/188.13 ! [V_a_2,V_D_2,V_C_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 187.88/188.13 => 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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__insertI2,axiom, % 187.88/188.13 ! [V_ba_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => 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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__insertI,axiom, % 187.88/188.13 ! [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))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__mono,axiom, % 187.88/188.13 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => 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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__image__iff,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 <=> ? [B_AA] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 187.88/188.13 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_double__diff,axiom, % 187.88/188.13 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.13 => 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 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Diff__mono,axiom, % 187.88/188.13 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Diff__subset,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__mono,axiom, % 187.88/188.13 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => 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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__UNIV,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_weaken,axiom, % 187.88/188.13 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] : % 187.88/188.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) % 187.88/188.13 => ( 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)) % 187.88/188.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_asm,axiom, % 187.88/188.13 ! [V_Ga_2,V_ts_2,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__vimage__singleton,axiom, % 187.88/188.13 ! [V_a_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => 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))))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_pred__subset__eq,axiom, % 187.88/188.13 ! [V_S_2,V_R_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_the__inv__into__into,axiom, % 187.88/188.13 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => 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)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_UNIV__def,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_range__composition,axiom, % 187.88/188.13 ! [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)))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_insert__subset,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_x_2,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 187.88/188.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__insert,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_x_2,T_b] : % 187.88/188.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_the__inv__into__f__f,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => 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 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_the__inv__into__f__eq,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_range__eqI,axiom, % 187.88/188.13 ! [T_c,T_b,V_x_2,V_f_2,V_ba_2] : % 187.88/188.13 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 187.88/188.13 => 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))))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_rangeI,axiom, % 187.88/188.13 ! [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))))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__singletonD,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,T_b] : % 187.88/188.13 ( 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))))) % 187.88/188.13 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.13 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_the__inv__into__onto,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => 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 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__the__inv__into,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Diff__UNIV,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__diff__subset,axiom, % 187.88/188.13 ! [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)))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__vimage__subset,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_surj__image__vimage__eq,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_b,T_c] : % 187.88/188.13 ( 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)) % 187.88/188.13 => 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 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_f__the__inv__into__f,axiom, % 187.88/188.13 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 187.88/188.13 => 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 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__iff__surj,axiom, % 187.88/188.13 ! [V_A_H_2,T_c,T_b,V_A_2] : % 187.88/188.13 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.13 => ( ? [B_f] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 187.88/188.13 & 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)) ) % 187.88/188.13 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_flat__lub__def,axiom, % 187.88/188.13 ! [V_ba_2,V_A_2,T_b] : % 187.88/188.13 ( ( 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))))) % 187.88/188.13 => c_Partial__Function_Oflat__lub(T_b,V_ba_2,V_A_2) = V_ba_2 ) % 187.88/188.13 & ( ~ 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))))) % 187.88/188.13 => 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)))))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_iso__tuple__UNIV__I,axiom, % 187.88/188.13 ! [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)))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 187.88/188.13 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.13 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 187.88/188.13 | ? [B_x,B_y] : % 187.88/188.13 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 187.88/188.13 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 187.88/188.13 & 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) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_psubset__insert__iff,axiom, % 187.88/188.13 ! [V_B_2,V_x_2,V_A_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 187.88/188.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 187.88/188.13 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => 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)) ) % 187.88/188.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Diff1__fold__graph,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__if,axiom, % 187.88/188.13 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] : % 187.88/188.13 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.13 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 187.88/188.13 => 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)) ) % 187.88/188.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 187.88/188.13 => 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 ) ) ) % 187.88/188.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.13 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 187.88/188.13 => 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) ) % 187.88/188.13 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 187.88/188.13 => 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)) ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_rangeE,axiom, % 187.88/188.13 ! [V_f_2,T_c,V_ba_2,T_b] : % 187.88/188.13 ( 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))))) % 187.88/188.13 => ~ ! [B_x] : V_ba_2 != hAPP(V_f_2,B_x) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__subset__eq,axiom, % 187.88/188.13 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => ( 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)) % 187.88/188.13 <=> 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__image__Compl__subset,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => 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)))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_the__inv__into__comp,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 187.88/188.13 => ( 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)))) % 187.88/188.13 => 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) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__uminus,axiom, % 187.88/188.13 ! [V_A_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_ComplI,axiom, % 187.88/188.13 ! [V_A_2,V_ca_2,T_b] : % 187.88/188.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.13 => 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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fun__Compl__def,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,T_c,T_b] : % 187.88/188.13 ( class_Groups_Ouminus(T_b) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_minus__minus,axiom, % 187.88/188.13 ! [V_a,T_a] : % 187.88/188.13 ( class_Groups_Ogroup__add(T_a) % 187.88/188.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_double__compl,axiom, % 187.88/188.13 ! [V_x,T_a] : % 187.88/188.13 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_uminus__apply,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,T_c,T_b] : % 187.88/188.13 ( class_Groups_Ouminus(T_b) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_equation__minus__iff,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Ogroup__add(T_b) % 187.88/188.13 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 187.88/188.13 <=> V_ba_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_less__minus__iff,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_minus__equation__iff,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Ogroup__add(T_b) % 187.88/188.13 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_ba_2 % 187.88/188.13 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) = V_a_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_minus__less__iff,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_neg__equal__iff__equal,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Ogroup__add(T_b) % 187.88/188.13 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 187.88/188.13 <=> V_a_2 = V_ba_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_compl__eq__compl__iff,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Lattices_Oboolean__algebra(T_b) % 187.88/188.13 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 187.88/188.13 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_neg__less__iff__less,axiom, % 187.88/188.13 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_o__assoc,axiom, % 187.88/188.13 ! [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) ). % 187.88/188.13 % 187.88/188.13 fof(fact_o__apply,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_o__eq__dest,axiom, % 187.88/188.13 ! [V_v_2,V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 187.88/188.13 ( 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) % 187.88/188.13 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_o__eq__elim,axiom, % 187.88/188.13 ! [V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 187.88/188.13 ( 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) % 187.88/188.13 => ! [B_v] : hAPP(V_a_2,hAPP(V_ba_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__comp__iff,axiom, % 187.88/188.13 ! [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] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 187.88/188.13 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) % 187.88/188.13 <=> 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) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__trans,axiom, % 187.88/188.13 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.13 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2) % 187.88/188.13 => 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) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__irrefl,axiom, % 187.88/188.13 ! [V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_double__complement,axiom, % 187.88/188.13 ! [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 ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__neq__iff,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Olinorder(T_b) % 187.88/188.13 => ( V_x_2 != V_y_2 % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_not__less__iff__gr__or__eq,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Olinorder(T_b) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 187.88/188.13 | V_x_2 = V_y_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__less__linear,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Olinorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 | V_x = V_y % 187.88/188.13 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__eq__Compl__iff,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,T_b] : % 187.88/188.13 ( 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) % 187.88/188.13 <=> V_A_2 = V_B_2 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__antisym__conv3,axiom, % 187.88/188.13 ! [V_x_2,V_y_2,T_b] : % 187.88/188.13 ( class_Orderings_Olinorder(T_b) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> V_x_2 = V_y_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__neqE,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Olinorder(T_a) % 187.88/188.13 => ( V_x != V_y % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_less__imp__neq,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => V_x != V_y ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__not__sym,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__imp__not__less,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__imp__not__eq,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => V_x != V_y ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__imp__not__eq2,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => V_y != V_x ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__asym_H,axiom, % 187.88/188.13 ! [V_b,V_a,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I9_J,axiom, % 187.88/188.13 ! [V_a,V_b,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_ord__eq__less__trans,axiom, % 187.88/188.13 ! [V_c,V_b,V_a,T_a] : % 187.88/188.13 ( class_Orderings_Oord(T_a) % 187.88/188.13 => ( V_a = V_b % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I1_J,axiom, % 187.88/188.13 ! [V_c,V_b,V_a,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( V_a = V_b % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_psubset__trans,axiom, % 187.88/188.13 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_ord__less__eq__trans,axiom, % 187.88/188.13 ! [V_c,V_b,V_a,T_a] : % 187.88/188.13 ( class_Orderings_Oord(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.13 => ( V_b = V_c % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I2_J,axiom, % 187.88/188.13 ! [V_c,V_a,V_b,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.88/188.13 => ( V_b = V_c % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__trans,axiom, % 187.88/188.13 ! [V_z,V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I10_J,axiom, % 187.88/188.13 ! [V_z,V_x,V_y,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__asym,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__cases,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Olinorder(T_a) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => ( V_x != V_y % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_o__eq__dest__lhs,axiom, % 187.88/188.13 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 187.88/188.13 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = V_ca_2 % 187.88/188.13 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_K__record__comp,axiom, % 187.88/188.13 ! [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 ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__comp,axiom, % 187.88/188.13 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => ( 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))) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_o__def,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__comp__iff2,axiom, % 187.88/188.13 ! [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] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) % 187.88/188.13 => ( 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)) % 187.88/188.13 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2) % 187.88/188.13 <=> 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) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__image__Compl__eq,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__compose,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_compl__mono,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_le__imp__neg__le,axiom, % 187.88/188.13 ! [V_b,V_a,T_a] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_compl__le__compl__iff,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Lattices_Oboolean__algebra(T_b) % 187.88/188.13 => ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_neg__le__iff__le,axiom, % 187.88/188.13 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_minus__le__iff,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( 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)) % 187.88/188.13 <=> 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)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_le__minus__iff,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( 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))) % 187.88/188.13 <=> 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__imageI2,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 187.88/188.13 ( 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) % 187.88/188.13 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__iff,axiom, % 187.88/188.13 ! [V_A_2,V_ca_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_ComplD,axiom, % 187.88/188.13 ! [V_A_2,V_ca_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_ComplE,axiom, % 187.88/188.13 ! [V_A_2,V_ca_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_minus__diff__eq,axiom, % 187.88/188.13 ! [V_b,V_a,T_a] : % 187.88/188.13 ( class_Groups_Oab__group__add(T_a) % 187.88/188.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__empty1,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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) % 187.88/188.13 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__empty2,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_less__fun__def,axiom, % 187.88/188.13 ! [V_g_2,V_f_2,T_b,T_c] : % 187.88/188.13 ( class_Orderings_Oord(T_c) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 187.88/188.13 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__subset__Compl__iff,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__anti__mono,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => 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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__not__less,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Olinorder(T_b) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__not__le,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Olinorder(T_b) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__le__less__linear,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Olinorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.13 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__le,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Oorder(T_b) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.13 & V_x_2 != V_y_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_less__le__not__le,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Opreorder(T_b) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.13 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__le__less,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Oorder(T_b) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 | V_x_2 = V_y_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_leI,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Olinorder(T_a) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_not__leE,axiom, % 187.88/188.13 ! [V_x,V_y,T_a] : % 187.88/188.13 ( class_Orderings_Olinorder(T_a) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__antisym__conv1,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Olinorder(T_b) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> V_x_2 = V_y_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__neq__le__trans,axiom, % 187.88/188.13 ! [V_b,V_a,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( V_a != V_b % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I12_J,axiom, % 187.88/188.13 ! [V_b,V_a,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( V_a != V_b % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_leD,axiom, % 187.88/188.13 ! [V_x,V_y,T_a] : % 187.88/188.13 ( class_Orderings_Olinorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.13 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__imp__le,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_linorder__antisym__conv2,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,T_b] : % 187.88/188.13 ( class_Orderings_Olinorder(T_b) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 187.88/188.13 <=> V_x_2 = V_y_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__le__imp__less__or__eq,axiom, % 187.88/188.13 ! [V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 | V_x = V_y ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__le__neq__trans,axiom, % 187.88/188.13 ! [V_b,V_a,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.13 => ( V_a != V_b % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I11_J,axiom, % 187.88/188.13 ! [V_a,V_b,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.88/188.13 => ( V_a != V_b % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__less__le__trans,axiom, % 187.88/188.13 ! [V_z,V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I7_J,axiom, % 187.88/188.13 ! [V_z,V_x,V_y,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_order__le__less__trans,axiom, % 187.88/188.13 ! [V_z,V_y,V_x,T_a] : % 187.88/188.13 ( class_Orderings_Opreorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_xt1_I8_J,axiom, % 187.88/188.13 ! [V_z,V_x,V_y,T_a] : % 187.88/188.13 ( class_Orderings_Oorder(T_a) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_psubsetD,axiom, % 187.88/188.13 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fun__upd__comp,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__compose,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__imp__inj__on,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.13 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_not__psubset__empty,axiom, % 187.88/188.13 ! [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)))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_diff__eq__diff__less,axiom, % 187.88/188.13 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.13 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.13 => ( 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) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 187.88/188.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_psubset__eq,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 & V_A_2 != V_B_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__iff__psubset__eq,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 | V_A_2 = V_B_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_psubset__imp__subset,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_psubset__subset__trans,axiom, % 187.88/188.13 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__psubset__trans,axiom, % 187.88/188.13 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_vimage__Compl,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 187.88/188.13 ! [V_x_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 187.88/188.13 => 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) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold__graph_Oequations_I1_J,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold__graph_OemptyI,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_empty__fold__graphE,axiom, % 187.88/188.13 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 => V_x_2 = V_z_2 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__the__inv__into,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.13 => 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) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Collect__neg__eq,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_comp__surj,axiom, % 187.88/188.13 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 187.88/188.13 ( 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)) % 187.88/188.13 => ( 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)) % 187.88/188.13 => 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)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__comp,axiom, % 187.88/188.13 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_comp__inj__on__iff,axiom, % 187.88/188.13 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( 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)) % 187.88/188.13 <=> 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) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_comp__inj__on,axiom, % 187.88/188.13 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( 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)) % 187.88/188.13 => 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) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__imageI,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 187.88/188.13 ( 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) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_compl__bot__eq,axiom, % 187.88/188.13 ! [T_a] : % 187.88/188.13 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_compl__top__eq,axiom, % 187.88/188.13 ! [T_a] : % 187.88/188.13 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_subset__Compl__self__eq,axiom, % 187.88/188.13 ! [V_A_2,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__UNIV__eq,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__empty__eq,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__subset,axiom, % 187.88/188.13 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.13 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2 % 187.88/188.13 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__is__surj,axiom, % 187.88/188.13 ! [V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__imp__surj,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__eq__Diff__UNIV,axiom, % 187.88/188.13 ! [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) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__is__inj,axiom, % 187.88/188.13 ! [V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__def,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.13 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__imp__bij__betw,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inj__on__strict__subset,axiom, % 187.88/188.13 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Compl__eq,axiom, % 187.88/188.13 ! [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))) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold__graph_OinsertI,axiom, % 187.88/188.13 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 187.88/188.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_surj__Compl__image__subset,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_b,T_c] : % 187.88/188.13 ( 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)) % 187.88/188.13 => 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)))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bijI,axiom, % 187.88/188.13 ! [V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 => ( 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)) % 187.88/188.13 => 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))) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__def,axiom, % 187.88/188.13 ! [V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.13 & 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)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold1Set_Ointros,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.13 => 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)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_Cantor__Bernstein,axiom, % 187.88/188.13 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( 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)) % 187.88/188.13 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 187.88/188.13 => ( 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)) % 187.88/188.13 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold__graph__permute__diff,axiom, % 187.88/188.13 ! [V_a_2,V_x_2,V_A_2,V_ba_2,T_b] : % 187.88/188.13 ( class_Groups_Oab__semigroup__mult(T_b) % 187.88/188.13 => ( 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)) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.13 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 187.88/188.13 => 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)) ) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__image__Collect__eq,axiom, % 187.88/188.13 ! [V_Pa_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => 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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__vimage__eq__inv__image,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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))) % 187.88/188.13 => 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) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inv__into__comp,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 187.88/188.13 => ( 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)))) % 187.88/188.13 => 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) ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_mk__less__def,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_R_2,T_b] : % 187.88/188.13 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2) % 187.88/188.13 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 187.88/188.13 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_psubset__imp__ex__mem,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.13 => ? [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))) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold1Set__sing,axiom, % 187.88/188.13 ! [V_ba_2,V_a_2,V_f_2,T_b] : % 187.88/188.13 ( 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)) % 187.88/188.13 <=> V_a_2 = V_ba_2 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_folding__one_Osingleton,axiom, % 187.88/188.13 ! [V_x_2,V_F_2,V_f_2,T_b] : % 187.88/188.13 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.13 => 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 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__subsetI,axiom, % 187.88/188.13 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] : % 187.88/188.13 ( ! [B_x] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.13 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) ) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 187.88/188.13 ! [V_c,V_b,V_a,T_a] : % 187.88/188.13 ( class_Groups_Oab__semigroup__mult(T_a) % 187.88/188.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_mult__left__idem,axiom, % 187.88/188.13 ! [V_b,V_a,T_a] : % 187.88/188.13 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.88/188.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_mult__idem,axiom, % 187.88/188.13 ! [V_x,T_a] : % 187.88/188.13 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.88/188.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_times_Oidem,axiom, % 187.88/188.13 ! [V_a,T_a] : % 187.88/188.13 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.88/188.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_bij__betw__inv__into,axiom, % 187.88/188.13 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.13 => 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) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fun__left__comm__idem,axiom, % 187.88/188.13 ! [T_b] : % 187.88/188.13 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 187.88/188.13 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_fold1Set__nonempty,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,V_f_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 187.88/188.13 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_empty__fold1SetE,axiom, % 187.88/188.13 ! [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)) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inv__into__injective,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] : % 187.88/188.13 ( 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) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 187.88/188.13 => V_x_2 = V_y_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inv__into__into,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 187.88/188.13 => 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)) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_f__inv__into__f,axiom, % 187.88/188.13 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] : % 187.88/188.13 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 187.88/188.13 => 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 ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inv__into__f__eq,axiom, % 187.88/188.13 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 187.88/188.13 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_inv__into__f__f,axiom, % 187.88/188.13 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.13 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.13 => 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 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__inv__into__cancel,axiom, % 187.88/188.13 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 187.88/188.13 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 187.88/188.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) % 187.88/188.13 => 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 ) ) ). % 187.88/188.13 % 187.88/188.13 fof(fact_image__surj__f__inv__f,axiom, % 187.88/188.14 ! [V_A_2,V_f_2,T_b,T_c] : % 187.88/188.14 ( 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)) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_surj__f__inv__f,axiom, % 187.88/188.14 ! [V_y_2,V_f_2,T_b,T_c] : % 187.88/188.14 ( 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)) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_surj__iff__all,axiom, % 187.88/188.14 ! [V_f_2,T_b,T_c] : % 187.88/188.14 ( 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)) % 187.88/188.14 <=> ! [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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inv__f__f,axiom, % 187.88/188.14 ! [V_x_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inv__f__eq,axiom, % 187.88/188.14 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 187.88/188.14 => 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 ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inv__into__inv__into__eq,axiom, % 187.88/188.14 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.14 => 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) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_bij__imp__bij__inv,axiom, % 187.88/188.14 ! [V_f_2,T_c,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 => 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))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inv__inv__eq,axiom, % 187.88/188.14 ! [V_f_2,T_c,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold__graph__insert__swap,axiom, % 187.88/188.14 ! [V_z_2,V_y_2,V_A_2,V_ba_2,T_b] : % 187.88/188.14 ( class_Groups_Oab__semigroup__mult(T_b) % 187.88/188.14 => ( 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)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 187.88/188.14 => 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))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inj__on__inv__into,axiom, % 187.88/188.14 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 => 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) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inv__into__image__cancel,axiom, % 187.88/188.14 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2)) % 187.88/188.14 => 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 ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_surj__imp__inj__inv,axiom, % 187.88/188.14 ! [V_f_2,T_b,T_c] : % 187.88/188.14 ( 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)) % 187.88/188.14 => 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))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inv__image__comp,axiom, % 187.88/188.14 ! [V_X_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_image__inv__f__f,axiom, % 187.88/188.14 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inj__imp__surj__inv,axiom, % 187.88/188.14 ! [V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => 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)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_o__inv__o__cancel,axiom, % 187.88/188.14 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_o__inv__distrib,axiom, % 187.88/188.14 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 => ( 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))) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_minus__mult__right,axiom, % 187.88/188.14 ! [V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Oring(T_a) % 187.88/188.14 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_minus__mult__left,axiom, % 187.88/188.14 ! [V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Oring(T_a) % 187.88/188.14 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_minus__mult__commute,axiom, % 187.88/188.14 ! [V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Oring(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_minus__mult__minus,axiom, % 187.88/188.14 ! [V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Oring(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_square__eq__iff,axiom, % 187.88/188.14 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.14 ( class_Rings_Oidom(T_b) % 187.88/188.14 => ( 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) % 187.88/188.14 <=> ( V_a_2 = V_ba_2 % 187.88/188.14 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inj__transfer,axiom, % 187.88/188.14 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => ( ! [B_y] : % 187.88/188.14 ( 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))))) % 187.88/188.14 => 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))) ) % 187.88/188.14 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one_Oremove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => ( ( 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)) % 187.88/188.14 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 187.88/188.14 & ( 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)) % 187.88/188.14 => 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)))))) ) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_insert__fold1SetE,axiom, % 187.88/188.14 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 187.88/188.14 ( 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)) % 187.88/188.14 => ~ ! [B_a,B_A] : % 187.88/188.14 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold1Set_Oequations,axiom, % 187.88/188.14 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 187.88/188.14 ( 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)) % 187.88/188.14 <=> ? [B_a,B_A] : % 187.88/188.14 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 187.88/188.14 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 187.88/188.14 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one_Oinsert__remove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( ( 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)) % 187.88/188.14 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 187.88/188.14 & ( 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)) % 187.88/188.14 => 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)))))) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite_OemptyI,axiom, % 187.88/188.14 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite_OinsertI,axiom, % 187.88/188.14 ! [V_a_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__imageI,axiom, % 187.88/188.14 ! [V_h_2,T_c,V_F_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Diff,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Collect__conjI,axiom, % 187.88/188.14 ! [V_Q_2,V_Pa_2,T_b] : % 187.88/188.14 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.14 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) % 187.88/188.14 => 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)))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Collect__subsets,axiom, % 187.88/188.14 ! [V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite,axiom, % 187.88/188.14 ! [V_A_2,T_b] : % 187.88/188.14 ( class_Finite__Set_Ofinite(T_b) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__code,axiom, % 187.88/188.14 ! [V_A_2,T_b] : % 187.88/188.14 ( class_Finite__Set_Ofinite(T_b) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__fun__UNIVD2,axiom, % 187.88/188.14 ! [T_c,T_b] : % 187.88/188.14 ( 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)))) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Plus__UNIV__iff,axiom, % 187.88/188.14 ! [T_c,T_b] : % 187.88/188.14 ( 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)))) % 187.88/188.14 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 187.88/188.14 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__option__UNIV,axiom, % 187.88/188.14 ! [T_b] : % 187.88/188.14 ( 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)))) % 187.88/188.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Prod__UNIV,axiom, % 187.88/188.14 ! [T_c,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 187.88/188.14 => 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)))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__seg__image__imp__finite,axiom, % 187.88/188.14 ! [V_n_2,V_f_2,T_b,V_A_2] : % 187.88/188.14 ( 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))) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite_Oequations_I1_J,axiom, % 187.88/188.14 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__insert,axiom, % 187.88/188.14 ! [V_A_2,V_a_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 187.88/188.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__subset,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_rev__finite__subset,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__UNIV,axiom, % 187.88/188.14 ! [T_b] : % 187.88/188.14 ( class_Finite__Set_Ofinite(T_b) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Diff2,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => ( 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))) % 187.88/188.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_bij__betw__finite,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold__graph__imp__finite,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Collect__disjI,axiom, % 187.88/188.14 ! [V_Q_2,V_Pa_2,T_b] : % 187.88/188.14 ( 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)))) % 187.88/188.14 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.14 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__surj,axiom, % 187.88/188.14 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( 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))) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Diff__insert,axiom, % 187.88/188.14 ! [V_B_2,V_a_2,V_A_2,T_b] : % 187.88/188.14 ( 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)))) % 187.88/188.14 <=> 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))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__imageD,axiom, % 187.88/188.14 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 187.88/188.14 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__compl,axiom, % 187.88/188.14 ! [V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 187.88/188.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Collect__not,axiom, % 187.88/188.14 ! [V_Pa_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.14 => ( 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)))) % 187.88/188.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__range__imageI,axiom, % 187.88/188.14 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 187.88/188.14 ( 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))))) % 187.88/188.14 => 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))))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_linorder__neqE__linordered__idom,axiom, % 187.88/188.14 ! [V_y,V_x,T_a] : % 187.88/188.14 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.14 => ( V_x != V_y % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__surj__inj,axiom, % 187.88/188.14 ! [V_f_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( 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))) % 187.88/188.14 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_endo__inj__surj,axiom, % 187.88/188.14 ! [V_f_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( 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)) % 187.88/188.14 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 187.88/188.14 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__UNIV__inj__surj,axiom, % 187.88/188.14 ! [V_f_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 187.88/188.14 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__UNIV__surj__inj,axiom, % 187.88/188.14 ! [V_f_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 187.88/188.14 => ( 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)) % 187.88/188.14 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__vimageD,axiom, % 187.88/188.14 ! [V_F_2,V_h_2,T_c,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 187.88/188.14 => ( 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)) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__vimageI,axiom, % 187.88/188.14 ! [V_h_2,T_c,V_F_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.14 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 187.88/188.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__vimage__iff,axiom, % 187.88/188.14 ! [V_F_2,V_h_2,T_c,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 187.88/188.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one_Oinsert,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => 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)) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Oremove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image__simple_Oremove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 187.88/188.14 => 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)))))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image_Oreindex,axiom, % 187.88/188.14 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.14 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 187.88/188.14 => 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) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Oinsert__remove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.14 => 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)))))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.14 => 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) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__idem_Oinsert__idem,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one_Oclosed,axiom, % 187.88/188.14 ! [V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => ( ! [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)))))) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__idem_Oin__comp__idem,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__empty__induct,axiom, % 187.88/188.14 ! [V_Pa_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 187.88/188.14 => ( ! [B_a,B_A] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 187.88/188.14 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 187.88/188.14 => 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)))))) ) ) ) % 187.88/188.14 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Collect__le__nat,axiom, % 187.88/188.14 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__Collect__less__nat,axiom, % 187.88/188.14 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Ocommute__left__comp,axiom, % 187.88/188.14 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => 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)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Ocommute__comp,axiom, % 187.88/188.14 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => 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)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 187.88/188.14 ! [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] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 187.88/188.14 => 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) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image__simple_Oempty,axiom, % 187.88/188.14 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.14 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__idem_Oidem__left__comp,axiom, % 187.88/188.14 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => 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) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__idem_Oidem__comp,axiom, % 187.88/188.14 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => 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) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image_Odistrib,axiom, % 187.88/188.14 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 187.88/188.14 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Ocommute__comp_H_H,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Ocommute__left__comp_H,axiom, % 187.88/188.14 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Ocommute__comp_H,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image__simple_Oinsert,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding_Oinsert,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__M__bounded__by__nat,axiom, % 187.88/188.14 ! [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))))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__subset__induct,axiom, % 187.88/188.14 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 187.88/188.14 => ( ! [B_a,B_F] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 187.88/188.14 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 187.88/188.14 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 187.88/188.14 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one__idem_Osubset__idem,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.14 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__conv__nat__seg__image,axiom, % 187.88/188.14 ! [V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 <=> ? [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))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Diff2__less,axiom, % 187.88/188.14 ! [V_y_2,V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.88/188.14 => 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))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Diff1__less,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold1__insert,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( class_Groups_Oab__semigroup__mult(T_b) % 187.88/188.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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)) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold__image__reindex,axiom, % 187.88/188.14 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 187.88/188.14 ( class_Groups_Oab__semigroup__mult(T_d) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 187.88/188.14 => 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) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_pigeonhole__infinite,axiom, % 187.88/188.14 ! [V_f_2,T_c,V_A_2,T_b] : % 187.88/188.14 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 187.88/188.14 => ? [B_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.14 & ~ 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)))))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 187.88/188.14 ! [V_N_2] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 187.88/188.14 <=> ? [B_m] : % 187.88/188.14 ! [B_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_infinite__UNIV__nat,axiom, % 187.88/188.14 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one__idem_Oidem,axiom, % 187.88/188.14 ! [V_x_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 187.88/188.14 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_bij__betw__same__card,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.14 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold__image__empty,axiom, % 187.88/188.14 ! [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 ). % 187.88/188.14 % 187.88/188.14 fof(fact_BIJ,axiom, % 187.88/188.14 ! [V_B_2,T_c,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.14 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2) % 187.88/188.14 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__insert__le,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__seteq,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.14 => ( 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))) % 187.88/188.14 => V_A_2 = V_B_2 ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__mono,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.14 => 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))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 187.88/188.14 ! [V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 187.88/188.14 => ( 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))) % 187.88/188.14 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__image__le,axiom, % 187.88/188.14 ! [V_f_2,T_c,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__card__le__card__Diff,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => 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)))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__image,axiom, % 187.88/188.14 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.14 => 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) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold1__singleton,axiom, % 187.88/188.14 ! [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 ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold1__singleton__def,axiom, % 187.88/188.14 ! [V_a_2,V_f_2,T_b,V_g_2] : % 187.88/188.14 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 187.88/188.14 => 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 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 187.88/188.14 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.14 => 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) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inj__on__iff__card__le,axiom, % 187.88/188.14 ! [V_B_2,T_c,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.14 => ( ? [B_f] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 187.88/188.14 & 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)) ) % 187.88/188.14 <=> 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))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__image_Oeq__fold,axiom, % 187.88/188.14 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.14 => 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) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one_Oeq__fold,axiom, % 187.88/188.14 ! [V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Diff__subset,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inj__on__iff__eq__card,axiom, % 187.88/188.14 ! [V_f_2,T_c,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.14 <=> 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) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_eq__card__imp__inj__on,axiom, % 187.88/188.14 ! [V_f_2,T_c,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( 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) % 187.88/188.14 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_pigeonhole,axiom, % 187.88/188.14 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_psubset__card__mono,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.14 => 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))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_finite__nat__set__iff__bounded,axiom, % 187.88/188.14 ! [V_N_2] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 187.88/188.14 <=> ? [B_m] : % 187.88/188.14 ! [B_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold1__def,axiom, % 187.88/188.14 ! [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)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Diff1__le,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__inj__on__le,axiom, % 187.88/188.14 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.14 => ( 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)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.14 => 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))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__bij__eq,axiom, % 187.88/188.14 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.14 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.14 => ( 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)) % 187.88/188.14 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 187.88/188.14 => ( 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)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.14 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__psubset,axiom, % 187.88/188.14 ! [V_A_2,V_B_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.14 => ( 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))) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one__idem_Oin__idem,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold__image__insert,axiom, % 187.88/188.14 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 187.88/188.14 ( class_Groups_Oab__semigroup__mult(T_c) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold1__insert__idem,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 187.88/188.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold1__in,axiom, % 187.88/188.14 ! [V_A_2,T_b] : % 187.88/188.14 ( class_Groups_Oab__semigroup__mult(T_b) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => ( ! [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)))))) % 187.88/188.14 => 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)) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 187.88/188.14 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 187.88/188.14 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OatLeastLessThan__iff,axiom, % 187.88/188.14 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 187.88/188.14 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 187.88/188.14 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 187.88/188.14 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OatLeastAtMost__iff,axiom, % 187.88/188.14 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 187.88/188.14 ( 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))) % 187.88/188.14 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 187.88/188.14 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OgreaterThan__iff,axiom, % 187.88/188.14 ! [V_k_2,V_less_2,V_i_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OlessThan__iff,axiom, % 187.88/188.14 ! [V_k_2,V_less_2,V_i_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OatLeast__iff,axiom, % 187.88/188.14 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ord_OatMost__iff,axiom, % 187.88/188.14 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__less__mono,axiom, % 187.88/188.14 ! [V_c,V_b,V_a] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__diff__iff,axiom, % 187.88/188.14 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Diff__singleton__if,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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)) ) % 187.88/188.14 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Diff__singleton,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__diff__iff,axiom, % 187.88/188.14 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_Nat_Odiff__diff__eq,axiom, % 187.88/188.14 ! [V_n,V_m,V_k] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 187.88/188.14 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_eq__diff__iff,axiom, % 187.88/188.14 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 187.88/188.14 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) % 187.88/188.14 <=> V_m_2 = V_n_2 ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__diff__cancel,axiom, % 187.88/188.14 ! [V_n,V_i] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 187.88/188.14 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__le__mono,axiom, % 187.88/188.14 ! [V_l,V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__UNIV__unit,axiom, % 187.88/188.14 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__mult__1,axiom, % 187.88/188.14 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__1__eq__mult__iff,axiom, % 187.88/188.14 ! [V_n_2,V_m_2] : % 187.88/188.14 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 187.88/188.14 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.88/188.14 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__mult__1__right,axiom, % 187.88/188.14 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__mult__eq__1__iff,axiom, % 187.88/188.14 ! [V_n_2,V_m_2] : % 187.88/188.14 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.88/188.14 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.88/188.14 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_one__reorient,axiom, % 187.88/188.14 ! [V_x_2,T_b] : % 187.88/188.14 ( class_Groups_Oone(T_b) % 187.88/188.14 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 187.88/188.14 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__1__left,axiom, % 187.88/188.14 ! [V_a,T_a] : % 187.88/188.14 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__1,axiom, % 187.88/188.14 ! [V_a,T_a] : % 187.88/188.14 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__1__right,axiom, % 187.88/188.14 ! [V_a,T_a] : % 187.88/188.14 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult_Ocomm__neutral,axiom, % 187.88/188.14 ! [V_a,T_a] : % 187.88/188.14 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__1__mult,axiom, % 187.88/188.14 ! [V_n,V_m,T_a] : % 187.88/188.14 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_square__eq__1__iff,axiom, % 187.88/188.14 ! [V_x_2,T_b] : % 187.88/188.14 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 187.88/188.14 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 187.88/188.14 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 187.88/188.14 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__less__cases,axiom, % 187.88/188.14 ! [V_Pa_2,V_n_2,V_m_2] : % 187.88/188.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 187.88/188.14 => ( ( V_m_2 = V_n_2 % 187.88/188.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 187.88/188.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.88/188.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 187.88/188.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__not__refl3,axiom, % 187.88/188.14 ! [V_t,V_s] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 187.88/188.14 => V_s != V_t ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__not__refl2,axiom, % 187.88/188.14 ! [V_m,V_n] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 187.88/188.14 => V_m != V_n ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__irrefl__nat,axiom, % 187.88/188.14 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_linorder__neqE__nat,axiom, % 187.88/188.14 ! [V_y,V_x] : % 187.88/188.14 ( V_x != V_y % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__neq__iff,axiom, % 187.88/188.14 ! [V_n_2,V_m_2] : % 187.88/188.14 ( V_m_2 != V_n_2 % 187.88/188.14 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__not__refl,axiom, % 187.88/188.14 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__square,axiom, % 187.88/188.14 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__cube,axiom, % 187.88/188.14 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__le__mono1,axiom, % 187.88/188.14 ! [V_k,V_j,V_i] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__le__mono2,axiom, % 187.88/188.14 ! [V_k,V_j,V_i] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__le__mono,axiom, % 187.88/188.14 ! [V_l,V_k,V_j,V_i] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__antisym,axiom, % 187.88/188.14 ! [V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.14 => V_m = V_n ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__trans,axiom, % 187.88/188.14 ! [V_k,V_j,V_i] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_eq__imp__le,axiom, % 187.88/188.14 ! [V_n,V_m] : % 187.88/188.14 ( V_m = V_n % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__le__linear,axiom, % 187.88/188.14 ! [V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__refl,axiom, % 187.88/188.14 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__mult__distrib2,axiom, % 187.88/188.14 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__mult__distrib,axiom, % 187.88/188.14 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__commute,axiom, % 187.88/188.14 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ). % 187.88/188.14 % 187.88/188.14 fof(fact_fold__image__distrib,axiom, % 187.88/188.14 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 187.88/188.14 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Diff__insert,axiom, % 187.88/188.14 ! [V_B_2,V_a_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.14 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 187.88/188.14 => 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)) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__less__le,axiom, % 187.88/188.14 ! [V_n_2,V_m_2] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.14 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.14 & V_m_2 != V_n_2 ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__eq__less__or__eq,axiom, % 187.88/188.14 ! [V_n_2,V_m_2] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.14 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.14 | V_m_2 = V_n_2 ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__imp__le__nat,axiom, % 187.88/188.14 ! [V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_le__neq__implies__less,axiom, % 187.88/188.14 ! [V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 => ( V_m != V_n % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__or__eq__imp__le,axiom, % 187.88/188.14 ! [V_n,V_m] : % 187.88/188.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 | V_m = V_n ) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__less__mono2,axiom, % 187.88/188.14 ! [V_l,V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__imp__diff__less,axiom, % 187.88/188.14 ! [V_n,V_k,V_j] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__le__self,axiom, % 187.88/188.14 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__le__mono2,axiom, % 187.88/188.14 ! [V_l,V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 187.88/188.14 ! [V_x,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__ring__1(T_a) % 187.88/188.14 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card_Oremove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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)))))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_termination__basic__simps_I5_J,axiom, % 187.88/188.14 ! [V_y,V_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 187.88/188.14 ! [V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 187.88/188.14 ! [V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_hom__fold1__commute,axiom, % 187.88/188.14 ! [V_N_2,V_h_2,T_b] : % 187.88/188.14 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 187.88/188.14 => ( ! [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)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.14 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => 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)) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card_Oinsert__remove,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => 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)))))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_card__Suc__Diff1,axiom, % 187.88/188.14 ! [V_x_2,V_A_2,T_b] : % 187.88/188.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.14 => 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) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_folding__one__idem_Ohom__commute,axiom, % 187.88/188.14 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 187.88/188.14 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 187.88/188.14 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 187.88/188.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.14 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.14 => 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)) ) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_lessI,axiom, % 187.88/188.14 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_Suc__mono,axiom, % 187.88/188.14 ! [V_n,V_m] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__add__Suc1,axiom, % 187.88/188.14 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__add__Suc2,axiom, % 187.88/188.14 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ). % 187.88/188.14 % 187.88/188.14 fof(fact_less__iff__Suc__add,axiom, % 187.88/188.14 ! [V_n_2,V_m_2] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.14 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__mult__commute,axiom, % 187.88/188.14 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__Suc__right,axiom, % 187.88/188.14 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__mult__distrib2,axiom, % 187.88/188.14 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_mult__Suc,axiom, % 187.88/188.14 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__mult__assoc,axiom, % 187.88/188.14 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__mult__distrib,axiom, % 187.88/188.14 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_Suc__mult__cancel1,axiom, % 187.88/188.14 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.14 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) % 187.88/188.14 <=> V_m_2 = V_n_2 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_Suc__inject,axiom, % 187.88/188.14 ! [V_y,V_x] : % 187.88/188.14 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 187.88/188.14 => V_x = V_y ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__add__right__cancel,axiom, % 187.88/188.14 ! [V_n_2,V_k_2,V_m_2] : % 187.88/188.14 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) % 187.88/188.14 <=> V_m_2 = V_n_2 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__add__left__cancel,axiom, % 187.88/188.14 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.14 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) % 187.88/188.14 <=> V_m_2 = V_n_2 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__add__assoc,axiom, % 187.88/188.14 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat_Oinject,axiom, % 187.88/188.14 ! [V_nat_H_2,V_nat_2] : % 187.88/188.14 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 187.88/188.14 <=> V_nat_2 = V_nat_H_2 ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__Suc__shift,axiom, % 187.88/188.14 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__Suc,axiom, % 187.88/188.14 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__add__left__commute,axiom, % 187.88/188.14 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__Suc__right,axiom, % 187.88/188.14 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.14 % 187.88/188.14 fof(fact_nat__add__commute,axiom, % 187.88/188.14 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ). % 187.88/188.14 % 187.88/188.14 fof(fact_Suc__n__not__n,axiom, % 187.88/188.14 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 187.88/188.14 % 187.88/188.14 fof(fact_n__not__Suc__n,axiom, % 187.88/188.14 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inj__on__add__nat,axiom, % 187.88/188.14 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ). % 187.88/188.14 % 187.88/188.14 fof(fact_inj__Suc,axiom, % 187.88/188.14 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 187.88/188.14 ! [V_c,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 187.88/188.14 ! [V_d,V_c,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 187.88/188.14 ! [V_d,V_c,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 187.88/188.14 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__right__imp__eq,axiom, % 187.88/188.14 ! [V_c,V_a,V_b,T_a] : % 187.88/188.14 ( class_Groups_Ocancel__semigroup__add(T_a) % 187.88/188.14 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) % 187.88/188.14 => V_b = V_c ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__imp__eq,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 187.88/188.14 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 187.88/188.14 => V_b = V_c ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__left__imp__eq,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Ocancel__semigroup__add(T_a) % 187.88/188.14 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 187.88/188.14 => V_b = V_c ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__right__cancel,axiom, % 187.88/188.14 ! [V_ca_2,V_a_2,V_ba_2,T_b] : % 187.88/188.14 ( class_Groups_Ocancel__semigroup__add(T_b) % 187.88/188.14 => ( 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) % 187.88/188.14 <=> V_ba_2 = V_ca_2 ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__left__cancel,axiom, % 187.88/188.14 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.14 ( class_Groups_Ocancel__semigroup__add(T_b) % 187.88/188.14 => ( 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) % 187.88/188.14 <=> V_ba_2 = V_ca_2 ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oab__semigroup__add(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_crossproduct__eq,axiom, % 187.88/188.14 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 187.88/188.14 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 187.88/188.14 => ( 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)) % 187.88/188.14 <=> ( V_w_2 = V_x_2 % 187.88/188.14 | V_y_2 = V_z_2 ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 187.88/188.14 ! [V_b,V_m,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_crossproduct__noteq,axiom, % 187.88/188.14 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.14 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 187.88/188.14 => ( ( V_a_2 != V_ba_2 % 187.88/188.14 & V_ca_2 != V_d_2 ) % 187.88/188.14 <=> 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)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 187.88/188.14 ! [V_z,V_y,V_x,T_a] : % 187.88/188.14 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_termination__basic__simps_I1_J,axiom, % 187.88/188.14 ! [V_z,V_y,V_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_termination__basic__simps_I2_J,axiom, % 187.88/188.14 ! [V_y,V_z,V_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_termination__basic__simps_I3_J,axiom, % 187.88/188.14 ! [V_z,V_y,V_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_termination__basic__simps_I4_J,axiom, % 187.88/188.14 ! [V_y,V_z,V_x] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__Suc__diff__eq1,axiom, % 187.88/188.14 ! [V_m,V_j,V_k] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.88/188.14 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_diff__Suc__diff__eq2,axiom, % 187.88/188.14 ! [V_m,V_j,V_k] : % 187.88/188.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.88/188.14 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__le__cancel__right,axiom, % 187.88/188.14 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 187.88/188.14 => ( 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))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__le__cancel__left,axiom, % 187.88/188.14 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 187.88/188.14 => ( 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))) % 187.88/188.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__right__mono,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__left__mono,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__mono,axiom, % 187.88/188.14 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__le__imp__le__right,axiom, % 187.88/188.14 ! [V_b,V_c,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__le__imp__le__left,axiom, % 187.88/188.14 ! [V_b,V_a,V_c,T_a] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__less__imp__less__left,axiom, % 187.88/188.14 ! [V_b,V_a,V_c,T_a] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__less__imp__less__right,axiom, % 187.88/188.14 ! [V_b,V_c,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__strict__mono,axiom, % 187.88/188.14 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__strict__left__mono,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__strict__right__mono,axiom, % 187.88/188.14 ! [V_c,V_b,V_a,T_a] : % 187.88/188.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.88/188.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 187.88/188.14 % 187.88/188.14 fof(fact_add__less__cancel__left,axiom, % 187.88/188.14 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 187.88/188.14 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__less__cancel__right,axiom, % 187.88/188.15 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__class_Odistrib,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_combine__common__factor,axiom, % 187.88/188.15 ! [V_c,V_b,V_e,V_a,T_a] : % 187.88/188.15 ( class_Rings_Osemiring(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__add__cancel,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__diff__cancel,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_minus__add__cancel,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__minus__cancel,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_minus__add,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_minus__add__distrib,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oab__group__add(T_a) % 187.88/188.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__less__eq,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__Suc__eq,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.15 | V_m_2 = V_n_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__less__eq,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__mult__less__cancel1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__less__less__Suc__eq,axiom, % 187.88/188.15 ! [V_m_2,V_n_2] : % 187.88/188.15 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 187.88/188.15 <=> V_n_2 = V_m_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__antisym,axiom, % 187.88/188.15 ! [V_m,V_n] : % 187.88/188.15 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 187.88/188.15 => V_m = V_n ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__SucI,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__lessI,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__trans__Suc,axiom, % 187.88/188.15 ! [V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__SucE,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 187.88/188.15 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => V_m = V_n ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__lessD,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__less__SucD,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__n__not__le__n,axiom, % 187.88/188.15 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__less__eq__eq,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__Suc__eq,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.15 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__le__mono,axiom, % 187.88/188.15 ! [V_m_2,V_n_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__SucI,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__SucE,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 187.88/188.15 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__leD,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__mult__le__cancel1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__add__less1,axiom, % 187.88/188.15 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__add__less2,axiom, % 187.88/188.15 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__add__left__cancel__less,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_trans__less__add1,axiom, % 187.88/188.15 ! [V_m,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_trans__less__add2,axiom, % 187.88/188.15 ! [V_m,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__less__mono1,axiom, % 187.88/188.15 ! [V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__less__mono,axiom, % 187.88/188.15 ! [V_l,V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__add__eq__less,axiom, % 187.88/188.15 ! [V_n,V_m,V_l,V_k] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__lessD1,axiom, % 187.88/188.15 ! [V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__Suc__Suc,axiom, % 187.88/188.15 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__diff__diff,axiom, % 187.88/188.15 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__add2,axiom, % 187.88/188.15 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__add1,axiom, % 187.88/188.15 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__iff__add,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.15 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__add__left__cancel__le,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_trans__le__add1,axiom, % 187.88/188.15 ! [V_m,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_trans__le__add2,axiom, % 187.88/188.15 ! [V_m,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__le__mono1,axiom, % 187.88/188.15 ! [V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__le__mono,axiom, % 187.88/188.15 ! [V_l,V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__leD2,axiom, % 187.88/188.15 ! [V_n,V_k,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__leD1,axiom, % 187.88/188.15 ! [V_n,V_k,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__leE,axiom, % 187.88/188.15 ! [V_n,V_k,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 187.88/188.15 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__add__inverse2,axiom, % 187.88/188.15 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__add__inverse,axiom, % 187.88/188.15 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__diff__left,axiom, % 187.88/188.15 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__cancel,axiom, % 187.88/188.15 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__cancel2,axiom, % 187.88/188.15 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 187.88/188.15 ! [V_m,V_a,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 187.88/188.15 ! [V_a,V_m,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 187.88/188.15 ! [V_m,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 187.88/188.15 ! [V_y,V_x,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__ring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__less__le__mono,axiom, % 187.88/188.15 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__le__less__mono,axiom, % 187.88/188.15 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__add__one,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_eq__add__iff2,axiom, % 187.88/188.15 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Oring(T_b) % 187.88/188.15 => ( 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) % 187.88/188.15 <=> 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) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_eq__add__iff1,axiom, % 187.88/188.15 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Oring(T_b) % 187.88/188.15 => ( 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) % 187.88/188.15 <=> 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 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__minus__eq__add,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_ab__diff__minus,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oab__group__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__def,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__le__lessD,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__less__Suc__eq,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 187.88/188.15 <=> V_n_2 = V_m_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__leI,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__imp__less__Suc,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__le__eq,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__Suc__eq__le,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__eq__Suc__le,axiom, % 187.88/188.15 ! [V_m_2,V_n_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__less__Suc,axiom, % 187.88/188.15 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__diff__le,axiom, % 187.88/188.15 ! [V_m,V_n] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__diff__conv,axiom, % 187.88/188.15 ! [V_k_2,V_j_2,V_i_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__diff__inverse,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__add__assoc2,axiom, % 187.88/188.15 ! [V_i,V_j,V_k] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__diff__assoc2,axiom, % 187.88/188.15 ! [V_i,V_j,V_k] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__add__assoc,axiom, % 187.88/188.15 ! [V_i,V_j,V_k] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__imp__diff__is__add,axiom, % 187.88/188.15 ! [V_k_2,V_j_2,V_i_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 187.88/188.15 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__add__diff__inverse2,axiom, % 187.88/188.15 ! [V_m,V_n] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__diff__conv2,axiom, % 187.88/188.15 ! [V_i_2,V_j_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__diff__assoc,axiom, % 187.88/188.15 ! [V_i,V_j,V_k] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__add__diff__inverse,axiom, % 187.88/188.15 ! [V_m,V_n] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__add__diff,axiom, % 187.88/188.15 ! [V_m,V_n,V_k] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__diff__conv,axiom, % 187.88/188.15 ! [V_i_2,V_k_2,V_j_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__diff__right,axiom, % 187.88/188.15 ! [V_i,V_j,V_k] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__Suc__1,axiom, % 187.88/188.15 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__eq__Suc__le__raw,axiom, % 187.88/188.15 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__add__iff1,axiom, % 187.88/188.15 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> 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)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__add__iff2,axiom, % 187.88/188.15 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> 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))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__add__iff2,axiom, % 187.88/188.15 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> 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))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__add__iff1,axiom, % 187.88/188.15 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> 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)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 187.88/188.15 ! [V_ry,V_rx,V_lx,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 187.88/188.15 ! [V_ry,V_rx,V_lx,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 187.88/188.15 ! [V_rx,V_ly,V_lx,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 187.88/188.15 ! [V_rx,V_ly,V_lx,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 187.88/188.15 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 187.88/188.15 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 187.88/188.15 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comp__cong,axiom, % 187.88/188.15 ! [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] : % 187.88/188.15 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) % 187.88/188.15 => 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) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card__insert__if,axiom, % 187.88/188.15 ! [V_x_2,V_A_2,T_b] : % 187.88/188.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.15 => 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) ) % 187.88/188.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.15 => 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)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card__insert__disjoint,axiom, % 187.88/188.15 ! [V_x_2,V_A_2,T_b] : % 187.88/188.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.15 => 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)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card__insert,axiom, % 187.88/188.15 ! [V_x_2,V_A_2,T_b] : % 187.88/188.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 => 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)))))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card_Oinsert,axiom, % 187.88/188.15 ! [V_x_2,V_A_2,T_b] : % 187.88/188.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.15 => 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)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__less__add__iff2,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__less__add__iff1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__eq__add__iff2,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 187.88/188.15 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__diff__add__eq2,axiom, % 187.88/188.15 ! [V_n,V_m,V_u,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__le__add__iff2,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__eq__add__iff1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 187.88/188.15 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__diff__add__eq1,axiom, % 187.88/188.15 ! [V_n,V_m,V_u,V_i,V_j] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__le__add__iff1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__Suc__eq__diff__pred,axiom, % 187.88/188.15 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ). % 187.88/188.15 % 187.88/188.15 fof(fact_left__add__mult__distrib,axiom, % 187.88/188.15 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__eq__plus1__left,axiom, % 187.88/188.15 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__eq__plus1,axiom, % 187.88/188.15 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_finite__fun__UNIVD1,axiom, % 187.88/188.15 ! [T_c,T_b] : % 187.88/188.15 ( 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)))) % 187.88/188.15 => ( 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)) % 187.88/188.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_inj__on__diff__nat,axiom, % 187.88/188.15 ! [V_k_2,V_N_2] : % 187.88/188.15 ( ! [B_x] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 187.88/188.15 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 187.88/188.15 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_convex__bound__lt,axiom, % 187.88/188.15 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_fold__image__1,axiom, % 187.88/188.15 ! [V_f_2,V_S_2,T_b,T_c] : % 187.88/188.15 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.15 => ( ! [B_x] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 187.88/188.15 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 187.88/188.15 => 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) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card__Plus,axiom, % 187.88/188.15 ! [V_B_2,T_c,V_A_2,T_b] : % 187.88/188.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.15 => 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)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_fold__image__cong,axiom, % 187.88/188.15 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 187.88/188.15 ( class_Groups_Oab__semigroup__mult(T_c) % 187.88/188.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 => ( ! [B_x] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.15 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 187.88/188.15 => 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) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 187.88/188.15 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.15 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.15 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__zeroE,axiom, % 187.88/188.15 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le0,axiom, % 187.88/188.15 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__less__Suc,axiom, % 187.88/188.15 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ). % 187.88/188.15 % 187.88/188.15 fof(fact_folding__image__simple__idem_Oidem,axiom, % 187.88/188.15 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.15 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.15 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_bot__nat__def,axiom, % 187.88/188.15 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__case__0,axiom, % 187.88/188.15 ! [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 ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__reorient,axiom, % 187.88/188.15 ! [V_x_2,T_b] : % 187.88/188.15 ( class_Groups_Ozero(T_b) % 187.88/188.15 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 187.88/188.15 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__0__iff,axiom, % 187.88/188.15 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.15 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 187.88/188.15 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2) % 187.88/188.15 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add_Ocomm__neutral,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Ocomm__monoid__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__0__right,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Omonoid__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_double__zero__sym,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 187.88/188.15 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__0,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Ocomm__monoid__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__0__left,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Omonoid__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__zero__left,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Omult__zero(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__zero__right,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Omult__zero(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__eq__0__iff,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Oring__no__zero__divisors(T_b) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.15 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.15 | V_ba_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_no__zero__divisors,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Ono__zero__divisors(T_a) % 187.88/188.15 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.15 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_divisors__zero,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Ono__zero__divisors(T_a) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.15 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.15 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__0__right,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__self,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_eq__iff__diff__eq__0,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oab__group__add(T_b) % 187.88/188.15 => ( V_a_2 = V_ba_2 % 187.88/188.15 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_right__minus__eq,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_b) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.15 <=> V_a_2 = V_ba_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__neq__one,axiom, % 187.88/188.15 ! [T_a] : % 187.88/188.15 ( class_Rings_Ozero__neq__one(T_a) % 187.88/188.15 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_one__neq__zero,axiom, % 187.88/188.15 ! [T_a] : % 187.88/188.15 ( class_Rings_Ozero__neq__one(T_a) % 187.88/188.15 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__equal__zero,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 187.88/188.15 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__equal__0__iff__equal,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_b) % 187.88/188.15 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.15 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_equal__neg__zero,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 187.88/188.15 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__0__equal__iff__equal,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_b) % 187.88/188.15 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 187.88/188.15 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_minus__zero,axiom, % 187.88/188.15 ! [T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__neq__Zero,axiom, % 187.88/188.15 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Zero__neq__Suc,axiom, % 187.88/188.15 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat_Osimps_I3_J,axiom, % 187.88/188.15 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Suc__not__Zero,axiom, % 187.88/188.15 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat_Osimps_I2_J,axiom, % 187.88/188.15 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Zero__not__Suc,axiom, % 187.88/188.15 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__less0,axiom, % 187.88/188.15 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neq0__conv,axiom, % 187.88/188.15 ! [V_n_2] : % 187.88/188.15 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__nat__zero__code,axiom, % 187.88/188.15 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.15 % 187.88/188.15 fof(fact_gr__implies__not0,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.15 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_gr0I,axiom, % 187.88/188.15 ! [V_n] : % 187.88/188.15 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__eq__self__zero,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 187.88/188.15 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__is__0,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_Nat_Oadd__0__right,axiom, % 187.88/188.15 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 187.88/188.15 % 187.88/188.15 fof(fact_plus__nat_Oadd__0,axiom, % 187.88/188.15 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 187.88/188.15 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__0__eq,axiom, % 187.88/188.15 ! [V_n_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 187.88/188.15 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__0__eq__0,axiom, % 187.88/188.15 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_minus__nat_Odiff__0,axiom, % 187.88/188.15 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__self__eq__0,axiom, % 187.88/188.15 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diffs0__imp__equal,axiom, % 187.88/188.15 ! [V_n,V_m] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 => V_m = V_n ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__0,axiom, % 187.88/188.15 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__0__right,axiom, % 187.88/188.15 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__is__0,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__cancel1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 187.88/188.15 <=> ( V_m_2 = V_n_2 % 187.88/188.15 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__cancel2,axiom, % 187.88/188.15 ! [V_n_2,V_k_2,V_m_2] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) % 187.88/188.15 <=> ( V_m_2 = V_n_2 % 187.88/188.15 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__mult__eq__cancel__disj,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 187.88/188.15 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 | V_m_2 = V_n_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card__Plus__conv__if,axiom, % 187.88/188.15 ! [V_B_2,T_c,V_A_2,T_b] : % 187.88/188.15 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 187.88/188.15 => 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)) ) % 187.88/188.15 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 187.88/188.15 => 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) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__nonneg__nonneg,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__nonneg__eq__0__iff,axiom, % 187.88/188.15 ! [V_y_2,V_x_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__comm__monoid__add(T_b) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.15 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.15 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__increasing,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__increasing2,axiom, % 187.88/188.15 ! [V_a,V_b,V_c,T_a] : % 187.88/188.15 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__nonpos__nonpos,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__le__square,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__ring(T_a) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__le__mult__iff,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 187.88/188.15 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__le__0__iff,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 187.88/188.15 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__nonneg__nonneg,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__nonneg__nonpos,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__nonneg__nonpos2,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__nonpos__nonneg,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__nonpos__nonpos,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__right__mono,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__left__mono,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__mult__left__mono,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__comm__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__right__mono__neg,axiom, % 187.88/188.15 ! [V_c,V_a,V_b,T_a] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__left__mono__neg,axiom, % 187.88/188.15 ! [V_c,V_a,V_b,T_a] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__mono_H,axiom, % 187.88/188.15 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__mono,axiom, % 187.88/188.15 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__semiring(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_split__mult__pos__le,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__ring(T_a) % 187.88/188.15 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 187.88/188.15 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_split__mult__neg__le,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.88/188.15 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 187.88/188.15 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__neg__neg,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__pos__pos,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_pos__add__strict,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__strict__left__mono__neg,axiom, % 187.88/188.15 ! [V_c,V_a,V_b,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__strict__right__mono__neg,axiom, % 187.88/188.15 ! [V_c,V_a,V_b,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_comm__mult__strict__left__mono,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__strict__left__mono,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__strict__right__mono,axiom, % 187.88/188.15 ! [V_c,V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__neg__neg,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__neg__pos,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__cancel__left__neg,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__less__mult__pos2,axiom, % 187.88/188.15 ! [V_a,V_b,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__less__mult__pos,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__pos__neg2,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__pos__neg,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__pos__pos,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__cancel__left__pos,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__cancel__left__disj,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 187.88/188.15 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__cancel__right__disj,axiom, % 187.88/188.15 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 187.88/188.15 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__square__less__zero,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Rings_Olinordered__ring(T_a) % 187.88/188.15 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__iff__diff__le__0,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 187.88/188.15 <=> 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))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__iff__diff__less__0,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 187.88/188.15 <=> 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))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__scale__eq__noteq,axiom, % 187.88/188.15 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 187.88/188.15 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 187.88/188.15 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.15 => ( ( V_a = V_b % 187.88/188.15 & V_c != V_d ) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_sum__squares__eq__zero__iff,axiom, % 187.88/188.15 ! [V_y_2,V_x_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.15 => ( 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) % 187.88/188.15 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.15 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__one__le__zero,axiom, % 187.88/188.15 ! [T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.15 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__le__one,axiom, % 187.88/188.15 ! [T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_not__one__less__zero,axiom, % 187.88/188.15 ! [T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.15 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__less__one,axiom, % 187.88/188.15 ! [T_a] : % 187.88/188.15 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__0__le__iff__le,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_le__minus__self__iff,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__le__0__iff__le,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_minus__le__self__iff,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( 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)) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__less__nonneg,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__less__0__iff__less,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_neg__0__less__iff__less,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.15 => ( 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))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__minus__self__iff,axiom, % 187.88/188.15 ! [V_a_2,T_b] : % 187.88/188.15 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_right__minus,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_eq__neg__iff__add__eq__0,axiom, % 187.88/188.15 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_b) % 187.88/188.15 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 187.88/188.15 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_left__minus,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_ab__left__minus,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Oab__group__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_minus__unique,axiom, % 187.88/188.15 ! [V_b,V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__0,axiom, % 187.88/188.15 ! [V_a,T_a] : % 187.88/188.15 ( class_Groups_Ogroup__add(T_a) % 187.88/188.15 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_gr0__conv__Suc,axiom, % 187.88/188.15 ! [V_n_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.88/188.15 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__Suc0,axiom, % 187.88/188.15 ! [V_n_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 187.88/188.15 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_less__Suc__eq__0__disj,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.15 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 | ? [B_j] : % 187.88/188.15 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__is__1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.88/188.15 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.88/188.15 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.15 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_one__is__add,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) % 187.88/188.15 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.88/188.15 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.15 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.15 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_add__gr__0,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) % 187.88/188.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 187.88/188.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card_Oempty,axiom, % 187.88/188.15 ! [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) ). % 187.88/188.15 % 187.88/188.15 fof(fact_card__infinite,axiom, % 187.88/188.15 ! [V_A_2,T_b] : % 187.88/188.15 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.15 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__eq__1__iff,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.88/188.15 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.88/188.15 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_zero__less__diff,axiom, % 187.88/188.15 ! [V_m_2,V_n_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 187.88/188.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_diff__less,axiom, % 187.88/188.15 ! [V_m,V_n] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__0__less__mult__iff,axiom, % 187.88/188.15 ! [V_n_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 187.88/188.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__cancel1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 187.88/188.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__cancel2,axiom, % 187.88/188.15 ! [V_n_2,V_k_2,V_m_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 187.88/188.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.88/188.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__mono1,axiom, % 187.88/188.15 ! [V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_mult__less__mono2,axiom, % 187.88/188.15 ! [V_k,V_j,V_i] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.88/188.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.88/188.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__mult__eq__cancel1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.88/188.15 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 187.88/188.15 <=> V_m_2 = V_n_2 ) ) ). % 187.88/188.15 % 187.88/188.15 fof(fact_nat__mult__less__cancel1,axiom, % 187.88/188.15 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__add__0,axiom, % 187.88/188.16 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__is__0__eq_H,axiom, % 187.88/188.16 ! [V_n,V_m] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__is__0__eq,axiom, % 187.88/188.16 ! [V_n_2,V_m_2] : % 187.88/188.16 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_One__nat__def,axiom, % 187.88/188.16 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__eq__self__implies__10,axiom, % 187.88/188.16 ! [V_n,V_m] : % 187.88/188.16 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 187.88/188.16 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.88/188.16 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__case__Suc,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__nonpos__neg,axiom, % 187.88/188.16 ! [V_b,V_a,T_a] : % 187.88/188.16 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__neg__nonpos,axiom, % 187.88/188.16 ! [V_b,V_a,T_a] : % 187.88/188.16 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__strict__increasing2,axiom, % 187.88/188.16 ! [V_c,V_b,V_a,T_a] : % 187.88/188.16 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__strict__increasing,axiom, % 187.88/188.16 ! [V_c,V_b,V_a,T_a] : % 187.88/188.16 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__nonneg__pos,axiom, % 187.88/188.16 ! [V_b,V_a,T_a] : % 187.88/188.16 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__pos__nonneg,axiom, % 187.88/188.16 ! [V_b,V_a,T_a] : % 187.88/188.16 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__left__le__imp__le,axiom, % 187.88/188.16 ! [V_b,V_a,V_c,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__right__le__imp__le,axiom, % 187.88/188.16 ! [V_b,V_c,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__less__imp__less__left,axiom, % 187.88/188.16 ! [V_b,V_a,V_c,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__left__less__imp__less,axiom, % 187.88/188.16 ! [V_b,V_a,V_c,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__less__imp__less__right,axiom, % 187.88/188.16 ! [V_b,V_c,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__right__less__imp__less,axiom, % 187.88/188.16 ! [V_b,V_c,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__le__less__imp__less,axiom, % 187.88/188.16 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__less__le__imp__less,axiom, % 187.88/188.16 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__strict__mono_H,axiom, % 187.88/188.16 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__strict__mono,axiom, % 187.88/188.16 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__le__cancel__left__neg,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__le__cancel__left__pos,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sum__squares__ge__zero,axiom, % 187.88/188.16 ! [V_y,V_x,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__ring(T_a) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sum__squares__le__zero__iff,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.16 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sum__squares__gt__zero__iff,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__ring__strict(T_b) % 187.88/188.16 => ( 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)))) % 187.88/188.16 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.16 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_not__sum__squares__lt__zero,axiom, % 187.88/188.16 ! [V_y,V_x,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__ring(T_a) % 187.88/188.16 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__right__le__one__le,axiom, % 187.88/188.16 ! [V_y,V_x,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__left__le__one__le,axiom, % 187.88/188.16 ! [V_y,V_x,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zero__less__two,axiom, % 187.88/188.16 ! [T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__eq__0__iff,axiom, % 187.88/188.16 ! [V_A_2,T_b] : % 187.88/188.16 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.16 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__ge__0__finite,axiom, % 187.88/188.16 ! [V_A_2,T_b] : % 187.88/188.16 ( 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))) % 187.88/188.16 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__Suc__less,axiom, % 187.88/188.16 ! [V_i,V_n] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Suc__pred,axiom, % 187.88/188.16 ! [V_n] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.16 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_n__less__m__mult__n,axiom, % 187.88/188.16 ! [V_m,V_n] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_n__less__n__mult__m,axiom, % 187.88/188.16 ! [V_m,V_n] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_one__less__mult,axiom, % 187.88/188.16 ! [V_m,V_n] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__diff__split,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,V_Pa_2] : % 187.88/188.16 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 187.88/188.16 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 187.88/188.16 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.88/188.16 & ! [B_d] : % 187.88/188.16 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 187.88/188.16 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__diff__split__asm,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,V_Pa_2] : % 187.88/188.16 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 187.88/188.16 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 187.88/188.16 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.88/188.16 | ? [B_d] : % 187.88/188.16 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 187.88/188.16 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_one__le__mult__iff,axiom, % 187.88/188.16 ! [V_n_2,V_m_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 187.88/188.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) % 187.88/188.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__le__cancel2,axiom, % 187.88/188.16 ! [V_n_2,V_k_2,V_m_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 187.88/188.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__le__cancel1,axiom, % 187.88/188.16 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 187.88/188.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__mult__le__cancel1,axiom, % 187.88/188.16 ! [V_n_2,V_m_2,V_k_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__less__Suc2,axiom, % 187.88/188.16 ! [V_i_2,V_M_2] : % 187.88/188.16 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 187.88/188.16 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__less,axiom, % 187.88/188.16 ! [V_i_2,V_M_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 187.88/188.16 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__less__Suc,axiom, % 187.88/188.16 ! [V_i_2,V_M_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 187.88/188.16 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_convex__bound__le,axiom, % 187.88/188.16 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__semiring__1(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 187.88/188.16 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_finite__PlusD_I2_J,axiom, % 187.88/188.16 ! [V_B_2,V_A_2,T_c,T_b] : % 187.88/188.16 ( 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))) % 187.88/188.16 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_finite__PlusD_I1_J,axiom, % 187.88/188.16 ! [V_B_2,V_A_2,T_c,T_b] : % 187.88/188.16 ( 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))) % 187.88/188.16 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_finite__Plus,axiom, % 187.88/188.16 ! [V_B_2,T_c,V_A_2,T_b] : % 187.88/188.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.16 => 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))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_finite__Plus__iff,axiom, % 187.88/188.16 ! [V_B_2,V_A_2,T_c,T_b] : % 187.88/188.16 ( 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))) % 187.88/188.16 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__gt__0__iff,axiom, % 187.88/188.16 ! [V_A_2,T_b] : % 187.88/188.16 ( 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))) % 187.88/188.16 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.16 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_finite__UNIV__card__ge__0,axiom, % 187.88/188.16 ! [T_b] : % 187.88/188.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 187.88/188.16 => 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))))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Suc__diff__1,axiom, % 187.88/188.16 ! [V_n] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.16 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Suc__pred_H,axiom, % 187.88/188.16 ! [V_n] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.16 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__eq__if,axiom, % 187.88/188.16 ! [V_n,V_m] : % 187.88/188.16 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 187.88/188.16 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__eq__if,axiom, % 187.88/188.16 ! [V_n,V_m] : % 187.88/188.16 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.16 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 187.88/188.16 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 187.88/188.16 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card_Oeq__fold__g,axiom, % 187.88/188.16 ! [V_A_2,T_b] : % 187.88/188.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__def,axiom, % 187.88/188.16 ! [V_A_2,T_b] : % 187.88/188.16 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 187.88/188.16 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.16 => 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)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_UNIV__Plus__UNIV,axiom, % 187.88/188.16 ! [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)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_triple_Osize_I1_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_even__less__0__iff,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_triple_Osize_I2_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Plus__eq__empty__conv,axiom, % 187.88/188.16 ! [V_B_2,V_A_2,T_c,T_b] : % 187.88/188.16 ( 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)) % 187.88/188.16 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.16 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card__Suc__eq,axiom, % 187.88/188.16 ! [V_k_2,V_A_2,T_b] : % 187.88/188.16 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 187.88/188.16 <=> ? [B_b,B_B] : % 187.88/188.16 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 187.88/188.16 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 187.88/188.16 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 187.88/188.16 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I4_J,axiom, % 187.88/188.16 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_double__eq__0__iff,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.16 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.16 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I2_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I1_J,axiom, % 187.88/188.16 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__Suc,axiom, % 187.88/188.16 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__odd__less__0,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I12_J,axiom, % 187.88/188.16 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_ex__least__nat__less,axiom, % 187.88/188.16 ! [V_n_2,V_Pa_2] : % 187.88/188.16 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 187.88/188.16 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 187.88/188.16 => ? [B_k] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 187.88/188.16 & ! [B_i] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 187.88/188.16 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 187.88/188.16 & 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)))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__1__neg,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.16 => ( 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)) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__neg,axiom, % 187.88/188.16 ! [V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__if,axiom, % 187.88/188.16 ! [V_x,T_a] : % 187.88/188.16 ( class_Groups_Osgn__if(T_a) % 187.88/188.16 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 187.88/188.16 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__odd__nonzero,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Int_Oring__char__0(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => 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) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__sgn,axiom, % 187.88/188.16 ! [V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__0__0,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.16 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.16 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn0,axiom, % 187.88/188.16 ! [T_a] : % 187.88/188.16 ( class_Groups_Osgn__if(T_a) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__times,axiom, % 187.88/188.16 ! [V_b,V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__0,axiom, % 187.88/188.16 ! [T_b] : % 187.88/188.16 ( class_Rings_Oring__1(T_b) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__add,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Oring__1(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => 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))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__mult,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Oring__1(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => 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))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__diff,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Oring__1(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => 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))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__1,axiom, % 187.88/188.16 ! [T_b] : % 187.88/188.16 ( class_Rings_Oring__1(T_b) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__minus,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Oring__1(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => 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))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__less,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__greater,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I10_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I9_J,axiom, % 187.88/188.16 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__double__eq__0__iff,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Int_Oring__char__0(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.16 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.16 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__1__pos,axiom, % 187.88/188.16 ! [V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.16 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_sgn__pos,axiom, % 187.88/188.16 ! [V_a,T_a] : % 187.88/188.16 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I13_J,axiom, % 187.88/188.16 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I5_J,axiom, % 187.88/188.16 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_card_Oneutral,axiom, % 187.88/188.16 ! [V_A_2,T_b] : % 187.88/188.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.16 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.16 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_expand__Suc,axiom, % 187.88/188.16 ! [V_v] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I11_J,axiom, % 187.88/188.16 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I3_J,axiom, % 187.88/188.16 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fold1__eq__fold,axiom, % 187.88/188.16 ! [V_a_2,V_A_2,T_b] : % 187.88/188.16 ( class_Groups_Oab__semigroup__mult(T_b) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.16 => 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) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I37_J,axiom, % 187.88/188.16 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I36_J,axiom, % 187.88/188.16 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I4_J,axiom, % 187.88/188.16 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 187.88/188.16 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) % 187.88/188.16 <=> ( V_fun_2 = V_fun_H_2 % 187.88/188.16 & V_com1_2 = V_com1_H_2 % 187.88/188.16 & V_com2_2 = V_com2_H_2 ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I2_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 187.88/188.16 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) % 187.88/188.16 <=> ( V_loc_2 = V_loc_H_2 % 187.88/188.16 & V_fun_2 = V_fun_H_2 % 187.88/188.16 & V_com_2 = V_com_H_2 ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__reorient,axiom, % 187.88/188.16 ! [V_x_2,V_w_2,T_b] : % 187.88/188.16 ( class_Int_Onumber(T_b) % 187.88/188.16 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 187.88/188.16 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_eq__number__of,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.16 & class_Int_Oring__char__0(T_b) ) % 187.88/188.16 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 187.88/188.16 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_le__number__of,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.16 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__number__of,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.16 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__number__of__left,axiom, % 187.88/188.16 ! [V_z,V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__number__of__eq,axiom, % 187.88/188.16 ! [V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__add,axiom, % 187.88/188.16 ! [V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__number__of__left,axiom, % 187.88/188.16 ! [V_z,V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_arith__simps_I32_J,axiom, % 187.88/188.16 ! [V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__mult,axiom, % 187.88/188.16 ! [V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__diff,axiom, % 187.88/188.16 ! [V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__number__of__eq,axiom, % 187.88/188.16 ! [V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fold__empty,axiom, % 187.88/188.16 ! [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 ). % 187.88/188.16 % 187.88/188.16 fof(fact_arith__simps_I30_J,axiom, % 187.88/188.16 ! [V_w,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__minus,axiom, % 187.88/188.16 ! [V_w,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I23_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I22_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I34_J,axiom, % 187.88/188.16 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I35_J,axiom, % 187.88/188.16 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I11_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I10_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I27_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I26_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I45_J,axiom, % 187.88/188.16 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I44_J,axiom, % 187.88/188.16 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I15_J,axiom, % 187.88/188.16 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I14_J,axiom, % 187.88/188.16 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fold__image__def,axiom, % 187.88/188.16 ! [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)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_le__number__of__eq__not__less,axiom, % 187.88/188.16 ! [V_w_2,V_v_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber(T_b) % 187.88/188.16 & class_Orderings_Olinorder(T_b) ) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> ~ 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))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_right__distrib__number__of,axiom, % 187.88/188.16 ! [V_c,V_b,V_v,T_b] : % 187.88/188.16 ( ( class_Int_Onumber(T_b) % 187.88/188.16 & class_Rings_Osemiring(T_b) ) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_left__distrib__number__of,axiom, % 187.88/188.16 ! [V_v,V_b,V_a,T_b] : % 187.88/188.16 ( ( class_Int_Onumber(T_b) % 187.88/188.16 & class_Rings_Osemiring(T_b) ) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__number__of__diff1,axiom, % 187.88/188.16 ! [V_c,V_w,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__number__of__diff2,axiom, % 187.88/188.16 ! [V_w,V_c,V_v,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_left__diff__distrib__number__of,axiom, % 187.88/188.16 ! [V_v,V_b,V_a,T_b] : % 187.88/188.16 ( ( class_Int_Onumber(T_b) % 187.88/188.16 & class_Rings_Oring(T_b) ) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_right__diff__distrib__number__of,axiom, % 187.88/188.16 ! [V_c,V_b,V_v,T_b] : % 187.88/188.16 ( ( class_Int_Onumber(T_b) % 187.88/188.16 & class_Rings_Oring(T_b) ) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_minus__number__of__mult,axiom, % 187.88/188.16 ! [V_z,V_w,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Ints__number__of,axiom, % 187.88/188.16 ! [V_w_2,T_b] : % 187.88/188.16 ( class_Int_Onumber__ring(T_b) % 187.88/188.16 => 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))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_folding_Oeq__fold,axiom, % 187.88/188.16 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fold__def,axiom, % 187.88/188.16 ! [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)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 187.88/188.16 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 187.88/188.16 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 187.88/188.16 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fold1__eq__fold__idem,axiom, % 187.88/188.16 ! [V_a_2,V_A_2,T_b] : % 187.88/188.16 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_minus__fold__remove,axiom, % 187.88/188.16 ! [V_B_2,V_A_2,T_b] : % 187.88/188.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_folding__one_Oeq__fold_H,axiom, % 187.88/188.16 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.16 => 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) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_hoare__derivs_OIf,axiom, % 187.88/188.16 ! [V_d_2,V_Q_2,V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 187.88/188.16 ( 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)))) % 187.88/188.16 => ( 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)))) % 187.88/188.16 => 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)))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__rec,axiom, % 187.88/188.16 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.16 => 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)))))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 187.88/188.16 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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)))))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__insert,axiom, % 187.88/188.16 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.16 => 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)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 187.88/188.16 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.16 => 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) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 187.88/188.16 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__pred,axiom, % 187.88/188.16 ! [V_w,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_plus__numeral__code_I9_J,axiom, % 187.88/188.16 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_minus__numeral__code_I6_J,axiom, % 187.88/188.16 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__eq__number__of__int__code,axiom, % 187.88/188.16 ! [V_l_2,V_k_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_minus__numeral__code_I5_J,axiom, % 187.88/188.16 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__number__of__int__code,axiom, % 187.88/188.16 ! [V_l_2,V_k_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_times__numeral__code_I5_J,axiom, % 187.88/188.16 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_odd__less__0,axiom, % 187.88/188.16 ! [V_z_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_odd__nonzero,axiom, % 187.88/188.16 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.16 % 187.88/188.16 fof(fact_le__imp__0__less,axiom, % 187.88/188.16 ! [V_z] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__0,axiom, % 187.88/188.16 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__0__right,axiom, % 187.88/188.16 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__zminus__inverse2,axiom, % 187.88/188.16 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zminus__0,axiom, % 187.88/188.16 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__bin__lemma,axiom, % 187.88/188.16 ! [V_l_2,V_k_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zmult__zless__mono2,axiom, % 187.88/188.16 ! [V_k,V_j,V_i] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_int__one__le__iff__zero__less,axiom, % 187.88/188.16 ! [V_z_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_pos__zmult__eq__1__iff,axiom, % 187.88/188.16 ! [V_n_2,V_m_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 187.88/188.16 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.88/188.16 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.88/188.16 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_int__0__less__1,axiom, % 187.88/188.16 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zle__diff1__eq,axiom, % 187.88/188.16 ! [V_z_2,V_w_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_pred__def,axiom, % 187.88/188.16 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zmult__1,axiom, % 187.88/188.16 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 187.88/188.16 % 187.88/188.16 fof(fact_zmult__1__right,axiom, % 187.88/188.16 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 187.88/188.16 % 187.88/188.16 fof(fact_zmult__assoc,axiom, % 187.88/188.16 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zmult__commute,axiom, % 187.88/188.16 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zmult__zminus,axiom, % 187.88/188.16 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zdiff__zmult__distrib2,axiom, % 187.88/188.16 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zdiff__zmult__distrib,axiom, % 187.88/188.16 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zless__linear,axiom, % 187.88/188.16 ! [V_y,V_x] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 187.88/188.16 | V_x = V_y % 187.88/188.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zminus__zminus,axiom, % 187.88/188.16 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 187.88/188.16 % 187.88/188.16 fof(fact_zle__refl,axiom, % 187.88/188.16 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zle__linear,axiom, % 187.88/188.16 ! [V_w,V_z] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 187.88/188.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zle__trans,axiom, % 187.88/188.16 ! [V_k,V_j,V_i] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zle__antisym,axiom, % 187.88/188.16 ! [V_w,V_z] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 187.88/188.16 => V_z = V_w ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_le__iff__pred__less,axiom, % 187.88/188.16 ! [V_l_2,V_k_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zless__le,axiom, % 187.88/188.16 ! [V_w_2,V_z_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 187.88/188.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 187.88/188.16 & V_z_2 != V_w_2 ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__int__def,axiom, % 187.88/188.16 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__int__def__symmetric,axiom, % 187.88/188.16 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__strict__right__mono,axiom, % 187.88/188.16 ! [V_k,V_j,V_i] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zminus__zadd__distrib,axiom, % 187.88/188.16 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__zmult__distrib2,axiom, % 187.88/188.16 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__zmult__distrib,axiom, % 187.88/188.16 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__assoc,axiom, % 187.88/188.16 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__left__commute,axiom, % 187.88/188.16 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__commute,axiom, % 187.88/188.16 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__left__mono,axiom, % 187.88/188.16 ! [V_k,V_j,V_i] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zadd__zless__mono,axiom, % 187.88/188.16 ! [V_z,V_z_H,V_w,V_w_H] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zless__imp__add1__zle,axiom, % 187.88/188.16 ! [V_z,V_w] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add1__zle__eq,axiom, % 187.88/188.16 ! [V_z_2,V_w_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zle__add1__eq__le,axiom, % 187.88/188.16 ! [V_z_2,V_w_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zless__add1__eq,axiom, % 187.88/188.16 ! [V_z_2,V_w_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 187.88/188.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 187.88/188.16 | V_w_2 = V_z_2 ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 187.88/188.16 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zsgn__def,axiom, % 187.88/188.16 ! [V_i] : % 187.88/188.16 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.16 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 187.88/188.16 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 187.88/188.16 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => 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)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_peek__and__def,axiom, % 187.88/188.16 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) % 187.88/188.16 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) % 187.88/188.16 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm,axiom, % 187.88/188.16 ! [T_b] : % 187.88/188.16 ( class_Groups_Oab__semigroup__mult(T_b) % 187.88/188.16 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => 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)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.88/188.16 => V_y_2 = V_x_2 ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 187.88/188.16 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.16 => 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) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__equality,axiom, % 187.88/188.16 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.88/188.16 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_q__pos__lemma,axiom, % 187.88/188.16 ! [V_r_H,V_q_H,V_b_H] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_q__neg__lemma,axiom, % 187.88/188.16 ! [V_r_H,V_q_H,V_b_H] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_unique__quotient__lemma,axiom, % 187.88/188.16 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zdiv__mono2__lemma,axiom, % 187.88/188.16 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 187.88/188.16 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_unique__quotient__lemma__neg,axiom, % 187.88/188.16 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zdiv__mono2__neg__lemma,axiom, % 187.88/188.16 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 187.88/188.16 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_self__quotient__aux1,axiom, % 187.88/188.16 ! [V_q,V_r,V_a] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.16 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__is__id,axiom, % 187.88/188.16 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 187.88/188.16 % 187.88/188.16 fof(fact_int__0__neq__1,axiom, % 187.88/188.16 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 187.88/188.16 % 187.88/188.16 fof(fact_self__quotient__aux2,axiom, % 187.88/188.16 ! [V_q,V_r,V_a] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.16 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 187.88/188.16 ! [V_y,V_x] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 187.88/188.16 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 187.88/188.16 ! [V_y,V_x] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Loop,axiom, % 187.88/188.16 ! [V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 187.88/188.16 ( 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)))) % 187.88/188.16 => 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)))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 187.88/188.16 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.16 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 187.88/188.16 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.16 => ? [B_y_H] : % 187.88/188.16 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 187.88/188.16 & 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)) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 187.88/188.16 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__number__of__diff__1,axiom, % 187.88/188.16 ! [V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I5_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 187.88/188.16 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 187.88/188.16 <=> ( V_fun_2 = V_fun_H_2 % 187.88/188.16 & V_com_2 = V_com_H_2 ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Pls__def,axiom, % 187.88/188.16 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.16 % 187.88/188.16 fof(fact_rel__simps_I19_J,axiom, % 187.88/188.16 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_rel__simps_I2_J,axiom, % 187.88/188.16 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__Pls__right,axiom, % 187.88/188.16 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__Pls,axiom, % 187.88/188.16 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__Pls,axiom, % 187.88/188.16 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 187.88/188.16 % 187.88/188.16 fof(fact_diff__bin__simps_I1_J,axiom, % 187.88/188.16 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 187.88/188.16 % 187.88/188.16 fof(fact_minus__Pls,axiom, % 187.88/188.16 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I52_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I53_J,axiom, % 187.88/188.16 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I28_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I29_J,axiom, % 187.88/188.16 ! [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) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I46_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I47_J,axiom, % 187.88/188.16 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I38_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I39_J,axiom, % 187.88/188.16 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I16_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osimps_I17_J,axiom, % 187.88/188.16 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__Pls,axiom, % 187.88/188.16 ! [T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_semiring__norm_I112_J,axiom, % 187.88/188.16 ! [T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__numeral__0,axiom, % 187.88/188.16 ! [V_a,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__numeral__0__right,axiom, % 187.88/188.16 ! [V_a,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_bin__less__0__simps_I1_J,axiom, % 187.88/188.16 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_semiring__norm_I113_J,axiom, % 187.88/188.16 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__number__of__Pls,axiom, % 187.88/188.16 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.16 % 187.88/188.16 fof(fact_zero__is__num__zero,axiom, % 187.88/188.16 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 187.88/188.16 % 187.88/188.16 fof(fact_eq__number__of__0,axiom, % 187.88/188.16 ! [V_v_2] : % 187.88/188.16 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_eq__0__number__of,axiom, % 187.88/188.16 ! [V_v_2] : % 187.88/188.16 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__nat__number__of,axiom, % 187.88/188.16 ! [V_v_H_2,V_v_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 187.88/188.16 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 187.88/188.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_le__nat__number__of,axiom, % 187.88/188.16 ! [V_v_H_2,V_v_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 187.88/188.16 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_le__special_I1_J,axiom, % 187.88/188.16 ! [V_y_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.16 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_le__special_I3_J,axiom, % 187.88/188.16 ! [V_x_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.16 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__special_I1_J,axiom, % 187.88/188.16 ! [V_y_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.16 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__special_I3_J,axiom, % 187.88/188.16 ! [V_x_2,T_b] : % 187.88/188.16 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.16 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.16 => ( 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))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_less__0__number__of,axiom, % 187.88/188.16 ! [V_v_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 187.88/188.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_add__nat__number__of,axiom, % 187.88/188.16 ! [V_v_H,V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I14_J,axiom, % 187.88/188.16 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_com_Osize_I6_J,axiom, % 187.88/188.16 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__number__of__mult__left,axiom, % 187.88/188.16 ! [V_k,V_v_H,V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_mult__nat__number__of,axiom, % 187.88/188.16 ! [V_v_H,V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Suc__diff__number__of,axiom, % 187.88/188.16 ! [V_m,V_v] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of2,axiom, % 187.88/188.16 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 187.88/188.16 % 187.88/188.16 fof(fact_eq__special_I1_J,axiom, % 187.88/188.16 ! [V_y_2,T_b] : % 187.88/188.16 ( class_Int_Onumber__ring(T_b) % 187.88/188.16 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 187.88/188.16 <=> 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)))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_eq__special_I3_J,axiom, % 187.88/188.16 ! [V_x_2,T_b] : % 187.88/188.16 ( class_Int_Onumber__ring(T_b) % 187.88/188.16 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.16 <=> 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)))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__1__add__number__of,axiom, % 187.88/188.16 ! [V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_nat__number__of__add__1,axiom, % 187.88/188.16 ! [V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.88/188.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nats__number__of,axiom, % 187.88/188.16 ! [V_w_2,T_b] : % 187.88/188.16 ( class_Int_Onumber__ring(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 187.88/188.16 => 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))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_tsub__def,axiom, % 187.88/188.16 ! [V_x,V_y] : % 187.88/188.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 187.88/188.16 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 187.88/188.16 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_iszero__def,axiom, % 187.88/188.16 ! [V_z_2,T_b] : % 187.88/188.16 ( class_Rings_Osemiring__1(T_b) % 187.88/188.16 => ( c_Int_Oiszero(T_b,V_z_2) % 187.88/188.16 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_iszero__0,axiom, % 187.88/188.16 ! [T_a] : % 187.88/188.16 ( class_Rings_Osemiring__1(T_a) % 187.88/188.16 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_not__iszero__1,axiom, % 187.88/188.16 ! [T_a] : % 187.88/188.16 ( class_Rings_Osemiring__1(T_a) % 187.88/188.16 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_succ__pred,axiom, % 187.88/188.16 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 187.88/188.16 % 187.88/188.16 fof(fact_succ__def,axiom, % 187.88/188.16 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.88/188.16 % 187.88/188.16 fof(fact_iszero__Numeral0,axiom, % 187.88/188.16 ! [T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nats__0,axiom, % 187.88/188.16 ! [T_b] : % 187.88/188.16 ( class_Rings_Osemiring__1(T_b) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nats__add,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Osemiring__1(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 187.88/188.16 => 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))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nats__mult,axiom, % 187.88/188.16 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.16 ( class_Rings_Osemiring__1(T_b) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 187.88/188.16 => 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))) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nats__1,axiom, % 187.88/188.16 ! [T_b] : % 187.88/188.16 ( class_Rings_Osemiring__1(T_b) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 187.88/188.16 ! [V_y,V_x] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_number__of__succ,axiom, % 187.88/188.16 ! [V_k,T_a] : % 187.88/188.16 ( class_Int_Onumber__ring(T_a) % 187.88/188.16 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_tsub__eq,axiom, % 187.88/188.16 ! [V_x,V_y] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 187.88/188.16 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_eq__number__of__eq,axiom, % 187.88/188.16 ! [V_y_2,V_x_2,T_b] : % 187.88/188.16 ( class_Int_Onumber__ring(T_b) % 187.88/188.16 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 187.88/188.16 <=> 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)))) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Suc__nat__number__of__add,axiom, % 187.88/188.16 ! [V_n,V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.16 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ) % 187.88/188.16 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.16 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_decr__mult__lemma,axiom, % 187.88/188.16 ! [V_k_2,V_Pa_2,V_d_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 187.88/188.16 => ( ! [B_x] : % 187.88/188.16 ( hBOOL(hAPP(V_Pa_2,B_x)) % 187.88/188.16 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.88/188.16 => ! [B_x] : % 187.88/188.16 ( hBOOL(hAPP(V_Pa_2,B_x)) % 187.88/188.16 => 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)))) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_incr__mult__lemma,axiom, % 187.88/188.16 ! [V_k_2,V_Pa_2,V_d_2] : % 187.88/188.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 187.88/188.16 => ( ! [B_x] : % 187.88/188.16 ( hBOOL(hAPP(V_Pa_2,B_x)) % 187.88/188.16 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 187.88/188.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.88/188.16 => ! [B_x] : % 187.88/188.16 ( hBOOL(hAPP(V_Pa_2,B_x)) % 187.88/188.16 => 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)))) ) ) ) ) ). % 187.88/188.16 % 187.88/188.16 fof(fact_Suc__nat__number__of,axiom, % 187.88/188.16 ! [V_v] : % 187.88/188.16 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_eq__special_I2_J,axiom, % 187.88/188.17 ! [V_y_2,T_b] : % 187.88/188.17 ( class_Int_Onumber__ring(T_b) % 187.88/188.17 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 187.88/188.17 <=> 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)))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_eq__special_I4_J,axiom, % 187.88/188.17 ! [V_x_2,T_b] : % 187.88/188.17 ( class_Int_Onumber__ring(T_b) % 187.88/188.17 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 187.88/188.17 <=> 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))))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__number__of__lemma,axiom, % 187.88/188.17 ! [V_v,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_negative__zle,axiom, % 187.88/188.17 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_negative__zless,axiom, % 187.88/188.17 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__number__of__Bit1,axiom, % 187.88/188.17 ! [V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 187.88/188.17 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I51_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 187.88/188.17 <=> V_k_2 = V_l_2 ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__neg__int,axiom, % 187.88/188.17 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__eq__iff,axiom, % 187.88/188.17 ! [V_n_2,V_m_2,T_b] : % 187.88/188.17 ( class_Nat_Osemiring__char__0(T_b) % 187.88/188.17 => ( 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) % 187.88/188.17 <=> V_m_2 = V_n_2 ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__zminus__int,axiom, % 187.88/188.17 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I34_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__eq__int__code_I16_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I17_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__int__code_I16_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I46_J,axiom, % 187.88/188.17 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I39_J,axiom, % 187.88/188.17 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 187.88/188.17 ! [V_A_2,V_x_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_inj__int,axiom, % 187.88/188.17 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__neg__0,axiom, % 187.88/188.17 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 187.88/188.17 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 187.88/188.17 ! [V_A_2] : % 187.88/188.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 187.88/188.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__neg__1,axiom, % 187.88/188.17 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__nat__number__of,axiom, % 187.88/188.17 ! [V_v] : % 187.88/188.17 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 187.88/188.17 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__eq__0__conv,axiom, % 187.88/188.17 ! [V_n_2] : % 187.88/188.17 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__0,axiom, % 187.88/188.17 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 187.88/188.17 ! [V_Pa_2] : % 187.88/188.17 ( ! [B_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.88/188.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 187.88/188.17 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 187.88/188.17 ! [V_Pa_2] : % 187.88/188.17 ( ? [B_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.88/188.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 187.88/188.17 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 187.88/188.17 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__zle__int,axiom, % 187.88/188.17 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__less__0__conv,axiom, % 187.88/188.17 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 187.88/188.17 ! [V_y_2,V_x_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zless__int,axiom, % 187.88/188.17 ! [V_n_2,V_m_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_bin__less__0__simps_I4_J,axiom, % 187.88/188.17 ! [V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 187.88/188.17 ! [V_y_2,V_x_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zle__int,axiom, % 187.88/188.17 ! [V_n_2,V_m_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 187.88/188.17 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zadd__int,axiom, % 187.88/188.17 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zadd__int__left,axiom, % 187.88/188.17 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zle__iff__zadd,axiom, % 187.88/188.17 ! [V_z_2,V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 187.88/188.17 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I22_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I12_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__le__imp__of__nat,axiom, % 187.88/188.17 ! [V_m,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__0__le__iff,axiom, % 187.88/188.17 ! [V_n,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_negative__eq__positive,axiom, % 187.88/188.17 ! [V_m_2,V_n_2] : % 187.88/188.17 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) % 187.88/188.17 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__less__0__iff,axiom, % 187.88/188.17 ! [V_m,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__number__of__eq,axiom, % 187.88/188.17 ! [V_v,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Bit1__def,axiom, % 187.88/188.17 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__int__zless__negative,axiom, % 187.88/188.17 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 187.88/188.17 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__mult,axiom, % 187.88/188.17 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmult__int,axiom, % 187.88/188.17 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__0,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__less__iff,axiom, % 187.88/188.17 ! [V_n_2,V_m_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_b) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__imp__of__nat__less,axiom, % 187.88/188.17 ! [V_n,V_m,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__less__imp__less,axiom, % 187.88/188.17 ! [V_n,V_m,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 187.88/188.17 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__1,axiom, % 187.88/188.17 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__le__iff,axiom, % 187.88/188.17 ! [V_n_2,V_m_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_b) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__add,axiom, % 187.88/188.17 ! [V_n,V_m,T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__mult,axiom, % 187.88/188.17 ! [V_n,V_m,T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__1,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_minus__Bit1,axiom, % 187.88/188.17 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_iszero__number__of__Bit1,axiom, % 187.88/188.17 ! [V_w,T_a] : % 187.88/188.17 ( ( class_Int_Onumber__ring(T_a) % 187.88/188.17 & class_Int_Oring__char__0(T_a) ) % 187.88/188.17 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Ints__of__nat,axiom, % 187.88/188.17 ! [V_n_2,T_b] : % 187.88/188.17 ( class_Rings_Oring__1(T_b) % 187.88/188.17 => 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))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_succ__Pls,axiom, % 187.88/188.17 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__neg__eq__ge__0,axiom, % 187.88/188.17 ! [V_x_2] : % 187.88/188.17 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__def,axiom, % 187.88/188.17 ! [V_Z_2] : % 187.88/188.17 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__in__Nats,axiom, % 187.88/188.17 ! [V_n_2,T_b] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_b) % 187.88/188.17 => 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))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__neg__number__of__Pls,axiom, % 187.88/188.17 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 187.88/188.17 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__number__of__Bit1,axiom, % 187.88/188.17 ! [V_w_2] : % 187.88/188.17 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_inj__of__nat,axiom, % 187.88/188.17 ! [T_b] : % 187.88/188.17 ( class_Nat_Osemiring__char__0(T_b) % 187.88/188.17 => 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))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_number__of__Bit1,axiom, % 187.88/188.17 ! [V_w,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mult__numeral__1,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mult__numeral__1__right,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__le__0__conv,axiom, % 187.88/188.17 ! [V_n_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_numeral__1__eq__1,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_semiring__norm_I110_J,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__Suc0__eq__1,axiom, % 187.88/188.17 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zless__iff__Suc__zadd,axiom, % 187.88/188.17 ! [V_z_2,V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 187.88/188.17 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I5_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I29_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__zle__neg,axiom, % 187.88/188.17 ! [V_m_2,V_n_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) % 187.88/188.17 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__Suc,axiom, % 187.88/188.17 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_negative__zle__0,axiom, % 187.88/188.17 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_one__is__num__one,axiom, % 187.88/188.17 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiff__int,axiom, % 187.88/188.17 ! [V_m,V_n] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__numeral__1__eq__1,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Numeral1__eq1__nat,axiom, % 187.88/188.17 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__Suc,axiom, % 187.88/188.17 ! [V_m,T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__diff,axiom, % 187.88/188.17 ! [V_m,V_n,T_a] : % 187.88/188.17 ( class_Rings_Oring__1(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__iszero__Numeral1,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 187.88/188.17 ! [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)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__imp__number__of__eq__0,axiom, % 187.88/188.17 ! [V_v] : % 187.88/188.17 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__less__int__conv,axiom, % 187.88/188.17 ! [V_n_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmult__zless__mono2__lemma,axiom, % 187.88/188.17 ! [V_k,V_j,V_i] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_numeral__3__eq__3,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_numeral__1__eq__Suc__0,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__zle__0__negative,axiom, % 187.88/188.17 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_negative__zless__0,axiom, % 187.88/188.17 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 187.88/188.17 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Suc3__eq__add__3,axiom, % 187.88/188.17 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__0__less__iff,axiom, % 187.88/188.17 ! [V_n_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_b) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_eq__nat__number__of,axiom, % 187.88/188.17 ! [V_v_H_2,V_v_2] : % 187.88/188.17 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) % 187.88/188.17 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 187.88/188.17 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 187.88/188.17 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 187.88/188.17 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__number__of__add__left,axiom, % 187.88/188.17 ! [V_k,V_v_H,V_v] : % 187.88/188.17 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_le__special_I2_J,axiom, % 187.88/188.17 ! [V_y_2,T_b] : % 187.88/188.17 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.17 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_le__special_I4_J,axiom, % 187.88/188.17 ! [V_x_2,T_b] : % 187.88/188.17 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.17 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__special_I2_J,axiom, % 187.88/188.17 ! [V_y_2,T_b] : % 187.88/188.17 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.17 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__special_I4_J,axiom, % 187.88/188.17 ! [V_x_2,T_b] : % 187.88/188.17 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.17 & class_Rings_Olinordered__idom(T_b) ) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__special_I2_J,axiom, % 187.88/188.17 ! [V_w,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__special_I3_J,axiom, % 187.88/188.17 ! [V_v,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__number__of__pred__iff__0,axiom, % 187.88/188.17 ! [V_v_2] : % 187.88/188.17 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 187.88/188.17 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Suc__diff__eq__diff__pred,axiom, % 187.88/188.17 ! [V_m,V_n] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiff__int__split,axiom, % 187.88/188.17 ! [V_y_2,V_x_2,V_Pa_2] : % 187.88/188.17 ( 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)))) % 187.88/188.17 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 187.88/188.17 => 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)))) ) % 187.88/188.17 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 187.88/188.17 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__special_I2_J,axiom, % 187.88/188.17 ! [V_v,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__special_I1_J,axiom, % 187.88/188.17 ! [V_w,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 187.88/188.17 ! [V_n_2,T_b] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_b) % 187.88/188.17 => 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)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__nat__number__of,axiom, % 187.88/188.17 ! [V_v_2,V_v_H_2] : % 187.88/188.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__number__of__odd__number__of,axiom, % 187.88/188.17 ! [V_v_2,V_w_2,T_b] : % 187.88/188.17 ( class_Int_Onumber__ring(T_b) % 187.88/188.17 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => 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))) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => 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) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zpower__number__of__odd,axiom, % 187.88/188.17 ! [V_z_2,V_w_2] : % 187.88/188.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_one__code__numeral__code,axiom, % 187.88/188.17 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__number__of__odd,axiom, % 187.88/188.17 ! [V_z_2,V_w_2,T_b] : % 187.88/188.17 ( class_Int_Onumber__ring(T_b) % 187.88/188.17 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => 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))) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.88/188.17 => 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) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__case__add__eq__if,axiom, % 187.88/188.17 ! [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)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__int__eq,axiom, % 187.88/188.17 ! [V_n_2,V_m_2] : % 187.88/188.17 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) % 187.88/188.17 <=> V_m_2 = V_n_2 ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zpower__int,axiom, % 187.88/188.17 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__power,axiom, % 187.88/188.17 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__int,axiom, % 187.88/188.17 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 187.88/188.17 ! [V_B_2,V_A_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 187.88/188.17 ! [V_B_2,V_A_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 187.88/188.17 ! [V_B_2,V_A_2] : % 187.88/188.17 ( V_A_2 = V_B_2 % 187.88/188.17 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__set__return__embed,axiom, % 187.88/188.17 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 187.88/188.17 ! [V_y_2,V_x_2] : % 187.88/188.17 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) % 187.88/188.17 <=> V_x_2 = V_y_2 ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 187.88/188.17 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 187.88/188.17 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 187.88/188.17 ! [V_n,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 187.88/188.17 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_infinite__UNIV__int,axiom, % 187.88/188.17 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_code__numeral__zero__minus__one,axiom, % 187.88/188.17 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__power__eq,axiom, % 187.88/188.17 ! [V_n,V_z] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.17 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 187.88/188.17 ! [V_q,V_y,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 187.88/188.17 ! [V_q,V_p,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zpower__zpower,axiom, % 187.88/188.17 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 187.88/188.17 ! [V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__neg__nat,axiom, % 187.88/188.17 ! [V_z] : % 187.88/188.17 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__nat__number__of,axiom, % 187.88/188.17 ! [V_n,V_v] : % 187.88/188.17 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__nat__number__of__number__of,axiom, % 187.88/188.17 ! [V_w,V_v] : % 187.88/188.17 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 187.88/188.17 ! [V_q,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 187.88/188.17 ! [V_q,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 187.88/188.17 ! [V_q,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__0,axiom, % 187.88/188.17 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 187.88/188.17 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 187.88/188.17 ! [V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 187.88/188.17 ! [V_q,V_p,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_eq__nat__nat__iff,axiom, % 187.88/188.17 ! [V_z_H_2,V_z_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 187.88/188.17 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 187.88/188.17 <=> V_z_2 = V_z_H_2 ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_ex__nat,axiom, % 187.88/188.17 ! [V_Pa_2] : % 187.88/188.17 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 187.88/188.17 <=> ? [B_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.88/188.17 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_all__nat,axiom, % 187.88/188.17 ! [V_Pa_2] : % 187.88/188.17 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 187.88/188.17 <=> ! [B_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.88/188.17 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 187.88/188.17 ! [V_y_2,V_x_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 187.88/188.17 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 187.88/188.17 <=> V_x_2 = V_y_2 ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__0__le,axiom, % 187.88/188.17 ! [V_z] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__eq__iff,axiom, % 187.88/188.17 ! [V_z_2,V_m_2] : % 187.88/188.17 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 187.88/188.17 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__nat__eq,axiom, % 187.88/188.17 ! [V_z] : % 187.88/188.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zless__nat__eq__int__zless,axiom, % 187.88/188.17 ! [V_z_2,V_m_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 187.88/188.17 ! [V_n,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__zminus__int,axiom, % 187.88/188.17 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__number__of,axiom, % 187.88/188.17 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__number__of__def,axiom, % 187.88/188.17 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zpower__zadd__distrib,axiom, % 187.88/188.17 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 187.88/188.17 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__nat,axiom, % 187.88/188.17 ! [V_z] : % 187.88/188.17 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 187.88/188.17 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Ints__power,axiom, % 187.88/188.17 ! [V_n_2,V_a_2,T_b] : % 187.88/188.17 ( class_Rings_Oring__1(T_b) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 187.88/188.17 => 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))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__le__0,axiom, % 187.88/188.17 ! [V_z] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__0__iff,axiom, % 187.88/188.17 ! [V_i_2] : % 187.88/188.17 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__eq__iff2,axiom, % 187.88/188.17 ! [V_w_2,V_m_2] : % 187.88/188.17 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 187.88/188.17 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.88/188.17 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.88/188.17 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__eq__iff,axiom, % 187.88/188.17 ! [V_m_2,V_w_2] : % 187.88/188.17 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 187.88/188.17 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.88/188.17 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.88/188.17 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_split__nat,axiom, % 187.88/188.17 ! [V_i_2,V_Pa_2] : % 187.88/188.17 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 187.88/188.17 <=> ( ! [B_n] : % 187.88/188.17 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 187.88/188.17 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 187.88/188.17 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__mono__iff,axiom, % 187.88/188.17 ! [V_w_2,V_z_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zless__nat__conj,axiom, % 187.88/188.17 ! [V_z_2,V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 187.88/188.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 187.88/188.17 ! [V_y_2,V_x_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__1,axiom, % 187.88/188.17 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__eq__iff__number__of,axiom, % 187.88/188.17 ! [V_v_2,V_m_2] : % 187.88/188.17 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) % 187.88/188.17 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 187.88/188.17 ! [V_i_2,V_inc_2,T_b] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_b) % 187.88/188.17 => 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 ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 187.88/188.17 ! [V_i_2,V_n_2,V_inc_2,T_b] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_b) % 187.88/188.17 => 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)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__code__numeral__code,axiom, % 187.88/188.17 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 187.88/188.17 ! [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)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__less__nat__eq,axiom, % 187.88/188.17 ! [V_z_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__less__eq__zless,axiom, % 187.88/188.17 ! [V_z_2,V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 187.88/188.17 ! [V_y_2,V_x_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__less__iff,axiom, % 187.88/188.17 ! [V_m_2,V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__le__eq__zle,axiom, % 187.88/188.17 ! [V_z_2,V_w_2] : % 187.88/188.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.88/188.17 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__add__distrib,axiom, % 187.88/188.17 ! [V_z_H,V_z] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 187.88/188.17 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 187.88/188.17 ! [V_y,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power3__eq__cube,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__mult__distrib,axiom, % 187.88/188.17 ! [V_z_H,V_z] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.17 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 187.88/188.17 ! [V_y,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__diff__distrib,axiom, % 187.88/188.17 ! [V_z,V_z_H] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 187.88/188.17 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__eq__if,axiom, % 187.88/188.17 ! [V_p,V_m] : % 187.88/188.17 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 187.88/188.17 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 187.88/188.17 ! [V_y,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__nat__eq__if,axiom, % 187.88/188.17 ! [V_z_2,V_z_H_2] : % 187.88/188.17 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 187.88/188.17 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_one__less__nat__eq,axiom, % 187.88/188.17 ! [V_z_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 187.88/188.17 ! [V_z] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.17 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__mult__distrib__neg,axiom, % 187.88/188.17 ! [V_z_H,V_z] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Suc__eq__number__of,axiom, % 187.88/188.17 ! [V_v_2,V_n_2] : % 187.88/188.17 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_eq__number__of__Suc,axiom, % 187.88/188.17 ! [V_n_2,V_v_2] : % 187.88/188.17 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__case__number__of,axiom, % 187.88/188.17 ! [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))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__Suc__number__of,axiom, % 187.88/188.17 ! [V_v_2,V_n_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__number__of__Suc,axiom, % 187.88/188.17 ! [V_n_2,V_v_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_le__Suc__number__of,axiom, % 187.88/188.17 ! [V_v_2,V_n_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_le__number__of__Suc,axiom, % 187.88/188.17 ! [V_n_2,V_v_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__strict__mono,axiom, % 187.88/188.17 ! [V_n,V_b,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_one__less__power,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__increasing__iff,axiom, % 187.88/188.17 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_b) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__le__imp__le__exp,axiom, % 187.88/188.17 ! [V_n,V_m,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__decreasing,axiom, % 187.88/188.17 ! [V_a,V_N,V_n,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__strict__decreasing,axiom, % 187.88/188.17 ! [V_a,V_N,V_n,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_field__power__not__zero,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 187.88/188.17 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 187.88/188.17 ! [V_m_2,V_x_2] : % 187.88/188.17 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.88/188.17 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__Suc__0,axiom, % 187.88/188.17 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__power__less__imp__less,axiom, % 187.88/188.17 ! [V_n,V_m,V_i] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__zero__less__power__iff,axiom, % 187.88/188.17 ! [V_n_2,V_x_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) % 187.88/188.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 187.88/188.17 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__mult__distrib,axiom, % 187.88/188.17 ! [V_n,V_b,V_a,T_a] : % 187.88/188.17 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__commutes,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__one,axiom, % 187.88/188.17 ! [V_n,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__power,axiom, % 187.88/188.17 ! [V_n,V_m,T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__mult,axiom, % 187.88/188.17 ! [V_n,V_m,V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__one__right,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__mono,axiom, % 187.88/188.17 ! [V_n,V_b,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__le__power,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__less__power,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__eq__0__iff,axiom, % 187.88/188.17 ! [V_n_2,V_a_2,T_b] : % 187.88/188.17 ( ( class_Power_Opower(T_b) % 187.88/188.17 & class_Rings_Omult__zero(T_b) % 187.88/188.17 & class_Rings_Ono__zero__divisors(T_b) % 187.88/188.17 & class_Rings_Ozero__neq__one(T_b) ) % 187.88/188.17 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.17 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.17 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_one__le__power,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__0__Suc,axiom, % 187.88/188.17 ! [V_n,T_a] : % 187.88/188.17 ( ( class_Power_Opower(T_a) % 187.88/188.17 & class_Rings_Osemiring__0(T_a) ) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__inject__exp,axiom, % 187.88/188.17 ! [V_n_2,V_m_2,V_a_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_b) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 187.88/188.17 => ( 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) % 187.88/188.17 <=> V_m_2 = V_n_2 ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__Suc2,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__Suc,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Power_Opower(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__one__le__power,axiom, % 187.88/188.17 ! [V_n,V_i] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__0,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Power_Opower(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__add,axiom, % 187.88/188.17 ! [V_n,V_m,V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__less__imp__less__base,axiom, % 187.88/188.17 ! [V_b,V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__inject__base,axiom, % 187.88/188.17 ! [V_b,V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.17 => V_a = V_b ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__le__imp__le__base,axiom, % 187.88/188.17 ! [V_b,V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__less__power__Suc,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__gt1__lemma,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__0__left,axiom, % 187.88/188.17 ! [V_n,T_a] : % 187.88/188.17 ( ( class_Power_Opower(T_a) % 187.88/188.17 & class_Rings_Osemiring__0(T_a) ) % 187.88/188.17 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) % 187.88/188.17 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__gt1,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__strict__increasing__iff,axiom, % 187.88/188.17 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_b) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__less__imp__less__exp,axiom, % 187.88/188.17 ! [V_n,V_m,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__strict__increasing,axiom, % 187.88/188.17 ! [V_a,V_N,V_n,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__increasing,axiom, % 187.88/188.17 ! [V_a,V_N,V_n,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__minus,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Oring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__Suc__less,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__eq__imp__eq__base,axiom, % 187.88/188.17 ! [V_b,V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.17 => V_a = V_b ) ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__Suc__less__one,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__aux__def,axiom, % 187.88/188.17 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__of__aux__code,axiom, % 187.88/188.17 ! [V_n,V_i] : % 187.88/188.17 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.88/188.17 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 187.88/188.17 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.88/188.17 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__rec__add__eq__if,axiom, % 187.88/188.17 ! [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))))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__rec__number__of,axiom, % 187.88/188.17 ! [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)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__morphism__nat__int,axiom, % 187.88/188.17 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_of__nat__double,axiom, % 187.88/188.17 ! [V_x,T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I48_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 187.88/188.17 <=> V_k_2 = V_l_2 ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__eq__int__code_I13_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I31_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__int__code_I13_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I14_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Bit0__Pls,axiom, % 187.88/188.17 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I38_J,axiom, % 187.88/188.17 ! [V_l_2] : % 187.88/188.17 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 187.88/188.17 <=> c_Int_OPls = V_l_2 ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I44_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 187.88/188.17 <=> V_k_2 = c_Int_OPls ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I49_J,axiom, % 187.88/188.17 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I50_J,axiom, % 187.88/188.17 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Bit0__def,axiom, % 187.88/188.17 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__Bit0__Bit0,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mult__Bit0,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__bin__simps_I7_J,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_minus__Bit0,axiom, % 187.88/188.17 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_bin__less__0__simps_I3_J,axiom, % 187.88/188.17 ! [V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__rec__0,axiom, % 187.88/188.17 ! [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 ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__rec__Suc,axiom, % 187.88/188.17 ! [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)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I21_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I27_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I32_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__eq__int__code_I14_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I4_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I10_J,axiom, % 187.88/188.17 ! [V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I16_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__int__code_I15_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__Bit1__Bit0,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__Bit0__Bit1,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__bin__simps_I3_J,axiom, % 187.88/188.17 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__bin__simps_I9_J,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__bin__simps_I10_J,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__number__of__Bit0,axiom, % 187.88/188.17 ! [V_w_2] : % 187.88/188.17 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 187.88/188.17 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pred__Bit0,axiom, % 187.88/188.17 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pred__Bit1,axiom, % 187.88/188.17 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 187.88/188.17 % 187.88/188.17 fof(fact_iszero__number__of__Bit0,axiom, % 187.88/188.17 ! [V_w_2,T_b] : % 187.88/188.17 ( ( class_Int_Onumber__ring(T_b) % 187.88/188.17 & class_Int_Oring__char__0(T_b) ) % 187.88/188.17 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 187.88/188.17 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_succ__Bit1,axiom, % 187.88/188.17 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_succ__Bit0,axiom, % 187.88/188.17 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__number__of__Bit0,axiom, % 187.88/188.17 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_number__of__Bit0,axiom, % 187.88/188.17 ! [V_w,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__eq__int__code_I15_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I33_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__int__code_I14_J,axiom, % 187.88/188.17 ! [V_k2_2,V_k1_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_rel__simps_I15_J,axiom, % 187.88/188.17 ! [V_l_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_card__UNIV__bool,axiom, % 187.88/188.17 hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mult__Bit1,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ). % 187.88/188.17 % 187.88/188.17 fof(fact_diff__bin__simps_I8_J,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__Bit1__Bit1,axiom, % 187.88/188.17 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__number__of__even,axiom, % 187.88/188.17 ! [V_w_2,V_z_2,T_b] : % 187.88/188.17 ( class_Int_Onumber__ring(T_b) % 187.88/188.17 => 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))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zpower__number__of__even,axiom, % 187.88/188.17 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_double__number__of__Bit0,axiom, % 187.88/188.17 ! [V_w,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_number__of1,axiom, % 187.88/188.17 ! [V_n] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__number__of__even__number__of,axiom, % 187.88/188.17 ! [V_w_2,V_v_2,T_b] : % 187.88/188.17 ( class_Int_Onumber__ring(T_b) % 187.88/188.17 => 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))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mult__2,axiom, % 187.88/188.17 ! [V_z,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mult__2__right,axiom, % 187.88/188.17 ! [V_z,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_one__add__one__is__two,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__power2,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__eq__power2,axiom, % 187.88/188.17 ! [V_a_2,T_b] : % 187.88/188.17 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 187.88/188.17 => ( 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) % 187.88/188.17 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_semiring__norm_I115_J,axiom, % 187.88/188.17 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_numeral__2__eq__2,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__eq__square,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 187.88/188.17 ! [V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 187.88/188.17 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__2__eq__Suc,axiom, % 187.88/188.17 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_add__2__eq__Suc_H,axiom, % 187.88/188.17 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_one__power2,axiom, % 187.88/188.17 ! [T_a] : % 187.88/188.17 ( class_Rings_Osemiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__minus,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Rings_Oring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__mult__2__right,axiom, % 187.88/188.17 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__mult__2,axiom, % 187.88/188.17 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__even__eq,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 187.88/188.17 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__1__add__1,axiom, % 187.88/188.17 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__eq__imp__eq,axiom, % 187.88/188.17 ! [V_y,V_x,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.17 => V_x = V_y ) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__le__imp__le,axiom, % 187.88/188.17 ! [V_y,V_x,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__le__power2,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__less__power2,axiom, % 187.88/188.17 ! [V_a_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.17 => ( 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)))))) % 187.88/188.17 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__less__0,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_sum__power2__eq__zero__iff,axiom, % 187.88/188.17 ! [V_y_2,V_x_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.17 => ( 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) % 187.88/188.17 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.17 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__eq__square__number__of,axiom, % 187.88/188.17 ! [V_w,T_b] : % 187.88/188.17 ( ( class_Groups_Omonoid__mult(T_b) % 187.88/188.17 & class_Int_Onumber(T_b) ) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_less__2__cases,axiom, % 187.88/188.17 ! [V_n] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) % 187.88/188.17 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.17 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nat__2,axiom, % 187.88/188.17 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__eq__1__iff,axiom, % 187.88/188.17 ! [V_a_2,T_b] : % 187.88/188.17 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 187.88/188.17 => ( 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) % 187.88/188.17 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 187.88/188.17 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 187.88/188.17 ! [V_n,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__minus__even,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Oring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__less__imp__less,axiom, % 187.88/188.17 ! [V_y,V_x,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__semidom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_sum__power2__le__zero__iff,axiom, % 187.88/188.17 ! [V_y_2,V_x_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.17 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_sum__power2__ge__zero,axiom, % 187.88/188.17 ! [V_y,V_x,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_sum__power2__gt__zero__iff,axiom, % 187.88/188.17 ! [V_y_2,V_x_2,T_b] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.17 => ( 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))))))) % 187.88/188.17 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.17 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_not__sum__power2__lt__zero,axiom, % 187.88/188.17 ! [V_y,V_x,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__sum,axiom, % 187.88/188.17 ! [V_y,V_x,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zero__le__even__power_H,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 187.88/188.17 ! [V_n,V_x,T_a] : % 187.88/188.17 ( class_Rings_Ocomm__semiring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__odd__eq,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Groups_Omonoid__mult(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__minus1__even,axiom, % 187.88/188.17 ! [V_n,T_a] : % 187.88/188.17 ( class_Rings_Oring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power2__diff,axiom, % 187.88/188.17 ! [V_y,V_x,T_a] : % 187.88/188.17 ( class_Int_Onumber__ring(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_odd__0__le__power__imp__0__le,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_odd__power__less__zero,axiom, % 187.88/188.17 ! [V_n,V_a,T_a] : % 187.88/188.17 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__minus1__odd,axiom, % 187.88/188.17 ! [V_n,T_a] : % 187.88/188.17 ( class_Rings_Oring__1(T_a) % 187.88/188.17 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__zmod__mult__2,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__number__of__Bit1,axiom, % 187.88/188.17 ! [V_v,V_w] : % 187.88/188.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 187.88/188.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__zmod__mult__2,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__zdiv__mult__2,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__zdiv__mult__2,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power__power__power,axiom, % 187.88/188.17 ! [T_b] : % 187.88/188.17 ( class_Power_Opower(T_b) % 187.88/188.17 => 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)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zmod__equality2,axiom, % 187.88/188.17 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zmod__equality,axiom, % 187.88/188.17 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zmult1__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zdiv__equality,axiom, % 187.88/188.17 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zadd1__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mod__trivial,axiom, % 187.88/188.17 ! [V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 187.88/188.17 ! [V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__div__equality2,axiom, % 187.88/188.17 ! [V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__div__equality,axiom, % 187.88/188.17 ! [V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mod__equality2,axiom, % 187.88/188.17 ! [V_c,V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mod__equality,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zdiv__trivial,axiom, % 187.88/188.17 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__div__trivial,axiom, % 187.88/188.17 ! [V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_DIVISION__BY__ZERO,axiom, % 187.88/188.17 ! [V_a] : % 187.88/188.17 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zdiv__equality_H,axiom, % 187.88/188.17 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmult__div__cancel,axiom, % 187.88/188.17 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__self,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__by__0,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__0,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__add__cong,axiom, % 187.88/188.17 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 187.88/188.17 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__simps_I1_J,axiom, % 187.88/188.17 ! [V_b,V_c,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__simps_I2_J,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__add__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__add__left__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__add__right__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__add__self1,axiom, % 187.88/188.17 ! [V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__add__self2,axiom, % 187.88/188.17 ! [V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__cong,axiom, % 187.88/188.17 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 187.88/188.17 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__simps_I4_J,axiom, % 187.88/188.17 ! [V_b,V_c,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__mult2,axiom, % 187.88/188.17 ! [V_b,V_c,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__mult1,axiom, % 187.88/188.17 ! [V_b,V_a,V_c,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__left__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__right__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__diff__cong,axiom, % 187.88/188.17 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 187.88/188.17 ( class_Divides_Oring__div(T_a) % 187.88/188.17 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 187.88/188.17 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__diff__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Oring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__diff__left__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Oring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__diff__right__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Oring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__minus__eq,axiom, % 187.88/188.17 ! [V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Oring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__minus__cong,axiom, % 187.88/188.17 ! [V_a_H,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Oring__div(T_a) % 187.88/188.17 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zero,axiom, % 187.88/188.17 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__self,axiom, % 187.88/188.17 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zero,axiom, % 187.88/188.17 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zminus__zminus,axiom, % 187.88/188.17 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zminus2,axiom, % 187.88/188.17 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__simps_I3_J,axiom, % 187.88/188.17 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zmult1__eq,axiom, % 187.88/188.17 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiff__zmod__right,axiom, % 187.88/188.17 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiff__zmod__left,axiom, % 187.88/188.17 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zminus__zmod,axiom, % 187.88/188.17 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zminus__zminus,axiom, % 187.88/188.17 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zminus2,axiom, % 187.88/188.17 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__by__0,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__0,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__by__1,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zpower__zmod,axiom, % 187.88/188.17 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__self2__is__0,axiom, % 187.88/188.17 ! [V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__self1__is__0,axiom, % 187.88/188.17 ! [V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zmult2__eq,axiom, % 187.88/188.17 ! [V_b,V_a,V_c] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__self1,axiom, % 187.88/188.17 ! [V_b,V_c,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__mult__self2,axiom, % 187.88/188.17 ! [V_c,V_b,V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__by__1,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zminus1__eq__if,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 187.88/188.17 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zminus2__eq__if,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 187.88/188.17 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 187.88/188.17 ! [V_y,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__neg__pos__less0,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 187.88/188.17 ! [V_a_2,V_ba_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 187.88/188.17 ! [V_a_2,V_ba_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__self,axiom, % 187.88/188.17 ! [V_a] : % 187.88/188.17 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 187.88/188.17 ! [V_y,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__le__nonneg__dividend,axiom, % 187.88/188.17 ! [V_k,V_m] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__mod__bound,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__mod__bound,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__number__of__Bit0,axiom, % 187.88/188.17 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__eq__0__iff,axiom, % 187.88/188.17 ! [V_d_2,V_m_2] : % 187.88/188.17 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zminus2__not__zero,axiom, % 187.88/188.17 ! [V_l,V_k] : % 187.88/188.17 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zminus1__not__zero,axiom, % 187.88/188.17 ! [V_l,V_k] : % 187.88/188.17 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mult__mult1__if,axiom, % 187.88/188.17 ! [V_b,V_a,V_c,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) % 187.88/188.17 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mult__self2__is__id,axiom, % 187.88/188.17 ! [V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mult__self1__is__id,axiom, % 187.88/188.17 ! [V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mult__mult2,axiom, % 187.88/188.17 ! [V_b,V_a,V_c,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mult__mult1,axiom, % 187.88/188.17 ! [V_b,V_a,V_c,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__self,axiom, % 187.88/188.17 ! [V_a,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_split__pos__lemma,axiom, % 187.88/188.17 ! [V_n_2,V_Pa_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> ! [B_i,B_j] : % 187.88/188.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 187.88/188.17 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 187.88/188.17 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_split__neg__lemma,axiom, % 187.88/188.17 ! [V_n_2,V_Pa_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> ! [B_i,B_j] : % 187.88/188.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 187.88/188.17 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__eq__0__iff,axiom, % 187.88/188.17 ! [V_k_2,V_i_2] : % 187.88/188.17 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 187.88/188.17 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 187.88/188.17 ! [V_a_2,V_ba_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 187.88/188.17 ! [V_i_2,V_k_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 187.88/188.17 ! [V_ba_2,V_a_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),V_a_2)) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__mono2,axiom, % 187.88/188.17 ! [V_b,V_b_H,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__nonneg__neg__le0,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__pos__pos__trivial,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 187.88/188.17 ! [V_a_2,V_ba_2] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( 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))) % 187.88/188.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__nonpos__pos__le0,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__mono2__neg,axiom, % 187.88/188.17 ! [V_b,V_b_H,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__neg__neg__trivial,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__mono1,axiom, % 187.88/188.17 ! [V_b,V_a_H,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__mono1__neg,axiom, % 187.88/188.17 ! [V_b,V_a_H,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_int__div__less__self,axiom, % 187.88/188.17 ! [V_k,V_x] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zdiv__zmult2__eq,axiom, % 187.88/188.17 ! [V_b,V_a,V_c] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__mod__sign,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_pos__mod__conj,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__pos__pos__trivial,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__mod__sign,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_neg__mod__conj,axiom, % 187.88/188.17 ! [V_a,V_b] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__neg__neg__trivial,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zminus2__eq__if,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.17 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_zmod__zminus1__eq__if,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.17 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_power_Opower_Opower__0,axiom, % 187.88/188.17 ! [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 ). % 187.88/188.17 % 187.88/188.17 fof(fact_power_Opower_Opower__Suc,axiom, % 187.88/188.17 ! [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)) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mult__self1,axiom, % 187.88/188.17 ! [V_c,V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__mult__self2,axiom, % 187.88/188.17 ! [V_c,V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__add__self1,axiom, % 187.88/188.17 ! [V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_div__add__self2,axiom, % 187.88/188.17 ! [V_a,V_b,T_a] : % 187.88/188.17 ( class_Divides_Osemiring__div(T_a) % 187.88/188.17 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_mod__pos__neg__trivial,axiom, % 187.88/188.17 ! [V_b,V_a] : % 187.88/188.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.17 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ). % 187.88/188.17 % 187.88/188.17 fof(fact_split__zdiv,axiom, % 187.88/188.17 ! [V_k_2,V_n_2,V_Pa_2] : % 187.88/188.17 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 187.88/188.18 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.18 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.88/188.18 => ! [B_i] : % 187.88/188.18 ( ? [B_j] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 187.88/188.18 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 187.88/188.18 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => ! [B_i] : % 187.88/188.18 ( ? [B_j] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_divmod__int__rel__div__eq,axiom, % 187.88/188.18 ! [V_r_1,V_y,V_b_1,V_a_1] : % 187.88/188.18 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) % 187.88/188.18 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 187.88/188.18 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_split__zmod,axiom, % 187.88/188.18 ! [V_k_2,V_n_2,V_Pa_2] : % 187.88/188.18 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 187.88/188.18 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 187.88/188.18 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.88/188.18 => ! [B_i,B_j] : % 187.88/188.18 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 187.88/188.18 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 187.88/188.18 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => ! [B_i,B_j] : % 187.88/188.18 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmult2__lemma__aux3,axiom, % 187.88/188.18 ! [V_q,V_b,V_r,V_c] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmult2__lemma__aux4,axiom, % 187.88/188.18 ! [V_q,V_b,V_r,V_c] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmult2__lemma__aux1,axiom, % 187.88/188.18 ! [V_q,V_r,V_b,V_c] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmult2__lemma__aux2,axiom, % 187.88/188.18 ! [V_q,V_r,V_b,V_c] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_divmod__int__rel__mod__eq,axiom, % 187.88/188.18 ! [V_y,V_q_1,V_b_1,V_a_1] : % 187.88/188.18 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) % 187.88/188.18 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 187.88/188.18 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmod__number__of__Bit0,axiom, % 187.88/188.18 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zdiv__number__of__Bit1,axiom, % 187.88/188.18 ! [V_v,V_w] : % 187.88/188.18 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_int__power__div__base,axiom, % 187.88/188.18 ! [V_k,V_m] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_z3div__def,axiom, % 187.88/188.18 ! [V_k,V_l] : % 187.88/188.18 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.88/188.18 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.88/188.18 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_z3mod__def,axiom, % 187.88/188.18 ! [V_k,V_l] : % 187.88/188.18 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.88/188.18 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.88/188.18 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_power__m1__odd,axiom, % 187.88/188.18 ! [V_n,T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_power__m1__even,axiom, % 187.88/188.18 ! [V_n,T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_one__mod__nat__number__of,axiom, % 187.88/188.18 ! [V_v_H] : % 187.88/188.18 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 187.88/188.18 ! [V_B_2,V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__add1__eq,axiom, % 187.88/188.18 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__mod__equality_H,axiom, % 187.88/188.18 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mult__div__cancel,axiom, % 187.88/188.18 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Divides_Omod__div__equality_H,axiom, % 187.88/188.18 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__mult2__eq,axiom, % 187.88/188.18 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__mult1__eq,axiom, % 187.88/188.18 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__le__mono,axiom, % 187.88/188.18 ! [V_k,V_n,V_m] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__le__dividend,axiom, % 187.88/188.18 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 187.88/188.18 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__mult2__eq,axiom, % 187.88/188.18 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__less,axiom, % 187.88/188.18 ! [V_n,V_m] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__less__eq__dividend,axiom, % 187.88/188.18 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__mult__distrib2,axiom, % 187.88/188.18 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__mult__distrib,axiom, % 187.88/188.18 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I24_J,axiom, % 187.88/188.18 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I7_J,axiom, % 187.88/188.18 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I40_J,axiom, % 187.88/188.18 c_Int_OMin != c_Int_OPls ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I37_J,axiom, % 187.88/188.18 c_Int_OPls != c_Int_OMin ). % 187.88/188.18 % 187.88/188.18 fof(fact_Bit1__Min,axiom, % 187.88/188.18 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I43_J,axiom, % 187.88/188.18 ! [V_l_2] : % 187.88/188.18 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 187.88/188.18 <=> c_Int_OMin = V_l_2 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I47_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 187.88/188.18 <=> V_k_2 = c_Int_OMin ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I42_J,axiom, % 187.88/188.18 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I45_J,axiom, % 187.88/188.18 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__1,axiom, % 187.88/188.18 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__less,axiom, % 187.88/188.18 ! [V_n,V_m] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nat__mult__div__cancel__disj,axiom, % 187.88/188.18 ! [V_n,V_m,V_k] : % 187.88/188.18 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.18 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__1,axiom, % 187.88/188.18 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__Suc,axiom, % 187.88/188.18 ! [V_n,V_m] : % 187.88/188.18 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.18 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__less__divisor,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__eq__0__iff,axiom, % 187.88/188.18 ! [V_d_2,V_m_2] : % 187.88/188.18 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__geq,axiom, % 187.88/188.18 ! [V_n,V_m] : % 187.88/188.18 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__if,axiom, % 187.88/188.18 ! [V_n,V_m] : % 187.88/188.18 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__mult__self3,axiom, % 187.88/188.18 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ). % 187.88/188.18 % 187.88/188.18 fof(fact_le__mod__geq,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zdiv__int,axiom, % 187.88/188.18 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 187.88/188.18 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_bin__less__0__simps_I2_J,axiom, % 187.88/188.18 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I23_J,axiom, % 187.88/188.18 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I20_J,axiom, % 187.88/188.18 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I26_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I30_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I6_J,axiom, % 187.88/188.18 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I3_J,axiom, % 187.88/188.18 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I9_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I13_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I28_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I8_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmod__int,axiom, % 187.88/188.18 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 187.88/188.18 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_eq__number__of__Pls__Min,axiom, % 187.88/188.18 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Int_OMin__def,axiom, % 187.88/188.18 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mult__Min,axiom, % 187.88/188.18 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ). % 187.88/188.18 % 187.88/188.18 fof(fact_neg__number__of__Min,axiom, % 187.88/188.18 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_pred__Pls,axiom, % 187.88/188.18 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 187.88/188.18 % 187.88/188.18 fof(fact_add__Min,axiom, % 187.88/188.18 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 187.88/188.18 % 187.88/188.18 fof(fact_add__Min__right,axiom, % 187.88/188.18 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 187.88/188.18 % 187.88/188.18 fof(fact_pred__Min,axiom, % 187.88/188.18 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 187.88/188.18 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nonzero__number__of__Min,axiom, % 187.88/188.18 ! [T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_succ__Min,axiom, % 187.88/188.18 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 187.88/188.18 % 187.88/188.18 fof(fact_diff__bin__simps_I2_J,axiom, % 187.88/188.18 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nat__set__def,axiom, % 187.88/188.18 ! [V_S_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_S_2) % 187.88/188.18 <=> ! [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__le__mono2,axiom, % 187.88/188.18 ! [V_k,V_n,V_m] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__mult__self__is__m,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__mult__self1__is__m,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nat__mult__div__cancel1,axiom, % 187.88/188.18 ! [V_n,V_m,V_k] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__less__dividend,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__le__divisor,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__mult__self4,axiom, % 187.88/188.18 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mult__minus1,axiom, % 187.88/188.18 ! [V_z,T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mult__minus1__right,axiom, % 187.88/188.18 ! [V_z,T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 187.88/188.18 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_arith__simps_I31_J,axiom, % 187.88/188.18 ! [T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_number__of__Min,axiom, % 187.88/188.18 ! [T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 187.88/188.18 ! [V_B_2,V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.18 => ( V_A_2 = V_B_2 % 187.88/188.18 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I11_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_rel__simps_I25_J,axiom, % 187.88/188.18 ! [V_k_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmod__minus1__right,axiom, % 187.88/188.18 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.88/188.18 % 187.88/188.18 fof(fact_diff__bin__simps_I4_J,axiom, % 187.88/188.18 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_minus__Min,axiom, % 187.88/188.18 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmult__eq__1__iff,axiom, % 187.88/188.18 ! [V_n_2,V_m_2] : % 187.88/188.18 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.88/188.18 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.88/188.18 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 187.88/188.18 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 187.88/188.18 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 187.88/188.18 ! [V_n,V_m] : % 187.88/188.18 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.88/188.18 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.88/188.18 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_diff__bin__simps_I5_J,axiom, % 187.88/188.18 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_diff__bin__simps_I6_J,axiom, % 187.88/188.18 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zdiv__minus1__right,axiom, % 187.88/188.18 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__geq,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__if,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_split__div,axiom, % 187.88/188.18 ! [V_k_2,V_n_2,V_Pa_2] : % 187.88/188.18 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 187.88/188.18 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.88/188.18 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 => ! [B_i,B_j] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 187.88/188.18 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nat__div__distrib,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.18 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_split__mod,axiom, % 187.88/188.18 ! [V_k_2,V_n_2,V_Pa_2] : % 187.88/188.18 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 187.88/188.18 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 187.88/188.18 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 => ! [B_i,B_j] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 187.88/188.18 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 187.88/188.18 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__lemma,axiom, % 187.88/188.18 ! [V_q,V_b,V_r,V_c] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Suc__times__mod__eq,axiom, % 187.88/188.18 ! [V_m,V_k] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nat__mod__distrib,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.88/188.18 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__eq__minus1,axiom, % 187.88/188.18 ! [V_b] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 187.88/188.18 ! [V_x_2,V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_le__div__geq,axiom, % 187.88/188.18 ! [V_m,V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_split__div_H,axiom, % 187.88/188.18 ! [V_n_2,V_m_2,V_Pa_2] : % 187.88/188.18 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 187.88/188.18 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.18 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.88/188.18 | ? [B_q] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q)))) % 187.88/188.18 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_split__div__lemma,axiom, % 187.88/188.18 ! [V_m_2,V_q_2,V_n_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) ) % 187.88/188.18 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 187.88/188.18 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Suc__div__eq__add3__div,axiom, % 187.88/188.18 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__Suc__eq__div__add3,axiom, % 187.88/188.18 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div2__Suc__Suc,axiom, % 187.88/188.18 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_add__self__div__2,axiom, % 187.88/188.18 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ). % 187.88/188.18 % 187.88/188.18 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 187.88/188.18 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Suc__mod__eq__add3__mod,axiom, % 187.88/188.18 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__Suc__eq__mod__add3,axiom, % 187.88/188.18 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod2__Suc__Suc,axiom, % 187.88/188.18 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 187.88/188.18 ! [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))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__nat__int__set__return__embed,axiom, % 187.88/188.18 ! [V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__nat__number__of,axiom, % 187.88/188.18 ! [V_v_H,V_v] : % 187.88/188.18 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod__nat__number__of,axiom, % 187.88/188.18 ! [V_v_H,V_v] : % 187.88/188.18 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.18 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__pos__neg__trivial,axiom, % 187.88/188.18 ! [V_b,V_a] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmod__minus1,axiom, % 187.88/188.18 ! [V_b] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.18 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 187.88/188.18 ! [V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 187.88/188.18 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 187.88/188.18 ! [V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_div__2__gt__zero,axiom, % 187.88/188.18 ! [V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_one__div__nat__number__of,axiom, % 187.88/188.18 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_mod2__gr__0,axiom, % 187.88/188.18 ! [V_m_2] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 187.88/188.18 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Suc__n__div__2__gt__zero,axiom, % 187.88/188.18 ! [V_n] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 187.88/188.18 ! [V_B_2,V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_int__of__code,axiom, % 187.88/188.18 ! [V_k] : % 187.88/188.18 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.88/188.18 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.18 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.88/188.18 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.88/188.18 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) % 187.88/188.18 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.88/188.18 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 187.88/188.18 ! [V_A_2,V_x_2] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x_2) % 187.88/188.18 => ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__Suc__number__of,axiom, % 187.88/188.18 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__number__of__Suc,axiom, % 187.88/188.18 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_code__numeral_Osize_I1_J,axiom, % 187.88/188.18 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__le__iff__disj,axiom, % 187.88/188.18 ! [V_z_2,V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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)) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 187.88/188.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__infE,axiom, % 187.88/188.18 ! [V_b,V_a,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) % 187.88/188.18 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.88/188.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__mono,axiom, % 187.88/188.18 ! [V_d,V_b,V_c,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__greatest,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__infI,axiom, % 187.88/188.18 ! [V_b,V_a,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__absorb2,axiom, % 187.88/188.18 ! [V_x,V_y,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__absorb1,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__infI2,axiom, % 187.88/188.18 ! [V_a,V_x,V_b,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__infI1,axiom, % 187.88/188.18 ! [V_b,V_x,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__inf__iff,axiom, % 187.88/188.18 ! [V_z_2,V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__iff__inf,axiom, % 187.88/188.18 ! [V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.18 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__le2,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__le1,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oless__infI1,axiom, % 187.88/188.18 ! [V_b,V_x,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oless__infI2,axiom, % 187.88/188.18 ! [V_a,V_x,V_b,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__less__iff__conj,axiom, % 187.88/188.18 ! [V_y_2,V_x_2,V_z_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__less__iff__disj,axiom, % 187.88/188.18 ! [V_z_2,V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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)) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 187.88/188.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__add__distrib__left,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.88/188.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__assoc,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf_Oassoc,axiom, % 187.88/188.18 ! [V_c,V_b,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__left__commute,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 187.88/188.18 ! [V_c,V_a,V_b,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__left__idem,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 187.88/188.18 ! [V_b,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__commute,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf_Ocommute,axiom, % 187.88/188.18 ! [V_b,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf_Oidem,axiom, % 187.88/188.18 ! [V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__diff__distrib__left,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Groups_Oordered__ab__group__add(T_a) % 187.88/188.18 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__0R,axiom, % 187.88/188.18 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__0L,axiom, % 187.88/188.18 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__Suc__Suc,axiom, % 187.88/188.18 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__diff,axiom, % 187.88/188.18 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 187.88/188.18 ! [T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 187.88/188.18 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x) % 187.88/188.18 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 187.88/188.18 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 187.88/188.18 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x) % 187.88/188.18 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x) % 187.88/188.18 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x) % 187.88/188.18 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 187.88/188.18 ! [V_n,V_x] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__number__of,axiom, % 187.88/188.18 ! [V_v,V_u,T_b] : % 187.88/188.18 ( ( class_Int_Onumber(T_b) % 187.88/188.18 & class_Orderings_Oord(T_b) ) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 187.88/188.18 ! [V_y,V_x] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x) % 187.88/188.18 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_is__nat__def,axiom, % 187.88/188.18 ! [V_x_2] : % 187.88/188.18 ( c_Nat__Transfer_Ois__nat(V_x_2) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 187.88/188.18 ! [V_x_2,V_A_2] : % 187.88/188.18 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__Suc2,axiom, % 187.88/188.18 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__Suc1,axiom, % 187.88/188.18 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 187.88/188.18 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 187.88/188.18 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_fold1__antimono,axiom, % 187.88/188.18 ! [V_B_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.18 => 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))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_fold1__strict__below__iff,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( 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)) % 187.88/188.18 <=> ? [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_strict__below__fold1__iff,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> ! [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_fold1__below__iff,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( 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)) % 187.88/188.18 <=> ? [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Obelow__fold1__iff,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> ! [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oidem,axiom, % 187.88/188.18 ! [V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ofold__inf__insert,axiom, % 187.88/188.18 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 187.88/188.18 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ofold1__belowI,axiom, % 187.88/188.18 ! [V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_semilattice__big_OF__eq,axiom, % 187.88/188.18 ! [V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.18 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_dual__max,axiom, % 187.88/188.18 ! [T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => 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) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_comm__monoid__big_OF__eq,axiom, % 187.88/188.18 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.18 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 187.88/188.18 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.18 => 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) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.18 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__ord__min,axiom, % 187.88/188.18 ! [T_b] : % 187.88/188.18 ( class_Orderings_Oord(T_b) % 187.88/188.18 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_code__numeral_Osize_I2_J,axiom, % 187.88/188.18 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_code__numeral_Oinject,axiom, % 187.88/188.18 ! [V_code__numeral_H_2,V_code__numeral_2] : % 187.88/188.18 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 187.88/188.18 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_code__numeral_Osimps_I3_J,axiom, % 187.88/188.18 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 187.88/188.18 % 187.88/188.18 fof(fact_code__numeral_Osimps_I2_J,axiom, % 187.88/188.18 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Suc__code__numeral__minus__one,axiom, % 187.88/188.18 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ). % 187.88/188.18 % 187.88/188.18 fof(fact_comm__monoid__big_Oinfinite,axiom, % 187.88/188.18 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.18 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 187.88/188.18 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.18 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_code__numeral_Osize_I4_J,axiom, % 187.88/188.18 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_card__greaterThanLessThan__int,axiom, % 187.88/188.18 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oremove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__of__nat,axiom, % 187.88/188.18 ! [V_k,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oremove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_finite__greaterThanLessThan__int,axiom, % 187.88/188.18 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__eq__iff,axiom, % 187.88/188.18 ! [V_z_2,V_w_2,T_b] : % 187.88/188.18 ( class_Int_Oring__char__0(T_b) % 187.88/188.18 => ( 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) % 187.88/188.18 <=> V_w_2 = V_z_2 ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_number__of__eq,axiom, % 187.88/188.18 ! [V_k,T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_int__number__of__def,axiom, % 187.88/188.18 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__int__eq,axiom, % 187.88/188.18 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__0,axiom, % 187.88/188.18 ! [T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__0__eq__iff,axiom, % 187.88/188.18 ! [V_z_2,T_b] : % 187.88/188.18 ( class_Int_Oring__char__0(T_b) % 187.88/188.18 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 187.88/188.18 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__eq__0__iff,axiom, % 187.88/188.18 ! [V_z_2,T_b] : % 187.88/188.18 ( class_Int_Oring__char__0(T_b) % 187.88/188.18 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.18 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__le__iff,axiom, % 187.88/188.18 ! [V_z_2,V_w_2,T_b] : % 187.88/188.18 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__less__iff,axiom, % 187.88/188.18 ! [V_z_2,V_w_2,T_b] : % 187.88/188.18 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__add,axiom, % 187.88/188.18 ! [V_z,V_w,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__number__of__eq,axiom, % 187.88/188.18 ! [V_v,T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__mult,axiom, % 187.88/188.18 ! [V_z,V_w,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__1,axiom, % 187.88/188.18 ! [T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__diff,axiom, % 187.88/188.18 ! [V_z,V_w,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Osingleton,axiom, % 187.88/188.18 ! [V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => 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 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__of__nat__eq,axiom, % 187.88/188.18 ! [V_n,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__minus,axiom, % 187.88/188.18 ! [V_z,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Ints__of__int,axiom, % 187.88/188.18 ! [V_z_2,T_b] : % 187.88/188.18 ( class_Rings_Oring__1(T_b) % 187.88/188.18 => 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))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__power,axiom, % 187.88/188.18 ! [V_n,V_z,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_greaterThanLessThan__empty,axiom, % 187.88/188.18 ! [V_k_2,V_l_2,T_b] : % 187.88/188.18 ( class_Orderings_Oorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 187.88/188.18 => 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)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_image__uminus__greaterThanLessThan,axiom, % 187.88/188.18 ! [V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.18 => 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)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min__le,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 187.88/188.18 ! [V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => 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 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min__in,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oin__idem,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__m1,axiom, % 187.88/188.18 ! [T_a] : % 187.88/188.18 ( class_Int_Onumber__ring(T_a) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_OF__eq,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__0__le__iff,axiom, % 187.88/188.18 ! [V_z_2,T_b] : % 187.88/188.18 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__le__0__iff,axiom, % 187.88/188.18 ! [V_z_2,T_b] : % 187.88/188.18 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__0__less__iff,axiom, % 187.88/188.18 ! [V_z_2,T_b] : % 187.88/188.18 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__less__0__iff,axiom, % 187.88/188.18 ! [V_z_2,T_b] : % 187.88/188.18 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 187.88/188.18 ! [V_B_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__nat__nat,axiom, % 187.88/188.18 ! [V_z,T_a] : % 187.88/188.18 ( class_Rings_Oring__1(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.88/188.18 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min__antimono,axiom, % 187.88/188.18 ! [V_N_2,V_M_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 187.88/188.18 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.18 => 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))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 187.88/188.18 ! [V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min__insert,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Osubset__idem,axiom, % 187.88/188.18 ! [V_B_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oeq__fold__idem_H,axiom, % 187.88/188.18 ! [V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => 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 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oinsert,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oinsert__remove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oeq__fold_H,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_code__numeral_Osize_I3_J,axiom, % 187.88/188.18 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__num,axiom, % 187.88/188.18 ! [V_k_2,T_b] : % 187.88/188.18 ( class_Rings_Oring__1(T_b) % 187.88/188.18 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 187.88/188.18 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => 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))) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.18 => 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))))) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( ! [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)))))) % 187.88/188.18 => 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)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Min_Oclosed,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( ! [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)))))) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__gen__delta,axiom, % 187.88/188.18 ! [V_ca_2,V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.18 => 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)))) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.18 => 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)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_add__Min__commute,axiom, % 187.88/188.18 ! [V_k_2,V_N_2,T_b] : % 187.88/188.18 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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))))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_finite__greaterThanLessThan,axiom, % 187.88/188.18 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__int__setprod,axiom, % 187.88/188.18 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.18 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 187.88/188.18 & class_Rings_Oring__1(T_b) ) % 187.88/188.18 => 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) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 187.88/188.18 ! [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)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_int__setprod,axiom, % 187.88/188.18 ! [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) ). % 187.88/188.18 % 187.88/188.18 fof(fact_of__nat__setprod,axiom, % 187.88/188.18 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.18 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 187.88/188.18 & class_Rings_Osemiring__1(T_b) ) % 187.88/188.18 => 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) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__timesf,axiom, % 187.88/188.18 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.88/188.18 => 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)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__1,axiom, % 187.88/188.18 ! [V_A_2,T_c,T_b] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.88/188.18 => 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) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 187.88/188.18 ! [V_A_2,V_f_2,T_b] : % 187.88/188.18 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.18 & class_Groups_Ocomm__monoid__mult(T_b) ) % 187.88/188.18 => 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)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__zero,axiom, % 187.88/188.18 ! [V_f_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Rings_Ocomm__semiring__1(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ? [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.18 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__zero__iff,axiom, % 187.88/188.18 ! [V_f_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( ( class_Rings_Ocomm__semiring__1(T_c) % 187.88/188.18 & class_Rings_Ono__zero__divisors(T_c) ) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( 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) % 187.88/188.18 <=> ? [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.18 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Oempty,axiom, % 187.88/188.18 ! [V_g_2,T_c,T_b] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.88/188.18 => 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) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__empty,axiom, % 187.88/188.18 ! [V_f_2,T_c,T_b] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.88/188.18 => 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) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Oinfinite,axiom, % 187.88/188.18 ! [V_g_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__infinite,axiom, % 187.88/188.18 ! [V_f_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__eq__1__iff,axiom, % 187.88/188.18 ! [V_f_2,V_F_2,T_b] : % 187.88/188.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.18 => ( 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) % 187.88/188.18 <=> ! [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 187.88/188.18 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 187.88/188.18 ! [V_f_2,V_A_2,T_b] : % 187.88/188.18 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.18 & class_Groups_Ocomm__monoid__mult(T_b) ) % 187.88/188.18 => ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.18 => 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)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Odistrib,axiom, % 187.88/188.18 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_finite__image__set,axiom, % 187.88/188.18 ! [V_f_2,T_c,V_Pa_2,T_b] : % 187.88/188.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.18 => 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))))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_finite__Collect__bounded__ex,axiom, % 187.88/188.18 ! [V_Q_2,T_c,V_Pa_2,T_b] : % 187.88/188.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 187.88/188.18 => ( 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))))) % 187.88/188.18 <=> ! [B_y] : % 187.88/188.18 ( hBOOL(hAPP(V_Pa_2,B_y)) % 187.88/188.18 => 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)))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__pos__nat__iff,axiom, % 187.88/188.18 ! [V_f_2,V_S_2,T_b] : % 187.88/188.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> ! [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__reindex__cong,axiom, % 187.88/188.18 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_d) % 187.88/188.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.18 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 187.88/188.18 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 187.88/188.18 => 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) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__reindex,axiom, % 187.88/188.18 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_d) % 187.88/188.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__delta,axiom, % 187.88/188.18 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.18 => 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) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.18 => 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) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__delta_H,axiom, % 187.88/188.18 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.18 => 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) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.18 => 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) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__constant,axiom, % 187.88/188.18 ! [V_y_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__insert,axiom, % 187.88/188.18 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Oinsert,axiom, % 187.88/188.18 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Oreindex,axiom, % 187.88/188.18 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Oeq__fold,axiom, % 187.88/188.18 ! [V_g_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_OF__eq,axiom, % 187.88/188.18 ! [V_g_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Oinsert__remove,axiom, % 187.88/188.18 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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)))))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_card__greaterThanLessThan,axiom, % 187.88/188.18 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod_Oremove,axiom, % 187.88/188.18 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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)))))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_int__ge__less__than2__def,axiom, % 187.88/188.18 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_int__ge__less__than__def,axiom, % 187.88/188.18 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_add__Max__commute,axiom, % 187.88/188.18 ! [V_k_2,V_N_2,T_b] : % 187.88/188.18 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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))))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_divmod__int__rel__def,axiom, % 187.88/188.18 ! [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))))))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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))))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__diff__distrib__left,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Groups_Oordered__ab__group__add(T_a) % 187.88/188.18 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__0R,axiom, % 187.88/188.18 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__0L,axiom, % 187.88/188.18 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__Suc__Suc,axiom, % 187.88/188.18 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup_Oidem,axiom, % 187.88/188.18 ! [V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup_Ocommute,axiom, % 187.88/188.18 ! [V_b,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__commute,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup_Oleft__idem,axiom, % 187.88/188.18 ! [V_b,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__left__idem,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup_Oleft__commute,axiom, % 187.88/188.18 ! [V_c,V_a,V_b,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__left__commute,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup_Oassoc,axiom, % 187.88/188.18 ! [V_c,V_b,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__assoc,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__add__distrib__left,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.88/188.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__less__iff__conj,axiom, % 187.88/188.18 ! [V_z_2,V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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)) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_less__max__iff__disj,axiom, % 187.88/188.18 ! [V_y_2,V_x_2,V_z_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 187.88/188.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oless__supI2,axiom, % 187.88/188.18 ! [V_a,V_b,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oless__supI1,axiom, % 187.88/188.18 ! [V_b,V_a,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_le__maxI1,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_le__maxI2,axiom, % 187.88/188.18 ! [V_x,V_y,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__iff__sup,axiom, % 187.88/188.18 ! [V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.18 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__sup__iff,axiom, % 187.88/188.18 ! [V_z_2,V_y_2,V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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)) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 187.88/188.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__supI1,axiom, % 187.88/188.18 ! [V_b,V_a,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__supI2,axiom, % 187.88/188.18 ! [V_a,V_b,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__absorb2,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__absorb1,axiom, % 187.88/188.18 ! [V_x,V_y,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__supI,axiom, % 187.88/188.18 ! [V_b,V_x,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__least,axiom, % 187.88/188.18 ! [V_z,V_x,V_y,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__mono,axiom, % 187.88/188.18 ! [V_d,V_b,V_c,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ole__supE,axiom, % 187.88/188.18 ! [V_x,V_b,V_a,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) % 187.88/188.18 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.88/188.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_le__max__iff__disj,axiom, % 187.88/188.18 ! [V_y_2,V_x_2,V_z_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( 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))) % 187.88/188.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 187.88/188.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_OF__eq,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oin__idem,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oidem,axiom, % 187.88/188.18 ! [V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__inf__absorb,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__sup__absorb,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__inf__distrib1,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__inf__distrib2,axiom, % 187.88/188.18 ! [V_x,V_z,V_y,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 187.88/188.18 ! [V_x,V_z,V_y,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 187.88/188.18 ! [T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max__insert,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Osubset__idem,axiom, % 187.88/188.18 ! [V_B_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oeq__fold__idem_H,axiom, % 187.88/188.18 ! [V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__number__of,axiom, % 187.88/188.18 ! [V_v,V_u,T_b] : % 187.88/188.18 ( ( class_Int_Onumber(T_b) % 187.88/188.18 & class_Orderings_Oord(T_b) ) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 187.88/188.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oinsert,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Odistrib__inf__le,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Odistrib__sup__le,axiom, % 187.88/188.18 ! [V_z,V_y,V_x,T_a] : % 187.88/188.18 ( class_Orderings_Olinorder(T_a) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oinsert__remove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oeq__fold_H,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_minus__max__eq__min,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.88/188.18 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_minus__min__eq__max,axiom, % 187.88/188.18 ! [V_y,V_x,T_a] : % 187.88/188.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.88/188.18 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nat__minus__add__max,axiom, % 187.88/188.18 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ). % 187.88/188.18 % 187.88/188.18 fof(fact_inj__graph,axiom, % 187.88/188.18 ! [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))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Osingleton,axiom, % 187.88/188.18 ! [V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => 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 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oremove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__Suc2,axiom, % 187.88/188.18 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__Suc1,axiom, % 187.88/188.18 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__ord__max,axiom, % 187.88/188.18 ! [T_b] : % 187.88/188.18 ( class_Orderings_Oord(T_b) % 187.88/188.18 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Ofold__sup__insert,axiom, % 187.88/188.18 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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)) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_divmod__int__correct,axiom, % 187.88/188.18 ! [V_a,V_b] : % 187.88/188.18 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_dual__min,axiom, % 187.88/188.18 ! [T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => 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) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max__ge,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max__in,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__le__fold__sup,axiom, % 187.88/188.18 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__Inf__absorb,axiom, % 187.88/188.18 ! [V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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 ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max__mono,axiom, % 187.88/188.18 ! [V_N_2,V_M_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 187.88/188.18 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.18 => 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))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_minus__Min__eq__Max,axiom, % 187.88/188.18 ! [V_S_2,T_b] : % 187.88/188.18 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.18 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_minus__Max__eq__Min,axiom, % 187.88/188.18 ! [V_S_2,T_b] : % 187.88/188.18 ( class_Groups_Olinordered__ab__group__add(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.18 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__number__of__Suc,axiom, % 187.88/188.18 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_max__Suc__number__of,axiom, % 187.88/188.18 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 187.88/188.18 ! [V_B_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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))))))) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nitpick_Oprod__def,axiom, % 187.88/188.18 ! [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)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Nitpick_OFrac__def,axiom, % 187.88/188.18 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 187.88/188.18 ! [V_f_2,V_A_2,T_b] : % 187.88/188.18 ( ! [B_x] : % 187.88/188.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.18 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 187.88/188.18 => 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)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 187.88/188.18 ! [V_B_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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))))))) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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))))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 187.88/188.18 ! [V_x_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => 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 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 187.88/188.18 ! [V_B_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 187.88/188.18 ! [V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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 ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 187.88/188.18 ! [V_a_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => 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) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => 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 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oremove,axiom, % 187.88/188.18 ! [V_x_2,V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.18 => ( ( 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)) % 187.88/188.18 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 187.88/188.18 & ( 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)) % 187.88/188.18 => 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)))))) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OInf__le__Sup,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => 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))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( ! [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)))))) % 187.88/188.18 => 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)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_Max_Oclosed,axiom, % 187.88/188.18 ! [V_A_2,T_b] : % 187.88/188.18 ( class_Orderings_Olinorder(T_b) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.18 => ( ! [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)))))) % 187.88/188.18 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_zmult2__lemma,axiom, % 187.88/188.18 ! [V_c,V_r,V_q,V_b,V_a] : % 187.88/188.18 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.18 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.88/188.18 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_setprod__diff1,axiom, % 187.88/188.18 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 187.88/188.18 ( class_Fields_Ofield(T_c) % 187.88/188.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.18 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 187.88/188.18 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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)) ) % 187.88/188.18 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.18 => 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) ) ) ) ) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_adjust__def,axiom, % 187.88/188.18 ! [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))))))) ). % 187.88/188.18 % 187.88/188.18 fof(fact_pred__equals__eq2,axiom, % 187.88/188.18 ! [V_S_2,V_R_2,T_c,T_b] : % 187.88/188.18 ( 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) % 187.88/188.18 <=> V_R_2 = V_S_2 ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_bot__empty__eq2,axiom, % 187.88/188.18 ! [V_y_2,V_x_2,T_c,T_b] : % 187.88/188.18 ( 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)) % 187.88/188.18 <=> 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)))) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_pred__subset__eq2,axiom, % 187.88/188.18 ! [V_S_2,V_R_2,T_c,T_b] : % 187.88/188.18 ( 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))) % 187.88/188.18 <=> 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)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_divide__1,axiom, % 187.88/188.18 ! [V_a,T_a] : % 187.88/188.18 ( class_Rings_Odivision__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_minus__divide__left,axiom, % 187.88/188.18 ! [V_b,V_a,T_a] : % 187.88/188.18 ( class_Rings_Odivision__ring(T_a) % 187.88/188.18 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_power__divide,axiom, % 187.88/188.18 ! [V_n,V_b,V_a,T_a] : % 187.88/188.18 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.18 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_diff__divide__distrib,axiom, % 187.88/188.18 ! [V_c,V_b,V_a,T_a] : % 187.88/188.18 ( class_Rings_Odivision__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_times__divide__eq__right,axiom, % 187.88/188.18 ! [V_c,V_b,V_a,T_a] : % 187.88/188.18 ( class_Rings_Odivision__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_add__divide__distrib,axiom, % 187.88/188.18 ! [V_c,V_b,V_a,T_a] : % 187.88/188.18 ( class_Rings_Odivision__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_divide__zero,axiom, % 187.88/188.18 ! [V_a,T_a] : % 187.88/188.18 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 187.88/188.18 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_divide__zero__left,axiom, % 187.88/188.18 ! [V_a,T_a] : % 187.88/188.18 ( class_Rings_Odivision__ring(T_a) % 187.88/188.18 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.18 % 187.88/188.18 fof(fact_nonzero__eq__divide__eq,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_b) % 187.88/188.19 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 187.88/188.19 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nonzero__divide__eq__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_b) % 187.88/188.19 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 187.88/188.19 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__eq__imp,axiom, % 187.88/188.19 ! [V_a,V_b,V_c,T_a] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_a) % 187.88/188.19 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_eq__divide__imp,axiom, % 187.88/188.19 ! [V_b,V_a,V_c,T_a] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_a) % 187.88/188.19 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 187.88/188.19 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__self__if,axiom, % 187.88/188.19 ! [V_a,T_a] : % 187.88/188.19 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 187.88/188.19 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 187.88/188.19 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__self,axiom, % 187.88/188.19 ! [V_a,T_a] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_a) % 187.88/188.19 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_right__inverse__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_b) % 187.88/188.19 => ( V_ba_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2) = c_Groups_Oone__class_Oone(T_b) % 187.88/188.19 <=> V_a_2 = V_ba_2 ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nonzero__minus__divide__right,axiom, % 187.88/188.19 ! [V_a,V_b,T_a] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_a) % 187.88/188.19 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nonzero__minus__divide__divide,axiom, % 187.88/188.19 ! [V_a,V_b,T_a] : % 187.88/188.19 ( class_Rings_Odivision__ring(T_a) % 187.88/188.19 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nonzero__power__divide,axiom, % 187.88/188.19 ! [V_n,V_a,V_b,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_power__one__over,axiom, % 187.88/188.19 ! [V_n,V_a,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__rel__0,axiom, % 187.88/188.19 ! [V_b] : % 187.88/188.19 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_self__remainder,axiom, % 187.88/188.19 ! [V_r,V_q,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.19 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_unique__quotient,axiom, % 187.88/188.19 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.19 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 187.88/188.19 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => V_q = V_q_H ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_unique__remainder,axiom, % 187.88/188.19 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.19 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 187.88/188.19 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => V_r = V_r_H ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_setprod__dividef,axiom, % 187.88/188.19 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_c) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_eq__divide__eq__number__of1,axiom, % 187.88/188.19 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( ( class_Fields_Ofield__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => 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 ) % 187.88/188.19 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_eq__divide__eq__number__of,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 187.88/188.19 ( ( class_Fields_Ofield__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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) % 187.88/188.19 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => 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 ) % 187.88/188.19 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__eq__eq__number__of,axiom, % 187.88/188.19 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 187.88/188.19 ( ( class_Fields_Ofield__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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) % 187.88/188.19 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => 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) ) % 187.88/188.19 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__eq__eq__number__of1,axiom, % 187.88/188.19 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 187.88/188.19 ( ( class_Fields_Ofield__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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 % 187.88/188.19 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__Numeral0,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 & class_Int_Onumber__ring(T_a) ) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__Numeral1,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( ( class_Fields_Ofield(T_a) % 187.88/188.19 & class_Int_Onumber__ring(T_a) ) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__numeral__1,axiom, % 187.88/188.19 ! [V_a,T_a] : % 187.88/188.19 ( ( class_Fields_Ofield(T_a) % 187.88/188.19 & class_Int_Onumber__ring(T_a) ) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__minus1,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 & class_Int_Onumber__ring(T_a) ) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_self__quotient,axiom, % 187.88/188.19 ! [V_r,V_q,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.19 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__rel__mod,axiom, % 187.88/188.19 ! [V_r,V_q,V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.19 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__rel__div,axiom, % 187.88/188.19 ! [V_r,V_q,V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.19 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__mod__div,axiom, % 187.88/188.19 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__less__eq__number__of1,axiom, % 187.88/188.19 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ( ( 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))) % 187.88/188.19 => 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)))) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => ( ( 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))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__less__eq__number__of,axiom, % 187.88/188.19 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__divide__eq__number__of,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__divide__eq__number__of1,axiom, % 187.88/188.19 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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)))) % 187.88/188.19 <=> ( ( 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))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => ( ( 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))) % 187.88/188.19 => 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)))) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_power__diff,axiom, % 187.88/188.19 ! [V_m,V_n,V_a,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.19 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_minus1__divide,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 & class_Int_Onumber__ring(T_a) ) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__rel__div__mod,axiom, % 187.88/188.19 ! [V_a,V_b] : % 187.88/188.19 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__le__eq__number__of1,axiom, % 187.88/188.19 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ( ( 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))) % 187.88/188.19 => 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)))) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => ( ( 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))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__le__eq__number__of,axiom, % 187.88/188.19 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__divide__eq__number__of,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__divide__eq__number__of1,axiom, % 187.88/188.19 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber(T_b) ) % 187.88/188.19 => ( 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)))) % 187.88/188.19 <=> ( ( 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))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => ( ( 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))) % 187.88/188.19 => 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)))) ) % 187.88/188.19 & ( ~ 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))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_zadd1__lemma,axiom, % 187.88/188.19 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar))) % 187.88/188.19 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br))) % 187.88/188.19 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_zminus1__lemma,axiom, % 187.88/188.19 ! [V_r_2,V_q_2,V_ba_2,V_a_2] : % 187.88/188.19 ( 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))) % 187.88/188.19 => 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))))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_half__gt__zero,axiom, % 187.88/188.19 ! [V_r,T_a] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.88/188.19 & class_Int_Onumber__ring(T_a) ) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_half__gt__zero__iff,axiom, % 187.88/188.19 ! [V_r_2,T_b] : % 187.88/188.19 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 & class_Int_Onumber__ring(T_b) ) % 187.88/188.19 => ( 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)))))) % 187.88/188.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__relI,axiom, % 187.88/188.19 ! [V_r,V_q,V_b,V_a] : % 187.88/188.19 ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) % 187.88/188.19 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_zmult1__lemma,axiom, % 187.88/188.19 ! [V_a,V_r,V_q,V_c,V_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 187.88/188.19 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_adjust__eq,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pair__imageI,axiom, % 187.88/188.19 ! [V_f_2,T_d,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_norm__frac_Osimps,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2] : % 187.88/188.19 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.19 => 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))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 187.88/188.19 ! [V_w] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 187.88/188.19 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 187.88/188.19 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_splitI,axiom, % 187.88/188.19 ! [T_c,T_b,V_ba_2,V_a_2,V_f_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_prod__caseI,axiom, % 187.88/188.19 ! [T_c,T_b,V_ba_2,V_a_2,V_f1_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_ba_2)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mem__splitI,axiom, % 187.88/188.19 ! [T_d,T_c,V_ba_2,V_a_2,V_ca_2,V_z_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_ba_2))) % 187.88/188.19 => 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)))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_bot2E,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_splitD_H,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_ba_2),V_ca_2)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__by__empty,axiom, % 187.88/188.19 ! [V_B_2,T_b,V_A_2] : % 187.88/188.19 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_predicate2D,axiom, % 187.88/188.19 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_rev__predicate2D,axiom, % 187.88/188.19 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 187.88/188.19 => ( 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)) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__paired__All,axiom, % 187.88/188.19 ! [T_c,T_b,V_Pa_2] : % 187.88/188.19 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 187.88/188.19 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Pair__eq,axiom, % 187.88/188.19 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 187.88/188.19 ( 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) % 187.88/188.19 <=> ( V_a_2 = V_a_H_2 % 187.88/188.19 & V_ba_2 = V_b_H_2 ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Pair__inject,axiom, % 187.88/188.19 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 187.88/188.19 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) % 187.88/188.19 => ~ ( V_a = V_a_H % 187.88/188.19 => V_b != V_b_H ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__weak__cong,axiom, % 187.88/188.19 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 187.88/188.19 ( V_p_2 = V_q_2 % 187.88/188.19 => 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) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg__correct,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_prod_Osimps_I2_J,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__conv,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_splitD,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg__div__mod,axiom, % 187.88/188.19 ! [V_l,V_k] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.88/188.19 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg__minus1,axiom, % 187.88/188.19 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__eta,axiom, % 187.88/188.19 ! [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 ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__paired__The,axiom, % 187.88/188.19 ! [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)))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_The__split__eq,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_swap__inj__on,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__twice,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg_Osimps,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 187.88/188.19 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg__eqn__number__of,axiom, % 187.88/188.19 ! [V_w,V_v] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 187.88/188.19 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 187.88/188.19 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg__eqn,axiom, % 187.88/188.19 ! [V_a,V_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 187.88/188.19 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 187.88/188.19 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_in__rel__def,axiom, % 187.88/188.19 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 187.88/188.19 <=> 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__mod__code__numeral__def,axiom, % 187.88/188.19 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__divide__eq,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__le__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_times__divide__times__eq,axiom, % 187.88/188.19 ! [V_w,V_z,V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_minus__divide__divide,axiom, % 187.88/188.19 ! [V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_minus__divide__right,axiom, % 187.88/188.19 ! [V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__right__mono__neg,axiom, % 187.88/188.19 ! [V_c,V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__right__mono,axiom, % 187.88/188.19 ! [V_c,V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__le__0__iff,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 187.88/188.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_zero__le__divide__iff,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 187.88/188.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__strict__right__mono__neg,axiom, % 187.88/188.19 ! [V_c,V_a,V_b,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__strict__right__mono,axiom, % 187.88/188.19 ! [V_c,V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__neg__neg,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__neg__pos,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__pos__neg,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__pos__pos,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__less__0__iff,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 187.88/188.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_zero__less__divide__iff,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 187.88/188.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_eq__divide__eq,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_b) % 187.88/188.19 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 187.88/188.19 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) % 187.88/188.19 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__eq__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_b) % 187.88/188.19 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 187.88/188.19 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) % 187.88/188.19 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mult__divide__mult__cancel__right,axiom, % 187.88/188.19 ! [V_b,V_a,V_c,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mult__divide__mult__cancel__left,axiom, % 187.88/188.19 ! [V_b,V_a,V_c,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_frac__eq__eq,axiom, % 187.88/188.19 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 187.88/188.19 ( class_Fields_Ofield(T_b) % 187.88/188.19 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.19 => ( 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) % 187.88/188.19 <=> 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) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__nonpos__neg,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__nonpos__pos,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_frac__le,axiom, % 187.88/188.19 ! [V_z,V_w,V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_frac__less,axiom, % 187.88/188.19 ! [V_z,V_w,V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_frac__less2,axiom, % 187.88/188.19 ! [V_z,V_w,V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__nonneg__neg,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__nonneg__pos,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__strict__left__mono__neg,axiom, % 187.88/188.19 ! [V_c,V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__strict__left__mono,axiom, % 187.88/188.19 ! [V_c,V_a,V_b,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_neg__divide__less__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_neg__less__divide__eq,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mult__imp__less__div__pos,axiom, % 187.88/188.19 ! [V_x,V_z,V_y,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mult__imp__div__pos__less,axiom, % 187.88/188.19 ! [V_z,V_x,V_y,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pos__divide__less__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pos__less__divide__eq,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__less__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__divide__eq,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_add__num__frac,axiom, % 187.88/188.19 ! [V_x,V_z,V_y,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_add__divide__eq__iff,axiom, % 187.88/188.19 ! [V_y,V_x,V_z,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_add__frac__num,axiom, % 187.88/188.19 ! [V_z,V_x,V_y,T_a] : % 187.88/188.19 ( class_Fields_Ofield__inverse__zero(T_a) % 187.88/188.19 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__add__eq__iff,axiom, % 187.88/188.19 ! [V_y,V_x,V_z,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_add__frac__eq,axiom, % 187.88/188.19 ! [V_w,V_x,V_z,V_y,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_diff__frac__eq,axiom, % 187.88/188.19 ! [V_w,V_x,V_z,V_y,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__diff__eq__iff,axiom, % 187.88/188.19 ! [V_y,V_x,V_z,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_diff__divide__eq__iff,axiom, % 187.88/188.19 ! [V_y,V_x,V_z,T_a] : % 187.88/188.19 ( class_Fields_Ofield(T_a) % 187.88/188.19 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.19 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__half__sum,axiom, % 187.88/188.19 ! [V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_gt__half__sum,axiom, % 187.88/188.19 ! [V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__left__mono__neg,axiom, % 187.88/188.19 ! [V_c,V_b,V_a,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divide__left__mono,axiom, % 187.88/188.19 ! [V_c,V_a,V_b,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_neg__divide__le__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_neg__le__divide__eq,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mult__imp__le__div__pos,axiom, % 187.88/188.19 ! [V_x,V_z,V_y,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mult__imp__div__pos__le,axiom, % 187.88/188.19 ! [V_z,V_x,V_y,T_a] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pos__divide__le__eq,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pos__le__divide__eq,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 187.88/188.19 ( class_Fields_Olinordered__field(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Nitpick_Orefl_H__def,axiom, % 187.88/188.19 ! [V_r_2,T_b] : % 187.88/188.19 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 187.88/188.19 <=> ! [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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 187.88/188.19 ! [V_w] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.19 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.19 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg_Osimps,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 187.88/188.19 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg__eqn__number__of,axiom, % 187.88/188.19 ! [V_w,V_v] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.19 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.88/188.19 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg__0,axiom, % 187.88/188.19 ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg__correct,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg__div__mod,axiom, % 187.88/188.19 ! [V_l,V_k] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.88/188.19 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg__eqn,axiom, % 187.88/188.19 ! [V_a,V_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.88/188.19 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.88/188.19 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__def,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 187.88/188.19 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__step,axiom, % 187.88/188.19 ! [V_m,V_n] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.88/188.19 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg_Opsimps,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2] : % 187.88/188.19 ( 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))) % 187.88/188.19 => ( ( ( 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))) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ ( 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))) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg_Opsimps,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2] : % 187.88/188.19 ( 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))) % 187.88/188.19 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => 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) ) % 187.88/188.19 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__zero,axiom, % 187.88/188.19 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__base,axiom, % 187.88/188.19 ! [V_n,V_m] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.88/188.19 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negateSnd__eq,axiom, % 187.88/188.19 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__div__mod,axiom, % 187.88/188.19 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__int__rel__neg,axiom, % 187.88/188.19 ! [V_qr,V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr)) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__if,axiom, % 187.88/188.19 ! [V_m_2,V_n_2] : % 187.88/188.19 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 187.88/188.19 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) % 187.88/188.19 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 187.88/188.19 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_norm__frac_Opsimps,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2] : % 187.88/188.19 ( 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))) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.19 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.88/188.19 => 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))) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negDivAlg_Opinduct,axiom, % 187.88/188.19 ! [V_Pa_2,V_a1_2,V_a0_2] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 187.88/188.19 => ( ! [B_a,B_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 187.88/188.19 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => 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))) ) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_posDivAlg_Opinduct,axiom, % 187.88/188.19 ! [V_Pa_2,V_a1_2,V_a0_2] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 187.88/188.19 => ( ! [B_a,B_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 187.88/188.19 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.88/188.19 => 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))) ) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_accp__subset,axiom, % 187.88/188.19 ! [V_R2_2,V_R1_2,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_accp_Osimps,axiom, % 187.88/188.19 ! [V_a_2,V_r_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 187.88/188.19 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_accp_Oequations,axiom, % 187.88/188.19 ! [V_a_2,V_r_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 187.88/188.19 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_accp__downward,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,V_r_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_ba_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 187.88/188.19 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 187.88/188.19 ! [V_c,V_r,V_q,V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 187.88/188.19 ! [V_a,V_r,V_q,V_c,V_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nat_Osize_I2_J,axiom, % 187.88/188.19 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__rel__add1__eq,axiom, % 187.88/188.19 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar))) % 187.88/188.19 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.88/188.19 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__rel__unique,axiom, % 187.88/188.19 ! [V_qr_H,V_qr,V_n,V_m] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 187.88/188.19 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 187.88/188.19 => V_qr = V_qr_H ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 187.88/188.19 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__eq,axiom, % 187.88/188.19 ! [V_qr,V_n,V_m] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 187.88/188.19 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__def,axiom, % 187.88/188.19 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__eq,axiom, % 187.88/188.19 ! [V_r,V_q,V_n,V_m] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__eq,axiom, % 187.88/188.19 ! [V_r,V_q,V_n,V_m] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nat_Osize_I1_J,axiom, % 187.88/188.19 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__rel,axiom, % 187.88/188.19 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__pos__neg__1__number__of,axiom, % 187.88/188.19 ! [V_w] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_in__measure,axiom, % 187.88/188.19 ! [V_f_2,V_y_2,V_x_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_norm__frac_Opinduct,axiom, % 187.88/188.19 ! [V_Pa_2,V_a1_2,V_a0_2] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 187.88/188.19 => ( ! [B_a,B_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => 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))) ) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__pos__neg__1__number__of,axiom, % 187.88/188.19 ! [V_w] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_surjective__pairing,axiom, % 187.88/188.19 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_fst__conv,axiom, % 187.88/188.19 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ). % 187.88/188.19 % 187.88/188.19 fof(fact_snd__conv,axiom, % 187.88/188.19 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ). % 187.88/188.19 % 187.88/188.19 fof(fact_pair__collapse,axiom, % 187.88/188.19 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ). % 187.88/188.19 % 187.88/188.19 fof(fact_fst__eqD,axiom, % 187.88/188.19 ! [V_a,V_y,V_x,T_b,T_a] : % 187.88/188.19 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a % 187.88/188.19 => V_x = V_a ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_snd__eqD,axiom, % 187.88/188.19 ! [V_a,V_y,V_x,T_a,T_b] : % 187.88/188.19 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a % 187.88/188.19 => V_y = V_a ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_prod__eqI,axiom, % 187.88/188.19 ! [V_q,V_p,T_b,T_a] : % 187.88/188.19 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 187.88/188.19 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 187.88/188.19 => V_p = V_q ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Pair__fst__snd__eq,axiom, % 187.88/188.19 ! [T_c,T_b,V_t_2,V_s_2] : % 187.88/188.19 ( V_s_2 = V_t_2 % 187.88/188.19 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 187.88/188.19 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__comp,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__beta,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_prod__case__beta,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__comp__eq,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_split__def,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_The__split,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_fst__def,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_snd__def,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__int__def,axiom, % 187.88/188.19 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__int__def,axiom, % 187.88/188.19 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__neg__pos,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__neg__pos,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__pos__pos,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__pos__pos,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__pos__pos__1__number__of,axiom, % 187.88/188.19 ! [V_w] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__pos__pos__1__number__of,axiom, % 187.88/188.19 ! [V_w] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__pos__neg,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__pos__neg,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__neg__neg,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__neg__neg,axiom, % 187.88/188.19 ! [V_b,V_a] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_prod__size__simp,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_conjI__realizer,axiom, % 187.88/188.19 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] : % 187.88/188.19 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 187.88/188.19 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 187.88/188.19 => ( 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)))) % 187.88/188.19 & 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)))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_exI__realizer,axiom, % 187.88/188.19 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 187.88/188.19 => 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)))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mlex__leq,axiom, % 187.88/188.19 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 187.88/188.19 => ( 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)) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_div__nat__def,axiom, % 187.88/188.19 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mod__nat__def,axiom, % 187.88/188.19 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_divmod__nat__rel__def,axiom, % 187.88/188.19 ! [V_qr_2,V_n_2,V_m_2] : % 187.88/188.19 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 187.88/188.19 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) % 187.88/188.19 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.19 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.19 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) ) % 187.88/188.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mlex__less,axiom, % 187.88/188.19 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_finite__psubset__def,axiom, % 187.88/188.19 ! [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)))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nat_Osize_I4_J,axiom, % 187.88/188.19 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_prod_Orecs,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_in__lex__prod,axiom, % 187.88/188.19 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 <=> ( 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)) % 187.88/188.19 | ( V_a_2 = V_a_H_2 % 187.88/188.19 & 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nat__size,axiom, % 187.88/188.19 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 187.88/188.19 % 187.88/188.19 fof(fact_nat_Osize_I3_J,axiom, % 187.88/188.19 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.88/188.19 % 187.88/188.19 fof(fact_in__finite__psubset,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_same__fstI,axiom, % 187.88/188.19 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 187.88/188.19 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 187.88/188.19 => ( 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))) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pair__lessI2,axiom, % 187.88/188.19 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 187.88/188.19 ! [V_N_2,V_h_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( ! [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)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.19 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 187.88/188.19 ! [V_N_2,V_h_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( ! [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)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.19 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pair__lessI1,axiom, % 187.88/188.19 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pair__leqI2,axiom, % 187.88/188.19 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_smax__insertI,axiom, % 187.88/188.19 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_smin__insertI,axiom, % 187.88/188.19 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pair__leqI1,axiom, % 187.88/188.19 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_smax__emptyI,axiom, % 187.88/188.19 ! [V_Y_2] : % 187.88/188.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 187.88/188.19 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_smin__emptyI,axiom, % 187.88/188.19 ! [V_X_2] : % 187.88/188.19 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_wmin__insertI,axiom, % 187.88/188.19 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_wmax__insertI,axiom, % 187.88/188.19 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_wmax__emptyI,axiom, % 187.88/188.19 ! [V_X_2] : % 187.88/188.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_wmin__emptyI,axiom, % 187.88/188.19 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_max__rpair__set,axiom, % 187.88/188.19 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_min__rpair__set,axiom, % 187.88/188.19 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_min__strict__def,axiom, % 187.88/188.19 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__than__iff,axiom, % 187.88/188.19 ! [V_y_2,V_x_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) % 187.88/188.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_pair__less__def,axiom, % 187.88/188.19 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mlex__prod__def,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_min__weak__def,axiom, % 187.88/188.19 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_intrel__iff,axiom, % 187.88/188.19 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) % 187.88/188.19 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_rp__inv__image__rp,axiom, % 187.88/188.19 ! [V_f_2,T_c,V_Pa_2,T_b] : % 187.88/188.19 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 187.88/188.19 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup1E,axiom, % 187.88/188.19 ! [V_x_2,V_B_2,V_A_2,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 187.88/188.19 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup1CI,axiom, % 187.88/188.19 ! [T_b,V_A_2,V_x_2,V_B_2] : % 187.88/188.19 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 187.88/188.19 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UnE,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UnCI,axiom, % 187.88/188.19 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 187.88/188.19 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UnI2,axiom, % 187.88/188.19 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UnI1,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__iff,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.19 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__insert__right,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__insert__left,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_fun__left__comm__idem__sup,axiom, % 187.88/188.19 ! [T_b] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_b) % 187.88/188.19 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__upper1,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__upper2,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_subset__Un__eq,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.19 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__absorb1,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__absorb2,axiom, % 187.88/188.19 ! [V_A_2,V_B_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__least,axiom, % 187.88/188.19 ! [V_B_2,V_C_2,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__mono,axiom, % 187.88/188.19 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_image__Un,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__supE,axiom, % 187.88/188.19 ! [V_x,V_b,V_a,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) % 187.88/188.19 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.88/188.19 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__mono,axiom, % 187.88/188.19 ! [V_d,V_b,V_c,V_a,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__least,axiom, % 187.88/188.19 ! [V_z,V_x,V_y,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__supI,axiom, % 187.88/188.19 ! [V_b,V_x,V_a,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__absorb1,axiom, % 187.88/188.19 ! [V_x,V_y,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__absorb2,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__supI2,axiom, % 187.88/188.19 ! [V_a,V_b,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__supI1,axiom, % 187.88/188.19 ! [V_b,V_a,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__sup__iff,axiom, % 187.88/188.19 ! [V_z_2,V_y_2,V_x_2,T_b] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_b) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__iff__sup,axiom, % 187.88/188.19 ! [V_y_2,V_x_2,T_b] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.19 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__ge2,axiom, % 187.88/188.19 ! [V_x,V_y,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inf__sup__ord_I4_J,axiom, % 187.88/188.19 ! [V_x,V_y,T_a] : % 187.88/188.19 ( class_Lattices_Olattice(T_a) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__ge1,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inf__sup__ord_I3_J,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Olattice(T_a) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__max,axiom, % 187.88/188.19 ! [T_b] : % 187.88/188.19 ( ( class_Lattices_Osemilattice__sup(T_b) % 187.88/188.19 & class_Orderings_Olinorder(T_b) ) % 187.88/188.19 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__fun__def,axiom, % 187.88/188.19 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_vimage__Un,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__Diff,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__Diff__cancel2,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__Diff__cancel,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__top__left,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Obounded__lattice__top(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__top__right,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Obounded__lattice__top(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup_Oidem,axiom, % 187.88/188.19 ! [V_a,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__idem,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup_Ocommute,axiom, % 187.88/188.19 ! [V_b,V_a,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inf__sup__aci_I5_J,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Olattice(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__commute,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup_Oleft__idem,axiom, % 187.88/188.19 ! [V_b,V_a,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inf__sup__aci_I8_J,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Olattice(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__left__idem,axiom, % 187.88/188.19 ! [V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup_Oleft__commute,axiom, % 187.88/188.19 ! [V_c,V_a,V_b,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inf__sup__aci_I7_J,axiom, % 187.88/188.19 ! [V_z,V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Olattice(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__left__commute,axiom, % 187.88/188.19 ! [V_z,V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup_Oassoc,axiom, % 187.88/188.19 ! [V_c,V_b,V_a,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inf__sup__aci_I6_J,axiom, % 187.88/188.19 ! [V_z,V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Olattice(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__assoc,axiom, % 187.88/188.19 ! [V_z,V_y,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__apply,axiom, % 187.88/188.19 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__absorb,axiom, % 187.88/188.19 ! [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 ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__commute,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__left__absorb,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__left__commute,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__assoc,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_bex__Un,axiom, % 187.88/188.19 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 187.88/188.19 ( ? [B_x] : % 187.88/188.19 ( 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))) % 187.88/188.19 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 187.88/188.19 <=> ( ? [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.19 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 187.88/188.19 | ? [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 187.88/188.19 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_ball__Un,axiom, % 187.88/188.19 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 187.88/188.19 ( ! [B_x] : % 187.88/188.19 ( 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))) % 187.88/188.19 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 187.88/188.19 <=> ( ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.19 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 187.88/188.19 & ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 187.88/188.19 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup1I1,axiom, % 187.88/188.19 ! [V_B_2,T_b,V_x_2,V_A_2] : % 187.88/188.19 ( hBOOL(hAPP(V_A_2,V_x_2)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup1I2,axiom, % 187.88/188.19 ! [V_A_2,T_b,V_x_2,V_B_2] : % 187.88/188.19 ( hBOOL(hAPP(V_B_2,V_x_2)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__supI2,axiom, % 187.88/188.19 ! [V_a,V_b,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__supI1,axiom, % 187.88/188.19 ! [V_b,V_a,V_x,T_a] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_a) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__UNIV__right,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__UNIV__left,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oidem,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Olattice(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_finite__Un,axiom, % 187.88/188.19 ! [V_Ga_2,V_F_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_finite__UnI,axiom, % 187.88/188.19 ! [V_Ga_2,V_F_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__empty,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__empty__right,axiom, % 187.88/188.19 ! [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 ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__empty__left,axiom, % 187.88/188.19 ! [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 ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__eq__bot__iff,axiom, % 187.88/188.19 ! [V_y_2,V_x_2,T_b] : % 187.88/188.19 ( class_Lattices_Obounded__lattice__bot(T_b) % 187.88/188.19 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 187.88/188.19 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 187.88/188.19 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__bot__right,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__bot__left,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__Un__eq,axiom, % 187.88/188.19 ! [V_x_2,V_S_2,V_R_2,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Collect__disj__eq,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_compl__sup__top,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__compl__top,axiom, % 187.88/188.19 ! [V_x,T_a] : % 187.88/188.19 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_insert__is__Un,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Diff__subset__conv,axiom, % 187.88/188.19 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Diff__partition,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.19 => 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 ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inj__on__Un__image__eq__iff,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => ( 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) % 187.88/188.19 <=> V_A_2 = V_B_2 ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Compl__partition,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Compl__partition2,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Compl__Diff__eq,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Un__def,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_insert__def,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Collect__imp__eq,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_rp__inv__image__def,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.19 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.19 => 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_fold__sup__insert,axiom, % 187.88/188.19 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_vimage__insert,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_folding__one__idem_Ounion__idem,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.19 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_folding__idem_Ounion__idem,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.19 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__le__fold__sup,axiom, % 187.88/188.19 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Osemilattice__sup(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.19 => 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_union__fold__insert,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_fold1__Un2,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Min__Un,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Max__Un,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_image__eq__fold__image,axiom, % 187.88/188.19 ! [V_f_2,T_c,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_inv__image__def,axiom, % 187.88/188.19 ! [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))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_max__weak__def,axiom, % 187.88/188.19 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_in__inv__image,axiom, % 187.88/188.19 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 <=> 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__Inf1__distrib,axiom, % 187.88/188.19 ! [V_x_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Odistrib__lattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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))))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__nat__def,axiom, % 187.88/188.19 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2] : % 187.88/188.19 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.19 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.19 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Inf__fin_Osingleton,axiom, % 187.88/188.19 ! [V_x_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => 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 ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2] : % 187.88/188.19 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.19 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.19 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__Un__eq2,axiom, % 187.88/188.19 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__Inf__absorb,axiom, % 187.88/188.19 ! [V_a_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.19 => 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 ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_max__strict__def,axiom, % 187.88/188.19 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 187.88/188.19 % 187.88/188.19 fof(fact_measure__def,axiom, % 187.88/188.19 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 187.88/188.19 % 187.88/188.19 fof(fact_max__ext__additive,axiom, % 187.88/188.19 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 => ( 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))) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__Inf2__distrib,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Odistrib__lattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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))))))) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_max__extp__max__ext__eq,axiom, % 187.88/188.19 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 187.88/188.19 ( 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) % 187.88/188.19 <=> 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_irrefl__def,axiom, % 187.88/188.19 ! [V_r_2,T_b] : % 187.88/188.19 ( c_Relation_Oirrefl(T_b,V_r_2) % 187.88/188.19 <=> ! [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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Field__insert,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_ivl__disj__un_I4_J,axiom, % 187.88/188.19 ! [V_u_2,V_l_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 187.88/188.19 => 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) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_finite__greaterThanAtMost,axiom, % 187.88/188.19 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup2E,axiom, % 187.88/188.19 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup2CI,axiom, % 187.88/188.19 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 187.88/188.19 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 187.88/188.19 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_finite__greaterThanAtMost__int,axiom, % 187.88/188.19 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup2I1,axiom, % 187.88/188.19 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup2I2,axiom, % 187.88/188.19 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_greaterThanAtMost__empty,axiom, % 187.88/188.19 ! [V_k_2,V_l_2,T_b] : % 187.88/188.19 ( class_Orderings_Oorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 187.88/188.19 ! [V_l_2,V_k_2,T_b] : % 187.88/188.19 ( class_Orderings_Oorder(T_b) % 187.88/188.19 => ( 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) % 187.88/188.19 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_greaterThanAtMost__empty__iff,axiom, % 187.88/188.19 ! [V_l_2,V_k_2,T_b] : % 187.88/188.19 ( class_Orderings_Oorder(T_b) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_ivl__disj__un_I20_J,axiom, % 187.88/188.19 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 187.88/188.19 => 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) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_card__greaterThanAtMost,axiom, % 187.88/188.19 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Field__empty,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_mono__Field,axiom, % 187.88/188.19 ! [V_s_2,V_r_2,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Field__Un,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_finite__Field,axiom, % 187.88/188.19 ! [V_r_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 187.88/188.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_card__greaterThanAtMost__int,axiom, % 187.88/188.19 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_ivl__disj__un_I16_J,axiom, % 187.88/188.19 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 187.88/188.19 => 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) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oremove,axiom, % 187.88/188.19 ! [V_x_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.19 => ( ( 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)) % 187.88/188.19 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 187.88/188.19 & ( 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)) % 187.88/188.19 => 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)))))) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Max_Ohom__commute,axiom, % 187.88/188.19 ! [V_N_2,V_h_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( ! [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)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.19 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Min_Ohom__commute,axiom, % 187.88/188.19 ! [V_N_2,V_h_2,T_b] : % 187.88/188.19 ( class_Orderings_Olinorder(T_b) % 187.88/188.19 => ( ! [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)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.19 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_negD,axiom, % 187.88/188.19 ! [V_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.19 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Osingleton,axiom, % 187.88/188.19 ! [V_x_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => 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 ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oin__idem,axiom, % 187.88/188.19 ! [V_x_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.19 => 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) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_OF__eq,axiom, % 187.88/188.19 ! [V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oinsert__idem,axiom, % 187.88/188.19 ! [V_x_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Osubset__idem,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.19 => 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) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Ounion__idem,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Inf__le__Sup,axiom, % 187.88/188.19 ! [V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 187.88/188.19 ! [V_a_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oinsert,axiom, % 187.88/188.19 ! [V_x_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oinsert__remove,axiom, % 187.88/188.19 ! [V_x_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( ( 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)) % 187.88/188.19 => 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 ) % 187.88/188.19 & ( 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)) % 187.88/188.19 => 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)))))) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 187.88/188.19 ! [V_x_2,V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.19 => 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) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Oclosed,axiom, % 187.88/188.19 ! [V_A_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => ( ! [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)))))) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Sup__fin_Ohom__commute,axiom, % 187.88/188.19 ! [V_N_2,V_h_2,T_b] : % 187.88/188.19 ( class_Lattices_Olattice(T_b) % 187.88/188.19 => ( ! [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)) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.19 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUPR__fold__sup,axiom, % 187.88/188.19 ! [V_f_2,V_A_2,T_b,T_c] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_strong__setprod__reindex__cong,axiom, % 187.88/188.19 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 187.88/188.19 ( class_Groups_Ocomm__monoid__mult(T_d) % 187.88/188.19 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.19 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 187.88/188.19 => ( ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.19 => 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) ) % 187.88/188.19 => 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) ) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP1__I,axiom, % 187.88/188.19 ! [T_c,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP2__I,axiom, % 187.88/188.19 ! [T_d,T_c,V_ca_2,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__o,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_finite__UN,axiom, % 187.88/188.19 ! [V_B_2,T_c,V_A_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP__UN__eq2,axiom, % 187.88/188.19 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP__UN__eq,axiom, % 187.88/188.19 ! [V_x_2,V_r_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_sup__SUPR__fold__sup,axiom, % 187.88/188.19 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.19 => 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) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_vimage__eq__UN,axiom, % 187.88/188.19 ! [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))))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_image__eq__UN,axiom, % 187.88/188.19 ! [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)))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__I,axiom, % 187.88/188.19 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_le__SUPI,axiom, % 187.88/188.19 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP2__iff,axiom, % 187.88/188.19 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> ? [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__extend__simps_I9_J,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__simps_I9_J,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__UN__flatten,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP1__iff,axiom, % 187.88/188.19 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> ? [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_ball__UN,axiom, % 187.88/188.19 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.19 ( ! [B_x] : % 187.88/188.19 ( 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))) % 187.88/188.19 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.19 => ! [B_xa] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 187.88/188.19 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__iff,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 187.88/188.19 ( 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))) % 187.88/188.19 <=> ? [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UNION__empty__conv_I2_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_b,T_c] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.19 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__constant,axiom, % 187.88/188.19 ! [V_ca_2,T_c,T_b,V_A_2] : % 187.88/188.19 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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 ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__empty2,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UNION__empty__conv_I1_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_c,T_b] : % 187.88/188.19 ( 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) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.19 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__subset__iff,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 187.88/188.19 ( 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)) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__simps_I10_J,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_image__UN,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__extend__simps_I10_J,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__Un__distrib,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__Un,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUPR__apply,axiom, % 187.88/188.19 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP__commute,axiom, % 187.88/188.19 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__extend__simps_I6_J,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__simps_I6_J,axiom, % 187.88/188.19 ! [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) ). % 187.88/188.19 % 187.88/188.19 fof(fact_vimage__UN,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__insert__distrib,axiom, % 187.88/188.19 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 187.88/188.19 => 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)) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__upper,axiom, % 187.88/188.19 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.19 => 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))) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__absorb,axiom, % 187.88/188.19 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 187.88/188.19 => 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) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__extend__simps_I1_J,axiom, % 187.88/188.19 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 187.88/188.19 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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))) ) % 187.88/188.19 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__singleton,axiom, % 187.88/188.19 ! [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 ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__simps_I1_J,axiom, % 187.88/188.19 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 187.88/188.19 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP__le__iff,axiom, % 187.88/188.19 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.19 => ( 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)) % 187.88/188.19 <=> ! [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_less__SUP__iff,axiom, % 187.88/188.19 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 187.88/188.19 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.19 & class_Orderings_Olinorder(T_b) ) % 187.88/188.19 => ( 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))) % 187.88/188.19 <=> ? [B_x] : % 187.88/188.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__extend__simps_I2_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.19 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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 ) % 187.88/188.19 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__extend__simps_I3_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.19 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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 ) % 187.88/188.19 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__simps_I2_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.19 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__simps_I3_J,axiom, % 187.88/188.19 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.19 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) % 187.88/188.19 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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)) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_UN__insert,axiom, % 187.88/188.19 ! [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)) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP__const,axiom, % 187.88/188.19 ! [V_M_2,T_b,V_A_2,T_c] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.19 => 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 ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_SUP__subset,axiom, % 187.88/188.19 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.19 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.19 => 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))) ) ) ). % 187.88/188.19 % 187.88/188.19 fof(fact_Id__on__def,axiom, % 187.88/188.19 ! [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)))) ). % 187.88/188.19 % 187.88/188.19 fof(fact_nat__def,axiom, % 187.88/188.19 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ). % 187.88/188.19 % 187.88/188.20 fof(fact_setprod__mono__one__right,axiom, % 187.88/188.20 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 187.88/188.20 => 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) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod__mono__one__left,axiom, % 187.88/188.20 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 187.88/188.20 => 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) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Rep__Integ__inject,axiom, % 187.88/188.20 ! [V_y_2,V_x_2] : % 187.88/188.20 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 187.88/188.20 <=> V_x_2 = V_y_2 ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Id__on__def_H,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Id__on__empty,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Id__on__eqI,axiom, % 187.88/188.20 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 187.88/188.20 ( V_a_2 = V_ba_2 % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Id__on__iff,axiom, % 187.88/188.20 ! [V_A_2,V_y_2,V_x_2,T_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 <=> ( V_x_2 = V_y_2 % 187.88/188.20 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Id__onE,axiom, % 187.88/188.20 ! [V_A_2,V_ca_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2))) % 187.88/188.20 => ~ ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_zero__less__imp__eq__int,axiom, % 187.88/188.20 ! [V_k] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.88/188.20 => ? [B_n] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 187.88/188.20 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__Pow,axiom, % 187.88/188.20 ! [V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I19_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__atLeastAtMost,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__atLeastAtMost__int,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_PowI,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__empty,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__insert,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 187.88/188.20 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Un__Pow__subset,axiom, % 187.88/188.20 ! [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)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__not__empty,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__bottom,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__Suc__atLeastAtMost,axiom, % 187.88/188.20 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Cantors__paradox,axiom, % 187.88/188.20 ! [V_A_2,T_b] : % 187.88/188.20 ~ ? [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__Pow__surj,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 187.88/188.20 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__UNIV,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__mono,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__iff,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_PowD,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__top,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__add__atLeastAtMost,axiom, % 187.88/188.20 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__Pow__subset,axiom, % 187.88/188.20 ! [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)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 187.88/188.20 ! [V_n_2,V_m_2] : % 187.88/188.20 ( c_Nat__Transfer_Ois__nat(V_m_2) % 187.88/188.20 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 187.88/188.20 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 187.88/188.20 ! [V_y_2,V_x_2] : % 187.88/188.20 ( c_Nat__Transfer_Ois__nat(V_x_2) % 187.88/188.20 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastatMost__empty__iff,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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)) % 187.88/188.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastatMost__empty__iff2,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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) % 187.88/188.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastatMost__empty,axiom, % 187.88/188.20 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastatMost__subset__iff,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 187.88/188.20 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastAtMost__singleton_H,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( V_a_2 = V_ba_2 % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastAtMost__singleton__iff,axiom, % 187.88/188.20 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> ( V_a_2 = V_ba_2 % 187.88/188.20 & V_ba_2 = V_ca_2 ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastAtMost__singleton,axiom, % 187.88/188.20 ! [V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__uminus__atLeastAtMost,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__Pow__mono,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__def,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__Pow__iff,axiom, % 187.88/188.20 ! [V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 187.88/188.20 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 187.88/188.20 ! [V_y_2,V_x_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.88/188.20 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__Compl,axiom, % 187.88/188.20 ! [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))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__atLeastAtMost,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastAtMostSuc__conv,axiom, % 187.88/188.20 ! [V_n_2,V_m_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.88/188.20 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastatMost__psubset__iff,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 187.88/188.20 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) % 187.88/188.20 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) % 187.88/188.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_d_2)) ) ) ) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I22_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_simp__from__to,axiom, % 187.88/188.20 ! [V_i_2,V_j_2] : % 187.88/188.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 187.88/188.20 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 187.88/188.20 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__atLeastAtMost__int,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I5_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_aset_I6_J,axiom, % 187.88/188.20 ! [V_A_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bset_I8_J,axiom, % 187.88/188.20 ! [V_B_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_aset_I4_J,axiom, % 187.88/188.20 ! [V_A_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( B_x != V_t_2 % 187.88/188.20 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bset_I4_J,axiom, % 187.88/188.20 ! [V_B_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( B_x != V_t_2 % 187.88/188.20 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_all__nat__less,axiom, % 187.88/188.20 ! [V_Pa_2,V_n_2] : % 187.88/188.20 ( ! [B_m] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 187.88/188.20 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 187.88/188.20 <=> ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 187.88/188.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ex__nat__less,axiom, % 187.88/188.20 ! [V_Pa_2,V_n_2] : % 187.88/188.20 ( ? [B_m] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 187.88/188.20 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 187.88/188.20 <=> ? [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 187.88/188.20 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Powp__Pow__eq,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bset_I3_J,axiom, % 187.88/188.20 ! [V_B_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 187.88/188.20 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 187.88/188.20 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Powp__mono,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bset_I7_J,axiom, % 187.88/188.20 ! [V_B_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_aset_I5_J,axiom, % 187.88/188.20 ! [V_A_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_aset_I3_J,axiom, % 187.88/188.20 ! [V_A_2,V_t_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 187.88/188.20 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 187.88/188.20 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bset_I6_J,axiom, % 187.88/188.20 ! [V_t_2,V_B_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_aset_I8_J,axiom, % 187.88/188.20 ! [V_t_2,V_A_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_periodic__finite__ex,axiom, % 187.88/188.20 ! [V_Pa_2,V_d_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 187.88/188.20 => ( ! [B_x,B_k] : % 187.88/188.20 ( hBOOL(hAPP(V_Pa_2,B_x)) % 187.88/188.20 <=> 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)))) ) % 187.88/188.20 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 187.88/188.20 <=> ? [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) % 187.88/188.20 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bset_I5_J,axiom, % 187.88/188.20 ! [V_t_2,V_B_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_aset_I7_J,axiom, % 187.88/188.20 ! [V_t_2,V_A_2,V_D_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.88/188.20 => ! [B_x] : % 187.88/188.20 ( ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 187.88/188.20 => ! [B_xb] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.88/188.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 187.88/188.20 ! [V_x_2,V_y_2,V_ca_2] : % 187.88/188.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 187.88/188.20 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 187.88/188.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 187.88/188.20 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 187.88/188.20 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 187.88/188.20 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_greaterThan__0,axiom, % 187.88/188.20 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I18_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__atLeastLessThan__int,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__atLeastLessThan,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__atMost,axiom, % 187.88/188.20 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atMost__eq__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 187.88/188.20 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_greaterThan__eq__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 187.88/188.20 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__greaterThan,axiom, % 187.88/188.20 ! [V_k_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__atMost,axiom, % 187.88/188.20 ! [V_k_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__eq__iff,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 187.88/188.20 => ( 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) % 187.88/188.20 <=> ( V_a_2 = V_ca_2 % 187.88/188.20 & V_ba_2 = V_d_2 ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( 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) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 187.88/188.20 => V_a_2 = V_ca_2 ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( 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) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 187.88/188.20 => V_ba_2 = V_d_2 ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_all__nat__less__eq,axiom, % 187.88/188.20 ! [V_Pa_2,V_n_2] : % 187.88/188.20 ( ! [B_m] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 187.88/188.20 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 187.88/188.20 <=> ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 187.88/188.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ex__nat__less__eq,axiom, % 187.88/188.20 ! [V_Pa_2,V_n_2] : % 187.88/188.20 ( ? [B_m] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 187.88/188.20 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 187.88/188.20 <=> ? [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 187.88/188.20 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__atMost__UNIV,axiom, % 187.88/188.20 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan0,axiom, % 187.88/188.20 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__atLeastLessThan,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__Suc__atLeastLessThan,axiom, % 187.88/188.20 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__empty,axiom, % 187.88/188.20 ! [V_a_2,V_ba_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__empty__iff2,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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) % 187.88/188.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__empty__iff,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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)) % 187.88/188.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__subset__iff,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 187.88/188.20 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I17_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__diff,axiom, % 187.88/188.20 ! [V_m_2,V_n_2,V_i_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__UN__finite__eq,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast0AtMost,axiom, % 187.88/188.20 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__add__atLeastLessThan,axiom, % 187.88/188.20 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 187.88/188.20 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__atMost,axiom, % 187.88/188.20 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atMost__Suc,axiom, % 187.88/188.20 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atMost__iff,axiom, % 187.88/188.20 ! [V_k_2,V_i_2,T_b] : % 187.88/188.20 ( class_Orderings_Oord(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atMost__subset__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_greaterThan__iff,axiom, % 187.88/188.20 ! [V_k_2,V_i_2,T_b] : % 187.88/188.20 ( class_Orderings_Oord(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_greaterThan__subset__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__le__add__shift,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__singleton,axiom, % 187.88/188.20 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I21_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThan__add__Un,axiom, % 187.88/188.20 ! [V_k_2,V_j_2,V_i_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.88/188.20 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_subset__card__intvl__is__intvl,axiom, % 187.88/188.20 ! [V_k_2,V_A_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) % 187.88/188.20 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__uminus__atLeastLessThan,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__uminus__greaterThanAtMost,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__add__int__atLeastLessThan,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__atLeastZeroLessThan__int,axiom, % 187.88/188.20 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__atLeastLessThan__int,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 187.88/188.20 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeastLessThanSuc,axiom, % 187.88/188.20 ! [V_n_2,V_m_2] : % 187.88/188.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atMost__0,axiom, % 187.88/188.20 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I9_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I15_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I11_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_greaterThan__Suc,axiom, % 187.88/188.20 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__le__eq__Un0,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I6_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I3_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__finite2__subset,axiom, % 187.88/188.20 ! [V_B_2,V_k_2,V_A_2,T_b] : % 187.88/188.20 ( ! [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))) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I12_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I7_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I13_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__lessThan,axiom, % 187.88/188.20 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__eq__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 187.88/188.20 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast__eq__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 187.88/188.20 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__atLeast,axiom, % 187.88/188.20 ! [V_k_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__lessThan,axiom, % 187.88/188.20 ! [V_k_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__lessThan,axiom, % 187.88/188.20 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__lessThan__UNIV,axiom, % 187.88/188.20 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__atLeast__UNIV,axiom, % 187.88/188.20 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast0LessThan,axiom, % 187.88/188.20 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__0,axiom, % 187.88/188.20 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__Suc,axiom, % 187.88/188.20 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__Suc__atMost,axiom, % 187.88/188.20 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast__iff,axiom, % 187.88/188.20 ! [V_k_2,V_i_2,T_b] : % 187.88/188.20 ( class_Orderings_Oord(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__iff,axiom, % 187.88/188.20 ! [V_k_2,V_i_2,T_b] : % 187.88/188.20 ( class_Orderings_Oord(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast__subset__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__subset__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast__0,axiom, % 187.88/188.20 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__strict__subset__iff,axiom, % 187.88/188.20 ! [V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast__Suc__greaterThan,axiom, % 187.88/188.20 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_single__Diff__lessThan,axiom, % 187.88/188.20 ! [V_k_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I8_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I14_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__uminus__atLeast,axiom, % 187.88/188.20 ! [V_x_2,T_b] : % 187.88/188.20 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__uminus__atMost,axiom, % 187.88/188.20 ! [V_x_2,T_b] : % 187.88/188.20 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atLeast__Suc,axiom, % 187.88/188.20 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__uminus__greaterThan,axiom, % 187.88/188.20 ! [V_x_2,T_b] : % 187.88/188.20 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__uminus__lessThan,axiom, % 187.88/188.20 ! [V_x_2,T_b] : % 187.88/188.20 ( class_Groups_Oordered__ab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 187.88/188.20 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I2_J,axiom, % 187.88/188.20 ! [V_u_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I10_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__atLeastZeroLessThan__int,axiom, % 187.88/188.20 ! [V_u_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 187.88/188.20 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__un_I1_J,axiom, % 187.88/188.20 ! [V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_arith__series__int,axiom, % 187.88/188.20 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__finite2__eq,axiom, % 187.88/188.20 ! [V_B_2,V_k_2,V_A_2,T_b] : % 187.88/188.20 ( ! [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) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__finite__subset,axiom, % 187.88/188.20 ! [V_C_2,V_A_2,T_b] : % 187.88/188.20 ( ! [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)) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_equiv__intrel__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2] : % 187.88/188.20 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__UN,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__subtractf,axiom, % 187.88/188.20 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Groups_Oab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__addf,axiom, % 187.88/188.20 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__product,axiom, % 187.88/188.20 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Rings_Osemiring__0(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__left__distrib,axiom, % 187.88/188.20 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Rings_Osemiring__0(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__right__distrib,axiom, % 187.88/188.20 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 187.88/188.20 ( class_Rings_Osemiring__0(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__negf,axiom, % 187.88/188.20 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Groups_Oab__group__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__commute,axiom, % 187.88/188.20 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_of__nat__setsum,axiom, % 187.88/188.20 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Rings_Osemiring__1(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_of__int__setsum,axiom, % 187.88/188.20 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Rings_Oring__1(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__0,axiom, % 187.88/188.20 ! [V_A_2,T_c,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__divide__distrib,axiom, % 187.88/188.20 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Fields_Ofield(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__Un,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__empty,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__empty,axiom, % 187.88/188.20 ! [V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Oempty,axiom, % 187.88/188.20 ! [V_g_2,T_c,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__infinite,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Oinfinite,axiom, % 187.88/188.20 ! [V_g_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Odistrib,axiom, % 187.88/188.20 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__lessThan__Suc,axiom, % 187.88/188.20 ! [V_n_2,V_f_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__mono,axiom, % 187.88/188.20 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Un__Image,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 187.88/188.20 ! [V_n_2,V_m_2,V_f_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 187.88/188.20 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 187.88/188.20 ! [V_n_2,V_m_2,V_f_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 187.88/188.20 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__reindex,axiom, % 187.88/188.20 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_d) % 187.88/188.20 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__add__nat__ivl,axiom, % 187.88/188.20 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__diff__nat__ivl,axiom, % 187.88/188.20 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Groups_Oab__group__add(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__delta_H,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.20 => 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) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.20 => 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) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__delta,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.20 => 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) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 187.88/188.20 => 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) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__setsum__restrict,axiom, % 187.88/188.20 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_d) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__iff,axiom, % 187.88/188.20 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 187.88/188.20 <=> ? [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.20 & 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_rev__ImageI,axiom, % 187.88/188.20 ! [V_r_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => ( 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)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__constant,axiom, % 187.88/188.20 ! [V_A_2,V_y_2,T_c,T_b] : % 187.88/188.20 ( class_Rings_Osemiring__1(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__atMost__Suc,axiom, % 187.88/188.20 ! [V_n_2,V_f_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__eq__UN,axiom, % 187.88/188.20 ! [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))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__insert,axiom, % 187.88/188.20 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Oinsert,axiom, % 187.88/188.20 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__diff,axiom, % 187.88/188.20 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Oab__group__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Oreindex,axiom, % 187.88/188.20 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_OF__eq,axiom, % 187.88/188.20 ! [V_g_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Oeq__fold,axiom, % 187.88/188.20 ! [V_g_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 187.88/188.20 ! [V_k_2,V_f_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__head__upt__Suc,axiom, % 187.88/188.20 ! [V_f_2,V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__head__Suc,axiom, % 187.88/188.20 ! [V_f_2,V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__restrict__set_H,axiom, % 187.88/188.20 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__image__gen,axiom, % 187.88/188.20 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Oinsert__remove,axiom, % 187.88/188.20 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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)))))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__op__ivl__Suc,axiom, % 187.88/188.20 ! [V_f_2,V_m_2,V_n_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.88/188.20 => 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) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__cl__ivl__Suc,axiom, % 187.88/188.20 ! [V_f_2,V_m_2,V_n_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 187.88/188.20 => 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) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 187.88/188.20 => 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))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__head,axiom, % 187.88/188.20 ! [V_Pa_2,V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__ub__add__nat,axiom, % 187.88/188.20 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 187.88/188.20 => 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)))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__singleton__iff,axiom, % 187.88/188.20 ! [V_a_2,V_r_2,T_c,V_ba_2,T_b] : % 187.88/188.20 ( 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)))))) % 187.88/188.20 <=> 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__diff1_H,axiom, % 187.88/188.20 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)))))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Oremove,axiom, % 187.88/188.20 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => 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)))))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__diff1,axiom, % 187.88/188.20 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Oab__group__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__diff1__ring,axiom, % 187.88/188.20 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Rings_Oring(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__singleton,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_arith__series__general,axiom, % 187.88/188.20 ! [V_n_2,V_d_2,V_a_2,T_b] : % 187.88/188.20 ( class_Rings_Ocomm__semiring__1(T_b) % 187.88/188.20 => 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)))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_geometric__sum,axiom, % 187.88/188.20 ! [V_n_2,V_x_2,T_b] : % 187.88/188.20 ( class_Fields_Ofield(T_b) % 187.88/188.20 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_gauss__sum,axiom, % 187.88/188.20 ! [V_n_2,T_b] : % 187.88/188.20 ( class_Rings_Ocomm__semiring__1(T_b) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__natinterval__difff,axiom, % 187.88/188.20 ! [V_f_2,V_n_2,V_m_2,T_b] : % 187.88/188.20 ( class_Groups_Oab__group__add(T_b) % 187.88/188.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => 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)))) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_of__int,axiom, % 187.88/188.20 ! [V_j_2,V_i_2,T_b] : % 187.88/188.20 ( class_Rings_Oring__1(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_One__int__def,axiom, % 187.88/188.20 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_mult,axiom, % 187.88/188.20 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__eq__0__iff,axiom, % 187.88/188.20 ! [V_f_2,V_F_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.20 => ( 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) % 187.88/188.20 <=> ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 187.88/188.20 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Rep__Integ__inverse,axiom, % 187.88/188.20 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__eq__setsum,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_int__setsum,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__eq__Suc0__iff,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( 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)) % 187.88/188.20 <=> ? [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.88/188.20 & ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 187.88/188.20 => ( B_x != B_xa % 187.88/188.20 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__eq__1__iff,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( 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) % 187.88/188.20 <=> ? [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.88/188.20 & ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 187.88/188.20 => ( B_x != B_xa % 187.88/188.20 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 187.88/188.20 ! [V_k_2,V_f_2] : % 187.88/188.20 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.20 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__diff__nat,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,V_B_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 187.88/188.20 ! [V_A_2,V_f_2,T_b] : % 187.88/188.20 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 & class_Groups_Ocomm__monoid__mult(T_b) ) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__diff1__nat,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,V_a_2,T_b] : % 187.88/188.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,T_b] : % 187.88/188.20 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.20 & class_Groups_Ocomm__monoid__mult(T_b) ) % 187.88/188.20 => ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_arith__series__nat,axiom, % 187.88/188.20 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_minus,axiom, % 187.88/188.20 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Zero__int__def,axiom, % 187.88/188.20 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_int__def,axiom, % 187.88/188.20 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_add,axiom, % 187.88/188.20 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_nat,axiom, % 187.88/188.20 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ). % 187.88/188.20 % 187.88/188.20 fof(fact_minus__int__def,axiom, % 187.88/188.20 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_less,axiom, % 187.88/188.20 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_le,axiom, % 187.88/188.20 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,T_b] : % 187.88/188.20 ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_eq__Abs__Integ,axiom, % 187.88/188.20 ! [V_z_2] : % 187.88/188.20 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__mono2,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Oordered__comm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.20 => ( ! [B_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 187.88/188.20 => 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))) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__multicount,axiom, % 187.88/188.20 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 187.88/188.20 => 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 ) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__bounded,axiom, % 187.88/188.20 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 187.88/188.20 & class_Rings_Osemiring__1(T_c) ) % 187.88/188.20 => ( ! [B_i] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__mono3,axiom, % 187.88/188.20 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 187.88/188.20 ( ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 187.88/188.20 => 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))) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__reindex__nonzero,axiom, % 187.88/188.20 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_d) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 187.88/188.20 => ! [B_y] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 187.88/188.20 => ( B_x != B_y % 187.88/188.20 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 187.88/188.20 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__multicount__gen,axiom, % 187.88/188.20 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 187.88/188.20 => 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) ) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__def,axiom, % 187.88/188.20 ! [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)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__is__empty,axiom, % 187.88/188.20 ! [V_r_2,V_A_2,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__is__empty2,axiom, % 187.88/188.20 ! [V_r_2,V_A_2,T_b] : % 187.88/188.20 ( 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) % 187.88/188.20 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__empty,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__diff1,axiom, % 187.88/188.20 ! [V_a_2,V_A_2,V_r_2,T_b] : % 187.88/188.20 ( 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) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotientI,axiom, % 187.88/188.20 ! [V_r_2,V_A_2,V_x_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_singleton__quotient,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__quotient__disjoint,axiom, % 187.88/188.20 ! [V_r_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( 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) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_subset__equiv__class,axiom, % 187.88/188.20 ! [V_a_2,V_ba_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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)))))) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotientE,axiom, % 187.88/188.20 ! [V_r_2,V_A_2,V_X_2,T_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 => ~ ! [B_x] : % 187.88/188.20 ( 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)))) % 187.88/188.20 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_eq__equiv__class__iff2,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.88/188.20 => ( 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) % 187.88/188.20 <=> 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_equiv__intrel,axiom, % 187.88/188.20 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ). % 187.88/188.20 % 187.88/188.20 fof(fact_equiv__class__self,axiom, % 187.88/188.20 ! [V_a_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)))))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_equiv__class__eq,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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)) % 187.88/188.20 => 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)))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__eqI,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 187.88/188.20 => ( 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)) % 187.88/188.20 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__eq__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 187.88/188.20 => ( V_X_2 = V_Y_2 % 187.88/188.20 <=> 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_eq__equiv__class__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.88/188.20 => ( 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)))) % 187.88/188.20 <=> 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_eq__equiv__class,axiom, % 187.88/188.20 ! [V_A_2,V_ba_2,V_a_2,V_r_2,T_b] : % 187.88/188.20 ( 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)))) % 187.88/188.20 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_equiv__class__eq__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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)) % 187.88/188.20 <=> ( 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)))) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_equiv__class__subset,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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)) % 187.88/188.20 => 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)))))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__equiv__class2,axiom, % 187.88/188.20 ! [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] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 187.88/188.20 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 187.88/188.20 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 187.88/188.20 => 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) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__equiv__class,axiom, % 187.88/188.20 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_equiv__class__nondisjoint,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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))))))) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf1I,axiom, % 187.88/188.20 ! [T_b,V_B_2,V_x_2,V_A_2] : % 187.88/188.20 ( hBOOL(hAPP(V_A_2,V_x_2)) % 187.88/188.20 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf1E,axiom, % 187.88/188.20 ! [V_x_2,V_B_2,V_A_2,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 187.88/188.20 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_IntE,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.20 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_IntI,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_finite__Int,axiom, % 187.88/188.20 ! [V_Ga_2,V_F_2,T_b] : % 187.88/188.20 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 187.88/188.20 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inj__on__Int,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.20 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__Int2,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__Int__distrib2,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__Diff,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__Int__distrib,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Pow__Int__eq,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Collect__conj__eq,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fun__left__comm__idem__inf,axiom, % 187.88/188.20 ! [T_b] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 187.88/188.20 ! [V_B_2,V_A_2] : % 187.88/188.20 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.20 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.20 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__fun__def,axiom, % 187.88/188.20 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_vimage__Int,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf_Oidem,axiom, % 187.88/188.20 ! [V_a,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__idem,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf_Ocommute,axiom, % 187.88/188.20 ! [V_b,V_a,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__aci_I1_J,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__commute,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf_Oleft__idem,axiom, % 187.88/188.20 ! [V_b,V_a,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__aci_I4_J,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__left__idem,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf_Oleft__commute,axiom, % 187.88/188.20 ! [V_c,V_a,V_b,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__aci_I3_J,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__left__commute,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf_Oassoc,axiom, % 187.88/188.20 ! [V_c,V_b,V_a,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__aci_I2_J,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__assoc,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__apply,axiom, % 187.88/188.20 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__absorb,axiom, % 187.88/188.20 ! [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 ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__commute,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__left__absorb,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__left__commute,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__assoc,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf1D1,axiom, % 187.88/188.20 ! [V_x_2,V_B_2,V_A_2,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf1D2,axiom, % 187.88/188.20 ! [V_x_2,V_B_2,V_A_2,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_less__infI2,axiom, % 187.88/188.20 ! [V_a,V_x,V_b,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_less__infI1,axiom, % 187.88/188.20 ! [V_b,V_x,V_a,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oidem,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__min,axiom, % 187.88/188.20 ! [T_b] : % 187.88/188.20 ( ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 & class_Orderings_Olinorder(T_b) ) % 187.88/188.20 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_insert__inter__insert,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__absorb,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_sup__inf__absorb,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__distrib1,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Odistrib__lattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_sup__inf__distrib1,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Odistrib__lattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__distrib2,axiom, % 187.88/188.20 ! [V_x,V_z,V_y,T_a] : % 187.88/188.20 ( class_Lattices_Odistrib__lattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_sup__inf__distrib2,axiom, % 187.88/188.20 ! [V_x,V_z,V_y,T_a] : % 187.88/188.20 ( class_Lattices_Odistrib__lattice(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__Un__distrib,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Un__Int__distrib,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__Un__distrib2,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Un__Int__distrib2,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Un__Int__crazy,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_disjoint__iff__not__equal,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 <=> ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 => ! [B_xa] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 187.88/188.20 => B_x != B_xa ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__empty__right,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__empty__left,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__bot__right,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__bot__left,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__UNIV__left,axiom, % 187.88/188.20 ! [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 ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__UNIV__right,axiom, % 187.88/188.20 ! [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 ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__eq__top__iff,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Lattices_Obounded__lattice__top(T_b) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 187.88/188.20 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 187.88/188.20 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__top__right,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Obounded__lattice__top(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__top__left,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Obounded__lattice__top(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__ord_I1_J,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__le1,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__sup__ord_I2_J,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__le2,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_le__iff__inf,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.20 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_le__inf__iff,axiom, % 187.88/188.20 ! [V_z_2,V_y_2,V_x_2,T_b] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_le__infI1,axiom, % 187.88/188.20 ! [V_b,V_x,V_a,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_le__infI2,axiom, % 187.88/188.20 ! [V_a,V_x,V_b,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__absorb1,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__absorb2,axiom, % 187.88/188.20 ! [V_x,V_y,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_le__infI,axiom, % 187.88/188.20 ! [V_b,V_a,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__greatest,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__mono,axiom, % 187.88/188.20 ! [V_d,V_b,V_c,V_a,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_le__infE,axiom, % 187.88/188.20 ! [V_b,V_a,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_a) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) % 187.88/188.20 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.88/188.20 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__mono,axiom, % 187.88/188.20 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__greatest,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_C_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__absorb1,axiom, % 187.88/188.20 ! [V_A_2,V_B_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__absorb2,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__lower2,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__lower1,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__iff,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 187.88/188.20 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_IntD1,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_IntD2,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__Int__eq,axiom, % 187.88/188.20 ! [V_x_2,V_S_2,V_R_2,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 <=> 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__UN__distrib2,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__extend__simps_I4_J,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__UN__distrib,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__extend__simps_I5_J,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__simps_I4_J,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__simps_I5_J,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_distrib__sup__le,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_distrib__inf__le,axiom, % 187.88/188.20 ! [V_z,V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Olattice(T_a) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__compl__bot,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_compl__inf__bot,axiom, % 187.88/188.20 ! [V_x,T_a] : % 187.88/188.20 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_diff__eq,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.20 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_compl__sup,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.20 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_compl__inf,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.20 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__insert__left__if1,axiom, % 187.88/188.20 ! [V_B_2,V_C_2,V_a_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__insert__right__if1,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_a_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__insert__left__if0,axiom, % 187.88/188.20 ! [V_B_2,V_C_2,V_a_2,T_b] : % 187.88/188.20 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__insert__right__if0,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_a_2,T_b] : % 187.88/188.20 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__insert__left,axiom, % 187.88/188.20 ! [V_B_2,V_C_2,V_a_2,T_b] : % 187.88/188.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 187.88/188.20 => 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)) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__insert__right,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_a_2,T_b] : % 187.88/188.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)) ) % 187.88/188.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__Int__subset,axiom, % 187.88/188.20 ! [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)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__triv,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__disjoint,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Un__Int__assoc__eq,axiom, % 187.88/188.20 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__Int,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__Un,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Un__Diff__Int,axiom, % 187.88/188.20 ! [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 ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I11_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 187.88/188.20 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__disjoint2,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__disjoint,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__Int__subset,axiom, % 187.88/188.20 ! [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)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__Int,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Compl__Un,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__eq,axiom, % 187.88/188.20 ! [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)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Diff__Compl,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I14_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__def,axiom, % 187.88/188.20 ! [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))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__Collect,axiom, % 187.88/188.20 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 187.88/188.20 ( 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)))) % 187.88/188.20 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Image__Id__on,axiom, % 187.88/188.20 ! [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) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 187.88/188.20 ! [V_B_2,V_A_2] : % 187.88/188.20 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.88/188.20 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.20 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_congruent2__implies__congruent,axiom, % 187.88/188.20 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 187.88/188.20 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fold__inf__insert,axiom, % 187.88/188.20 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oin__idem,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__Sup__absorb,axiom, % 187.88/188.20 ! [V_a_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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 ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inj__on__image__Int,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__Int,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_disjoint__eq__subset__Compl,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 <=> 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bij__betw__Disj__Un,axiom, % 187.88/188.20 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( 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)) % 187.88/188.20 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 187.88/188.20 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_bij__betw__combine,axiom, % 187.88/188.20 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 187.88/188.20 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2) % 187.88/188.20 => ( 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)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I15_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_OF__eq,axiom, % 187.88/188.20 ! [V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_image__vimage__eq,axiom, % 187.88/188.20 ! [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)))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__atLeastAtMost,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__atLeastLessThan,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I4_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I2_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I16_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I13_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I12_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__greaterThanAtMost,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I9_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__greaterThanLessThan,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__atLeastAtMostR1,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_ba_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__atLeastAtMostL1,axiom, % 187.88/188.20 ! [V_d_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I8_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I7_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__atLeastAtMostR2,axiom, % 187.88/188.20 ! [V_d_2,V_ca_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Int__atLeastAtMostL2,axiom, % 187.88/188.20 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => 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) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I3_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I1_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I10_J,axiom, % 187.88/188.20 ! [V_u_2,V_m_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I6_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_if__image__distrib,axiom, % 187.88/188.20 ! [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))))) ). % 187.88/188.20 % 187.88/188.20 fof(fact_ivl__disj__int_I5_J,axiom, % 187.88/188.20 ! [V_u_2,V_l_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_folding__image__simple_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_compl__unique,axiom, % 187.88/188.20 ! [V_y,V_x,T_a] : % 187.88/188.20 ( class_Lattices_Oboolean__algebra(T_a) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 187.88/188.20 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fold__inf__le__inf,axiom, % 187.88/188.20 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fold1__belowI,axiom, % 187.88/188.20 ! [V_a_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_below__fold1__iff,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Osemilattice__inf(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( 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))) % 187.88/188.20 <=> ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oinsert__idem,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Osubset__idem,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.20 => 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) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Ounion__idem,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__Un__Int,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 187.88/188.20 ! [V_a_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod_Ounion__inter,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod__Un__Int,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__Un__Int,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__Diff__subset__Int,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( 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))) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__restrict__set,axiom, % 187.88/188.20 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_folding_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_quotient__disj,axiom, % 187.88/188.20 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( V_X_2 = V_Y_2 % 187.88/188.20 | 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_atMost__Int__atLeast,axiom, % 187.88/188.20 ! [V_n_2,T_b] : % 187.88/188.20 ( class_Orderings_Oorder(T_b) % 187.88/188.20 => 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_folding__one_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.20 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_folding__one_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 187.88/188.20 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 187.88/188.20 => ( 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)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oinsert,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oinsert__remove,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( ( 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)) % 187.88/188.20 => 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 ) % 187.88/188.20 & ( 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)) % 187.88/188.20 => 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)))))) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => 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) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__Un__disjoint,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__Un,axiom, % 187.88/188.20 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Oab__group__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod__Un__disjoint,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card__Un__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inj__on__Un,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 187.88/188.20 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 187.88/188.20 & 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fold__image__Un__Int,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fold1__Un,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Groups_Oab__semigroup__mult(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Sup__fin_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Min_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Min_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Max_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Max_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Orderings_Olinorder(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_congruent2D,axiom, % 187.88/188.20 ! [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] : % 187.88/188.20 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 187.88/188.20 => ( 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)) % 187.88/188.20 => ( 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)) % 187.88/188.20 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__Un__nat,axiom, % 187.88/188.20 ! [V_f_2,V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => 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))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_folding_Ounion,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 187.88/188.20 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum__cases,axiom, % 187.88/188.20 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => 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))))) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oremove,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.20 => ( ( 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)) % 187.88/188.20 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 187.88/188.20 & ( 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)) % 187.88/188.20 => 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)))))) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_congruentD,axiom, % 187.88/188.20 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 187.88/188.20 => ( 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)) % 187.88/188.20 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fold__Un__disjoint,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__Sup1__distrib,axiom, % 187.88/188.20 ! [V_x_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Odistrib__lattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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))))) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__Sup2__distrib,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Odistrib__lattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => 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))))))) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_congruent2__implies__congruent__UN,axiom, % 187.88/188.20 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 187.88/188.20 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 187.88/188.20 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__equiv__class__inject,axiom, % 187.88/188.20 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 187.88/188.20 => ( 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) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 => ! [B_y] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 187.88/188.20 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 187.88/188.20 => 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)) ) ) ) % 187.88/188.20 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__equiv__class__type2,axiom, % 187.88/188.20 ! [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] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 187.88/188.20 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 187.88/188.20 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( ! [B_x1] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 187.88/188.20 => ! [B_x2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 187.88/188.20 => 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)) ) ) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_UN__equiv__class__type,axiom, % 187.88/188.20 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 187.88/188.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 187.88/188.20 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 187.88/188.20 => ( 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))) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__nat__def,axiom, % 187.88/188.20 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf__Int__eq2,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 <=> 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))) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_card_Ounion__inter__neutral,axiom, % 187.88/188.20 ! [V_B_2,V_A_2,T_b] : % 187.88/188.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( ( ? [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))) % 187.88/188.20 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.88/188.20 => 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)) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod__Un,axiom, % 187.88/188.20 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Fields_Ofield(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.88/188.20 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 187.88/188.20 => 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))) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_fold__image__Un__one,axiom, % 187.88/188.20 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf2I,axiom, % 187.88/188.20 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.88/188.20 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 187.88/188.20 => 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)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf2E,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.88/188.20 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf2D1,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_inf2D2,axiom, % 187.88/188.20 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.20 ( 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)) % 187.88/188.20 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Integ__def,axiom, % 187.88/188.20 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Inf__fin_Oclosed,axiom, % 187.88/188.20 ! [V_A_2,T_b] : % 187.88/188.20 ( class_Lattices_Olattice(T_b) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.20 => ( ! [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)))))) % 187.88/188.20 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod__Un__one,axiom, % 187.88/188.20 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( 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))) % 187.88/188.20 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_Rep__Integ,axiom, % 187.88/188.20 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setprod_Ounion__inter__neutral,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.20 => ( ! [B_x] : % 187.88/188.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.88/188.20 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 187.88/188.20 => 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)) ) ) ) ) ). % 187.88/188.20 % 187.88/188.20 fof(fact_setsum_Ounion__inter__neutral,axiom, % 187.88/188.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.20 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.88/188.21 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 187.88/188.21 => 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)) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__Un__zero,axiom, % 187.88/188.21 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 187.88/188.21 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) % 187.88/188.21 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 187.88/188.21 => 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)) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_equivp__equiv,axiom, % 187.88/188.21 ! [V_A_2,T_b] : % 187.88/188.21 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 187.88/188.21 <=> 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition__Integ,axiom, % 187.88/188.21 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__nonneg__0,axiom, % 187.88/188.21 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 187.88/188.21 => ( ! [B_i] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 187.88/188.21 => ( 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) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 187.88/188.21 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_equivp__transp,axiom, % 187.88/188.21 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 187.88/188.21 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_equivp__symp,axiom, % 187.88/188.21 ! [V_y_2,V_x_2,V_R_2,T_b] : % 187.88/188.21 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_equivp__reflp,axiom, % 187.88/188.21 ! [V_x_2,V_R_2,T_b] : % 187.88/188.21 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_equivp__def,axiom, % 187.88/188.21 ! [V_R_2,T_b] : % 187.88/188.21 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 187.88/188.21 <=> ! [B_x,B_y] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 187.88/188.21 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_identity__equivp,axiom, % 187.88/188.21 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition_OAbs__image,axiom, % 187.88/188.21 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 187.88/188.21 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 187.88/188.21 => 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition_ORep__range,axiom, % 187.88/188.21 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 187.88/188.21 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 187.88/188.21 => 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 ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition_OAbs__inject,axiom, % 187.88/188.21 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 187.88/188.21 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 187.88/188.21 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 187.88/188.21 <=> V_x_2 = V_y_2 ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition_ORep__inject,axiom, % 187.88/188.21 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 187.88/188.21 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 187.88/188.21 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 187.88/188.21 <=> V_x_2 = V_y_2 ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition_ORep__inverse,axiom, % 187.88/188.21 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 187.88/188.21 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 187.88/188.21 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition_ORep,axiom, % 187.88/188.21 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 187.88/188.21 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_type__definition_OAbs__inverse,axiom, % 187.88/188.21 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 187.88/188.21 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 187.88/188.21 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__nonneg__leq__bound,axiom, % 187.88/188.21 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 187.88/188.21 => ( ! [B_i] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 187.88/188.21 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_sum__diff__distrib,axiom, % 187.88/188.21 ! [V_n_2,V_Pa_2,V_Q_2] : % 187.88/188.21 ( ! [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))) % 187.88/188.21 => 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INFI__fold__inf,axiom, % 187.88/188.21 ! [V_f_2,V_A_2,T_b,T_c] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => 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) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF1__E,axiom, % 187.88/188.21 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 187.88/188.21 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF1__D,axiom, % 187.88/188.21 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__E,axiom, % 187.88/188.21 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 187.88/188.21 ( 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))) % 187.88/188.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) % 187.88/188.21 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__D,axiom, % 187.88/188.21 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 187.88/188.21 ( 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))) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF2__D,axiom, % 187.88/188.21 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF2__E,axiom, % 187.88/188.21 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 187.88/188.21 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_finite__INT,axiom, % 187.88/188.21 ! [V_A_2,T_c,V_I_2,T_b] : % 187.88/188.21 ( ? [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 187.88/188.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__iff,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 187.88/188.21 ( 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))) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF__INT__eq2,axiom, % 187.88/188.21 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 <=> 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__Int__distrib,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_b,T_c] : % 187.88/188.21 ( 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)) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.21 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b] : % 187.88/188.21 ( 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) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.21 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I9_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I9_J,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I7_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I6_J,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I7_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Un__INT__distrib,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I6_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Un__INT__distrib2,axiom, % 187.88/188.21 ! [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))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__subset__iff,axiom, % 187.88/188.21 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 187.88/188.21 ( 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))) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 187.88/188.21 => 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))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I5_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I5_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_vimage__INT,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF__commute,axiom, % 187.88/188.21 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INFI__apply,axiom, % 187.88/188.21 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Pow__INT__eq,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I10_J,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I10_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_le__INF__iff,axiom, % 187.88/188.21 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => ( 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))) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF__less__iff,axiom, % 187.88/188.21 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 187.88/188.21 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 & class_Orderings_Olinorder(T_b) ) % 187.88/188.21 => ( 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)) % 187.88/188.21 <=> ? [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.88/188.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__insert__distrib,axiom, % 187.88/188.21 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 187.88/188.21 => 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__lower,axiom, % 187.88/188.21 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF__INT__eq,axiom, % 187.88/188.21 ! [V_x_2,V_r_2,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 <=> 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__absorb,axiom, % 187.88/188.21 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 187.88/188.21 => 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) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF__const,axiom, % 187.88/188.21 ! [V_M_2,T_b,V_A_2,T_c] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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 ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__constant,axiom, % 187.88/188.21 ! [V_ca_2,T_c,T_b,V_A_2] : % 187.88/188.21 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) % 187.88/188.21 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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 ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__empty,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I1_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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 ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I2_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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 ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__insert,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__Un,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_UN__extend__simps_I7_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_UN__simps_I7_J,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Image__INT__subset,axiom, % 187.88/188.21 ! [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)))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Compl__UN,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Compl__INT,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF__subset,axiom, % 187.88/188.21 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.88/188.21 => 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))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I2_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I1_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I3_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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) ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I3_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__extend__simps_I4_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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 ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_bij__image__INT,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : % 187.88/188.21 ( 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))) % 187.88/188.21 => 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF__leI,axiom, % 187.88/188.21 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 187.88/188.21 => 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))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__greaterThan__UNIV,axiom, % 187.88/188.21 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INT__simps_I4_J,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 187.88/188.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) % 187.88/188.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_inf__INFI__fold__inf,axiom, % 187.88/188.21 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => 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) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__fin_Ohom__commute,axiom, % 187.88/188.21 ! [V_N_2,V_h_2,T_b] : % 187.88/188.21 ( class_Lattices_Olattice(T_b) % 187.88/188.21 => ( ! [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)) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 187.88/188.21 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => 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)) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_ImageE,axiom, % 187.88/188.21 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 187.88/188.21 => ~ ! [B_x] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__mono__zero__right,axiom, % 187.88/188.21 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 187.88/188.21 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( 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))) % 187.88/188.21 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 187.88/188.21 => 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) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF1__iff,axiom, % 187.88/188.21 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INF2__iff,axiom, % 187.88/188.21 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_image__INT,axiom, % 187.88/188.21 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 187.88/188.21 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 187.88/188.21 => 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)) ) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 187.88/188.21 => 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)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__mono__zero__left,axiom, % 187.88/188.21 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 187.88/188.21 ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( 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))) % 187.88/188.21 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 187.88/188.21 => 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) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__strict__mono,axiom, % 187.88/188.21 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 187.88/188.21 ( ( class_Groups_Ocomm__monoid__add(T_c) % 187.88/188.21 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 187.88/188.21 => 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))) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_field__le__mult__one__interval,axiom, % 187.88/188.21 ! [V_y,V_x,T_a] : % 187.88/188.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.88/188.21 => ( ! [B_z] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) ) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 187.88/188.21 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 187.88/188.21 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.21 & class_Groups_Ocomm__monoid__mult(T_b) ) % 187.88/188.21 => ( V_A_2 = V_B_2 % 187.88/188.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.88/188.21 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 187.88/188.21 => 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) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_code__numeral_Osimps_I5_J,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_code__numeral_Osimps_I4_J,axiom, % 187.88/188.21 ! [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 ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__fold__inf,axiom, % 187.88/188.21 ! [V_A_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => 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) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_divmod__int__pdivmod,axiom, % 187.88/188.21 ! [V_l_2,V_k_2] : % 187.88/188.21 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 187.88/188.21 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 187.88/188.21 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_decr__lemma,axiom, % 187.88/188.21 ! [V_z,V_x,V_d] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_finite__Inter,axiom, % 187.88/188.21 ! [V_M_2,T_b] : % 187.88/188.21 ( ? [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 187.88/188.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 187.88/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_InterE,axiom, % 187.88/188.21 ! [V_X_2,V_C_2,V_A_2,T_b] : % 187.88/188.21 ( 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))) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_InterD,axiom, % 187.88/188.21 ! [V_X_2,V_C_2,V_A_2,T_b] : % 187.88/188.21 ( 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))) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__abs,axiom, % 187.88/188.21 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_setsum__abs__ge__zero,axiom, % 187.88/188.21 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Un__Inter,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__less__iff,axiom, % 187.88/188.21 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_b) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2)) % 187.88/188.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 187.88/188.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_nonzero__abs__divide,axiom, % 187.88/188.21 ! [V_a,V_b,T_a] : % 187.88/188.21 ( class_Fields_Olinordered__field(T_a) % 187.88/188.21 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__le__D2,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__leI,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__le__iff,axiom, % 187.88/188.21 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 187.88/188.21 => ( 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)) % 187.88/188.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 187.88/188.21 & 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)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__ge__minus__self,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__setsum__abs,axiom, % 187.88/188.21 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 187.88/188.21 => 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) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apsnd__conv,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__le__D1,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__ge__self,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__divide,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__zero,axiom, % 187.88/188.21 ! [T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__eq__0,axiom, % 187.88/188.21 ! [V_a_2,T_b] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 187.88/188.21 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 187.88/188.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__add__abs,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__mult__self,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__mult,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__one,axiom, % 187.88/188.21 ! [T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__minus__cancel,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__idempotent,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__int__eq,axiom, % 187.88/188.21 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__of__nat,axiom, % 187.88/188.21 ! [V_n,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_power__abs,axiom, % 187.88/188.21 ! [V_n,V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__setprod,axiom, % 187.88/188.21 ! [V_A_2,V_f_2,T_c,T_b] : % 187.88/188.21 ( class_Fields_Olinordered__field(T_b) % 187.88/188.21 => 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) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__less__iff,axiom, % 187.88/188.21 ! [V_a_2,V_S_2,T_b] : % 187.88/188.21 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 & class_Orderings_Olinorder(T_b) ) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 187.88/188.21 <=> ? [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 187.88/188.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_le__Inf__iff,axiom, % 187.88/188.21 ! [V_A_2,V_ba_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => ( 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))) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__minus__commute,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__triangle__ineq3,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__triangle__ineq2,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__triangle__ineq2__sym,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_fst__apsnd,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__mult__less,axiom, % 187.88/188.21 ! [V_d,V_b,V_c,V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__triangle__ineq,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__not__less__zero,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_zero__less__abs__iff,axiom, % 187.88/188.21 ! [V_a_2,T_b] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 187.88/188.21 => ( 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))) % 187.88/188.21 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__of__pos,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__of__nonneg,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__le__zero__iff,axiom, % 187.88/188.21 ! [V_a_2,T_b] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 187.88/188.21 => ( 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))) % 187.88/188.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__ge__zero,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apsnd__compose,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_snd__apsnd,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apsnd__eq__conv,axiom, % 187.88/188.21 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 187.88/188.21 ( 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) % 187.88/188.21 <=> 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__power__minus,axiom, % 187.88/188.21 ! [V_n,V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__zmult__eq__1,axiom, % 187.88/188.21 ! [V_n,V_m] : % 187.88/188.21 ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_pdivmod__def,axiom, % 187.88/188.21 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_mult__sgn__abs,axiom, % 187.88/188.21 ! [V_x,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__sgn,axiom, % 187.88/188.21 ! [V_k,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_pdivmod__posDivAlg,axiom, % 187.88/188.21 ! [V_k,V_l] : % 187.88/188.21 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) ) % 187.88/188.21 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__lower,axiom, % 187.88/188.21 ! [V_A_2,V_B_2,T_b] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.88/188.21 => 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__anti__mono,axiom, % 187.88/188.21 ! [V_A_2,V_B_2,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__empty,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__insert,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__mult__pos,axiom, % 187.88/188.21 ! [V_y,V_x,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.88/188.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__eq__mult,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Rings_Oordered__ring__abs(T_a) % 187.88/188.21 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.88/188.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 187.88/188.21 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.88/188.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__diff__triangle__ineq,axiom, % 187.88/188.21 ! [V_d,V_c,V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__triangle__ineq4,axiom, % 187.88/188.21 ! [V_b,V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__of__nonpos,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__minus__le__zero,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__of__neg,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__if,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Groups_Oabs__if(T_a) % 187.88/188.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 187.88/188.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_zero__le__power__abs,axiom, % 187.88/188.21 ! [V_n,V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__div__pos,axiom, % 187.88/188.21 ! [V_x,V_y,T_a] : % 187.88/188.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.88/188.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__UNIV,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__minus__one,axiom, % 187.88/188.21 ! [T_a] : % 187.88/188.21 ( ( class_Int_Onumber__ring(T_a) % 187.88/188.21 & class_Rings_Olinordered__idom(T_a) ) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__lower,axiom, % 187.88/188.21 ! [V_A_2,V_x_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__Un__distrib,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_zabs__less__one__iff,axiom, % 187.88/188.21 ! [V_z_2] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 187.88/188.21 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_zabs__def,axiom, % 187.88/188.21 ! [V_i] : % 187.88/188.21 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 187.88/188.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__singleton,axiom, % 187.88/188.21 ! [V_a_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => 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 ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__empty,axiom, % 187.88/188.21 ! [T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => 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) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__UNIV,axiom, % 187.88/188.21 ! [T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => 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) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__insert,axiom, % 187.88/188.21 ! [V_A_2,V_a_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_nat__abs__mult__distrib,axiom, % 187.88/188.21 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_INTER__eq__Inter__image,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__image__eq,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_zero__le__zpower__abs,axiom, % 187.88/188.21 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_negateSnd__def,axiom, % 187.88/188.21 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__number__of,axiom, % 187.88/188.21 ! [V_x,T_a] : % 187.88/188.21 ( ( class_Int_Onumber__ring(T_a) % 187.88/188.21 & class_Rings_Olinordered__idom(T_a) ) % 187.88/188.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) % 187.88/188.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__power__minus__one,axiom, % 187.88/188.21 ! [V_n,T_a] : % 187.88/188.21 ( ( class_Int_Onumber__ring(T_a) % 187.88/188.21 & class_Rings_Olinordered__idom(T_a) ) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_zero__less__zpower__abs__iff,axiom, % 187.88/188.21 ! [V_n_2,V_x_2] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) % 187.88/188.21 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Int__eq__Inter,axiom, % 187.88/188.21 ! [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))))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Int__Inter__image,axiom, % 187.88/188.21 ! [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))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__Un__subset,axiom, % 187.88/188.21 ! [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)))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__binary,axiom, % 187.88/188.21 ! [V_ba_2,V_a_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => 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) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_inf__Inf__fold__inf,axiom, % 187.88/188.21 ! [V_B_2,V_A_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => 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) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inf__fin__Inf,axiom, % 187.88/188.21 ! [V_A_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_power2__abs,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_abs__power2,axiom, % 187.88/188.21 ! [V_a,T_a] : % 187.88/188.21 ( class_Rings_Olinordered__idom(T_a) % 187.88/188.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_divmod__int__code,axiom, % 187.88/188.21 ! [V_l_2,V_k_2] : % 187.88/188.21 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 187.88/188.21 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 187.88/188.21 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.88/188.21 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_incr__lemma,axiom, % 187.88/188.21 ! [V_x,V_z,V_d] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Nitpick_Oint__gcd__def,axiom, % 187.88/188.21 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Nitpick_Oint__lcm__def,axiom, % 187.88/188.21 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apfst__apsnd,axiom, % 187.88/188.21 ! [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))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Inter__def,axiom, % 187.88/188.21 ! [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))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apfst__compose,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apfst__eq__conv,axiom, % 187.88/188.21 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 187.88/188.21 ( 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) % 187.88/188.21 <=> 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)) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_fst__apfst,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_snd__apfst,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apfst__conv,axiom, % 187.88/188.21 ! [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) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apsnd__apfst__commute,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Nitpick_Onat__lcm__def,axiom, % 187.88/188.21 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_nat__gcd_Osimps,axiom, % 187.88/188.21 ! [V_x,V_y] : % 187.88/188.21 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.21 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 187.88/188.21 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.21 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_apsnd__apfst,axiom, % 187.88/188.21 ! [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))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_nat__gcd_Opsimps,axiom, % 187.88/188.21 ! [V_y_2,V_x_2] : % 187.88/188.21 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) % 187.88/188.21 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.21 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 187.88/188.21 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.21 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 187.88/188.21 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 187.88/188.21 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.88/188.21 & class_Groups_Ocomm__monoid__mult(T_b) ) % 187.88/188.21 => ( V_A_2 = V_B_2 % 187.88/188.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.88/188.21 => ( ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.88/188.21 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 187.88/188.21 => 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) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_accp__acc__eq,axiom, % 187.88/188.21 ! [V_x_2,V_r_2,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_acc__subset,axiom, % 187.88/188.21 ! [V_R2_2,V_R1_2,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_acc__downward,axiom, % 187.88/188.21 ! [V_a_2,V_r_2,V_ba_2,T_b] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 187.88/188.21 => ( 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)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_acc_Osimps,axiom, % 187.88/188.21 ! [V_r_2,V_a_2,T_b] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 187.88/188.21 <=> ! [B_x] : % 187.88/188.21 ( 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)) % 187.88/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_nat__gcd_Opinduct,axiom, % 187.88/188.21 ! [V_Pa_2,V_a1_2,V_a0_2] : % 187.88/188.21 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) % 187.88/188.21 => ( ! [B_x,B_y] : % 187.88/188.21 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) % 187.88/188.21 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 187.88/188.21 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__def,axiom, % 187.88/188.21 ! [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))))) ). % 187.88/188.21 % 187.88/188.21 fof(fact_max__extp_Oequations,axiom, % 187.88/188.21 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 187.88/188.21 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 187.88/188.21 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 187.88/188.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 187.88/188.21 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.88/188.21 & ! [B_x] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 187.88/188.21 => ? [B_xa] : % 187.88/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 187.88/188.21 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__compI,axiom, % 187.88/188.21 ! [V_s_2,V_ca_2,T_d,V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( 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)) % 187.88/188.21 => 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))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__UNION__distrib2,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__UNION__distrib,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_O__assoc,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__distrib2,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__distrib,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__mono,axiom, % 187.88/188.21 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( 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)) % 187.88/188.21 => 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))) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__empty2,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_rel__comp__empty1,axiom, % 187.88/188.21 ! [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)) ). % 187.88/188.21 % 187.88/188.21 fof(fact_union__comp__emptyL,axiom, % 187.88/188.21 ! [V_B_2,V_C_2,V_A_2,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( 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)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_union__comp__emptyR,axiom, % 187.88/188.21 ! [V_C_2,V_B_2,V_A_2,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => ( 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)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_max__ext__compat,axiom, % 187.88/188.21 ! [V_S_2,V_R_2,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_min__ext__compat,axiom, % 187.88/188.21 ! [V_S_2,V_R_2,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 => 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_pred__comp__rel__comp__eq,axiom, % 187.88/188.21 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 187.88/188.21 ( 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)) % 187.88/188.21 <=> 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))) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_reduction__pairI,axiom, % 187.88/188.21 ! [V_S_2,V_R_2,T_b] : % 187.88/188.21 ( c_Wellfounded_Owf(T_b,V_R_2) % 187.88/188.21 => ( 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)) % 187.88/188.21 => 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)) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_Sup__fold__sup,axiom, % 187.88/188.21 ! [V_A_2,T_b] : % 187.88/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.88/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.88/188.21 => 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) ) ) ). % 187.88/188.21 % 187.88/188.21 fof(fact_wf__less__than,axiom, % 187.88/188.21 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 188.18/188.21 % 188.18/188.21 fof(fact_pred__comp_Ointros,axiom, % 188.18/188.21 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_ba_2,V_a_2,V_r_2] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(V_s_2,V_ba_2),V_ca_2)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_UnionI,axiom, % 188.18/188.21 ! [V_A_2,V_C_2,V_X_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__empty,axiom, % 188.18/188.21 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__inv__image,axiom, % 188.18/188.21 ! [V_f_2,T_c,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__lex__prod,axiom, % 188.18/188.21 ! [V_rb_2,T_c,V_ra_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_ra_2) % 188.18/188.21 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 188.18/188.21 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__measure,axiom, % 188.18/188.21 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__comp__self,axiom, % 188.18/188.21 ! [V_R_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_R_2) % 188.18/188.21 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__Int1,axiom, % 188.18/188.21 ! [V_r_H_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__Int2,axiom, % 188.18/188.21 ! [V_r_H_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Int__Union,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Int__Union2,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_UN__simps_I8_J,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_UN__extend__simps_I8_J,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_image__Union,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_vimage__Union,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__less,axiom, % 188.18/188.21 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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__subset,axiom, % 188.18/188.21 ! [V_p_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__le__iff,axiom, % 188.18/188.21 ! [V_ba_2,V_A_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => ( 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)) % 188.18/188.21 <=> ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__pair__less,axiom, % 188.18/188.21 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 188.18/188.21 % 188.18/188.21 fof(fact_max__ext__wf,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_pred__comp_Oequations,axiom, % 188.18/188.21 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> ? [B_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 188.18/188.21 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_min__ext__wf,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__Pow__eq,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_less__Sup__iff,axiom, % 188.18/188.21 ! [V_S_2,V_a_2,T_b] : % 188.18/188.21 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 & class_Orderings_Olinorder(T_b) ) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 188.18/188.21 <=> ? [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 188.18/188.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Field__Union,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__mlex,axiom, % 188.18/188.21 ! [V_f_2,V_R_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_R_2) % 188.18/188.21 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__finite__psubset,axiom, % 188.18/188.21 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__irrefl,axiom, % 188.18/188.21 ! [V_a_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ~ 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__asym,axiom, % 188.18/188.21 ! [V_x_2,V_a_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => ~ 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__not__sym,axiom, % 188.18/188.21 ! [V_x_2,V_a_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => ~ 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__not__refl,axiom, % 188.18/188.21 ! [V_a_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ~ 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__disjoint,axiom, % 188.18/188.21 ! [V_A_2,V_C_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__upper,axiom, % 188.18/188.21 ! [V_A_2,V_B_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__int__ge__less__than2,axiom, % 188.18/188.21 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__int__ge__less__than,axiom, % 188.18/188.21 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__acc__iff,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acc__wfD,axiom, % 188.18/188.21 ! [V_x_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__no__loop,axiom, % 188.18/188.21 ! [V_R_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__union__merge,axiom, % 188.18/188.21 ! [V_S_2,V_R_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__empty,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__mono,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__quotient,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 188.18/188.21 => 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 ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__insert,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__UnionD,axiom, % 188.18/188.21 ! [V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_subset__Pow__Union,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__UNIV,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__Un__distrib,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_UNION__eq__Union__image,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__image__eq,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__upper,axiom, % 188.18/188.21 ! [V_A_2,V_x_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__empty,axiom, % 188.18/188.21 ! [T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => 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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__singleton,axiom, % 188.18/188.21 ! [V_a_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => 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 ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__insert,axiom, % 188.18/188.21 ! [V_A_2,V_a_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__UNIV,axiom, % 188.18/188.21 ! [T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => 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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 <=> ~ ? [B_f] : % 188.18/188.21 ! [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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfE__pf,axiom, % 188.18/188.21 ! [V_A_2,V_R_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_R_2) % 188.18/188.21 => ( 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))) % 188.18/188.21 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_INT__extend__simps_I8_J,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_INT__simps_I8_J,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__union__compatible,axiom, % 188.18/188.21 ! [V_S_2,V_R_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_R_2) % 188.18/188.21 => ( c_Wellfounded_Owf(T_b,V_S_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Un__eq__Union,axiom, % 188.18/188.21 ! [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))))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Un__Union__image,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf,axiom, % 188.18/188.21 ! [T_b] : % 188.18/188.21 ( class_Orderings_Owellorder(T_b) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_reduction__pair__def,axiom, % 188.18/188.21 ! [V_Pa_2,T_b] : % 188.18/188.21 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 188.18/188.21 <=> ( 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)) % 188.18/188.21 & 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_reduction__pair__lemma,axiom, % 188.18/188.21 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 188.18/188.21 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 188.18/188.21 => ( 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))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => ( c_Wellfounded_Owf(T_b,V_S_2) % 188.18/188.21 => 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)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__Int__subset,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__binary,axiom, % 188.18/188.21 ! [V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => 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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_sup__Sup__fold__sup,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => 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) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__fin__Sup,axiom, % 188.18/188.21 ! [V_A_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__lenlex,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__if__measure,axiom, % 188.18/188.21 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 188.18/188.21 ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.21 => 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))) ) % 188.18/188.21 => 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))))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_max__ext_Ointros,axiom, % 188.18/188.21 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 188.18/188.21 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 188.18/188.21 => ? [B_xa] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 188.18/188.21 & 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)) ) ) % 188.18/188.21 => 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))) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Union__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_pred__nat__def,axiom, % 188.18/188.21 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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__lex,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__Union,axiom, % 188.18/188.21 ! [V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 188.18/188.21 => ( ! [B_M] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__pred__nat,axiom, % 188.18/188.21 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 188.18/188.21 % 188.18/188.21 fof(fact_lex__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_insert__partition,axiom, % 188.18/188.21 ! [V_F_2,V_x_2,T_b] : % 188.18/188.21 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ! [B_xa] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( B_x != B_xa % 188.18/188.21 => 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)) ) ) ) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__lexn,axiom, % 188.18/188.21 ! [V_n_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_lexn_Osimps_I1_J,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_card__partition,axiom, % 188.18/188.21 ! [V_k_2,V_C_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 188.18/188.21 => ( ! [B_c] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 188.18/188.21 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 188.18/188.21 => ( ! [B_c1] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 188.18/188.21 => ! [B_c2] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 188.18/188.21 => ( B_c1 != B_c2 % 188.18/188.21 => 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)) ) ) ) % 188.18/188.21 => 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)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__same__fst,axiom, % 188.18/188.21 ! [T_b,V_R_2,T_c,V_Pa_2] : % 188.18/188.21 ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.21 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 188.18/188.21 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Ozero__frac__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Oone__frac__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Ofrac__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inj__on__Inter,axiom, % 188.18/188.21 ! [V_f_2,T_c,T_b,V_S_2] : % 188.18/188.21 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 188.18/188.21 => ( ! [B_A] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 188.18/188.21 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__Collect__split,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Inter__subset,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_b] : % 188.18/188.21 ( ! [B_X] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 188.18/188.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_RangeI,axiom, % 188.18/188.21 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__Id__on,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__Diff__subset,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__Union,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__empty__iff,axiom, % 188.18/188.21 ! [V_r_2,T_b,T_c] : % 188.18/188.21 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__empty,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__Un__eq,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__Range,axiom, % 188.18/188.21 ! [V_r_2,T_c,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_snd__eq__Range,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__iff,axiom, % 188.18/188.21 ! [V_r_2,T_c,V_a_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 188.18/188.21 <=> ? [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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__insert,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__Int__subset,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_RangeP__Range__eq,axiom, % 188.18/188.21 ! [V_x_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_RangeE,axiom, % 188.18/188.21 ! [V_r_2,T_c,V_ba_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 188.18/188.21 => ~ ! [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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__Un,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ( c_Wellfounded_Owf(T_b,V_s_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_RangeP_Ointros,axiom, % 188.18/188.21 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 188.18/188.21 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_ba_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_DomainI,axiom, % 188.18/188.21 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__Id__on,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_RangeP_Oequations,axiom, % 188.18/188.21 ! [V_a2_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 188.18/188.21 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__Diff__subset,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__Union,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__empty,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__empty__iff,axiom, % 188.18/188.21 ! [V_r_2,T_c,T_b] : % 188.18/188.21 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__mono,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__Un__eq,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__Domain,axiom, % 188.18/188.21 ! [V_r_2,T_c,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_fst__eq__Domain,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__iff,axiom, % 188.18/188.21 ! [V_r_2,T_c,V_a_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 188.18/188.21 <=> ? [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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__insert,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__Int__subset,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Field__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__Collect__split,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_DomainP__Domain__eq,axiom, % 188.18/188.21 ! [V_x_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_DomainE,axiom, % 188.18/188.21 ! [V_r_2,T_c,V_a_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 188.18/188.21 => ~ ! [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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_image__split__eq__Sigma,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_DomainP_Ointros,axiom, % 188.18/188.21 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 188.18/188.21 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_SigmaI,axiom, % 188.18/188.21 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__Union,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Times__eq__cancel2,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 188.18/188.21 => ( 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)) % 188.18/188.21 <=> V_A_2 = V_B_2 ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__empty1,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_card__cartesian__product,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setsum__cartesian__product,axiom, % 188.18/188.21 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__empty2,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Times__empty,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Compl__Times__UNIV2,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Compl__Times__UNIV1,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setprod__cartesian__product,axiom, % 188.18/188.21 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__Un__distrib2,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Times__Un__distrib1,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__Un__distrib1,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__comp__subset__Sigma,axiom, % 188.18/188.21 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => ( 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)))) % 188.18/188.21 => 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)))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_swap__product,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__cartesian__product,axiom, % 188.18/188.21 ! [V_B_2,T_c,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 188.18/188.21 => 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)))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_equiv__type,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__Int__distrib2,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Times__Int__distrib1,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__Int__distrib1,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Id__on__subset__Times,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__Diff__distrib2,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Times__Diff__distrib1,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__Diff__distrib1,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_DomainP_Oequations,axiom, % 188.18/188.21 ! [V_a1_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 188.18/188.21 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_UNIV__Times__UNIV,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_mem__Sigma__iff,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 188.18/188.21 & hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_SigmaD1,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_SigmaD2,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_SigmaE2,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 188.18/188.21 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_card__cartesian__product__singleton,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Times__subset__cancel2,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 188.18/188.21 => ( 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)))) % 188.18/188.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Image__subset,axiom, % 188.18/188.21 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__cartesian__productD2,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_c,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__cartesian__productD1,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_c,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Collect__split,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_SetCompr__Sigma__eq,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_fst__image__times,axiom, % 188.18/188.21 ! [V_A_2,T_c,T_b,V_B_2] : % 188.18/188.21 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => 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)) ) % 188.18/188.21 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => 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 ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_snd__image__times,axiom, % 188.18/188.21 ! [V_B_2,T_c,T_b,V_A_2] : % 188.18/188.21 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => 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)) ) % 188.18/188.21 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => 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 ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_insert__times__insert,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__equiv__class,axiom, % 188.18/188.21 ! [V_X_2,V_r_2,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( 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)))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_vimage__Times,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_UN__Times__distrib,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__def,axiom, % 188.18/188.21 ! [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))))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__quotient,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( 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)))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setsum__mult__setsum__if__inj,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 188.18/188.21 ( class_Rings_Osemiring__0(T_d) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))))))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 188.18/188.21 ! [V_A_2,V_I_2,T_c,T_b] : % 188.18/188.21 ? [B_f] : % 188.18/188.21 ( 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)) % 188.18/188.21 & 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_fold__image__Sigma,axiom, % 188.18/188.21 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__mult(T_d) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 188.18/188.21 => 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_bij__betw__id,axiom, % 188.18/188.21 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ). % 188.18/188.21 % 188.18/188.21 fof(fact_image__id,axiom, % 188.18/188.21 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 188.18/188.21 % 188.18/188.21 fof(fact_inj__on__id,axiom, % 188.18/188.21 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 188.18/188.21 % 188.18/188.21 fof(fact_o__eq__id__dest,axiom, % 188.18/188.21 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 188.18/188.21 ( 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) % 188.18/188.21 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_o__id,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_id__o,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_bij__betw__id__iff,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_b] : % 188.18/188.21 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2) % 188.18/188.21 <=> V_A_2 = V_B_2 ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_vimage__id,axiom, % 188.18/188.21 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 188.18/188.21 % 188.18/188.21 fof(fact_id__def,axiom, % 188.18/188.21 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 188.18/188.21 % 188.18/188.21 fof(fact_id__apply,axiom, % 188.18/188.21 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 188.18/188.21 % 188.18/188.21 fof(fact_apfst__id,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_apsnd__id,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_of__int__eq__id,axiom, % 188.18/188.21 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 188.18/188.21 % 188.18/188.21 fof(fact_surj__id,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_bij__id,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inv__id,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_folding_Oempty,axiom, % 188.18/188.21 ! [V_F_2,V_f_2,T_c,T_b] : % 188.18/188.21 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 188.18/188.21 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_split__Pair,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setsum__reindex__id,axiom, % 188.18/188.21 ! [V_B_2,V_f_2,T_b,T_c] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__add(T_c) % 188.18/188.21 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setprod__reindex__id,axiom, % 188.18/188.21 ! [V_B_2,V_f_2,T_b,T_c] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__mult(T_c) % 188.18/188.21 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_surj__iff,axiom, % 188.18/188.21 ! [V_f_2,T_b,T_c] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> 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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inv__o__cancel,axiom, % 188.18/188.21 ! [V_f_2,T_c,T_b] : % 188.18/188.21 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 188.18/188.21 => 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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inj__iff,axiom, % 188.18/188.21 ! [V_f_2,T_c,T_b] : % 188.18/188.21 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 188.18/188.21 <=> 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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setprod__Sigma,axiom, % 188.18/188.21 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__mult(T_d) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 188.18/188.21 => 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setsum__Sigma,axiom, % 188.18/188.21 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__add(T_d) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 188.18/188.21 => 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_card__SigmaI,axiom, % 188.18/188.21 ! [V_B_2,T_c,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 188.18/188.21 => 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) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__SigmaI,axiom, % 188.18/188.21 ! [V_B_2,T_c,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_a] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_SigmaE,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => ! [B_y] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 188.18/188.21 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__surj,axiom, % 188.18/188.21 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__imageI,axiom, % 188.18/188.21 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__simp,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__ident,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_snd__prod__fun,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_fst__map__pair,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_fst__comp__map__pair,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_snd__comp__map__pair,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair_Ocomp,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__compose,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair_Ocompositionality,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair_Oidentity,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_apfst__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_apsnd__def,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair_Oid,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__surj__on,axiom, % 188.18/188.21 ! [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] : % 188.18/188.21 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 188.18/188.21 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__map__pair__image,axiom, % 188.18/188.21 ! [V_f_2,T_c,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_map__pair__inj__on,axiom, % 188.18/188.21 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 188.18/188.21 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 188.18/188.21 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_prod__fun__imageE,axiom, % 188.18/188.21 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_x,B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ~ 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__def,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 <=> ( 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)))) % 188.18/188.21 & ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_nat0__intermed__int__val,axiom, % 188.18/188.21 ! [V_k_2,V_f_2,V_n_2] : % 188.18/188.21 ( ! [B_i] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 188.18/188.21 => ? [B_i] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 188.18/188.21 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__Id__on,axiom, % 188.18/188.21 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__empty,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__Un,axiom, % 188.18/188.21 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__Int,axiom, % 188.18/188.21 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__onD2,axiom, % 188.18/188.21 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__onD1,axiom, % 188.18/188.21 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__onD,axiom, % 188.18/188.21 ! [V_a_2,V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_reflp__def,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Predicate_Oreflp(T_b,V_r_2) % 188.18/188.21 <=> 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__onI,axiom, % 188.18/188.21 ! [V_A_2,V_r_2,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => 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)) ) % 188.18/188.21 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_int__val__lemma,axiom, % 188.18/188.21 ! [V_k_2,V_f_2,V_n_2] : % 188.18/188.21 ( ! [B_i] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 188.18/188.21 => ? [B_i] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 188.18/188.21 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_reflpE,axiom, % 188.18/188.21 ! [V_x_2,V_r_2,T_b] : % 188.18/188.21 ( c_Predicate_Oreflp(T_b,V_r_2) % 188.18/188.21 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfP__def,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_OwfP(T_b,V_r_2) % 188.18/188.21 <=> 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setprod__pos__nat,axiom, % 188.18/188.21 ! [V_f_2,V_S_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfP__empty,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_accp__wfPD,axiom, % 188.18/188.21 ! [V_x_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_OwfP(T_b,V_r_2) % 188.18/188.21 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfP__accp__iff,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_OwfP(T_b,V_r_2) % 188.18/188.21 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfP__subset,axiom, % 188.18/188.21 ! [V_p_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_OwfP(T_b,V_r_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__in__rel,axiom, % 188.18/188.21 ! [V_R_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_R_2) % 188.18/188.21 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfP__wf__eq,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfP__acyclicP,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_OwfP(T_b,V_r_2) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Rep__Integ__cases,axiom, % 188.18/188.21 ! [V_y_2] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 188.18/188.21 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acyclic__subset,axiom, % 188.18/188.21 ! [V_r_2,V_s_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__acyclic,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__acyclic__wf,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 188.18/188.21 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__iff__acyclic__if__finite,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 188.18/188.21 => ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Owf_H__def,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Nitpick_Owf_H(T_b,V_r_2) % 188.18/188.21 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 188.18/188.21 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 188.18/188.21 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Rep__Integ__induct,axiom, % 188.18/188.21 ! [V_Pa_2,V_y_2] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 188.18/188.21 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inj__on__INTER,axiom, % 188.18/188.21 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 188.18/188.21 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 => ( ! [B_i] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 188.18/188.21 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 188.18/188.21 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( 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))) % 188.18/188.21 => hAPP(V_g_2,B_x) = V_z_2 ) % 188.18/188.21 => 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)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 188.18/188.21 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 188.18/188.21 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 188.18/188.21 => ~ ! [B_y] : % 188.18/188.21 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 188.18/188.21 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__def_H,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 <=> ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 188.18/188.21 => 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)) ) % 188.18/188.21 & ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Powp__def,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 188.18/188.21 <=> ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 188.18/188.21 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_INFI__bool__eq,axiom, % 188.18/188.21 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 188.18/188.21 % 188.18/188.21 fof(fact_ball__empty,axiom, % 188.18/188.21 ! [V_Pa_2,T_b,B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Collect__ball__eq,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_congruent__def,axiom, % 188.18/188.21 ! [V_f_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 188.18/188.21 <=> ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_INTER__def,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sup__Inf,axiom, % 188.18/188.21 ! [V_A_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => 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)))))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Inf__Sup,axiom, % 188.18/188.21 ! [V_A_2,T_b] : % 188.18/188.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.21 => 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))))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Abs__Integ__induct,axiom, % 188.18/188.21 ! [V_x_2,V_Pa_2] : % 188.18/188.21 ( ! [B_y] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Abs__Integ__cases,axiom, % 188.18/188.21 ! [V_x_2] : % 188.18/188.21 ~ ! [B_y] : % 188.18/188.21 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 188.18/188.21 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Inter__eq,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__UN__I,axiom, % 188.18/188.21 ! [V_B_2,T_c,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_a] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_ex__bij__betw__nat__finite__1,axiom, % 188.18/188.21 ! [V_M_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 188.18/188.21 => ? [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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_ex__bij__betw__nat__finite,axiom, % 188.18/188.21 ! [V_M_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 188.18/188.21 => ? [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) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfP__SUP,axiom, % 188.18/188.21 ! [T_b,V_r_2,T_c] : % 188.18/188.21 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 188.18/188.21 => ( ! [B_i,B_j] : % 188.18/188.21 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 188.18/188.21 => 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)) ) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_mem__splitI2,axiom, % 188.18/188.21 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 188.18/188.21 ( ! [B_a,B_b] : % 188.18/188.21 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_mem__splitE,axiom, % 188.18/188.21 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_x,B_y] : % 188.18/188.21 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 188.18/188.21 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setsum__SucD,axiom, % 188.18/188.21 ! [V_n_2,V_A_2,V_f_2,T_b] : % 188.18/188.21 ( 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) % 188.18/188.21 => ? [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Eps__split,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_exE__some,axiom, % 188.18/188.21 ! [T_b,V_ca_2,V_Pa_2] : % 188.18/188.21 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 188.18/188.21 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_someI__ex,axiom, % 188.18/188.21 ! [T_b,V_Pa_2] : % 188.18/188.21 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_some__eq__ex,axiom, % 188.18/188.21 ! [T_b,V_Pa_2] : % 188.18/188.21 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 188.18/188.21 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_some__eq__trivial,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_some__sym__eq__trivial,axiom, % 188.18/188.21 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 188.18/188.21 % 188.18/188.21 fof(fact_tfl__some,axiom, % 188.18/188.21 ! [T_b,B_P] : % 188.18/188.21 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 188.18/188.21 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_someI,axiom, % 188.18/188.21 ! [T_b,V_x_2,V_Pa_2] : % 188.18/188.21 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Eps__split__eq,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_split__paired__Eps,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inv__into__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inv__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_nat__mod__eq__lemma,axiom, % 188.18/188.21 ! [V_y,V_n,V_x] : % 188.18/188.21 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 188.18/188.21 => ? [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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wfI__pf,axiom, % 188.18/188.21 ! [V_R_2,T_b] : % 188.18/188.21 ( ! [B_A] : % 188.18/188.21 ( 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))) % 188.18/188.21 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 188.18/188.21 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_ex__bij__betw__finite__nat,axiom, % 188.18/188.21 ! [V_M_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 188.18/188.21 => ? [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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Sigma__mono,axiom, % 188.18/188.21 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => 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))) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_not__acc__down,axiom, % 188.18/188.21 ! [V_R_2,V_x_2,T_b] : % 188.18/188.21 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 188.18/188.21 => ~ ! [B_z] : % 188.18/188.21 ( 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)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acc_OaccI,axiom, % 188.18/188.21 ! [V_r_2,V_x_2,T_b] : % 188.18/188.21 ( ! [B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_max__ext_Osimps,axiom, % 188.18/188.21 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 188.18/188.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 188.18/188.21 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.21 & ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 188.18/188.21 => ? [B_xa] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 188.18/188.21 & 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)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 188.18/188.21 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 188.18/188.21 ( class_Orderings_Olinorder(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 188.18/188.21 => 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))) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 188.18/188.21 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 188.18/188.21 ( class_Orderings_Olinorder(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 188.18/188.21 => 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))) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_mod__induct__0,axiom, % 188.18/188.21 ! [V_i_2,V_Pa_2,V_p_2] : % 188.18/188.21 ( ! [B_i] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 188.18/188.21 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 188.18/188.21 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 188.18/188.21 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_InterI,axiom, % 188.18/188.21 ! [V_A_2,V_C_2,T_b] : % 188.18/188.21 ( ! [B_X] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Min__eqI,axiom, % 188.18/188.21 ! [V_x_2,V_A_2,T_b] : % 188.18/188.21 ( class_Orderings_Olinorder(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_y] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 188.18/188.21 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Max__eqI,axiom, % 188.18/188.21 ! [V_x_2,V_A_2,T_b] : % 188.18/188.21 ( class_Orderings_Olinorder(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_y] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 188.18/188.21 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inf__le__fold__inf,axiom, % 188.18/188.21 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 188.18/188.21 ( class_Lattices_Osemilattice__inf(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 188.18/188.21 => 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))) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_fold__sup__le__sup,axiom, % 188.18/188.21 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 188.18/188.21 ( class_Lattices_Osemilattice__sup(T_b) % 188.18/188.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 188.18/188.21 => 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))) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__no__infinite__down__chainE,axiom, % 188.18/188.21 ! [V_f_2,V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => ~ ! [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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setsum__reindex__cong,axiom, % 188.18/188.21 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 188.18/188.21 ( class_Groups_Ocomm__monoid__add(T_d) % 188.18/188.21 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 188.18/188.21 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 188.18/188.21 => ( ! [B_a] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 188.18/188.21 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 188.18/188.21 => 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) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_scomp__unfold,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_scomp__apply,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Pair__scomp,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_scomp__scomp,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_scomp__Pair,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_scomp__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_iterate_Osimps,axiom, % 188.18/188.21 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 188.18/188.21 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.21 => 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) ) % 188.18/188.21 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setsum__ivl__cong,axiom, % 188.18/188.21 ! [V_g_2,V_f_2,V_d_2,V_ba_2,V_ca_2,V_a_2,T_b,T_c] : % 188.18/188.21 ( ( class_Groups_Ocomm__monoid__add(T_c) % 188.18/188.21 & class_Orderings_Oord(T_b) ) % 188.18/188.21 => ( V_a_2 = V_ca_2 % 188.18/188.21 => ( V_ba_2 = V_d_2 % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 188.18/188.21 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 188.18/188.21 => 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)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_log_Osimps,axiom, % 188.18/188.21 ! [V_i,V_b] : % 188.18/188.21 ( ( ( 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))) % 188.18/188.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 188.18/188.21 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 188.18/188.21 & ( ~ ( 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))) % 188.18/188.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_minus__shift__def,axiom, % 188.18/188.21 ! [V_r,V_l,V_k] : % 188.18/188.21 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 188.18/188.21 => 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) ) % 188.18/188.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 188.18/188.21 => 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) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_inc__shift__def,axiom, % 188.18/188.21 ! [V_k,V_v] : % 188.18/188.21 ( ( V_v = V_k % 188.18/188.21 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 188.18/188.21 & ( V_v != V_k % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_range,axiom, % 188.18/188.21 ! [V_s,V_k] : % 188.18/188.21 ( 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)) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_less__eq,axiom, % 188.18/188.21 ! [V_n_2,V_m_2] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_nat__intermed__int__val,axiom, % 188.18/188.21 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 188.18/188.21 ( ! [B_i] : % 188.18/188.21 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 188.18/188.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 188.18/188.21 => ? [B_i] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 188.18/188.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 188.18/188.21 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__trancl,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_less__than__def,axiom, % 188.18/188.21 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acyclic__def,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 188.18/188.21 <=> ! [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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl_Or__into__trancl,axiom, % 188.18/188.21 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__subset__Field2,axiom, % 188.18/188.21 ! [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))))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_r__into__trancl_H,axiom, % 188.18/188.21 ! [V_r_2,V_p_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__empty,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__domain,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__range,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__trancl,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 188.18/188.21 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_r__r__into__trancl,axiom, % 188.18/188.21 ! [V_ca_2,V_R_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__into__trancl2,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__trans,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__mono,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,V_p_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 188.18/188.21 => ( 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)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__unfold,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__subset__Sigma,axiom, % 188.18/188.21 ! [V_A_2,V_r_2,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__Int__subset,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__insert,axiom, % 188.18/188.21 ! [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)))))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_reflcl__set__eq,axiom, % 188.18/188.21 ! [V_y_2,V_x_2,V_r_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_r__into__rtrancl,axiom, % 188.18/188.21 ! [V_r_2,V_p_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl_Ortrancl__refl,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_IdI,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__into__rtrancl,axiom, % 188.18/188.21 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__trancl__absorb,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__rtrancl__absorb,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_reflcl__trancl,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__reflcl,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__unfold__left,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__unfold__right,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Image__closed__trancl,axiom, % 188.18/188.21 ! [V_X_2,V_r_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__Un__subset,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__mono,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__subset,axiom, % 188.18/188.21 ! [V_S_2,V_R_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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))) % 188.18/188.21 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__subset__rtrancl,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__Int__subset,axiom, % 188.18/188.21 ! [V_r_2,V_s_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__rtrancl,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__rtrancl,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__empty,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__idemp__self__comp,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_r__comp__rtrancl__eq,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__unfold,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_in__rtrancl__UnI,axiom, % 188.18/188.21 ! [V_S_2,V_R_2,V_x_2,T_b] : % 188.18/188.21 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 188.18/188.21 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__reflcl,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__Un__rtrancl,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__reflcl__absorb,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__idemp,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__trans,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__rtrancl,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__r__diff__Id,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Image__Id,axiom, % 188.18/188.21 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 188.18/188.21 % 188.18/188.21 fof(fact_R__O__Id,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_Id__O__R,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_pair__in__Id__conv,axiom, % 188.18/188.21 ! [V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> V_a_2 = V_ba_2 ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__eq__or__trancl,axiom, % 188.18/188.21 ! [V_R_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> ( V_x_2 = V_y_2 % 188.18/188.21 | ( V_x_2 != V_y_2 % 188.18/188.21 & 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))) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__into__trancl2,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtranclD,axiom, % 188.18/188.21 ! [V_R_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( V_a_2 = V_ba_2 % 188.18/188.21 | ( V_a_2 != V_ba_2 % 188.18/188.21 & 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))) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__into__trancl1,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__rtrancl__trancl,axiom, % 188.18/188.21 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__trancl__trancl,axiom, % 188.18/188.21 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__Id,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__Id,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__Id,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_pair__leq__def,axiom, % 188.18/188.21 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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Not__Domain__rtrancl,axiom, % 188.18/188.21 ! [V_y_2,V_R_2,V_x_2,T_b] : % 188.18/188.21 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 188.18/188.21 => ( 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))) % 188.18/188.21 <=> V_x_2 = V_y_2 ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acc__downwards,axiom, % 188.18/188.21 ! [V_ba_2,V_r_2,V_a_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acc__downwards__aux,axiom, % 188.18/188.21 ! [V_r_2,V_a_2,V_ba_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__insert,axiom, % 188.18/188.21 ! [V_r_2,V_x_2,V_y_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 & ~ 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acyclic__insert,axiom, % 188.18/188.21 ! [V_r_2,V_x_2,V_y_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 188.18/188.21 & ~ 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__reflcl,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Id__def,axiom, % 188.18/188.21 ! [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))))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_irrefl__diff__Id,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_pred__nat__trancl__eq__le,axiom, % 188.18/188.21 ! [V_n_2,V_m_2] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__subset__Sigma__aux,axiom, % 188.18/188.21 ! [V_A_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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)))) % 188.18/188.21 => ( V_a_2 = V_ba_2 % 188.18/188.21 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_irrefl__tranclI,axiom, % 188.18/188.21 ! [V_x_2,V_r_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ~ 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_sequence__trans,axiom, % 188.18/188.21 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 188.18/188.21 ( ! [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))) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__converse,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__Id,axiom, % 188.18/188.21 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__converse,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 188.18/188.21 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converseD,axiom, % 188.18/188.21 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converseI,axiom, % 188.18/188.21 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__iff,axiom, % 188.18/188.21 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__rel__comp,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__Un,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__inv__image,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__converse,axiom, % 188.18/188.21 ! [V_r_2,T_c,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 188.18/188.21 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__converse,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_Field__converse,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__Id__on,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__Int,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__UNION,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acyclic__converse,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 188.18/188.21 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__INTER,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__converse,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__converse__trancl,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 188.18/188.21 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_equiv__comp__eq,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 188.18/188.21 => 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 ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Domain__converse,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Range__converse,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__converseD,axiom, % 188.18/188.21 ! [V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__converseI,axiom, % 188.18/188.21 ! [V_r_2,V_x_2,V_y_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__converseD,axiom, % 188.18/188.21 ! [V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__converseI,axiom, % 188.18/188.21 ! [V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Image__subset__eq,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 <=> 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))))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_refl__on__comp__subset,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_comp__equivI,axiom, % 188.18/188.21 ! [V_A_2,V_r_2,T_b] : % 188.18/188.21 ( 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 % 188.18/188.21 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 188.18/188.21 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__acyclic__wf__converse,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 188.18/188.21 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 188.18/188.21 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converse__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Image__INT__eq,axiom, % 188.18/188.21 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 188.18/188.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_total__on__diff__Id,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valued__Id,axiom, % 188.18/188.21 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valued__rel__comp,axiom, % 188.18/188.21 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 188.18/188.21 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 188.18/188.21 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 188.18/188.21 => 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valued__subset,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 188.18/188.21 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valued__Id__on,axiom, % 188.18/188.21 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_total__on__empty,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_total__on__converse,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 188.18/188.21 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valued__def,axiom, % 188.18/188.21 ! [V_r_2,T_c,T_b] : % 188.18/188.21 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 188.18/188.21 <=> ! [B_x,B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ! [B_z] : % 188.18/188.21 ( 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)) % 188.18/188.21 => B_y = B_z ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valuedD,axiom, % 188.18/188.21 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 188.18/188.21 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 188.18/188.21 => ( 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)) % 188.18/188.21 => ( 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)) % 188.18/188.21 => V_y_2 = V_z_2 ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_total__on__def,axiom, % 188.18/188.21 ! [V_r_2,V_A_2,T_b] : % 188.18/188.21 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 188.18/188.21 <=> ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => ! [B_xa] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 188.18/188.21 => ( B_x != B_xa % 188.18/188.21 => ( 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)) % 188.18/188.21 | 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)) ) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valued__confluent,axiom, % 188.18/188.21 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 188.18/188.21 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 188.18/188.21 => ( 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))) % 188.18/188.21 => ( 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))) % 188.18/188.21 => ( 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))) % 188.18/188.21 | 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))) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Image__Int__eq,axiom, % 188.18/188.21 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 188.18/188.21 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 188.18/188.21 ! [V_R_2,V_p_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_acyclicI,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( ! [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))) % 188.18/188.21 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_single__valued__rel__pow,axiom, % 188.18/188.21 ! [V_n_2,V_R_2,T_b] : % 188.18/188.21 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_comp__funpow,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_funpow__mult,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_funpow__swap1,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__exp,axiom, % 188.18/188.21 ! [V_R_2,V_n_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__1,axiom, % 188.18/188.21 ! [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 ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__commute,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__power,axiom, % 188.18/188.21 ! [V_R_2,V_p_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 188.18/188.21 <=> ? [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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__imp__rtrancl,axiom, % 188.18/188.21 ! [V_R_2,V_n_2,V_p_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_relpow_Osimps_I2_J,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__add,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_relpow_Osimps_I1_J,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__0__I,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__0__E,axiom, % 188.18/188.21 ! [V_R_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => V_x_2 = V_y_2 ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__Suc__I2,axiom, % 188.18/188.21 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ( 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))) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__Suc__I,axiom, % 188.18/188.21 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( 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)) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_funpow_Osimps_I2_J,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_funpow__add,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_funpow_Osimps_I1_J,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_trancl__power,axiom, % 188.18/188.21 ! [V_R_2,V_p_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 188.18/188.21 <=> ? [B_n] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 188.18/188.21 & 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_funpow__code__def,axiom, % 188.18/188.21 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__E2,axiom, % 188.18/188.21 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.21 => V_x_2 != V_z_2 ) % 188.18/188.21 => ~ ! [B_y,B_m] : % 188.18/188.21 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 188.18/188.21 => ( 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)) % 188.18/188.21 => ~ 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))) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__E,axiom, % 188.18/188.21 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.21 => V_x_2 != V_z_2 ) % 188.18/188.21 => ~ ! [B_y,B_m] : % 188.18/188.21 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 188.18/188.21 => ( 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))) % 188.18/188.21 => ~ 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)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__Un__separatorE,axiom, % 188.18/188.21 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ! [B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 => B_x = B_y ) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rtrancl__Un__separator__converseE,axiom, % 188.18/188.21 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 188.18/188.21 ( 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)))) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ! [B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 => B_y = B_x ) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__Suc__D2,axiom, % 188.18/188.21 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ? [B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 & 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__Suc__E,axiom, % 188.18/188.21 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_y] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__pow__Suc__E2,axiom, % 188.18/188.21 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ~ 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_tranclD,axiom, % 188.18/188.21 ! [V_R_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ? [B_z] : % 188.18/188.21 ( 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)) % 188.18/188.21 & 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_tranclD2,axiom, % 188.18/188.21 ! [V_R_2,V_y_2,V_x_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ? [B_z] : % 188.18/188.21 ( 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))) % 188.18/188.21 & 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_IdE,axiom, % 188.18/188.21 ! [V_p_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 188.18/188.21 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_mod__div__decomp,axiom, % 188.18/188.21 ! [V_b,V_a,T_a] : % 188.18/188.21 ( class_Divides_Osemiring__div(T_a) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_wf__eq__minimal,axiom, % 188.18/188.21 ! [V_r_2,T_b] : % 188.18/188.21 ( c_Wellfounded_Owf(T_b,V_r_2) % 188.18/188.21 <=> ! [B_Q] : % 188.18/188.21 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 188.18/188.21 => ? [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 188.18/188.21 & ! [B_y] : % 188.18/188.21 ( 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)) % 188.18/188.21 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_transfer__nat__int__set__cong,axiom, % 188.18/188.21 ! [V_P_H_2,V_Pa_2] : % 188.18/188.21 ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 188.18/188.21 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.21 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 188.18/188.21 => 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)) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Int__Collect__mono,axiom, % 188.18/188.21 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.21 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 188.18/188.21 => 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)))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_UnionE,axiom, % 188.18/188.21 ! [V_C_2,V_A_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_X] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 188.18/188.21 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_converseE,axiom, % 188.18/188.21 ! [V_r_2,V_yx_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_x,B_y] : % 188.18/188.21 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 188.18/188.21 => ~ 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)) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_rel__compE,axiom, % 188.18/188.21 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ~ ! [B_x,B_y,B_z] : % 188.18/188.21 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 188.18/188.21 => ( 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)) % 188.18/188.21 => ~ 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)) ) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Oplus__frac__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setprod__pos,axiom, % 188.18/188.21 ! [V_f_2,V_A_2,T_b,T_c] : % 188.18/188.21 ( class_Rings_Olinordered__semidom(T_c) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Otimes__frac__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Oof__frac__def,axiom, % 188.18/188.21 ! [V_q,T_a,T_b] : % 188.18/188.21 ( ( class_Rings_Oinverse(T_b) % 188.18/188.21 & class_Rings_Oring__1(T_b) ) % 188.18/188.21 => 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 188.18/188.21 ! [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))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Oless__frac__def,axiom, % 188.18/188.21 ! [V_r_2,V_q_2,T_b] : % 188.18/188.21 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 188.18/188.21 <=> 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 188.18/188.21 ! [V_r_2,V_q_2,T_b] : % 188.18/188.21 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 188.18/188.21 <=> 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))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Onum__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_Nitpick_Odenom__def,axiom, % 188.18/188.21 ! [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)) ). % 188.18/188.21 % 188.18/188.21 fof(fact_internal__split__def,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_setprod__nonneg,axiom, % 188.18/188.21 ! [V_f_2,V_A_2,T_b,T_c] : % 188.18/188.21 ( class_Rings_Olinordered__semidom(T_c) % 188.18/188.21 => ( ! [B_x] : % 188.18/188.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 188.18/188.21 => 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))) ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_internal__split__conv,axiom, % 188.18/188.21 ! [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) ). % 188.18/188.21 % 188.18/188.21 fof(fact_bool_Osize_I1_J,axiom, % 188.18/188.21 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 188.18/188.21 % 188.18/188.21 fof(fact_bool_Osize_I2_J,axiom, % 188.18/188.21 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 188.18/188.21 % 188.18/188.21 fof(fact_finite__less__ub,axiom, % 188.18/188.21 ! [V_u_2,V_f_2] : % 188.18/188.21 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 188.18/188.21 => 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)))) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_lenlex__def,axiom, % 188.18/188.21 ! [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)))) ). % 188.18/188.21 % 188.18/188.21 fof(fact_lexn__length,axiom, % 188.18/188.21 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.21 ( 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))) % 188.18/188.21 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 % 188.18/188.21 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_neq__if__length__neq,axiom, % 188.18/188.21 ! [V_ys,V_xs,T_a] : % 188.18/188.21 ( 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) % 188.18/188.21 => V_xs != V_ys ) ). % 188.18/188.21 % 188.18/188.21 fof(fact_lenlex__conv,axiom, % 188.18/188.22 ! [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)))))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__sublist,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexn_Osimps_I2_J,axiom, % 188.18/188.22 ! [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)))))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_impossible__Cons,axiom, % 188.18/188.22 ! [V_x,V_ys,V_xs,T_a] : % 188.18/188.22 ( 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))) % 188.18/188.22 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_not__Cons__self,axiom, % 188.18/188.22 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 188.18/188.22 % 188.18/188.22 fof(fact_not__Cons__self2,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Oinject,axiom, % 188.18/188.22 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> ( V_a_2 = V_a_H_2 % 188.18/188.22 & V_list_2 = V_list_H_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osize_I4_J,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Cons__in__lex,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( ( 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)) % 188.18/188.22 & 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) ) % 188.18/188.22 | ( V_x_2 = V_y_2 % 188.18/188.22 & 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))) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__Cons__def,axiom, % 188.18/188.22 ! [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)))))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_pick_Osimps,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a,V_i] : % 188.18/188.22 ( ( 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))) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( ~ 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))) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_select__weight__cons__zero,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__cons__cons,axiom, % 188.18/188.22 ! [V_r_2,V_y_2,V_ba_2,V_x_2,V_a_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( 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)) % 188.18/188.22 | ( V_a_2 = V_ba_2 % 188.18/188.22 & 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))) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__lex,axiom, % 188.18/188.22 ! [V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( 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))) % 188.18/188.22 & 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( 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)))) % 188.18/188.22 => 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)))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osize_I2_J,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Cons__acc__listrel1I,axiom, % 188.18/188.22 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 188.18/188.22 => ( 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)))) % 188.18/188.22 => 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)))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1__converse,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1__mono,axiom, % 188.18/188.22 ! [V_s_2,V_r_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1I2,axiom, % 188.18/188.22 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 188.18/188.22 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1__eq__len,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rtrancl__listrel1__eq__len,axiom, % 188.18/188.22 ! [V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__listrel1__converse,axiom, % 188.18/188.22 ! [V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 <=> 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1I1,axiom, % 188.18/188.22 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Cons__listrel1__Cons,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( ( 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)) % 188.18/188.22 & V_xs_2 = V_ys_2 ) % 188.18/188.22 | ( V_x_2 = V_y_2 % 188.18/188.22 & 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))) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__Cons,axiom, % 188.18/188.22 ! [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))))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__irreflexive,axiom, % 188.18/188.22 ! [V_y_2,V_r_2,T_b] : % 188.18/188.22 ( ! [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)) % 188.18/188.22 => ~ 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__rtrancl__refl,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__mono,axiom, % 188.18/188.22 ! [V_s_2,V_r_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__eq__len,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__rtrancl__trans,axiom, % 188.18/188.22 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => ( 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)))) % 188.18/188.22 => 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)))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__reflcl__if__listrel1,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1__subset__listrel,axiom, % 188.18/188.22 ! [V_r_H_2,V_r_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel_OCons,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => ( 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))) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrelp__listrel__eq,axiom, % 188.18/188.22 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__Cons2,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ~ ! [B_x,B_xs] : % 188.18/188.22 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 188.18/188.22 => ( 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)) % 188.18/188.22 => ~ 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))) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrelp_OCons,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 188.18/188.22 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrelp_Oequations_I2_J,axiom, % 188.18/188.22 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 188.18/188.22 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__Cons1,axiom, % 188.18/188.22 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ~ ! [B_y,B_ys] : % 188.18/188.22 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 188.18/188.22 => ( 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)) % 188.18/188.22 => ~ 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))) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__subset,axiom, % 188.18/188.22 ! [V_A_2,V_r_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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))))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists__UNIV,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists__mono,axiom, % 188.18/188.22 ! [V_B_2,V_A_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_equiv__listrel,axiom, % 188.18/188.22 ! [V_r_2,V_A_2,T_b] : % 188.18/188.22 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__refl__on,axiom, % 188.18/188.22 ! [V_r_2,V_A_2,T_b] : % 188.18/188.22 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Cons__in__lists__iff,axiom, % 188.18/188.22 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 188.18/188.22 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists__accD,axiom, % 188.18/188.22 ! [V_r_2,V_xs_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists__accI,axiom, % 188.18/188.22 ! [V_r_2,V_xs_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__iff__nth,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( 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) % 188.18/188.22 & ! [B_n] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__linear,axiom, % 188.18/188.22 ! [V_y_2,V_x_2,V_r_2,T_b] : % 188.18/188.22 ( ! [B_a,B_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 | B_a = B_b % 188.18/188.22 | 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)) ) % 188.18/188.22 => ( 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))) % 188.18/188.22 | V_x_2 = V_y_2 % 188.18/188.22 | 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_infinite__UNIV__listI,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__eq__iff__nth__eq,axiom, % 188.18/188.22 ! [T_b,V_ys_2,V_xs_2] : % 188.18/188.22 ( V_xs_2 = V_ys_2 % 188.18/188.22 <=> ( 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) % 188.18/188.22 & ! [B_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__Cons__0,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__Cons__Suc,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth_Osimps,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__Cons_H,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a,V_n] : % 188.18/188.22 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 188.18/188.22 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__Cons__number__of,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a,V_v] : % 188.18/188.22 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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 ) % 188.18/188.22 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__take__index__conv,axiom, % 188.18/188.22 ! [V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( ( 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))) % 188.18/188.22 & 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 ) % 188.18/188.22 | ? [B_i] : % 188.18/188.22 ( 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)))) % 188.18/188.22 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 188.18/188.22 & 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)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__sublist,axiom, % 188.18/188.22 ! [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))))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_finite__set,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__subset__Cons,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__all,axiom, % 188.18/188.22 ! [V_n,V_xs,T_a] : % 188.18/188.22 ( 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)) % 188.18/188.22 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__take__subset__set__take,axiom, % 188.18/188.22 ! [V_xs_2,T_b,V_n_2,V_m_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__take__subset,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__sublist__subset,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__take,axiom, % 188.18/188.22 ! [V_xs,T_a,V_n,V_i] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sublist__upt__eq__take,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__Suc__Cons,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__ConsD,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => ( V_y_2 = V_x_2 % 188.18/188.22 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__sublistD,axiom, % 188.18/188.22 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__takeD,axiom, % 188.18/188.22 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_notin__set__sublistI,axiom, % 188.18/188.22 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => ~ 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__take,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__take,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_List_Oset_Osimps_I2_J,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_card__length,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_all__set__conv__all__nth,axiom, % 188.18/188.22 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.22 ( ! [B_x] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.22 <=> ! [B_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__size__estimation,axiom, % 188.18/188.22 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__size__estimation_H,axiom, % 188.18/188.22 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__lists__conv__set,axiom, % 188.18/188.22 ! [V_A_2,V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 188.18/188.22 <=> ! [B_x] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__pos__if__in__set,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__conv__nth,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 <=> ? [B_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__mem,axiom, % 188.18/188.22 ! [V_xs_2,T_b,V_n_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists__eq__set,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__conv__nth,axiom, % 188.18/188.22 ! [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))))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_finite__lists__length__eq,axiom, % 188.18/188.22 ! [V_n_2,V_A_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => 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))))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_finite__lists__length__le,axiom, % 188.18/188.22 ! [V_n_2,V_A_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => 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))))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__iff__zip,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( 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) % 188.18/188.22 & ! [B_x] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__zip,axiom, % 188.18/188.22 ! [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)))))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__zip,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__zip,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__Cons__Cons,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__eq__iff__zip__eq,axiom, % 188.18/188.22 ! [T_b,V_ys_2,V_xs_2] : % 188.18/188.22 ( V_xs_2 = V_ys_2 % 188.18/188.22 <=> ( 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) % 188.18/188.22 & ! [B_x] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__same,axiom, % 188.18/188.22 ! [V_xs_2,V_ba_2,V_a_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 & V_a_2 = V_ba_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__zip__leftD,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__zip__rightD,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__zipE,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__zip,axiom, % 188.18/188.22 ! [V_ys,T_b,V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( 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))) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_greaterThanLessThan__upto,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__setsum__nth,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__upto,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_atLeastAtMost__upto,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 188.18/188.22 ! [V_ns_2] : % 188.18/188.22 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 <=> ! [B_x] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 188.18/188.22 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_elem__le__listsum__nat,axiom, % 188.18/188.22 ! [V_ns,V_k] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__simps_I2_J,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a] : % 188.18/188.22 ( class_Groups_Omonoid__add(T_a) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_atLeastLessThan__upto,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_greaterThanAtMost__upto,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nat__list__def,axiom, % 188.18/188.22 ! [V_l_2] : % 188.18/188.22 ( c_List_Onat__list(V_l_2) % 188.18/188.22 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__size__pointwise,axiom, % 188.18/188.22 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 188.18/188.22 ( ! [B_x] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__update__nat,axiom, % 188.18/188.22 ! [V_n,V_ns,V_k] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast__take,axiom, % 188.18/188.22 ! [V_xs,T_a,V_n] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__beyond,axiom, % 188.18/188.22 ! [V_x,V_i,V_xs,T_a] : % 188.18/188.22 ( 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)) % 188.18/188.22 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__list__update__neq,axiom, % 188.18/188.22 ! [V_x,V_xs,T_a,V_j,V_i] : % 188.18/188.22 ( V_i != V_j % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__id,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast__list__update,axiom, % 188.18/188.22 ! [V_x,V_xs,T_a,V_k] : % 188.18/188.22 ( ( 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)) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( 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)) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__list__update,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__update,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_update__zip,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__overwrite,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__swap,axiom, % 188.18/188.22 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 188.18/188.22 ( V_i != V_i_H % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update_Osimps_I2_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__code_I2_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__code_I3_J,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__butlastD,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__update__subsetI,axiom, % 188.18/188.22 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__update__subset__insert,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__list__update,axiom, % 188.18/188.22 ! [V_x,V_j,V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( ( V_i = V_j % 188.18/188.22 => 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 ) % 188.18/188.22 & ( V_i != V_j % 188.18/188.22 => 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) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__same__conv,axiom, % 188.18/188.22 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 188.18/188.22 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__list__update__eq,axiom, % 188.18/188.22 ! [V_x,V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__butlast,axiom, % 188.18/188.22 ! [V_xs,T_a,V_n] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__butlast,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__update__memI,axiom, % 188.18/188.22 ! [V_x_2,V_xs_2,T_b,V_n_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast__conv__take,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1__iff__update,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ? [B_y,B_n] : % 188.18/188.22 ( 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)) % 188.18/188.22 & 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))) % 188.18/188.22 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__list__update,axiom, % 188.18/188.22 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => ( ~ 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)))))) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__upto,axiom, % 188.18/188.22 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__take,axiom, % 188.18/188.22 ! [V_i,V_xs,T_a] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__sublistI,axiom, % 188.18/188.22 ! [V_I_2,V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__zipI1,axiom, % 188.18/188.22 ! [V_ys,T_b,V_xs,T_a] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__zipI2,axiom, % 188.18/188.22 ! [V_xs,T_b,V_ys,T_a] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct_Osimps_I2_J,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 188.18/188.22 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_card__distinct,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__card,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__conv__nth,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 <=> ! [B_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ! [B_j] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( B_i != B_j % 188.18/188.22 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__eq__iff__index__eq,axiom, % 188.18/188.22 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => ( 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))) % 188.18/188.22 => ( 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))) % 188.18/188.22 => ( 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) % 188.18/188.22 <=> V_i_2 = V_j_2 ) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__listsum__conv__Setsum,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.22 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Nitpick_Ocard_H__def,axiom, % 188.18/188.22 ! [V_A_2,T_b] : % 188.18/188.22 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => 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)))) ) % 188.18/188.22 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__take__lemma,axiom, % 188.18/188.22 ! [V_ys,V_xs,T_a,V_k] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( 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))) % 188.18/188.22 => ( ! [B_i] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 188.18/188.22 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 188.18/188.22 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__remove1__eq,axiom, % 188.18/188.22 ! [V_x_2,V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__Cons__number__of,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a,V_v] : % 188.18/188.22 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists_ONil,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__Nil1,axiom, % 188.18/188.22 ! [V_r_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__Nil2,axiom, % 188.18/188.22 ! [V_r_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__butlast,axiom, % 188.18/188.22 ! [T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__remove1,axiom, % 188.18/188.22 ! [V_x,V_xs,T_a] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct_Osimps_I1_J,axiom, % 188.18/188.22 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast_Osimps_I1_J,axiom, % 188.18/188.22 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast_Osimps_I2_J,axiom, % 188.18/188.22 ! [V_x,T_a,V_xs] : % 188.18/188.22 ( ( V_xs = c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 188.18/188.22 & ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osimps_I2_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osimps_I3_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_remove1_Osimps_I2_J,axiom, % 188.18/188.22 ! [V_xs,T_a,V_y,V_x] : % 188.18/188.22 ( ( V_x = V_y % 188.18/188.22 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 188.18/188.22 & ( V_x != V_y % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_upto__empty,axiom, % 188.18/188.22 ! [V_i,V_j] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 188.18/188.22 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__0,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__eq__Nil,axiom, % 188.18/188.22 ! [V_xs_2,V_n_2,T_b] : % 188.18/188.22 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.22 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__Nil,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sublist__nil,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_remove1__commute,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_remove1_Osimps_I1_J,axiom, % 188.18/188.22 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osize_I1_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrelp_Oequations_I1_J,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrelp_ONil,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__Nil,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip_Osimps_I1_J,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__simps_I1_J,axiom, % 188.18/188.22 ! [T_a] : % 188.18/188.22 ( class_Groups_Omonoid__add(T_a) % 188.18/188.22 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__0__conv,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osize_I3_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__empty,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__empty2,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_List_Oset_Osimps_I1_J,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__code_I1_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update_Osimps_I1_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__nonempty,axiom, % 188.18/188.22 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 188.18/188.22 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__remove1,axiom, % 188.18/188.22 ! [V_xs_2,T_b,V_ba_2,V_a_2] : % 188.18/188.22 ( V_a_2 != V_ba_2 % 188.18/188.22 => ( 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)))) % 188.18/188.22 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_notin__set__remove1,axiom, % 188.18/188.22 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => ~ 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_remove1__idem,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sublist__empty,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__remove1__subset,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__greater__0__conv,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__1__Cons,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_not__Nil__listrel1,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_not__listrel1__Nil,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel_ONil,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__Nil__right,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Nil__notin__lex,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Nil2__notin__lex,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__Cons,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_upto_Osimps,axiom, % 188.18/188.22 ! [V_j,V_i] : % 188.18/188.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 188.18/188.22 => 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)) ) % 188.18/188.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 188.18/188.22 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sublist__singleton,axiom, % 188.18/188.22 ! [V_x_2,T_b,V_A_2] : % 188.18/188.22 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 188.18/188.22 => 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)) ) % 188.18/188.22 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists__empty,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__Cons_H,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a,V_n] : % 188.18/188.22 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_upto__rec__number__of,axiom, % 188.18/188.22 ! [V_n,V_m] : % 188.18/188.22 ( ( 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))) % 188.18/188.22 => 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))) ) % 188.18/188.22 & ( ~ 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))) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel__Nil,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__Cons__sing__Nil,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__remove1,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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)) ) % 188.18/188.22 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_upto_Opsimps,axiom, % 188.18/188.22 ! [V_j_2,V_i_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 188.18/188.22 => 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)) ) % 188.18/188.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 188.18/188.22 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_select,axiom, % 188.18/188.22 ! [V_s_2,T_b,V_xs_2] : % 188.18/188.22 ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listset_Osimps_I1_J,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__Cons1,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osimps_I5_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list_Osimps_I4_J,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_listset_Osimps_I2_J,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__Cons,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sorted__list__of__set__remove,axiom, % 188.18/188.22 ! [V_x_2,V_A_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_upto_Opinduct,axiom, % 188.18/188.22 ! [V_Pa_2,V_a1_2,V_a0_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( ! [B_i,B_j] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 188.18/188.22 => 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)) ) % 188.18/188.22 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 188.18/188.22 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sorted__list__of__set__empty,axiom, % 188.18/188.22 ! [T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_anamorph_Osimps,axiom, % 188.18/188.22 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 188.18/188.22 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sublist__Cons,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__eq__Cons__conv,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 188.18/188.22 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 188.18/188.22 | ? [B_ys_H] : % 188.18/188.22 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 188.18/188.22 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Cons__eq__append__conv,axiom, % 188.18/188.22 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 188.18/188.22 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 188.18/188.22 | ? [B_ys_H] : % 188.18/188.22 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 188.18/188.22 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append1__eq__conv,axiom, % 188.18/188.22 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( V_xs_2 = V_ys_2 % 188.18/188.22 & V_x_2 = V_y_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__Cons,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Cons__eq__appendI,axiom, % 188.18/188.22 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 188.18/188.22 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 188.18/188.22 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 188.18/188.22 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__in__lists__conv,axiom, % 188.18/188.22 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 188.18/188.22 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__eq__appendI,axiom, % 188.18/188.22 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 188.18/188.22 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 188.18/188.22 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 188.18/188.22 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__same__eq,axiom, % 188.18/188.22 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> V_ys_2 = V_zs_2 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_same__append__eq,axiom, % 188.18/188.22 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> V_ys_2 = V_zs_2 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__eq__append__conv2,axiom, % 188.18/188.22 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> ? [B_us] : % 188.18/188.22 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 188.18/188.22 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 188.18/188.22 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 188.18/188.22 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__assoc,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__append,axiom, % 188.18/188.22 ! [V_ys,V_xs,T_a] : % 188.18/188.22 ( class_Groups_Omonoid__add(T_a) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__append,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__append,axiom, % 188.18/188.22 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 188.18/188.22 ( 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) % 188.18/188.22 => ( 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) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__append,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__Nil,axiom, % 188.18/188.22 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 188.18/188.22 % 188.18/188.22 fof(fact_Nil__is__append__conv,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 188.18/188.22 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 188.18/188.22 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__Nil2,axiom, % 188.18/188.22 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 188.18/188.22 % 188.18/188.22 fof(fact_self__append__conv,axiom, % 188.18/188.22 ! [V_ys_2,T_b,V_xs_2] : % 188.18/188.22 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 188.18/188.22 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_self__append__conv2,axiom, % 188.18/188.22 ! [V_xs_2,T_b,V_ys_2] : % 188.18/188.22 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__is__Nil__conv,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 188.18/188.22 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 188.18/188.22 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__self__conv,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 188.18/188.22 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__self__conv2,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_eq__Nil__appendI,axiom, % 188.18/188.22 ! [T_a,V_ys,V_xs] : % 188.18/188.22 ( V_xs = V_ys % 188.18/188.22 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast__append,axiom, % 188.18/188.22 ! [V_xs,T_a,V_ys] : % 188.18/188.22 ( ( V_ys = c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 188.18/188.22 & ( V_ys != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__append__length,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__append__length__plus,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__append,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__append1,axiom, % 188.18/188.22 ! [V_x,V_ys,V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__length,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_remove1__append,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__butlast__appendI,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 188.18/188.22 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 188.18/188.22 => 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))))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast__snoc,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__listrel1I,axiom, % 188.18/188.22 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( ( ( 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))) % 188.18/188.22 & V_us_2 = V_vs_2 ) % 188.18/188.22 | ( V_xs_2 = V_ys_2 % 188.18/188.22 & 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))) ) ) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__append__leftI,axiom, % 188.18/188.22 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__append,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 188.18/188.22 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 188.18/188.22 & 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__append,axiom, % 188.18/188.22 ! [V_ys,V_xs,T_a,V_n] : % 188.18/188.22 ( ( 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))) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( ~ 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))) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__update__append,axiom, % 188.18/188.22 ! [V_x,V_ys,V_xs,T_a,V_n] : % 188.18/188.22 ( ( 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))) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( ~ 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))) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sublist__append,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1I,axiom, % 188.18/188.22 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => ( 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)) % 188.18/188.22 => ( 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)) % 188.18/188.22 => 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))) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__append__left__rightI,axiom, % 188.18/188.22 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_ba_2,V_a_2,T_b] : % 188.18/188.22 ( 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)) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__Suc__conv__app__nth,axiom, % 188.18/188.22 ! [V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_snoc__listrel1__snoc__iff,axiom, % 188.18/188.22 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ( ( 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))) % 188.18/188.22 & V_x_2 = V_y_2 ) % 188.18/188.22 | ( V_xs_2 = V_ys_2 % 188.18/188.22 & 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)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listrel1E,axiom, % 188.18/188.22 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ~ ! [B_x,B_y] : % 188.18/188.22 ( 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)) % 188.18/188.22 => ! [B_us,B_vs] : % 188.18/188.22 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 188.18/188.22 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__append__leftD,axiom, % 188.18/188.22 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( ! [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)) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate1__def,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_upd__conv__take__nth__drop,axiom, % 188.18/188.22 ! [V_a,V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__take__drop__id,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__1__Cons,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__Suc__Cons,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__via__drop,axiom, % 188.18/188.22 ! [V_ys,V_y,V_xs,V_n,T_a] : % 188.18/188.22 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 188.18/188.22 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__drop,axiom, % 188.18/188.22 ! [V_i,V_xs,T_a] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct1__rotate,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 188.18/188.22 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_butlast__drop,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__butlast,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__take,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__drop,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__0,axiom, % 188.18/188.22 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__drop,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__zip,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__rotate1,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__drop,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__rotate1,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_in__set__dropD,axiom, % 188.18/188.22 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__drop__subset,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__Nil,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate1__is__Nil__conv,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__drop__subset__set__drop,axiom, % 188.18/188.22 ! [V_xs_2,T_b,V_m_2,V_n_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__all,axiom, % 188.18/188.22 ! [V_n,V_xs,T_a] : % 188.18/188.22 ( 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)) % 188.18/188.22 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__eq__Nil,axiom, % 188.18/188.22 ! [V_xs_2,V_n_2,T_b] : % 188.18/188.22 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.22 <=> 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__append,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__eq__conv__conj,axiom, % 188.18/188.22 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 188.18/188.22 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 188.18/188.22 <=> ( 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) % 188.18/188.22 & 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__Cons,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__Cons_H,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a,V_n] : % 188.18/188.22 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__drop,axiom, % 188.18/188.22 ! [V_xs,T_a,V_i,V_n] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__eq__append__conv__if,axiom, % 188.18/188.22 ! [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] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> ( ( 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))) % 188.18/188.22 => ( 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) % 188.18/188.22 & 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) ) ) % 188.18/188.22 & ( ~ 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))) % 188.18/188.22 => ( 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 % 188.18/188.22 & 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 ) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__drop_H,axiom, % 188.18/188.22 ! [V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__simps,axiom, % 188.18/188.22 ! [V_xs,V_x,T_b,T_a] : % 188.18/188.22 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 188.18/188.22 & 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__Cons__number__of,axiom, % 188.18/188.22 ! [V_xs,V_x,T_a,V_v] : % 188.18/188.22 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__add,axiom, % 188.18/188.22 ! [V_xs,T_a,V_j,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate1__length01,axiom, % 188.18/188.22 ! [V_xs,T_a] : % 188.18/188.22 ( 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))) % 188.18/188.22 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__append2,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__append1,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_id__take__nth__drop,axiom, % 188.18/188.22 ! [V_xs,T_a,V_i] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__hd__drop,axiom, % 188.18/188.22 ! [V_xs,T_a,V_n] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd__drop__conv__nth,axiom, % 188.18/188.22 ! [V_n,T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => ( 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))) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd_Osimps,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd__append2,axiom, % 188.18/188.22 ! [V_ys,T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd__append,axiom, % 188.18/188.22 ! [V_ys,T_a,V_xs] : % 188.18/188.22 ( ( V_xs = c_List_Olist_ONil(T_a) % 188.18/188.22 => 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) ) % 188.18/188.22 & ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd__in__set,axiom, % 188.18/188.22 ! [T_b,V_xs_2] : % 188.18/188.22 ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd__conv__nth,axiom, % 188.18/188.22 ! [T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate1__hd__tl,axiom, % 188.18/188.22 ! [T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd__rotate__conv__nth,axiom, % 188.18/188.22 ! [V_n,T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__tl,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_tl__drop,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_tl_Osimps_I2_J,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__tl,axiom, % 188.18/188.22 ! [V_xs,T_a] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.22 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__rotate,axiom, % 188.18/188.22 ! [V_xs_2,V_n_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) % 188.18/188.22 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__add,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate0,axiom, % 188.18/188.22 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__rotate,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__rotate,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__rotate,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_tl_Osimps_I1_J,axiom, % 188.18/188.22 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__is__Nil__conv,axiom, % 188.18/188.22 ! [V_xs_2,V_n_2,T_b] : % 188.18/188.22 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__def,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate1__rotate__swap,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_tl__append2,axiom, % 188.18/188.22 ! [V_ys,T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__tl,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__conv__mod,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__Suc,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__Suc,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_tl__append,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__id,axiom, % 188.18/188.22 ! [V_xs,T_a,V_n] : % 188.18/188.22 ( 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) % 188.18/188.22 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__length01,axiom, % 188.18/188.22 ! [V_n,V_xs,T_a] : % 188.18/188.22 ( 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))) % 188.18/188.22 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__tl,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_tl__take,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__Suc,axiom, % 188.18/188.22 ! [V_n,T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__drop__take,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_fold1__set,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 188.18/188.22 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sorted__list__of__set__insert,axiom, % 188.18/188.22 ! [V_x_2,V_A_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => 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)))))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_foldl__Nil,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__not__Nil,axiom, % 188.18/188.22 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( class_Orderings_Olinorder(T_c) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_remove1__insort,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__insort,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( class_Orderings_Olinorder(T_c) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__insort,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( class_Orderings_Olinorder(T_c) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_start__le__sum,axiom, % 188.18/188.22 ! [V_ns_2,V_n_2,V_m_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_foldl__assoc,axiom, % 188.18/188.22 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( class_Groups_Osemigroup__add(T_b) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_foldl__absorb0,axiom, % 188.18/188.22 ! [V_zs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Groups_Omonoid__add(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__key__left__comm,axiom, % 188.18/188.22 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_fun__left__comm__insort,axiom, % 188.18/188.22 ! [T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__left__comm,axiom, % 188.18/188.22 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_foldl__Cons,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__key_Osimps_I2_J,axiom, % 188.18/188.22 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( ( 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))) % 188.18/188.22 => 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)) ) % 188.18/188.22 & ( ~ 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))) % 188.18/188.22 => 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)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__key_Osimps_I1_J,axiom, % 188.18/188.22 ! [V_x_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( class_Orderings_Olinorder(T_c) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_foldl__append,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__foldl,axiom, % 188.18/188.22 ! [T_b] : % 188.18/188.22 ( class_Groups_Omonoid__add(T_b) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_sum__eq__0__conv,axiom, % 188.18/188.22 ! [V_ns_2,V_m_2] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.22 & ! [B_x] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 188.18/188.22 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__insort,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( class_Orderings_Olinorder(T_c) % 188.18/188.22 => ( 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))) % 188.18/188.22 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 188.18/188.22 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Sup__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Inf__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Sup__fin__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Lattices_Olattice(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Inf__fin__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Lattices_Olattice(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Min__fin__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Max__fin__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_min__max_OInf__fin__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_min__max_OSup__fin__set__fold,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_SUPR__set__fold,axiom, % 188.18/188.22 ! [V_f_2,V_xs_2,T_c,T_b] : % 188.18/188.22 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_INFI__set__fold,axiom, % 188.18/188.22 ! [V_f_2,V_xs_2,T_c,T_b] : % 188.18/188.22 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_elem__le__sum,axiom, % 188.18/188.22 ! [V_ns_2,V_n_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__insert__insort__key,axiom, % 188.18/188.22 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( ~ 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)))) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__append__rightI,axiom, % 188.18/188.22 ! [V_r_2,V_x_2,T_b,V_y_2] : % 188.18/188.22 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__insort__insert,axiom, % 188.18/188.22 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 188.18/188.22 ( class_Orderings_Olinorder(T_c) % 188.18/188.22 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => 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))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__insert__triv,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__insort__insert,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__insert__key__triv,axiom, % 188.18/188.22 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( 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)))) % 188.18/188.22 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_insort__insert__insort,axiom, % 188.18/188.22 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.22 ( class_Orderings_Olinorder(T_b) % 188.18/188.22 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lexord__Nil__left,axiom, % 188.18/188.22 ! [V_r_2,V_y_2,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__list__update,axiom, % 188.18/188.22 ! [V_x,V_k,T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => ( ( 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)) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 188.18/188.22 & ( 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)) % 188.18/188.22 => 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) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__append,axiom, % 188.18/188.22 ! [V_xs,T_a,V_ys] : % 188.18/188.22 ( ( V_ys = c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 188.18/188.22 & ( V_ys != c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__appendR,axiom, % 188.18/188.22 ! [V_xs,T_a,V_ys] : % 188.18/188.22 ( V_ys != c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__appendL,axiom, % 188.18/188.22 ! [V_xs,T_a,V_ys] : % 188.18/188.22 ( V_ys = c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last_Osimps,axiom, % 188.18/188.22 ! [V_x,T_a,V_xs] : % 188.18/188.22 ( ( V_xs = c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 188.18/188.22 & ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__ConsR,axiom, % 188.18/188.22 ! [V_x,T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__ConsL,axiom, % 188.18/188.22 ! [V_x,T_a,V_xs] : % 188.18/188.22 ( V_xs = c_List_Olist_ONil(T_a) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__in__set,axiom, % 188.18/188.22 ! [T_b,V_as_2] : % 188.18/188.22 ( V_as_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__snoc,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__drop,axiom, % 188.18/188.22 ! [V_xs,T_a,V_n] : % 188.18/188.22 ( 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))) % 188.18/188.22 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_snoc__eq__iff__butlast,axiom, % 188.18/188.22 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 188.18/188.22 ( 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 % 188.18/188.22 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 188.18/188.22 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_append__butlast__last__id,axiom, % 188.18/188.22 ! [T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__conv__nth,axiom, % 188.18/188.22 ! [T_a,V_xs] : % 188.18/188.22 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_lists_Osimps,axiom, % 188.18/188.22 ! [V_A_2,V_a_2,T_b] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 188.18/188.22 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 188.18/188.22 | ? [B_a,B_l] : % 188.18/188.22 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 188.18/188.22 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 188.18/188.22 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_select__weigth__select,axiom, % 188.18/188.22 ! [T_b,V_xs_2] : % 188.18/188.22 ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_inj__mapI,axiom, % 188.18/188.22 ! [V_f_2,T_c,T_b] : % 188.18/188.22 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_last__map,axiom, % 188.18/188.22 ! [V_f_2,T_c,T_b,V_xs_2] : % 188.18/188.22 ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_inj__on__map__eq__map,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => ( 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) % 188.18/188.22 <=> V_xs_2 = V_ys_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__inj__on,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( 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) % 188.18/188.22 => ( 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))) % 188.18/188.22 => V_xs_2 = V_ys_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__size__map,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_List_Omap_Oid,axiom, % 188.18/188.22 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_List_Omap_Oidentity,axiom, % 188.18/188.22 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_List_Omap_Ocomp,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__comp__map,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_List_Omap_Ocompositionality,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__map,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_drop__map,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_hd__map,axiom, % 188.18/188.22 ! [V_f_2,T_c,T_b,V_xs_2] : % 188.18/188.22 ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__append,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map_Osimps_I2_J,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_set__map,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__butlast,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_take__map,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__ident,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 188.18/188.22 % 188.18/188.22 fof(fact_inj__map__eq__map,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 188.18/188.22 => ( 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) % 188.18/188.22 <=> V_xs_2 = V_ys_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__injective,axiom, % 188.18/188.22 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( 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) % 188.18/188.22 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 188.18/188.22 => V_xs_2 = V_ys_2 ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__subtractf,axiom, % 188.18/188.22 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( class_Groups_Oab__group__add(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__mult__const,axiom, % 188.18/188.22 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( class_Rings_Osemiring__0(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__const__mult,axiom, % 188.18/188.22 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] : % 188.18/188.22 ( class_Rings_Osemiring__0(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__0,axiom, % 188.18/188.22 ! [V_xs_2,T_c,T_b] : % 188.18/188.22 ( class_Groups_Omonoid__add(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__addf,axiom, % 188.18/188.22 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_length__map,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__eq__imp__length__eq,axiom, % 188.18/188.22 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( 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) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__eq__conv,axiom, % 188.18/188.22 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( 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) % 188.18/188.22 <=> ! [B_x] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 188.18/188.22 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__update,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Nil__is__map__conv,axiom, % 188.18/188.22 ! [V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map_Osimps_I1_J,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__is__Nil__conv,axiom, % 188.18/188.22 ! [V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.22 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.22 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__same__conv__map,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__map2,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__zip__map2,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__zip__map,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__map1,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__map__map,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__tl,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_rotate__map,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_foldl__map,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nth__map,axiom, % 188.18/188.22 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__fun__upd,axiom, % 188.18/188.22 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 188.18/188.22 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_distinct__map,axiom, % 188.18/188.22 ! [V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 188.18/188.22 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 188.18/188.22 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__abs,axiom, % 188.18/188.22 ! [V_xs_2,T_b] : % 188.18/188.22 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_uminus__listsum__map,axiom, % 188.18/188.22 ! [V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( class_Groups_Oab__group__add(T_b) % 188.18/188.22 => 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_inj__on__mapI,axiom, % 188.18/188.22 ! [V_A_2,V_f_2,T_c,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_inj__mapD,axiom, % 188.18/188.22 ! [V_f_2,T_c,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_inj__map,axiom, % 188.18/188.22 ! [V_f_2,T_c,T_b] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 188.18/188.22 ! [V_f_2,V_xs_2,T_b,T_c] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_c) % 188.18/188.22 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.22 => 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)) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__triv,axiom, % 188.18/188.22 ! [V_xs_2,V_r_2,T_c,T_b] : % 188.18/188.22 ( class_Rings_Osemiring__1(T_b) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__map__remove1,axiom, % 188.18/188.22 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_c) % 188.18/188.22 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => 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)))) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Nitpick_Osetsum_H__def,axiom, % 188.18/188.22 ! [V_f_2,V_A_2,T_b,T_c] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_c) % 188.18/188.22 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => 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))))) ) % 188.18/188.22 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.22 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_pick__same,axiom, % 188.18/188.22 ! [V_xs_2,T_b,V_l_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 => 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) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_one__code__numeral__def,axiom, % 188.18/188.22 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_less__code__numeral__code,axiom, % 188.18/188.22 ! [V_m_2,V_n_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_times__code__numeral__code,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 188.18/188.22 ! [V_m_2,V_n_2] : % 188.18/188.22 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 188.18/188.22 <=> V_n_2 = V_m_2 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 188.18/188.22 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zero__code__numeral__def,axiom, % 188.18/188.22 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_code__numeral_Oof__nat__inject,axiom, % 188.18/188.22 ! [V_y_2,V_x_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 188.18/188.22 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 188.18/188.22 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 188.18/188.22 <=> V_x_2 = V_y_2 ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__fst__zip,axiom, % 188.18/188.22 ! [V_ys_2,T_c,V_xs_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 => 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 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_map__snd__zip,axiom, % 188.18/188.22 ! [V_ys_2,T_c,V_xs_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 => 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 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_number__of__code__numeral__def,axiom, % 188.18/188.22 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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__map__fst__snd,axiom, % 188.18/188.22 ! [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 ). % 188.18/188.22 % 188.18/188.22 fof(fact_plus__code__numeral__code,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_less__eq__code__numeral__code,axiom, % 188.18/188.22 ! [V_m_2,V_n_2] : % 188.18/188.22 ( 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))) % 188.18/188.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_pick__member,axiom, % 188.18/188.22 ! [V_xs_2,T_b,V_i_2] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_zip__eq__conv,axiom, % 188.18/188.22 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 188.18/188.22 ( 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) % 188.18/188.22 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 188.18/188.22 <=> ( 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 % 188.18/188.22 & 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 ) ) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_list__size__conv__listsum,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_code__numeral__not__eq__zero,axiom, % 188.18/188.22 ! [V_i_2] : % 188.18/188.22 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 188.18/188.22 <=> 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)) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 188.18/188.22 ! [V_l_2,V_k_2,V_f_2,T_b] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 188.18/188.22 ! [V_j_2,V_i_2,V_f_2,T_b] : % 188.18/188.22 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_select__weight__member,axiom, % 188.18/188.22 ! [V_s_2,V_xs_2,T_b] : % 188.18/188.22 ( 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)))) % 188.18/188.22 => 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)))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_select__weight__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_select__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_subtract__code__numeral__code,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nat__of__of__nat,axiom, % 188.18/188.22 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 188.18/188.22 % 188.18/188.22 fof(fact_of__nat__nat__of,axiom, % 188.18/188.22 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 188.18/188.22 % 188.18/188.22 fof(fact_nat__of__inverse,axiom, % 188.18/188.22 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 188.18/188.22 % 188.18/188.22 fof(fact_times__code__numeral__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_code__numeral_Onat__of__inject,axiom, % 188.18/188.22 ! [V_y_2,V_x_2] : % 188.18/188.22 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 188.18/188.22 <=> V_x_2 = V_y_2 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 188.18/188.22 ! [V_l_2,V_k_2] : % 188.18/188.22 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 188.18/188.22 <=> V_k_2 = V_l_2 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_type__definition__code__numeral,axiom, % 188.18/188.22 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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_less__code__numeral__def,axiom, % 188.18/188.22 ! [V_m_2,V_n_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 188.18/188.22 <=> 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nat__of,axiom, % 188.18/188.22 ! [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)))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nat__of__number,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_int__of__def,axiom, % 188.18/188.22 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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_less__eq__code__numeral__def,axiom, % 188.18/188.22 ! [V_m_2,V_n_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 188.18/188.22 <=> 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nat__of__code,axiom, % 188.18/188.22 ! [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)) ). % 188.18/188.22 % 188.18/188.22 fof(fact_nat__of__aux__def,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_Suc__code__numeral__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_minus__code__numeral__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_of__nat__inverse,axiom, % 188.18/188.22 ! [V_y_2] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 188.18/188.22 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_plus__code__numeral__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_div__code__numeral__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_subtract__code__numeral__def,axiom, % 188.18/188.22 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.22 % 188.18/188.22 fof(fact_minus__code__numeral__code,axiom, % 188.18/188.22 ! [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) ). % 188.18/188.22 % 188.18/188.22 fof(fact_mod__code__numeral__def,axiom, % 188.18/188.22 ! [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))) ). % 188.18/188.22 % 188.18/188.22 fof(fact_code__numeral__decr,axiom, % 188.18/188.22 ! [V_k] : % 188.18/188.22 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 188.18/188.22 => 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))) ) ). % 188.18/188.22 % 188.18/188.22 fof(fact_listsum__mono,axiom, % 188.18/188.22 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 188.18/188.22 ( ( class_Groups_Omonoid__add(T_c) % 188.18/188.22 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 188.18/188.22 => ( ! [B_x] : % 188.18/188.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 188.18/188.23 => 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)))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_partition__set,axiom, % 188.18/188.23 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lists__IntI,axiom, % 188.18/188.23 ! [V_B_2,V_A_2,V_l_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2))) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2))) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp_ONil,axiom, % 188.18/188.23 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_append__in__listsp__conv,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_A_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 188.18/188.23 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 188.18/188.23 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp_Oequations_I2_J,axiom, % 188.18/188.23 ! [V_a2_2,V_a1_2,V_A_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2))) % 188.18/188.23 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 188.18/188.23 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp__infI,axiom, % 188.18/188.23 ! [V_B_2,V_l_2,V_A_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2)) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2)) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp__inf__eq,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp__conj__eq,axiom, % 188.18/188.23 ! [V_x_2,V_B_2,V_A_2,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) % 188.18/188.23 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__listsp__conv__set,axiom, % 188.18/188.23 ! [V_xs_2,V_A_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp_Oequations_I1_J,axiom, % 188.18/188.23 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp__mono,axiom, % 188.18/188.23 ! [V_B_2,V_A_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_partition__P,axiom, % 188.18/188.23 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 & ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 188.18/188.23 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_partition_Osimps_I1_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsp__lists__eq,axiom, % 188.18/188.23 ! [V_x_2,V_A_2,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_partition_Osimps_I2_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lists__Int__eq,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_product_Osimps_I2_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__def,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 <=> ( 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) % 188.18/188.23 & ! [B_x] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__map2,axiom, % 188.18/188.23 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__map1,axiom, % 188.18/188.23 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__Nil2,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c)) % 188.18/188.23 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__Nil,axiom, % 188.18/188.23 ! [V_ys_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2) % 188.18/188.23 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__lengthD,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__eq,axiom, % 188.18/188.23 ! [T_b,V_ys_2,V_xs_2] : % 188.18/188.23 ( V_xs_2 = V_ys_2 % 188.18/188.23 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__takeI,axiom, % 188.18/188.23 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__Cons,axiom, % 188.18/188.23 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 188.18/188.23 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__append,axiom, % 188.18/188.23 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 => ( 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)) % 188.18/188.23 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__appendI,axiom, % 188.18/188.23 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_ba_2) % 188.18/188.23 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__dropI,axiom, % 188.18/188.23 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_product_Osimps_I1_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__nthD2,axiom, % 188.18/188.23 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__nthD,axiom, % 188.18/188.23 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__conv__all__nth,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 <=> ( 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) % 188.18/188.23 & ! [B_i] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__update__cong2,axiom, % 188.18/188.23 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__update__cong,axiom, % 188.18/188.23 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 188.18/188.23 => 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)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__product,axiom, % 188.18/188.23 ! [V_ys,T_b,V_xs,T_a] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_product__list__set,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sublists__powset,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__sublists,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sublists_Osimps_I1_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sublists_Osimps_I2_J,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__set__sublists,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => 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)))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__n__lists,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_enum__the__def,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__n__lists,axiom, % 188.18/188.23 ! [V_n,V_xs,T_a] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_n__lists__Nil,axiom, % 188.18/188.23 ! [T_a,V_n] : % 188.18/188.23 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => 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))) ) % 188.18/188.23 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_n__lists_Osimps_I1_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__n__lists,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__n__lists__elem,axiom, % 188.18/188.23 ! [V_xs_2,V_n_2,V_ys_2,T_b] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2I,axiom, % 188.18/188.23 ! [V_Pa_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) % 188.18/188.23 => ( 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) % 188.18/188.23 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_ba_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_all__nth__imp__all__set,axiom, % 188.18/188.23 ! [V_x_2,V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( ! [B_i] : % 188.18/188.23 ( 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))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 188.18/188.23 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__removeAll__inj__on,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__remdups,axiom, % 188.18/188.23 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__remdups__leq,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups__id__iff__distinct,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2 % 188.18/188.23 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__removeAll,axiom, % 188.18/188.23 ! [V_x,V_xs,T_a] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__remdups__id,axiom, % 188.18/188.23 ! [V_xs,T_a] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.23 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__remdups__eq,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__remdups,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups__remdups,axiom, % 188.18/188.23 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 188.18/188.23 % 188.18/188.23 fof(fact_removeAll__append,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_removeAll_Osimps_I2_J,axiom, % 188.18/188.23 ! [V_xs,T_a,V_y,V_x] : % 188.18/188.23 ( ( V_x = V_y % 188.18/188.23 => 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) ) % 188.18/188.23 & ( V_x != V_y % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups_Osimps_I1_J,axiom, % 188.18/188.23 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups__eq__nil__right__iff,axiom, % 188.18/188.23 ! [V_x_2,T_b] : % 188.18/188.23 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2) % 188.18/188.23 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_removeAll_Osimps_I1_J,axiom, % 188.18/188.23 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups__eq__nil__iff,axiom, % 188.18/188.23 ! [V_x_2,T_b] : % 188.18/188.23 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b) % 188.18/188.23 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups__map__remdups,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remove1__remdups,axiom, % 188.18/188.23 ! [V_x,V_xs,T_a] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_removeAll__id,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__remove1__removeAll,axiom, % 188.18/188.23 ! [V_x,V_xs,T_a] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.23 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups_Osimps_I2_J,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => 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) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__remdups__card__conv,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__removeAll__inj,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__removeAll,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__remdups__concat,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__conv__foldl,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldl__conv__concat,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sort__key__simps_I1_J,axiom, % 188.18/188.23 ! [V_f_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat_Osimps_I1_J,axiom, % 188.18/188.23 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__sort,axiom, % 188.18/188.23 ! [V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__sort,axiom, % 188.18/188.23 ! [V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__sort,axiom, % 188.18/188.23 ! [V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))) % 188.18/188.23 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat_Osimps_I2_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Nil__eq__concat__conv,axiom, % 188.18/188.23 ! [V_xss_2,T_b] : % 188.18/188.23 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 188.18/188.23 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__eq__Nil__conv,axiom, % 188.18/188.23 ! [V_xss_2,T_b] : % 188.18/188.23 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 188.18/188.23 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__concat,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__concat,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__concat,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sort__key__simps_I2_J,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__append,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sort__foldl__insort,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__eq__concat__iff,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => 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)) ) % 188.18/188.23 => ( 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) % 188.18/188.23 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 188.18/188.23 <=> V_xs_2 = V_ys_2 ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__injective,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.23 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 188.18/188.23 => ( 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) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => 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)) ) % 188.18/188.23 => V_xs_2 = V_ys_2 ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__map__singleton,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_n__lists_Osimps_I2_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose_Osimps_I3_J,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__aux__filter__head,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__concat,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__sort,axiom, % 188.18/188.23 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__filter,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sum__length__filter__compl,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__filter__le,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__id__conv,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__is__subset,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_partition__filter1,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remove1__filter__not,axiom, % 188.18/188.23 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 188.18/188.23 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__remove1,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__filter,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__insort__triv,axiom, % 188.18/188.23 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__map,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__append,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter_Osimps_I2_J,axiom, % 188.18/188.23 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 188.18/188.23 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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)) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose_Osimps_I1_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter_Osimps_I1_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__empty__conv,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_removeAll__filter__not__eq,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_removeAll__filter__not,axiom, % 188.18/188.23 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 188.18/188.23 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_remdups__filter,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_partition__filter2,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose_Osimps_I2_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_nth__transpose,axiom, % 188.18/188.23 ! [V_xs_2,T_b,V_i_2] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__map__map,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__filter,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__filter__map,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__filter__less,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_partition__filter__conv,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__minus__filter__out,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__in__sublist,axiom, % 188.18/188.23 ! [V_s_2,V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__empty,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 188.18/188.23 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__filter__conv__card,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__aux__filter__tail,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose_Opsimps_I3_J,axiom, % 188.18/188.23 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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))))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose_Opsimps_I2_J,axiom, % 188.18/188.23 ! [V_xss_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sublist__shift__lemma__Suc,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pick__drop__zero,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_select__weigth__drop__zero,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose_Opsimps_I1_J,axiom, % 188.18/188.23 ! [T_b] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__max__length,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__aux__max,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldr__append,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldr_Osimps_I2_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldr_Osimps_I1_J,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldr__conv__foldl,axiom, % 188.18/188.23 ! [V_a_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Groups_Oab__semigroup__add(T_b) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldr__map,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldl__foldr1__lemma,axiom, % 188.18/188.23 ! [V_xs_2,V_a_2,T_b] : % 188.18/188.23 ( class_Groups_Omonoid__add(T_b) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldl__foldr1,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( class_Groups_Omonoid__add(T_b) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__transpose,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sublist__def,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sublist__shift__lemma,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_atLeastLessThan__upt,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__upt,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__0,axiom, % 188.18/188.23 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__eq__Nil__conv,axiom, % 188.18/188.23 ! [V_j_2,V_i_2] : % 188.18/188.23 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 188.18/188.23 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__conv__Nil,axiom, % 188.18/188.23 ! [V_i,V_j] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 188.18/188.23 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__conv__Cons,axiom, % 188.18/188.23 ! [V_j,V_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__rec,axiom, % 188.18/188.23 ! [V_j,V_i] : % 188.18/188.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => 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)) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__add__eq__append,axiom, % 188.18/188.23 ! [V_k,V_j,V_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__Suc__append,axiom, % 188.18/188.23 ! [V_j,V_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__Suc,axiom, % 188.18/188.23 ! [V_j,V_i] : % 188.18/188.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => 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))) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_drop__upt,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_hd__upt,axiom, % 188.18/188.23 ! [V_j,V_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__list__of__set__range,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_take__upt,axiom, % 188.18/188.23 ! [V_n,V_m,V_i] : % 188.18/188.23 ( 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)) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__upt,axiom, % 188.18/188.23 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__upt,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__rec__number__of,axiom, % 188.18/188.23 ! [V_n,V_m] : % 188.18/188.23 ( ( 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))) % 188.18/188.23 => 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))) ) % 188.18/188.23 & ( ~ 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))) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_upt__eq__Cons__conv,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 188.18/188.23 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 188.18/188.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 188.18/188.23 & V_i_2 = V_x_2 % 188.18/188.23 & 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 ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_last__upt,axiom, % 188.18/188.23 ! [V_j,V_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__Suc__upt,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_atLeastAtMost__upt,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_atLeast__upt,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_nth__upt,axiom, % 188.18/188.23 ! [V_j,V_k,V_i] : % 188.18/188.23 ( 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)) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_greaterThanAtMost__upt,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_greaterThanLessThan__upt,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_atMost__upto,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__nth,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 188.18/188.23 ! [V_n_2,V_m_2,V_f_2,T_b] : % 188.18/188.23 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 188.18/188.23 ! [V_n_2,V_m_2,V_f_2,T_b] : % 188.18/188.23 ( class_Groups_Ocomm__monoid__add(T_b) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_nth__map__upt,axiom, % 188.18/188.23 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__rectangle,axiom, % 188.18/188.23 ! [V_n_2,T_b,V_xs_2] : % 188.18/188.23 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 188.18/188.23 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 188.18/188.23 => ( ! [B_i] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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 ) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_insort__key__remove1,axiom, % 188.18/188.23 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 188.18/188.23 => ( 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 % 188.18/188.23 => 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 ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted_ONil,axiom, % 188.18/188.23 ! [T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__single,axiom, % 188.18/188.23 ! [V_x,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__upt,axiom, % 188.18/188.23 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__sort,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__insort__insert,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__tl,axiom, % 188.18/188.23 ! [V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__remove1,axiom, % 188.18/188.23 ! [V_a,V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__take,axiom, % 188.18/188.23 ! [V_n,V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__upto,axiom, % 188.18/188.23 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__drop,axiom, % 188.18/188.23 ! [V_n,V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__insort,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( 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)) % 188.18/188.23 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__many,axiom, % 188.18/188.23 ! [V_zs,V_y,V_x,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 188.18/188.23 => 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))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__many__eq,axiom, % 188.18/188.23 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( 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))) % 188.18/188.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 188.18/188.23 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted_Oequations_I1_J,axiom, % 188.18/188.23 ! [T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__butlast,axiom, % 188.18/188.23 ! [V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__remdups,axiom, % 188.18/188.23 ! [V_l,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__distinct__set__unique,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 188.18/188.23 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 188.18/188.23 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__sort__key,axiom, % 188.18/188.23 ! [V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__insort__insert__key,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__map__remove1,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__insort__key,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( 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))) % 188.18/188.23 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__map__same,axiom, % 188.18/188.23 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__filter,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__same,axiom, % 188.18/188.23 ! [V_xs_2,V_g_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__Cons,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 188.18/188.23 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 & ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__append,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 188.18/188.23 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 188.18/188.23 & ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ! [B_xa] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__insort,axiom, % 188.18/188.23 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 188.18/188.23 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted_Oequations_I2_J,axiom, % 188.18/188.23 ! [V_a1_2,V_a2_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 188.18/188.23 <=> ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 188.18/188.23 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__list__of__set,axiom, % 188.18/188.23 ! [V_A_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.23 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 188.18/188.23 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 188.18/188.23 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_insort__remove1,axiom, % 188.18/188.23 ! [V_xs_2,V_a_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 => 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 ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__equals__nth__mono,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 <=> ! [B_j] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ! [B_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 188.18/188.23 => 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))) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__nth__mono,axiom, % 188.18/188.23 ! [V_j,V_i,V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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))) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__sorted__distinct__set__unique,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => ( 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))) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 188.18/188.23 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 188.18/188.23 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__column,axiom, % 188.18/188.23 ! [V_i_2,V_xs_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_nth__nth__transpose__sorted,axiom, % 188.18/188.23 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( 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)))) % 188.18/188.23 => ( 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)))) % 188.18/188.23 => 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) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_inj__on__rev,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__rev,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 188.18/188.23 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__append,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__singleton__conv,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_singleton__rev__conv,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev_Osimps_I1_J,axiom, % 188.18/188.23 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Nil__is__rev__conv,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 188.18/188.23 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__is__Nil__conv,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.23 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__concat,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__map,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__filter,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_zip__rev,axiom, % 188.18/188.23 ! [V_ys,T_b,V_xs,T_a] : % 188.18/188.23 ( 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) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__rev,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__rev1,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) % 188.18/188.23 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__rev,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__is__rev__conv,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.23 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 188.18/188.23 <=> V_xs_2 = V_ys_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__swap,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,T_b] : % 188.18/188.23 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 188.18/188.23 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__rev__ident,axiom, % 188.18/188.23 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsum__rev,axiom, % 188.18/188.23 ! [V_xs,T_a] : % 188.18/188.23 ( class_Groups_Ocomm__monoid__add(T_a) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__rev,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldl__foldr,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldr__foldl,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev_Osimps_I2_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__eq__Cons__iff,axiom, % 188.18/188.23 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 188.18/188.23 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 188.18/188.23 <=> 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_last__rev,axiom, % 188.18/188.23 ! [T_a,V_xs] : % 188.18/188.23 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.23 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_hd__rev,axiom, % 188.18/188.23 ! [T_a,V_xs] : % 188.18/188.23 ( V_xs != c_List_Olist_ONil(T_a) % 188.18/188.23 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__transpose,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__foldl__cons,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__take,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__drop,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rotate__rev,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__nth,axiom, % 188.18/188.23 ! [V_xs,T_a,V_n] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__update,axiom, % 188.18/188.23 ! [V_y,V_xs,T_a,V_k] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__rev__nth__mono,axiom, % 188.18/188.23 ! [V_j,V_i,V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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))) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldr__max__sorted,axiom, % 188.18/188.23 ! [V_y_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 188.18/188.23 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 188.18/188.23 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 188.18/188.23 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.23 => 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) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__transpose__sorted,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 188.18/188.23 => 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) ) % 188.18/188.23 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 188.18/188.23 => 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))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__column__length,axiom, % 188.18/188.23 ! [V_i_2,V_xs_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpose__transpose,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 188.18/188.23 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__takeWhile,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__takeWhile__le,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__takeWhileD,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__eq__all__conv,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_zip__takeWhile__fst,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_zip__takeWhile__snd,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__map,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile_Osimps_I1_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile_Osimps_I2_J,axiom, % 188.18/188.23 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 188.18/188.23 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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)) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__tail,axiom, % 188.18/188.23 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] : % 188.18/188.23 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__eq__take,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__takeWhile,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_return__list__def,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__append1,axiom, % 188.18/188.23 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_nth__length__takeWhile,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ~ 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))))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__nth,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__not__last,axiom, % 188.18/188.23 ! [T_b,V_xs_2] : % 188.18/188.23 ( V_xs_2 != c_List_Olist_ONil(T_b) % 188.18/188.23 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 188.18/188.23 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transfer__nat__int__list__return__embed,axiom, % 188.18/188.23 ! [V_l] : % 188.18/188.23 ( c_List_Onat__list(V_l) % 188.18/188.23 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_embed__list__def,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__neq__rev,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__neq__rev,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__dropWhile__id,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__dropWhile,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__dropWhile__le,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_hd__dropWhile,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) % 188.18/188.23 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__eq__Nil__conv,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile_Osimps_I1_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile_Osimps_I2_J,axiom, % 188.18/188.23 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 188.18/188.23 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__dropWhile,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__map,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__append1,axiom, % 188.18/188.23 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__eq__Cons__conv,axiom, % 188.18/188.23 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> ( 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)) % 188.18/188.23 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__eq__drop,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__nth,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => 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)))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listsum__map__filter,axiom, % 188.18/188.23 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] : % 188.18/188.23 ( class_Groups_Omonoid__add(T_c) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => ( ~ hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.23 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted__nth__monoI,axiom, % 188.18/188.23 ! [V_xs,T_a] : % 188.18/188.23 ( class_Orderings_Olinorder(T_a) % 188.18/188.23 => ( ! [B_i,B_j] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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))) ) ) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__eq__filter,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__eq__take__P__nth,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 188.18/188.23 ( ! [B_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 188.18/188.23 => ( 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))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) % 188.18/188.23 => ( ( 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))) % 188.18/188.23 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) % 188.18/188.23 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__takeWhile__less__P__nth,axiom, % 188.18/188.23 ! [V_xs_2,T_b,V_Pa_2,V_j_2] : % 188.18/188.23 ( ! [B_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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)))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted_Osimps,axiom, % 188.18/188.23 ! [V_a_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2) % 188.18/188.23 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 188.18/188.23 | ? [B_xs,B_x] : % 188.18/188.23 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 188.18/188.23 & ! [B_xa] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) % 188.18/188.23 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_List_Oinsert__def,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) % 188.18/188.23 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_not__in__set__insert,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_insert__remdups,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__insert,axiom, % 188.18/188.23 ! [V_x,V_xs,T_a] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__set__insert,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_List_Oset__insert,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_insert__Nil,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__map__maps,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_maps__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_maps__simps_I2_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_maps__simps_I1_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_distinct__concat,axiom, % 188.18/188.23 ! [V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2)) % 188.18/188.23 => ( ! [B_ys] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) ) % 188.18/188.23 => ( ! [B_ys] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 188.18/188.23 => ! [B_zs] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 188.18/188.23 => ( B_ys != B_zs % 188.18/188.23 => 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)) ) ) ) % 188.18/188.23 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_measures__lesseq,axiom, % 188.18/188.23 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 188.18/188.23 => ( 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))) % 188.18/188.23 => 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)))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_wf__measures,axiom, % 188.18/188.23 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__measures_I1_J,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_measures__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_measures__less,axiom, % 188.18/188.23 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 188.18/188.23 => 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)))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__measures_I2_J,axiom, % 188.18/188.23 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] : % 188.18/188.23 ( 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)))) % 188.18/188.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 188.18/188.23 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 188.18/188.23 & 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))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_foldl__apply,axiom, % 188.18/188.23 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => 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)) ) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_order__fun_I2_J,axiom, % 188.18/188.23 ! [V_g_2,V_f_2,T_b,T_c] : % 188.18/188.23 ( ( class_Orderings_Oorder(T_c) % 188.18/188.23 & class_Enum_Oenum(T_b) ) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 188.18/188.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 188.18/188.23 & 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)))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_enum__ex__prod__def,axiom, % 188.18/188.23 ! [V_Pa_2,T_b,T_c] : % 188.18/188.23 ( ( class_Enum_Oenum(T_c) % 188.18/188.23 & class_Enum_Oenum(T_b) ) % 188.18/188.23 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2)) % 188.18/188.23 <=> 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))))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_exists__code,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : % 188.18/188.23 ( class_Enum_Oenum(T_b) % 188.18/188.23 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 188.18/188.23 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_enum__ex,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : % 188.18/188.23 ( class_Enum_Oenum(T_b) % 188.18/188.23 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) % 188.18/188.23 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_zip__obtain__same__length,axiom, % 188.18/188.23 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 188.18/188.23 ( ( 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)) % 188.18/188.23 => 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)))) ) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pos__not__random__dseq__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_dropWhile__append2,axiom, % 188.18/188.23 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all2__all__nthI,axiom, % 188.18/188.23 ! [V_Pa_2,V_ba_2,T_c,V_a_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 => ( ! [B_n] : % 188.18/188.23 ( 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))) % 188.18/188.23 => 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))) ) % 188.18/188.23 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_ba_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_finite__sorted__distinct__unique,axiom, % 188.18/188.23 ! [V_A_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.23 => ? [B_x] : % 188.18/188.23 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2 % 188.18/188.23 & c_List_Olinorder__class_Osorted(T_b,B_x) % 188.18/188.23 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x)) % 188.18/188.23 & ! [B_y] : % 188.18/188.23 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2 % 188.18/188.23 & c_List_Olinorder__class_Osorted(T_b,B_y) % 188.18/188.23 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) ) % 188.18/188.23 => B_y = B_x ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_takeWhile__append2,axiom, % 188.18/188.23 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_insort__is__Cons,axiom, % 188.18/188.23 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] : % 188.18/188.23 ( class_Orderings_Olinorder(T_c) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__eq__Cons__iff,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> ? [B_us,B_vs] : % 188.18/188.23 ( 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)) % 188.18/188.23 & ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 188.18/188.23 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Cons__eq__filter__iff,axiom, % 188.18/188.23 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> ? [B_us,B_vs] : % 188.18/188.23 ( 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)) % 188.18/188.23 & ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 188.18/188.23 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_order__fun_I1_J,axiom, % 188.18/188.23 ! [V_g_2,V_f_2,T_b,T_c] : % 188.18/188.23 ( ( class_Orderings_Oorder(T_c) % 188.18/188.23 & class_Enum_Oenum(T_b) ) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 188.18/188.23 <=> 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_enum__all,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : % 188.18/188.23 ( class_Enum_Oenum(T_b) % 188.18/188.23 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) % 188.18/188.23 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_all__code,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : % 188.18/188.23 ( class_Enum_Oenum(T_b) % 188.18/188.23 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 188.18/188.23 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_enum__all__prod__def,axiom, % 188.18/188.23 ! [V_Pa_2,T_b,T_c] : % 188.18/188.23 ( ( class_Enum_Oenum(T_c) % 188.18/188.23 & class_Enum_Oenum(T_b) ) % 188.18/188.23 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2)) % 188.18/188.23 <=> 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))))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ball__nth,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sorted_OCons,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,T_b] : % 188.18/188.23 ( class_Orderings_Olinorder(T_b) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) % 188.18/188.23 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 188.18/188.23 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__length,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ? [B_n] : % 188.18/188.23 ( 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))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__set__conv__decomp,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 <=> ? [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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__simps_I2_J,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__append,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 188.18/188.23 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__iff,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__rev,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 188.18/188.23 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__simps_I1_J,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 188.18/188.23 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__set__conv__decomp__first,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 <=> ? [B_ys] : % 188.18/188.23 ( ? [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)) % 188.18/188.23 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__set__conv__decomp__last,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 <=> ? [B_ys,B_zs] : % 188.18/188.23 ( 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)) % 188.18/188.23 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__length,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ! [B_n] : % 188.18/188.23 ( 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))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_finite__induct,axiom, % 188.18/188.23 ! [V_Pa_2,V_F_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 188.18/188.23 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 188.18/188.23 => ( ! [B_x,B_F] : % 188.18/188.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 188.18/188.23 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F)) % 188.18/188.23 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) ) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__simps_I2_J,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__append,axiom, % 188.18/188.23 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 188.18/188.23 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__iff,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__rev,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 188.18/188.23 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__simps_I1_J,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 188.18/188.23 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Ball__set__list__all,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__iff__raw,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex1__simps_I2_J,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 188.18/188.23 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_measure__function__int,axiom, % 188.18/188.23 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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_measure__fst,axiom, % 188.18/188.23 ! [T_c,V_f_2,T_b] : % 188.18/188.23 ( c_FunDef_Ois__measure(T_b,V_f_2) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_measure__snd,axiom, % 188.18/188.23 ! [T_c,V_f_2,T_b] : % 188.18/188.23 ( c_FunDef_Ois__measure(T_b,V_f_2) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_is__measure_Osimps,axiom, % 188.18/188.23 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 188.18/188.23 % 188.18/188.23 fof(fact_is__measure_Oequations,axiom, % 188.18/188.23 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 188.18/188.23 % 188.18/188.23 fof(fact_is__measure_Ointros,axiom, % 188.18/188.23 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ). % 188.18/188.23 % 188.18/188.23 fof(fact_measure__size,axiom, % 188.18/188.23 ! [T_b] : % 188.18/188.23 ( class_Nat_Osize(T_b) % 188.18/188.23 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex1__simps_I1_J,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex1__iff,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.23 & ! [B_y] : % 188.18/188.23 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 188.18/188.23 => B_y = B_x ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transfer__morphism__int__nat,axiom, % 188.18/188.23 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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 188.18/188.23 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 188.18/188.23 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.23 => 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) ) % 188.18/188.23 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_bool_Osize_I4_J,axiom, % 188.18/188.23 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 188.18/188.23 % 188.18/188.23 fof(fact_bool_Osize_I3_J,axiom, % 188.18/188.23 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_neg__bind__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 188.18/188.23 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 188.18/188.23 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.23 => 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) ) % 188.18/188.23 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Opos__empty__def,axiom, % 188.18/188.23 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pos__empty__def,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Opos__bind__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pos__bind__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_neg__map__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_neg__single__def,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pos__map__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Oneg__single__def,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pos__single__def,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Opos__single__def,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__splice,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_splice_Osimps_I1_J,axiom, % 188.18/188.23 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 188.18/188.23 % 188.18/188.23 fof(fact_splice__Nil2,axiom, % 188.18/188.23 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 188.18/188.23 % 188.18/188.23 fof(fact_splice_Osimps_I3_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_splice_Osimps_I2_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_acyclicP__converse,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( 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)))) % 188.18/188.23 <=> 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_converse__meet,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_converse__join,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversepD,axiom, % 188.18/188.23 ! [V_ba_2,V_a_2,V_r_2,T_c,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_ba_2)) % 188.18/188.23 => hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_a_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversep_Ointros,axiom, % 188.18/188.23 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_ba_2),V_a_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversep_Oequations,axiom, % 188.18/188.23 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) % 188.18/188.23 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversep__iff,axiom, % 188.18/188.23 ! [V_ba_2,V_a_2,V_r_2,T_c,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_ba_2)) % 188.18/188.23 <=> hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_a_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversep__conversep,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversep__eq,axiom, % 188.18/188.23 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversep__noteq,axiom, % 188.18/188.23 ! [V_y_2,V_x_2,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> V_x_2 != V_y_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_converse__pred__comp,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_conversep__converse__eq,axiom, % 188.18/188.23 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_small__lazy__list_Osimps,axiom, % 188.18/188.23 ! [V_d_2,T_b] : % 188.18/188.23 ( class_Lazy__Sequence_Osmall__lazy(T_b) % 188.18/188.23 => 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)))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_tl__replicate,axiom, % 188.18/188.23 ! [V_x,T_a,V_n] : % 188.18/188.23 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_small__lazy__prod__def,axiom, % 188.18/188.23 ! [V_d,T_b,T_a] : % 188.18/188.23 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 188.18/188.23 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__replicate__const,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_length__replicate,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__length__filter,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__replicate,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__empty,axiom, % 188.18/188.23 ! [V_x_2,V_n_2,T_b] : % 188.18/188.23 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b) % 188.18/188.23 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_empty__replicate,axiom, % 188.18/188.23 ! [V_x_2,V_n_2,T_b] : % 188.18/188.23 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2) % 188.18/188.23 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__0,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_concat__replicate__trivial,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_filter__replicate,axiom, % 188.18/188.23 ! [V_n_2,T_b,V_x_2,V_Pa_2] : % 188.18/188.23 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 188.18/188.23 => 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) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_append__replicate__commute,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__add,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_nth__replicate,axiom, % 188.18/188.23 ! [V_x,T_a,V_n,V_i] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 188.18/188.23 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__eq__replicate,axiom, % 188.18/188.23 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] : % 188.18/188.23 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2) % 188.18/188.23 <=> ( V_m_2 = V_n_2 % 188.18/188.23 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => V_x_2 = V_y_2 ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Ball__set__replicate,axiom, % 188.18/188.23 ! [V_Pa_2,V_a_2,V_n_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( 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)))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 188.18/188.23 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Bex__set__replicate,axiom, % 188.18/188.23 ! [V_Pa_2,V_a_2,V_n_2,T_b] : % 188.18/188.23 ( ? [B_x] : % 188.18/188.23 ( 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)))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 188.18/188.23 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_zip__replicate,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_last__replicate,axiom, % 188.18/188.23 ! [V_x,T_a,V_n] : % 188.18/188.23 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_drop__replicate,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_hd__replicate,axiom, % 188.18/188.23 ! [V_x,T_a,V_n] : % 188.18/188.23 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_take__replicate,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_rev__replicate,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__Suc,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__app__Cons__same,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__set__replicate,axiom, % 188.18/188.23 ! [V_y_2,V_n_2,V_x_2,T_b] : % 188.18/188.23 ( 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)))) % 188.18/188.23 <=> ( V_x_2 = V_y_2 % 188.18/188.23 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_replicate__append__same,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_map__replicate__trivial,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__replicate,axiom, % 188.18/188.23 ! [V_x_2,T_b,V_n_2] : % 188.18/188.23 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__replicate__conv__if,axiom, % 188.18/188.23 ! [V_x_2,T_b,V_n_2] : % 188.18/188.23 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => 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)) ) % 188.18/188.23 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_set__replicate__Suc,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_New__DSequence_Opos__union__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_eq__comp__r,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_pos__union__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_small__lazy_H_Osimps,axiom, % 188.18/188.23 ! [V_i,V_d] : % 188.18/188.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 188.18/188.23 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 188.18/188.23 => 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)))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_small__lazy__int__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_small__lazy_H_Opsimps,axiom, % 188.18/188.23 ! [V_i_2,V_d_2] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 188.18/188.23 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 188.18/188.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 188.18/188.23 => 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)))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_field__le__epsilon,axiom, % 188.18/188.23 ! [V_y,V_x,T_a] : % 188.18/188.23 ( class_Fields_Olinordered__field(T_a) % 188.18/188.23 => ( ! [B_e] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 188.18/188.23 => 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))) ) % 188.18/188.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_small__lazy_H_Opinduct,axiom, % 188.18/188.23 ! [V_Pa_2,V_a1_2,V_a0_2] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( ! [B_d,B_i] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 188.18/188.23 => 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)))) ) % 188.18/188.23 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) ) % 188.18/188.23 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Oinject,axiom, % 188.18/188.23 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> ( V_a_2 = V_a_H_2 % 188.18/188.23 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact__01,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_size__code,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence__size__code,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_seq__case,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_yieldn__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_refl__on__INTER,axiom, % 188.18/188.23 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 188.18/188.23 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_in__set__member,axiom, % 188.18/188.23 ! [V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_member__rec_I1_J,axiom, % 188.18/188.23 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 <=> ( V_x_2 = V_y_2 % 188.18/188.23 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_member__set,axiom, % 188.18/188.23 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ). % 188.18/188.23 % 188.18/188.23 fof(fact_member__rec_I2_J,axiom, % 188.18/188.23 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_List_Omember__def,axiom, % 188.18/188.23 ! [V_x_2,V_xs_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) % 188.18/188.23 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pair__box_Osize_I1_J,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex1__iff__raw,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.23 & ! [B_y] : % 188.18/188.23 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 188.18/188.23 => B_y = B_x ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pair__box_Oinject,axiom, % 188.18/188.23 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 188.18/188.23 ( 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) % 188.18/188.23 <=> ( V_a_2 = V_a_H_2 % 188.18/188.23 & V_ba_2 = V_b_H_2 ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pair__box_Osize_I2_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pair__box_Orecs,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_pair__box_Osimps_I2_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_THE__default__def,axiom, % 188.18/188.23 ! [V_d_2,T_b,V_Pa_2] : % 188.18/188.23 ( ( ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.23 & ! [B_y] : % 188.18/188.23 ( hBOOL(hAPP(V_Pa_2,B_y)) % 188.18/188.23 => B_y = B_x ) ) % 188.18/188.23 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ) % 188.18/188.23 & ( ~ ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(V_Pa_2,B_x)) % 188.18/188.23 & ! [B_y] : % 188.18/188.23 ( hBOOL(hAPP(V_Pa_2,B_y)) % 188.18/188.23 => B_y = B_x ) ) % 188.18/188.23 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_setsum__UNION__zero,axiom, % 188.18/188.23 ! [V_f_2,V_S_2,T_b,T_c] : % 188.18/188.23 ( class_Groups_Ocomm__monoid__add(T_c) % 188.18/188.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2)) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2)) % 188.18/188.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 188.18/188.23 => ( ! [B_T1] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2)) % 188.18/188.23 => ! [B_T2] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2)) % 188.18/188.23 => ( B_T1 != B_T2 % 188.18/188.23 => ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1)) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2)) % 188.18/188.23 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) % 188.18/188.23 => 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) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_INF2__I,axiom, % 188.18/188.23 ! [T_d,T_c,V_ca_2,V_ba_2,V_B_2,V_A_2,T_b] : % 188.18/188.23 ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.23 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_SUP2__E,axiom, % 188.18/188.23 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 => ~ ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.23 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_finite__maxlen,axiom, % 188.18/188.23 ! [V_M_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2)) % 188.18/188.23 => ? [B_n] : % 188.18/188.23 ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2)) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osize_I1_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact__02,axiom, % 188.18/188.23 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osimps_I3_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osimps_I2_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osimps_I4_J,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_lazy__sequence_Osize_I3_J,axiom, % 188.18/188.23 ! [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) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__all__iff__all__interval__int,axiom, % 188.18/188.23 ! [V_j_2,V_i_2,V_Pa_2] : % 188.18/188.23 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 188.18/188.23 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__iff__not__all__inverval__int,axiom, % 188.18/188.23 ! [V_j_2,V_i_2,V_Pa_2] : % 188.18/188.23 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 188.18/188.23 <=> ~ 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) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_all__interval__int__def,axiom, % 188.18/188.23 ! [V_j_2,V_i_2,V_Pa_2] : % 188.18/188.23 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) % 188.18/188.23 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_code__numeral_Orecs_I2_J,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Random_Osimps,axiom, % 188.18/188.23 ! [V_size_2,V_g_2,T_b,V_nrandom_2] : % 188.18/188.23 ( ( 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))) % 188.18/188.23 => 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)) ) % 188.18/188.23 & ( ~ 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))) % 188.18/188.23 => 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))))))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_code__numeral_Orecs_I1_J,axiom, % 188.18/188.23 ! [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 ). % 188.18/188.23 % 188.18/188.23 fof(fact_Random__Sequence_Oempty__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Random__Sequence_Osingle__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Random__Sequence_Omap__def,axiom, % 188.18/188.23 ! [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)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_exE__realizer,axiom, % 188.18/188.23 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( ! [B_x,B_y] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 188.18/188.23 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Image__Collect__split,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lexord__trans,axiom, % 188.18/188.23 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 => ( 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))) % 188.18/188.23 => ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => 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))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__less__than,axiom, % 188.18/188.23 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__lex__prod,axiom, % 188.18/188.23 ! [V_R2_2,T_c,V_R1_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_R1_2) % 188.18/188.23 => ( c_Relation_Otrans(T_c,V_R2_2) % 188.18/188.23 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transD,axiom, % 188.18/188.23 ! [V_ca_2,V_ba_2,V_a_2,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => ( 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)) % 188.18/188.23 => ( 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)) % 188.18/188.23 => 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)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__def,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 <=> ! [B_x,B_y] : % 188.18/188.23 ( 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)) % 188.18/188.23 => ! [B_z] : % 188.18/188.23 ( 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)) % 188.18/188.23 => 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)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Union__eq,axiom, % 188.18/188.23 ! [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)))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__Int,axiom, % 188.18/188.23 ! [V_s_2,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => ( c_Relation_Otrans(T_b,V_s_2) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_bex__UNIV,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : % 188.18/188.23 ( ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_finite__Collect__bex,axiom, % 188.18/188.23 ! [V_Q_2,T_c,V_A_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.23 => ( 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))))) % 188.18/188.23 <=> ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.23 => 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)))) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_bex__empty,axiom, % 188.18/188.23 ! [V_Pa_2,T_b] : % 188.18/188.23 ~ ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listrel__trans,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__converse,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 188.18/188.23 <=> c_Relation_Otrans(T_b,V_r_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_lexord__transI,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__Id,axiom, % 188.18/188.23 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__finite__psubset,axiom, % 188.18/188.23 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__trancl,axiom, % 188.18/188.23 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trancl__id,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__Id__on,axiom, % 188.18/188.23 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__rtrancl,axiom, % 188.18/188.23 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__O__subset,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => 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)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_SUPR__bool__eq,axiom, % 188.18/188.23 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__reflclI,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__inv__image,axiom, % 188.18/188.23 ! [V_f_2,T_c,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_UN__eq,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_list__ex__iff__raw,axiom, % 188.18/188.23 ! [V_xs_2,V_Pa_2,T_b] : % 188.18/188.23 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 188.18/188.23 <=> ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Bex__set__list__ex,axiom, % 188.18/188.23 ! [V_Pa_2,V_xs_2,T_b] : % 188.18/188.23 ( ? [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 188.18/188.23 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.23 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_INT__eq,axiom, % 188.18/188.23 ! [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))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Sup__apply,axiom, % 188.18/188.23 ! [V_x_2,V_A_2,T_c,T_b] : % 188.18/188.23 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.23 => 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)))))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Sup__fun__def,axiom, % 188.18/188.23 ! [V_x_2,V_A_2,T_c,T_b] : % 188.18/188.23 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.23 => 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)))))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Inf__apply,axiom, % 188.18/188.23 ! [V_x_2,V_A_2,T_c,T_b] : % 188.18/188.23 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.23 => 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)))))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_Inf__fun__def,axiom, % 188.18/188.23 ! [V_x_2,V_A_2,T_c,T_b] : % 188.18/188.23 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 188.18/188.23 => 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)))))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_max__extp_Ointros,axiom, % 188.18/188.23 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 188.18/188.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 188.18/188.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 188.18/188.23 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.23 => ( ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 188.18/188.23 => ? [B_xa] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 188.18/188.23 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) % 188.18/188.23 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transp__def,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Predicate_Otransp(T_b,V_r_2) % 188.18/188.23 <=> 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))) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_transpE,axiom, % 188.18/188.23 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 188.18/188.23 ( c_Predicate_Otransp(T_b,V_r_2) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2)) % 188.18/188.23 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_equivp__reflp__symp__transp,axiom, % 188.18/188.23 ! [V_R_2,T_b] : % 188.18/188.23 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 188.18/188.23 <=> ( c_Predicate_Oreflp(T_b,V_R_2) % 188.18/188.23 & c_Predicate_Osymp(T_b,V_R_2) % 188.18/188.23 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_equivpI,axiom, % 188.18/188.23 ! [V_R_2,T_b] : % 188.18/188.23 ( c_Predicate_Oreflp(T_b,V_R_2) % 188.18/188.23 => ( c_Predicate_Osymp(T_b,V_R_2) % 188.18/188.23 => ( c_Predicate_Otransp(T_b,V_R_2) % 188.18/188.23 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sympE,axiom, % 188.18/188.23 ! [V_y_2,V_x_2,V_r_2,T_b] : % 188.18/188.23 ( c_Predicate_Osymp(T_b,V_r_2) % 188.18/188.23 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 188.18/188.23 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_equivpE,axiom, % 188.18/188.23 ! [V_R_2,T_b] : % 188.18/188.23 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 188.18/188.23 => ~ ( c_Predicate_Oreflp(T_b,V_R_2) % 188.18/188.23 => ( c_Predicate_Osymp(T_b,V_R_2) % 188.18/188.23 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_max__extp_Osimps,axiom, % 188.18/188.23 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 188.18/188.23 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 188.18/188.23 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 188.18/188.23 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 188.18/188.23 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.23 & ! [B_x] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 188.18/188.23 => ? [B_xa] : % 188.18/188.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 188.18/188.23 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_trans__diff__Id,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => ( c_Relation_Oantisym(T_b,V_r_2) % 188.18/188.23 => 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))) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisym__subset,axiom, % 188.18/188.23 ! [V_s_2,V_r_2,T_b] : % 188.18/188.23 ( 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)) % 188.18/188.23 => ( c_Relation_Oantisym(T_b,V_s_2) % 188.18/188.23 => c_Relation_Oantisym(T_b,V_r_2) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisym__Id__on,axiom, % 188.18/188.23 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisym__Id,axiom, % 188.18/188.23 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisym__converse,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 188.18/188.23 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisym__empty,axiom, % 188.18/188.23 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisymD,axiom, % 188.18/188.23 ! [V_ba_2,V_a_2,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Oantisym(T_b,V_r_2) % 188.18/188.23 => ( 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)) % 188.18/188.23 => ( 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)) % 188.18/188.23 => V_a_2 = V_ba_2 ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisym__def,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Oantisym(T_b,V_r_2) % 188.18/188.23 <=> ! [B_x,B_y] : % 188.18/188.23 ( 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)) % 188.18/188.23 => ( 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)) % 188.18/188.23 => B_x = B_y ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_antisym__reflcl,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( 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))) % 188.18/188.23 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_acyclic__impl__antisym__rtrancl,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 188.18/188.23 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_fun__lub__def,axiom, % 188.18/188.23 ! [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)))))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__trans__comp__subset,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_symD,axiom, % 188.18/188.23 ! [V_ba_2,V_a_2,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => ( 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)) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__def,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 <=> ! [B_x,B_y] : % 188.18/188.23 ( 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)) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__Int,axiom, % 188.18/188.23 ! [V_s_2,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => ( c_Relation_Osym(T_b,V_s_2) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_listrel__sym,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__converse,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 188.18/188.23 <=> c_Relation_Osym(T_b,V_r_2) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__conv__converse__eq,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__Id,axiom, % 188.18/188.23 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__Un,axiom, % 188.18/188.23 ! [V_s_2,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => ( c_Relation_Osym(T_b,V_s_2) % 188.18/188.23 => 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)) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__trancl,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__Id__on,axiom, % 188.18/188.23 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__rtrancl,axiom, % 188.18/188.23 ! [V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__Un__converse,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__Int__converse,axiom, % 188.18/188.23 ! [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))) ). % 188.18/188.23 % 188.18/188.23 fof(fact_sym__inv__image,axiom, % 188.18/188.23 ! [V_f_2,T_c,V_r_2,T_b] : % 188.18/188.23 ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_equivE,axiom, % 188.18/188.23 ! [V_r_2,V_A_2,T_b] : % 188.18/188.23 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 188.18/188.23 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.23 => ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.23 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ). % 188.18/188.23 % 188.18/188.23 fof(fact_equivI,axiom, % 188.18/188.23 ! [V_r_2,V_A_2,T_b] : % 188.18/188.24 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.24 => ( c_Relation_Osym(T_b,V_r_2) % 188.18/188.24 => ( c_Relation_Otrans(T_b,V_r_2) % 188.18/188.24 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_equiv__def,axiom, % 188.18/188.24 ! [V_r_2,V_A_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 188.18/188.24 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 188.18/188.24 & c_Relation_Osym(T_b,V_r_2) % 188.18/188.24 & c_Relation_Otrans(T_b,V_r_2) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_symp__def,axiom, % 188.18/188.24 ! [V_r_2,T_b] : % 188.18/188.24 ( c_Predicate_Osymp(T_b,V_r_2) % 188.18/188.24 <=> 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))) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_part__equivp__refl__symp__transp,axiom, % 188.18/188.24 ! [V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 188.18/188.24 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 188.18/188.24 & c_Predicate_Osymp(T_b,V_R_2) % 188.18/188.24 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_part__equivpI,axiom, % 188.18/188.24 ! [T_b,V_R_2] : % 188.18/188.24 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 188.18/188.24 => ( c_Predicate_Osymp(T_b,V_R_2) % 188.18/188.24 => ( c_Predicate_Otransp(T_b,V_R_2) % 188.18/188.24 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_part__equivp__def,axiom, % 188.18/188.24 ! [V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 188.18/188.24 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 188.18/188.24 & ! [B_x,B_y] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 188.18/188.24 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 188.18/188.24 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y)) % 188.18/188.24 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_part__equivp__symp,axiom, % 188.18/188.24 ! [V_y_2,V_x_2,V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 188.18/188.24 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_part__equivp__transp,axiom, % 188.18/188.24 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 188.18/188.24 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_equivp__implies__part__equivp,axiom, % 188.18/188.24 ! [V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 188.18/188.24 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_part__equivpE,axiom, % 188.18/188.24 ! [V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 188.18/188.24 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 188.18/188.24 => ( c_Predicate_Osymp(T_b,V_R_2) % 188.18/188.24 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_part__equivp__typedef,axiom, % 188.18/188.24 ! [V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 188.18/188.24 => ? [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))))) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_fold__image__UN__disjoint,axiom, % 188.18/188.24 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] : % 188.18/188.24 ( class_Groups_Ocomm__monoid__mult(T_d) % 188.18/188.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2)) % 188.18/188.24 => ( ! [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 188.18/188.24 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 188.18/188.24 => ( ! [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 188.18/188.24 => ! [B_xa] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2)) % 188.18/188.24 => ( B_x != B_xa % 188.18/188.24 => 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)) ) ) ) % 188.18/188.24 => 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) ) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_nat__of__cases,axiom, % 188.18/188.24 ! [V_y_2] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 188.18/188.24 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_nat__of__induct,axiom, % 188.18/188.24 ! [V_Pa_2,V_y_2] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 188.18/188.24 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x))) % 188.18/188.24 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_of__nat__induct,axiom, % 188.18/188.24 ! [V_x_2,V_Pa_2] : % 188.18/188.24 ( ! [B_y] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 188.18/188.24 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) ) % 188.18/188.24 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_of__nat__cases,axiom, % 188.18/188.24 ! [V_x_2] : % 188.18/188.24 ~ ! [B_y] : % 188.18/188.24 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y) % 188.18/188.24 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_lazy__sequence_Orecs_I1_J,axiom, % 188.18/188.24 ! [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 ). % 188.18/188.24 % 188.18/188.24 fof(fact_lazy__sequence_Orecs_I2_J,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(fact_beyond__def,axiom, % 188.18/188.24 ! [V_l,V_k] : % 188.18/188.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 188.18/188.24 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 188.18/188.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 188.18/188.24 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_curry__def,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(fact_curryI,axiom, % 188.18/188.24 ! [V_ba_2,V_a_2,T_c,T_b,V_f_2] : % 188.18/188.24 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) % 188.18/188.24 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_curryD,axiom, % 188.18/188.24 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 188.18/188.24 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_curryE,axiom, % 188.18/188.24 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 188.18/188.24 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_curry__conv,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(fact_split__curry,axiom, % 188.18/188.24 ! [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 ). % 188.18/188.24 % 188.18/188.24 fof(fact_curry__split,axiom, % 188.18/188.24 ! [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 ). % 188.18/188.24 % 188.18/188.24 fof(fact_beyond__zero,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_refl__on__UNION,axiom, % 188.18/188.24 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 188.18/188.24 ( ! [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 188.18/188.24 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 188.18/188.24 => 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)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_bex__reg__eqv,axiom, % 188.18/188.24 ! [V_Pa_2,V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 188.18/188.24 => ( ? [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 188.18/188.24 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.24 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_Respects__def,axiom, % 188.18/188.24 ! [V_x_2,V_R_2,T_b] : % 188.18/188.24 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2)) % 188.18/188.24 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_in__respects,axiom, % 188.18/188.24 ! [V_R_2,V_x_2,T_b] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2))) % 188.18/188.24 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_bex__reg__right,axiom, % 188.18/188.24 ! [V_Pa_2,V_Q_2,V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 188.18/188.24 => ( ! [B_x] : % 188.18/188.24 ( hBOOL(hAPP(V_Q_2,B_x)) % 188.18/188.24 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 188.18/188.24 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1)) % 188.18/188.24 => ? [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 188.18/188.24 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_babs__reg__eqv,axiom, % 188.18/188.24 ! [V_Pa_2,T_c,V_R_2,T_b] : % 188.18/188.24 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 188.18/188.24 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_Babs__def,axiom, % 188.18/188.24 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2)) % 188.18/188.24 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_wf__weak__decr__stable,axiom, % 188.18/188.24 ! [V_r_2,V_f_2,T_b] : % 188.18/188.24 ( ! [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))) % 188.18/188.24 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) % 188.18/188.24 => ? [B_i] : % 188.18/188.24 ! [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) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_INT__greatest,axiom, % 188.18/188.24 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : % 188.18/188.24 ( ! [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.24 => 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))) ) % 188.18/188.24 => 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))) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_INT__anti__mono,axiom, % 188.18/188.24 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 188.18/188.24 => ( ! [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 188.18/188.24 => 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))) ) % 188.18/188.24 => 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))) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_hoare__derivs_OLocal,axiom, % 188.18/188.24 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 188.18/188.24 ( 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)))) % 188.18/188.24 => 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)))) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osimps_I2_J,axiom, % 188.18/188.24 ! [V_loc_H_2,V_loc_2] : % 188.18/188.24 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2) % 188.18/188.24 <=> V_loc_2 = V_loc_H_2 ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osize_I4_J,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osize_I2_J,axiom, % 188.18/188.24 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osimps_I6_J,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osize_I3_J,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osize_I1_J,axiom, % 188.18/188.24 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osimps_I1_J,axiom, % 188.18/188.24 ! [V_glb_H_2,V_glb_2] : % 188.18/188.24 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2) % 188.18/188.24 <=> V_glb_2 = V_glb_H_2 ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osimps_I3_J,axiom, % 188.18/188.24 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osimps_I4_J,axiom, % 188.18/188.24 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Osimps_I5_J,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Orecs_I1_J,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_vname_Orecs_I2_J,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_converse__rtranclE2,axiom, % 188.18/188.24 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] : % 188.18/188.24 ( 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))) % 188.18/188.24 => ( 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) % 188.18/188.24 => ~ ! [B_a,B_b] : % 188.18/188.24 ( 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)) % 188.18/188.24 => ~ 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))) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_converse__rtrancl__induct2,axiom, % 188.18/188.24 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 188.18/188.24 ( 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))) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) % 188.18/188.24 => ( ! [B_a,B_b,B_aa,B_ba] : % 188.18/188.24 ( 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)) % 188.18/188.24 => ( 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))) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) % 188.18/188.24 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) ) % 188.18/188.24 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_rtrancl__induct2,axiom, % 188.18/188.24 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 188.18/188.24 ( 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))) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) % 188.18/188.24 => ( ! [B_a,B_b] : % 188.18/188.24 ( 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))) % 188.18/188.24 => ! [B_aa,B_ba] : % 188.18/188.24 ( 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)) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) % 188.18/188.24 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) ) % 188.18/188.24 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_congruentI,axiom, % 188.18/188.24 ! [T_c,V_f_2,V_r_2,T_b] : % 188.18/188.24 ( ! [B_y,B_z] : % 188.18/188.24 ( 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)) % 188.18/188.24 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) ) % 188.18/188.24 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_congruent2I_H,axiom, % 188.18/188.24 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] : % 188.18/188.24 ( ! [B_y1,B_z1] : % 188.18/188.24 ( 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)) % 188.18/188.24 => ! [B_y2,B_z2] : % 188.18/188.24 ( 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)) % 188.18/188.24 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) ) % 188.18/188.24 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact__03,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(fact__04,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact__05,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(fact_all__interval__nat__def,axiom, % 188.18/188.24 ! [V_j_2,V_i_2,V_Pa_2] : % 188.18/188.24 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) % 188.18/188.24 <=> ! [B_x] : % 188.18/188.24 ( 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))) % 188.18/188.24 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact__06,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(fact__07,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(fact_list__all__iff__all__interval__nat,axiom, % 188.18/188.24 ! [V_j_2,V_i_2,V_Pa_2] : % 188.18/188.24 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 188.18/188.24 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_list__ex__iff__not__all__inverval__nat,axiom, % 188.18/188.24 ! [V_j_2,V_i_2,V_Pa_2] : % 188.18/188.24 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 188.18/188.24 <=> ~ 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) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_New__DSequence_Opos__map__def,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(fact_folding__image_Ocong,axiom, % 188.18/188.24 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 188.18/188.24 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 188.18/188.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 188.18/188.24 => ( ! [B_x] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 188.18/188.24 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 188.18/188.24 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_power__dvd__imp__le,axiom, % 188.18/188.24 ! [V_n,V_m,V_i] : % 188.18/188.24 ( 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)) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 188.18/188.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_finite__nonempty__imp__fold1Set,axiom, % 188.18/188.24 ! [V_f_2,V_A_2,T_b] : % 188.18/188.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 188.18/188.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 188.18/188.24 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd_Oorder__refl,axiom, % 188.18/188.24 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__0__right,axiom, % 188.18/188.24 ! [V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__1__left,axiom, % 188.18/188.24 ! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__imp__le,axiom, % 188.18/188.24 ! [V_n,V_k] : % 188.18/188.24 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 188.18/188.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult__cancel,axiom, % 188.18/188.24 ! [V_n,V_m,V_k] : % 188.18/188.24 ( c_Rings_Odvd__class_Odvd(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)) % 188.18/188.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_nat__mult__dvd__cancel1,axiom, % 188.18/188.24 ! [V_n_2,V_m_2,V_k_2] : % 188.18/188.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(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)) % 188.18/188.24 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_inf__period_I3_J,axiom, % 188.18/188.24 ! [V_t_2,V_D_2,V_d_2,T_b] : % 188.18/188.24 ( ( class_Rings_Ocomm__ring(T_b) % 188.18/188.24 & class_Rings_Odvd(T_b) ) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2) % 188.18/188.24 => ! [B_x,B_k] : % 188.18/188.24 ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)) % 188.18/188.24 <=> c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_inf__period_I4_J,axiom, % 188.18/188.24 ! [V_t_2,V_D_2,V_d_2,T_b] : % 188.18/188.24 ( ( class_Rings_Ocomm__ring(T_b) % 188.18/188.24 & class_Rings_Odvd(T_b) ) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2) % 188.18/188.24 => ! [B_x,B_k] : % 188.18/188.24 ( c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)) % 188.18/188.24 <=> c_Rings_Odvd__class_Odvd(T_b,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_unity__coeff__ex,axiom, % 188.18/188.24 ! [V_l_2,V_Pa_2,T_b] : % 188.18/188.24 ( ( class_Rings_Odvd(T_b) % 188.18/188.24 & class_Rings_Osemiring__0(T_b) ) % 188.18/188.24 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) % 188.18/188.24 <=> ? [B_x] : % 188.18/188.24 ( c_Rings_Odvd__class_Odvd(T_b,V_l_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))) % 188.18/188.24 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_nat__mult__dvd__cancel__disj,axiom, % 188.18/188.24 ! [V_n_2,V_m_2,V_k_2] : % 188.18/188.24 ( c_Rings_Odvd__class_Odvd(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)) % 188.18/188.24 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 188.18/188.24 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_div__mult__div__if__dvd,axiom, % 188.18/188.24 ! [V_w,V_z,V_x,V_y,T_a] : % 188.18/188.24 ( class_Divides_Osemiring__div(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_w) % 188.18/188.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__div__mult,axiom, % 188.18/188.24 ! [V_c,V_b,V_a,T_a] : % 188.18/188.24 ( class_Divides_Osemiring__div(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) % 188.18/188.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__div__mult__self,axiom, % 188.18/188.24 ! [V_b,V_a,T_a] : % 188.18/188.24 ( class_Divides_Osemiring__div(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) % 188.18/188.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_div__mult__swap,axiom, % 188.18/188.24 ! [V_a,V_b,V_c,T_a] : % 188.18/188.24 ( class_Divides_Osemiring__div(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_b) % 188.18/188.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult__div__cancel,axiom, % 188.18/188.24 ! [V_b,V_a,T_a] : % 188.18/188.24 ( class_Divides_Osemiring__div(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) % 188.18/188.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult__right,axiom, % 188.18/188.24 ! [V_c,V_b,V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult__left,axiom, % 188.18/188.24 ! [V_c,V_b,V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvdI,axiom, % 188.18/188.24 ! [V_k,V_b,V_a,T_a] : % 188.18/188.24 ( class_Rings_Odvd(T_a) % 188.18/188.24 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_mult__dvd__mono,axiom, % 188.18/188.24 ! [V_d,V_c,V_b,V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(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)) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult,axiom, % 188.18/188.24 ! [V_b,V_c,V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult2,axiom, % 188.18/188.24 ! [V_c,V_b,V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__triv__right,axiom, % 188.18/188.24 ! [V_b,V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__triv__left,axiom, % 188.18/188.24 ! [V_b,V_a,T_a] : % 188.18/188.24 ( class_Rings_Ocomm__semiring__1(T_a) % 188.18/188.24 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult__cancel__right,axiom, % 188.18/188.24 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 188.18/188.24 ( class_Rings_Oidom(T_b) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(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)) % 188.18/188.24 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 188.18/188.24 | c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_ba_2) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__mult__cancel__left,axiom, % 188.18/188.24 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 188.18/188.24 ( class_Rings_Oidom(T_b) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(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)) % 188.18/188.24 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 188.18/188.24 | c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_ba_2) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__div__div__eq__mult,axiom, % 188.18/188.24 ! [V_d_2,V_ba_2,V_ca_2,V_a_2,T_b] : % 188.18/188.24 ( class_Divides_Osemiring__div(T_b) % 188.18/188.24 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 188.18/188.24 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_ba_2) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_b,V_ca_2,V_d_2) % 188.18/188.24 => ( 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_d_2),V_ca_2) % 188.18/188.24 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ). % 188.18/188.24 % 188.18/188.24 fof(fact_dvd__div__eq__mult,axiom, % 188.18/188.24 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 188.18/188.24 ( class_Divides_Osemiring__div(T_b) % 188.18/188.24 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 188.18/188.24 => ( c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_ba_2) % 188.18/188.24 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2) = V_ca_2 % 188.18/188.24 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ). % 188.18/188.24 % 188.18/188.24 %----Arity declarations (223) % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 188.18/188.24 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Obounded__lattice(T_1) % 188.18/188.24 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 188.18/188.24 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Obounded__lattice(T_1) % 188.18/188.24 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Obounded__lattice(T_1) % 188.18/188.24 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Olattice(T_1) % 188.18/188.24 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Olattice(T_1) % 188.18/188.24 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Odistrib__lattice(T_1) % 188.18/188.24 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Oboolean__algebra(T_1) % 188.18/188.24 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Orderings_Opreorder,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Orderings_Opreorder(T_1) % 188.18/188.24 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Finite__Set_Ofinite,axiom, % 188.18/188.24 ! [T_1,T_2] : % 188.18/188.24 ( ( class_Finite__Set_Ofinite(T_2) % 188.18/188.24 & class_Finite__Set_Ofinite(T_1) ) % 188.18/188.24 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Lattices_Olattice,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Lattices_Olattice(T_1) % 188.18/188.24 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Orderings_Oorder,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Orderings_Oorder(T_1) % 188.18/188.24 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Orderings_Otop,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Orderings_Otop(T_1) % 188.18/188.24 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Orderings_Oord,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Orderings_Oord(T_1) % 188.18/188.24 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Orderings_Obot,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Orderings_Obot(T_1) % 188.18/188.24 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Groups_Ouminus,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Groups_Ouminus(T_1) % 188.18/188.24 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Groups_Ominus,axiom, % 188.18/188.24 ! [T_2,T_1] : % 188.18/188.24 ( class_Groups_Ominus(T_1) % 188.18/188.24 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_fun__Enum_Oenum,axiom, % 188.18/188.24 ! [T_1,T_2] : % 188.18/188.24 ( ( class_Enum_Oenum(T_2) % 188.18/188.24 & class_Enum_Oenum(T_1) ) % 188.18/188.24 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Com__Ocom__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_Com_Ocom) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 188.18/188.24 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 188.18/188.24 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 188.18/188.24 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 188.18/188.24 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 188.18/188.24 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 188.18/188.24 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 188.18/188.24 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 188.18/188.24 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 188.18/188.24 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 188.18/188.24 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 188.18/188.24 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 188.18/188.24 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 188.18/188.24 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 188.18/188.24 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 188.18/188.24 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 188.18/188.24 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 188.18/188.24 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 188.18/188.24 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 188.18/188.24 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 188.18/188.24 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 188.18/188.24 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 188.18/188.24 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 188.18/188.24 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 188.18/188.24 class_Divides_Osemiring__div(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 188.18/188.24 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 188.18/188.24 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 188.18/188.24 class_Groups_Oab__group__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 188.18/188.24 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 188.18/188.24 class_Rings_Oordered__ring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 188.18/188.24 class_Orderings_Opreorder(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 188.18/188.24 class_Orderings_Olinorder(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 188.18/188.24 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 188.18/188.24 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 188.18/188.24 class_Groups_Omonoid__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 188.18/188.24 class_Rings_Osemiring__1(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 188.18/188.24 class_Rings_Osemiring__0(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 188.18/188.24 class_Lattices_Olattice(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 188.18/188.24 class_Groups_Ogroup__add(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 188.18/188.24 class_Divides_Oring__div(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 188.18/188.24 class_Rings_Omult__zero(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 188.18/188.24 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 188.18/188.24 class_Orderings_Oorder(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 188.18/188.24 class_Int_Oring__char__0(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 188.18/188.24 class_Int_Onumber__ring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 188.18/188.24 class_Rings_Osemiring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Orderings_Oord,axiom, % 188.18/188.24 class_Orderings_Oord(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 188.18/188.24 class_Groups_Ouminus(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 188.18/188.24 class_Groups_Osgn__if(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 188.18/188.24 class_Groups_Oabs__if(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 188.18/188.24 class_Rings_Oring__1(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ominus,axiom, % 188.18/188.24 class_Groups_Ominus(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Power_Opower,axiom, % 188.18/188.24 class_Power_Opower(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Ozero,axiom, % 188.18/188.24 class_Groups_Ozero(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oring,axiom, % 188.18/188.24 class_Rings_Oring(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Oidom,axiom, % 188.18/188.24 class_Rings_Oidom(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Int_Onumber,axiom, % 188.18/188.24 class_Int_Onumber(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Groups_Oone,axiom, % 188.18/188.24 class_Groups_Oone(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Int__Oint__Rings_Odvd,axiom, % 188.18/188.24 class_Rings_Odvd(tc_Int_Oint) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 188.18/188.24 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 188.18/188.24 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 188.18/188.24 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 188.18/188.24 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 188.18/188.24 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 188.18/188.24 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 188.18/188.24 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 188.18/188.24 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 188.18/188.24 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 188.18/188.24 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 188.18/188.24 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 188.18/188.24 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 188.18/188.24 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 188.18/188.24 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 188.18/188.24 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 188.18/188.24 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 188.18/188.24 class_Orderings_Owellorder(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 188.18/188.24 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 188.18/188.24 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 188.18/188.24 class_Orderings_Opreorder(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 188.18/188.24 class_Orderings_Olinorder(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 188.18/188.24 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 188.18/188.24 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 188.18/188.24 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 188.18/188.24 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 188.18/188.24 class_Lattices_Olattice(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 188.18/188.24 class_Rings_Omult__zero(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 188.18/188.24 class_Orderings_Oorder(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 188.18/188.24 class_Rings_Osemiring(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 188.18/188.24 class_Orderings_Oord(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 188.18/188.24 class_Orderings_Obot(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 188.18/188.24 class_Groups_Ominus(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Power_Opower,axiom, % 188.18/188.24 class_Power_Opower(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 188.18/188.24 class_Groups_Ozero(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Int_Onumber,axiom, % 188.18/188.24 class_Int_Onumber(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Groups_Oone,axiom, % 188.18/188.24 class_Groups_Oone(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 188.18/188.24 class_Rings_Odvd(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nat__Onat__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_Nat_Onat) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 188.18/188.24 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 188.18/188.24 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 188.18/188.24 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 188.18/188.24 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 188.18/188.24 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 188.18/188.24 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 188.18/188.24 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 188.18/188.24 class_Orderings_Opreorder(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 188.18/188.24 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 188.18/188.24 class_Lattices_Olattice(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 188.18/188.24 class_Orderings_Oorder(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 188.18/188.24 class_Orderings_Otop(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 188.18/188.24 class_Orderings_Oord(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 188.18/188.24 class_Orderings_Obot(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 188.18/188.24 class_Groups_Ouminus(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 188.18/188.24 class_Groups_Ominus(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 188.18/188.24 class_Enum_Oenum(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_HOL__Obool__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_HOL_Obool) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Com__Ostate__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_Com_Ostate) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Com__Ovname__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_Com_Ovname) ). % 188.18/188.24 % 188.18/188.24 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 188.18/188.24 ! [T_1] : % 188.18/188.24 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 188.18/188.24 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_List__Olist__Nat_Osize,axiom, % 188.18/188.24 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 188.18/188.24 % 188.18/188.24 fof(arity_sum__Finite__Set_Ofinite,axiom, % 188.18/188.24 ! [T_1,T_2] : % 188.18/188.24 ( ( class_Finite__Set_Ofinite(T_2) % 188.18/188.24 & class_Finite__Set_Ofinite(T_1) ) % 188.18/188.24 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_sum__Enum_Oenum,axiom, % 188.18/188.24 ! [T_1,T_2] : % 188.18/188.24 ( ( class_Enum_Oenum(T_2) % 188.18/188.24 & class_Enum_Oenum(T_1) ) % 188.18/188.24 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_sum__Nat_Osize,axiom, % 188.18/188.24 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 188.18/188.24 ! [T_1] : % 188.18/188.24 ( class_Finite__Set_Ofinite(T_1) % 188.18/188.24 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 188.18/188.24 ! [T_1] : % 188.18/188.24 ( class_Enum_Oenum(T_1) % 188.18/188.24 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Option__Ooption__Nat_Osize,axiom, % 188.18/188.24 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 188.18/188.24 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 188.18/188.24 % 188.18/188.24 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 188.18/188.24 ! [T_1,T_2] : % 188.18/188.24 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 188.18/188.24 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 188.18/188.24 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_prod__Finite__Set_Ofinite,axiom, % 188.18/188.24 ! [T_1,T_2] : % 188.18/188.24 ( ( class_Finite__Set_Ofinite(T_2) % 188.18/188.24 & class_Finite__Set_Ofinite(T_1) ) % 188.18/188.24 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_prod__Enum_Oenum,axiom, % 188.18/188.24 ! [T_1,T_2] : % 188.18/188.24 ( ( class_Enum_Oenum(T_2) % 188.18/188.24 & class_Enum_Oenum(T_1) ) % 188.18/188.24 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 188.18/188.24 % 188.18/188.24 fof(arity_prod__Nat_Osize,axiom, % 188.18/188.24 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 188.18/188.24 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 188.18/188.24 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 188.18/188.24 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_Product__Type_Ounit) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 188.18/188.24 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 188.18/188.24 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 188.18/188.24 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 188.18/188.24 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 188.18/188.24 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 188.18/188.24 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 188.18/188.24 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 188.18/188.24 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 188.18/188.24 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 188.18/188.24 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 188.18/188.24 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 188.18/188.24 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 188.18/188.24 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 188.18/188.24 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 188.18/188.24 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 188.18/188.24 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 188.18/188.24 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 188.18/188.24 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 188.18/188.24 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 188.18/188.24 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 188.18/188.24 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 188.18/188.24 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 188.18/188.24 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 188.18/188.24 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 188.18/188.24 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 188.18/188.24 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 188.18/188.24 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 188.18/188.24 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 188.18/188.24 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 188.18/188.24 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 188.18/188.24 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 188.18/188.24 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 188.18/188.24 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 188.18/188.24 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 188.18/188.24 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 188.18/188.24 % 188.18/188.24 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 188.18/188.24 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 188.18/188.24 % 188.18/188.24 %----Helper facts (20) % 188.18/188.24 fof(help_c__COMBI__1,axiom, % 188.18/188.24 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 188.18/188.24 % 188.18/188.24 fof(help_c__COMBK__1,axiom, % 188.18/188.24 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 188.18/188.24 % 188.18/188.24 fof(help_c__COMBB__1,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__COMBC__1,axiom, % 188.18/188.24 ! [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) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__COMBS__1,axiom, % 188.18/188.24 ! [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)) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fequal__1,axiom, % 188.18/188.24 ! [V_y_2,V_x_2] : % 188.18/188.24 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 188.18/188.24 | V_x_2 = V_y_2 ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fequal__2,axiom, % 188.18/188.24 ! [V_y_2,V_x_2] : % 188.18/188.24 ( V_x_2 != V_y_2 % 188.18/188.24 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fFalse__1,axiom, % 188.18/188.24 ~ hBOOL(c_fFalse) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fTrue__1,axiom, % 188.18/188.24 hBOOL(c_fTrue) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fNot__1,axiom, % 188.18/188.24 ! [V_Pa_2] : % 188.18/188.24 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 188.18/188.24 | ~ hBOOL(V_Pa_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fNot__2,axiom, % 188.18/188.24 ! [V_Pa_2] : % 188.18/188.24 ( ~ ~ hBOOL(V_Pa_2) % 188.18/188.24 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fconj__1,axiom, % 188.18/188.24 ! [V_Q_2,V_Pa_2] : % 188.18/188.24 ( ~ hBOOL(V_Pa_2) % 188.18/188.24 | ~ hBOOL(V_Q_2) % 188.18/188.24 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fconj__2,axiom, % 188.18/188.24 ! [V_Q_2,V_Pa_2] : % 188.18/188.24 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 188.18/188.24 | hBOOL(V_Pa_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fconj__3,axiom, % 188.18/188.24 ! [V_Q_2,V_Pa_2] : % 188.18/188.24 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 188.18/188.24 | hBOOL(V_Q_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fdisj__1,axiom, % 188.18/188.24 ! [V_Q_2,V_Pa_2] : % 188.18/188.24 ( ~ hBOOL(V_Pa_2) % 188.18/188.24 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fdisj__2,axiom, % 188.18/188.24 ! [V_Pa_2,V_Q_2] : % 188.18/188.24 ( ~ hBOOL(V_Q_2) % 188.18/188.24 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fdisj__3,axiom, % 188.18/188.24 ! [V_Q_2,V_Pa_2] : % 188.18/188.24 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) % 188.18/188.24 | hBOOL(V_Pa_2) % 188.18/188.24 | hBOOL(V_Q_2) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fimplies__1,axiom, % 188.18/188.24 ! [V_Q_2,V_Pa_2] : % 188.18/188.24 ( hBOOL(V_Pa_2) % 188.18/188.24 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fimplies__2,axiom, % 188.18/188.24 ! [V_Pa_2,V_Q_2] : % 188.18/188.24 ( ~ hBOOL(V_Q_2) % 188.18/188.24 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 188.18/188.24 % 188.18/188.24 fof(help_c__fimplies__3,axiom, % 188.18/188.24 ! [V_Q_2,V_Pa_2] : % 188.18/188.24 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) % 188.18/188.24 | ~ hBOOL(V_Pa_2) % 188.18/188.24 | hBOOL(V_Q_2) ) ). % 188.18/188.24 % 188.18/188.24 %----Conjectures (1) % 188.18/188.24 fof(conj_0,conjecture, % 188.18/188.24 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,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse)),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)))) ). % 188.18/188.24 % 188.18/188.24 %------------------------------------------------------------------------------ % 188.18/188.24 %------------------------------------------- % 188.18/188.24 % Proof found % 188.18/188.24 % SZS status Theorem for theBenchmark % 188.18/188.24 % SZS output start Proof % 188.18/188.24 %ClaNum:10488(EqnAxiom:3147) % 188.18/188.24 %VarNum:70959(SingletonVarNum:20562) % 188.18/188.24 %MaxLitNum:8 % 188.18/188.24 %MaxfuncDepth:15 % 188.18/188.24 %SharedTerms:1034 % 188.18/188.24 %goalClause: 4812 % 188.18/188.24 %singleGoalClaCount:1 % 188.18/188.24 [3151]P1(a922) % 188.18/188.24 [3152]P1(a927) % 188.18/188.24 [3153]P107(a194) % 188.18/188.24 [3154]P2(a922) % 188.18/188.24 [3155]P2(a927) % 188.18/188.24 [3156]P2(a1) % 188.18/188.24 [3157]P2(a106) % 188.18/188.24 [3158]P3(a1) % 188.18/188.24 [3159]P108(a922) % 188.18/188.24 [3160]P108(a927) % 188.18/188.24 [3161]P108(a1) % 188.18/188.24 [3162]P108(a106) % 188.18/188.24 [3163]P109(a927) % 188.18/188.24 [3164]P109(a1) % 188.18/188.24 [3165]P109(a106) % 188.18/188.24 [3166]P110(a922) % 188.18/188.24 [3167]P110(a927) % 188.18/188.24 [3168]P110(a1) % 188.18/188.24 [3169]P110(a106) % 188.18/188.24 [3170]P111(a922) % 188.18/188.24 [3171]P111(a927) % 188.18/188.24 [3172]P111(a1) % 188.18/188.24 [3173]P111(a106) % 188.18/188.24 [3174]P112(a922) % 188.18/188.24 [3175]P79(a1) % 188.18/188.24 [3176]P83(a922) % 188.18/188.24 [3177]P83(a1) % 188.18/188.24 [3178]P69(a1) % 188.18/188.24 [3179]P91(a922) % 188.18/188.24 [3180]P70(a927) % 188.18/188.24 [3181]P70(a1) % 188.18/188.24 [3182]P70(a106) % 188.18/188.24 [3183]P113(a1) % 188.18/188.24 [3184]P114(a1) % 188.18/188.24 [3185]P4(a922) % 188.18/188.24 [3186]P4(a930) % 188.18/188.24 [3187]P124(a1) % 188.18/188.24 [3188]P80(a927) % 188.18/188.24 [3189]P80(a1) % 188.18/188.24 [3190]P80(a106) % 188.18/188.24 [3191]P81(a927) % 188.18/188.24 [3192]P81(a1) % 188.18/188.24 [3193]P81(a106) % 188.18/188.24 [3194]P72(a927) % 188.18/188.24 [3195]P72(a1) % 188.18/188.24 [3196]P72(a106) % 188.18/188.24 [3197]P127(a927) % 188.18/188.24 [3198]P127(a1) % 188.18/188.24 [3199]P127(a106) % 188.18/188.24 [3200]P141(a1) % 188.18/188.24 [3201]P115(a1) % 188.18/188.24 [3202]P119(a927) % 188.18/188.24 [3203]P119(a1) % 188.18/188.24 [3204]P119(a106) % 188.18/188.24 [3205]P73(a927) % 188.18/188.24 [3206]P73(a1) % 188.18/188.24 [3207]P73(a106) % 188.18/188.24 [3208]P74(a927) % 188.18/188.24 [3209]P74(a1) % 188.18/188.24 [3210]P74(a106) % 188.18/188.24 [3211]P71(a927) % 188.18/188.24 [3212]P71(a1) % 188.18/188.24 [3213]P71(a106) % 188.18/188.24 [3214]P143(a927) % 188.18/188.24 [3215]P143(a1) % 188.18/188.24 [3216]P84(a927) % 188.18/188.24 [3217]P84(a1) % 188.18/188.24 [3218]P84(a106) % 188.18/188.24 [3219]P85(a927) % 188.18/188.24 [3220]P85(a1) % 188.18/188.24 [3221]P85(a106) % 188.18/188.24 [3222]P87(a927) % 188.18/188.24 [3223]P87(a1) % 188.18/188.24 [3224]P87(a106) % 188.18/188.24 [3225]P120(a927) % 188.18/188.24 [3226]P120(a1) % 188.18/188.24 [3227]P120(a106) % 188.18/188.24 [3228]P144(a927) % 188.18/188.24 [3229]P144(a1) % 188.18/188.24 [3230]P144(a106) % 188.18/188.24 [3231]P130(a1) % 188.18/188.24 [3232]P131(a1) % 188.18/188.24 [3233]P92(a927) % 188.18/188.24 [3234]P92(a1) % 188.18/188.24 [3235]P92(a106) % 188.18/188.24 [3236]P76(a927) % 188.18/188.24 [3237]P76(a1) % 188.18/188.24 [3238]P76(a106) % 188.18/188.24 [3239]P82(a927) % 188.18/188.24 [3240]P82(a1) % 188.18/188.24 [3241]P82(a106) % 188.18/188.24 [3242]P77(a1) % 188.18/188.24 [3243]P134(a927) % 188.18/188.24 [3244]P134(a1) % 188.18/188.24 [3245]P134(a106) % 188.18/188.24 [3246]P145(a1) % 188.18/188.24 [3247]P136(a927) % 188.18/188.24 [3248]P136(a1) % 188.18/188.24 [3249]P136(a106) % 188.18/188.24 [3250]P146(a927) % 188.18/188.24 [3251]P146(a1) % 188.18/188.24 [3252]P146(a106) % 188.18/188.24 [3253]P88(a927) % 188.18/188.24 [3254]P88(a1) % 188.18/188.24 [3255]P88(a106) % 188.18/188.24 [3256]P128(a1) % 188.18/188.24 [3257]P129(a1) % 188.18/188.24 [3258]P137(a927) % 188.18/188.24 [3259]P137(a1) % 188.18/188.24 [3260]P137(a106) % 188.18/188.24 [3261]P139(a927) % 188.18/188.24 [3262]P139(a1) % 188.18/188.24 [3263]P139(a106) % 188.18/188.24 [3264]P138(a927) % 188.18/188.24 [3265]P138(a1) % 188.18/188.24 [3266]P138(a106) % 188.18/188.24 [3267]P125(a927) % 188.18/188.24 [3268]P125(a1) % 188.18/188.24 [3269]P125(a106) % 188.18/188.24 [3270]P135(a927) % 188.18/188.24 [3271]P135(a1) % 188.18/188.24 [3272]P135(a106) % 188.18/188.24 [3273]P132(a927) % 188.18/188.24 [3274]P132(a1) % 188.18/188.24 [3275]P132(a106) % 188.18/188.24 [3276]P133(a1) % 188.18/188.24 [3277]P89(a1) % 188.18/188.24 [3278]P93(a1) % 188.18/188.24 [3279]P142(a1) % 188.18/188.24 [3280]P94(a927) % 188.18/188.24 [3281]P94(a1) % 188.18/188.24 [3282]P94(a106) % 188.18/188.24 [3283]P95(a1) % 188.18/188.24 [3284]P147(a927) % 188.18/188.24 [3285]P147(a1) % 188.18/188.24 [3286]P147(a106) % 188.18/188.24 [3287]P97(a927) % 188.18/188.24 [3288]P97(a1) % 188.18/188.24 [3289]P97(a106) % 188.18/188.24 [3290]P116(a927) % 188.18/188.24 [3291]P116(a1) % 188.18/188.24 [3292]P116(a106) % 188.18/188.24 [3293]P148(a927) % 188.18/188.24 [3294]P148(a1) % 188.18/188.24 [3295]P148(a106) % 188.18/188.24 [3296]P5(a927) % 188.18/188.24 [3297]P5(a1) % 188.18/188.24 [3298]P5(a106) % 188.18/188.24 [3299]P6(a1) % 188.18/188.24 [3300]P78(a927) % 188.18/188.24 [3301]P78(a1) % 188.18/188.24 [3302]P78(a106) % 188.18/188.24 [3303]P98(a922) % 188.18/188.24 [3304]P98(a927) % 188.18/188.24 [3305]P98(a1) % 188.18/188.24 [3306]P99(a922) % 188.18/188.24 [3307]P99(a927) % 188.18/188.24 [3308]P99(a1) % 188.18/188.24 [3309]P100(a922) % 188.18/188.24 [3310]P101(a922) % 188.18/188.24 [3311]P103(a922) % 188.18/188.24 [3312]P103(a927) % 188.18/188.24 [3313]P103(a1) % 188.18/188.24 [3314]P7(a922) % 188.18/188.24 [3315]P104(a922) % 188.18/188.24 [3316]P104(a927) % 188.18/188.24 [3317]P104(a1) % 188.18/188.24 [3318]P86(a1) % 188.18/188.24 [3319]P140(a1) % 188.18/188.24 [3320]P75(a1) % 188.18/188.24 [3321]P117(a927) % 188.18/188.24 [3322]P90(a927) % 188.18/188.24 [3323]P90(a1) % 188.18/188.24 [3324]P90(a106) % 188.18/188.24 [3325]P64(a922) % 188.18/188.24 [3326]P64(a930) % 188.18/188.24 [3327]P106(a922) % 188.18/188.24 [3328]P106(a923) % 188.18/188.24 [3329]P106(a927) % 188.18/188.24 [3330]P106(a925) % 188.18/188.24 [3331]P106(a930) % 188.18/188.24 [3332]P106(a924) % 188.18/188.24 [3333]P106(a106) % 188.18/188.24 [3334]P106(a330) % 188.18/188.24 [3335]P105(a930) % 188.18/188.24 [3336]P105(a1) % 188.18/188.24 [3337]P118(a1) % 188.18/188.24 [3338]P121(a927) % 188.18/188.24 [3339]P121(a1) % 188.18/188.24 [3340]P121(a106) % 188.18/188.24 [3341]P102(a922) % 188.18/188.24 [3357]P39(a927,a248) % 188.18/188.24 [3358]P39(a927,a324) % 188.18/188.24 [3359]P40(a927,a248) % 188.18/188.24 [4711]~E(a104,a89) % 188.18/188.24 [4712]~P107(a247) % 188.18/188.24 [3148]E(f2(a1),a89) % 188.18/188.24 [3149]E(f107(a106),a3) % 188.18/188.24 [3150]E(f23(a106),a24) % 188.18/188.24 [3342]E(f195(a927),f2(a927)) % 188.18/188.24 [3343]E(f29(a25),f2(a927)) % 188.18/188.24 [3344]E(f241(a927),f108(a927)) % 188.18/188.24 [3345]E(f246(a927),f109(a927)) % 188.18/188.24 [3346]E(f110(a1),f32(a1)) % 188.18/188.24 [3347]E(f90(a247),f2(a927)) % 188.18/188.24 [3348]E(f90(a194),f2(a927)) % 188.18/188.24 [3349]P8(f84(a1)) % 188.18/188.24 [3350]P8(f2(a1)) % 188.18/188.24 [3411]P39(f934(a927,a927),a38) % 188.18/188.24 [3754]E(f326(a927,a927,a248,a248),a38) % 188.18/188.24 [4713]~E(f84(a1),f2(a1)) % 188.18/188.24 [3351]E(f4(f2(a106)),f2(a927)) % 188.18/188.24 [3352]E(f118(f2(a927)),f2(a927)) % 188.18/188.24 [3363]E(f334(f85(a1),a89),a89) % 188.18/188.24 [3366]E(f334(a119,f2(a927)),f84(a927)) % 188.18/188.24 [3367]E(f334(a112,f84(a1)),f84(a927)) % 188.18/188.24 [3368]E(f334(a3,f84(a927)),f84(a106)) % 188.18/188.24 [3370]E(f334(a3,f2(a927)),f2(a106)) % 188.18/188.24 [3372]E(f334(f111(a1),a89),f2(a1)) % 188.18/188.24 [3373]E(f334(f111(a106),a89),f2(a106)) % 188.18/188.24 [3374]E(f334(a112,f2(a1)),f2(a927)) % 188.18/188.24 [3375]E(f334(f196(a922),a247),f2(a927)) % 188.18/188.24 [3376]E(f334(f196(a922),a194),f2(a927)) % 188.18/188.24 [3377]E(f334(f196(a924),a25),f2(a927)) % 188.18/188.24 [3378]E(f334(f111(a927),a89),f2(a927)) % 188.18/188.24 [3384]E(f334(f85(a1),f84(a1)),a104) % 188.18/188.24 [3391]E(f334(f85(a1),f2(a1)),f2(a1)) % 188.18/188.24 [3393]E(f334(f196(a106),f2(a106)),f2(a927)) % 188.18/188.24 [3394]E(f334(f107(a1),f84(a927)),f84(a1)) % 188.18/188.24 [3395]E(f334(f107(a1),f2(a927)),f2(a1)) % 188.18/188.24 [3407]E(f334(a112,f84(a1)),f334(a119,f2(a927))) % 188.18/188.24 [3409]E(f325(f934(a927,a927),a38),a39) % 188.18/188.24 [3410]E(f327(f934(a927,a927),a38),a74) % 188.18/188.24 [3436]E(f334(f290(a927),f2(a927)),f250(f935(a927,a922))) % 188.18/188.24 [3437]E(f334(f307(a927),f2(a927)),f195(f935(a927,a922))) % 188.18/188.24 [3446]P42(f195(f935(a1,a922))) % 188.18/188.24 [3481]E(f334(f334(f23(a106),f2(a106)),f84(a106)),f2(a106)) % 188.18/188.24 [3556]P107(f334(f334(f243(a1),a104),f2(a1))) % 188.18/188.24 [3580]P107(f334(f334(f242(a1),f2(a1)),f84(a1))) % 188.18/188.24 [3582]P107(f334(f334(f243(a1),f2(a1)),f84(a1))) % 188.18/188.24 [3784]E(f334(f334(f295(a927,a927,a927),a324),f314(a927,a324)),a248) % 188.18/188.24 [3827]P43(a1,a927,a112,f334(f242(a1),f2(a1))) % 188.18/188.24 [3831]E(f334(f334(f44(a927,f935(a927,a922)),f250(f935(a927,a922))),f309(a927)),f250(f935(a927,a922))) % 188.18/188.24 [3832]E(f334(f334(f44(a927,f935(a927,a922)),f250(f935(a927,a922))),f290(a927)),f250(f935(a927,a922))) % 188.18/188.24 [3833]E(f334(f334(f44(a927,f935(a927,a922)),f250(f935(a927,a922))),f307(a927)),f250(f935(a927,a922))) % 188.18/188.24 [3834]E(f334(f334(f45(a927,f935(a927,a922)),f250(f935(a927,a922))),f308(a927)),f195(f935(a927,a922))) % 188.18/188.24 [3850]P27(a927,a1,f107(a1),f250(f935(a927,a922))) % 188.18/188.24 [3864]P43(a927,a1,f107(a1),f334(f16(a922,a927),a194)) % 188.18/188.24 [3993]E(f334(f78(a927,a106,a1,a3),a112),f111(a106)) % 188.18/188.24 [4219]P60(a106,a927,a20,a3,f250(f935(a927,a922))) % 188.18/188.24 [4223]P60(a1,f935(f934(a927,a927),a922),a115,a95,a105) % 188.18/188.24 [4475]E(f266(a1,a1,a1,a1,f32(a1),f85(a1)),a56) % 188.18/188.24 [4736]~E(f334(f111(a1),a104),f334(f111(a1),a89)) % 188.18/188.24 [4737]~P107(f334(a200,f84(a1))) % 188.18/188.24 [4738]~P107(f334(a200,f2(a1))) % 188.18/188.24 [4777]~P107(f334(f334(f243(a1),a89),f2(a1))) % 188.18/188.24 [3429]E(f334(f334(f23(a1),a104),a104),a89) % 188.18/188.24 [3444]E(f334(f107(a1),f334(a119,f2(a927))),f84(a1)) % 188.18/188.24 [3510]E(f334(f40(a930),f250(f935(a930,a922))),f84(a927)) % 188.18/188.24 [3531]P107(f334(a200,f334(f111(a1),a104))) % 188.18/188.24 [3533]P107(f334(f334(f242(a1),a104),a89)) % 188.18/188.24 [3535]P107(f334(f334(f243(a1),a104),a89)) % 188.18/188.24 [3591]E(f334(f334(f316(a927),f2(a927)),f195(f935(a927,a922))),f334(f309(a927),f2(a927))) % 188.18/188.24 [3646]P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),a89))) % 188.18/188.24 [3658]E(f334(f317(a927,a927,a119),f250(f935(a927,a922))),f334(f308(a927),f2(a927))) % 188.18/188.24 [3695]P10(f934(a927,a927),f250(f935(f934(a927,a927),a922)),a116) % 188.18/188.24 [4000]E(f334(f78(a927,a1,a106,f107(a1)),a20),a22) % 188.18/188.24 [4065]P39(a927,f334(f270(f934(a927,a927)),f334(f265(a927,a927,a922),f243(a927)))) % 188.18/188.24 [4768]~P107(f334(a200,f334(f111(a1),a89))) % 188.18/188.24 [4769]~P107(f334(f334(f242(a1),a89),a104)) % 188.18/188.24 [4770]~P107(f334(f334(f243(a1),a89),a89)) % 188.18/188.24 [4771]~P107(f334(f334(f243(a1),a89),a104)) % 188.18/188.24 [4772]~P107(f334(f334(f243(a1),a104),a104)) % 188.18/188.24 [4783]~P107(f334(f66(a927),f250(f935(a927,a922)))) % 188.18/188.24 [4784]~P107(f334(f66(a1),f250(f935(a1,a922)))) % 188.18/188.24 [4650]E(f334(f265(a1,a1,a922),f334(f334(f8(f935(a1,a922),f935(a1,a922),a1),f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f243(a1),f2(a1))))),f334(f334(f7(a1,a1,f935(a1,a922)),f334(f334(f8(f935(a1,f935(a1,a922)),f935(a1,f935(a1,a922)),a1),f7(a1,a1,a922)),f334(f334(f8(f935(a1,a1),f935(a1,f935(a1,a922)),a1),f334(f8(a1,f935(a1,a922),a1),a331)),a226))),f84(a1)))),a222) % 188.18/188.24 [4812]~P26(a921,a936,f334(f334(f316(f926(a921)),f98(a921,f334(f16(f935(a923,a922),a921),f334(f16(a922,a923),a247)),a937,f334(f334(f7(a921,f935(a923,a922),f935(a923,a922)),f334(f334(f8(f935(a923,f935(a922,a922)),f935(f935(a923,a922),f935(a923,a922)),a921),f18(a923,a922,a922)),f334(f334(f8(f935(a923,a922),f935(a923,f935(a922,a922)),a921),f334(f8(a922,f935(a922,a922),a923),a332)),a938))),f334(f334(f8(a922,a922,a923),a329),a939)))),f195(f935(f926(a921),a922)))) % 188.18/188.24 [3756]E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a104)),a104),a104) % 188.18/188.24 [3794]E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89),f334(f85(a1),a104)) % 188.18/188.24 [3836]E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89),f334(f334(f23(a1),a89),a104)) % 188.18/188.24 [3933]E(f334(f334(f65(f934(a927,a927)),f250(f935(f934(a927,a927),a922))),a116),a105) % 188.18/188.24 [4002]E(f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f84(a1)) % 188.18/188.24 [4003]E(f334(f111(a106),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f84(a106)) % 188.18/188.24 [4004]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f84(a927)) % 188.18/188.24 [4011]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f334(a119,f2(a927))) % 188.18/188.24 [4341]E(f334(f334(f108(f935(f934(f934(a927,a927),f934(a927,a927)),a922)),a38),f314(f934(a927,a927),f195(f935(f934(f934(a927,a927),f934(a927,a927)),a922)))),a76) % 188.18/188.24 [4403]E(f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),f84(a927)),f2(a927))),f195(f935(f934(a927,a927),a922))))),f84(a1)) % 188.18/188.24 [4404]E(f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),f2(a927)),f2(a927))),f195(f935(f934(a927,a927),a922))))),f2(a1)) % 188.18/188.24 [4417]E(f334(f270(f934(a927,a927)),f334(f265(a927,a927,a922),f334(f334(f8(a927,f935(a927,a922),a927),f334(f7(a927,a927,a922),a331)),a119))),a324) % 188.18/188.24 [4169]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),a104),a89) % 188.18/188.24 [4468]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(a119,f334(a119,f334(a119,f2(a927))))) % 188.18/188.24 [4533]P29(f935(f934(a927,a927),a922),f334(f334(f260(f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922),f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922)),a39),a75)) % 188.18/188.24 [4534]P29(f935(f934(a927,a927),a922),f334(f334(f260(f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922),f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922)),a74),a77)) % 188.18/188.24 [4544]P8(f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))) % 188.18/188.24 [4571]E(f334(f334(f108(f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922)),f327(f934(a927,a927),a76)),f334(f334(f316(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),f195(f935(f934(a927,a927),a922))),f195(f935(f934(a927,a927),a922)))),f195(f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922)))),a77) % 188.18/188.24 [4572]E(f334(f334(f108(f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922)),f325(f934(a927,a927),a76)),f334(f334(f316(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),f195(f935(f934(a927,a927),a922))),f195(f935(f934(a927,a927),a922)))),f195(f935(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a922)))),a75) % 188.18/188.24 [4578]E(f334(f107(a1),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))) % 188.18/188.24 [4591]P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))))) % 188.18/188.24 [4588]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)),f334(a119,f334(a119,f2(a927)))) % 188.18/188.24 [4589]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)),f334(f334(f86(a927),f84(a927)),f84(a927))) % 188.18/188.24 [4590]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)),f334(f40(a922),f250(f935(a922,a922)))) % 188.18/188.24 [4630]P8(f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))) % 188.18/188.24 [4631]E(f334(a112,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(a119,f334(a119,f2(a927)))) % 188.18/188.24 [4652]E(f334(f107(a1),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))) % 188.18/188.24 [4665]P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.24 [3360]P9(x33601,a331) % 188.18/188.24 [3459]P59(a927,x34591,x34591) % 188.18/188.24 [3755]P27(a927,a927,a119,x37551) % 188.18/188.24 [3353]P106(f926(x33531)) % 188.18/188.24 [3354]P106(f931(x33541)) % 188.18/188.24 [3355]P106(f928(x33551)) % 188.18/188.24 [3356]P106(f929(x33561)) % 188.18/188.24 [3379]P39(a1,f113(x33791)) % 188.18/188.24 [3380]P39(a1,f114(x33801)) % 188.18/188.24 [3432]P39(f935(x34321,a922),f321(x34321)) % 188.18/188.24 [3433]P40(f935(x34331,a922),f321(x34331)) % 188.18/188.24 [3458]E(f251(x34581,x34581,a331),a331) % 188.18/188.24 [3474]E(f50(a1,x34741,x34741),f2(a1)) % 188.18/188.24 [3528]P16(x35281,f935(x35281,a922),f316(x35281)) % 188.18/188.24 [4717]~E(f334(a119,x47171),x47171) % 188.18/188.24 [4729]~E(f334(a119,x47291),f2(a927)) % 188.18/188.24 [3361]E(f35(f33(x33611)),f2(a927)) % 188.18/188.24 [3362]E(f35(f34(x33621)),f2(a927)) % 188.18/188.24 [3364]E(f334(f196(a927),x33641),x33641) % 188.18/188.24 [3365]E(f334(f111(a1),x33651),x33651) % 188.18/188.24 [3381]E(f334(a95,f335(x33811)),x33811) % 188.18/188.24 [3382]E(f334(a3,f579(x33821)),x33821) % 188.18/188.24 [3383]E(f249(x33831,f2(a106)),f2(a106)) % 188.18/188.24 [3396]E(f121(x33961,f120(x33961)),f120(x33961)) % 188.18/188.24 [3397]E(f159(x33971,f120(x33971)),f120(x33971)) % 188.18/188.24 [3399]E(f334(f196(a925),f33(x33991)),f2(a927)) % 188.18/188.24 [3400]E(f334(f196(a925),f34(x34001)),f2(a927)) % 188.18/188.24 [3404]E(f334(f174(x34041),f120(x34041)),f120(x34041)) % 188.18/188.24 [3405]E(f334(f178(x34051),f120(x34051)),f120(x34051)) % 188.18/188.24 [3406]E(f334(f175(x34061),f120(x34061)),f120(x34061)) % 188.18/188.24 [3412]E(f334(f111(a1),x34121),f334(f110(a1),x34121)) % 188.18/188.24 [3413]E(f334(a95,f334(a115,x34131)),x34131) % 188.18/188.24 [3415]E(f334(a3,f334(a20,x34151)),x34151) % 188.18/188.24 [3416]E(f334(a20,f334(a3,x34161)),x34161) % 188.18/188.24 [3418]P8(f334(f107(a1),x34181)) % 188.18/188.24 [3427]E(f334(f196(f928(x34271)),f120(x34271)),f2(a927)) % 188.18/188.24 [3428]E(f334(f196(f929(x34281)),f126(x34281)),f2(a927)) % 188.18/188.24 [3449]E(f334(f334(f23(a927),x34491),f2(a927)),x34491) % 188.18/188.24 [3450]E(f334(f334(f87(a927),x34501),f84(a927)),x34501) % 188.18/188.24 [3451]E(f334(f334(f87(a1),x34511),f84(a1)),x34511) % 188.18/188.24 [3452]E(f334(f334(f86(a927),x34521),f2(a927)),x34521) % 188.18/188.24 [3453]E(f334(f334(f86(a1),x34531),f2(a1)),x34531) % 188.18/188.24 [3454]E(f334(f334(f241(a927),x34541),f2(a927)),x34541) % 188.18/188.24 [3455]E(f334(f334(f87(a927),x34551),f2(a927)),f2(a927)) % 188.18/188.24 [3456]E(f334(f334(f41(a1),x34561),f2(a1)),f2(a1)) % 188.18/188.24 [3457]E(f334(f334(f246(a927),x34571),f2(a927)),f2(a927)) % 188.18/188.24 [3465]E(f334(f179(x34651),f120(x34651)),f195(f935(x34651,a922))) % 188.18/188.24 [3469]P107(f334(f144(x34691),f120(x34691))) % 188.18/188.24 [3475]E(f334(f161(x34751,x34751),f5(x34751)),f32(f928(x34751))) % 188.18/188.24 [3476]E(f334(f161(x34761,x34761),f32(x34761)),f32(f928(x34761))) % 188.18/188.24 [3477]E(f50(a1,x34771,f2(a1)),x34771) % 188.18/188.24 [3478]E(f334(f242(a927),f334(a119,x34781)),f334(f243(a927),x34781)) % 188.18/188.24 [3479]E(f334(f290(a927),f334(a119,x34791)),f334(f308(a927),x34791)) % 188.18/188.24 [3480]E(f334(f307(a927),f334(a119,x34801)),f334(f309(a927),x34801)) % 188.18/188.24 [3482]E(f50(a1,f2(a1),x34821),f2(a1)) % 188.18/188.24 [3495]E(f334(f334(f86(a927),x34951),f84(a927)),f334(a119,x34951)) % 188.18/188.24 [3504]E(f334(f310(a927,x35041),f2(a927)),f195(f935(a927,a922))) % 188.18/188.24 [3516]E(f311(a927,f2(a927),x35161),f334(f309(a927),x35161)) % 188.18/188.24 [3525]P59(a927,f334(a119,f2(a927)),x35251) % 188.18/188.24 [3559]E(f334(f334(f23(a927),f334(a119,x35591)),f84(a927)),x35591) % 188.18/188.24 [3571]E(f52(f2(a1),x35711),f334(f334(f260(a1,a1),f2(a1)),f2(a1))) % 188.18/188.24 [3621]P107(f334(f334(f243(a927),x36211),f334(a119,x36211))) % 188.18/188.24 [3633]P107(f334(f334(f243(a927),f2(a927)),f334(a119,x36331))) % 188.18/188.24 [3863]E(f97(x38631,x38631,f250(f935(x38631,a922)),f32(x38631)),f32(x38631)) % 188.18/188.24 [3920]E(f334(f334(f23(a106),f334(a3,f334(a119,f334(a20,x39201)))),f84(a106)),x39201) % 188.18/188.24 [3984]P107(f334(f334(f242(a1),f334(f85(a1),f334(f107(a1),x39841))),f2(a1))) % 188.18/188.24 [4132]P107(f334(f334(f243(a1),f334(f85(a1),f334(f107(a1),f334(a119,x41321)))),f2(a1))) % 188.18/188.24 [4741]~E(f250(f935(x47411,a922)),f195(f935(x47411,a922))) % 188.18/188.24 [4780]~P107(f334(f334(f243(a927),x47801),f2(a927))) % 188.18/188.24 [4791]~P107(f334(f334(f243(a1),f334(f107(a1),x47911)),f2(a1))) % 188.18/188.24 [3417]E(f127(x34171,f126(f929(x34171))),f126(x34171)) % 188.18/188.24 [3431]E(f186(x34311,f120(f928(x34311))),f120(f928(x34311))) % 188.18/188.24 [3434]E(f334(f334(f87(a1),a89),x34341),a89) % 188.18/188.24 [3435]E(f334(f334(f86(a1),a89),x34351),x34351) % 188.18/188.24 [3438]E(f334(a112,f334(f107(a1),x34381)),x34381) % 188.18/188.24 [3439]E(f334(f334(f23(a1),x34391),a89),x34391) % 188.18/188.24 [3440]E(f334(f334(f86(a1),x34401),a89),x34401) % 188.18/188.24 [3443]E(f334(f334(f23(a927),x34431),x34431),f2(a927)) % 188.18/188.24 [3447]E(f334(f85(a1),f334(f85(a1),x34471)),x34471) % 188.18/188.24 [3448]E(f334(f40(a927),f334(f307(a927),x34481)),x34481) % 188.18/188.24 [3460]E(f334(f334(f87(a927),f84(a927)),x34601),x34601) % 188.18/188.24 [3461]E(f334(f334(f87(a1),f84(a1)),x34611),x34611) % 188.18/188.24 [3462]E(f334(f334(f86(a927),f2(a927)),x34621),x34621) % 188.18/188.24 [3463]E(f334(f334(f86(a1),f2(a1)),x34631),x34631) % 188.18/188.24 [3464]E(f334(f334(f241(a927),f2(a927)),x34641),x34641) % 188.18/188.24 [3470]E(f334(f334(f23(a927),f2(a927)),x34701),f2(a927)) % 188.18/188.24 [3471]E(f334(f334(f87(a927),f2(a927)),x34711),f2(a927)) % 188.18/188.24 [3472]E(f334(f334(f41(a1),f2(a1)),x34721),f2(a1)) % 188.18/188.24 [3473]E(f334(f334(f246(a927),f2(a927)),x34731),f2(a927)) % 188.18/188.24 [3483]E(f135(x34831,f334(f85(a1),x34831)),f139(a1,x34831)) % 188.18/188.24 [3488]E(f334(f310(a927,f2(a927)),x34881),f334(f307(a927),x34881)) % 188.18/188.24 [3489]E(f334(f334(f87(a1),a104),x34891),f334(f85(a1),x34891)) % 188.18/188.24 [3497]E(f334(a112,f334(f111(a1),x34971)),f334(f111(a927),x34971)) % 188.18/188.24 [3498]E(f334(a20,f334(f111(a106),x34981)),f334(f111(a927),x34981)) % 188.18/188.24 [3499]E(f334(f40(a927),f334(f309(a927),x34991)),f334(a119,x34991)) % 188.18/188.24 [3508]E(f334(f334(f86(a927),f84(a927)),x35081),f334(a119,x35081)) % 188.18/188.24 [3512]E(f334(f110(a1),f334(f107(a1),x35121)),f334(f107(a1),x35121)) % 188.18/188.24 [3513]E(f334(f81(a1),f334(f107(a1),x35131)),f334(f107(a1),x35131)) % 188.18/188.24 [3517]E(f334(f40(x35171),f195(f935(x35171,a922))),f2(a927)) % 188.18/188.24 [3519]E(f334(f334(f41(a927),x35191),f334(a119,f2(a927))),x35191) % 188.18/188.24 [3529]E(f50(a927,x35291,f334(a119,f2(a927))),f2(a927)) % 188.18/188.24 [3530]E(f50(a1,x35301,f334(f111(a1),a104)),f2(a1)) % 188.18/188.24 [3544]E(f334(f334(f41(a1),x35441),f334(f111(a1),a104)),f334(f85(a1),x35441)) % 188.18/188.24 [3548]E(f146(a927,f334(f310(a927,x35481),f2(a927))),f120(a927)) % 188.18/188.24 [3549]E(f334(f334(f86(a1),x35491),f84(a1)),f334(f334(f23(a1),x35491),a104)) % 188.18/188.24 [3550]E(f334(f334(f23(a1),x35501),f84(a1)),f334(f334(f86(a1),x35501),a104)) % 188.18/188.24 [3554]P107(f334(f334(f242(a927),x35541),x35541)) % 188.18/188.24 [3555]P107(f334(f334(f242(a1),x35551),x35551)) % 188.18/188.24 [3560]E(f334(f85(a1),f334(f111(a1),x35601)),f334(f111(a1),f334(f85(a1),x35601))) % 188.18/188.24 [3561]P107(f334(f66(a927),f334(f309(a927),x35611))) % 188.18/188.24 [3562]P107(f334(f66(a927),f334(f307(a927),x35621))) % 188.18/188.24 [3569]E(f168(x35691,f250(f935(x35691,a922))),f250(f935(f928(x35691),a922))) % 188.18/188.24 [3574]P107(f334(f334(f242(a927),f2(a927)),x35741)) % 188.18/188.24 [3584]E(f334(f334(f86(a927),f118(x35841)),f334(a119,f2(a927))),f118(f334(a119,x35841))) % 188.18/188.24 [3585]E(f334(f270(x35851),f334(f16(a922,x35851),a247)),f195(f935(x35851,a922))) % 188.18/188.24 [3586]E(f334(f270(x35861),f334(f16(a922,x35861),a194)),f250(f935(x35861,a922))) % 188.18/188.24 [3590]E(f334(f334(f316(a927),x35901),f334(f307(a927),x35901)),f334(f307(a927),f334(a119,x35901))) % 188.18/188.24 [3602]E(f334(f334(f86(a1),f84(a1)),f334(f107(a1),x36021)),f334(f107(a1),f334(a119,x36021))) % 188.18/188.24 [3604]E(f334(f334(f158(f928(x36041)),f120(x36041)),f120(f928(x36041))),f59(x36041,f120(x36041))) % 188.18/188.24 [3624]E(f195(f935(f934(x36241,x36241),a922)),f271(x36241,f195(f935(x36241,a922)))) % 188.18/188.24 [3625]E(f334(f315(x36251),f250(f935(x36251,a922))),f250(f935(f935(x36251,a922),a922))) % 188.18/188.24 [3626]E(f334(f85(f935(x36261,a922)),f195(f935(x36261,a922))),f250(f935(x36261,a922))) % 188.18/188.24 [3627]E(f334(f85(f935(x36271,a922)),f250(f935(x36271,a922))),f195(f935(x36271,a922))) % 188.18/188.24 [3629]P107(f334(f66(x36291),f195(f935(x36291,a922)))) % 188.18/188.24 [3631]E(f334(f310(a927,x36311),f334(a119,x36311)),f334(f334(f316(a927),x36311),f195(f935(a927,a922)))) % 188.18/188.24 [3632]E(f91(f934(a927,a927),f53(x36321,f2(a927))),f334(f334(f260(a927,a927),f2(a927)),x36321)) % 188.18/188.24 [3645]E(f334(f334(f316(a927),f334(a119,x36451)),f334(f309(a927),x36451)),f334(f309(a927),f334(a119,x36451))) % 188.18/188.24 [3649]P39(x36491,f195(f935(f934(x36491,x36491),a922))) % 188.18/188.24 [3650]P41(x36501,f195(f935(f934(x36501,x36501),a922))) % 188.18/188.24 [3653]P107(f334(f334(f242(a1),f2(a1)),f334(f107(a1),x36531))) % 188.18/188.24 [3660]E(f334(f334(f86(a927),f334(f196(a927),x36601)),f334(a119,f2(a927))),f334(f196(a927),f334(a119,x36601))) % 188.18/188.24 [3763]P42(f334(f317(a927,a1,f107(a1)),x37631)) % 188.18/188.24 [3800]P55(x38001,f195(f935(x38001,a922)),f195(f935(f934(x38001,x38001),a922))) % 188.18/188.24 [3823]E(f334(f334(f260(a1,a1),f334(f111(a1),a104)),f334(f334(f23(a1),x38231),f84(a1))),f55(f334(f111(a1),a104),x38231)) % 188.18/188.24 [3876]P63(x38761,f334(f16(f935(x38761,a922),x38761),f334(f16(a922,x38761),a247))) % 188.18/188.24 [4077]P107(f334(f334(f336(f935(f934(a927,a927),a922)),f335(x40771)),a105)) % 188.18/188.24 [4101]P107(f334(f334(f336(f935(f934(a927,a927),a922)),f334(a115,x41011)),a105)) % 188.18/188.24 [4232]P27(x42321,f935(x42321,a922),f334(f334(f7(x42321,f935(x42321,a922),f935(x42321,a922)),f316(x42321)),f195(f935(x42321,a922))),f250(f935(x42321,a922))) % 188.18/188.24 [4767]~E(f334(a3,f334(a119,f334(a20,x47671))),f2(a106)) % 188.18/188.24 [4773]~P107(f334(a200,f334(f107(a1),x47731))) % 188.18/188.24 [4776]~P107(f334(f334(f243(a927),x47761),x47761)) % 188.18/188.24 [4786]~P107(f334(f334(f242(a927),f334(a119,x47861)),x47861)) % 188.18/188.24 [3576]E(f334(a112,f334(f85(a1),f334(f107(a1),x35761))),f2(a927)) % 188.18/188.24 [3579]E(f334(f334(f86(a1),f334(f85(a1),x35791)),x35791),f2(a1)) % 188.18/188.24 [3583]E(f334(f40(a1),f334(f310(a1,f2(a1)),x35831)),f334(a112,x35831)) % 188.18/188.24 [3595]E(f334(f334(f252(a927),f334(a119,f2(a927))),x35951),f334(a119,f2(a927))) % 188.18/188.24 [3692]E(f334(f289(x36921),f195(f935(f934(x36921,x36921),a922))),f195(f935(x36921,a922))) % 188.18/188.24 [3699]E(f43(f935(x36991,a922),f195(f935(f935(x36991,a922),a922))),f250(f935(x36991,a922))) % 188.18/188.24 [3700]E(f43(f935(x37001,a922),f250(f935(f935(x37001,a922),a922))),f195(f935(x37001,a922))) % 188.18/188.24 [3701]E(f42(f935(x37011,a922),f195(f935(f935(x37011,a922),a922))),f195(f935(x37011,a922))) % 188.18/188.24 [3702]E(f42(f935(x37021,a922),f250(f935(f935(x37021,a922),a922))),f250(f935(x37021,a922))) % 188.18/188.24 [3745]E(f334(f334(f316(f928(x37451)),f120(x37451)),f195(f935(f928(x37451),a922))),f168(x37451,f195(f935(x37451,a922)))) % 188.18/188.24 [3746]E(f334(f334(f316(f928(x37461)),f120(x37461)),f195(f935(f928(x37461),a922))),f169(x37461,f120(f935(x37461,a922)))) % 188.18/188.24 [3783]E(f334(f334(f86(a927),f4(x37831)),f334(a119,f2(a927))),f4(f334(a3,f334(a119,f334(a20,x37831))))) % 188.18/188.24 [3814]E(f334(f40(a1),f334(f317(a927,a1,f107(a1)),x38141)),f334(f40(a927),x38141)) % 188.18/188.24 [3815]P107(f334(f334(f242(a927),x38151),f334(f334(f87(a927),x38151),x38151))) % 188.18/188.24 [3854]E(f334(f317(a1,a927,a112),f311(a1,f2(a1),f334(f107(a1),x38541))),f334(f309(a927),x38541)) % 188.18/188.24 [3871]E(f334(f334(f41(a927),f334(a119,f2(a927))),f334(f111(a927),x38711)),f334(a112,f334(f334(f41(a1),f84(a1)),f334(f111(a1),x38711)))) % 188.18/188.24 [3873]E(f334(f179(a927),f146(a927,f334(f310(a927,f2(a927)),f334(a119,x38731)))),f334(f309(a927),x38731)) % 188.18/188.24 [3874]E(f334(f334(f86(a927),f334(f196(a106),x38741)),f334(a119,f2(a927))),f334(f196(a106),f334(a3,f334(a119,f334(a20,x38741))))) % 188.18/188.24 [3893]P41(x38931,f314(x38931,f195(f935(f934(x38931,x38931),a922)))) % 188.18/188.24 [3894]P54(x38941,f314(x38941,f195(f935(f934(x38941,x38941),a922)))) % 188.18/188.24 [3895]E(f334(f317(a1,a927,a112),f334(f317(a927,a1,f107(a1)),x38951)),x38951) % 188.18/188.24 [3926]E(f334(f334(f316(a927),f2(a927)),f334(f317(a927,a927,a119),f334(f307(a927),x39261))),f334(f307(a927),f334(a119,x39261))) % 188.18/188.24 [3932]P57(x39321,x39321,f314(x39321,f195(f935(f934(x39321,x39321),a922)))) % 188.18/188.24 [3938]P107(f334(a200,f334(f85(a1),f334(f107(a1),f334(a119,x39381))))) % 188.18/188.24 [3948]E(f334(f334(f23(f935(a927,a922)),f334(f290(a927),x39481)),f334(f334(f316(a927),x39481),f195(f935(a927,a922)))),f334(f290(a927),f334(a119,x39481))) % 188.18/188.24 [3974]E(f334(f334(f316(f935(x39741,a922)),f195(f935(x39741,a922))),f195(f935(f935(x39741,a922),a922))),f334(f315(x39741),f195(f935(x39741,a922)))) % 188.18/188.24 [4005]E(f334(f334(f23(f935(a927,a922)),f334(f308(a927),x40051)),f334(f334(f316(a927),f334(a119,x40051)),f195(f935(a927,a922)))),f334(f308(a927),f334(a119,x40051))) % 188.18/188.24 [4483]P16(x44831,f935(x44831,a922),f334(f334(f8(f935(x44831,a922),f935(f935(x44831,a922),f935(x44831,a922)),x44831),f334(f7(f935(x44831,a922),f935(x44831,a922),f935(x44831,a922)),f23(f935(x44831,a922)))),f334(f334(f7(x44831,f935(x44831,a922),f935(x44831,a922)),f316(x44831)),f195(f935(x44831,a922))))) % 188.18/188.24 [4570]E(f334(f270(f934(a1,a1)),f334(f265(a1,a1,a922),f334(f334(f8(f935(a1,a922),f935(a1,a922),a1),f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),x45701)))),f243(a1)))),f113(x45701)) % 188.18/188.24 [4609]E(f334(f270(f934(a1,a1)),f334(f265(a1,a1,a922),f334(f334(f18(a1,f935(a1,a922),f935(a1,a922)),f334(f334(f8(f935(a922,a922),f935(f935(a1,a922),f935(a1,a922)),a1),f8(a922,a922,a1)),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),x46091)))),f243(a1)))),f114(x46091)) % 188.18/188.24 [4672]E(f334(f270(f934(f935(x46721,a922),f935(x46721,a922))),f334(f265(f935(x46721,a922),f935(x46721,a922),a922),f334(f334(f7(f935(x46721,a922),f935(f935(x46721,a922),a922),f935(f935(x46721,a922),a922)),f334(f334(f8(f935(f935(x46721,a922),f935(a922,a922)),f935(f935(f935(x46721,a922),a922),f935(f935(x46721,a922),a922)),f935(x46721,a922)),f18(f935(x46721,a922),a922,a922)),f334(f334(f8(f935(f935(x46721,a922),a922),f935(f935(x46721,a922),f935(a922,a922)),f935(x46721,a922)),f334(f8(a922,f935(a922,a922),f935(x46721,a922)),a332)),f243(f935(x46721,a922))))),f66(x46721)))),f321(x46721)) % 188.18/188.24 [4790]~P107(f334(f66(f928(x47901)),f250(f935(f928(x47901),a922)))) % 188.18/188.24 [4800]~P107(f334(f334(f242(a1),f2(a1)),f334(f85(a1),f334(f107(a1),f334(a119,x48001))))) % 188.18/188.24 [3725]E(f334(f334(f23(a1),f334(f334(f86(a1),x37251),a104)),a104),x37251) % 188.18/188.24 [3738]E(f334(f179(a927),f146(a927,f334(f310(a927,f2(a927)),x37381))),f334(f307(a927),x37381)) % 188.18/188.24 [4033]E(f334(f293(x40331,x40331),f314(x40331,f195(f935(f934(x40331,x40331),a922)))),f314(x40331,f195(f935(f934(x40331,x40331),a922)))) % 188.18/188.24 [4078]P107(f334(f334(f242(a927),x40781),f334(f334(f87(a927),x40781),f334(f334(f87(a927),x40781),x40781)))) % 188.18/188.24 [4345]P107(f334(f66(a927),f334(f270(a927),f334(f334(f7(a927,a927,a922),f242(a927)),x43451)))) % 188.18/188.24 [4346]P107(f334(f66(a927),f334(f270(a927),f334(f334(f7(a927,a927,a922),f243(a927)),x43461)))) % 188.18/188.24 [4623]E(f334(f270(f934(x46231,x46231)),f334(f334(f8(f935(x46231,a922),a922,f934(x46231,x46231)),f92(x46231)),f334(f334(f7(f934(x46231,x46231),f935(x46231,f934(x46231,x46231)),f935(x46231,a922)),f334(f334(f8(f935(f934(x46231,x46231),a922),f935(f935(x46231,f934(x46231,x46231)),f935(x46231,a922)),f934(x46231,x46231)),f8(f934(x46231,x46231),a922,x46231)),a331)),f334(f334(f18(x46231,x46231,f934(x46231,x46231)),f260(x46231,x46231)),f5(x46231))))),f314(x46231,f195(f935(f934(x46231,x46231),a922)))) % 188.18/188.24 [4793]~E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x47931)),x47931),a89) % 188.18/188.24 [4794]~E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x47941)),x47941),f2(a1)) % 188.18/188.24 [4211]E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),a104),x42111))),f334(f334(f23(a1),a104),x42111)),f334(f334(f23(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x42111)),x42111))) % 188.18/188.24 [4326]E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f85(a1),x43261)),a104))),f334(f334(f86(a1),f334(f85(a1),x43261)),a104)),f334(f85(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x43261)),x43261))) % 188.18/188.24 [4398]E(f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x43981),f2(a927))),f195(f935(f934(a927,a927),a922))))),f334(f107(a1),x43981)) % 188.18/188.24 [4409]E(f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),f339(x44091)),f460(x44091))),f195(f935(f934(a927,a927),a922))))),x44091) % 188.18/188.24 [4415]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),a104),x44151))),f334(f334(f23(a1),a104),x44151))),a104),f334(f334(f23(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44151)),x44151))) % 188.18/188.24 [4447]E(f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x44471)),f334(f317(a927,a1,f107(a1)),f334(f270(a927),f334(f334(f8(a1,a922,a927),x44471),f107(a1))))) % 188.18/188.24 [4491]P42(f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x44911))) % 188.18/188.24 [4512]P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x45121),f195(f935(f934(a927,a927),a922)))),a77)) % 188.18/188.24 [4517]E(f334(f317(a1,a927,a112),f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),f334(f334(f8(a927,a922,a1),x45171),a112)))),f334(f270(a927),x45171)) % 188.18/188.24 [4688]E(f319(a927,f334(f334(f44(f934(a927,a927),f935(a927,a922)),f334(a115,x46881)),f334(f265(a927,a927,f935(a927,a922)),f334(f334(f7(a927,f935(a927,a922),f935(a927,f935(a927,a922))),f334(f334(f8(f935(a927,f935(f935(a927,a922),f935(a927,a922))),f935(f935(a927,a922),f935(a927,f935(a927,a922))),a927),f7(a927,f935(a927,a922),f935(a927,a922))),f334(f334(f8(f935(a927,a927),f935(a927,f935(f935(a927,a922),f935(a927,a922))),a927),f334(f8(a927,f935(f935(a927,a922),f935(a927,a922)),a927),f316(a927))),f23(a927)))),f195(f935(a927,a922)))))),f334(a112,x46881)) % 188.18/188.24 [4184]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x41841)),x41841)),a104),f334(f334(f86(a1),x41841),x41841)) % 188.18/188.24 [4432]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),x44321),a104))),f334(f334(f23(a1),x44321),a104))),a104),f334(f334(f23(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44321)),x44321)),a104)) % 188.18/188.24 [4803]~E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x48031)),x48031)),a104),a104) % 188.18/188.24 [4394]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x43941)),x43941)),a104)),f334(f334(f94(a927,a927),f334(f111(a927),x43941)),f334(f334(f18(a927,a927,a927),f86(a927)),f5(a927)))) % 188.18/188.24 [4400]E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),a104),x44001))),f334(f334(f23(a1),a104),x44001)),f334(f334(f23(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44001)),x44001)),a104))) % 188.18/188.24 [4430]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f85(a1),x44301))),f334(f85(a1),x44301))),a104),f334(f85(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44301)),x44301)),a104))) % 188.18/188.24 [4456]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),a89),x44561))),f334(f334(f23(a1),a89),x44561))),a104),f334(f334(f23(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44561)),x44561)),a104))) % 188.18/188.24 [4702]E(f334(a95,f334(f334(f44(f934(a927,a927),f935(f934(a927,a927),a922)),f334(a115,x47021)),f334(f265(a927,a927,f935(f934(a927,a927),a922)),f334(f334(f8(f935(a927,f935(f934(a927,a927),a922)),f935(a927,f935(f934(a927,a927),a922)),a927),f334(f8(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922),a927),f292(f934(a927,a927),f934(a927,a927),a116))),f334(f334(f7(a927,f935(f934(a927,a927),a922),f935(a927,f935(f934(a927,a927),a922))),f334(f334(f8(f935(a927,f935(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f935(f935(f934(a927,a927),a922),f935(a927,f935(f934(a927,a927),a922))),a927),f7(a927,f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f8(f935(a927,f934(a927,a927)),f935(a927,f935(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),a927),f334(f8(f934(a927,a927),f935(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),a927),f316(f934(a927,a927)))),f334(f7(a927,a927,f934(a927,a927)),f260(a927,a927))))),f195(f935(f934(a927,a927),a922))))))),f334(f85(a1),x47021)) % 188.18/188.24 [4459]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44591)),x44591)),a104)),a104),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),x44591),a104))),f334(f334(f86(a1),x44591),a104))) % 188.18/188.24 [4592]E(f334(f334(f86(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),x45921),f334(a119,f334(a119,f334(a119,x45921)))) % 188.18/188.24 [4632]E(f334(f334(f86(a927),x46321),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(a119,f334(a119,x46321))) % 188.18/188.24 [4633]E(f334(f334(f87(a927),x46331),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f86(a927),x46331),x46331)) % 188.18/188.24 [4634]E(f334(f334(f41(a927),f334(f334(f86(a927),x46341),x46341)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x46341) % 188.18/188.24 [4666]E(f50(a927,f334(a119,f334(a119,x46661)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f50(a927,x46661,f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.24 [4663]E(f334(f334(f86(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x46631),f334(a119,f334(a119,x46631))) % 188.18/188.24 [4664]E(f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x46641),f334(f334(f86(a927),x46641),x46641)) % 188.18/188.24 [4678]E(f334(f334(f41(a927),f334(a119,f334(a119,x46781))),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(a119,f334(f334(f41(a927),x46781),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.24 [4709]E(f334(f265(a1,a1,f934(a1,a1)),f334(f334(f18(a1,f935(a1,f934(a1,a1)),f935(a1,f934(a1,a1))),f334(f334(f8(f935(a1,f935(f934(a1,a1),f934(a1,a1))),f935(f935(a1,f934(a1,a1)),f935(a1,f934(a1,a1))),a1),f18(a1,f934(a1,a1),f934(a1,a1))),f334(f334(f8(f935(a1,f934(a1,a1)),f935(a1,f935(f934(a1,a1),f934(a1,a1))),a1),f334(f18(a1,f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),f334(f334(f8(a922,f935(f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),a1),f103(f934(a1,a1))),f334(f334(f8(a1,a922,a1),f334(f242(a1),f2(a1))),f334(f334(f7(a1,a1,a1),f23(a1)),x47091))))),f334(f334(f7(a1,f935(a1,a1),f935(a1,f934(a1,a1))),f334(f334(f8(f935(a1,f934(a1,a1)),f935(f935(a1,a1),f935(a1,f934(a1,a1))),a1),f8(a1,f934(a1,a1),a1)),f334(f334(f8(a1,f935(a1,f934(a1,a1)),a1),f260(a1,a1)),f334(f334(f7(a1,a1,a1),f334(f334(f8(a1,f935(a1,a1),a1),f86(a1)),f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f84(a1))))),f334(f334(f7(a1,a1,a1),f23(a1)),x47091))))),f334(f334(f8(a1,f935(a1,f934(a1,a1)),a1),f260(a1,a1)),f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))))),f48(x47091)) % 188.18/188.24 [3401]P106(f933(x34011,x34012)) % 188.18/188.24 [3402]P106(f934(x34021,x34022)) % 188.18/188.24 [3403]P106(f932(x34031,x34032)) % 188.18/188.24 [3421]P15(a1,f185(x34211,x34212)) % 188.18/188.24 [3422]P39(x34221,f160(x34221,x34222)) % 188.18/188.24 [3423]P40(x34231,f271(x34231,x34232)) % 188.18/188.24 [3424]P40(x34241,f314(x34241,x34242)) % 188.18/188.24 [3425]P41(x34251,f271(x34251,x34252)) % 188.18/188.24 [3426]P54(x34261,f271(x34261,x34262)) % 188.18/188.24 [3490]P33(x34901,x34902,f120(x34901)) % 188.18/188.24 [3523]P55(x35231,x35232,f271(x35231,x35232)) % 188.18/188.24 [3524]P57(x35241,x35241,f271(x35241,x35242)) % 188.18/188.24 [3786]P27(x37861,x37861,f5(x37861),x37862) % 188.18/188.24 [3787]P27(x37871,x37871,f32(x37871),x37872) % 188.18/188.24 [3796]P34(x37961,x37962,f120(x37961),f120(x37961)) % 188.18/188.24 [3804]P27(f928(x38041),f928(x38041),f175(x38041),x38042) % 188.18/188.24 [4209]P28(x42091,x42091,f32(x42091),x42092,x42092) % 188.18/188.24 [4715]~E(f34(x47151),f33(x47152)) % 188.18/188.24 [4721]~E(f31(x47211,x47212),a25) % 188.18/188.24 [4722]~E(f26(x47221,x47222),a25) % 188.18/188.24 [4723]~E(f30(x47231,x47232),a25) % 188.18/188.24 [4750]~P35(x47501,x47502,f120(x47501)) % 188.18/188.24 [4751]~P37(x47511,x47512,f120(x47511)) % 188.18/188.24 [3385]E(f334(f270(x33851),x33852),x33852) % 188.18/188.24 [3386]E(f334(f5(x33861),x33862),x33862) % 188.18/188.24 [3388]E(f334(f32(x33881),x33882),x33882) % 188.18/188.24 [3398]E(f334(f198(x33981),x33982),f122(x33981)) % 188.18/188.24 [3408]E(f29(f26(x34081,x34082)),f2(a927)) % 188.18/188.24 [3419]E(f91(x34191,f334(a331,x34192)),x34192) % 188.18/188.24 [3420]E(f96(x34201,f334(a331,x34202)),x34202) % 188.18/188.24 [3441]E(f334(f196(a924),f26(x34411,x34412)),f2(a927)) % 188.18/188.24 [3442]E(f334(f132(x34421,x34422),f126(x34421)),f2(a927)) % 188.18/188.24 [3445]E(f334(f143(x34451,x34452),f120(x34451)),f120(x34451)) % 188.18/188.24 [3466]E(f314(x34661,f314(x34661,x34662)),f314(x34661,x34662)) % 188.18/188.24 [3467]E(f159(x34671,f159(x34671,x34672)),f159(x34671,x34672)) % 188.18/188.24 [3485]E(f334(f334(f141(x34851),x34852),f120(x34851)),x34852) % 188.18/188.24 [3491]E(f180(x34911,x34912,f120(x34911)),x34912) % 188.18/188.24 [3492]E(f180(x34921,f120(x34921),x34922),x34922) % 188.18/188.24 [3493]E(f123(x34931,f126(x34931),x34932),x34932) % 188.18/188.24 [3494]E(f176(x34941,f2(a927),x34942),f120(x34941)) % 188.18/188.24 [3500]E(f334(f334(f182(x35001),x35002),f120(x35001)),f120(x35001)) % 188.18/188.24 [3501]E(f334(f334(f145(x35011),x35012),f120(x35011)),f120(x35011)) % 188.18/188.24 [3503]E(f162(x35031,x35032,f120(x35031)),f2(a927)) % 188.18/188.24 [3505]E(f177(x35051,x35052,f120(x35051)),f120(x35051)) % 188.18/188.24 [3506]E(f184(x35061,x35062,f120(x35061)),f120(x35061)) % 188.18/188.24 [3507]E(f183(x35071,f120(x35071),x35072),f120(x35071)) % 188.18/188.24 [3511]E(f334(f179(x35111),f159(x35111,x35112)),f334(f179(x35111),x35112)) % 188.18/188.24 [3514]E(f334(f291(x35141,x35141),f271(x35141,x35142)),x35142) % 188.18/188.24 [3515]E(f334(f272(x35151,x35151),f271(x35151,x35152)),x35152) % 188.18/188.24 [3522]E(f334(f293(x35221,x35221),f271(x35221,x35222)),f271(x35221,x35222)) % 188.18/188.24 [3536]E(f314(f928(x35361),f164(x35361,x35362)),f165(x35361,f314(x35361,x35362))) % 188.18/188.24 [3538]P107(f334(f144(a1),f185(x35381,x35382))) % 188.18/188.24 [3546]E(f334(f291(x35461,x35461),f314(x35461,x35462)),f250(f935(x35461,a922))) % 188.18/188.24 [3547]E(f334(f272(x35471,x35471),f314(x35471,x35472)),f250(f935(x35471,a922))) % 188.18/188.24 [3551]P107(f334(f144(x35511),f159(x35511,x35512))) % 188.18/188.24 [3553]P107(f334(f167(x35531,x35532),f120(x35531))) % 188.18/188.24 [3558]E(f334(f179(a1),f185(x35581,x35582)),f311(a1,x35581,x35582)) % 188.18/188.24 [3572]P58(x35721,f195(f935(x35721,a922)),x35722) % 188.18/188.24 [3577]E(f334(f264(a1,a1),f51(x35771,x35772)),f50(a1,x35771,x35772)) % 188.18/188.24 [3578]E(f334(f310(a927,x35781),f334(a119,x35782)),f311(a927,x35781,x35782)) % 188.18/188.24 [3594]E(f334(f334(f158(x35941),x35942),f120(x35941)),f147(x35941,x35942,f120(x35941))) % 188.18/188.24 [3606]E(f311(a927,f334(a119,x36061),x36062),f312(a927,x36061,x36062)) % 188.18/188.24 [3609]P55(x36091,f250(f935(x36091,a922)),f314(x36091,x36092)) % 188.18/188.24 [3672]E(f334(f334(f23(a927),x36721),f334(a119,x36722)),f334(f40(a927),f313(a927,x36722,x36721))) % 188.18/188.24 [3726]E(f173(x37261,x37262,f120(x37261)),f334(f334(f260(f928(x37261),f928(x37261)),f120(x37261)),f120(x37261))) % 188.18/188.24 [3743]E(f334(f265(x37431,x37432,f934(x37431,x37432)),f260(x37431,x37432)),f32(f934(x37431,x37432))) % 188.18/188.24 [3747]P107(f334(f334(f336(f928(x37471)),f120(x37471)),f168(x37471,x37472))) % 188.18/188.24 [3748]E(f334(f196(f928(x37481)),f121(x37481,x37482)),f334(f334(f23(a927),f334(f196(f928(x37481)),x37482)),f84(a927))) % 188.18/188.24 [3757]P107(f334(f66(a927),f313(a927,x37571,x37572))) % 188.18/188.24 [3758]P107(f334(f66(a927),f312(a927,x37581,x37582))) % 188.18/188.24 [3759]P107(f334(f66(a927),f311(a927,x37591,x37592))) % 188.18/188.24 [3760]P107(f334(f66(a1),f313(a1,x37601,x37602))) % 188.18/188.24 [3761]P107(f334(f66(a1),f312(a1,x37611,x37612))) % 188.18/188.24 [3762]P107(f334(f66(a1),f311(a1,x37621,x37622))) % 188.18/188.24 [3870]E(f334(f317(a927,a927,a119),f311(a927,x38701,x38702)),f311(a927,f334(a119,x38701),f334(a119,x38702))) % 188.18/188.24 [3889]E(f334(f334(f295(x38891,x38891,x38891),f314(x38891,x38892)),f314(x38891,x38892)),f314(x38891,x38892)) % 188.18/188.24 [3924]E(f334(f334(f260(a1,a1),f334(f334(f41(a1),x39241),x39242)),f50(a1,x39241,x39242)),f51(x39241,x39242)) % 188.18/188.24 [3925]E(f334(f334(f260(a106,a106),f334(f334(f41(a106),x39251),x39252)),f50(a106,x39251,x39252)),f21(x39251,x39252)) % 188.18/188.24 [3952]E(f334(f334(f260(a927,a927),f334(f334(f41(a927),x39521),x39522)),f50(a927,x39521,x39522)),f91(f934(a927,a927),f53(x39521,x39522))) % 188.18/188.24 [3997]P107(f334(f334(f243(a927),f334(f334(f23(a927),x39971),x39972)),f334(a119,x39971))) % 188.18/188.24 [4051]P40(x40511,f334(f334(f295(x40511,x40511,x40511),x40512),f314(x40511,x40512))) % 188.18/188.24 [4100]E(f334(f334(f86(a1),f334(f334(f87(a1),x41001),f334(f334(f41(a1),x41002),x41001))),f50(a1,x41002,x41001)),x41002) % 188.18/188.24 [4104]E(f334(f334(f44(a927,f935(f934(f928(x41041),f928(x41041)),a922)),f250(f935(a927,a922))),f150(x41041,x41042)),f152(x41041,x41042)) % 188.18/188.24 [4322]P107(f334(f334(f336(f934(f928(x43221),f928(x43221))),f334(f334(f260(f928(x43221),f928(x43221)),f120(x43221)),f120(x43221))),f165(x43221,x43222))) % 188.18/188.24 [4427]E(f261(x44271,x44271,x44271,a331,f261(x44271,x44271,x44271,x44272,a331)),x44272) % 188.18/188.24 [4477]E(f266(x44771,x44771,x44772,x44772,f5(x44771),f5(x44772)),f32(f934(x44771,x44772))) % 188.18/188.24 [4479]E(f266(x44791,x44791,x44792,x44792,f32(x44791),f32(x44792)),f32(f934(x44791,x44792))) % 188.18/188.24 [3484]E(f334(f175(x34841),f334(f175(x34841),x34842)),x34842) % 188.18/188.24 [3486]E(f334(f334(f145(x34861),f2(a927)),x34862),x34862) % 188.18/188.24 [3502]E(f334(f334(f182(x35021),f2(a927)),x35022),f120(x35021)) % 188.18/188.24 [3509]E(f334(f334(f141(x35091),f120(x35091)),x35092),x35092) % 188.18/188.24 [3518]E(f42(f935(x35181,a922),f334(f315(x35181),x35182)),x35182) % 188.18/188.24 [3520]E(f334(f179(x35201),f334(f174(x35201),x35202)),f334(f179(x35201),x35202)) % 188.18/188.24 [3521]E(f334(f179(x35211),f334(f175(x35211),x35212)),f334(f179(x35211),x35212)) % 188.18/188.24 [3527]E(f334(f334(f23(a106),x35271),x35272),f334(f334(a24,x35271),x35272)) % 188.18/188.24 [3540]E(f334(f334(f87(a927),x35401),x35402),f334(f334(f87(a927),x35402),x35401)) % 188.18/188.24 [3541]E(f334(f334(f87(a1),x35411),x35412),f334(f334(f87(a1),x35412),x35411)) % 188.18/188.24 [3542]E(f334(f334(f86(a927),x35421),x35422),f334(f334(f86(a927),x35422),x35421)) % 188.18/188.24 [3543]E(f334(f334(f86(a1),x35431),x35432),f334(f334(f86(a1),x35432),x35431)) % 188.18/188.24 [3564]E(f334(f334(f190(x35641,x35641),f2(a927)),x35642),f32(x35641)) % 188.18/188.24 [3565]E(f334(f196(f928(x35651)),f334(f174(x35651),x35652)),f334(f196(f928(x35651)),x35652)) % 188.18/188.24 [3566]E(f334(f196(f928(x35661)),f334(f175(x35661),x35662)),f334(f196(f928(x35661)),x35662)) % 188.18/188.24 [3567]E(f183(x35671,x35672,f195(f935(a927,a922))),f120(x35671)) % 188.18/188.24 [3568]E(f334(f334(f161(x35681,x35681),f5(x35681)),x35682),x35682) % 188.18/188.24 [3570]E(f334(f259(a1,a1),f51(x35701,x35702)),f334(f334(f41(a1),x35701),x35702)) % 188.18/188.24 [3587]E(f334(f196(f928(x35871)),f159(x35871,x35872)),f334(f40(x35871),f334(f179(x35871),x35872))) % 188.18/188.24 [3588]E(f29(f30(x35881,x35882)),f334(f334(f86(a927),f29(x35882)),f334(a119,f2(a927)))) % 188.18/188.24 [3589]E(f334(f289(x35891),f334(f293(x35891,x35891),x35892)),f334(f289(x35891),x35892)) % 188.18/188.24 [3593]P107(f334(f66(x35931),f334(f179(x35931),x35932))) % 188.18/188.24 [3601]E(f334(f334(f86(a1),x36011),f334(f85(a1),x36012)),f334(f334(f23(a1),x36011),x36012)) % 188.18/188.24 [3608]P26(x36081,x36082,f195(f935(f926(x36081),a922))) % 188.18/188.24 [3610]E(f334(f317(x36101,x36101,f5(x36101)),x36102),x36102) % 188.18/188.24 [3611]E(f334(f317(x36111,x36111,f32(x36111)),x36112),x36112) % 188.18/188.24 [3612]E(f334(f318(x36121,x36121,f5(x36121)),x36122),x36122) % 188.18/188.24 [3613]E(f334(f318(x36131,x36131,f32(x36131)),x36132),x36132) % 188.18/188.24 [3614]P107(f334(f250(f935(x36141,a922)),x36142)) % 188.18/188.24 [3616]E(f334(f40(a927),f334(f310(a927,x36161),x36162)),f334(f334(f23(a927),x36162),x36161)) % 188.18/188.24 [3617]E(f334(f310(a927,f334(a119,x36171)),x36172),f313(a927,x36171,x36172)) % 188.18/188.24 [3630]E(f334(f334(f316(x36301),x36302),f195(f935(x36301,a922))),f334(f270(x36301),f334(a331,x36302))) % 188.18/188.24 [3635]E(f314(x36351,f334(f293(x36351,x36351),x36352)),f334(f293(x36351,x36351),f314(x36351,x36352))) % 188.18/188.24 [3640]E(f334(f334(f86(a927),f334(a119,x36401)),x36402),f334(f334(f86(a927),x36401),f334(a119,x36402))) % 188.18/188.24 [3641]E(f334(f334(f23(a927),f334(a119,x36411)),f334(a119,x36412)),f334(f334(f23(a927),x36411),x36412)) % 188.18/188.24 [3647]E(f60(x36471,f2(a927),x36472),f334(f334(f158(f928(x36471)),f120(x36471)),f120(f928(x36471)))) % 188.18/188.24 [3648]E(f334(f40(a927),f312(a927,x36481,x36482)),f334(f334(f23(a927),x36482),x36481)) % 188.18/188.24 [3657]P39(x36571,f334(f334(f294(a927,x36571),a248),x36572)) % 188.18/188.24 [3659]P15(a927,f146(a927,f334(f310(a927,x36591),x36592))) % 188.18/188.24 [3661]P107(f334(f66(a927),f334(f310(a927,x36611),x36612))) % 188.18/188.24 [3662]P107(f334(f66(a1),f334(f310(a1,x36621),x36622))) % 188.18/188.24 [3665]E(f334(f293(f928(x36651),f928(x36651)),f164(x36651,x36652)),f164(x36651,f334(f293(x36651,x36651),x36652))) % 188.18/188.24 [3666]E(f334(f196(a924),f30(x36661,x36662)),f334(f334(f86(a927),f334(f196(a924),x36662)),f334(a119,f2(a927)))) % 188.18/188.24 [3668]E(f334(f310(a1,x36681),f334(f334(f86(a1),x36682),f84(a1))),f311(a1,x36681,x36682)) % 188.18/188.24 [3671]E(f334(f334(f41(a1),f334(f85(a1),x36711)),f334(f85(a1),x36712)),f334(f334(f41(a1),x36711),x36712)) % 188.18/188.24 [3679]E(f334(f334(f190(f934(x36791,x36791),a922),f84(a927)),x36792),x36792) % 188.18/188.24 [3681]E(f334(f334(f23(f935(x36811,a922)),x36812),f195(f935(x36811,a922))),x36812) % 188.18/188.24 [3682]E(f334(f334(f108(f935(x36821,a922)),x36822),f195(f935(x36821,a922))),x36822) % 188.18/188.24 [3683]E(f334(f334(f109(f935(x36831,a922)),x36832),f250(f935(x36831,a922))),x36832) % 188.18/188.24 [3684]E(f334(f259(a927,a927),f91(f934(a927,a927),f53(x36841,x36842))),f334(f334(f41(a927),x36841),x36842)) % 188.18/188.24 [3691]E(f311(a1,f334(f334(f86(a1),x36911),f84(a1)),x36912),f312(a1,x36911,x36912)) % 188.18/188.24 [3696]E(f334(f264(a927,a927),f91(f934(a927,a927),f53(x36961,x36962))),f50(a927,x36961,x36962)) % 188.18/188.24 [3705]P107(f334(f334(f336(x37051),x37052),f250(f935(x37051,a922)))) % 188.18/188.24 [3709]E(f334(f334(f23(a927),f334(a119,x37091)),x37092),f334(f40(a927),f311(a927,x37092,x37091))) % 188.18/188.24 [3734]E(f334(f334(f23(f935(x37341,a922)),x37342),f250(f935(x37341,a922))),f195(f935(x37341,a922))) % 188.18/188.24 [3735]E(f334(f334(f108(f935(x37351,a922)),x37352),f250(f935(x37351,a922))),f250(f935(x37351,a922))) % 188.18/188.24 [3736]E(f334(f334(f109(f935(x37361,a922)),x37362),f195(f935(x37361,a922))),f195(f935(x37361,a922))) % 188.18/188.24 [3751]E(f50(a1,f334(f85(a1),x37511),f334(f85(a1),x37512)),f334(f85(a1),f50(a1,x37511,x37512))) % 188.18/188.24 [3752]E(f50(a1,f334(f107(a1),x37521),f334(f107(a1),x37522)),f334(f107(a1),f50(a927,x37521,x37522))) % 188.18/188.24 [3764]E(f334(f196(f928(x37641)),f334(f178(x37641),x37642)),f334(f334(f23(a927),f334(f196(f928(x37641)),x37642)),f84(a927))) % 188.18/188.24 [3788]E(f334(f334(f41(a1),f50(a1,x37881,x37882)),x37882),f2(a1)) % 188.18/188.24 [3798]E(f334(a3,f50(a927,f334(a20,x37981),f334(a20,x37982))),f50(a106,x37981,x37982)) % 188.18/188.24 [3837]E(f334(a3,f334(f334(f23(a927),f334(a20,x38371)),f334(a20,x38372))),f334(f334(f23(a106),x38371),x38372)) % 188.18/188.24 [3838]E(f334(a3,f334(f334(f87(a927),f334(a20,x38381)),f334(a20,x38382))),f334(f334(f87(a106),x38381),x38382)) % 188.18/188.24 [3839]E(f334(a3,f334(f334(f86(a927),f334(a20,x38391)),f334(a20,x38392))),f334(f334(f86(a106),x38391),x38392)) % 188.18/188.24 [3840]E(f334(a3,f334(f334(f41(a927),f334(a20,x38401)),f334(a20,x38402))),f334(f334(f41(a106),x38401),x38402)) % 188.18/188.24 [3848]E(f334(f317(a927,a927,a119),f334(f310(a927,x38481),x38482)),f334(f310(a927,f334(a119,x38481)),f334(a119,x38482))) % 188.18/188.24 [3875]P107(f334(f53(x38751,x38752),f91(f934(a927,a927),f53(x38751,x38752)))) % 188.18/188.24 [3898]E(f334(f334(f86(a927),f334(f334(f86(a927),f29(x38981)),f29(x38982))),f334(a119,f2(a927))),f29(f31(x38981,x38982))) % 188.18/188.24 [3899]E(f50(a927,f334(a119,f50(a927,x38991,x38992)),x38992),f50(a927,f334(a119,x38991),x38992)) % 188.18/188.24 [3911]E(f334(f334(f45(f935(x39111,a922),f935(x39111,a922)),x39112),f5(f935(x39111,a922))),f43(f935(x39111,a922),x39112)) % 188.18/188.24 [3912]E(f334(f334(f44(f935(x39121,a922),f935(x39121,a922)),x39122),f5(f935(x39121,a922))),f42(f935(x39121,a922),x39122)) % 188.18/188.24 [3913]E(f334(f317(f928(x39131),f935(x39131,a922),f179(x39131)),f334(f179(f928(x39131)),f59(x39131,x39132))),f334(f315(x39131),f334(f179(x39131),x39132))) % 188.18/188.24 [3917]P107(f334(f334(f336(f935(x39171,a922)),x39172),f334(f315(x39171),x39172))) % 188.18/188.24 [3923]E(f50(a1,f334(f85(a1),f50(a1,x39231,x39232)),x39232),f50(a1,f334(f85(a1),x39231),x39232)) % 188.18/188.24 [3934]P107(f334(f334(f242(f935(x39341,a922)),x39342),f250(f935(x39341,a922)))) % 188.18/188.24 [3936]E(f334(f334(f295(x39361,x39361,x39361),f314(x39361,x39362)),f314(x39361,f314(x39361,x39362))),f314(x39361,x39362)) % 188.18/188.24 [3937]E(f334(f334(f108(f935(x39371,a922)),f334(f272(x39371,x39371),x39372)),f334(f291(x39371,x39371),x39372)),f334(f289(x39371),x39372)) % 188.18/188.24 [3958]E(f320(x39581,x39582,f250(f935(x39581,a922)),f250(f935(x39582,a922))),f250(f935(f933(x39581,x39582),a922))) % 188.18/188.24 [4006]P107(f334(f334(f242(a927),f50(a927,x40061,x40062)),x40061)) % 188.18/188.24 [4031]P107(f334(f334(f242(a1),f334(f85(a1),f334(f107(a1),x40311))),f334(f107(a1),x40312))) % 188.18/188.24 [4056]P107(f334(f334(f336(f935(x40561,a922)),f195(f935(x40561,a922))),f334(f315(x40561),x40562))) % 188.18/188.24 [4061]E(f314(x40611,f334(f334(f295(x40611,x40611,x40611),x40612),f314(x40611,x40612))),f314(x40611,x40612)) % 188.18/188.24 [4064]E(f334(f334(f295(x40641,x40641,x40641),f314(x40641,x40642)),x40642),f334(f334(f295(x40641,x40641,x40641),x40642),f314(x40641,x40642))) % 188.18/188.24 [4066]E(f334(a112,f334(f334(f86(a1),f334(f334(f23(a1),x40661),x40662)),f84(a1))),f334(f40(a1),f311(a1,x40662,x40661))) % 188.18/188.24 [4079]E(f334(f291(x40791,x40791),f334(f334(f295(x40791,x40791,x40791),x40792),f314(x40791,x40792))),f334(f291(x40791,x40791),x40792)) % 188.18/188.24 [4080]E(f334(f272(x40801,x40801),f334(f334(f295(x40801,x40801,x40801),x40802),f314(x40801,x40802))),f334(f272(x40801,x40801),x40802)) % 188.18/188.24 [4096]E(f334(f334(f86(a927),f334(f334(f86(a927),f334(f196(a924),x40961)),f334(f196(a924),x40962))),f334(a119,f2(a927))),f334(f196(a924),f31(x40961,x40962))) % 188.18/188.24 [4099]E(f334(f149(f928(x40991),f928(x40991),f141(x40991),f120(x40991)),f176(f928(x40991),x40992,f120(x40991))),f120(x40991)) % 188.18/188.24 [4108]P27(a927,a927,f334(f334(f7(a927,a927,a927),f86(a927)),x41081),x41082) % 188.18/188.24 [4110]P15(a927,f334(f175(a927),f334(f334(f161(f928(x41101),a927),f196(f928(x41101))),f186(x41101,x41102)))) % 188.18/188.24 [4140]P54(x41401,f334(f334(f108(f935(f934(x41401,x41401),a922)),x41402),f334(f293(x41401,x41401),x41402))) % 188.18/188.24 [4141]P54(x41411,f334(f334(f109(f935(f934(x41411,x41411),a922)),x41412),f334(f293(x41411,x41411),x41412))) % 188.18/188.24 [4152]P107(f334(f334(f243(a1),f334(f85(a1),f334(f107(a1),f334(a119,x41521)))),f334(f107(a1),x41522))) % 188.18/188.24 [4198]E(f334(f149(f928(x41981),x41981,f334(f7(x41981,f928(x41981),f928(x41981)),f158(x41981)),f120(x41981)),x41982),f334(f175(x41981),x41982)) % 188.18/188.24 [4246]P107(f334(f334(f242(f935(f934(f928(x42461),f928(x42461)),a922)),f165(x42461,x42462)),f314(f928(x42461),f164(x42461,x42462)))) % 188.18/188.24 [4274]P107(f334(f53(x42741,x42742),f334(f334(f260(a927,a927),f334(f334(f41(a927),x42741),x42742)),f50(a927,x42741,x42742)))) % 188.18/188.24 [4286]P107(f334(f334(f242(f935(f934(f928(x42861),f928(x42861)),a922)),f164(x42861,f314(x42861,x42862))),f314(f928(x42861),f164(x42861,x42862)))) % 188.18/188.24 [4503]E(f334(f334(f267(f934(a106,a106),a106,f934(a106,a106),f934(x45031,f934(a106,a106))),f275(f334(f172(a106),f334(f334(f161(f934(a106,x45031),a106),f259(a106,x45031)),x45032)))),f334(f334(f8(x45031,f935(f934(a106,a106),f934(x45031,f934(a106,a106))),a106),f260(x45031,f934(a106,a106))),f276(x45031,x45032))),f274(x45031,x45032)) % 188.18/188.24 [4579]E(f232(a927,f934(x45791,f929(x45791)),f2(a927),f334(f265(x45791,f929(x45791),a927),f334(f16(f935(f929(x45791),a927),x45791),f334(f334(f7(f929(x45791),a927,a927),f334(f334(f8(a927,f935(a927,a927),f929(x45791)),f86(a927)),f196(f929(x45791)))),f84(a927)))),f334(f142(x45791),x45792)),f334(f196(f929(x45791)),x45792)) % 188.18/188.24 [4701]E(f334(f265(f935(f934(x47011,x47011),a922),f935(f934(x47011,x47011),a922),f935(f935(x47012,x47011),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922)))),f334(f334(f7(f935(f934(x47011,x47011),a922),f935(f935(f934(x47011,x47011),a922),f935(f935(x47012,x47011),f935(f934(x47012,x47012),a922))),f935(f935(f934(x47011,x47011),a922),f935(f935(x47012,x47011),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922))))),f334(f334(f8(f935(f935(f935(x47012,x47011),f935(f934(x47012,x47012),a922)),f935(f935(x47012,x47011),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922)))),f935(f935(f935(f934(x47011,x47011),a922),f935(f935(x47012,x47011),f935(f934(x47012,x47012),a922))),f935(f935(f934(x47011,x47011),a922),f935(f935(x47012,x47011),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922))))),f935(f934(x47011,x47011),a922)),f8(f935(f935(x47012,x47011),f935(f934(x47012,x47012),a922)),f935(f935(x47012,x47011),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922))),f935(f934(x47011,x47011),a922))),f334(f334(f8(f935(f935(x47012,x47011),f935(f935(f934(x47012,x47012),a922),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922)))),f935(f935(f935(x47012,x47011),f935(f934(x47012,x47012),a922)),f935(f935(x47012,x47011),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922)))),f935(f934(x47011,x47011),a922)),f18(f935(x47012,x47011),f935(f934(x47012,x47012),a922),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922)))),f334(f334(f8(f935(f935(x47012,x47011),f935(f934(x47012,x47012),a922)),f935(f935(x47012,x47011),f935(f935(f934(x47012,x47012),a922),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922)))),f935(f934(x47011,x47011),a922)),f334(f8(f935(f934(x47012,x47012),a922),f935(f935(f934(x47012,x47012),a922),f934(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922))),f935(x47012,x47011)),f260(f935(f934(x47012,x47012),a922),f935(f934(x47012,x47012),a922)))),f294(x47011,x47012))))),f294(x47011,x47012))),f79(x47011,x47012)) % 188.18/188.24 [4774]~E(f334(f315(x47741),x47742),f195(f935(f935(x47741,a922),a922))) % 188.18/188.24 [4785]~P107(f334(f334(f179(x47851),f120(x47851)),x47852)) % 188.18/188.24 [4789]~P107(f334(f334(f336(x47891),x47892),f195(f935(x47891,a922)))) % 188.18/188.24 [4795]~P107(f334(f334(f243(f935(x47951,a922)),x47952),f195(f935(x47951,a922)))) % 188.18/188.24 [3619]E(f334(f334(f23(a927),x36191),f334(f334(f86(a927),x36191),x36192)),f2(a927)) % 188.18/188.24 [3622]E(f334(f334(f108(f935(x36221,a922)),x36222),x36222),x36222) % 188.18/188.24 [3623]E(f334(f334(f109(f935(x36231,a922)),x36232),x36232),x36232) % 188.18/188.24 [3651]E(f334(f334(f23(f935(x36511,a922)),x36512),x36512),f195(f935(x36511,a922))) % 188.18/188.24 [3654]E(f334(f150(x36541,x36542),f2(a927)),f195(f935(f934(f928(x36541),f928(x36541)),a922))) % 188.18/188.24 [3655]E(f334(f334(f86(a927),x36551),f334(a119,x36552)),f334(a119,f334(f334(f86(a927),x36551),x36552))) % 188.18/188.24 [3667]E(f201(f334(f107(a1),x36671),f334(f107(a1),x36672)),f334(f107(a1),f334(f334(f23(a927),x36671),x36672))) % 188.18/188.24 [3670]E(f334(f334(f41(a1),f334(f85(a1),x36701)),x36702),f334(f334(f41(a1),x36701),f334(f85(a1),x36702))) % 188.18/188.24 [3674]E(f334(f40(a1),f334(f310(a1,x36741),x36742)),f334(a112,f334(f334(f23(a1),x36742),x36741))) % 188.18/188.24 [3677]E(f334(f334(f86(a927),f334(a119,x36771)),x36772),f334(a119,f334(f334(f86(a927),x36771),x36772))) % 188.18/188.24 [3680]E(f334(f85(f935(x36801,a922)),f334(f85(f935(x36801,a922)),x36802)),x36802) % 188.18/188.24 [3693]E(f186(x36931,f334(f334(f158(f928(x36931)),f120(x36931)),x36932)),f186(x36931,x36932)) % 188.18/188.24 [3697]E(f334(f334(f86(a927),x36971),f334(f334(f87(a927),x36971),x36972)),f334(f334(f87(a927),x36971),f334(a119,x36972))) % 188.18/188.24 [3703]E(f334(f334(a24,f334(a3,x37031)),f334(a3,x37032)),f334(a3,f334(f334(f23(a927),x37031),x37032))) % 188.18/188.24 [3717]E(f334(f334(f87(a1),f334(f85(a1),x37171)),x37172),f334(f85(a1),f334(f334(f87(a1),x37171),x37172))) % 188.18/188.24 [3719]E(f334(f334(f252(a1),f334(f107(a1),x37191)),x37192),f334(f107(a1),f334(f334(f252(a927),x37191),x37192))) % 188.18/188.24 [3720]E(f334(f334(f87(a106),f334(a3,x37201)),f334(a3,x37202)),f334(a3,f334(f334(f87(a927),x37201),x37202))) % 188.18/188.24 [3721]E(f334(f334(f86(a106),f334(a3,x37211)),f334(a3,x37212)),f334(a3,f334(f334(f86(a927),x37211),x37212))) % 188.18/188.24 [3722]E(f334(f334(f246(a927),f334(a119,x37221)),f334(a119,x37222)),f334(a119,f334(f334(f246(a927),x37221),x37222))) % 188.18/188.24 [3723]E(f334(f334(f241(a927),f334(a119,x37231)),f334(a119,x37232)),f334(a119,f334(f334(f241(a927),x37231),x37232))) % 188.18/188.24 [3728]E(f334(f179(a927),f146(a927,f334(f310(a927,x37281),x37282))),f334(f310(a927,x37281),x37282)) % 188.18/188.24 [3729]E(f319(x37291,f334(f334(f316(x37291),x37292),f195(f935(x37291,a922)))),x37292) % 188.18/188.24 [3732]E(f334(f291(x37321,x37322),f195(f935(f934(x37321,x37322),a922))),f195(f935(x37322,a922))) % 188.18/188.24 [3733]E(f334(f272(x37331,x37332),f195(f935(f934(x37331,x37332),a922))),f195(f935(x37331,a922))) % 188.18/188.24 [3737]E(f334(a112,f334(f334(f23(a1),x37371),x37372)),f334(f40(a1),f312(a1,x37372,x37371))) % 188.18/188.24 [3742]E(f334(f334(f86(a927),x37421),f334(f334(f87(a927),x37422),x37421)),f334(f334(f87(a927),f334(a119,x37422)),x37421)) % 188.18/188.24 [3744]E(f334(f334(f65(x37441),f195(f935(x37441,a922))),x37442),f195(f935(f935(x37441,a922),a922))) % 188.18/188.24 [3753]E(f334(f196(f928(a927)),f146(a927,f334(f310(a927,x37531),x37532))),f334(f334(f23(a927),x37532),x37531)) % 188.18/188.24 [3768]E(f334(f334(f108(f935(x37681,a922)),f195(f935(x37681,a922))),x37682),x37682) % 188.18/188.24 [3769]E(f334(f334(f109(f935(x37691,a922)),f250(f935(x37691,a922))),x37692),x37692) % 188.18/188.24 [3770]E(f334(f334(f86(a1),f334(f85(a1),x37701)),f334(f85(a1),x37702)),f334(f85(a1),f334(f334(f86(a1),x37701),x37702))) % 188.18/188.24 [3773]E(f334(f334(f87(a1),f334(f111(a1),x37731)),f334(f111(a1),x37732)),f334(f111(a1),f334(f334(f87(a1),x37731),x37732))) % 188.18/188.24 [3775]E(f334(f334(f87(a1),f334(f107(a1),x37751)),f334(f107(a1),x37752)),f334(f107(a1),f334(f334(f87(a927),x37751),x37752))) % 188.18/188.24 [3776]E(f334(f334(f86(a1),f334(f111(a1),x37761)),f334(f111(a1),x37762)),f334(f111(a1),f334(f334(f86(a1),x37761),x37762))) % 188.18/188.24 [3778]E(f334(f334(f86(a1),f334(f107(a1),x37781)),f334(f107(a1),x37782)),f334(f107(a1),f334(f334(f86(a927),x37781),x37782))) % 188.18/188.24 [3779]E(f334(f334(f41(a1),f334(f107(a1),x37791)),f334(f107(a1),x37792)),f334(f107(a1),f334(f334(f41(a927),x37791),x37792))) % 188.18/188.24 [3799]E(f334(f334(f6(x37991,a927),f334(f16(a927,x37991),f84(a927))),x37992),f334(f40(x37991),x37992)) % 188.18/188.24 [3809]E(f334(f85(a1),f50(a1,f334(f85(a1),x38091),x38092)),f50(a1,x38091,f334(f85(a1),x38092))) % 188.18/188.24 [3811]E(f334(f179(a1),f185(x38111,f334(f334(f23(a1),x38112),f84(a1)))),f334(f310(a1,x38111),x38112)) % 188.18/188.24 [3816]P107(f334(f334(f242(a927),x38161),f334(f334(f86(a927),x38162),x38161))) % 188.18/188.24 [3817]P107(f334(f334(f242(a927),x38171),f334(f334(f86(a927),x38171),x38172))) % 188.18/188.24 [3819]E(f334(f334(f23(f935(x38191,a922)),f195(f935(x38191,a922))),x38192),f195(f935(x38191,a922))) % 188.18/188.24 [3820]E(f334(f334(f108(f935(x38201,a922)),f250(f935(x38201,a922))),x38202),f250(f935(x38201,a922))) % 188.18/188.24 [3821]E(f334(f334(f109(f935(x38211,a922)),f195(f935(x38211,a922))),x38212),f195(f935(x38211,a922))) % 188.18/188.24 [3828]E(f334(f334(f260(a1,a1),x38281),f334(f85(a1),x38282)),f334(a56,f334(f334(f260(a1,a1),x38281),x38282))) % 188.18/188.24 [3829]E(f334(f310(a1,f334(f334(f86(a1),x38291),f84(a1))),x38292),f313(a1,x38291,x38292)) % 188.18/188.24 [3841]E(f334(f334(f87(a927),x38411),f334(f334(f41(a927),x38412),x38411)),f334(f334(f23(a927),x38412),f50(a927,x38412,x38411))) % 188.18/188.24 [3842]E(f334(f334(f87(a1),x38421),f334(f334(f41(a1),x38422),x38421)),f334(f334(f23(a1),x38422),f50(a1,x38422,x38421))) % 188.18/188.24 [3845]E(f334(f179(a1),f185(f334(f334(f86(a1),x38451),f84(a1)),x38452)),f312(a1,x38451,x38452)) % 188.18/188.24 [3849]P107(f334(f334(f242(f935(x38491,a922)),x38492),x38492)) % 188.18/188.24 [3852]E(f334(f334(f108(f935(x38521,a922)),x38522),f334(f85(f935(x38521,a922)),x38522)),f250(f935(x38521,a922))) % 188.18/188.24 [3853]E(f334(f334(f109(f935(x38531,a922)),x38532),f334(f85(f935(x38531,a922)),x38532)),f195(f935(x38531,a922))) % 188.18/188.24 [3861]E(f334(f334(f23(a927),f334(f334(f23(a927),x38611),f84(a927))),x38612),f334(f334(f23(a927),x38611),f334(a119,x38612))) % 188.18/188.24 [3867]E(f334(f334(f23(f935(x38671,a922)),f250(f935(x38671,a922))),x38672),f334(f85(f935(x38671,a922)),x38672)) % 188.18/188.24 [3868]E(f334(f334(f23(a1),f334(f111(a1),x38681)),f334(f111(a1),x38682)),f334(f111(a1),f334(f334(f86(a1),x38681),f334(f85(a1),x38682)))) % 188.18/188.24 [3881]E(f334(f179(a927),f146(a927,f334(f310(a927,x38811),f334(a119,x38812)))),f311(a927,x38811,x38812)) % 188.18/188.24 [3896]E(f334(f196(f928(f928(x38961))),f59(x38961,x38962)),f334(f334(f252(a927),f334(a119,f334(a119,f2(a927)))),f334(f196(f928(x38961)),x38962))) % 188.18/188.24 [3915]E(f334(f334(f190(f934(x39151,x39151),a922),f2(a927)),x39152),f314(x39151,f195(f935(f934(x39151,x39151),a922)))) % 188.18/188.24 [3919]P107(f334(f144(a927),f146(a927,f334(f310(a927,x39191),x39192)))) % 188.18/188.24 [3935]E(f334(f317(a1,a927,a112),f311(a1,f334(f107(a1),x39351),f334(f107(a1),x39352))),f311(a927,x39351,x39352)) % 188.18/188.24 [3944]E(f192(a927,f2(a927),f5(a927),f334(f334(f23(a927),x39441),x39442)),f334(f334(f23(a927),x39441),f334(a119,x39442))) % 188.18/188.24 [3945]E(f334(a112,f334(f334(f23(a1),x39451),f334(f334(f86(a1),x39452),f84(a1)))),f334(f40(a1),f313(a1,x39452,x39451))) % 188.18/188.24 [3975]E(f334(f334(f161(a927,a927),a119),f146(a927,f334(f310(a927,x39751),x39752))),f146(a927,f334(f310(a927,f334(a119,x39751)),f334(a119,x39752)))) % 188.18/188.24 [3982]E(f334(f179(a1),f185(f334(f334(f86(a1),x39821),f84(a1)),f334(f334(f23(a1),x39822),f84(a1)))),f313(a1,x39821,x39822)) % 188.18/188.24 [3994]P107(f334(f334(f242(f935(x39941,a922)),f195(f935(x39941,a922))),x39942)) % 188.18/188.24 [3998]E(f91(x39981,f334(f334(f7(x39981,x39981,a922),a331),x39982)),x39982) % 188.18/188.24 [3999]E(f96(x39991,f334(f334(f7(x39991,x39991,a922),a331),x39992)),x39992) % 188.18/188.24 [4007]E(f334(f179(a927),f146(a927,f334(f310(a927,f334(a119,x40071)),f334(a119,x40072)))),f312(a927,x40071,x40072)) % 188.18/188.24 [4034]E(f334(f334(f262(x40341,x40342),f250(f935(x40341,a922))),f334(f16(f935(x40342,a922),x40341),f250(f935(x40342,a922)))),f250(f935(f934(x40341,x40342),a922))) % 188.18/188.24 [4068]E(f334(f270(x40681),f334(f334(f8(a922,a922,x40681),a329),x40682)),f334(f85(f935(x40681,a922)),f334(f270(x40681),x40682))) % 188.18/188.24 [4071]E(f334(f270(x40711),f334(f334(f7(x40711,x40711,a922),a331),x40712)),f334(f334(f316(x40711),x40712),f195(f935(x40711,a922)))) % 188.18/188.24 [4093]P107(f334(f334(f242(a927),f334(f40(x40931),f334(f179(x40931),x40932))),f334(f196(f928(x40931)),x40932))) % 188.18/188.24 [4094]P107(f334(f334(f242(a927),f334(f196(f928(x40941)),f159(x40941,x40942))),f334(f196(f928(x40941)),x40942))) % 188.18/188.24 [4105]E(f334(f270(x41051),f334(f334(f7(x41051,f935(x41051,a922),a922),f336(x41051)),x41052)),x41052) % 188.18/188.24 [4118]E(f334(f334(f182(x41181),f334(f334(f23(a927),f334(f196(f928(x41181)),x41182)),f84(a927))),x41182),f121(x41181,x41182)) % 188.18/188.24 [4139]E(f192(a927,f2(a927),f334(f334(f8(a927,a927,a927),a119),f334(f246(a927),x41391)),x41392),f334(f334(f246(a927),f334(a119,x41391)),x41392)) % 188.18/188.24 [4144]E(f42(f935(x41441,a922),f334(f317(f935(f934(x41441,x41441),a922),f935(x41441,a922),f289(x41441)),x41442)),f334(f289(x41441),f42(f935(f934(x41441,x41441),a922),x41442))) % 188.18/188.24 [4145]E(f192(a927,f334(a119,x41451),f334(f334(f8(a927,a927,a927),a119),f334(f241(a927),x41451)),x41452),f334(f334(f241(a927),f334(a119,x41451)),x41452)) % 188.18/188.24 [4147]E(f334(f334(f260(a1,a1),f334(f334(f41(a1),f334(f81(a1),x41471)),f334(f81(a1),x41472))),f50(a1,f334(f81(a1),x41471),f334(f81(a1),x41472))),f58(x41471,x41472)) % 188.18/188.24 [4170]P107(f334(f334(f242(f935(f935(x41701,a922),a922)),x41702),f334(f315(x41701),f42(f935(x41701,a922),x41702)))) % 188.18/188.24 [4203]E(f334(f334(f44(x42031,f935(x42031,a922)),x42032),f334(f334(f7(x42031,f935(x42031,a922),f935(x42031,a922)),f316(x42031)),f195(f935(x42031,a922)))),x42032) % 188.18/188.24 [4204]E(f334(f334(f295(x42041,x42041,x42041),f334(f293(x42041,x42041),x42042)),f314(x42041,f334(f293(x42041,x42041),x42042))),f334(f293(x42041,x42041),f334(f334(f295(x42041,x42041,x42041),x42042),f314(x42041,x42042)))) % 188.18/188.24 [4267]E(f334(f179(x42671),f334(f149(f928(x42671),f928(x42671),f141(x42671),f120(x42671)),x42672)),f334(f334(f44(f928(x42671),f935(x42671,a922)),f334(f179(f928(x42671)),x42672)),f179(x42671))) % 188.18/188.24 [4297]E(f334(f334(f108(f935(f934(x42971,x42971),a922)),f314(x42971,f195(f935(f934(x42971,x42971),a922)))),f334(f334(f295(x42971,x42971,x42971),f314(x42971,x42972)),x42972)),f314(x42971,x42972)) % 188.18/188.24 [4332]E(f334(f334(f188(x43321,x43321),x43322),x43322),f334(f334(f161(x43321,f934(x43321,x43321)),f334(f334(f18(x43321,x43321,f934(x43321,x43321)),f260(x43321,x43321)),f5(x43321))),x43322)) % 188.18/188.24 [4442]E(f334(f149(a927,f928(x44421),f334(f7(f928(x44421),a927,a927),f334(f334(f8(a927,f935(a927,a927),f928(x44421)),f241(a927)),f196(f928(x44421)))),f2(a927)),f334(f175(f928(x44421)),x44422)),f334(f196(f928(f928(x44421))),f186(x44421,x44422))) % 188.18/188.24 [4516]E(f334(f334(f294(f934(a927,f928(x45161)),f928(x45161)),f326(a927,f928(x45161),a248,f152(x45161,x45162))),f334(f334(f18(f928(x45161),f928(x45161),f934(a927,f928(x45161))),f334(f334(f8(a927,f935(f928(x45161),f934(a927,f928(x45161))),f928(x45161)),f260(a927,f928(x45161))),f196(f928(x45161)))),f5(f928(x45161)))),f153(x45161,x45162)) % 188.18/188.24 [4654]E(f334(f270(x46541),f334(f334(f8(f935(f935(x46541,a922),a922),a922,x46541),f93(f935(x46541,a922))),f334(f334(f8(f935(f935(x46541,a922),a922),f935(f935(x46541,a922),a922),x46541),f334(f18(f935(x46541,a922),a922,a922),f334(f334(f8(a922,f935(a922,a922),f935(x46541,a922)),a337),f334(f334(f7(f935(x46541,a922),f935(f935(x46541,a922),a922),a922),f336(f935(x46541,a922))),x46542)))),f336(x46541)))),f43(f935(x46541,a922),x46542)) % 188.18/188.24 [4655]E(f334(f270(x46551),f334(f334(f8(f935(f935(x46551,a922),a922),a922,x46551),f92(f935(x46551,a922))),f334(f334(f8(f935(f935(x46551,a922),a922),f935(f935(x46551,a922),a922),x46551),f334(f18(f935(x46551,a922),a922,a922),f334(f334(f8(a922,f935(a922,a922),f935(x46551,a922)),a332),f334(f334(f7(f935(x46551,a922),f935(f935(x46551,a922),a922),a922),f336(f935(x46551,a922))),x46552)))),f336(x46551)))),f42(f935(x46551,a922),x46552)) % 188.18/188.24 [4796]~P107(f334(f334(f243(a1),f334(f107(a1),x47961)),f334(f85(a1),f334(f107(a1),x47962)))) % 188.18/188.24 [3740]E(f334(f334(f23(a927),f334(f334(f86(a927),x37401),x37402)),x37402),x37401) % 188.18/188.24 [3741]E(f334(f334(f23(a927),f334(f334(f86(a927),x37411),x37412)),x37411),x37412) % 188.18/188.24 [3810]E(f334(f334(f86(a927),f334(f334(f23(a927),x38101),x38102)),x38102),f334(f334(f241(a927),x38101),x38102)) % 188.18/188.24 [3922]E(f334(f334(f87(a927),f334(f334(f41(a927),x39221),x39222)),x39222),f334(f334(f23(a927),x39221),f50(a927,x39221,x39222))) % 188.18/188.24 [3949]E(f334(f179(a927),f146(a927,f334(f310(a927,f334(a119,x39491)),x39492))),f313(a927,x39491,x39492)) % 188.18/188.24 [3957]E(f334(f107(a1),f225(f334(a112,f334(f81(a1),x39571)),f334(a112,f334(f81(a1),x39572)))),f334(f334(a226,x39571),x39572)) % 188.18/188.24 [3959]E(f334(f334(f108(f935(x39591,a922)),f334(f85(f935(x39591,a922)),x39592)),x39592),f250(f935(x39591,a922))) % 188.18/188.24 [3960]E(f334(f334(f109(f935(x39601,a922)),f334(f85(f935(x39601,a922)),x39602)),x39602),f195(f935(x39601,a922))) % 188.18/188.24 [3971]P107(f334(f334(f242(a927),f334(f334(f23(a927),x39711),x39712)),x39711)) % 188.18/188.24 [3972]P107(f334(f334(f242(a927),f334(f334(f41(a927),x39721),x39722)),x39721)) % 188.18/188.24 [3995]P107(f334(f334(f243(a927),x39951),f334(a119,f334(f334(f86(a927),x39952),x39951)))) % 188.18/188.24 [3996]P107(f334(f334(f243(a927),x39961),f334(a119,f334(f334(f86(a927),x39961),x39962)))) % 188.18/188.24 [4019]E(f334(f334(f87(a927),f334(a112,f334(f81(a1),x40191))),f334(a112,f334(f81(a1),x40192))),f334(a112,f334(f81(a1),f334(f334(f87(a1),x40191),x40192)))) % 188.18/188.24 [4030]P107(f334(f334(f242(a1),f2(a1)),f334(f334(f252(a1),f334(f81(a1),x40301)),x40302))) % 188.18/188.24 [4098]E(f334(f292(f928(x40981),f928(x40981),f165(x40981,x40982)),f334(f334(f316(f928(x40981)),f120(x40981)),f195(f935(f928(x40981),a922)))),f334(f334(f316(f928(x40981)),f120(x40981)),f195(f935(f928(x40981),a922)))) % 188.18/188.24 [4116]E(f334(f334(f108(f935(f934(x41161,x41161),a922)),f314(x41161,x41162)),f314(x41161,f195(f935(f934(x41161,x41161),a922)))),f314(x41161,x41162)) % 188.18/188.24 [4199]E(f334(f270(f935(x41991,a922)),f334(f334(f7(f935(x41991,a922),f935(x41991,a922),a922),f242(f935(x41991,a922))),x41992)),f334(f315(x41991),x41992)) % 188.18/188.24 [4216]E(f334(f334(f161(a1,a927),a112),f334(f334(f141(a1),f334(f334(f161(a927,a1),f107(a1)),x42161)),f334(f334(f161(a927,a1),f107(a1)),x42162))),f334(f334(f141(a927),x42161),x42162)) % 188.18/188.24 [4245]E(f334(f317(a1,a1,f334(f334(f7(a1,a1,a1),f86(a1)),x42451)),f334(f310(a1,f2(a1)),f334(f334(f23(a1),x42452),x42451))),f334(f310(a1,x42451),x42452)) % 188.18/188.24 [4247]P56(x42471,f334(f334(f23(f935(f934(x42471,x42471),a922)),x42472),f314(x42471,f195(f935(f934(x42471,x42471),a922))))) % 188.18/188.24 [4265]E(f334(f196(f928(x42651)),f334(f149(f928(x42651),f928(x42651),f141(x42651),f120(x42651)),x42652)),f334(f172(a927),f334(f334(f161(f928(x42651),a927),f196(f928(x42651))),x42652))) % 188.18/188.24 [4269]P55(x42691,f250(f935(x42691,a922)),f334(f334(f108(f935(f934(x42691,x42691),a922)),x42692),f314(x42691,f195(f935(f934(x42691,x42691),a922))))) % 188.18/188.24 [4311]E(f192(a927,f2(a927),f334(f334(f8(a927,a927,a927),a119),f334(f334(f7(a927,a927,a927),f246(a927)),x43111)),x43112),f334(f334(f246(a927),x43112),f334(a119,x43111))) % 188.18/188.24 [4314]E(f192(a927,f334(a119,x43141),f334(f334(f8(a927,a927,a927),a119),f334(f334(f7(a927,a927,a927),f241(a927)),x43141)),x43142),f334(f334(f241(a927),x43142),f334(a119,x43141))) % 188.18/188.24 [4317]E(f334(f317(x43171,f928(x43171),f334(f334(f7(x43171,f928(x43171),f928(x43171)),f158(x43171)),f120(x43171))),x43172),f181(x43171,x43172,f334(f334(f316(f928(x43171)),f120(x43171)),f195(f935(f928(x43171),a922))))) % 188.18/188.24 [4319]E(f334(f334(f108(f935(f934(x43191,x43191),a922)),f334(f334(f295(x43191,x43191,x43191),x43192),f314(x43191,x43192))),f314(x43191,f195(f935(f934(x43191,x43191),a922)))),f314(x43191,x43192)) % 188.18/188.24 [4327]P107(f334(f334(f242(f935(f934(x43271,x43271),a922)),f271(x43271,x43272)),f334(f334(f262(x43271,x43271),x43272),f334(f16(f935(x43271,a922),x43271),x43272)))) % 188.18/188.24 [4330]E(f334(f317(a1,a927,a112),f334(f334(f108(f935(a1,a922)),f334(f317(a927,a1,f107(a1)),x43301)),f334(f317(a927,a1,f107(a1)),x43302))),f334(f334(f108(f935(a927,a922)),x43301),x43302)) % 188.18/188.24 [4331]E(f334(f317(a1,a927,a112),f334(f334(f109(f935(a1,a922)),f334(f317(a927,a1,f107(a1)),x43311)),f334(f317(a927,a1,f107(a1)),x43312))),f334(f334(f109(f935(a927,a922)),x43311),x43312)) % 188.18/188.24 [4334]E(f334(f270(x43341),f334(f334(f8(a922,a922,x43341),a329),f334(f334(f7(x43341,f935(x43341,a922),a922),f336(x43341)),x43342))),f334(f85(f935(x43341,a922)),x43342)) % 188.18/188.24 [4360]E(f334(f149(f928(x43601),f928(x43601),f141(x43601),f120(x43601)),f334(f334(f161(f928(x43601),f928(x43601)),f175(x43601)),f334(f175(f928(x43601)),x43602))),f334(f175(x43601),f334(f149(f928(x43601),f928(x43601),f141(x43601),f120(x43601)),x43602))) % 188.18/188.24 [4384]E(f334(f334(f44(a927,f935(f934(x43841,x43841),a922)),f250(f935(a927,a922))),f334(f334(f7(a927,f935(f934(x43841,x43841),a922),f935(f934(x43841,x43841),a922)),f190(f934(x43841,x43841),a922)),x43842)),f314(x43841,x43842)) % 188.18/188.24 [4399]E(f91(x43991,f334(f334(f8(f935(x43991,a922),a922,x43991),f334(a331,x43992)),f334(f334(f7(x43991,f935(x43991,a922),f935(x43991,a922)),f316(x43991)),f195(f935(x43991,a922))))),f319(x43991,x43992)) % 188.18/188.24 [4408]E(f334(f196(f928(x44081)),f159(x44081,f334(f149(f928(x44081),f928(x44081),f141(x44081),f120(x44081)),x44082))),f334(f40(x44081),f334(f334(f44(f928(x44081),f935(x44081,a922)),f334(f179(f928(x44081)),x44082)),f179(x44081)))) % 188.18/188.24 [4422]E(f334(f334(f108(f935(f934(x44221,x44221),a922)),x44222),f334(f334(f295(x44221,x44221,x44221),f334(f334(f295(x44221,x44221,x44221),x44222),f314(x44221,x44222))),x44222)),f334(f334(f295(x44221,x44221,x44221),x44222),f314(x44221,x44222))) % 188.18/188.24 [4452]P107(f334(f334(f242(f935(f934(x44521,x44521),a922)),f334(f334(f295(x44521,x44521,x44521),x44522),f314(x44521,x44522))),f334(f334(f262(x44521,x44521),f334(f289(x44521),x44522)),f334(f16(f935(x44521,a922),x44521),f334(f289(x44521),x44522))))) % 188.18/188.24 [4492]E(f334(f270(f928(x44921)),f334(f334(f7(f928(x44921),f935(x44921,a922),a922),f334(f334(f8(f935(x44921,a922),f935(f935(x44921,a922),a922),f928(x44921)),f242(f935(x44921,a922))),f179(x44921))),x44922)),f168(x44921,x44922)) % 188.18/188.24 [4505]E(f334(f163(f928(x45051),x45051,f120(x45051),f334(f334(f8(f928(x45051),f935(f928(x45051),f928(x45051)),x45051),f334(f7(f928(x45051),f928(x45051),f928(x45051)),f141(x45051))),f334(f334(f7(x45051,f928(x45051),f928(x45051)),f158(x45051)),f120(x45051)))),x45052),f334(f174(x45051),x45052)) % 188.18/188.24 [4542]P27(f935(x45421,x45422),f935(f934(x45421,x45422),a922),f334(f334(f8(f935(f934(x45421,x45422),a922),f935(f934(x45421,x45422),a922),f935(x45421,x45422)),f270(f934(x45421,x45422))),f334(f334(f8(f935(x45421,f935(x45422,a922)),f935(f934(x45421,x45422),a922),f935(x45421,x45422)),f265(x45421,x45422,a922)),f334(f8(x45422,f935(x45422,a922),x45421),f334(f7(x45422,x45422,a922),a331)))),f250(f935(f935(x45421,x45422),a922))) % 188.18/188.24 [4598]E(f334(f334(f44(x45981,f935(f934(x45981,x45981),a922)),x45982),f334(f334(f7(x45981,f935(f934(x45981,x45981),a922),f935(f934(x45981,x45981),a922)),f334(f334(f8(f934(x45981,x45981),f935(f935(f934(x45981,x45981),a922),f935(f934(x45981,x45981),a922)),x45981),f316(f934(x45981,x45981))),f334(f334(f18(x45981,x45981,f934(x45981,x45981)),f260(x45981,x45981)),f5(x45981)))),f195(f935(f934(x45981,x45981),a922)))),f271(x45981,x45982)) % 188.18/188.24 [4606]E(f211(x46061,f334(f334(f260(a1,a1),f334(f85(a1),f334(f334(f78(f934(a1,a1),a1,x46061,f259(a1,a1)),f221(x46061)),x46062))),f334(f334(f78(f934(a1,a1),a1,x46061,f264(a1,a1)),f221(x46061)),x46062))),f236(x46061,x46062)) % 188.18/188.24 [4698]E(f334(f270(f935(x46981,a922)),f334(f334(f8(f935(f935(x46981,a922),a922),a922,f935(x46981,a922)),f92(f935(x46981,a922))),f334(f334(f7(f935(x46981,a922),f935(f935(x46981,a922),a922),f935(f935(x46981,a922),a922)),f334(f334(f8(f935(f935(x46981,a922),f935(a922,a922)),f935(f935(f935(x46981,a922),a922),f935(f935(x46981,a922),a922)),f935(x46981,a922)),f18(f935(x46981,a922),a922,a922)),f334(f334(f8(f935(f935(x46981,a922),a922),f935(f935(x46981,a922),f935(a922,a922)),f935(x46981,a922)),f334(f8(a922,f935(a922,a922),f935(x46981,a922)),a332)),f334(f334(f7(f935(x46981,a922),f935(f935(x46981,a922),f935(x46981,a922)),f935(f935(x46981,a922),a922)),f334(f334(f8(f935(f935(x46981,a922),a922),f935(f935(f935(x46981,a922),f935(x46981,a922)),f935(f935(x46981,a922),a922)),f935(x46981,a922)),f8(f935(x46981,a922),a922,f935(x46981,a922))),a331)),f85(f935(x46981,a922)))))),f334(f334(f8(f935(f935(x46981,a922),a922),a922,f935(x46981,a922)),f334(f336(f935(x46981,a922)),x46982)),f315(x46981))))),f334(f315(x46981),f334(f85(f935(x46981,a922)),x46982))) % 188.18/188.24 [4798]~P107(f334(f334(f243(a927),f334(f334(f86(a927),x47981),x47982)),x47982)) % 188.18/188.24 [4799]~P107(f334(f334(f243(a927),f334(f334(f86(a927),x47991),x47992)),x47991)) % 188.18/188.24 [4035]E(f334(f334(f23(a927),x40351),f334(f334(f87(a927),f334(f334(f41(a927),x40351),x40352)),x40352)),f50(a927,x40351,x40352)) % 188.18/188.24 [4036]E(f334(f334(f23(a1),x40361),f334(f334(f87(a1),f334(f334(f41(a1),x40361),x40362)),x40362)),f50(a1,x40361,x40362)) % 188.18/188.24 [4069]E(f334(f334(f161(a927,x40691),f334(f171(x40691),x40692)),f146(a927,f334(f310(a927,f2(a927)),f334(f196(f928(x40691)),x40692)))),x40692) % 188.18/188.24 [4124]E(f334(f292(x41241,x41241,f314(x41241,f195(f935(f934(x41241,x41241),a922)))),x41242),x41242) % 188.18/188.24 [4250]E(f314(x42501,f334(f334(f23(f935(f934(x42501,x42501),a922)),x42502),f314(x42501,f195(f935(f934(x42501,x42501),a922))))),f314(x42501,x42502)) % 188.18/188.24 [4251]E(f314(x42511,f334(f334(f108(f935(f934(x42511,x42511),a922)),x42512),f314(x42511,f195(f935(f934(x42511,x42511),a922))))),f314(x42511,x42512)) % 188.18/188.24 [4419]E(f334(f107(a1),f334(f334(f41(a927),f334(f334(f87(a927),f334(a112,f334(f81(a1),x44191))),f334(a112,f334(f81(a1),x44192)))),f225(f334(a112,f334(f81(a1),x44191)),f334(a112,f334(f81(a1),x44192))))),f227(x44191,x44192)) % 188.18/188.24 [4444]E(f334(f334(f23(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44441)),x44441)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44442)),x44442)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),x44441),x44442))),f334(f334(f23(a1),x44441),x44442))),a104)) % 188.18/188.24 [4467]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44671)),x44671)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44672)),x44672)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),x44671),x44672))),f334(f334(f86(a1),x44671),x44672))) % 188.18/188.24 [4470]E(f334(f334(f267(f934(a106,a106),a106,f934(a106,a106),f934(x44701,f934(a106,a106))),f275(f334(a3,f334(f196(f928(x44701)),x44702)))),f334(f334(f8(x44701,f935(f934(a106,a106),f934(x44701,f934(a106,a106))),a106),f260(x44701,f934(a106,a106))),f334(f334(f8(a927,x44701,a106),f334(f171(x44701),x44702)),a20))),f283(x44701,x44702)) % 188.18/188.24 [4498]E(f334(f334(f23(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44981)),x44981)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44982)),x44982)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),f334(f334(f86(a1),x44981),a104)),x44982))),f334(f334(f23(a1),f334(f334(f86(a1),x44981),a104)),x44982))) % 188.18/188.24 [4547]E(f334(f149(a927,f928(x45471),f334(f7(f928(x45471),a927,a927),f334(f334(f8(a927,f935(a927,a927),f928(x45471)),f241(a927)),f196(f928(x45471)))),f2(a927)),f334(f175(f928(x45471)),f186(x45471,x45472))),f334(f196(f928(f928(x45471))),f334(f143(f928(x45471),f334(f334(f8(a922,a922,f928(x45471)),a329),f334(f334(f7(f928(x45471),f928(x45471),a922),a331),f120(x45471)))),x45472))) % 188.18/188.24 [4553]E(f334(f334(f44(a927,f935(x45531,a922)),f250(f935(a927,a922))),f334(f334(f7(a927,f935(a927,f935(x45531,a922)),f935(x45531,a922)),f334(f334(f8(f935(a927,a922),f935(f935(a927,f935(x45531,a922)),f935(x45531,a922)),a927),f44(a927,f935(x45531,a922))),f310(a927,f2(a927)))),x45532)),f334(f334(f44(a927,f935(x45531,a922)),f250(f935(a927,a922))),x45532)) % 188.18/188.24 [4576]P107(f334(f66(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),x45761)),f334(f334(f7(a927,a927,a922),f243(a927)),x45762))))) % 188.18/188.24 [4705]E(f334(f270(f934(f928(x47051),f928(x47051))),f334(f265(f928(x47051),f928(x47051),a922),f334(f334(f18(f928(x47051),f935(f928(x47051),a922),f935(f928(x47051),a922)),f334(f334(f8(f935(f928(x47051),f935(a922,a922)),f935(f935(f928(x47051),a922),f935(f928(x47051),a922)),f928(x47051)),f18(f928(x47051),a922,a922)),f334(f334(f8(f935(f928(x47051),a922),f935(f928(x47051),f935(a922,a922)),f928(x47051)),f334(f8(a922,f935(a922,a922),f928(x47051)),a333)),f334(f334(f7(f928(x47051),f935(f928(x47051),a927),f935(f928(x47051),a922)),f334(f334(f8(f935(a927,a922),f935(f935(f928(x47051),a927),f935(f928(x47051),a922)),f928(x47051)),f8(a927,a922,f928(x47051))),f334(f334(f8(a927,f935(a927,a922),f928(x47051)),f243(a927)),f196(f928(x47051))))),f196(f928(x47051)))))),f334(f334(f18(f928(x47051),f935(f928(x47051),a922),f935(f928(x47051),a922)),f334(f334(f8(f935(f928(x47051),f935(a922,a922)),f935(f935(f928(x47051),a922),f935(f928(x47051),a922)),f928(x47051)),f18(f928(x47051),a922,a922)),f334(f334(f8(f935(f928(x47051),a922),f935(f928(x47051),f935(a922,a922)),f928(x47051)),f334(f8(a922,f935(a922,a922),f928(x47051)),a332)),f334(f334(f7(f928(x47051),f935(f928(x47051),a927),f935(f928(x47051),a922)),f334(f334(f8(f935(a927,a922),f935(f935(f928(x47051),a927),f935(f928(x47051),a922)),f928(x47051)),f8(a927,a922,f928(x47051))),f334(f334(f8(a927,f935(a927,a922),f928(x47051)),a331),f196(f928(x47051))))),f196(f928(x47051)))))),f334(f334(f7(f928(x47051),f935(f934(f928(x47051),f928(x47051)),a922),f935(f928(x47051),a922)),f334(f334(f8(f935(f928(x47051),f935(f935(f934(f928(x47051),f928(x47051)),a922),a922)),f935(f935(f934(f928(x47051),f928(x47051)),a922),f935(f928(x47051),a922)),f928(x47051)),f7(f928(x47051),f935(f934(f928(x47051),f928(x47051)),a922),a922)),f334(f334(f8(f935(f928(x47051),f934(f928(x47051),f928(x47051))),f935(f928(x47051),f935(f935(f934(f928(x47051),f928(x47051)),a922),a922)),f928(x47051)),f334(f8(f934(f928(x47051),f928(x47051)),f935(f935(f934(f928(x47051),f928(x47051)),a922),a922),f928(x47051)),f336(f934(f928(x47051),f928(x47051))))),f260(f928(x47051),f928(x47051))))),f152(x47051,x47052)))))),f153(x47051,x47052)) % 188.18/188.24 [4469]E(f334(a112,f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x44691),x44692)),f195(f935(f934(a927,a927),a922)))))),f334(f334(f23(a927),x44691),x44692)) % 188.18/188.24 [4473]E(f334(f334(f295(x44731,x44731,x44731),f334(f334(f108(f935(f934(x44731,x44731),a922)),x44732),f314(x44731,f195(f935(f934(x44731,x44731),a922))))),f314(x44731,f334(f334(f108(f935(f934(x44731,x44731),a922)),x44732),f314(x44731,f195(f935(f934(x44731,x44731),a922)))))),f314(x44731,x44732)) % 188.18/188.24 [4509]E(f276(x45091,f334(f143(f934(a106,x45091),f334(f265(a106,x45091,a922),f334(f334(f8(a922,f935(x45091,a922),a106),f16(a922,x45091)),f334(f243(a106),f2(a106))))),x45092)),f276(x45091,x45092)) % 188.18/188.24 [4510]E(f274(x45101,f334(f143(f934(a106,x45101),f334(f265(a106,x45101,a922),f334(f334(f8(a922,f935(x45101,a922),a106),f16(a922,x45101)),f334(f243(a106),f2(a106))))),x45102)),f274(x45101,x45102)) % 188.18/188.24 [4511]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),x45111),f334(f334(f23(a1),x45112),a104)))),f334(f334(f86(a1),x45111),f334(f334(f23(a1),x45112),a104)))),a104),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45111)),x45111)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45112)),x45112))) % 188.18/188.24 [4513]E(f334(f85(a1),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x45131),x45132)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x45132),x45131)),f195(f935(f934(a927,a927),a922)))))) % 188.18/188.24 [4568]E(f334(f334(f294(f928(a927),x45681),f152(a927,a248)),f334(f334(f7(x45681,f928(f935(x45681,a927)),f928(a927)),f334(f334(f8(f935(f935(x45681,a927),a927),f935(f928(f935(x45681,a927)),f928(a927)),x45681),f161(f935(x45681,a927),a927)),f334(f7(f935(x45681,a927),x45681,a927),f5(f935(x45681,a927))))),x45682)),f160(x45681,x45682)) % 188.18/188.24 [4595]E(f334(f334(f94(a1,a927),f334(f111(a1),f334(f334(f86(a1),x45951),a104))),f334(f334(f18(a1,a927,a927),f334(f334(f7(a1,a927,f935(a927,a927)),f334(f334(f8(a922,f935(a927,f935(a927,a927)),a1),f103(a927)),a200)),f2(a927))),f334(f334(f8(a927,a927,a1),a119),f334(f334(f8(a927,a927,a1),f334(f246(a927),x45952)),a112)))),f334(f334(f246(a927),f334(a119,x45952)),f334(f111(a927),x45951))) % 188.18/188.24 [4596]E(f334(f334(f94(a1,a927),f334(f111(a1),f334(f334(f86(a1),x45961),a104))),f334(f334(f18(a1,a927,a927),f334(f334(f7(a1,a927,f935(a927,a927)),f334(f334(f8(a922,f935(a927,f935(a927,a927)),a1),f103(a927)),a200)),f334(a119,x45962))),f334(f334(f8(a927,a927,a1),a119),f334(f334(f8(a927,a927,a1),f334(f241(a927),x45962)),a112)))),f334(f334(f241(a927),f334(a119,x45962)),f334(f111(a927),x45961))) % 188.18/188.24 [4616]E(f334(f149(f928(x46161),f928(x46161),f141(x46161),f120(x46161)),f334(f334(f161(f928(x46161),f928(x46161)),f163(f928(x46161),x46161,f120(x46161),f334(f334(f8(f928(x46161),f935(f928(x46161),f928(x46161)),x46161),f16(f928(x46161),f928(x46161))),f334(f334(f7(x46161,f928(x46161),f928(x46161)),f158(x46161)),f120(x46161))))),x46162)),f334(f334(f161(f928(x46161),x46161),f148(x46161)),f334(f143(f928(x46161),f334(f334(f8(a922,a922,f928(x46161)),a329),f334(f334(f7(f928(x46161),f928(x46161),a922),a331),f120(x46161)))),x46162))) % 188.18/188.24 [4689]E(f334(f265(a1,a1,a922),f334(f334(f7(a1,f935(a1,a922),f935(a1,a922)),f334(f334(f8(f935(a1,f935(a922,a922)),f935(f935(a1,a922),f935(a1,a922)),a1),f18(a1,a922,a922)),f334(f334(f8(f935(a1,a922),f935(a1,f935(a922,a922)),a1),f334(f8(a922,f935(a922,a922),a1),a332)),f334(f334(f8(f935(a1,a1),f935(a1,a922),a1),f334(f8(a1,a922,a1),f334(a331,x46891))),f334(f334(f8(a1,f935(a1,a1),a1),f86(a1)),f334(f87(a1),x46892)))))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),f334(a337,f334(f334(f243(a1),f2(a1)),x46892))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),f334(f334(f7(a1,a1,a922),f243(a1)),x46892))))),f334(f334(f8(a922,a922,a1),f334(a337,f334(a329,f334(f334(f243(a1),f2(a1)),x46892)))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f243(a1),x46892))),f334(f334(f7(a1,a1,a922),f242(a1)),f2(a1))))))),f54(x46891,x46892)) % 188.18/188.24 [4692]E(f334(f270(x46921),f334(f334(f8(f935(a927,a922),a922,x46921),f92(a927)),f334(f334(f7(x46921,f935(a927,a922),f935(a927,a922)),f334(f334(f8(f935(a927,f935(a922,a922)),f935(f935(a927,a922),f935(a927,a922)),x46921),f18(a927,a922,a922)),f334(f334(f8(f935(a927,a922),f935(a927,f935(a922,a922)),x46921),f334(f8(a922,f935(a922,a922),a927),a332)),f334(f334(f7(x46921,f935(a927,x46921),f935(a927,a922)),f334(f334(f8(f935(x46921,a922),f935(f935(a927,x46921),f935(a927,a922)),x46921),f8(x46921,a922,a927)),a331)),f334(f171(x46921),x46922))))),f334(f334(f7(a927,a927,a922),f243(a927)),f334(f196(f928(x46921)),x46922))))),f334(f179(x46921),x46922)) % 188.18/188.24 [4805]~E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x48051)),x48051)),a104),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x48052)),x48052)) % 188.18/188.24 [4433]E(f334(f334(f23(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44331)),x44331)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44332)),x44332)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),x44331),x44332))),f334(f334(f23(a1),x44331),x44332))) % 188.18/188.24 [4434]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44341)),x44341)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44342)),x44342)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),x44341),x44342))),f334(f334(f86(a1),x44341),x44342))) % 188.18/188.24 [4521]E(f334(f334(f23(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45211)),x45211)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45212)),x45212)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f23(a1),x45211),x45212))),f334(f334(f23(a1),x45211),x45212))),a104)) % 188.18/188.24 [4522]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45221)),x45221)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45222)),x45222)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),x45221),x45222))),f334(f334(f86(a1),x45221),x45222))),a104)) % 188.18/188.24 [4554]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f87(a1),x45541),x45542))),f334(f334(f87(a1),x45541),x45542))),a104)),x45542),f334(f334(f87(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45541)),x45541)),x45542)) % 188.18/188.24 [4611]E(f334(f149(f928(f928(x46111)),f928(f928(x46111)),f141(f928(x46111)),f120(f928(x46111))),f334(f334(f161(f928(x46111),f928(f928(x46111))),f163(f928(f928(x46111)),x46111,f120(f928(x46111)),f334(f16(f935(f928(x46111),f928(f928(x46111))),x46111),f334(f334(f7(f928(x46111),f928(f928(x46111)),f928(f928(x46111))),f158(f928(x46111))),f120(f928(x46111)))))),x46112)),f334(f334(f161(f928(x46111),f928(x46111)),f178(x46111)),f334(f143(f928(x46111),f334(f334(f8(a922,a922,f928(x46111)),a329),f334(f334(f7(f928(x46111),f928(x46111),a922),a331),f120(x46111)))),x46112))) % 188.18/188.24 [4619]E(f334(f334(f94(a1,a927),f334(f111(a1),f334(f334(f86(a1),x46191),a104))),f334(f334(f18(a1,a927,a927),f334(f334(f7(a1,a927,f935(a927,a927)),f334(f334(f8(a922,f935(a927,f935(a927,a927)),a1),f103(a927)),a200)),f2(a927))),f334(f334(f8(a927,a927,a1),a119),f334(f334(f7(a1,a927,a927),f334(f334(f8(a927,f935(a927,a927),a1),f246(a927)),a112)),x46192)))),f334(f334(f246(a927),f334(f111(a927),x46191)),f334(a119,x46192))) % 188.18/188.24 [4620]E(f334(f334(f94(a1,a927),f334(f111(a1),f334(f334(f86(a1),x46201),a104))),f334(f334(f18(a1,a927,a927),f334(f334(f7(a1,a927,f935(a927,a927)),f334(f334(f8(a922,f935(a927,f935(a927,a927)),a1),f103(a927)),a200)),f334(a119,x46202))),f334(f334(f8(a927,a927,a1),a119),f334(f334(f7(a1,a927,a927),f334(f334(f8(a927,f935(a927,a927),a1),f241(a927)),a112)),x46202)))),f334(f334(f241(a927),f334(f111(a927),x46201)),f334(a119,x46202))) % 188.18/188.24 [4462]E(f334(f334(f252(a1),x44621),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44622)),x44622)),a104))),f334(f334(f94(a1,a1),f334(f334(f252(a1),x44621),f334(f111(a927),x44622))),f334(f334(f18(a1,a1,a1),f87(a1)),f5(a1)))) % 188.18/188.24 [4497]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f87(a1),x44971),x44972))),f334(f334(f87(a1),x44971),x44972))),a104),f334(f334(f87(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x44971)),x44971)),a104)),x44972)) % 188.18/188.24 [4556]E(f334(f334(f41(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45561)),x45561)),a104))),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x45562)),x45562)),a104))),f334(f334(f41(a1),f334(f111(a1),x45561)),f334(f111(a1),x45562))) % 188.18/188.24 [4610]E(f334(f265(x46101,x46101,a922),f334(f334(f18(x46101,a922,f935(x46101,a922)),f334(f334(f8(f935(x46101,f935(a922,a922)),f935(a922,f935(x46101,a922)),x46101),f7(x46101,a922,a922)),f334(f334(f8(f935(x46101,a922),f935(x46101,f935(a922,a922)),x46101),f334(f8(a922,f935(a922,a922),x46101),a332)),a331))),x46102)),f271(x46101,x46102)) % 188.18/188.24 [4669]E(f50(a1,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x46691)),x46691)),a104)),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x46692)),x46692)),a104))),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f50(a1,f334(f111(a1),x46691),f334(f111(a1),x46692)))) % 188.18/188.24 [4635]E(f334(f334(f41(a927),x46351),f334(f334(f86(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),x46352)),f334(f334(f41(a927),x46351),f334(a119,f334(a119,f334(a119,x46352))))) % 188.18/188.24 [4636]E(f50(a927,x46361,f334(f334(f86(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),x46362)),f50(a927,x46361,f334(a119,f334(a119,f334(a119,x46362))))) % 188.18/188.24 [4637]E(f50(a927,f334(f334(f86(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),x46371),x46372),f50(a927,f334(a119,f334(a119,f334(a119,x46371))),x46372)) % 188.18/188.24 [4662]E(f130(f334(x46621,f334(f334(f87(a106),f334(f111(a106),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),x46622))),f334(f209(x46621),x46622)) % 188.18/188.24 [4667]E(f334(f334(f41(a927),f334(f334(f86(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),x46671)),x46672),f334(f334(f41(a927),f334(a119,f334(a119,f334(a119,x46671)))),x46672)) % 188.18/188.24 [4744]~E(f28(x47441,x47442,x47443),a25) % 188.18/188.24 [4745]~E(f27(x47451,x47452,x47453),a25) % 188.18/188.24 [4749]~E(f133(x47491,x47492,x47493),f126(x47491)) % 188.18/188.24 [3468]E(f334(f199(x34681,x34682),x34683),f128(x34681,x34682)) % 188.18/188.24 [3487]E(f334(f208(x34871,x34872),x34873),f334(f136(x34871),x34872)) % 188.18/188.24 [3563]E(f334(f334(f161(x35631,x35632),x35633),f120(x35631)),f120(x35632)) % 188.18/188.24 [3603]E(f334(f191(x36031,x36032,x36033),f2(a927)),x36032) % 188.18/188.24 [3605]E(f334(f334(f188(x36051,x36052),x36053),f120(x36052)),f120(f934(x36051,x36052))) % 188.18/188.24 [3620]E(f334(f196(f928(x36201)),f176(x36201,x36202,x36203)),x36202) % 188.18/188.24 [3639]E(f91(x36391,f67(x36391,x36392,x36393)),f334(f68(x36391,x36392),x36393)) % 188.18/188.24 [3643]E(f251(x36431,x36432,f251(x36432,x36431,x36433)),x36433) % 188.18/188.24 [3663]E(f334(f175(x36631),f176(x36631,x36632,x36633)),f176(x36631,x36632,x36633)) % 188.18/188.24 [3690]E(f147(x36901,x36902,f159(x36901,x36903)),f159(x36901,f147(x36901,x36902,x36903))) % 188.18/188.24 [3707]E(f334(f259(f928(x37071),f928(x37071)),f173(x37071,x37072,x37073)),f334(f143(x37071,x37072),x37073)) % 188.18/188.24 [3749]E(f334(f334(f158(x37491),x37492),f176(x37491,x37493,x37492)),f176(x37491,f334(a119,x37493),x37492)) % 188.18/188.24 [3780]E(f192(x37801,x37802,x37803,f2(a927)),x37802) % 188.18/188.24 [3781]E(f17(x37811,x37812,x37813,f2(a106)),x37812) % 188.18/188.24 [3782]E(f19(x37821,x37822,x37823,f2(a106)),x37822) % 188.18/188.24 [3789]E(f170(x37891,x37892,x37893,f120(x37891)),f120(x37892)) % 188.18/188.24 [3790]E(f137(x37901,x37902,x37903,f126(x37901)),f126(x37902)) % 188.18/188.24 [3797]E(f334(f334(f171(x37971),f334(f334(f158(x37971),x37972),x37973)),f2(a927)),x37972) % 188.18/188.24 [3830]E(f64(x38301,x38302,f120(x38301),x38303),f120(f934(x38301,x38302))) % 188.18/188.24 [3851]P27(x38511,x38512,x38513,f195(f935(x38511,a922))) % 188.18/188.24 [3953]E(f273(x39531,x39532,x39533),f334(f260(f935(a106,f935(a922,f931(f929(x39531)))),f934(a106,a106)),f46(x39531))) % 188.18/188.24 [4008]E(f334(f78(x40081,x40082,x40081,x40083),f32(x40081)),x40083) % 188.18/188.24 [4186]P107(f334(f334(f336(f934(x41861,x41861)),f334(f334(f260(x41861,x41861),x41862),x41862)),f314(x41861,x41863))) % 188.18/188.24 [4807]~P107(f334(f334(f336(f934(f928(x48071),f928(x48071))),f334(f334(f260(f928(x48071),f928(x48071)),x48072),f120(x48071))),f152(x48071,x48073))) % 188.18/188.24 [4808]~P107(f334(f334(f336(f934(f928(x48081),f928(x48081))),f334(f334(f260(f928(x48081),f928(x48081)),x48082),f120(x48081))),f154(x48081,x48083))) % 188.18/188.24 [4809]~P107(f334(f334(f336(f934(f928(x48091),f928(x48091))),f334(f334(f260(f928(x48091),f928(x48091)),x48092),f120(x48091))),f164(x48091,x48093))) % 188.18/188.24 [4810]~P107(f334(f334(f336(f934(f928(x48101),f928(x48101))),f334(f334(f260(f928(x48101),f928(x48101)),f120(x48101)),x48102)),f152(x48101,x48103))) % 188.18/188.24 [4811]~P107(f334(f334(f336(f934(f928(x48111),f928(x48111))),f334(f334(f260(f928(x48111),f928(x48111)),f120(x48111)),x48112)),f164(x48111,x48113))) % 188.18/188.24 [3539]E(f334(f334(f210(x35391),x35392),x35393),f211(x35391,f224(x35392,x35393))) % 188.18/188.24 [3592]E(f334(f293(x35921,x35922),f334(f293(x35922,x35921),x35923)),x35923) % 188.18/188.24 [3615]E(f334(f334(f188(x36151,x36152),f120(x36151)),x36153),f120(f934(x36151,x36152))) % 188.18/188.24 [3618]E(f183(x36181,x36182,f334(f307(a927),x36183)),f334(f334(f182(x36181),x36183),x36182)) % 188.18/188.24 [3636]E(f159(x36361,f334(f143(x36361,x36362),x36363)),f334(f143(x36361,x36362),f159(x36361,x36363))) % 188.18/188.24 [3637]E(f334(f291(x36371,x36372),f334(f293(x36372,x36371),x36373)),f334(f272(x36372,x36371),x36373)) % 188.18/188.24 [3638]E(f334(f272(x36381,x36382),f334(f293(x36382,x36381),x36383)),f334(f291(x36382,x36381),x36383)) % 188.18/188.24 [3656]E(f334(f143(x36561,x36562),f334(f175(x36561),x36563)),f334(f175(x36561),f334(f143(x36561,x36562),x36563))) % 188.18/188.24 [3669]E(f334(f334(f145(x36691),x36692),f334(f178(x36691),x36693)),f334(f334(f145(x36691),f334(a119,x36692)),x36693)) % 188.18/188.24 [3685]E(f29(f27(x36851,x36852,x36853)),f334(f334(f86(a927),f29(x36853)),f334(a119,f2(a927)))) % 188.18/188.24 [3686]E(f334(f317(x36861,x36862,x36863),f195(f935(x36861,a922))),f195(f935(x36862,a922))) % 188.18/188.24 [3687]E(f334(f318(x36871,x36872,x36873),f195(f935(x36872,a922))),f195(f935(x36871,a922))) % 188.18/188.24 [3688]E(f334(f318(x36881,x36882,x36883),f250(f935(x36882,a922))),f250(f935(x36881,a922))) % 188.18/188.24 [3689]E(f334(f292(x36891,x36892,x36893),f195(f935(x36891,a922))),f195(f935(x36892,a922))) % 188.18/188.24 [3713]E(f127(x37131,f133(f929(x37131),x37132,x37133)),f123(x37131,x37132,f127(x37131,x37133))) % 188.18/188.24 [3715]E(f334(f334(f316(x37151),x37152),f334(f179(x37151),x37153)),f334(f179(x37151),f147(x37151,x37152,x37153))) % 188.18/188.24 [3801]E(f334(f196(a924),f27(x38011,x38012,x38013)),f334(f334(f86(a927),f334(f196(a924),x38013)),f334(a119,f2(a927)))) % 188.18/188.24 [3802]E(f334(f317(f934(x38021,x38022),x38022,f264(x38021,x38022)),x38023),f334(f291(x38021,x38022),x38023)) % 188.18/188.24 [3803]E(f334(f317(f934(x38031,x38032),x38031,f259(x38031,x38032)),x38033),f334(f272(x38031,x38032),x38033)) % 188.18/188.24 [3822]E(f334(f179(x38221),f176(x38221,f334(a119,x38222),x38223)),f334(f334(f316(x38221),x38223),f195(f935(x38221,a922)))) % 188.18/188.24 [3880]E(f334(f334(f260(x38801,x38802),f334(f259(x38801,x38802),x38803)),f334(f264(x38801,x38802),x38803)),x38803) % 188.18/188.24 [3887]E(f334(f196(f929(x38871)),f133(x38871,x38872,x38873)),f334(f334(f86(a927),f334(f196(f929(x38871)),x38873)),f334(a119,f2(a927)))) % 188.18/188.24 [3888]E(f334(f334(f265(x38881,x38882,x38881),f16(x38881,x38882)),x38883),f334(f259(x38881,x38882),x38883)) % 188.18/188.24 [3961]E(f29(f28(x39611,x39612,x39613)),f334(f334(f86(a927),f334(f334(f86(a927),f29(x39612)),f29(x39613))),f334(a119,f2(a927)))) % 188.18/188.24 [4014]E(f334(f78(x40141,x40141,x40142,f32(x40141)),x40143),x40143) % 188.18/188.24 [4022]E(f334(f334(f141(x40221),f176(x40221,x40222,x40223)),f334(f334(f158(x40221),x40223),f120(x40221))),f334(f334(f158(x40221),x40223),f176(x40221,x40222,x40223))) % 188.18/188.24 [4119]E(f334(f196(a924),f28(x41191,x41192,x41193)),f334(f334(f86(a927),f334(f334(f86(a927),f334(f196(a924),x41192)),f334(f196(a924),x41193))),f334(a119,f2(a927)))) % 188.18/188.24 [4194]P107(f334(f334(f242(f935(x41941,a922)),f334(f179(x41941),f334(f143(x41941,x41942),x41943))),f334(f179(x41941),x41943))) % 188.18/188.24 [4237]P107(f334(f334(f242(f935(x42371,a922)),f334(f179(x42371),f334(f334(f182(x42371),x42372),x42373))),f334(f179(x42371),x42373))) % 188.18/188.24 [4238]P107(f334(f334(f242(f935(x42381,a922)),f334(f179(x42381),f334(f334(f145(x42381),x42382),x42383))),f334(f179(x42381),x42383))) % 188.18/188.24 [4241]P107(f334(f334(f242(f935(x42411,a922)),f334(f179(x42411),f183(x42411,x42412,x42413))),f334(f179(x42411),x42412))) % 188.18/188.24 [4242]P107(f334(f334(f242(f935(x42421,a922)),f334(f179(x42421),f177(x42421,x42422,x42423))),f334(f179(x42421),x42423))) % 188.18/188.24 [4263]P27(f934(x42631,x42632),f934(x42632,x42631),f334(f265(x42631,x42632,f934(x42632,x42631)),f334(f7(x42632,x42631,f934(x42632,x42631)),f260(x42632,x42631))),x42633) % 188.18/188.24 [4273]E(f334(f334(f334(f190(f928(x42731),f928(x42731)),f50(a927,x42732,f334(f196(f928(x42731)),x42733))),f174(x42731)),x42733),f334(f334(f334(f190(f928(x42731),f928(x42731)),x42732),f174(x42731)),x42733)) % 188.18/188.24 [4315]P107(f334(f334(f336(f934(f928(x43151),f928(x43151))),f334(f334(f260(f928(x43151),f928(x43151)),x43152),x43152)),f165(x43151,f314(x43151,x43153)))) % 188.18/188.24 [4457]E(f91(f934(x44571,x44572),f334(f334(f18(f934(x44571,x44572),x44572,a922),f334(f334(f8(x44571,f935(x44572,a922),f934(x44571,x44572)),x44573),f259(x44571,x44572))),f264(x44571,x44572))),f91(f934(x44571,x44572),f334(f265(x44571,x44572,a922),x44573))) % 188.18/188.24 [4458]E(f96(f934(x44581,x44582),f334(f334(f18(f934(x44581,x44582),x44582,a922),f334(f334(f8(x44581,f935(x44582,a922),f934(x44581,x44582)),x44583),f259(x44581,x44582))),f264(x44581,x44582))),f96(f934(x44581,x44582),f334(f265(x44581,x44582,a922),x44583))) % 188.18/188.24 [4489]E(f334(f334(f294(f934(a927,x44891),x44891),f326(a927,x44891,a248,x44892)),f334(f334(f18(x44891,x44891,f934(a927,x44891)),f334(f334(f8(a927,f935(x44891,f934(a927,x44891)),x44891),f260(a927,x44891)),x44893)),f5(x44891))),f328(x44891,x44893,x44892)) % 188.18/188.24 [4549]E(f334(f266(x45491,x45491,x45492,x45492,f5(x45491),f5(x45492)),x45493),x45493) % 188.18/188.24 [4628]E(f334(f149(f928(f928(x46281)),f928(f928(x46281)),f141(f928(x46281)),f120(f928(x46281))),f334(f334(f161(f928(x46281),f928(f928(x46281))),f334(f334(f7(f928(x46281),f928(x46281),f928(f928(x46281))),f334(f334(f8(f935(x46281,f928(x46281)),f935(f928(x46281),f928(f928(x46281))),f928(x46281)),f161(x46281,f928(x46281))),f334(f7(x46281,f928(x46281),f928(x46281)),f158(x46281)))),x46282)),f60(x46281,x46283,x46282))),f60(x46281,f334(a119,x46283),x46282)) % 188.18/188.24 [4697]E(f232(a927,f934(x46971,f929(x46971)),f2(a927),f334(f265(x46971,f929(x46971),a927),f334(f334(f7(x46971,a927,f935(f929(x46971),a927)),f334(f334(f8(f935(f929(x46971),f935(a927,a927)),f935(a927,f935(f929(x46971),a927)),x46971),f7(f929(x46971),a927,a927)),f334(f334(f8(f935(f929(x46971),a927),f935(f929(x46971),f935(a927,a927)),x46971),f334(f8(a927,f935(a927,a927),f929(x46971)),f86(a927))),f334(f334(f7(x46971,f935(f929(x46971),a927),f935(f929(x46971),a927)),f334(f334(f8(f935(a927,a927),f935(f935(f929(x46971),a927),f935(f929(x46971),a927)),x46971),f8(a927,a927,f929(x46971))),f334(f334(f8(a927,f935(a927,a927),x46971),f86(a927)),x46972))),f132(x46971,x46972))))),f84(a927))),f334(f142(x46971),x46973)),f334(f132(x46971,x46972),x46973)) % 188.18/188.24 [4704]E(f334(f334(f94(a1,x47041),f227(f334(f334(f78(f934(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47042),f334(f334(f78(f934(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47043))),f334(f334(f18(a1,a1,x47041),f334(f334(f8(a1,f935(a1,x47041),a1),f210(x47041)),f334(f334(f18(a1,a1,a1),f334(f334(f8(a1,f935(a1,a1),a1),f86(a1)),f334(f334(f8(a1,a1,a1),f334(f87(a1),f334(f334(f78(f934(a1,a1),a1,x47041,f259(a1,a1)),f221(x47041)),x47042))),f334(f334(f7(a1,a1,a1),f41(a1)),f334(f334(f78(f934(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47042))))),f334(f334(f8(a1,a1,a1),f334(f87(a1),f334(f334(f78(f934(a1,a1),a1,x47041,f259(a1,a1)),f221(x47041)),x47043))),f334(f334(f7(a1,a1,a1),f41(a1)),f334(f334(f78(f934(a1,a1),a1,x47041,f264(a1,a1)),f221(x47041)),x47043)))))),f5(a1))),f239(x47041,x47042,x47043)) % 188.18/188.24 [4740]~E(f334(f334(f158(x47401),x47402),x47403),x47403) % 188.18/188.24 [4747]~E(f334(f334(f158(x47471),x47472),x47473),f120(x47471)) % 188.18/188.24 [4765]~E(f334(f334(f316(x47651),x47652),x47653),f195(f935(x47651,a922))) % 188.18/188.24 [4787]~E(f334(f317(x47871,f935(x47871,a922),x47872),x47873),f334(f315(x47871),x47873)) % 188.18/188.24 [3597]E(f334(f334(f166(x35971,f120(x35971)),x35972),x35973),f120(x35971)) % 188.18/188.24 [3598]E(f334(f148(x35981),f334(f334(f158(x35981),x35982),x35983)),x35982) % 188.18/188.24 [3599]E(f334(f178(x35991),f334(f334(f158(x35991),x35992),x35993)),x35993) % 188.18/188.24 [3642]E(f334(f334(f145(x36421),f84(a927)),f334(f334(f158(x36421),x36422),x36423)),x36423) % 188.18/188.24 [3676]E(f121(x36761,f334(f334(f145(x36761),x36762),x36763)),f334(f334(f145(x36761),x36762),f121(x36761,x36763))) % 188.18/188.24 [3678]E(f334(f334(f166(x36781,x36782),x36783),f334(f334(f171(x36781),x36782),x36783)),x36782) % 188.18/188.24 [3698]E(f334(f334(f316(x36981),x36982),f334(f334(f316(x36981),x36982),x36983)),f334(f334(f316(x36981),x36982),x36983)) % 188.18/188.24 [3710]E(f334(f334(f316(x37101),x37102),f334(f179(x37101),x37103)),f334(f179(x37101),f334(f334(f158(x37101),x37102),x37103))) % 188.18/188.24 [3712]E(f334(f334(f145(x37121),x37122),f334(f178(x37121),x37123)),f334(f178(x37121),f334(f334(f145(x37121),x37122),x37123))) % 188.18/188.24 [3724]E(f334(f334(f182(x37241),f84(a927)),f334(f334(f158(x37241),x37242),x37243)),f334(f334(f158(x37241),x37242),f120(x37241))) % 188.18/188.24 [3767]E(f334(f68(x37671,x37672),f334(f334(f316(x37671),x37673),f195(f935(x37671,a922)))),x37673) % 188.18/188.24 [3812]E(f334(f334(f86(a927),x38121),f334(f334(f86(a927),x38122),x38123)),f334(f334(f86(a927),x38122),f334(f334(f86(a927),x38121),x38123))) % 188.18/188.24 [3813]E(f334(f334(f86(a1),x38131),f334(f334(f86(a1),x38132),x38133)),f334(f334(f86(a1),x38132),f334(f334(f86(a1),x38131),x38133))) % 188.18/188.24 [3818]E(f334(f334(f262(x38181,x38182),f195(f935(x38181,a922))),x38183),f195(f935(f934(x38181,x38182),a922))) % 188.18/188.24 [3843]E(f334(f334(f108(f935(x38431,a922)),x38432),x38433),f334(f334(f108(f935(x38431,a922)),x38433),x38432)) % 188.18/188.24 [3844]E(f334(f334(f109(f935(x38441,a922)),x38442),x38443),f334(f334(f109(f935(x38441,a922)),x38443),x38442)) % 188.18/188.24 [3846]E(f334(f334(f141(x38461),x38462),f334(f334(f158(x38461),x38463),f120(x38461))),f334(f174(x38461),f334(f334(f158(x38461),x38463),x38462))) % 188.18/188.24 [3847]E(f334(f334(f141(x38471),f334(f175(x38471),x38472)),f334(f175(x38471),x38473)),f334(f175(x38471),f334(f334(f141(x38471),x38473),x38472))) % 188.18/188.24 [3857]E(f334(f178(x38571),f334(f334(f182(x38571),f334(a119,x38572)),x38573)),f334(f334(f182(x38571),x38572),f334(f178(x38571),x38573))) % 188.18/188.24 [3865]P107(f334(f334(f336(x38651),x38652),f334(f334(f316(x38651),x38652),x38653))) % 188.18/188.24 [3869]E(f334(f334(f45(x38691,f935(x38692,a922)),f195(f935(x38691,a922))),x38693),f250(f935(x38692,a922))) % 188.18/188.24 [3872]E(f334(f292(x38721,x38721,f271(x38721,x38722)),x38723),f334(f334(f109(f935(x38721,a922)),x38722),x38723)) % 188.18/188.24 [3886]E(f334(f196(f928(x38861)),f334(f334(f158(x38861),x38862),x38863)),f334(f334(f86(a927),f334(f196(f928(x38861)),x38863)),f334(a119,f2(a927)))) % 188.18/188.24 [3890]E(f121(x38901,f334(f334(f141(x38901),x38902),f334(f334(f158(x38901),x38903),f120(x38901)))),x38902) % 188.18/188.24 [3891]E(f151(x38911,f334(f334(f141(x38911),x38912),f334(f334(f158(x38911),x38913),f120(x38911)))),x38913) % 188.18/188.24 [3900]E(f334(f334(f141(x39001),f334(f334(f182(x39001),x39002),x39003)),f334(f334(f145(x39001),x39002),x39003)),x39003) % 188.18/188.24 [3909]E(f334(f334(f23(a927),f334(f334(f86(a927),x39091),x39092)),f334(f334(f86(a927),x39093),x39092)),f334(f334(f23(a927),x39091),x39093)) % 188.18/188.24 [3910]E(f334(f334(f23(a927),f334(f334(f86(a927),x39101),x39102)),f334(f334(f86(a927),x39101),x39103)),f334(f334(f23(a927),x39102),x39103)) % 188.18/188.24 [3916]E(f334(f334(f141(x39161),f334(f175(x39161),x39162)),f334(f334(f158(x39161),x39163),f120(x39161))),f334(f175(x39161),f334(f334(f158(x39161),x39163),x39162))) % 188.18/188.24 [3918]E(f334(f334(f86(a927),f334(f196(f928(x39181)),x39182)),f334(f196(f928(x39181)),x39183)),f334(f196(f928(x39181)),f334(f334(f141(x39181),x39182),x39183))) % 188.18/188.24 [3921]E(f334(f334(f86(a927),f334(f196(f928(x39211)),x39212)),f334(f196(f928(x39211)),x39213)),f334(f196(f928(x39211)),f180(x39211,x39212,x39213))) % 188.18/188.24 [3928]E(f334(f334(f108(f935(x39281,a922)),f334(f179(x39281),x39282)),f334(f179(x39281),x39283)),f334(f179(x39281),f334(f334(f141(x39281),x39282),x39283))) % 188.18/188.24 [3929]E(f50(a927,f334(f334(f87(a927),x39291),x39292),f334(f334(f87(a927),x39291),x39293)),f334(f334(f87(a927),x39291),f50(a927,x39292,x39293))) % 188.18/188.24 [3941]E(f334(f334(f182(x39411),f334(f334(f23(a927),x39412),f84(a927))),f334(f178(x39411),x39413)),f334(f178(x39411),f334(f334(f182(x39411),x39412),x39413))) % 188.18/188.24 [3946]E(f334(f334(f109(f935(x39461,a922)),x39462),f334(f85(f935(x39461,a922)),x39463)),f334(f334(f23(f935(x39461,a922)),x39462),x39463)) % 188.18/188.24 [3947]E(f334(f334(f23(f935(x39471,a922)),x39472),f334(f85(f935(x39471,a922)),x39473)),f334(f334(f109(f935(x39471,a922)),x39472),x39473)) % 188.18/188.24 [3964]E(f334(f334(f262(x39641,x39642),x39643),f334(f16(f935(x39642,a922),x39641),f195(f935(x39642,a922)))),f195(f935(f934(x39641,x39642),a922))) % 188.18/188.24 [3966]E(f334(f334(f23(a927),f334(f334(f87(a927),x39661),x39662)),f334(f334(f87(a927),x39661),x39663)),f334(f334(f87(a927),x39661),f334(f334(f23(a927),x39662),x39663))) % 188.18/188.24 [3967]E(f334(f334(f86(a927),f334(f334(f87(a927),x39671),x39672)),f334(f334(f87(a927),x39671),x39673)),f334(f334(f87(a927),x39671),f334(f334(f86(a927),x39672),x39673))) % 188.18/188.24 [3968]E(f334(f334(f23(a1),f334(f334(f87(a1),x39681),x39682)),f334(f334(f87(a1),x39681),x39683)),f334(f334(f87(a1),x39681),f334(f334(f23(a1),x39682),x39683))) % 188.18/188.24 [3969]E(f334(f334(f86(a1),f334(f334(f87(a1),x39691),x39692)),f334(f334(f87(a1),x39691),x39693)),f334(f334(f87(a1),x39691),f334(f334(f86(a1),x39692),x39693))) % 188.18/188.24 [3970]E(f334(f334(f87(a1),f334(f334(f252(a1),x39701),x39702)),f334(f334(f252(a1),x39701),x39703)),f334(f334(f252(a1),x39701),f334(f334(f86(a927),x39702),x39703))) % 188.18/188.24 [3983]E(f334(f334(f44(x39831,f935(x39832,a922)),x39833),f334(f16(f935(x39832,a922),x39831),f195(f935(x39832,a922)))),f195(f935(x39832,a922))) % 188.18/188.24 [3985]E(f50(a927,f334(f334(f87(a927),x39851),x39852),f334(f334(f87(a927),x39853),x39852)),f334(f334(f87(a927),f50(a927,x39851,x39853)),x39852)) % 188.18/188.24 [3990]E(f50(a1,f334(f334(f23(a1),x39901),f50(a1,x39902,x39903)),x39903),f50(a1,f334(f334(f23(a1),x39901),x39902),x39903)) % 188.18/188.24 [3991]E(f50(a1,f334(f334(f87(a1),x39911),f50(a1,x39912,x39913)),x39913),f50(a1,f334(f334(f87(a1),x39911),x39912),x39913)) % 188.18/188.24 [3992]P107(f334(f334(f242(f935(x39921,a922)),x39922),f334(f334(f316(x39921),x39923),x39922))) % 188.18/188.24 [4073]E(f334(f334(f45(f935(x40731,a922),f935(x40731,a922)),x40732),f334(f108(f935(x40731,a922)),x40733)),f334(f334(f108(f935(x40731,a922)),x40733),f43(f935(x40731,a922),x40732))) % 188.18/188.24 [4074]E(f334(f334(f44(f935(x40741,a922),f935(x40741,a922)),x40742),f334(f109(f935(x40741,a922)),x40743)),f334(f334(f109(f935(x40741,a922)),x40743),f42(f935(x40741,a922),x40742))) % 188.18/188.24 [4084]E(f334(f179(x40841),f334(f334(f334(f190(f928(x40841),f928(x40841)),x40842),f174(x40841)),x40843)),f334(f179(x40841),x40843)) % 188.18/188.24 [4088]E(f334(f334(f182(x40881),f334(f196(f928(x40881)),f184(x40881,x40882,x40883))),x40883),f184(x40881,x40882,x40883)) % 188.18/188.24 [4092]E(f334(f196(f928(x40921)),f334(f334(f334(f190(f928(x40921),f928(x40921)),x40922),f174(x40921)),x40923)),f334(f196(f928(x40921)),x40923)) % 188.18/188.24 [4095]E(f334(f334(f265(x40951,x40952,x40952),f334(f16(f935(x40952,x40952),x40951),f5(x40952))),x40953),f334(f264(x40951,x40952),x40953)) % 188.18/188.24 [4102]E(f50(a1,f334(f334(f23(a1),f50(a1,x41021,x41022)),x41023),x41022),f50(a1,f334(f334(f23(a1),x41021),x41023),x41022)) % 188.18/188.24 [4103]E(f50(a1,f334(f334(f252(a1),f50(a1,x41031,x41032)),x41033),x41032),f50(a1,f334(f334(f252(a1),x41031),x41033),x41032)) % 188.18/188.24 [4106]E(f334(f334(f44(f935(f934(x41061,x41062),a922),f935(x41062,a922)),x41063),f291(x41061,x41062)),f334(f291(x41061,x41062),f42(f935(f934(x41061,x41062),a922),x41063))) % 188.18/188.24 [4107]E(f334(f334(f44(f935(f934(x41071,x41072),a922),f935(x41071,a922)),x41073),f272(x41071,x41072)),f334(f272(x41071,x41072),f42(f935(f934(x41071,x41072),a922),x41073))) % 188.18/188.24 [4128]E(f334(f78(x41281,x41281,x41281,x41282),f334(f334(f190(x41281,x41281),x41283),x41282)),f334(f334(f190(x41281,x41281),f334(a119,x41283)),x41282)) % 188.18/188.24 [4148]E(f334(f334(f145(x41481),f334(f334(f23(a927),f334(f196(f928(x41481)),x41482)),x41483)),f334(f175(x41481),x41482)),f334(f175(x41481),f334(f334(f182(x41481),x41483),x41482))) % 188.18/188.24 [4149]E(f334(f334(f182(x41491),f334(f334(f23(a927),f334(f196(f928(x41491)),x41492)),x41493)),f334(f175(x41491),x41492)),f334(f175(x41491),f334(f334(f145(x41491),x41493),x41492))) % 188.18/188.24 [4151]E(f334(f334(f86(a927),f334(f172(a927),f334(f334(f161(x41511,a927),x41512),x41513))),f334(f196(f928(x41511)),x41513)),f162(x41511,x41512,x41513)) % 188.18/188.24 [4171]E(f334(f174(x41711),f334(f334(f334(f190(f928(x41711),f928(x41711)),x41712),f174(x41711)),x41713)),f334(f334(f334(f190(f928(x41711),f928(x41711)),f334(a119,x41712)),f174(x41711)),x41713)) % 188.18/188.24 [4187]P107(f334(f334(f242(a927),f334(f196(f928(x41871)),f334(f143(x41871,x41872),x41873))),f334(f196(f928(x41871)),x41873))) % 188.18/188.24 [4202]E(f334(f334(f108(f935(f935(x42021,a922),a922)),f334(f315(x42021),x42022)),f334(f317(f935(x42021,a922),f935(x42021,a922),f334(f316(x42021),x42023)),f334(f315(x42021),x42022))),f334(f315(x42021),f334(f334(f316(x42021),x42023),x42022))) % 188.18/188.24 [4234]P107(f334(f334(f242(a927),f334(f196(f928(x42341)),f184(x42341,x42342,x42343))),f334(f196(f928(x42341)),x42343))) % 188.18/188.24 [4240]E(f334(f272(x42401,x42402),f334(f270(f934(x42401,x42402)),f334(f265(x42401,x42402,a922),x42403))),f334(f270(x42401),f334(f334(f8(f935(x42402,a922),a922,x42401),f92(x42402)),x42403))) % 188.18/188.24 [4252]E(f334(f317(a927,a927,f334(f334(f7(a927,a927,a927),f86(a927)),x42521)),f311(a927,x42522,x42523)),f311(a927,f334(f334(f86(a927),x42522),x42521),f334(f334(f86(a927),x42523),x42521))) % 188.18/188.24 [4266]E(f334(f317(a927,a927,f334(f334(f7(a927,a927,a927),f86(a927)),x42661)),f334(f310(a927,x42662),x42663)),f334(f310(a927,f334(f334(f86(a927),x42662),x42661)),f334(f334(f86(a927),x42663),x42661))) % 188.18/188.24 [4283]E(f334(f334(f188(x42831,x42832),f334(f334(f161(f934(x42831,x42832),x42831),f259(x42831,x42832)),x42833)),f334(f334(f161(f934(x42831,x42832),x42832),f264(x42831,x42832)),x42833)),x42833) % 188.18/188.24 [4288]E(f334(f334(f86(a927),f334(f334(f87(a927),x42881),f50(a927,f334(f334(f41(a927),x42882),x42881),x42883))),f50(a927,x42882,x42881)),f50(a927,x42882,f334(f334(f87(a927),x42881),x42883))) % 188.18/188.24 [4300]E(f334(f334(f141(x43001),x43002),f334(f149(f928(x43001),f928(x43001),f141(x43001),f120(x43001)),x43003)),f334(f149(f928(x43001),f928(x43001),f141(x43001),x43002),x43003)) % 188.18/188.24 [4320]P107(f334(f334(f336(f934(x43201,x43201)),f334(f334(f260(x43201,x43201),x43202),x43202)),f334(f334(f190(f934(x43201,x43201),a922),f2(a927)),x43203))) % 188.18/188.24 [4325]E(f334(f270(x43251),f334(f334(f8(f935(x43252,a922),a922,x43251),f92(x43252)),f334(f7(x43252,x43251,a922),x43253))),f334(f291(x43252,x43251),f334(f270(f934(x43252,x43251)),f334(f265(x43252,x43251,a922),x43253)))) % 188.18/188.24 [4342]E(f334(f334(f108(f935(x43421,a922)),f334(f334(f44(a927,f935(x43421,a922)),f311(a927,f84(a927),x43422)),x43423)),f334(x43423,f2(a927))),f334(f334(f44(a927,f935(x43421,a922)),f334(f309(a927),x43422)),x43423)) % 188.18/188.24 [4357]E(f334(f149(f928(x43571),f928(x43571),f141(x43571),f120(x43571)),f334(f334(f161(f928(x43571),f928(x43571)),f143(x43571,x43572)),x43573)),f334(f143(x43571,x43572),f334(f149(f928(x43571),f928(x43571),f141(x43571),f120(x43571)),x43573))) % 188.18/188.24 [4361]E(f334(f264(f928(x43611),f928(x43611)),f173(x43611,x43612,x43613)),f334(f143(x43611,f334(f78(a922,a922,x43611,a329),x43612)),x43613)) % 188.18/188.24 [4369]P26(x43691,x43692,f334(f334(f316(f926(x43691)),f98(x43691,x43693,a25,x43693)),f195(f935(f926(x43691),a922)))) % 188.18/188.24 [4402]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f87(a1),x44021),f334(f334(f41(a1),x44022),x44021))),f50(a1,x44022,x44021))),x44023),f334(f334(f86(a1),x44022),x44023)) % 188.18/188.24 [4443]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f87(a1),f334(f334(f41(a1),x44431),x44432)),x44432)),f50(a1,x44431,x44432))),x44433),f334(f334(f86(a1),x44431),x44433)) % 188.18/188.24 [4471]E(f91(f934(x44711,x44712),f334(f265(x44711,x44712,a922),f334(f334(f8(f935(x44712,f934(x44711,x44712)),f935(x44712,a922),x44711),f334(f8(f934(x44711,x44712),a922,x44712),x44713)),f260(x44711,x44712)))),f91(f934(x44711,x44712),x44713)) % 188.18/188.24 [4472]E(f96(f934(x44721,x44722),f334(f265(x44721,x44722,a922),f334(f334(f8(f935(x44722,f934(x44721,x44722)),f935(x44722,a922),x44721),f334(f8(f934(x44721,x44722),a922,x44722),x44723)),f260(x44721,x44722)))),f96(f934(x44721,x44722),x44723)) % 188.18/188.24 [4500]P107(f334(f334(f242(f935(x45001,a922)),f42(f935(x45001,a922),f334(f334(f109(f935(f935(x45001,a922),a922)),x45002),x45003))),f334(f334(f109(f935(x45001,a922)),f42(f935(x45001,a922),x45002)),f42(f935(x45001,a922),x45003)))) % 188.18/188.24 [4501]E(f334(f175(x45011),f334(f334(f334(f190(f928(x45011),f928(x45011)),f334(f334(f23(a927),f334(f196(f928(x45011)),x45012)),f50(a927,x45013,f334(f196(f928(x45011)),x45012)))),f174(x45011)),x45012)),f334(f334(f334(f190(f928(x45011),f928(x45011)),x45013),f174(x45011)),f334(f175(x45011),x45012))) % 188.18/188.24 [4539]P107(f334(f334(f242(a927),f334(f196(f928(x45391)),f334(f334(f145(x45391),f334(f196(f928(x45391)),f184(x45391,x45392,x45393))),x45393))),f334(f196(f928(x45391)),x45393))) % 188.18/188.24 [4797]~P107(f334(f67(x47971,x47972,f195(f935(x47971,a922))),x47973)) % 188.18/188.24 [4806]~P107(f334(f334(f336(f934(x48061,x48061)),f334(f334(f260(x48061,x48061),x48062),x48063)),f160(x48061,f120(f935(x48061,a927))))) % 188.18/188.24 [3858]E(f334(f196(f928(x38581)),f334(f334(f182(x38581),x38582),x38583)),f334(f334(f246(a927),f334(f196(f928(x38581)),x38583)),x38582)) % 188.18/188.24 [3859]E(f334(f196(f928(x38591)),f334(f334(f145(x38591),x38592),x38593)),f334(f334(f23(a927),f334(f196(f928(x38591)),x38593)),x38592)) % 188.18/188.24 [3885]E(f334(f196(f928(f928(x38851))),f60(x38851,x38852,x38853)),f334(f334(f252(a927),f334(f196(f928(x38851)),x38853)),x38852)) % 188.18/188.24 [3902]E(f334(f334(f41(a927),f334(f334(f41(a927),x39021),x39022)),x39023),f334(f334(f41(a927),x39021),f334(f334(f87(a927),x39022),x39023))) % 188.18/188.24 [3903]E(f334(f334(f23(a927),f334(f334(f23(a927),x39031),x39032)),x39033),f334(f334(f23(a927),x39031),f334(f334(f86(a927),x39032),x39033))) % 188.18/188.24 [3904]E(f334(f334(f87(a927),f334(f334(f87(a927),x39041),x39042)),x39043),f334(f334(f87(a927),x39041),f334(f334(f87(a927),x39042),x39043))) % 188.18/188.24 [3905]E(f334(f334(f87(a1),f334(f334(f87(a1),x39051),x39052)),x39053),f334(f334(f87(a1),x39051),f334(f334(f87(a1),x39052),x39053))) % 188.18/188.24 [3906]E(f334(f334(f86(a927),f334(f334(f86(a927),x39061),x39062)),x39063),f334(f334(f86(a927),x39061),f334(f334(f86(a927),x39062),x39063))) % 188.18/188.24 [3907]E(f334(f334(f86(a1),f334(f334(f86(a1),x39071),x39072)),x39073),f334(f334(f86(a1),x39071),f334(f334(f86(a1),x39072),x39073))) % 188.18/188.24 [3908]E(f334(f334(f252(a1),f334(f334(f252(a1),x39081),x39082)),x39083),f334(f334(f252(a1),x39081),f334(f334(f87(a927),x39082),x39083))) % 188.18/188.24 [3927]E(f169(x39271,f334(f334(f158(f935(x39271,a922)),x39272),x39273)),f181(x39271,x39272,f169(x39271,x39273))) % 188.18/188.24 [3965]E(f334(f334(f23(a927),f334(f334(f23(a927),x39651),x39652)),x39653),f334(f334(f23(a927),f334(f334(f23(a927),x39651),x39653)),x39652)) % 188.18/188.24 [3973]E(f334(f334(f109(f935(x39731,a922)),x39732),f334(f334(f23(f935(x39731,a922)),x39733),x39732)),f195(f935(x39731,a922))) % 188.18/188.24 [3977]E(f334(f334(f161(a927,x39771),f334(f16(x39771,a927),x39772)),f146(a927,f334(f310(a927,f2(a927)),x39773))),f176(x39771,x39773,x39772)) % 188.18/188.24 [4020]E(f43(f935(x40201,a922),f334(f334(f316(f935(x40201,a922)),x40202),x40203)),f334(f334(f109(f935(x40201,a922)),x40202),f43(f935(x40201,a922),x40203))) % 188.18/188.24 [4021]E(f42(f935(x40211,a922),f334(f334(f316(f935(x40211,a922)),x40212),x40213)),f334(f334(f108(f935(x40211,a922)),x40212),f42(f935(x40211,a922),x40213))) % 188.18/188.24 [4023]E(f176(x40231,f334(f196(f928(x40231)),f334(f143(x40231,f334(a331,x40232)),x40233)),x40232),f334(f143(x40231,f334(a331,x40232)),x40233)) % 188.18/188.24 [4025]E(f334(f334(f23(a927),f334(f334(f87(a927),x40251),x40252)),f334(f334(f87(a927),x40253),x40252)),f334(f334(f87(a927),f334(f334(f23(a927),x40251),x40253)),x40252)) % 188.18/188.24 [4026]E(f334(f334(f86(a927),f334(f334(f87(a927),x40261),x40262)),f334(f334(f87(a927),x40263),x40262)),f334(f334(f87(a927),f334(f334(f86(a927),x40261),x40263)),x40262)) % 188.18/188.24 [4027]E(f334(f334(f23(a1),f334(f334(f87(a1),x40271),x40272)),f334(f334(f87(a1),x40273),x40272)),f334(f334(f87(a1),f334(f334(f23(a1),x40271),x40273)),x40272)) % 188.18/188.24 [4028]E(f334(f334(f86(a1),f334(f334(f87(a1),x40281),x40282)),f334(f334(f87(a1),x40283),x40282)),f334(f334(f87(a1),f334(f334(f86(a1),x40281),x40283)),x40282)) % 188.18/188.24 [4029]E(f334(f334(f246(a927),f334(f334(f23(a927),x40291),x40292)),f334(f334(f23(a927),x40293),x40292)),f334(f334(f23(a927),f334(f334(f246(a927),x40291),x40293)),x40292)) % 188.18/188.24 [4050]E(f334(f334(f109(f935(f928(x40501),a922)),f167(x40501,x40502)),f167(x40501,x40503)),f167(x40501,f334(f334(f109(f935(x40501,a922)),x40502),x40503))) % 188.18/188.24 [4053]E(f334(f334(f108(f935(x40531,a922)),x40532),f334(f334(f23(f935(x40531,a922)),x40533),x40532)),f334(f334(f108(f935(x40531,a922)),x40532),x40533)) % 188.18/188.24 [4054]E(f334(f334(f108(f935(x40541,a922)),x40542),f334(f334(f108(f935(x40541,a922)),x40542),x40543)),f334(f334(f108(f935(x40541,a922)),x40542),x40543)) % 188.18/188.24 [4055]E(f334(f334(f109(f935(x40551,a922)),x40552),f334(f334(f109(f935(x40551,a922)),x40552),x40553)),f334(f334(f109(f935(x40551,a922)),x40552),x40553)) % 188.18/188.24 [4067]E(f334(f334(f295(x40671,x40672,x40672),x40673),f314(x40672,f195(f935(f934(x40672,x40672),a922)))),x40673) % 188.18/188.24 [4070]E(f334(f334(f108(f935(x40701,a922)),f334(f334(f316(x40701),x40702),f195(f935(x40701,a922)))),x40703),f334(f334(f316(x40701),x40702),x40703)) % 188.18/188.24 [4087]E(f334(f334(f23(a927),f334(f334(f23(a927),f334(a119,x40871)),x40872)),f334(a119,x40873)),f334(f334(f23(a927),f334(f334(f23(a927),x40871),x40872)),x40873)) % 188.18/188.24 [4114]E(f334(f334(f109(f935(f935(x41141,a922),a922)),f334(f315(x41141),x41142)),f334(f315(x41141),x41143)),f334(f315(x41141),f334(f334(f109(f935(x41141,a922)),x41142),x41143))) % 188.18/188.24 [4117]E(f334(f334(f108(f935(x41171,a922)),f334(f85(f935(x41171,a922)),x41172)),x41173),f334(f85(f935(x41171,a922)),f334(f334(f23(f935(x41171,a922)),x41172),x41173))) % 188.18/188.24 [4126]E(f334(f334(f316(x41261),x41262),f334(f334(f23(f935(x41261,a922)),x41263),f334(f334(f316(x41261),x41262),f195(f935(x41261,a922))))),f334(f334(f316(x41261),x41262),x41263)) % 188.18/188.24 [4137]P107(f334(f334(f242(f935(x41371,a922)),x41372),f334(f334(f108(f935(x41371,a922)),x41373),x41372))) % 188.18/188.24 [4138]P107(f334(f334(f242(f935(x41381,a922)),x41382),f334(f334(f108(f935(x41381,a922)),x41382),x41383))) % 188.18/188.24 [4142]E(f334(f334(f109(f935(x41421,a922)),f334(f85(f935(x41421,a922)),x41422)),f334(f85(f935(x41421,a922)),x41423)),f334(f85(f935(x41421,a922)),f334(f334(f108(f935(x41421,a922)),x41422),x41423))) % 188.18/188.24 [4143]E(f334(f334(f108(f935(x41431,a922)),f334(f85(f935(x41431,a922)),x41432)),f334(f85(f935(x41431,a922)),x41433)),f334(f85(f935(x41431,a922)),f334(f334(f109(f935(x41431,a922)),x41432),x41433))) % 188.18/188.24 [4157]P107(f334(f334(f242(f935(x41571,a922)),f334(f179(x41571),x41572)),f334(f179(x41571),f334(f334(f158(x41571),x41573),x41572)))) % 188.18/188.24 [4168]E(f334(f334(f108(f935(x41681,a922)),f334(f334(f23(f935(x41681,a922)),x41682),x41683)),f334(f334(f109(f935(x41681,a922)),x41682),x41683)),x41682) % 188.18/188.24 [4221]E(f334(f334(f9(x42211,a1),f334(f334(f8(a927,a1,x42211),f107(a1)),x42212)),x42213),f334(f107(a1),f334(f334(f9(x42211,a927),x42212),x42213))) % 188.18/188.24 [4222]E(f334(f334(f6(x42221,a1),f334(f334(f8(a927,a1,x42221),f107(a1)),x42222)),x42223),f334(f107(a1),f334(f334(f6(x42221,a927),x42222),x42223))) % 188.18/188.24 [4268]E(f334(f334(f141(x42681),f184(x42681,x42682,x42683)),f334(f334(f145(x42681),f334(f196(f928(x42681)),f184(x42681,x42682,x42683))),x42683)),x42683) % 188.18/188.24 [4271]E(f334(f85(f935(f934(x42711,x42712),a922)),f334(f334(f262(x42711,x42712),x42713),f334(f16(f935(x42712,a922),x42711),f250(f935(x42712,a922))))),f334(f334(f262(x42711,x42712),f334(f85(f935(x42711,a922)),x42713)),f334(f16(f935(x42712,a922),x42711),f250(f935(x42712,a922))))) % 188.18/188.24 [4272]E(f334(f85(f935(f934(x42721,x42722),a922)),f334(f334(f262(x42721,x42722),f250(f935(x42721,a922))),f334(f16(f935(x42722,a922),x42721),x42723))),f334(f334(f262(x42721,x42722),f250(f935(x42721,a922))),f334(f16(f935(x42722,a922),x42721),f334(f85(f935(x42722,a922)),x42723)))) % 188.18/188.24 [4321]E(f334(f334(f44(f935(x43211,a922),f935(x43211,a922)),x43212),f334(f334(f7(f935(x43211,a922),f935(x43211,a922),f935(x43211,a922)),f109(f935(x43211,a922))),x43213)),f334(f334(f109(f935(x43211,a922)),f42(f935(x43211,a922),x43212)),x43213)) % 188.18/188.24 [4328]E(f334(f149(f928(x43281),f928(x43281),f141(x43281),f120(x43281)),f334(f334(f158(f928(x43281)),x43282),x43283)),f334(f334(f141(x43281),x43282),f334(f149(f928(x43281),f928(x43281),f141(x43281),f120(x43281)),x43283))) % 188.18/188.24 [4348]E(f334(f334(f316(f935(x43481,a922)),f334(f292(x43481,x43481,x43482),f334(f334(f316(x43481),x43483),f195(f935(x43481,a922))))),f195(f935(f935(x43481,a922),a922))),f334(f334(f65(x43481),f334(f334(f316(x43481),x43483),f195(f935(x43481,a922)))),x43482)) % 188.18/188.24 [4358]E(f334(f334(f86(a927),f334(f334(f87(a927),x43581),f334(f334(f41(a927),x43582),x43583))),f334(f334(f41(a927),f334(f334(f87(a927),x43581),f50(a927,x43582,x43583))),x43583)),f334(f334(f41(a927),f334(f334(f87(a927),x43581),x43582)),x43583)) % 188.18/188.24 [4359]E(f334(f334(f86(a1),f334(f334(f87(a1),x43591),f334(f334(f41(a1),x43592),x43593))),f334(f334(f41(a1),f334(f334(f87(a1),x43591),f50(a1,x43592,x43593))),x43593)),f334(f334(f41(a1),f334(f334(f87(a1),x43591),x43592)),x43593)) % 188.18/188.24 [4389]E(f334(f334(f23(f935(x43891,a922)),f334(f179(x43891),x43892)),f334(f334(f316(x43891),x43893),f195(f935(x43891,a922)))),f334(f179(x43891),f334(f143(x43891,f334(f334(f8(a922,a922,x43891),a329),f334(a331,x43893))),x43892))) % 188.18/188.24 [4441]E(f334(f334(f141(x44411),f334(f149(f928(x44411),f928(x44411),f141(x44411),f120(x44411)),x44412)),f334(f149(f928(x44411),f928(x44411),f141(x44411),f120(x44411)),x44413)),f334(f149(f928(x44411),f928(x44411),f141(x44411),f120(x44411)),f334(f334(f141(f928(x44411)),x44412),x44413))) % 188.18/188.24 [4445]E(f334(f334(f260(f928(x44451),f928(x44451)),f334(f143(x44451,x44452),x44453)),f334(f143(x44451,f334(f78(a922,a922,x44451,a329),x44452)),x44453)),f173(x44451,x44452,x44453)) % 188.18/188.24 [4449]E(f334(f334(f86(a927),f334(f334(f86(a927),f334(f334(f41(a927),x44491),x44492)),f334(f334(f41(a927),x44493),x44492))),f334(f334(f41(a927),f334(f334(f86(a927),f50(a927,x44491,x44492)),f50(a927,x44493,x44492))),x44492)),f334(f334(f41(a927),f334(f334(f86(a927),x44491),x44493)),x44492)) % 188.18/188.24 [4450]E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f41(a1),x44501),x44502)),f334(f334(f41(a1),x44503),x44502))),f334(f334(f41(a1),f334(f334(f86(a1),f50(a1,x44501,x44502)),f50(a1,x44503,x44502))),x44502)),f334(f334(f41(a1),f334(f334(f86(a1),x44501),x44503)),x44502)) % 188.18/188.24 [4504]E(f334(f334(f109(f935(f928(x45041),a922)),f334(f334(f7(f928(x45041),f935(f928(x45041),a922),a922),f336(f928(x45041))),f168(x45041,x45042))),f334(f334(f7(f928(x45041),f935(f928(x45041),a922),a922),f336(f928(x45041))),f168(x45041,x45043))),f167(x45041,f334(f334(f109(f935(x45041,a922)),f334(f334(f7(x45041,f935(x45041,a922),a922),f336(x45041)),x45042)),f334(f334(f7(x45041,f935(x45041,a922),a922),f336(x45041)),x45043)))) % 188.18/188.24 [4515]E(f334(f270(x45151),f334(f334(f18(x45151,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45151),a333),f334(f334(f7(x45151,x45151,a922),a331),x45152))),f334(f334(f7(x45151,f935(x45151,a922),a922),f336(x45151)),x45153))),f334(f334(f316(x45151),x45152),x45153)) % 188.18/188.24 [4537]E(f334(f334(f94(f928(f928(x45371)),f928(f928(x45371))),f59(x45371,x45372)),f334(f334(f18(f928(f928(x45371)),f928(f928(x45371)),f928(f928(x45371))),f334(f334(f8(f928(f928(x45371)),f935(f928(f928(x45371)),f928(f928(x45371))),f928(f928(x45371))),f141(f928(x45371))),f334(f161(f928(x45371),f928(x45371)),f334(f158(x45371),x45373)))),f5(f928(f928(x45371))))),f59(x45371,f334(f334(f158(x45371),x45373),x45372))) % 188.18/188.24 [4540]E(f334(f270(x45401),f334(f334(f18(x45401,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45401),a333),f334(f334(f7(x45401,f935(x45401,a922),a922),f336(x45401)),x45402))),f334(f334(f7(x45401,f935(x45401,a922),a922),f336(x45401)),x45403))),f334(f334(f108(f935(x45401,a922)),x45402),x45403)) % 188.18/188.24 [4541]E(f334(f270(x45411),f334(f334(f18(x45411,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45411),a332),f334(f334(f7(x45411,f935(x45411,a922),a922),f336(x45411)),x45412))),f334(f334(f7(x45411,f935(x45411,a922),a922),f336(x45411)),x45413))),f334(f334(f109(f935(x45411,a922)),x45412),x45413)) % 188.18/188.24 [4629]E(f334(f334(f44(x46291,f935(f935(x46291,a922),a922)),x46292),f334(f334(f7(x46291,f935(f935(x46291,a922),a922),f935(f935(x46291,a922),a922)),f334(f334(f8(f935(x46291,a922),f935(f935(f935(x46291,a922),a922),f935(f935(x46291,a922),a922)),x46291),f316(f935(x46291,a922))),f334(f334(f8(f935(x46291,a922),f935(x46291,a922),x46291),f292(x46291,x46291,x46293)),f334(f334(f7(x46291,f935(x46291,a922),f935(x46291,a922)),f316(x46291)),f195(f935(x46291,a922)))))),f195(f935(f935(x46291,a922),a922)))),f334(f334(f65(x46291),x46292),x46293)) % 188.18/188.24 [4638]E(f334(f334(f210(x46381),f334(f334(f87(a1),f334(f334(f78(f934(a1,a1),a1,x46381,f259(a1,a1)),f221(x46381)),x46382)),f334(f334(f78(f934(a1,a1),a1,x46381,f259(a1,a1)),f221(x46381)),x46383))),f334(f334(f87(a1),f334(f334(f78(f934(a1,a1),a1,x46381,f264(a1,a1)),f221(x46381)),x46382)),f334(f334(f78(f934(a1,a1),a1,x46381,f264(a1,a1)),f221(x46381)),x46383))),f237(x46381,x46382,x46383)) % 188.18/188.24 [4642]E(f334(f270(f928(x46421)),f334(f334(f18(f928(x46421),a922,a922),f334(f334(f8(a922,f935(a922,a922),f928(x46421)),a332),f334(f334(f7(f928(x46421),a927,a922),f334(f334(f8(a927,f935(a927,a922),f928(x46421)),a331),f196(f928(x46421)))),x46422))),f334(f334(f7(f928(x46421),f935(x46421,a922),a922),f334(f334(f8(f935(x46421,a922),f935(f935(x46421,a922),a922),f928(x46421)),f242(f935(x46421,a922))),f179(x46421))),f334(f179(x46421),x46423)))),f334(f179(f928(x46421)),f60(x46421,x46422,x46423))) % 188.18/188.24 [4043]E(f50(a927,f334(f334(f86(a927),f334(f334(f87(a927),x40431),x40432)),x40433),x40432),f50(a927,x40433,x40432)) % 188.18/188.24 [4086]E(f146(a927,f334(f310(a927,f334(f334(f86(a927),x40861),x40862)),x40863)),f334(f334(f145(a927),x40862),f146(a927,f334(f310(a927,x40861),x40863)))) % 188.18/188.24 [4125]E(f334(f334(f86(a1),f334(f107(a1),x41251)),f334(f334(f86(a1),f334(f107(a1),x41252)),x41253)),f334(f334(f86(a1),f334(f107(a1),f334(f334(f86(a927),x41251),x41252))),x41253)) % 188.18/188.24 [4133]E(f334(f334(f23(f935(x41331,a922)),f334(f334(f23(f935(x41331,a922)),x41332),x41333)),x41333),f334(f334(f23(f935(x41331,a922)),x41332),x41333)) % 188.18/188.24 [4134]E(f334(f334(f108(f935(x41341,a922)),f334(f334(f23(f935(x41341,a922)),x41342),x41343)),x41343),f334(f334(f108(f935(x41341,a922)),x41342),x41343)) % 188.18/188.24 [4158]E(f334(f334(f295(x41581,x41581,x41582),f314(x41581,f195(f935(f934(x41581,x41581),a922)))),x41583),x41583) % 188.18/188.24 [4166]E(f334(f334(f108(f935(x41661,a922)),f334(f289(x41661),x41662)),f334(f289(x41661),x41663)),f334(f289(x41661),f334(f334(f108(f935(f934(x41661,x41661),a922)),x41662),x41663))) % 188.18/188.24 [4176]E(f274(x41761,f334(f334(f158(f934(a106,x41761)),f334(f334(f260(a106,x41761),f2(a106)),x41762)),x41763)),f274(x41761,x41763)) % 188.18/188.24 [4178]E(f334(f334(f109(f935(x41781,a922)),f43(f935(x41781,a922),x41782)),f43(f935(x41781,a922),x41783)),f43(f935(x41781,a922),f334(f334(f108(f935(f935(x41781,a922),a922)),x41782),x41783))) % 188.18/188.24 [4179]E(f334(f334(f108(f935(x41791,a922)),f42(f935(x41791,a922),x41792)),f42(f935(x41791,a922),x41793)),f42(f935(x41791,a922),f334(f334(f108(f935(f935(x41791,a922),a922)),x41792),x41793))) % 188.18/188.24 [4218]E(f334(f334(f295(x42181,x42181,x42181),f334(f334(f190(f934(x42181,x42181),a922),x42182),x42183)),x42183),f334(f334(f190(f934(x42181,x42181),a922),f334(a119,x42182)),x42183)) % 188.18/188.25 [4260]P107(f334(f334(f242(f935(x42601,a922)),f334(f334(f23(f935(x42601,a922)),x42602),x42603)),x42602)) % 188.18/188.25 [4261]P107(f334(f334(f242(f935(x42611,a922)),f334(f334(f109(f935(x42611,a922)),x42612),x42613)),x42613)) % 188.18/188.25 [4262]P107(f334(f334(f242(f935(x42621,a922)),f334(f334(f109(f935(x42621,a922)),x42622),x42623)),x42622)) % 188.18/188.25 [4285]E(f314(x42851,f334(f334(f108(f935(f934(x42851,x42851),a922)),f314(x42851,x42852)),f314(x42851,x42853))),f314(x42851,f334(f334(f108(f935(f934(x42851,x42851),a922)),x42852),x42853))) % 188.18/188.25 [4289]E(f42(f935(x42891,a922),f334(f334(f316(f935(x42891,a922)),x42892),f334(f334(f316(f935(x42891,a922)),x42893),f195(f935(f935(x42891,a922),a922))))),f334(f334(f108(f935(x42891,a922)),x42892),x42893)) % 188.18/188.25 [4290]E(f43(f935(x42901,a922),f334(f334(f316(f935(x42901,a922)),x42902),f334(f334(f316(f935(x42901,a922)),x42903),f195(f935(f935(x42901,a922),a922))))),f334(f334(f109(f935(x42901,a922)),x42902),x42903)) % 188.18/188.25 [4295]E(f334(f334(f295(x42951,x42951,x42951),f334(f334(f190(f934(x42951,x42951),a922),x42952),x42953)),x42953),f334(f334(f295(x42951,x42951,x42951),x42953),f334(f334(f190(f934(x42951,x42951),a922),x42952),x42953))) % 188.18/188.25 [4362]E(f334(f334(f108(f935(x43621,a922)),f334(f270(x43621),f334(f334(f7(x43621,x43621,a922),a331),x43622))),x43623),f334(f334(f316(x43621),x43622),x43623)) % 188.18/188.25 [4363]E(f334(a112,f334(f334(f9(x43631,a1),f334(f334(f8(a927,a1,x43631),f107(a1)),x43632)),x43633)),f334(f334(f9(x43631,a927),x43632),x43633)) % 188.18/188.25 [4364]E(f334(a112,f334(f334(f6(x43641,a1),f334(f334(f8(a927,a1,x43641),f107(a1)),x43642)),x43643)),f334(f334(f6(x43641,a927),x43642),x43643)) % 188.18/188.25 [4438]E(f334(f163(f928(x44381),x44381,f334(f178(x44381),x44382),f334(f16(f935(f928(x44381),f928(x44381)),x44381),f334(f334(f7(f928(x44381),f928(x44381),f928(x44381)),f141(x44381)),x44382))),x44383),f334(f178(x44381),f334(f334(f141(x44381),x44383),x44382))) % 188.18/188.25 [4466]P107(f334(f334(f242(f935(f935(x44661,a922),a922)),f334(f334(f108(f935(f935(x44661,a922),a922)),f334(f315(x44661),x44662)),f334(f315(x44661),x44663))),f334(f315(x44661),f334(f334(f108(f935(x44661,a922)),x44662),x44663)))) % 188.18/188.25 [4555]E(f334(f270(x45551),f334(f334(f18(x45551,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45551),a332),f334(f334(f7(x45551,f935(x45551,a922),a922),f336(x45551)),x45552))),f334(f334(f8(a922,a922,x45551),a329),f334(f334(f7(x45551,f935(x45551,a922),a922),f336(x45551)),x45553)))),f334(f334(f23(f935(x45551,a922)),x45552),x45553)) % 188.18/188.25 [4581]E(f334(f40(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,a927,a922),f243(a927)),f334(f196(f928(x45811)),x45812)))),f334(f334(f8(x45811,a922,a927),x45813),f334(f171(x45811),x45812))))),f334(f196(f928(x45811)),f334(f143(x45811,x45813),x45812))) % 188.18/188.25 [4583]E(f334(f196(f928(x45831)),f183(x45831,x45832,x45833)),f334(f40(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,a927,a922),f243(a927)),f334(f196(f928(x45831)),x45832)))),f334(f334(f7(a927,f935(a927,a922),a922),f336(a927)),x45833))))) % 188.18/188.25 [4695]E(f334(f334(f109(f935(f934(f928(x46951),f928(x46951)),a922)),f334(f317(f934(f934(x46951,f928(x46951)),f934(x46951,f928(x46951))),f934(f928(x46951),f928(x46951)),f266(f934(x46951,f928(x46951)),f928(x46951),f934(x46951,f928(x46951)),f928(x46951),f334(f265(x46951,f928(x46951),f928(x46951)),f158(x46951)),f334(f265(x46951,f928(x46951),f928(x46951)),f158(x46951)))),f326(x46951,f928(x46951),x46952,f334(f150(x46951,x46952),x46953)))),f334(f270(f934(f928(x46951),f928(x46951))),f334(f265(f928(x46951),f928(x46951),a922),f334(f334(f7(f928(x46951),f935(f928(x46951),a922),f935(f928(x46951),a922)),f334(f334(f8(f935(a922,a922),f935(f935(f928(x46951),a922),f935(f928(x46951),a922)),f928(x46951)),f8(a922,a922,f928(x46951))),f334(f334(f8(a922,f935(a922,a922),f928(x46951)),a332),f334(f334(f7(f928(x46951),a927,a922),f334(f334(f8(a927,f935(a927,a922),f928(x46951)),a331),f196(f928(x46951)))),f334(a119,x46953))))),f334(f334(f7(f928(x46951),a927,a922),f334(f334(f8(a927,f935(a927,a922),f928(x46951)),a331),f196(f928(x46951)))),f334(a119,x46953)))))),f334(f150(x46951,x46952),f334(a119,x46953))) % 188.18/188.25 [4180]E(f50(a927,f334(a119,f334(f334(f86(a927),f334(f334(f87(a927),x41801),x41802)),x41803)),x41802),f50(a927,f334(a119,x41803),x41802)) % 188.18/188.25 [4420]E(f334(f270(x44201),f334(f334(f18(x44201,a922,a922),f334(f334(f8(a922,f935(a922,a922),x44201),a332),x44202)),x44203)),f334(f334(f109(f935(x44201,a922)),f334(f270(x44201),x44202)),f334(f270(x44201),x44203))) % 188.18/188.25 [4421]E(f334(f270(x44211),f334(f334(f18(x44211,a922,a922),f334(f334(f8(a922,f935(a922,a922),x44211),a333),x44212)),x44213)),f334(f334(f108(f935(x44211,a922)),f334(f270(x44211),x44212)),f334(f270(x44211),x44213))) % 188.18/188.25 [4423]E(f334(f334(f141(x44231),f334(f334(f145(x44231),f50(a927,x44232,f334(f196(f928(x44231)),x44233))),x44233)),f334(f334(f182(x44231),f50(a927,x44232,f334(f196(f928(x44231)),x44233))),x44233)),f334(f334(f334(f190(f928(x44231),f928(x44231)),x44232),f174(x44231)),x44233)) % 188.18/188.25 [4429]E(f334(f270(x44291),f334(f334(f18(x44291,a922,a922),f334(f334(f8(a922,f935(a922,a922),x44291),a337),x44292)),x44293)),f334(f334(f108(f935(x44291,a922)),f334(f85(f935(x44291,a922)),f334(f270(x44291),x44292))),f334(f270(x44291),x44293))) % 188.18/188.25 [4451]E(f334(f334(f86(a927),f334(f196(f928(x44511)),f334(f143(x44511,x44512),x44513))),f334(f196(f928(x44511)),f334(f143(x44511,f334(f334(f8(a922,a922,x44511),a329),x44512)),x44513))),f334(f196(f928(x44511)),x44513)) % 188.18/188.25 [4474]P107(f334(f334(f242(f935(x44741,a922)),f334(f334(f108(f935(x44741,a922)),f43(f935(x44741,a922),x44742)),f43(f935(x44741,a922),x44743))),f43(f935(x44741,a922),f334(f334(f109(f935(f935(x44741,a922),a922)),x44742),x44743)))) % 188.18/188.25 [4487]E(f334(f179(x44871),f334(f143(x44871,f334(f334(f8(a922,a922,x44871),a329),f334(f334(f7(x44871,x44871,a922),a331),x44872))),x44873)),f334(f334(f23(f935(x44871,a922)),f334(f179(x44871),x44873)),f334(f334(f316(x44871),x44872),f195(f935(x44871,a922))))) % 188.18/188.25 [4496]P107(f334(f334(f242(f935(f934(x44961,x44961),a922)),f334(f334(f108(f935(f934(x44961,x44961),a922)),f314(x44961,x44962)),f314(x44961,x44963))),f314(x44961,f334(f334(f108(f935(f934(x44961,x44961),a922)),x44962),x44963)))) % 188.18/188.25 [4520]E(f334(f334(f87(a927),f334(a119,f334(a119,f2(a927)))),f334(f334(f6(a927,a927),f334(f334(f8(a927,a927,a927),f334(f86(a927),x45201)),f334(f334(f7(a927,a927,a927),f87(a927)),x45202))),f334(f307(a927),x45203))),f334(f334(f87(a927),x45203),f334(f334(f86(a927),x45201),f334(f334(f86(a927),x45201),f334(f334(f87(a927),f334(f334(f23(a927),x45203),f84(a927))),x45202))))) % 188.18/188.25 [4532]E(f334(f270(x45321),f334(f334(f18(x45321,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45321),a332),f334(f334(f7(x45321,f935(x45321,a922),a922),f336(x45321)),f334(f179(x45321),x45322)))),x45323)),f334(f179(x45321),f334(f143(x45321,x45323),x45322))) % 188.18/188.25 [4694]E(f334(f270(x46941),f334(f334(f8(f935(a927,a922),a922,x46941),f92(a927)),f334(f334(f7(x46941,f935(a927,a922),f935(a927,a922)),f334(f334(f8(f935(a927,f935(a922,a922)),f935(f935(a927,a922),f935(a927,a922)),x46941),f18(a927,a922,a922)),f334(f334(f8(f935(a927,a922),f935(a927,f935(a922,a922)),x46941),f334(f8(a922,f935(a922,a922),a927),a332)),f334(f334(f7(x46941,f935(a927,x46941),f935(a927,a922)),f334(f334(f8(f935(x46941,a922),f935(f935(a927,x46941),f935(a927,a922)),x46941),f8(x46941,a922,a927)),a331)),f334(f171(x46941),x46942))))),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,a927,a922),f243(a927)),f334(f196(f928(x46941)),x46942)))),f334(f334(f7(a927,f935(a927,a922),a922),f336(a927)),x46943))))),f334(f179(x46941),f183(x46941,x46942,x46943))) % 188.18/188.25 [4569]E(f334(f270(x45691),f334(f334(f18(x45691,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45691),a337),f334(f334(f8(a922,a922,x45691),a329),f334(f334(f7(x45691,x45691,a922),a331),x45692)))),x45693)),f334(f334(f316(x45691),x45692),f334(f270(x45691),x45693))) % 188.18/188.25 [4607]E(f334(f334(f161(f934(x46071,a927),x46071),f259(x46071,a927)),f334(f143(f934(x46071,a927),f334(f334(f7(f934(x46071,a927),f935(a927,a922),a922),f334(f334(f8(a927,f935(f935(a927,a922),a922),f934(x46071,a927)),f336(a927)),f264(x46071,a927))),x46072)),f334(f334(f188(x46071,a927),x46073),f146(a927,f334(f310(a927,f2(a927)),f334(f196(f928(x46071)),x46073)))))),f183(x46071,x46073,x46072)) % 188.18/188.25 [4675]E(f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f6(a927,a1),f334(f334(f8(a1,a1,a927),f334(f86(a1),x46751)),f334(f334(f7(a927,a1,a1),f334(f334(f8(a1,f935(a1,a1),a927),f87(a1)),f107(a1))),x46752))),f334(f307(a927),x46753))),f334(f334(f87(a1),f334(f107(a1),x46753)),f334(f334(f86(a1),x46751),f334(f334(f86(a1),x46751),f334(f334(f87(a1),f334(f107(a1),f334(f334(f23(a927),x46753),f84(a927)))),x46752))))) % 188.18/188.25 [4687]E(f334(f270(f934(x46871,x46872)),f334(f265(x46871,x46872,a922),f334(f334(f7(x46871,f935(f934(x46872,x46871),a922),f935(x46872,a922)),f334(f334(f8(f935(x46872,f935(f935(f934(x46872,x46871),a922),a922)),f935(f935(f934(x46872,x46871),a922),f935(x46872,a922)),x46871),f7(x46872,f935(f934(x46872,x46871),a922),a922)),f334(f334(f8(f935(x46872,f934(x46872,x46871)),f935(x46872,f935(f935(f934(x46872,x46871),a922),a922)),x46871),f334(f8(f934(x46872,x46871),f935(f935(f934(x46872,x46871),a922),a922),x46872),f336(f934(x46872,x46871)))),f334(f7(x46872,x46871,f934(x46872,x46871)),f260(x46872,x46871))))),x46873))),f334(f293(x46872,x46871),x46873)) % 188.18/188.25 [4706]E(f334(f270(f928(x47061)),f334(f334(f8(f935(x47061,a922),a922,f928(x47061)),f92(x47061)),f334(f334(f8(f935(x47061,f935(f928(x47061),a922)),f935(x47061,a922),f928(x47061)),f334(f8(f935(f928(x47061),a922),a922,x47061),f92(f928(x47061)))),f334(f334(f7(f928(x47061),f935(x47061,f935(f928(x47061),a922)),f935(x47061,f935(f928(x47061),a922))),f334(f334(f8(f935(x47061,f935(f935(f928(x47061),a922),f935(f928(x47061),a922))),f935(f935(x47061,f935(f928(x47061),a922)),f935(x47061,f935(f928(x47061),a922))),f928(x47061)),f18(x47061,f935(f928(x47061),a922),f935(f928(x47061),a922))),f334(f334(f8(f935(x47061,f935(f928(x47061),f935(a922,a922))),f935(x47061,f935(f935(f928(x47061),a922),f935(f928(x47061),a922))),f928(x47061)),f334(f8(f935(f928(x47061),f935(a922,a922)),f935(f935(f928(x47061),a922),f935(f928(x47061),a922)),x47061),f18(f928(x47061),a922,a922))),f334(f334(f8(f935(x47061,f935(f928(x47061),a922)),f935(x47061,f935(f928(x47061),f935(a922,a922))),f928(x47061)),f334(f8(f935(f928(x47061),a922),f935(f928(x47061),f935(a922,a922)),x47061),f334(f8(a922,f935(a922,a922),f928(x47061)),a332))),f334(f334(f7(f928(x47061),f935(x47061,f935(f928(x47061),f928(x47061))),f935(x47061,f935(f928(x47061),a922))),f334(f334(f8(f935(f935(f928(x47061),f928(x47061)),f935(f928(x47061),a922)),f935(f935(x47061,f935(f928(x47061),f928(x47061))),f935(x47061,f935(f928(x47061),a922))),f928(x47061)),f8(f935(f928(x47061),f928(x47061)),f935(f928(x47061),a922),x47061)),f334(f334(f8(f935(f928(x47061),a922),f935(f935(f928(x47061),f928(x47061)),f935(f928(x47061),a922)),f928(x47061)),f8(f928(x47061),a922,f928(x47061))),a331))),f158(x47061)))))),f334(f334(f7(x47061,f935(f928(x47061),a922),f935(f928(x47061),a922)),f334(f334(f8(f935(a922,a922),f935(f935(f928(x47061),a922),f935(f928(x47061),a922)),x47061),f8(a922,a922,f928(x47061))),f334(f334(f8(a922,f935(a922,a922),x47061),a332),f334(f334(f7(x47061,f935(x47061,a922),a922),f336(x47061)),x47062)))),f334(f334(f7(f928(x47061),f935(f928(x47061),a922),a922),f336(f928(x47061))),x47063)))))),f181(x47061,x47062,x47063)) % 188.18/188.25 [4707]E(f334(f334(f94(a1,f934(a1,a1)),f334(f334(f23(a1),x47071),x47072)),f334(f334(f7(a1,f934(a1,a1),f934(a1,a1)),f334(f334(f18(a1,f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),f334(f334(f8(a922,f935(f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),a1),f103(f934(a1,a1))),f334(f242(a1),f2(a1)))),f334(f260(a1,a1),f334(f334(f86(a1),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x47073)),f84(a1))))),f334(f334(f260(a1,a1),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x47073)),x47071))),f334(f48(x47072),f334(f334(f260(a1,a1),x47073),x47071))) % 188.18/188.25 [4731]~E(f26(x47311,x47312),f31(x47313,x47314)) % 188.18/188.25 [4734]~E(f30(x47341,x47342),f31(x47343,x47344)) % 188.18/188.25 [4735]~E(f30(x47351,x47352),f26(x47353,x47354)) % 188.18/188.25 [3739]E(f123(x37391,f334(x37392,x37393),f334(x37394,x37393)),f334(f212(x37391,x37392,x37394),x37393)) % 188.18/188.25 [3791]E(f334(f334(f253(x37911,x37912,x37913),x37914),f2(a927)),x37912) % 188.18/188.25 [3805]E(f36(x38051,x38052,x38053,f33(x38054)),f334(x38053,x38054)) % 188.18/188.25 [3806]E(f36(x38061,x38062,x38063,f34(x38064)),f334(x38062,x38064)) % 188.18/188.25 [3807]E(f37(x38071,x38072,x38073,f33(x38074)),f334(x38073,x38074)) % 188.18/188.25 [3808]E(f37(x38081,x38082,x38083,f34(x38084)),f334(x38082,x38084)) % 188.18/188.25 [3835]E(f192(x38351,x38352,x38353,f334(a119,x38354)),f334(x38353,x38354)) % 188.18/188.25 [3877]E(f177(x38771,x38772,f177(x38771,x38773,x38774)),f177(x38771,x38773,f177(x38771,x38772,x38774))) % 188.18/188.25 [3878]E(f133(x38781,x38782,f123(x38781,x38783,x38784)),f123(x38781,f133(x38781,x38782,x38783),x38784)) % 188.18/188.25 [4009]E(f334(f163(x40091,x40092,x40093,x40094),f120(x40092)),x40093) % 188.18/188.25 [4010]E(f334(f149(x40101,x40102,x40103,x40104),f120(x40102)),x40104) % 188.18/188.25 [4018]E(f334(f196(f926(x40181)),f98(x40181,x40182,x40183,x40184)),f2(a927)) % 188.18/188.25 [4049]E(f334(f196(f932(x40491,x40492)),f229(x40491,x40492,x40493,x40494)),f2(a927)) % 188.18/188.25 [4072]E(f334(f265(x40721,x40722,x40723),f263(x40721,x40722,x40723,x40724)),x40724) % 188.18/188.25 [4113]E(f334(f334(f141(x41131),f176(x41131,x41132,x41133)),f176(x41131,x41134,x41133)),f334(f334(f141(x41131),f176(x41131,x41134,x41133)),f176(x41131,x41132,x41133))) % 188.18/188.25 [4200]E(f334(f334(f267(x42001,x42002,x42003,f934(x42002,x42003)),x42004),f260(x42002,x42003)),x42004) % 188.18/188.25 [4210]E(f134(x42101,x42102,x42103,x42104,f126(x42102)),x42103) % 188.18/188.25 [4217]E(f80(x42171,x42172,x42173,x42174,f334(x42173,x42174)),x42173) % 188.18/188.25 [4481]P44(x44811,x44812,x44813,x44814,f195(f935(x44811,a922)),x44814) % 188.18/188.25 [3545]E(f334(f334(f16(x35451,x35452),x35453),x35454),x35453) % 188.18/188.25 [3825]E(f177(x38251,x38252,f334(f143(x38251,x38253),x38254)),f334(f143(x38251,x38253),f177(x38251,x38252,x38254))) % 188.18/188.25 [3860]E(f334(f334(f69(x38601,x38602,x38603),x38604),f195(f935(x38601,a922))),x38604) % 188.18/188.25 [3884]E(f334(f334(f171(x38841),f334(f334(f158(x38841),x38842),x38843)),f334(a119,x38844)),f334(f334(f171(x38841),x38843),x38844)) % 188.18/188.25 [3951]E(f334(f334(x39511,x39512),f334(f191(x39513,x39514,x39511),x39512)),f334(f191(x39513,x39514,x39511),f334(a119,x39512))) % 188.18/188.25 [3986]E(f263(x39861,x39862,x39863,f334(f265(x39861,x39862,x39863),x39864)),x39864) % 188.18/188.25 [4047]E(f334(f334(f166(x40471,f334(f334(f158(x40471),x40472),x40473)),f2(a927)),x40474),f334(f334(f158(x40471),x40474),x40473)) % 188.18/188.25 [4057]E(f334(f334(f44(f935(x40571,a922),f935(x40572,a922)),x40573),f317(x40571,x40572,x40574)),f334(f317(x40571,x40572,x40574),f42(f935(x40571,a922),x40573))) % 188.18/188.25 [4058]E(f334(f334(f44(f935(x40581,a922),f935(x40582,a922)),x40583),f318(x40582,x40581,x40584)),f334(f318(x40582,x40581,x40584),f42(f935(x40581,a922),x40583))) % 188.18/188.25 [4081]E(f127(x40811,f137(x40812,f929(x40811),x40813,x40814)),f334(f125(x40812,x40811,x40814),x40813)) % 188.18/188.25 [4154]E(f334(f132(x41541,x41542),f133(x41541,x41543,x41544)),f334(f334(f86(a927),f334(f334(f86(a927),f334(x41542,x41543)),f334(f132(x41541,x41542),x41544))),f334(a119,f2(a927)))) % 188.18/188.25 [4175]E(f334(f149(x41751,x41752,f334(f7(x41752,x41751,x41751),x41753),x41754),f334(f175(x41752),f120(x41752))),x41754) % 188.18/188.25 [4220]E(f82(x42201,x42202,x42203,x42204,f195(f935(x42201,a922))),x42203) % 188.18/188.25 [4279]E(f232(x42791,f934(x42792,f929(x42792)),x42793,f334(f265(x42792,f929(x42792),x42791),x42794),f334(f142(x42792),f126(x42792))),x42793) % 188.18/188.25 [4405]E(f334(f265(x44051,x44052,x44053),f334(f334(f8(f935(x44052,f934(x44051,x44052)),f935(x44052,x44053),x44051),f334(f8(f934(x44051,x44052),x44053,x44052),x44054)),f260(x44051,x44052))),x44054) % 188.18/188.25 [3730]E(f334(f264(x37301,x37302),f334(f334(f260(x37301,x37302),x37303),x37304)),x37304) % 188.18/188.25 [3731]E(f334(f259(x37311,x37312),f334(f334(f260(x37311,x37312),x37313),x37314)),x37313) % 188.18/188.25 [3765]E(f334(f196(f928(x37651)),f334(f334(f166(x37651,x37652),x37653),x37654)),f334(f196(f928(x37651)),x37652)) % 188.18/188.25 [3766]E(f334(f196(f928(x37661)),f334(f334(f161(x37662,x37661),x37663),x37664)),f334(f196(f928(x37662)),x37664)) % 188.18/188.25 [3785]E(f334(f334(f145(x37851),f334(a119,x37852)),f334(f334(f158(x37851),x37853),x37854)),f334(f334(f145(x37851),x37852),x37854)) % 188.18/188.25 [3855]E(f334(f334(f182(x38551),x38552),f176(x38551,x38553,x38554)),f176(x38551,f334(f334(f246(a927),x38552),x38553),x38554)) % 188.18/188.25 [3856]E(f334(f334(f145(x38561),x38562),f176(x38561,x38563,x38564)),f176(x38561,f334(f334(f23(a927),x38563),x38562),x38564)) % 188.18/188.25 [3862]E(f334(f334(f316(x38621),x38622),f334(f334(f316(x38621),x38623),x38624)),f334(f334(f316(x38621),x38623),f334(f334(f316(x38621),x38622),x38624))) % 188.18/188.25 [3866]E(f334(f334(f161(x38661,x38662),x38663),f121(x38661,x38664)),f121(x38662,f334(f334(f161(x38661,x38662),x38663),x38664))) % 188.18/188.25 [3882]E(f334(f175(x38821),f334(f334(f161(x38822,x38821),x38823),x38824)),f334(f334(f161(x38822,x38821),x38823),f334(f175(x38822),x38824))) % 188.18/188.25 [3883]E(f334(f334(f161(x38831,x38832),x38833),f334(f178(x38831),x38834)),f334(f178(x38832),f334(f334(f161(x38831,x38832),x38833),x38834))) % 188.18/188.25 [3897]E(f334(f334(f182(x38971),f334(a119,x38972)),f334(f334(f158(x38971),x38973),x38974)),f334(f334(f158(x38971),x38973),f334(f334(f182(x38971),x38972),x38974))) % 188.18/188.25 [3901]E(f334(f179(x39011),f334(f334(f161(x39012,x39011),x39013),x39014)),f334(f317(x39012,x39011,x39013),f334(f179(x39012),x39014))) % 188.18/188.25 [3914]E(f334(f334(f161(x39141,x39142),f334(f16(x39142,x39141),x39143)),x39144),f176(x39142,f334(f196(f928(x39141)),x39144),x39143)) % 188.18/188.25 [3950]E(f17(x39501,x39502,x39503,f334(a3,f334(a119,f334(a20,x39504)))),f334(x39503,x39504)) % 188.18/188.25 [3954]E(f334(f334(f141(x39541),f334(f143(x39541,x39542),x39543)),f334(f143(x39541,x39542),x39544)),f334(f143(x39541,x39542),f334(f334(f141(x39541),x39543),x39544))) % 188.18/188.25 [3962]E(f159(x39621,f334(f334(f161(x39622,x39621),x39623),f159(x39622,x39624))),f159(x39621,f334(f334(f161(x39622,x39621),x39623),x39624))) % 188.18/188.25 [3976]E(f334(f293(x39761,x39761),f334(f334(f294(x39762,x39761),x39763),x39764)),f334(f334(f294(x39762,x39761),f334(f293(x39762,x39762),x39763)),x39764)) % 188.18/188.25 [3987]E(f334(f334(f295(x39871,x39872,x39873),x39874),f195(f935(f934(x39872,x39873),a922))),f195(f935(f934(x39871,x39873),a922))) % 188.18/188.25 [3988]E(f334(f334(f182(x39881),f334(f334(f23(a927),x39882),x39883)),f334(f334(f145(x39881),x39883),x39884)),f334(f334(f145(x39881),x39883),f334(f334(f182(x39881),x39882),x39884))) % 188.18/188.25 [4012]E(f334(f334(f141(x40121),f176(x40121,x40122,x40123)),f176(x40121,x40124,x40123)),f176(x40121,f334(f334(f86(a927),x40122),x40124),x40123)) % 188.18/188.25 [4013]E(f334(f334(f334(f286(x40131),x40132),x40133),x40134),f334(f260(f935(a106,f935(a922,f931(f929(x40131)))),f934(a106,a106)),f334(f47(x40131),x40132))) % 188.18/188.25 [4040]E(f43(f935(x40401,a922),f334(f317(x40402,f935(x40401,a922),x40403),x40404)),f334(f334(f45(x40402,f935(x40401,a922)),x40404),x40403)) % 188.18/188.25 [4041]E(f42(f935(x40411,a922),f334(f317(x40412,f935(x40411,a922),x40413),x40414)),f334(f334(f44(x40412,f935(x40411,a922)),x40414),x40413)) % 188.18/188.25 [4042]E(f334(f196(f928(f934(x40421,x40422))),f334(f334(f188(x40421,x40422),x40423),x40424)),f334(f334(f246(a927),f334(f196(f928(x40421)),x40423)),f334(f196(f928(x40422)),x40424))) % 188.18/188.25 [4044]E(f334(f318(x40441,x40442,x40443),f334(f85(f935(x40442,a922)),x40444)),f334(f85(f935(x40441,a922)),f334(f318(x40441,x40442,x40443),x40444))) % 188.18/188.25 [4091]E(f334(f318(x40911,x40912,x40913),f334(f270(x40912),x40914)),f334(f270(x40911),f334(f334(f8(x40912,a922,x40911),x40914),x40913))) % 188.18/188.25 [4109]E(f334(f334(f171(x41091),f334(f334(f141(x41091),x41092),f334(f334(f158(x41091),x41093),x41094))),f334(f196(f928(x41091)),x41092)),x41093) % 188.18/188.25 [4131]E(f334(f317(x41311,x41312,x41313),f334(f318(x41311,x41312,x41313),x41314)),f334(f334(f109(f935(x41312,a922)),x41314),f334(f317(x41311,x41312,x41313),f250(f935(x41311,a922))))) % 188.18/188.25 [4150]P107(f334(f334(f336(x41501),f334(x41502,x41503)),f334(f317(x41504,x41501,x41502),f250(f935(x41504,a922))))) % 188.18/188.25 [4159]E(f19(x41591,x41592,x41593,f334(a3,f334(a119,f334(a20,x41594)))),f334(f334(x41593,x41594),f19(x41591,x41592,x41593,x41594))) % 188.18/188.25 [4163]E(f334(f334(f141(x41631),f176(x41631,x41632,x41633)),f334(f334(f158(x41631),x41633),x41634)),f334(f334(f158(x41631),x41633),f334(f334(f141(x41631),f176(x41631,x41632,x41633)),x41634))) % 188.18/188.25 [4165]E(f334(f334(f262(x41651,x41652),f334(f179(x41651),x41653)),f334(f16(f935(x41652,a922),x41651),f334(f179(x41652),x41654))),f334(f179(f934(x41651,x41652)),f64(x41651,x41652,x41653,x41654))) % 188.18/188.25 [4177]E(f162(x41771,x41772,f334(f334(f158(x41771),x41773),x41774)),f334(f334(f86(a927),f334(f334(f86(a927),f334(x41772,x41773)),f162(x41771,x41772,x41774))),f334(a119,f2(a927)))) % 188.18/188.25 [4192]E(f192(f928(x41921),f334(f334(f158(x41921),x41922),x41923),f334(f334(f7(a927,f928(x41921),f928(x41921)),f145(x41921)),x41923),x41924),f334(f334(f145(x41921),x41924),f334(f334(f158(x41921),x41922),x41923))) % 188.18/188.25 [4193]P27(x41931,f934(x41932,x41931),f338(x41933,x41934,x41932,x41931),f334(f334(f44(x41932,f935(x41931,a922)),x41934),x41933)) % 188.18/188.25 [4201]E(f334(f334(f23(f935(x42011,a922)),f334(f334(f23(f935(x42011,a922)),x42012),x42013)),f334(f334(f316(x42011),x42014),f195(f935(x42011,a922)))),f334(f334(f23(f935(x42011,a922)),x42012),f334(f334(f316(x42011),x42014),x42013))) % 188.18/188.25 [4215]E(f334(f334(f190(f935(x42151,x42152),f935(x42151,x42152)),x42153),f78(x42152,x42152,x42151,x42154)),f78(x42152,x42152,x42151,f334(f334(f190(x42152,x42152),x42153),x42154))) % 188.18/188.25 [4284]E(f334(f334(f334(f190(f928(x42841),f928(x42841)),x42842),f174(x42841)),f334(f334(f334(f190(f928(x42841),f928(x42841)),x42843),f174(x42841)),x42844)),f334(f334(f334(f190(f928(x42841),f928(x42841)),f334(f334(f86(a927),x42842),x42843)),f174(x42841)),x42844)) % 188.18/188.25 [4365]P107(f334(f334(f242(f935(x43651,a922)),f334(f179(x43651),f334(f334(f166(x43651,x43652),x43653),x43654))),f334(f334(f316(x43651),x43654),f334(f179(x43651),x43652)))) % 188.18/188.25 [4393]E(f334(f334(f44(f935(x43931,a922),f935(f934(x43931,x43932),a922)),x43933),f334(f334(f7(f935(x43931,a922),f935(x43931,f935(x43932,a922)),f935(f934(x43931,x43932),a922)),f262(x43931,x43932)),x43934)),f334(f334(f262(x43931,x43932),f42(f935(x43931,a922),x43933)),x43934)) % 188.18/188.25 [4437]E(f218(x44371,x44372,x44373,f334(f78(x44372,f935(a106,f935(a106,f935(f934(a106,a106),f935(a106,f929(x44372))))),x44371,f217(x44372)),x44374)),f219(x44371,x44372,x44374,x44373)) % 188.18/188.25 [4454]E(f214(x44541,x44542,x44543,f334(f78(x44542,f935(a106,f935(a106,f935(f934(a106,a106),f935(a106,f929(f931(x44542)))))),x44541,f213(x44542)),x44544)),f215(x44541,x44542,x44544,x44543)) % 188.18/188.25 [4461]P107(f334(f71(x44611,x44612,x44613,x44614,f195(f935(x44611,a922))),x44614)) % 188.18/188.25 [4499]E(f334(f334(f44(x44991,f935(x44992,a922)),x44993),f334(f334(f7(x44991,f935(x44992,a922),f935(x44992,a922)),f334(f334(f8(x44992,f935(f935(x44992,a922),f935(x44992,a922)),x44991),f316(x44992)),x44994)),f195(f935(x44992,a922)))),f334(f317(x44991,x44992,x44994),x44993)) % 188.18/188.25 [4506]P107(f334(f334(f242(f935(x45061,a922)),f334(f291(x45062,x45061),f334(f334(f109(f935(f934(x45062,x45061),a922)),x45063),x45064))),f334(f334(f109(f935(x45061,a922)),f334(f291(x45062,x45061),x45063)),f334(f291(x45062,x45061),x45064)))) % 188.18/188.25 [4507]P107(f334(f334(f242(f935(x45071,a922)),f334(f272(x45071,x45072),f334(f334(f109(f935(f934(x45071,x45072),a922)),x45073),x45074))),f334(f334(f109(f935(x45071,a922)),f334(f272(x45071,x45072),x45073)),f334(f272(x45071,x45072),x45074)))) % 188.18/188.25 [4565]P107(f334(f334(f242(f935(f934(x45651,x45652),a922)),f334(f317(x45652,f934(x45651,x45652),f338(x45653,x45654,x45651,x45652)),f334(f334(f44(x45651,f935(x45652,a922)),x45654),x45653))),f334(f334(f262(x45651,x45652),x45654),x45653))) % 188.18/188.25 [4566]E(f334(f125(x45661,f934(x45661,x45662),x45663),f334(f334(f8(f935(x45662,f929(f934(x45661,x45662))),f929(f934(x45661,x45662)),x45661),f125(x45662,f934(x45661,x45662),x45664)),f334(f334(f8(f935(x45662,f934(x45661,x45662)),f935(x45662,f929(f934(x45661,x45662))),x45661),f334(f8(f934(x45661,x45662),f929(f934(x45661,x45662)),x45662),f136(f934(x45661,x45662)))),f260(x45661,x45662)))),f138(x45661,x45662,x45663,x45664)) % 188.18/188.25 [4567]E(f284(x45671,x45672,x45673,f334(f78(x45672,f935(a106,f935(a106,f935(f934(a106,a106),f934(f935(a106,f935(a922,f931(f929(x45672)))),f934(a106,a106))))),x45671,f286(x45672)),x45674)),f287(x45671,x45672,x45674,x45673)) % 188.18/188.25 [4613]E(f91(f934(x46131,x46132),f334(f265(x46131,x46132,a922),f334(f334(f7(x46131,f935(x46132,a922),f935(x46132,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x46132,a922),f935(x46132,a922)),x46131),f8(a922,a922,x46132)),f334(f334(f8(a922,f935(a922,a922),x46131),a332),f334(a331,x46133)))),f334(a331,x46134)))),f334(f334(f260(x46131,x46132),x46133),x46134)) % 188.18/188.25 [4614]E(f96(f934(x46141,x46142),f334(f265(x46141,x46142,a922),f334(f334(f7(x46141,f935(x46142,a922),f935(x46142,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x46142,a922),f935(x46142,a922)),x46141),f8(a922,a922,x46142)),f334(f334(f8(a922,f935(a922,a922),x46141),a332),f334(a331,x46143)))),f334(a331,x46144)))),f334(f334(f260(x46141,x46142),x46143),x46144)) % 188.18/188.25 [4696]E(f334(f334(f265(f928(x46961),f928(x46961),f934(f928(x46961),f928(x46961))),f334(f334(f18(f928(x46961),f935(f928(x46961),f934(f928(x46961),f928(x46961))),f935(f928(x46961),f934(f928(x46961),f928(x46961)))),f334(f334(f8(f935(f928(x46961),f935(f934(f928(x46961),f928(x46961)),f934(f928(x46961),f928(x46961)))),f935(f935(f928(x46961),f934(f928(x46961),f928(x46961))),f935(f928(x46961),f934(f928(x46961),f928(x46961)))),f928(x46961)),f18(f928(x46961),f934(f928(x46961),f928(x46961)),f934(f928(x46961),f928(x46961)))),f334(f334(f8(f935(f928(x46961),f934(f928(x46961),f928(x46961))),f935(f928(x46961),f935(f934(f928(x46961),f928(x46961)),f934(f928(x46961),f928(x46961)))),f928(x46961)),f334(f8(f934(f928(x46961),f928(x46961)),f935(f934(f928(x46961),f928(x46961)),f934(f928(x46961),f928(x46961))),f928(x46961)),f334(f103(f934(f928(x46961),f928(x46961))),f334(x46962,x46963)))),f334(f334(f8(f928(x46961),f935(f928(x46961),f934(f928(x46961),f928(x46961))),f928(x46961)),f260(f928(x46961),f928(x46961))),f334(f158(x46961),x46963))))),f334(f334(f7(f928(x46961),f935(f928(x46961),f928(x46961)),f935(f928(x46961),f934(f928(x46961),f928(x46961)))),f334(f334(f8(f935(f928(x46961),f934(f928(x46961),f928(x46961))),f935(f935(f928(x46961),f928(x46961)),f935(f928(x46961),f934(f928(x46961),f928(x46961)))),f928(x46961)),f8(f928(x46961),f934(f928(x46961),f928(x46961)),f928(x46961))),f260(f928(x46961),f928(x46961)))),f334(f158(x46961),x46963)))),f173(x46961,x46962,x46964)),f173(x46961,x46962,f334(f334(f158(x46961),x46963),x46964))) % 188.18/188.25 [3930]E(f334(f334(f182(x39301),x39302),f334(f334(f182(x39301),x39303),x39304)),f334(f334(f182(x39301),f334(f334(f246(a927),x39302),x39303)),x39304)) % 188.18/188.25 [3931]E(f334(f334(f145(x39311),x39312),f334(f334(f145(x39311),x39313),x39314)),f334(f334(f145(x39311),f334(f334(f86(a927),x39312),x39313)),x39314)) % 188.18/188.25 [3942]E(f334(f334(f141(x39421),f334(f334(f158(x39421),x39422),x39423)),x39424),f334(f334(f158(x39421),x39422),f334(f334(f141(x39421),x39423),x39424))) % 188.18/188.25 [3943]E(f334(f334(f141(x39431),f334(f334(f141(x39431),x39432),x39433)),x39434),f334(f334(f141(x39431),x39432),f334(f334(f141(x39431),x39433),x39434))) % 188.18/188.25 [4024]E(f334(f334(f171(x40241),f334(f334(f158(x40241),x40242),x40243)),x40244),f192(x40241,x40242,f334(f171(x40241),x40243),x40244)) % 188.18/188.25 [4032]E(f334(f334(f190(x40321,x40321),x40322),f334(f334(f190(x40321,x40321),x40323),x40324)),f334(f334(f190(x40321,x40321),f334(f334(f87(a927),x40323),x40322)),x40324)) % 188.18/188.25 [4060]E(f334(f334(f108(f935(x40601,a922)),x40602),f334(f334(f316(x40601),x40603),x40604)),f334(f334(f316(x40601),x40603),f334(f334(f108(f935(x40601,a922)),x40602),x40604))) % 188.18/188.25 [4075]E(f334(f334(f334(f190(x40751,x40751),x40752),x40753),f334(x40753,x40754)),f334(x40753,f334(f334(f334(f190(x40751,x40751),x40752),x40753),x40754))) % 188.18/188.25 [4082]E(f334(f334(f295(x40821,x40822,x40823),f195(f935(f934(x40821,x40822),a922))),x40824),f195(f935(f934(x40821,x40823),a922))) % 188.18/188.25 [4097]E(f334(f334(f108(f935(x40971,a922)),f334(f334(f316(x40971),x40972),x40973)),x40974),f334(f334(f316(x40971),x40972),f334(f334(f108(f935(x40971,a922)),x40973),x40974))) % 188.18/188.25 [4115]E(f334(f40(f934(x41151,x41152)),f334(f334(f262(x41151,x41152),x41153),f334(f16(f935(x41152,a922),x41151),x41154))),f334(f334(f87(a927),f334(f40(x41151),x41153)),f334(f40(x41152),x41154))) % 188.18/188.25 [4122]E(f334(f334(f109(f935(x41221,a922)),f334(f334(f316(x41221),x41222),x41223)),f334(f334(f316(x41221),x41222),x41224)),f334(f334(f316(x41221),x41222),f334(f334(f109(f935(x41221,a922)),x41223),x41224))) % 188.18/188.25 [4135]E(f334(f334(f108(f935(x41351,a922)),x41352),f334(f334(f108(f935(x41351,a922)),x41353),x41354)),f334(f334(f108(f935(x41351,a922)),x41353),f334(f334(f108(f935(x41351,a922)),x41352),x41354))) % 188.18/188.25 [4136]E(f334(f334(f109(f935(x41361,a922)),x41362),f334(f334(f109(f935(x41361,a922)),x41363),x41364)),f334(f334(f109(f935(x41361,a922)),x41363),f334(f334(f109(f935(x41361,a922)),x41362),x41364))) % 188.18/188.25 [4146]E(f69(x41461,x41462,f334(f334(f8(x41462,f935(x41462,x41462),x41461),x41463),x41464)),f334(f70(x41462,x41461,x41463),x41464)) % 188.18/188.25 [4155]E(f186(x41551,f334(f334(f161(f928(x41552),f928(x41551)),f334(f161(x41552,x41551),x41553)),x41554)),f334(f334(f161(f928(x41552),f928(x41551)),f334(f161(x41552,x41551),x41553)),f186(x41552,x41554))) % 188.18/188.25 [4174]E(f334(f149(f928(x41741),f928(x41741),f141(x41741),f120(x41741)),f334(f334(f161(x41742,f928(x41741)),x41743),x41744)),f170(x41742,x41741,x41743,x41744)) % 188.18/188.25 [4233]E(f334(f78(x42331,x42331,x42331,f334(f334(f190(x42331,x42331),x42332),x42333)),f334(f334(f190(x42331,x42331),x42334),x42333)),f334(f334(f190(x42331,x42331),f334(f334(f86(a927),x42332),x42334)),x42333)) % 188.18/188.25 [4255]E(f334(f334(f109(f935(x42551,a922)),f334(f334(f23(f935(x42551,a922)),x42552),x42553)),f334(f334(f23(f935(x42551,a922)),x42552),x42554)),f334(f334(f23(f935(x42551,a922)),x42552),f334(f334(f108(f935(x42551,a922)),x42553),x42554))) % 188.18/188.25 [4256]E(f334(f334(f108(f935(x42561,a922)),f334(f334(f23(f935(x42561,a922)),x42562),x42563)),f334(f334(f23(f935(x42561,a922)),x42562),x42564)),f334(f334(f23(f935(x42561,a922)),x42562),f334(f334(f109(f935(x42561,a922)),x42563),x42564))) % 188.18/188.25 [4257]E(f334(f334(f109(f935(x42571,a922)),f334(f334(f108(f935(x42571,a922)),x42572),x42573)),f334(f334(f108(f935(x42571,a922)),x42572),x42574)),f334(f334(f108(f935(x42571,a922)),x42572),f334(f334(f109(f935(x42571,a922)),x42573),x42574))) % 188.18/188.25 [4258]E(f334(f334(f23(f935(x42581,a922)),f334(f334(f109(f935(x42581,a922)),x42582),x42583)),f334(f334(f109(f935(x42581,a922)),x42582),x42584)),f334(f334(f109(f935(x42581,a922)),x42582),f334(f334(f23(f935(x42581,a922)),x42583),x42584))) % 188.18/188.25 [4259]E(f334(f334(f108(f935(x42591,a922)),f334(f334(f109(f935(x42591,a922)),x42592),x42593)),f334(f334(f109(f935(x42591,a922)),x42592),x42594)),f334(f334(f109(f935(x42591,a922)),x42592),f334(f334(f108(f935(x42591,a922)),x42593),x42594))) % 188.18/188.25 [4264]E(f334(f40(f934(x42641,x42642)),f334(f334(f262(x42641,x42642),f334(f334(f316(x42641),x42643),f195(f935(x42641,a922)))),f334(f16(f935(x42642,a922),x42641),x42644))),f334(f40(x42642),x42644)) % 188.18/188.25 [4298]E(f334(f334(f45(x42981,f935(x42982,a922)),x42983),f334(f334(f8(f935(x42982,a922),f935(x42982,a922),x42981),f85(f935(x42982,a922))),x42984)),f334(f85(f935(x42982,a922)),f334(f334(f44(x42981,f935(x42982,a922)),x42983),x42984))) % 188.18/188.25 [4299]E(f334(f334(f44(x42991,f935(x42992,a922)),x42993),f334(f334(f8(f935(x42992,a922),f935(x42992,a922),x42991),f85(f935(x42992,a922))),x42994)),f334(f85(f935(x42992,a922)),f334(f334(f45(x42991,f935(x42992,a922)),x42993),x42994))) % 188.18/188.25 [4313]E(f334(f334(f295(x43131,x43131,x43131),f334(f334(f190(f934(x43131,x43131),a922),x43132),x43133)),f334(f334(f190(f934(x43131,x43131),a922),x43134),x43133)),f334(f334(f190(f934(x43131,x43131),a922),f334(f334(f86(a927),x43132),x43134)),x43133)) % 188.18/188.25 [4343]E(f334(f334(f45(x43431,f935(f935(x43432,a922),a922)),x43433),f334(f334(f8(f935(x43432,a922),f935(f935(x43432,a922),a922),x43431),f315(x43432)),x43434)),f334(f315(x43432),f334(f334(f45(x43431,f935(x43432,a922)),x43433),x43434))) % 188.18/188.25 [4372]E(f334(f334(f44(f935(x43721,a922),f935(x43722,a922)),x43723),f334(f334(f7(f935(x43721,a922),f935(x43721,f935(x43722,a922)),f935(x43722,a922)),f44(x43721,f935(x43722,a922))),x43724)),f334(f334(f44(x43721,f935(x43722,a922)),f42(f935(x43721,a922),x43723)),x43724)) % 188.18/188.25 [4373]E(f334(f334(f45(f935(x43731,a922),f935(x43732,a922)),x43733),f334(f334(f7(f935(x43731,a922),f935(x43731,f935(x43732,a922)),f935(x43732,a922)),f45(x43731,f935(x43732,a922))),x43734)),f334(f334(f45(x43731,f935(x43732,a922)),f42(f935(x43731,a922),x43733)),x43734)) % 188.18/188.25 [4376]E(f334(f334(f161(x43761,x43762),x43763),f334(f149(f928(x43761),f928(x43761),f141(x43761),f120(x43761)),x43764)),f334(f149(f928(x43762),f928(x43762),f141(x43762),f120(x43762)),f334(f334(f161(f928(x43761),f928(x43762)),f334(f161(x43761,x43762),x43763)),x43764))) % 188.18/188.25 [4378]E(f192(f928(x43781),f120(x43781),f334(f334(f8(f928(x43781),f928(x43781),a927),f334(f158(x43781),x43782)),f334(f334(f7(a927,f928(x43781),f928(x43781)),f182(x43781)),x43783)),x43784),f334(f334(f182(x43781),x43784),f334(f334(f158(x43781),x43782),x43783))) % 188.18/188.25 [4414]P107(f334(f334(f242(f935(x44141,a922)),f334(f317(x44142,x44141,x44143),f334(f318(x44142,x44141,x44143),x44144))),x44144)) % 188.18/188.25 [4416]E(f334(f317(f934(x44161,x44162),f934(x44162,x44161),f334(f265(x44161,x44162,f934(x44162,x44161)),f334(f7(x44162,x44161,f934(x44162,x44161)),f260(x44162,x44161)))),f334(f334(f262(x44161,x44162),x44163),f334(f16(f935(x44162,a922),x44161),x44164))),f334(f334(f262(x44162,x44161),x44164),f334(f16(f935(x44161,a922),x44162),x44163))) % 188.18/188.25 [4425]E(f334(f334(f44(x44251,f935(x44252,a922)),x44253),f334(f334(f8(f935(x44251,a922),f935(x44252,a922),x44251),f318(x44252,x44251,x44254)),f334(f334(f7(x44251,f935(x44251,a922),f935(x44251,a922)),f316(x44251)),f195(f935(x44251,a922))))),f334(f318(x44252,x44251,x44254),x44253)) % 188.18/188.25 [4426]E(f334(f334(f44(x44261,f935(x44262,a922)),x44263),f334(f334(f8(f935(x44261,a922),f935(x44262,a922),x44261),f292(x44261,x44262,x44264)),f334(f334(f7(x44261,f935(x44261,a922),f935(x44261,a922)),f316(x44261)),f195(f935(x44261,a922))))),f334(f292(x44261,x44262,x44264),x44263)) % 188.18/188.25 [4519]E(f334(f334(f109(f935(x45191,a922)),f334(f334(f109(f935(x45191,a922)),f334(f334(f108(f935(x45191,a922)),x45192),x45193)),f334(f334(f108(f935(x45191,a922)),x45193),x45194))),f334(f334(f108(f935(x45191,a922)),x45194),x45192)),f334(f334(f108(f935(x45191,a922)),f334(f334(f108(f935(x45191,a922)),f334(f334(f109(f935(x45191,a922)),x45192),x45193)),f334(f334(f109(f935(x45191,a922)),x45193),x45194))),f334(f334(f109(f935(x45191,a922)),x45194),x45192))) % 188.18/188.25 [4582]E(f334(f149(f928(x45821),f928(x45821),f141(x45821),f120(x45821)),f334(f334(f161(x45822,f928(x45821)),f334(f334(f7(x45822,f928(x45821),f928(x45821)),f334(f334(f8(x45821,f935(f928(x45821),f928(x45821)),x45822),f158(x45821)),x45823)),f120(x45821))),x45824)),f334(f334(f161(x45822,x45821),x45823),x45824)) % 188.18/188.25 [4597]E(f334(f334(f94(a1,x45971),f334(f111(a1),f334(f334(f86(a1),x45972),a104))),f334(f334(f18(a1,x45971,x45971),f334(f334(f7(a1,x45971,f935(x45971,x45971)),f334(f334(f8(a922,f935(x45971,f935(x45971,x45971)),a1),f103(x45971)),a200)),x45973)),f334(f334(f8(a927,x45971,a1),x45974),a112))),f192(x45971,x45973,x45974,f334(f111(a927),x45972))) % 188.18/188.25 [4626]E(f334(f270(x46261),f334(f334(f8(f935(x46262,a922),a922,x46261),f92(x46262)),f334(f334(f8(f935(x46262,a922),f935(x46262,a922),x46261),f334(f18(x46262,a922,a922),f334(f334(f8(a922,f935(a922,a922),x46262),a332),f334(f334(f7(x46262,f935(x46262,a922),a922),f336(x46262)),x46263)))),f334(f7(x46262,x46261,a922),x46264)))),f334(f292(x46262,x46261,f334(f270(f934(x46262,x46261)),f334(f265(x46262,x46261,a922),x46264))),x46263)) % 188.18/188.25 [4801]~P107(f334(f334(f195(f935(x48011,f935(x48012,a922))),x48013),x48014)) % 188.18/188.25 [4085]E(f334(f334(f171(x40851),f334(f334(f141(x40851),x40852),x40853)),f334(f334(f86(a927),f334(f196(f928(x40851)),x40852)),x40854)),f334(f334(f171(x40851),x40853),x40854)) % 188.18/188.25 [4090]E(f334(f334(f145(x40901),x40902),f334(f334(f182(x40901),f334(f334(f86(a927),x40903),x40902)),x40904)),f334(f334(f182(x40901),x40903),f334(f334(f145(x40901),x40902),x40904))) % 188.18/188.25 [4190]E(f334(f334(f108(f935(x41901,a922)),f334(f291(x41902,x41901),x41903)),f334(f291(x41902,x41901),x41904)),f334(f291(x41902,x41901),f334(f334(f108(f935(f934(x41902,x41901),a922)),x41903),x41904))) % 188.18/188.25 [4191]E(f334(f334(f108(f935(x41911,a922)),f334(f272(x41911,x41912),x41913)),f334(f272(x41911,x41912),x41914)),f334(f272(x41911,x41912),f334(f334(f108(f935(f934(x41911,x41912),a922)),x41913),x41914))) % 188.18/188.25 [4195]E(f334(f334(f23(f935(x41951,a922)),f334(f334(f109(f935(x41951,a922)),x41952),x41953)),x41954),f334(f334(f109(f935(x41951,a922)),x41952),f334(f334(f23(f935(x41951,a922)),x41953),x41954))) % 188.18/188.25 [4196]E(f334(f334(f108(f935(x41961,a922)),f334(f334(f108(f935(x41961,a922)),x41962),x41963)),x41964),f334(f334(f108(f935(x41961,a922)),x41962),f334(f334(f108(f935(x41961,a922)),x41963),x41964))) % 188.18/188.25 [4197]E(f334(f334(f109(f935(x41971,a922)),f334(f334(f109(f935(x41971,a922)),x41972),x41973)),x41974),f334(f334(f109(f935(x41971,a922)),x41972),f334(f334(f109(f935(x41971,a922)),x41973),x41974))) % 188.18/188.25 [4235]E(f334(f334(f108(f935(f934(x42351,x42352),a922)),f334(f293(x42352,x42351),x42353)),f334(f293(x42352,x42351),x42354)),f334(f293(x42352,x42351),f334(f334(f108(f935(f934(x42352,x42351),a922)),x42353),x42354))) % 188.18/188.25 [4236]E(f334(f334(f109(f935(f934(x42361,x42362),a922)),f334(f293(x42362,x42361),x42363)),f334(f293(x42362,x42361),x42364)),f334(f293(x42362,x42361),f334(f334(f109(f935(f934(x42362,x42361),a922)),x42363),x42364))) % 188.18/188.25 [4248]E(f334(f334(f108(f935(x42481,f935(x42482,a922))),f251(x42482,x42481,x42483)),f251(x42482,x42481,x42484)),f251(x42482,x42481,f334(f334(f108(f935(x42482,f935(x42481,a922))),x42483),x42484))) % 188.18/188.25 [4249]E(f334(f334(f109(f935(x42491,f935(x42492,a922))),f251(x42492,x42491,x42493)),f251(x42492,x42491,x42494)),f251(x42492,x42491,f334(f334(f109(f935(x42492,f935(x42491,a922))),x42493),x42494))) % 188.18/188.25 [4301]E(f334(f334(f108(f935(x43011,a922)),f334(f334(f23(f935(x43011,a922)),x43012),x43013)),f334(f334(f23(f935(x43011,a922)),x43014),x43013)),f334(f334(f23(f935(x43011,a922)),f334(f334(f108(f935(x43011,a922)),x43012),x43014)),x43013)) % 188.18/188.25 [4302]E(f334(f334(f109(f935(x43021,a922)),f334(f334(f108(f935(x43021,a922)),x43022),x43023)),f334(f334(f108(f935(x43021,a922)),x43024),x43023)),f334(f334(f108(f935(x43021,a922)),f334(f334(f109(f935(x43021,a922)),x43022),x43024)),x43023)) % 188.18/188.25 [4303]E(f334(f334(f23(f935(x43031,a922)),f334(f334(f109(f935(x43031,a922)),x43032),x43033)),f334(f334(f109(f935(x43031,a922)),x43034),x43033)),f334(f334(f109(f935(x43031,a922)),f334(f334(f23(f935(x43031,a922)),x43032),x43034)),x43033)) % 188.18/188.25 [4304]E(f334(f334(f108(f935(x43041,a922)),f334(f334(f109(f935(x43041,a922)),x43042),x43043)),f334(f334(f109(f935(x43041,a922)),x43044),x43043)),f334(f334(f109(f935(x43041,a922)),f334(f334(f108(f935(x43041,a922)),x43042),x43044)),x43043)) % 188.18/188.25 [4305]E(f334(f334(f23(f935(x43051,a922)),f334(f334(f109(f935(x43051,a922)),x43052),x43053)),f334(f334(f109(f935(x43051,a922)),x43054),x43053)),f334(f334(f23(f935(x43051,a922)),f334(f334(f109(f935(x43051,a922)),x43052),x43053)),x43054)) % 188.18/188.25 [4316]E(f334(f334(f23(f935(x43161,a922)),f334(f334(f23(f935(x43161,a922)),x43162),f334(f334(f316(x43161),x43163),f195(f935(x43161,a922))))),x43164),f334(f334(f23(f935(x43161,a922)),x43162),f334(f334(f316(x43161),x43163),x43164))) % 188.18/188.25 [4367]E(f334(f334(f108(f935(x43671,a922)),f334(f334(f316(x43671),x43672),f334(f334(f316(x43671),x43673),f195(f935(x43671,a922))))),f334(f289(x43671),x43674)),f334(f289(x43671),f334(f334(f316(f934(x43671,x43671)),f334(f334(f260(x43671,x43671),x43672),x43673)),x43674))) % 188.18/188.25 [4390]E(f334(f334(f44(a927,f935(x43901,a922)),f334(f309(a927),x43902)),f334(f334(f8(a927,f935(x43901,a922),a927),x43903),f334(f334(f7(a927,a927,a927),f86(a927)),x43904))),f334(f334(f44(a927,f935(x43901,a922)),f311(a927,x43904,f334(f334(f86(a927),x43902),x43904))),x43903)) % 188.18/188.25 [4391]E(f181(x43911,f334(f292(x43911,x43911,x43912),f334(f334(f316(x43911),x43913),f195(f935(x43911,a922)))),f334(f292(f928(x43911),f928(x43911),f165(x43911,x43912)),f334(f334(f316(f928(x43911)),x43914),f195(f935(f928(x43911),a922))))),f334(f292(f928(x43911),f928(x43911),f165(x43911,x43912)),f334(f334(f316(f928(x43911)),f334(f334(f158(x43911),x43913),x43914)),f195(f935(f928(x43911),a922))))) % 188.18/188.25 [4464]E(f334(f270(x44641),f334(f334(f7(x44641,f935(x44642,a922),a922),f334(f334(f8(x44642,f935(f935(x44642,a922),a922),x44641),f336(x44642)),x44643)),x44644)),f334(f318(x44641,x44642,x44643),x44644)) % 188.18/188.25 [4548]E(f334(f270(x45481),f334(f334(f7(x45481,f935(f934(x45482,x45481),a922),a922),f334(f334(f8(f934(x45482,x45481),f935(f935(f934(x45482,x45481),a922),a922),x45481),f336(f934(x45482,x45481))),f334(f260(x45482,x45481),x45483))),x45484)),f334(f292(x45482,x45481,x45484),f334(f334(f316(x45482),x45483),f195(f935(x45482,a922))))) % 188.18/188.25 [4564]E(f334(f334(f161(f934(x45641,a927),x45641),f259(x45641,a927)),f334(f143(f934(x45641,a927),f334(f334(f8(a927,a922,f934(x45641,a927)),x45642),f334(f334(f8(a927,a927,f934(x45641,a927)),a119),f264(x45641,a927)))),f334(f334(f188(x45641,a927),x45643),x45644))),f334(f334(f161(f934(x45641,a927),x45641),f259(x45641,a927)),f334(f143(f934(x45641,a927),f334(f334(f8(a927,a922,f934(x45641,a927)),x45642),f264(x45641,a927))),f334(f334(f188(x45641,a927),x45643),f334(f334(f161(a927,a927),a119),x45644))))) % 188.18/188.25 [4573]P107(f334(f334(f242(f935(f935(x45731,a922),a922)),f334(f334(f44(x45732,f935(f935(x45731,a922),a922)),x45733),f334(f334(f8(f935(x45731,a922),f935(f935(x45731,a922),a922),x45732),f315(x45731)),x45734))),f334(f315(x45731),f334(f334(f44(x45732,f935(x45731,a922)),x45733),x45734)))) % 188.18/188.25 [4618]E(f334(f334(f94(a1,x46181),f334(f111(a1),f334(f334(f86(a1),x46182),a104))),f334(f334(f18(a1,x46181,x46181),f334(f334(f7(a1,x46181,f935(x46181,x46181)),f334(f334(f8(a922,f935(x46181,f935(x46181,x46181)),a1),f103(x46181)),a200)),x46183)),f334(f334(f18(a1,x46181,x46181),f334(f334(f8(a927,f935(x46181,x46181),a1),x46184),a112)),f334(f334(f8(a927,x46181,a1),f191(x46181,x46183,x46184)),a112)))),f334(f191(x46181,x46183,x46184),f334(f111(a927),x46182))) % 188.18/188.25 [4648]E(f334(f270(f934(x46481,x46482)),f334(f265(x46481,x46482,a922),f334(f334(f7(x46481,f935(x46482,a922),f935(x46482,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x46482,a922),f935(x46482,a922)),x46481),f8(a922,a922,x46482)),f334(f334(f8(a922,f935(a922,a922),x46481),a332),f334(f334(f7(x46481,f935(x46481,a922),a922),f336(x46481)),x46483)))),f334(f334(f7(x46482,f935(x46482,a922),a922),f336(x46482)),x46484)))),f238(x46481,x46482,x46483,x46484)) % 188.18/188.25 [4691]E(f334(f334(f44(x46911,f935(f934(x46911,x46912),a922)),x46913),f334(f334(f18(x46911,f935(x46912,f935(f934(x46911,x46912),a922)),f935(f934(x46911,x46912),a922)),f334(f334(f8(f935(x46912,a922),f935(f935(x46912,f935(f934(x46911,x46912),a922)),f935(f934(x46911,x46912),a922)),x46911),f44(x46912,f935(f934(x46911,x46912),a922))),x46914)),f334(f334(f7(x46911,f935(f934(x46911,x46912),a922),f935(x46912,f935(f934(x46911,x46912),a922))),f334(f334(f8(f935(x46912,f935(f935(f934(x46911,x46912),a922),f935(f934(x46911,x46912),a922))),f935(f935(f934(x46911,x46912),a922),f935(x46912,f935(f934(x46911,x46912),a922))),x46911),f7(x46912,f935(f934(x46911,x46912),a922),f935(f934(x46911,x46912),a922))),f334(f334(f8(f935(x46912,f934(x46911,x46912)),f935(x46912,f935(f935(f934(x46911,x46912),a922),f935(f934(x46911,x46912),a922))),x46911),f334(f8(f934(x46911,x46912),f935(f935(f934(x46911,x46912),a922),f935(f934(x46911,x46912),a922)),x46912),f316(f934(x46911,x46912)))),f260(x46911,x46912)))),f195(f935(f934(x46911,x46912),a922))))),f334(f334(f262(x46911,x46912),x46913),x46914)) % 188.18/188.25 [4243]E(f334(f334(f141(x42431),f334(f334(f182(x42431),x42432),x42433)),f334(f334(f182(x42431),f334(f334(f23(a927),x42432),f334(f196(f928(x42431)),x42433))),x42434)),f334(f334(f182(x42431),x42432),f334(f334(f141(x42431),x42433),x42434))) % 188.18/188.25 [4244]E(f334(f334(f141(x42441),f334(f334(f145(x42441),x42442),x42443)),f334(f334(f145(x42441),f334(f334(f23(a927),x42442),f334(f196(f928(x42441)),x42443))),x42444)),f334(f334(f145(x42441),x42442),f334(f334(f141(x42441),x42443),x42444))) % 188.18/188.25 [4292]E(f334(f334(f86(a927),f334(f334(f87(a927),x42921),x42922)),f334(f334(f86(a927),f334(f334(f87(a927),x42923),x42922)),x42924)),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f86(a927),x42921),x42923)),x42922)),x42924)) % 188.18/188.25 [4435]E(f96(x44351,f334(f334(f7(x44351,x44352,a922),f334(f334(f8(x44352,f935(x44352,a922),x44351),a331),x44353)),x44354)),f334(f97(x44351,x44352,f250(f935(x44351,a922)),x44353),x44354)) % 188.18/188.25 [4484]P107(f334(f334(f242(f935(x44841,a922)),f334(f334(f23(f935(x44841,a922)),f334(f291(x44842,x44841),x44843)),f334(f291(x44842,x44841),x44844))),f334(f291(x44842,x44841),f334(f334(f23(f935(f934(x44842,x44841),a922)),x44843),x44844)))) % 188.18/188.25 [4485]P107(f334(f334(f242(f935(x44851,a922)),f334(f334(f23(f935(x44851,a922)),f334(f272(x44851,x44852),x44853)),f334(f272(x44851,x44852),x44854))),f334(f272(x44851,x44852),f334(f334(f23(f935(f934(x44851,x44852),a922)),x44853),x44854)))) % 188.18/188.25 [4599]E(f334(f334(f86(a1),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x45991),x45992)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x45993),x45994)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),f334(f334(f86(a927),x45991),x45993)),f334(f334(f86(a927),x45992),x45994))),f195(f935(f934(a927,a927),a922)))))) % 188.18/188.25 [4643]E(f334(f334(f87(a1),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x46431),x46432)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x46433),x46434)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),f334(f334(f86(a927),f334(f334(f87(a927),x46431),x46433)),f334(f334(f87(a927),x46432),x46434))),f334(f334(f86(a927),f334(f334(f87(a927),x46431),x46434)),f334(f334(f87(a927),x46432),x46433)))),f195(f935(f934(a927,a927),a922)))))) % 188.18/188.25 [4670]E(f334(f270(x46701),f334(f334(f8(f935(x46702,a922),a922,x46701),f93(x46702)),f334(f334(f8(f935(x46702,a922),f935(x46702,a922),x46701),f334(f18(x46702,a922,a922),f334(f334(f8(a922,f935(a922,a922),x46702),a337),f334(f334(f7(x46702,f935(x46702,a922),a922),f336(x46702)),x46703)))),f334(f334(f7(x46701,f935(x46702,f935(x46701,a922)),f935(x46702,a922)),f334(f334(f8(f935(f935(x46701,a922),a922),f935(f935(x46702,f935(x46701,a922)),f935(x46702,a922)),x46701),f8(f935(x46701,a922),a922,x46702)),f336(x46701))),x46704)))),f334(f334(f45(x46702,f935(x46701,a922)),x46703),x46704)) % 188.18/188.25 [4703]E(f334(f334(f295(x47031,x47031,x47031),f334(f334(f316(f934(x47031,x47031)),f334(f334(f260(x47031,x47031),x47032),x47033)),x47034)),f314(x47031,f334(f334(f316(f934(x47031,x47031)),f334(f334(f260(x47031,x47031),x47032),x47033)),x47034))),f334(f334(f108(f935(f934(x47031,x47031),a922)),f334(f334(f295(x47031,x47031,x47031),x47034),f314(x47031,x47034))),f334(f270(f934(x47031,x47031)),f334(f265(x47031,x47031,a922),f334(f334(f7(x47031,f935(x47031,a922),f935(x47031,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x47031,a922),f935(x47031,a922)),x47031),f8(a922,a922,x47031)),f334(f334(f8(a922,f935(a922,a922),x47031),a332),f334(f334(f7(x47031,f935(f934(x47031,x47031),a922),a922),f334(f334(f8(f934(x47031,x47031),f935(f935(f934(x47031,x47031),a922),a922),x47031),f336(f934(x47031,x47031))),f334(f334(f7(x47031,x47031,f934(x47031,x47031)),f260(x47031,x47031)),x47032))),f314(x47031,x47034))))),f334(f334(f7(x47031,f935(f934(x47031,x47031),a922),a922),f334(f334(f8(f934(x47031,x47031),f935(f935(f934(x47031,x47031),a922),a922),x47031),f336(f934(x47031,x47031))),f334(f260(x47031,x47031),x47033))),f314(x47031,x47034))))))) % 188.18/188.25 [4486]E(f334(f143(x44861,f334(f334(f18(x44861,a922,a922),f334(f334(f8(a922,f935(a922,a922),x44861),a332),x44862)),x44863)),x44864),f334(f143(x44861,x44863),f334(f143(x44861,x44862),x44864))) % 188.18/188.25 [4593]E(f334(f334(f141(x45931),f334(f334(f334(f103(f928(x45931)),f334(f334(f336(a927),f2(a927)),x45932)),f334(f334(f158(x45931),x45933),f120(x45931))),f120(x45931))),f183(x45931,x45934,f334(f270(a927),f334(f334(f7(a927,f935(a927,a922),a922),f334(f334(f8(a927,f935(f935(a927,a922),a922),a927),f336(a927)),a119)),x45932)))),f183(x45931,f334(f334(f158(x45931),x45933),x45934),x45932)) % 188.18/188.25 [4699]E(f334(f270(f934(x46991,x46992)),f334(f334(f8(f935(a927,a922),a922,f934(x46991,x46992)),f92(a927)),f334(f334(f7(f934(x46991,x46992),f935(a927,a922),f935(a927,a922)),f334(f334(f8(f935(a927,f935(a922,a922)),f935(f935(a927,a922),f935(a927,a922)),f934(x46991,x46992)),f18(a927,a922,a922)),f334(f334(f8(f935(a927,a922),f935(a927,f935(a922,a922)),f934(x46991,x46992)),f334(f8(a922,f935(a922,a922),a927),a332)),f334(f334(f7(f934(x46991,x46992),f935(a927,f934(x46991,x46992)),f935(a927,a922)),f334(f334(f8(f935(f934(x46991,x46992),a922),f935(f935(a927,f934(x46991,x46992)),f935(a927,a922)),f934(x46991,x46992)),f8(f934(x46991,x46992),a922,a927)),a331)),f334(f334(f18(a927,x46992,f934(x46991,x46992)),f334(f334(f8(x46991,f935(x46992,f934(x46991,x46992)),a927),f260(x46991,x46992)),f334(f171(x46991),x46993))),f334(f171(x46992),x46994)))))),f334(f334(f7(a927,a927,a922),f243(a927)),f334(f334(f246(a927),f334(f196(f928(x46991)),x46993)),f334(f196(f928(x46992)),x46994)))))),f334(f179(f934(x46991,x46992)),f334(f334(f188(x46991,x46992),x46993),x46994))) % 188.18/188.25 [4612]E(f334(f270(f934(x46121,x46122)),f334(f265(x46121,x46122,a922),f334(f334(f7(x46121,f935(x46122,a922),f935(x46122,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x46122,a922),f935(x46122,a922)),x46121),f8(a922,a922,x46122)),f334(f334(f8(a922,f935(a922,a922),x46121),a332),x46123))),x46124))),f334(f334(f262(x46121,x46122),f334(f270(x46121),x46123)),f334(f16(f935(x46122,a922),x46121),f334(f270(x46122),x46124)))) % 188.18/188.25 [4615]E(f334(f270(f934(x46151,x46152)),f334(f265(x46151,x46152,a922),f334(f334(f18(x46151,f935(x46152,a922),f935(x46152,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x46152,a922),f935(x46152,a922)),x46151),f8(a922,a922,x46152)),f334(f334(f8(a922,f935(a922,a922),x46151),a332),x46153))),x46154))),f334(f334(f262(x46151,x46152),f334(f270(x46151),x46153)),f334(f334(f8(f935(x46152,a922),f935(x46152,a922),x46151),f270(x46152)),x46154))) % 188.18/188.25 [4625]E(f334(f270(x46251),f334(f334(f8(f935(x46252,a922),a922,x46251),f93(x46252)),f334(f334(f8(f935(x46252,a922),f935(x46252,a922),x46251),f334(f18(x46252,a922,a922),f334(f334(f8(a922,f935(a922,a922),x46252),a337),f334(f334(f7(x46252,f935(x46252,a922),a922),f336(x46252)),x46253)))),x46254))),f334(f334(f45(x46252,f935(x46251,a922)),x46253),f334(f334(f8(f935(x46251,a922),f935(x46251,a922),x46252),f270(x46251)),f334(f7(x46251,x46252,a922),x46254)))) % 188.18/188.25 [4683]E(f334(f334(f161(f934(x46831,a927),x46831),f259(x46831,a927)),f334(f143(f934(x46831,a927),f334(f334(f7(f934(x46831,a927),f935(a927,a922),a922),f334(f334(f8(a927,f935(f935(a927,a922),a922),f934(x46831,a927)),f336(a927)),f264(x46831,a927))),x46832)),f334(f334(f188(x46831,a927),x46833),f146(a927,f334(f310(a927,x46834),f334(f334(f86(a927),x46834),f334(f196(f928(x46831)),x46833))))))),f334(f334(f161(f934(x46831,a927),x46831),f259(x46831,a927)),f334(f143(f934(x46831,a927),f334(f334(f7(f934(x46831,a927),f935(a927,a922),a922),f334(f334(f8(a927,f935(f935(a927,a922),a922),f934(x46831,a927)),f336(a927)),f334(f334(f7(f934(x46831,a927),a927,a927),f334(f334(f8(a927,f935(a927,a927),f934(x46831,a927)),f86(a927)),f264(x46831,a927))),x46834))),x46832)),f334(f334(f188(x46831,a927),x46833),f146(a927,f334(f310(a927,f2(a927)),f334(f196(f928(x46831)),x46833))))))) % 188.18/188.25 [4684]E(f334(a119,f334(f334(f241(a927),f334(f196(f928(x46841)),x46842)),f334(f149(a927,f928(x46843),f334(f7(f928(x46843),a927,a927),f334(f334(f8(a927,f935(a927,a927),f928(x46843)),f241(a927)),f334(f334(f7(f928(x46843),a927,a927),f334(f334(f8(a927,f935(a927,a927),f928(x46843)),f23(a927)),f196(f928(x46843)))),f334(a119,f2(a927))))),f2(a927)),f334(f175(f928(x46843)),f334(f143(f928(x46843),f334(f334(f8(a922,a922,f928(x46843)),a329),f334(f334(f7(f928(x46843),f928(x46843),a922),a331),f120(x46843)))),x46844))))),f334(f334(f241(a927),f334(a119,f334(f196(f928(x46841)),x46842))),f334(f149(a927,f928(x46843),f334(f7(f928(x46843),a927,a927),f334(f334(f8(a927,f935(a927,a927),f928(x46843)),f241(a927)),f196(f928(x46843)))),f2(a927)),f334(f175(f928(x46843)),x46844)))) % 188.18/188.25 [4624]E(f334(f334(f141(x46241),f183(x46241,x46242,x46243)),f183(x46241,x46244,f334(f270(a927),f334(f334(f7(a927,f935(a927,a922),a922),f334(f334(f8(a927,f935(f935(a927,a922),a922),a927),f336(a927)),f334(f334(f7(a927,a927,a927),f86(a927)),f334(f196(f928(x46241)),x46242)))),x46243)))),f183(x46241,f334(f334(f141(x46241),x46242),x46244),x46243)) % 188.18/188.25 [4685]E(f42(f935(x46851,a922),f334(f270(f935(x46851,a922)),f334(f334(f8(f935(x46852,a922),a922,f935(x46851,a922)),f92(x46852)),f334(f334(f8(f935(x46852,a922),f935(x46852,a922),f935(x46851,a922)),f334(f18(x46852,a922,a922),f334(f334(f8(a922,f935(a922,a922),x46852),a332),f334(f334(f7(x46852,f935(x46852,a922),a922),f336(x46852)),x46853)))),f334(f334(f7(f935(x46851,a922),f935(x46852,f935(x46851,a922)),f935(x46852,a922)),f334(f334(f8(f935(f935(x46851,a922),a922),f935(f935(x46852,f935(x46851,a922)),f935(x46852,a922)),f935(x46851,a922)),f8(f935(x46851,a922),a922,x46852)),a331)),x46854))))),f334(f334(f44(x46852,f935(x46851,a922)),x46853),x46854)) % 188.18/188.25 [4686]E(f43(f935(x46861,a922),f334(f270(f935(x46861,a922)),f334(f334(f8(f935(x46862,a922),a922,f935(x46861,a922)),f92(x46862)),f334(f334(f8(f935(x46862,a922),f935(x46862,a922),f935(x46861,a922)),f334(f18(x46862,a922,a922),f334(f334(f8(a922,f935(a922,a922),x46862),a332),f334(f334(f7(x46862,f935(x46862,a922),a922),f336(x46862)),x46863)))),f334(f334(f7(f935(x46861,a922),f935(x46862,f935(x46861,a922)),f935(x46862,a922)),f334(f334(f8(f935(f935(x46861,a922),a922),f935(f935(x46862,f935(x46861,a922)),f935(x46862,a922)),f935(x46861,a922)),f8(f935(x46861,a922),a922,x46862)),a331)),x46864))))),f334(f334(f45(x46862,f935(x46861,a922)),x46863),x46864)) % 188.18/188.25 [4693]E(f334(f334(f158(f928(x46931)),f334(f334(f158(x46931),x46932),f334(f149(f928(x46931),f928(x46931),f141(x46931),f120(x46931)),f334(f334(f161(f928(x46931),f928(x46931)),f163(f928(x46931),x46931,f120(x46931),f334(f334(f8(f928(x46931),f935(f928(x46931),f928(x46931)),x46931),f16(f928(x46931),f928(x46931))),f334(f334(f7(x46931,f928(x46931),f928(x46931)),f158(x46931)),f120(x46931))))),x46933)))),f186(x46931,f334(f334(f158(f928(x46931)),x46934),f334(f149(f928(f928(x46931)),f928(f928(x46931)),f141(f928(x46931)),f120(f928(x46931))),f334(f334(f161(f928(x46931),f928(f928(x46931))),f163(f928(f928(x46931)),x46931,f120(f928(x46931)),f334(f16(f935(f928(x46931),f928(f928(x46931))),x46931),f334(f334(f7(f928(x46931),f928(f928(x46931)),f928(f928(x46931))),f158(f928(x46931))),f120(f928(x46931)))))),x46933))))),f186(x46931,f334(f334(f158(f928(x46931)),f334(f334(f158(x46931),x46932),x46934)),x46933))) % 188.18/188.25 [4700]E(f334(f270(f934(x47001,x47001)),f334(f265(x47001,x47001,a922),f334(f334(f7(x47001,f935(f934(x47002,x47002),a922),f935(x47001,a922)),f334(f334(f8(f935(x47001,f935(f935(f934(x47002,x47002),a922),a922)),f935(f935(f934(x47002,x47002),a922),f935(x47001,a922)),x47001),f7(x47001,f935(f934(x47002,x47002),a922),a922)),f334(f334(f8(f935(x47001,f934(x47002,x47002)),f935(x47001,f935(f935(f934(x47002,x47002),a922),a922)),x47001),f334(f8(f934(x47002,x47002),f935(f935(f934(x47002,x47002),a922),a922),x47001),f336(f934(x47002,x47002)))),f334(f334(f7(x47001,f935(x47001,x47002),f935(x47001,f934(x47002,x47002))),f334(f334(f8(f935(x47002,f934(x47002,x47002)),f935(f935(x47001,x47002),f935(x47001,f934(x47002,x47002))),x47001),f8(x47002,f934(x47002,x47002),x47001)),f334(f334(f8(x47002,f935(x47002,f934(x47002,x47002)),x47001),f260(x47002,x47002)),x47003))),x47003)))),x47004))),f334(f334(f294(x47002,x47001),x47004),x47003)) % 188.18/188.25 [4752]~E(f31(x47521,x47522),f28(x47523,x47524,x47525)) % 188.18/188.25 [4753]~E(f31(x47531,x47532),f27(x47533,x47534,x47535)) % 188.18/188.25 [4754]~E(f26(x47541,x47542),f28(x47543,x47544,x47545)) % 188.18/188.25 [4755]~E(f26(x47551,x47552),f27(x47553,x47554,x47555)) % 188.18/188.25 [4756]~E(f30(x47561,x47562),f28(x47563,x47564,x47565)) % 188.18/188.25 [4757]~E(f30(x47571,x47572),f27(x47573,x47574,x47575)) % 188.18/188.25 [4758]~E(f28(x47581,x47582,x47583),f31(x47584,x47585)) % 188.18/188.25 [4759]~E(f28(x47591,x47592,x47593),f26(x47594,x47595)) % 188.18/188.25 [4760]~E(f28(x47601,x47602,x47603),f30(x47604,x47605)) % 188.18/188.25 [4761]~E(f27(x47611,x47612,x47613),f31(x47614,x47615)) % 188.18/188.25 [4762]~E(f27(x47621,x47622,x47623),f26(x47624,x47625)) % 188.18/188.25 [4763]~E(f27(x47631,x47632,x47633),f30(x47634,x47635)) % 188.18/188.25 [3826]E(f334(f334(f161(x38261,x38262),x38263),f176(x38261,x38264,x38265)),f176(x38262,x38264,f334(x38263,x38265))) % 188.18/188.25 [4037]E(f100(x40371,x40372,f98(x40371,x40373,x40374,x40375)),f2(a927)) % 188.18/188.25 [4156]E(f137(x41561,x41562,x41563,f133(x41561,x41564,x41565)),f133(x41562,f334(x41563,x41564),f137(x41561,x41562,x41563,x41565))) % 188.18/188.25 [4382]E(f334(f80(x43821,x43822,x43823,x43824,x43825),x43824),x43825) % 188.18/188.25 [4436]E(f261(x44361,x44362,x44363,f251(x44362,x44361,x44364),f251(x44363,x44362,x44365)),f251(x44363,x44361,f261(x44363,x44362,x44361,x44365,x44364))) % 188.18/188.25 [4017]E(f334(f334(f265(x40171,x40172,x40173),x40174),x40175),f334(f334(x40174,f334(f259(x40171,x40172),x40175)),f334(f264(x40171,x40172),x40175))) % 188.18/188.25 [4052]E(f334(f334(f334(f70(x40521,x40522,x40523),x40524),x40525),f195(f935(x40522,a922))),x40525) % 188.18/188.25 [4324]E(f334(f78(f928(x43241),f928(x43242),f928(x43243),f334(f161(x43241,x43242),x43244)),f334(f161(x43243,x43241),x43245)),f334(f161(x43243,x43242),f334(f78(x43241,x43242,x43243,x43244),x43245))) % 188.18/188.25 [4392]E(f91(x43921,f71(x43922,x43921,x43923,x43924,x43925)),f334(f334(f69(x43922,x43921,x43923),x43924),x43925)) % 188.18/188.25 [4428]E(f334(f334(f86(a927),f334(f334(f86(a927),f334(x44281,f334(f259(x44282,x44283),x44284))),f334(x44285,f334(f264(x44282,x44283),x44284)))),f334(a119,f2(a927))),f269(x44282,x44283,x44281,x44285,x44284)) % 188.18/188.25 [3955]E(f334(f334(f182(x39551),x39552),f334(f334(f161(x39553,x39551),x39554),x39555)),f334(f334(f161(x39553,x39551),x39554),f334(f334(f182(x39553),x39552),x39555))) % 188.18/188.25 [3956]E(f334(f334(f145(x39561),x39562),f334(f334(f161(x39563,x39561),x39564),x39565)),f334(f334(f161(x39563,x39561),x39564),f334(f334(f145(x39563),x39562),x39565))) % 188.18/188.25 [3981]E(f334(f334(f161(x39811,x39812),x39813),f334(f334(f158(x39811),x39814),x39815)),f334(f334(f158(x39812),f334(x39813,x39814)),f334(f334(f161(x39811,x39812),x39813),x39815))) % 188.18/188.25 [4048]E(f334(f317(x40481,x40482,x40483),f334(f334(f316(x40481),x40484),x40485)),f334(f334(f316(x40482),f334(x40483,x40484)),f334(f317(x40481,x40482,x40483),x40485))) % 188.18/188.25 [4076]E(f180(x40761,f334(f334(f158(x40761),x40762),x40763),f334(f334(f158(x40761),x40764),x40765)),f334(f334(f158(x40761),x40762),f334(f334(f158(x40761),x40764),f180(x40761,x40763,x40765)))) % 188.18/188.25 [4111]E(f334(f334(f188(x41111,x41112),f334(f334(f182(x41111),x41113),x41114)),f334(f334(f182(x41112),x41113),x41115)),f334(f334(f182(f934(x41111,x41112)),x41113),f334(f334(f188(x41111,x41112),x41114),x41115))) % 188.18/188.25 [4112]E(f334(f334(f188(x41121,x41122),f334(f334(f145(x41121),x41123),x41124)),f334(f334(f145(x41122),x41123),x41125)),f334(f334(f145(f934(x41121,x41122)),x41123),f334(f334(f188(x41121,x41122),x41124),x41125))) % 188.18/188.25 [4121]E(f334(f334(f166(x41211,f334(f334(f158(x41211),x41212),x41213)),f334(a119,x41214)),x41215),f334(f334(f158(x41211),x41212),f334(f334(f166(x41211,x41213),x41214),x41215))) % 188.18/188.25 [4123]E(f334(f334(f141(x41231),f334(f334(f161(x41232,x41231),x41233),x41234)),f334(f334(f161(x41232,x41231),x41233),x41235)),f334(f334(f161(x41232,x41231),x41233),f334(f334(f141(x41232),x41234),x41235))) % 188.18/188.25 [4127]E(f334(f334(x41271,x41272),f334(f334(f253(x41273,x41274,x41271),x41272),x41275)),f334(f334(f253(x41273,x41274,x41271),x41272),f334(a119,x41275))) % 188.18/188.25 [4160]E(f170(x41601,x41602,x41603,f334(f334(f158(x41601),x41604),x41605)),f334(f334(f141(x41602),f334(x41603,x41604)),f170(x41601,x41602,x41603,x41605))) % 188.18/188.25 [4172]E(f334(f334(f295(x41721,x41722,x41723),f334(f293(x41722,x41721),x41724)),f334(f293(x41723,x41722),x41725)),f334(f293(x41723,x41721),f334(f334(f295(x41723,x41722,x41721),x41725),x41724))) % 188.18/188.25 [4205]E(f334(f334(f334(f190(f928(x42051),f928(x42051)),x42052),f174(x42051)),f334(f334(f161(x42053,x42051),x42054),x42055)),f334(f334(f161(x42053,x42051),x42054),f334(f334(f334(f190(f928(x42053),f928(x42053)),x42052),f174(x42053)),x42055))) % 188.18/188.25 [4206]E(f334(f334(f267(x42061,x42062,x42061,x42063),f334(f260(x42062,x42061),x42064)),x42065),f334(x42065,x42064)) % 188.18/188.25 [4230]E(f162(x42301,x42302,f334(f334(f161(x42303,x42301),x42304),x42305)),f162(x42303,f334(f78(x42301,a927,x42303,x42302),x42304),x42305)) % 188.18/188.25 [4291]E(f184(f934(x42911,x42912),f334(f78(x42912,a922,f934(x42911,x42912),x42913),f264(x42911,x42912)),f334(f334(f188(x42911,x42912),x42914),x42915)),f334(f334(f188(x42911,x42912),x42914),f184(x42912,x42913,x42915))) % 188.18/188.25 [4296]E(f334(f317(x42961,x42962,f334(f334(f8(x42963,x42962,x42961),x42964),x42965)),f250(f935(x42961,a922))),f334(f317(x42963,x42962,x42964),f334(f317(x42961,x42963,x42965),f250(f935(x42961,a922))))) % 188.18/188.25 [4307]E(f184(f934(x43071,x43072),f334(f78(x43071,a922,f934(x43071,x43072),x43073),f259(x43071,x43072)),f334(f334(f188(x43071,x43072),x43074),x43075)),f334(f334(f188(x43071,x43072),f184(x43071,x43073,x43074)),x43075)) % 188.18/188.25 [4329]E(f334(f334(f108(f935(x43291,a922)),f334(f318(x43291,x43292,x43293),f334(f334(f316(x43292),x43294),f195(f935(x43292,a922))))),f334(f318(x43291,x43292,x43293),x43295)),f334(f318(x43291,x43292,x43293),f334(f334(f316(x43292),x43294),x43295))) % 188.18/188.25 [4381]E(f334(f334(f141(f934(x43811,x43812)),f334(f334(f161(x43812,f934(x43811,x43812)),f334(f260(x43811,x43812),x43813)),x43814)),f64(x43811,x43812,x43815,x43814)),f64(x43811,x43812,f334(f334(f158(x43811),x43813),x43815),x43814)) % 188.18/188.25 [4383]E(f334(f334(f161(x43831,x43832),x43833),f184(x43831,f334(f78(x43832,a922,x43831,x43834),x43833),x43835)),f184(x43832,x43834,f334(f334(f161(x43831,x43832),x43833),x43835))) % 188.18/188.25 [4388]E(f334(f149(x43881,x43882,f334(f7(x43882,x43881,x43881),f334(f7(x43881,x43882,x43881),x43883)),x43884),f334(f175(x43882),f334(f175(x43882),x43885))),f334(f149(x43881,x43882,x43883,x43884),x43885)) % 188.18/188.25 [4494]P107(f334(f334(f242(f935(x44941,a922)),f334(f317(x44942,x44941,x44943),f334(f334(f109(f935(x44942,a922)),x44944),x44945))),f334(f334(f109(f935(x44941,a922)),f334(f317(x44942,x44941,x44943),x44944)),f334(f317(x44942,x44941,x44943),x44945)))) % 188.18/188.25 [4495]P107(f334(f334(f242(f935(x44951,a922)),f334(f292(x44952,x44951,x44953),f334(f334(f109(f935(x44952,a922)),x44954),x44955))),f334(f334(f109(f935(x44951,a922)),f334(f292(x44952,x44951,x44953),x44954)),f334(f292(x44952,x44951,x44953),x44955)))) % 188.18/188.25 [4600]E(f334(f264(x46001,x46002),f334(f266(x46003,x46001,x46002,x46002,x46004,f32(x46002)),x46005)),f334(f264(x46003,x46002),x46005)) % 188.18/188.25 [4601]E(f334(f259(x46011,x46012),f334(f266(x46011,x46011,x46013,x46012,f32(x46011),x46014),x46015)),f334(f259(x46011,x46013),x46015)) % 188.18/188.25 [4677]P26(x46771,x46772,f334(f334(f316(f926(x46771)),f98(x46771,f334(f334(f7(x46771,f935(a923,a923),f935(a923,a922)),f334(f334(f8(f935(a923,a922),f935(f935(a923,a923),f935(a923,a922)),x46771),f8(a923,a922,a923)),x46773)),f334(f334(f18(a923,a927,a923),f334(f334(f7(a923,a925,f935(a927,a923)),a203),x46774)),x46775)),f26(x46774,x46775),x46773)),f195(f935(f926(x46771),a922)))) % 188.18/188.25 [3792]E(f334(f334(f334(f334(f213(x37921),x37922),x37923),x37924),x37925),f199(x37921,x37922)) % 188.18/188.25 [3793]E(f334(f334(f334(f334(f217(x37931),x37932),x37933),x37934),x37935),f208(x37931,x37932)) % 188.18/188.25 [4161]E(f334(f334(f44(x41611,f935(x41612,a922)),f334(f334(f316(x41611),x41613),x41614)),x41615),f334(f334(f108(f935(x41612,a922)),f334(x41615,x41613)),f334(f334(f44(x41611,f935(x41612,a922)),x41614),x41615))) % 188.18/188.25 [4162]E(f334(f334(f45(x41621,f935(x41622,a922)),f334(f334(f316(x41621),x41623),x41624)),x41625),f334(f334(f109(f935(x41622,a922)),f334(x41625,x41623)),f334(f334(f45(x41621,f935(x41622,a922)),x41624),x41625))) % 188.18/188.25 [4214]E(f334(f125(x42141,x42142,f334(x42143,x42144)),f334(f334(f7(x42141,a106,f929(x42142)),x42145),x42144)),f334(f206(x42141,x42142,x42143,x42145),x42144)) % 188.18/188.25 [4224]E(f334(f334(f108(f935(x42241,a922)),f334(f317(x42242,x42241,x42243),x42244)),f334(f317(x42242,x42241,x42243),x42245)),f334(f317(x42242,x42241,x42243),f334(f334(f108(f935(x42242,a922)),x42244),x42245))) % 188.18/188.25 [4225]E(f334(f334(f23(f935(x42251,a922)),f334(f318(x42251,x42252,x42253),x42254)),f334(f318(x42251,x42252,x42253),x42255)),f334(f318(x42251,x42252,x42253),f334(f334(f23(f935(x42252,a922)),x42254),x42255))) % 188.18/188.25 [4226]E(f334(f334(f108(f935(x42261,a922)),f334(f318(x42261,x42262,x42263),x42264)),f334(f318(x42261,x42262,x42263),x42265)),f334(f318(x42261,x42262,x42263),f334(f334(f108(f935(x42262,a922)),x42264),x42265))) % 188.18/188.25 [4227]E(f334(f334(f109(f935(x42271,a922)),f334(f318(x42271,x42272,x42273),x42274)),f334(f318(x42271,x42272,x42273),x42275)),f334(f318(x42271,x42272,x42273),f334(f334(f109(f935(x42272,a922)),x42274),x42275))) % 188.18/188.25 [4228]E(f334(f334(f108(f935(x42281,a922)),f334(f292(x42282,x42281,x42283),x42284)),f334(f292(x42282,x42281,x42283),x42285)),f334(f292(x42282,x42281,x42283),f334(f334(f108(f935(x42282,a922)),x42284),x42285))) % 188.18/188.25 [4287]E(f334(f334(f166(x42871,f334(f334(f141(x42871),x42872),f334(f334(f158(x42871),x42873),x42874))),f334(f196(f928(x42871)),x42872)),x42875),f334(f334(f141(x42871),x42872),f334(f334(f158(x42871),x42875),x42874))) % 188.18/188.25 [4294]E(f334(f334(f45(x42941,f935(x42942,a922)),x42943),f334(f334(f8(f935(x42942,a922),f935(x42942,a922),x42941),f334(f316(x42942),x42944)),x42945)),f334(f334(f316(x42942),x42944),f334(f334(f45(x42941,f935(x42942,a922)),x42943),x42945))) % 188.18/188.25 [4446]E(f334(f334(f161(x44461,x44462),x44463),f334(f143(x44461,f334(f78(x44462,a922,x44461,x44464),x44463)),x44465)),f334(f143(x44462,x44464),f334(f334(f161(x44461,x44462),x44463),x44465))) % 188.18/188.25 [4453]E(f334(f196(f928(x44531)),f334(f143(x44531,x44532),f334(f334(f161(x44533,x44531),x44534),x44535))),f334(f196(f928(x44533)),f334(f143(x44533,f334(f78(x44531,a922,x44533,x44532),x44534)),x44535))) % 188.18/188.25 [4679]E(f334(f163(f928(f934(x46791,x46792)),x46792,f120(f934(x46791,x46792)),f334(f334(f7(x46792,f935(f928(x46792),f928(f934(x46791,x46792))),f935(f928(x46792),f928(f934(x46791,x46792)))),f334(f334(f8(f935(f928(f934(x46791,x46792)),f928(f934(x46791,x46792))),f935(f935(f928(x46792),f928(f934(x46791,x46792))),f935(f928(x46792),f928(f934(x46791,x46792)))),x46792),f8(f928(f934(x46791,x46792)),f928(f934(x46791,x46792)),f928(x46792))),f334(f334(f8(f934(x46791,x46792),f935(f928(f934(x46791,x46792)),f928(f934(x46791,x46792))),x46792),f158(f934(x46791,x46792))),f334(f260(x46791,x46792),x46793)))),f334(f188(x46791,x46792),x46794))),x46795),f334(f334(f188(x46791,x46792),f334(f334(f158(x46791),x46793),x46794)),x46795)) % 188.18/188.25 [4153]E(f334(f334(f166(x41531,f334(f334(f166(x41531,x41532),x41533),x41534)),x41533),x41535),f334(f334(f166(x41531,x41532),x41533),x41535)) % 188.18/188.25 [4207]E(f334(f291(x42071,x42072),f334(f334(f316(f934(x42071,x42072)),f334(f334(f260(x42071,x42072),x42073),x42074)),x42075)),f334(f334(f316(x42072),x42074),f334(f291(x42071,x42072),x42075))) % 188.18/188.25 [4208]E(f334(f272(x42081,x42082),f334(f334(f316(f934(x42081,x42082)),f334(f334(f260(x42081,x42082),x42083),x42084)),x42085)),f334(f334(f316(x42081),x42083),f334(f272(x42081,x42082),x42085))) % 188.18/188.25 [4253]E(f129(x42531,x42532,f334(x42533,x42534),f334(f334(f7(x42531,a106,f929(f931(x42532))),x42535),x42534)),f334(f202(x42531,x42532,x42533,x42535),x42534)) % 188.18/188.25 [4280]E(f334(f334(f23(f935(f934(x42801,x42802),a922)),f334(f334(f262(x42801,x42802),x42803),x42804)),f334(f334(f262(x42801,x42802),x42805),x42804)),f334(f334(f262(x42801,x42802),f334(f334(f23(f935(x42801,a922)),x42803),x42805)),x42804)) % 188.18/188.25 [4281]E(f334(f334(f108(f935(f934(x42811,x42812),a922)),f334(f334(f262(x42811,x42812),x42813),x42814)),f334(f334(f262(x42811,x42812),x42815),x42814)),f334(f334(f262(x42811,x42812),f334(f334(f108(f935(x42811,a922)),x42813),x42815)),x42814)) % 188.18/188.25 [4282]E(f334(f334(f109(f935(f934(x42821,x42822),a922)),f334(f334(f262(x42821,x42822),x42823),x42824)),f334(f334(f262(x42821,x42822),x42825),x42824)),f334(f334(f262(x42821,x42822),f334(f334(f109(f935(x42821,a922)),x42823),x42825)),x42824)) % 188.18/188.25 [4339]E(f334(f334(f108(f935(x43391,a922)),f334(f334(f44(x43392,f935(x43391,a922)),x43393),x43394)),f334(f334(f44(x43392,f935(x43391,a922)),x43395),x43394)),f334(f334(f44(x43392,f935(x43391,a922)),f334(f334(f108(f935(x43392,a922)),x43393),x43395)),x43394)) % 188.18/188.25 [4340]E(f334(f334(f109(f935(x43401,a922)),f334(f334(f45(x43402,f935(x43401,a922)),x43403),x43404)),f334(f334(f45(x43402,f935(x43401,a922)),x43405),x43404)),f334(f334(f45(x43402,f935(x43401,a922)),f334(f334(f108(f935(x43402,a922)),x43403),x43405)),x43404)) % 188.18/188.25 [4354]E(f334(f334(f44(x43541,f935(x43542,a922)),x43543),f334(f334(f8(f935(x43542,a922),f935(x43542,a922),x43541),f334(f23(f935(x43542,a922)),x43544)),x43545)),f334(f334(f23(f935(x43542,a922)),x43544),f334(f334(f45(x43541,f935(x43542,a922)),x43543),x43545))) % 188.18/188.25 [4355]E(f334(f334(f44(x43551,f935(x43552,a922)),x43553),f334(f334(f8(f935(x43552,a922),f935(x43552,a922),x43551),f334(f109(f935(x43552,a922)),x43554)),x43555)),f334(f334(f109(f935(x43552,a922)),x43554),f334(f334(f44(x43551,f935(x43552,a922)),x43553),x43555))) % 188.18/188.25 [4356]E(f334(f334(f45(x43561,f935(x43562,a922)),x43563),f334(f334(f8(f935(x43562,a922),f935(x43562,a922),x43561),f334(f108(f935(x43562,a922)),x43564)),x43565)),f334(f334(f108(f935(x43562,a922)),x43564),f334(f334(f45(x43561,f935(x43562,a922)),x43563),x43565))) % 188.18/188.25 [4406]E(f192(f928(x44061),f334(f334(f158(x44061),x44062),x44063),f334(f334(f8(f928(x44061),f928(x44061),a927),f334(f158(x44061),x44064)),f334(f334(f7(a927,x44061,f928(x44061)),f166(x44061,x44063)),x44062)),x44065),f334(f334(f166(x44061,f334(f334(f158(x44061),x44064),x44063)),x44065),x44062)) % 188.18/188.25 [4410]E(f334(f334(f44(x44101,f935(f934(x44102,x44103),a922)),x44104),f334(f334(f8(f935(f934(x44103,x44102),a922),f935(f934(x44102,x44103),a922),x44101),f293(x44103,x44102)),x44105)),f334(f293(x44103,x44102),f334(f334(f44(x44101,f935(f934(x44103,x44102),a922)),x44104),x44105))) % 188.18/188.25 [4411]E(f334(f334(f45(x44111,f935(f934(x44112,x44113),a922)),x44114),f334(f334(f8(f935(f934(x44113,x44112),a922),f935(f934(x44112,x44113),a922),x44111),f293(x44113,x44112)),x44115)),f334(f293(x44113,x44112),f334(f334(f45(x44111,f935(f934(x44113,x44112),a922)),x44114),x44115))) % 188.18/188.25 [4518]P107(f334(f334(f242(f935(x45181,a922)),f334(f334(f23(f935(x45181,a922)),f334(f317(x45182,x45181,x45183),x45184)),f334(f317(x45182,x45181,x45183),x45185))),f334(f317(x45182,x45181,x45183),f334(f334(f23(f935(x45182,a922)),x45184),x45185)))) % 188.18/188.25 [4682]E(f334(f163(f928(f934(x46821,x46822)),x46821,f120(f934(x46821,x46822)),f334(f334(f7(x46821,f935(f928(x46821),f928(f934(x46821,x46822))),f935(f928(x46821),f928(f934(x46821,x46822)))),f334(f334(f8(f935(f928(f934(x46821,x46822)),f928(f934(x46821,x46822))),f935(f935(f928(x46821),f928(f934(x46821,x46822))),f935(f928(x46821),f928(f934(x46821,x46822)))),x46821),f8(f928(f934(x46821,x46822)),f928(f934(x46821,x46822)),f928(x46821))),f334(f334(f8(f934(x46821,x46822),f935(f928(f934(x46821,x46822)),f928(f934(x46821,x46822))),x46821),f158(f934(x46821,x46822))),f334(f334(f7(x46821,x46822,f934(x46821,x46822)),f260(x46821,x46822)),x46823)))),f334(f334(f7(f928(x46821),f928(x46822),f928(f934(x46821,x46822))),f188(x46821,x46822)),x46824))),x46825),f334(f334(f188(x46821,x46822),x46825),f334(f334(f158(x46822),x46823),x46824))) % 188.18/188.25 [4377]E(f334(f334(f108(f935(x43771,a922)),f334(f292(x43772,x43771,x43773),x43774)),f334(f292(x43772,x43771,x43775),x43774)),f334(f292(x43772,x43771,f334(f334(f108(f935(f934(x43772,x43771),a922)),x43773),x43775)),x43774)) % 188.18/188.25 [4412]E(f334(f334(f141(f934(x44121,x44122)),f334(f334(f188(x44121,x44122),x44123),f334(f334(f182(x44122),f334(f196(f928(x44121)),x44123)),x44124))),f334(f334(f188(x44121,x44122),x44125),f334(f334(f145(x44122),f334(f196(f928(x44121)),x44123)),x44124))),f334(f334(f188(x44121,x44122),f334(f334(f141(x44121),x44123),x44125)),x44124)) % 188.18/188.25 [4523]E(f334(f334(f262(x45231,x45232),x45233),f334(f334(f18(x45231,f935(x45232,a922),f935(x45232,a922)),f334(f334(f8(f935(x45232,a922),f935(f935(x45232,a922),f935(x45232,a922)),x45231),f23(f935(x45232,a922))),x45234)),x45235)),f334(f334(f23(f935(f934(x45231,x45232),a922)),f334(f334(f262(x45231,x45232),x45233),x45234)),f334(f334(f262(x45231,x45232),x45233),x45235))) % 188.18/188.25 [4524]E(f334(f334(f262(x45241,x45242),x45243),f334(f334(f18(x45241,f935(x45242,a922),f935(x45242,a922)),f334(f334(f8(f935(x45242,a922),f935(f935(x45242,a922),f935(x45242,a922)),x45241),f108(f935(x45242,a922))),x45244)),x45245)),f334(f334(f108(f935(f934(x45241,x45242),a922)),f334(f334(f262(x45241,x45242),x45243),x45244)),f334(f334(f262(x45241,x45242),x45243),x45245))) % 188.18/188.25 [4525]E(f334(f334(f262(x45251,x45252),x45253),f334(f334(f18(x45251,f935(x45252,a922),f935(x45252,a922)),f334(f334(f8(f935(x45252,a922),f935(f935(x45252,a922),f935(x45252,a922)),x45251),f109(f935(x45252,a922))),x45254)),x45255)),f334(f334(f109(f935(f934(x45251,x45252),a922)),f334(f334(f262(x45251,x45252),x45253),x45254)),f334(f334(f262(x45251,x45252),x45253),x45255))) % 188.18/188.25 [4529]E(f334(f334(f44(x45291,f935(x45292,a922)),x45293),f334(f334(f7(x45291,f935(x45292,a922),f935(x45292,a922)),f334(f334(f8(f935(x45292,a922),f935(f935(x45292,a922),f935(x45292,a922)),x45291),f23(f935(x45292,a922))),x45294)),x45295)),f334(f334(f23(f935(x45292,a922)),f334(f334(f44(x45291,f935(x45292,a922)),x45293),x45294)),x45295)) % 188.18/188.25 [4530]E(f334(f334(f44(x45301,f935(x45302,a922)),x45303),f334(f334(f7(x45301,f935(x45302,a922),f935(x45302,a922)),f334(f334(f8(f935(x45302,a922),f935(f935(x45302,a922),f935(x45302,a922)),x45301),f109(f935(x45302,a922))),x45304)),x45305)),f334(f334(f109(f935(x45302,a922)),f334(f334(f44(x45301,f935(x45302,a922)),x45303),x45304)),x45305)) % 188.18/188.25 [4531]E(f334(f334(f45(x45311,f935(x45312,a922)),x45313),f334(f334(f7(x45311,f935(x45312,a922),f935(x45312,a922)),f334(f334(f8(f935(x45312,a922),f935(f935(x45312,a922),f935(x45312,a922)),x45311),f108(f935(x45312,a922))),x45314)),x45315)),f334(f334(f108(f935(x45312,a922)),f334(f334(f45(x45311,f935(x45312,a922)),x45313),x45314)),x45315)) % 188.18/188.25 [4535]E(f334(f334(f44(x45351,f935(x45352,a922)),x45353),f334(f334(f18(x45351,f935(x45352,a922),f935(x45352,a922)),f334(f334(f8(f935(x45352,a922),f935(f935(x45352,a922),f935(x45352,a922)),x45351),f108(f935(x45352,a922))),x45354)),x45355)),f334(f334(f108(f935(x45352,a922)),f334(f334(f44(x45351,f935(x45352,a922)),x45353),x45354)),f334(f334(f44(x45351,f935(x45352,a922)),x45353),x45355))) % 188.18/188.25 [4536]E(f334(f334(f45(x45361,f935(x45362,a922)),x45363),f334(f334(f18(x45361,f935(x45362,a922),f935(x45362,a922)),f334(f334(f8(f935(x45362,a922),f935(f935(x45362,a922),f935(x45362,a922)),x45361),f109(f935(x45362,a922))),x45364)),x45365)),f334(f334(f109(f935(x45362,a922)),f334(f334(f45(x45361,f935(x45362,a922)),x45363),x45364)),f334(f334(f45(x45361,f935(x45362,a922)),x45363),x45365))) % 188.18/188.25 [4545]E(f334(f334(f44(x45451,f935(x45452,a922)),x45453),f334(f334(f18(x45451,f935(x45452,a922),f935(x45452,a922)),f334(f334(f8(f935(x45452,a922),f935(f935(x45452,a922),f935(x45452,a922)),x45451),f108(f935(x45452,a922))),x45454)),x45455)),f334(f334(f108(f935(x45452,a922)),f42(f935(x45452,a922),f334(f317(x45451,f935(x45452,a922),x45454),x45453))),f42(f935(x45452,a922),f334(f317(x45451,f935(x45452,a922),x45455),x45453)))) % 188.18/188.25 [4546]E(f334(f334(f45(x45461,f935(x45462,a922)),x45463),f334(f334(f18(x45461,f935(x45462,a922),f935(x45462,a922)),f334(f334(f8(f935(x45462,a922),f935(f935(x45462,a922),f935(x45462,a922)),x45461),f109(f935(x45462,a922))),x45464)),x45465)),f334(f334(f109(f935(x45462,a922)),f43(f935(x45462,a922),f334(f317(x45461,f935(x45462,a922),x45464),x45463))),f43(f935(x45462,a922),f334(f317(x45461,f935(x45462,a922),x45465),x45463)))) % 188.18/188.25 [4584]E(f334(f334(f145(x45841),f334(f196(f928(x45841)),f184(x45841,x45842,f334(f334(f161(x45843,x45841),x45844),x45845)))),f334(f334(f161(x45843,x45841),x45844),x45845)),f334(f334(f161(x45843,x45841),x45844),f334(f334(f145(x45843),f334(f196(f928(x45843)),f184(x45843,f334(f78(x45841,a922,x45843,x45842),x45844),x45845))),x45845))) % 188.18/188.25 [4463]E(f334(f334(f141(f934(x44631,x44632)),f334(f334(f188(x44631,x44632),f334(f334(f182(x44631),f334(f196(f928(x44632)),x44633)),x44634)),x44633)),f334(f334(f188(x44631,x44632),f334(f334(f145(x44631),f334(f196(f928(x44632)),x44633)),x44634)),x44635)),f334(f334(f188(x44631,x44632),x44634),f334(f334(f141(x44632),x44633),x44635))) % 188.18/188.25 [4574]E(f91(x45741,f334(f334(f18(x45741,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45741),a332),f334(f334(f7(x45741,f935(x45741,a922),a922),f336(x45741)),x45742))),f334(f334(f7(x45741,x45743,a922),f334(f334(f8(x45743,f935(x45743,a922),x45741),a331),x45744)),x45745))),f334(f83(x45741,x45743,x45742,x45744),x45745)) % 188.18/188.25 [4575]E(f96(x45751,f334(f334(f18(x45751,a922,a922),f334(f334(f8(a922,f935(a922,a922),x45751),a332),f334(f334(f7(x45751,f935(x45751,a922),a922),f336(x45751)),x45752))),f334(f334(f7(x45751,x45753,a922),f334(f334(f8(x45753,f935(x45753,a922),x45751),a331),x45754)),x45755))),f334(f97(x45751,x45753,x45752,x45754),x45755)) % 188.18/188.25 [4627]E(f334(f334(f94(a1,x46271),f334(f111(a1),f334(f334(f86(a1),x46272),a104))),f334(f334(f18(a1,x46271,x46271),f334(f334(f7(a1,x46271,f935(x46271,x46271)),f334(f334(f8(a922,f935(x46271,f935(x46271,x46271)),a1),f103(x46271)),a200)),f192(x46271,x46273,x46274,x46275))),f334(f334(f8(a927,x46271,a1),x46274),f334(f334(f7(a1,a927,a927),f334(f334(f8(a927,f935(a927,a927),a1),f86(a927)),a112)),x46275)))),f192(x46271,x46273,x46274,f334(f334(f86(a927),f334(f111(a927),x46272)),x46275))) % 188.18/188.25 [4674]E(f334(f334(f94(a1,x46741),f334(f111(a1),f334(f334(f86(a1),x46742),a104))),f334(f334(f18(a1,x46741,x46741),f334(f334(f7(a1,x46741,f935(x46741,x46741)),f334(f334(f8(a922,f935(x46741,f935(x46741,x46741)),a1),f103(x46741)),a200)),f334(f191(x46741,x46743,x46744),x46745))),f334(f334(f18(a1,x46741,x46741),f334(f334(f8(a927,f935(x46741,x46741),a1),x46744),f334(f334(f7(a1,a927,a927),f334(f334(f8(a927,f935(a927,a927),a1),f86(a927)),a112)),x46745))),f334(f334(f8(a927,x46741,a1),f191(x46741,x46743,x46744)),f334(f334(f7(a1,a927,a927),f334(f334(f8(a927,f935(a927,a927),a1),f86(a927)),a112)),x46745))))),f334(f191(x46741,x46743,x46744),f334(f334(f86(a927),f334(f111(a927),x46742)),x46745))) % 188.18/188.25 [4708]E(f334(f270(f934(x47081,x47082)),f334(f265(x47081,x47082,a922),f334(f334(f8(f935(x47082,f935(x47083,a922)),f935(x47082,a922),x47081),f334(f8(f935(x47083,a922),a922,x47082),f92(x47083))),f334(f334(f7(x47081,f935(x47082,f935(x47083,a922)),f935(x47082,f935(x47083,a922))),f334(f334(f8(f935(f935(x47083,a922),f935(x47083,a922)),f935(f935(x47082,f935(x47083,a922)),f935(x47082,f935(x47083,a922))),x47081),f8(f935(x47083,a922),f935(x47083,a922),x47082)),f334(f334(f8(f935(x47083,f935(a922,a922)),f935(f935(x47083,a922),f935(x47083,a922)),x47081),f18(x47083,a922,a922)),f334(f334(f8(f935(x47083,a922),f935(x47083,f935(a922,a922)),x47081),f334(f8(a922,f935(a922,a922),x47083),a332)),f334(f334(f7(x47081,f935(f934(x47081,x47083),a922),f935(x47083,a922)),f334(f334(f8(f935(x47083,f935(f935(f934(x47081,x47083),a922),a922)),f935(f935(f934(x47081,x47083),a922),f935(x47083,a922)),x47081),f7(x47083,f935(f934(x47081,x47083),a922),a922)),f334(f334(f8(f935(x47083,f934(x47081,x47083)),f935(x47083,f935(f935(f934(x47081,x47083),a922),a922)),x47081),f334(f8(f934(x47081,x47083),f935(f935(f934(x47081,x47083),a922),a922),x47083),f336(f934(x47081,x47083)))),f260(x47081,x47083)))),x47084))))),f334(f334(f7(x47082,f935(f934(x47083,x47082),a922),f935(x47083,a922)),f334(f334(f8(f935(x47083,f935(f935(f934(x47083,x47082),a922),a922)),f935(f935(f934(x47083,x47082),a922),f935(x47083,a922)),x47082),f7(x47083,f935(f934(x47083,x47082),a922),a922)),f334(f334(f8(f935(x47083,f934(x47083,x47082)),f935(x47083,f935(f935(f934(x47083,x47082),a922),a922)),x47082),f334(f8(f934(x47083,x47082),f935(f935(f934(x47083,x47082),a922),a922),x47083),f336(f934(x47083,x47082)))),f334(f7(x47083,x47082,f934(x47083,x47082)),f260(x47083,x47082))))),x47085))))),f334(f334(f295(x47081,x47083,x47082),x47084),x47085)) % 188.18/188.25 [4782]~E(f27(x47821,x47822,x47823),f28(x47824,x47825,x47826)) % 188.18/188.25 [4308]E(f233(x43081,x43082,x43083,x43084,f229(x43081,x43082,x43085,x43086)),f334(f334(x43084,x43085),x43086)) % 188.18/188.25 [4309]E(f234(x43091,x43092,x43093,x43094,f229(x43091,x43092,x43095,x43096)),f334(f334(x43094,x43095),x43096)) % 188.18/188.25 [4431]E(f134(x44311,x44312,x44313,x44314,f133(x44312,x44315,x44316)),f334(f334(f334(x44314,x44315),x44316),f134(x44311,x44312,x44313,x44314,x44316))) % 188.18/188.25 [4455]E(f80(x44551,x44552,f80(x44551,x44552,x44553,x44554,x44555),x44554,x44556),f80(x44551,x44552,x44553,x44554,x44556)) % 188.18/188.25 [4562]E(f334(f78(f934(x45621,x45622),x45622,f934(x45623,x45624),f264(x45621,x45622)),f266(x45623,x45621,x45624,x45622,x45625,x45626)),f334(f78(x45624,x45622,f934(x45623,x45624),x45626),f264(x45623,x45624))) % 188.18/188.25 [4563]E(f334(f78(f934(x45631,x45632),x45631,f934(x45633,x45634),f259(x45631,x45632)),f266(x45633,x45631,x45634,x45632,x45635,x45636)),f334(f78(x45633,x45631,f934(x45633,x45634),x45635),f259(x45633,x45634))) % 188.18/188.25 [4129]E(f101(x41291,x41292,x41293,f98(x41291,x41294,x41295,x41296)),f334(f334(f334(x41293,x41294),x41295),x41296)) % 188.18/188.25 [4130]E(f102(x41301,x41302,x41303,f98(x41301,x41304,x41305,x41306)),f334(f334(f334(x41303,x41304),x41305),x41306)) % 188.18/188.25 [4183]E(f334(f334(f78(x41831,x41832,x41833,x41834),x41835),x41836),f334(x41834,f334(x41835,x41836))) % 188.18/188.25 [4318]E(f232(x43181,f934(x43182,f929(x43182)),x43183,f334(f265(x43182,f929(x43182),x43181),x43184),f334(f142(x43182),f133(x43182,x43185,x43186))),f334(f334(x43184,x43185),x43186)) % 188.18/188.25 [4366]E(f235(x43661,x43662,x43663,x43664,f229(x43661,x43662,x43665,x43666)),f334(f334(f86(a927),f334(f334(f86(a927),f334(x43663,x43665)),f334(x43664,x43666))),f334(a119,f2(a927)))) % 188.18/188.25 [3980]E(f334(f334(f265(x39801,x39802,x39803),x39804),f334(f334(f260(x39801,x39802),x39805),x39806)),f334(f334(x39804,x39805),x39806)) % 188.18/188.25 [4045]E(f334(f334(f334(f8(x40451,x40452,x40453),x40454),x40455),x40456),f334(x40454,f334(x40455,x40456))) % 188.18/188.25 [4046]E(f334(f334(f334(f7(x40461,x40462,x40463),x40464),x40465),x40466),f334(f334(x40464,x40466),x40465)) % 188.18/188.25 [4062]E(f334(f334(f334(f18(x40621,x40622,x40623),x40624),x40625),x40626),f334(f334(x40624,x40626),f334(x40625,x40626))) % 188.18/188.25 [4083]E(f334(f163(x40831,x40832,x40833,x40834),f334(f334(f158(x40832),x40835),x40836)),f334(f334(x40834,x40835),x40836)) % 188.18/188.25 [4120]E(f176(f934(x41201,x41202),f334(f334(f246(a927),x41203),x41204),f334(f334(f260(x41201,x41202),x41205),x41206)),f334(f334(f188(x41201,x41202),f176(x41201,x41203,x41205)),f176(x41202,x41204,x41206))) % 188.18/188.25 [4188]E(f334(f334(f158(f934(x41881,x41882)),f334(f334(f260(x41881,x41882),x41883),x41884)),f334(f334(f188(x41881,x41882),x41885),x41886)),f334(f334(f188(x41881,x41882),f334(f334(f158(x41881),x41883),x41885)),f334(f334(f158(x41882),x41884),x41886))) % 188.18/188.25 [4189]E(f334(f334(f161(x41891,x41892),x41893),f334(f334(f166(x41891,x41894),x41895),x41896)),f334(f334(f166(x41892,f334(f334(f161(x41891,x41892),x41893),x41894)),x41895),f334(x41893,x41896))) % 188.18/188.25 [4213]E(f334(f334(f263(x42131,x42132,x42133,x42134),x42135),x42136),f334(x42134,f334(f334(f260(x42131,x42132),x42135),x42136))) % 188.18/188.25 [4229]E(f334(f149(x42291,x42292,x42293,x42294),f334(f334(f158(x42292),x42295),x42296)),f334(f149(x42291,x42292,x42293,f334(f334(x42293,x42294),x42295)),x42296)) % 188.18/188.25 [4254]E(f268(x42541,x42542,x42543,x42544,f334(f334(f260(x42541,x42542),x42545),x42546)),f334(f334(x42544,x42545),x42546)) % 188.18/188.25 [4333]E(f334(f334(f44(x43331,f935(x43332,a922)),x43333),f334(f78(x43334,f935(x43332,a922),x43331,x43335),x43336)),f334(f334(f44(x43334,f935(x43332,a922)),f334(f317(x43331,x43334,x43336),x43333)),x43335)) % 188.18/188.25 [4380]E(f334(f334(f161(x43801,x43802),x43803),f334(f334(f161(x43804,x43801),x43805),x43806)),f334(f334(f161(x43804,x43802),f334(f78(x43801,x43802,x43804,x43803),x43805)),x43806)) % 188.18/188.25 [4386]E(f334(f317(x43861,x43862,f334(f78(x43863,x43862,x43861,x43864),x43865)),x43866),f334(f317(x43863,x43862,x43864),f334(f317(x43861,x43863,x43865),x43866))) % 188.18/188.25 [4387]E(f334(f318(x43871,x43872,f334(f78(x43873,x43872,x43871,x43874),x43875)),x43876),f334(f318(x43871,x43873,x43875),f334(f318(x43873,x43872,x43874),x43876))) % 188.18/188.25 [4413]E(f334(f149(x44131,x44132,x44133,f334(f149(x44131,x44132,x44133,x44134),x44135)),x44136),f334(f149(x44131,x44132,x44133,x44134),f334(f334(f141(x44132),x44135),x44136))) % 188.18/188.25 [4550]E(f334(f266(x45501,x45501,x45502,x45503,f32(x45501),x45504),f334(f334(f260(x45501,x45502),x45505),x45506)),f334(f334(f260(x45501,x45503),x45505),f334(x45504,x45506))) % 188.18/188.25 [4551]E(f334(f266(x45511,x45512,x45513,x45513,x45514,f32(x45513)),f334(f334(f260(x45511,x45513),x45515),x45516)),f334(f334(f260(x45512,x45513),f334(x45514,x45515)),x45516)) % 188.18/188.25 [4653]E(f334(f334(f161(f934(x46531,x46532),f934(x46531,x46533)),f334(f265(x46531,x46532,f934(x46531,x46533)),f334(f334(f7(x46531,f935(x46532,x46533),f935(x46532,f934(x46531,x46533))),f334(f334(f8(f935(x46533,f934(x46531,x46533)),f935(f935(x46532,x46533),f935(x46532,f934(x46531,x46533))),x46531),f8(x46533,f934(x46531,x46533),x46532)),f260(x46531,x46533))),x46534))),f334(f334(f188(x46531,x46532),x46535),x46536)),f334(f334(f188(x46531,x46533),x46535),f334(f334(f161(x46532,x46533),x46534),x46536))) % 188.18/188.25 [4239]E(f334(f334(f78(x42391,x42392,x42393,f334(f16(x42392,x42391),x42394)),x42395),x42396),x42394) % 188.18/188.25 [4270]E(f334(f317(x42701,x42702,x42703),f334(f317(x42704,x42701,x42705),x42706)),f334(f317(x42704,x42702,f334(f334(f8(x42701,x42702,x42704),x42703),x42705)),x42706)) % 188.18/188.25 [4275]E(f334(f334(f44(x42751,f935(x42752,a922)),f334(f317(x42753,x42751,x42754),x42755)),x42756),f334(f334(f44(x42753,f935(x42752,a922)),x42755),f334(f334(f8(x42751,f935(x42752,a922),x42753),x42756),x42754))) % 188.18/188.25 [4276]E(f334(f334(f45(x42761,f935(x42762,a922)),f334(f317(x42763,x42761,x42764),x42765)),x42766),f334(f334(f45(x42763,f935(x42762,a922)),x42765),f334(f334(f8(x42761,f935(x42762,a922),x42763),x42766),x42764))) % 188.18/188.25 [4277]E(f334(f334(f44(x42771,f935(x42772,a922)),x42773),f334(f334(f8(x42774,f935(x42772,a922),x42771),x42775),x42776)),f334(f334(f44(x42774,f935(x42772,a922)),f334(f317(x42771,x42774,x42776),x42773)),x42775)) % 188.18/188.25 [4278]E(f334(f334(f45(x42781,f935(x42782,a922)),x42783),f334(f334(f8(x42784,f935(x42782,a922),x42781),x42785),x42786)),f334(f334(f45(x42784,f935(x42782,a922)),f334(f317(x42781,x42784,x42786),x42783)),x42785)) % 188.18/188.25 [4335]E(f334(f334(f44(x43351,f935(x43352,a922)),x43353),f334(f334(f8(f935(x43354,a922),f935(x43352,a922),x43351),f317(x43354,x43352,x43355)),x43356)),f334(f317(x43354,x43352,x43355),f334(f334(f44(x43351,f935(x43354,a922)),x43353),x43356))) % 188.18/188.25 [4336]E(f334(f334(f44(x43361,f935(x43362,a922)),x43363),f334(f334(f8(f935(x43364,a922),f935(x43362,a922),x43361),f318(x43362,x43364,x43365)),x43366)),f334(f318(x43362,x43364,x43365),f334(f334(f44(x43361,f935(x43364,a922)),x43363),x43366))) % 188.18/188.25 [4337]E(f334(f334(f45(x43371,f935(x43372,a922)),x43373),f334(f334(f8(f935(x43374,a922),f935(x43372,a922),x43371),f318(x43372,x43374,x43375)),x43376)),f334(f318(x43372,x43374,x43375),f334(f334(f45(x43371,f935(x43374,a922)),x43373),x43376))) % 188.18/188.25 [4338]E(f334(f334(f44(x43381,f935(x43382,a922)),x43383),f334(f334(f8(f935(x43384,a922),f935(x43382,a922),x43381),f292(x43384,x43382,x43385)),x43386)),f334(f292(x43384,x43382,x43385),f334(f334(f44(x43381,f935(x43384,a922)),x43383),x43386))) % 188.18/188.25 [4418]E(f334(f149(x44181,x44182,f334(f7(x44182,x44181,x44181),x44183),x44184),f334(f175(x44182),f334(f334(f158(x44182),x44185),x44186))),f334(f334(x44183,x44185),f334(f149(x44181,x44182,f334(f7(x44182,x44181,x44181),x44183),x44184),f334(f175(x44182),x44186)))) % 188.18/188.25 [4482]E(f334(f334(f18(f934(x44821,x44822),x44822,x44823),f334(f334(f8(x44824,f935(x44822,x44823),f934(x44821,x44822)),x44825),f334(f334(f8(x44821,x44824,f934(x44821,x44822)),x44826),f259(x44821,x44822)))),f264(x44821,x44822)),f334(f265(x44821,x44822,x44823),f334(f334(f8(x44824,f935(x44822,x44823),x44821),x44825),x44826))) % 188.18/188.25 [4488]E(f334(f149(x44881,x44882,f334(f7(x44882,x44881,x44881),x44883),f334(f149(x44881,x44882,f334(f7(x44882,x44881,x44881),x44883),x44884),f334(f175(x44882),x44885))),f334(f175(x44882),x44886)),f334(f149(x44881,x44882,f334(f7(x44882,x44881,x44881),x44883),x44884),f334(f175(x44882),f334(f334(f141(x44882),x44886),x44885)))) % 188.18/188.25 [4490]E(f334(f334(f161(f934(x44901,x44902),f934(x44903,x44902)),f334(f265(x44901,x44902,f934(x44903,x44902)),f334(f334(f8(x44903,f935(x44902,f934(x44903,x44902)),x44901),f260(x44903,x44902)),x44904))),f334(f334(f188(x44901,x44902),x44905),x44906)),f334(f334(f188(x44903,x44902),f334(f334(f161(x44901,x44903),x44904),x44905)),x44906)) % 188.18/188.25 [4538]P107(f334(f334(f242(f935(x45381,a922)),f334(f292(x45382,x45381,x45383),f334(f334(f45(x45384,f935(x45382,a922)),x45385),x45386))),f334(f334(f45(x45384,f935(x45381,a922)),x45385),f334(f334(f8(f935(x45382,a922),f935(x45381,a922),x45384),f292(x45382,x45381,x45383)),x45386)))) % 188.18/188.25 [4347]E(f334(f334(f188(x43471,x43472),f334(f334(f166(x43471,x43473),x43474),f334(f259(x43471,x43472),x43475))),f334(f334(f166(x43472,x43476),x43474),f334(f264(x43471,x43472),x43475))),f334(f334(f166(f934(x43471,x43472),f334(f334(f188(x43471,x43472),x43473),x43476)),x43474),x43475)) % 188.18/188.25 [4401]E(f334(f334(f108(f935(f934(x44011,x44012),a922)),f334(f334(f295(x44011,x44013,x44012),x44014),x44015)),f334(f334(f295(x44011,x44013,x44012),x44014),x44016)),f334(f334(f295(x44011,x44013,x44012),x44014),f334(f334(f108(f935(f934(x44013,x44012),a922)),x44015),x44016))) % 188.18/188.25 [4502]E(f334(f334(f316(f934(x45021,x45022)),f334(f334(f260(x45021,x45022),x45023),x45024)),f334(f334(f108(f935(f934(x45021,x45022),a922)),f334(f334(f262(x45021,x45022),x45025),f334(f16(f935(x45022,a922),x45021),f334(f334(f316(x45022),x45024),x45026)))),f334(f334(f262(x45021,x45022),f334(f334(f316(x45021),x45023),x45025)),f334(f16(f935(x45022,a922),x45021),x45026)))),f334(f334(f262(x45021,x45022),f334(f334(f316(x45021),x45023),x45025)),f334(f16(f935(x45022,a922),x45021),f334(f334(f316(x45022),x45024),x45026)))) % 188.18/188.25 [4580]E(f334(f334(f109(f935(x45801,a922)),f334(f318(x45801,x45802,f334(f78(f934(x45802,x45803),x45802,x45801,f259(x45802,x45803)),x45804)),x45805)),f334(f318(x45801,x45803,f334(f78(f934(x45802,x45803),x45803,x45801,f264(x45802,x45803)),x45804)),x45806)),f334(f318(x45801,f934(x45802,x45803),x45804),f334(f334(f262(x45802,x45803),x45805),f334(f16(f935(x45803,a922),x45802),x45806)))) % 188.18/188.25 [4424]E(f334(f334(f108(f935(f934(x44241,x44242),a922)),f334(f334(f295(x44241,x44243,x44242),x44244),x44245)),f334(f334(f295(x44241,x44243,x44242),x44246),x44245)),f334(f334(f295(x44241,x44243,x44242),f334(f334(f108(f935(f934(x44241,x44243),a922)),x44244),x44246)),x44245)) % 188.18/188.25 [4560]E(f334(f334(f44(x45601,f935(x45602,a922)),x45603),f334(f334(f7(x45601,f935(x45604,f935(x45602,a922)),f935(x45602,a922)),f334(f334(f8(f935(x45604,a922),f935(f935(x45604,f935(x45602,a922)),f935(x45602,a922)),x45601),f44(x45604,f935(x45602,a922))),x45605)),x45606)),f334(f334(f44(x45604,f935(x45602,a922)),f334(f334(f44(x45601,f935(x45604,a922)),x45603),x45605)),x45606)) % 188.18/188.25 [4561]E(f334(f334(f45(x45611,f935(x45612,a922)),x45613),f334(f334(f7(x45611,f935(x45614,f935(x45612,a922)),f935(x45612,a922)),f334(f334(f8(f935(x45614,a922),f935(f935(x45614,f935(x45612,a922)),f935(x45612,a922)),x45611),f45(x45614,f935(x45612,a922))),x45615)),x45616)),f334(f334(f45(x45614,f935(x45612,a922)),f334(f334(f44(x45611,f935(x45614,a922)),x45613),x45615)),x45616)) % 188.18/188.25 [4617]E(f334(f265(x46171,x46172,f934(x46173,x46174)),f334(f334(f7(x46171,f935(x46172,x46174),f935(x46172,f934(x46173,x46174))),f334(f334(f8(f935(x46174,f934(x46173,x46174)),f935(f935(x46172,x46174),f935(x46172,f934(x46173,x46174))),x46171),f8(x46174,f934(x46173,x46174),x46172)),f334(f334(f8(x46173,f935(x46174,f934(x46173,x46174)),x46171),f260(x46173,x46174)),x46175))),x46176)),f266(x46171,x46173,x46172,x46174,x46175,x46176)) % 188.18/188.25 [4646]E(f334(f317(x46461,x46462,f334(f334(f18(x46461,x46462,x46462),f334(f334(f18(x46461,x46462,f935(x46462,x46462)),f334(f334(f8(a922,f935(x46462,f935(x46462,x46462)),x46461),f103(x46462)),x46463)),x46464)),x46465)),x46466),f334(f334(f108(f935(x46462,a922)),f334(f317(x46461,x46462,x46464),f334(f334(f109(f935(x46461,a922)),x46466),f334(f270(x46461),x46463)))),f334(f317(x46461,x46462,x46465),f334(f334(f109(f935(x46461,a922)),x46466),f334(f270(x46461),f334(f334(f8(a922,a922,x46461),a329),x46463)))))) % 188.18/188.25 [4660]E(f334(f317(x46601,f934(x46602,x46603),f334(f334(f18(x46601,x46603,f934(x46602,x46603)),f334(f334(f8(x46602,f935(x46603,f934(x46602,x46603)),x46601),f260(x46602,x46603)),x46604)),x46605)),x46606),f334(f334(f262(x46602,x46603),f334(f317(x46601,x46602,x46604),x46606)),f334(f334(f8(f935(x46601,a922),f935(x46603,a922),x46602),f317(x46601,x46603,x46605)),f334(f334(f7(x46602,f935(x46601,a922),f935(x46601,a922)),f334(f334(f8(f935(x46601,a922),f935(f935(x46601,a922),f935(x46601,a922)),x46602),f109(f935(x46601,a922))),f334(f334(f8(f935(x46602,a922),f935(x46601,a922),x46602),f318(x46601,x46602,x46604)),f334(f334(f7(x46602,f935(x46602,a922),f935(x46602,a922)),f316(x46602)),f195(f935(x46602,a922)))))),x46606)))) % 188.18/188.25 [4690]E(f254(x46901,x46902,x46903,x46904,x46905,x46906),f334(x46904,f334(f270(x46901),f334(f334(f8(f935(f935(x46903,x46901),a922),a922,x46901),f92(f935(x46903,x46901))),f334(f334(f8(f935(f935(x46903,x46901),a922),f935(f935(x46903,x46901),a922),x46901),f334(f18(f935(x46903,x46901),a922,a922),f334(f334(f8(a922,f935(a922,a922),f935(x46903,x46901)),a332),f334(f334(f7(f935(x46903,x46901),f935(f935(x46903,x46901),a922),a922),f336(f935(x46903,x46901))),x46905)))),f334(f334(f7(x46901,f935(f935(x46903,x46901),x46901),f935(f935(x46903,x46901),a922)),f334(f334(f8(f935(x46901,a922),f935(f935(f935(x46903,x46901),x46901),f935(f935(x46903,x46901),a922)),x46901),f8(x46901,a922,f935(x46903,x46901))),a331)),f334(f334(f7(f935(x46903,x46901),x46903,x46901),f5(f935(x46903,x46901))),x46906))))))) % 188.18/188.25 [4465]E(f334(f78(x44651,x44652,x44653,x44654),f80(x44653,x44651,x44655,x44656,x44657)),f80(x44653,x44652,f334(f78(x44651,x44652,x44653,x44654),x44655),x44656,f334(x44654,x44657))) % 188.18/188.25 [4602]E(f334(f264(x46021,x46022),f334(f266(x46023,x46021,x46024,x46022,x46025,x46026),x46027)),f334(x46026,f334(f264(x46023,x46024),x46027))) % 188.18/188.25 [4603]E(f334(f259(x46031,x46032),f334(f266(x46033,x46031,x46034,x46032,x46035,x46036),x46037)),f334(x46035,f334(f259(x46033,x46034),x46037))) % 188.18/188.25 [4310]E(f334(f334(f188(x43101,x43102),f334(f334(f166(x43101,x43103),x43104),x43105)),f334(f334(f166(x43102,x43106),x43104),x43107)),f334(f334(f166(f934(x43101,x43102),f334(f334(f188(x43101,x43102),x43103),x43106)),x43104),f334(f334(f260(x43101,x43102),x43105),x43107))) % 188.18/188.25 [4375]E(f334(f334(f334(f267(x43751,x43752,x43753,x43754),x43755),x43756),x43757),f334(f334(f265(x43752,x43753,x43754),x43756),f334(x43755,x43757))) % 188.18/188.25 [4385]E(f334(f334(f334(f267(x43851,x43852,x43853,x43854),x43855),x43856),x43857),f334(f334(x43856,f334(f259(x43852,x43853),f334(x43855,x43857))),f334(f264(x43852,x43853),f334(x43855,x43857)))) % 188.18/188.25 [4439]E(f334(f78(x44391,x44392,x44393,x44394),f334(f78(x44395,x44391,x44393,x44396),x44397)),f334(f78(x44395,x44392,x44393,f334(f78(x44391,x44392,x44395,x44394),x44396)),x44397)) % 188.18/188.25 [4621]E(f334(f266(x46211,x46212,x46213,x46213,x46214,f32(x46213)),f334(f266(x46211,x46211,x46215,x46213,f32(x46211),x46216),x46217)),f334(f334(f260(x46212,x46213),f334(x46214,f334(f259(x46211,x46215),x46217))),f334(x46216,f334(f264(x46211,x46215),x46217)))) % 188.18/188.25 [4622]E(f334(f266(x46221,x46221,x46222,x46223,f32(x46221),x46224),f334(f266(x46225,x46221,x46222,x46222,x46226,f32(x46222)),x46227)),f334(f334(f260(x46221,x46223),f334(x46226,f334(f259(x46225,x46222),x46227))),f334(x46224,f334(f264(x46225,x46222),x46227)))) % 188.18/188.25 [4644]E(f334(f266(x46441,x46442,x46443,x46443,x46444,f32(x46443)),f334(f266(x46445,x46441,x46443,x46443,x46446,f32(x46443)),x46447)),f334(f266(x46445,x46442,x46443,x46443,f334(f78(x46441,x46442,x46445,x46444),x46446),f32(x46443)),x46447)) % 188.18/188.25 [4645]E(f334(f266(x46451,x46451,x46452,x46453,f32(x46451),x46454),f334(f266(x46451,x46451,x46455,x46452,f32(x46451),x46456),x46457)),f334(f266(x46451,x46451,x46455,x46453,f32(x46451),f334(f78(x46452,x46453,x46455,x46454),x46456)),x46457)) % 188.18/188.25 [4657]E(f334(f266(x46571,x46572,x46573,x46573,x46574,f32(x46573)),f334(f266(x46571,x46571,x46575,x46573,f32(x46571),x46576),x46577)),f334(f266(x46572,x46572,x46575,x46573,f32(x46572),x46576),f334(f266(x46571,x46572,x46575,x46575,x46574,f32(x46575)),x46577))) % 188.18/188.25 [4344]E(f334(f334(f295(x43441,x43442,x43443),f334(f334(f295(x43441,x43444,x43442),x43445),x43446)),x43447),f334(f334(f295(x43441,x43444,x43443),x43445),f334(f334(f295(x43444,x43442,x43443),x43446),x43447))) % 188.18/188.25 [4407]E(f334(f334(f265(x44071,x44072,x44073),f334(f78(x44074,f935(x44072,x44073),x44071,x44075),x44076)),x44077),f334(f334(x44075,f334(x44076,f334(f259(x44071,x44072),x44077))),f334(f264(x44071,x44072),x44077))) % 188.18/188.25 [4493]E(f334(f149(x44931,x44932,f334(f7(x44932,x44931,x44931),x44933),x44934),f334(f175(x44932),f334(f334(f161(x44935,x44932),x44936),x44937))),f334(f149(x44931,x44935,f334(f7(x44935,x44931,x44931),f334(f78(x44932,f935(x44931,x44931),x44935,x44933),x44936)),x44934),f334(f175(x44935),x44937))) % 188.18/188.25 [4440]E(f334(f334(f44(x44401,f935(f934(x44402,x44403),a922)),x44404),f334(f334(f8(f935(f934(x44405,x44403),a922),f935(f934(x44402,x44403),a922),x44401),f334(f295(x44402,x44405,x44403),x44406)),x44407)),f334(f334(f295(x44402,x44405,x44403),x44406),f334(f334(f44(x44401,f935(f934(x44405,x44403),a922)),x44404),x44407))) % 188.18/188.25 [4585]E(f334(f334(f44(x45851,f935(f934(x45852,x45853),a922)),x45854),f334(f334(f7(x45851,f935(f934(x45855,x45853),a922),f935(f934(x45852,x45853),a922)),f334(f334(f8(f935(f934(x45852,x45855),a922),f935(f935(f934(x45855,x45853),a922),f935(f934(x45852,x45853),a922)),x45851),f295(x45852,x45855,x45853)),x45856)),x45857)),f334(f334(f295(x45852,x45855,x45853),f334(f334(f44(x45851,f935(f934(x45852,x45855),a922)),x45854),x45856)),x45857)) % 188.18/188.25 [4586]E(f334(f149(x45861,x45862,f334(f334(f7(x45861,f935(x45862,x45863),f935(x45862,x45861)),f334(f334(f8(f935(x45863,x45861),f935(f935(x45862,x45863),f935(x45862,x45861)),x45861),f8(x45863,x45861,x45862)),x45864)),x45865),x45866),x45867),f334(f149(x45861,x45863,x45864,x45866),f334(f334(f161(x45862,x45863),x45865),x45867))) % 188.18/188.25 [4658]E(f334(f334(f45(x46581,f935(x46582,a922)),x46583),f334(f334(f8(f935(x46584,f935(x46582,a922)),f935(x46582,a922),x46581),f334(f45(x46584,f935(x46582,a922)),x46585)),f334(f334(f7(x46581,f935(x46584,f935(x46582,a922)),f935(x46584,f935(x46582,a922))),f334(f334(f8(f935(f935(x46582,a922),f935(x46582,a922)),f935(f935(x46584,f935(x46582,a922)),f935(x46584,f935(x46582,a922))),x46581),f8(f935(x46582,a922),f935(x46582,a922),x46584)),f334(f334(f8(f935(x46582,a922),f935(f935(x46582,a922),f935(x46582,a922)),x46581),f108(f935(x46582,a922))),x46586))),x46587))),f334(f334(f108(f935(x46582,a922)),f334(f334(f45(x46581,f935(x46582,a922)),x46583),x46586)),f334(f334(f45(x46584,f935(x46582,a922)),x46585),x46587))) % 188.18/188.25 [4659]E(f334(f334(f44(x46591,f935(x46592,a922)),x46593),f334(f334(f8(f935(x46594,f935(x46592,a922)),f935(x46592,a922),x46591),f334(f44(x46594,f935(x46592,a922)),x46595)),f334(f334(f7(x46591,f935(x46594,f935(x46592,a922)),f935(x46594,f935(x46592,a922))),f334(f334(f8(f935(f935(x46592,a922),f935(x46592,a922)),f935(f935(x46594,f935(x46592,a922)),f935(x46594,f935(x46592,a922))),x46591),f8(f935(x46592,a922),f935(x46592,a922),x46594)),f334(f334(f8(f935(x46592,a922),f935(f935(x46592,a922),f935(x46592,a922)),x46591),f109(f935(x46592,a922))),x46596))),x46597))),f334(f334(f109(f935(x46592,a922)),f334(f334(f44(x46591,f935(x46592,a922)),x46593),x46596)),f334(f334(f44(x46594,f935(x46592,a922)),x46595),x46597))) % 188.18/188.25 [4649]E(f206(x46491,x46492,f334(f334(f334(x46493,x46494),x46495),x46496),f334(f334(f7(x46491,f934(a106,a106),f935(a106,f929(x46492))),f334(f334(f7(x46491,a106,f935(f934(a106,a106),f935(a106,f929(x46492)))),f334(f334(f7(x46491,a106,f935(a106,f935(f934(a106,a106),f935(a106,f929(x46492))))),x46497),x46494)),x46495)),x46496)),f334(f334(f334(f218(x46491,x46492,x46493,x46497),x46494),x46495),x46496)) % 188.18/188.25 [4661]E(f207(x46611,x46612,f334(f334(f334(x46613,x46614),x46615),x46616),f334(f334(f7(x46611,f934(a106,a106),f935(a106,f929(x46612))),f334(f334(f7(x46611,a106,f935(f934(a106,a106),f935(a106,f929(x46612)))),f334(f334(f7(x46611,a106,f935(a106,f935(f934(a106,a106),f935(a106,f929(x46612))))),x46617),x46614)),x46615)),x46616)),f220(x46611,x46612,x46613,x46617,x46614,x46615,x46616)) % 188.18/188.25 [4656]E(f202(x46561,x46562,f334(f334(f334(x46563,x46564),x46565),x46566),f334(f334(f7(x46561,f934(a106,a106),f935(a106,f929(f931(x46562)))),f334(f334(f7(x46561,a106,f935(f934(a106,a106),f935(a106,f929(f931(x46562))))),f334(f334(f7(x46561,a106,f935(a106,f935(f934(a106,a106),f935(a106,f929(f931(x46562)))))),x46567),x46564)),x46565)),x46566)),f334(f334(f334(f214(x46561,x46562,x46563,x46567),x46564),x46565),x46566)) % 188.18/188.25 [4671]E(f205(x46711,x46712,f334(f334(f334(x46713,x46714),x46715),x46716),f334(f334(f7(x46711,f934(a106,a106),f935(a106,f929(f931(x46712)))),f334(f334(f7(x46711,a106,f935(f934(a106,a106),f935(a106,f929(f931(x46712))))),f334(f334(f7(x46711,a106,f935(a106,f935(f934(a106,a106),f935(a106,f929(f931(x46712)))))),x46717),x46714)),x46715)),x46716)),f216(x46711,x46712,x46713,x46717,x46714,x46715,x46716)) % 188.18/188.25 [4552]E(f334(f266(x45521,x45522,x45523,x45524,x45525,x45526),f334(f334(f260(x45521,x45523),x45527),x45528)),f334(f334(f260(x45522,x45524),f334(x45525,x45527)),f334(x45526,x45528))) % 188.18/188.25 [4673]E(f334(f334(f161(f934(x46731,x46732),f934(x46733,x46734)),f334(f265(x46731,x46732,f934(x46733,x46734)),f334(f334(f7(x46731,f935(x46732,x46734),f935(x46732,f934(x46733,x46734))),f334(f334(f8(f935(x46734,f934(x46733,x46734)),f935(f935(x46732,x46734),f935(x46732,f934(x46733,x46734))),x46731),f8(x46734,f934(x46733,x46734),x46732)),f334(f334(f8(x46733,f935(x46734,f934(x46733,x46734)),x46731),f260(x46733,x46734)),x46735))),x46736))),f334(f334(f188(x46731,x46732),x46737),x46738)),f334(f334(f188(x46733,x46734),f334(f334(f161(x46731,x46733),x46735),x46737)),f334(f334(f161(x46732,x46734),x46736),x46738))) % 188.18/188.25 [4680]E(f334(f334(f161(f934(x46801,x46802),x46803),f334(f265(x46801,x46802,x46803),f334(f334(f8(f935(x46802,f934(x46801,x46804)),f935(x46802,x46803),x46801),f334(f8(f934(x46801,x46804),x46803,x46802),x46805)),f334(f334(f7(x46801,f935(x46802,x46804),f935(x46802,f934(x46801,x46804))),f334(f334(f8(f935(x46804,f934(x46801,x46804)),f935(f935(x46802,x46804),f935(x46802,f934(x46801,x46804))),x46801),f8(x46804,f934(x46801,x46804),x46802)),f260(x46801,x46804))),x46806)))),f334(f334(f188(x46801,x46802),x46807),x46808)),f334(f334(f161(f934(x46801,x46804),x46803),x46805),f334(f334(f188(x46801,x46804),x46807),f334(f334(f161(x46802,x46804),x46806),x46808)))) % 188.18/188.25 [4594]E(f334(f334(f161(f934(x45941,x45942),x45943),f334(f265(x45941,x45942,x45943),f334(f334(f8(f935(x45942,f934(x45944,x45942)),f935(x45942,x45943),x45941),f334(f8(f934(x45944,x45942),x45943,x45942),x45945)),f334(f334(f8(x45944,f935(x45942,f934(x45944,x45942)),x45941),f260(x45944,x45942)),x45946)))),f334(f334(f188(x45941,x45942),x45947),x45948)),f334(f334(f161(f934(x45944,x45942),x45943),x45945),f334(f334(f188(x45944,x45942),f334(f334(f161(x45941,x45944),x45946),x45947)),x45948))) % 188.18/188.25 [4543]E(f334(f334(f265(x45431,x45432,x45433),f334(f334(f8(f935(x45432,f934(x45434,x45435)),f935(x45432,x45433),x45431),f334(f8(f934(x45434,x45435),x45433,x45432),f334(f265(x45434,x45435,x45433),x45436))),x45437)),x45438),f334(f334(f265(x45434,x45435,x45433),x45436),f334(f334(f265(x45431,x45432,f934(x45434,x45435)),x45437),x45438))) % 188.18/188.25 [4681]E(f334(f334(f44(f934(x46811,x46812),f935(f934(x46813,x46814),a922)),f334(f334(f262(x46811,x46812),x46815),f334(f16(f935(x46812,a922),x46811),x46816))),f334(f265(x46811,x46812,f935(f934(x46813,x46814),a922)),f334(f334(f7(x46811,f935(x46812,f935(x46813,f935(x46814,a922))),f935(x46812,f935(f934(x46813,x46814),a922))),f334(f334(f8(f935(f935(x46813,f935(x46814,a922)),f935(f934(x46813,x46814),a922)),f935(f935(x46812,f935(x46813,f935(x46814,a922))),f935(x46812,f935(f934(x46813,x46814),a922))),x46811),f8(f935(x46813,f935(x46814,a922)),f935(f934(x46813,x46814),a922),x46812)),f334(f334(f8(f935(x46813,a922),f935(f935(x46813,f935(x46814,a922)),f935(f934(x46813,x46814),a922)),x46811),f262(x46813,x46814)),x46817))),f334(f334(f8(f935(x46814,a922),f935(x46813,f935(x46814,a922)),x46812),f16(f935(x46814,a922),x46813)),x46818)))),f334(f334(f262(x46813,x46814),f334(f334(f44(x46811,f935(x46813,a922)),x46815),x46817)),f334(f16(f935(x46814,a922),x46813),f334(f334(f44(x46812,f935(x46814,a922)),x46816),x46818)))) % 188.18/188.25 [4608]E(f334(f334(f267(x46081,x46082,x46083,x46084),f334(f334(f267(x46081,x46085,x46086,f934(x46082,x46083)),x46087),x46088)),x46089),f334(f334(f267(x46081,x46085,x46086,x46084),x46087),f334(f334(f7(x46085,f935(x46082,f935(x46083,x46084)),f935(x46086,x46084)),f334(f334(f8(f935(x46086,f934(x46082,x46083)),f935(f935(x46082,f935(x46083,x46084)),f935(x46086,x46084)),x46085),f267(x46086,x46082,x46083,x46084)),x46088)),x46089))) % 188.18/188.25 [4641]E(f334(f78(f934(x46411,x46412),f934(x46413,x46414),f934(x46415,x46416),f266(x46411,x46413,x46412,x46414,x46417,x46418)),f266(x46415,x46411,x46416,x46412,x46419,x464110)),f266(x46415,x46413,x46416,x46414,f334(f78(x46411,x46413,x46415,x46417),x46419),f334(f78(x46412,x46414,x46416,x46418),x464110))) % 188.18/188.25 [4647]E(f334(f266(x46471,x46472,x46473,x46474,x46475,x46476),f334(f266(x46477,x46471,x46478,x46473,x46479,x464710),x464711)),f334(f266(x46477,x46472,x46478,x46474,f334(f78(x46471,x46472,x46477,x46475),x46479),f334(f78(x46473,x46474,x46478,x46476),x464710)),x464711)) % 188.18/188.25 [4815]~P4(x48151)+P4(f931(x48151)) % 188.18/188.25 [4816]~P64(x48161)+P64(f931(x48161)) % 188.18/188.25 [4817]~P105(x48171)+P105(f928(x48171)) % 188.18/188.25 [4820]~P146(x48201)+~E(f84(x48201),f2(x48201)) % 188.18/188.25 [4822]~E(x48221,f2(a106))+E(f334(a22,x48221),f2(a1)) % 188.18/188.25 [4823]~E(x48231,f2(a1))+E(f88(a1,x48231),f2(a1)) % 188.18/188.25 [4829]~P147(x48291)+P30(x48291,f2(x48291)) % 188.18/188.25 [4831]~P109(x48311)+P15(x48311,f120(x48311)) % 188.18/188.25 [4840]P107(x48401)+P107(f334(a329,x48401)) % 188.18/188.25 [4894]~P147(x48941)+~P30(x48941,f84(x48941)) % 188.18/188.25 [4935]~P107(x49351)+~P107(f334(a329,x49351)) % 188.18/188.25 [4956]E(f334(a112,x49561),f2(a927))+~P107(f334(a200,x49561)) % 188.18/188.25 [5022]~P96(x50221)+P16(x50221,x50221,f87(x50221)) % 188.18/188.25 [5023]~P109(x50231)+P16(x50231,x50231,f246(x50231)) % 188.18/188.25 [5024]~P109(x50241)+P16(x50241,x50241,f241(x50241)) % 188.18/188.25 [5025]~P98(x50251)+P16(x50251,x50251,f108(x50251)) % 188.18/188.25 [5026]~P104(x50261)+P16(x50261,x50261,f109(x50261)) % 188.18/188.25 [5027]~P70(x50271)+P18(x50271,x50271,f87(x50271)) % 188.18/188.25 [4826]~E(x48261,f2(a927))+E(f334(f107(a1),x48261),f2(a1)) % 188.18/188.25 [4833]~P95(x48331)+E(f334(f111(x48331),a89),f2(x48331)) % 188.18/188.25 [4836]~E(f580(x48361),f2(a927))+E(f334(f172(a927),x48361),f2(a927)) % 188.18/188.25 [4837]~P110(x48371)+E(f244(x48371,f242(x48371)),f246(x48371)) % 188.18/188.25 [4838]~P110(x48381)+E(f245(x48381,f242(x48381)),f241(x48381)) % 188.18/188.25 [4839]~P89(x48391)+E(f88(x48391,f2(x48391)),f2(x48391)) % 188.18/188.25 [4848]~P147(x48481)+E(f334(f107(x48481),f84(a927)),f84(x48481)) % 188.18/188.25 [4849]~P147(x48491)+E(f334(f107(x48491),f2(a927)),f2(x48491)) % 188.18/188.25 [4850]~P142(x48501)+E(f334(f110(x48501),f84(a1)),f84(x48501)) % 188.18/188.25 [4851]~P142(x48511)+E(f334(f110(x48511),f2(a1)),f2(x48511)) % 188.18/188.25 [4852]E(x48521,f2(a927))+~E(f334(f107(a1),x48521),f2(a1)) % 188.18/188.25 [4888]~P91(x48881)+E(f334(f85(x48881),f195(x48881)),f250(x48881)) % 188.18/188.25 [4889]~P91(x48891)+E(f334(f85(x48891),f250(x48891)),f195(x48891)) % 188.18/188.25 [4890]~P69(x48901)+E(f334(f85(x48901),f2(x48901)),f2(x48901)) % 188.18/188.25 [4891]~P124(x48911)+E(f334(f81(x48911),f84(x48911)),f84(x48911)) % 188.18/188.25 [4892]~P86(x48921)+E(f334(f81(x48921),f2(x48921)),f2(x48921)) % 188.18/188.25 [4893]~P82(x48931)+E(f334(f172(x48931),f120(x48931)),f2(x48931)) % 188.18/188.25 [4911]~P38(x49111)+P42(f334(f179(a1),x49111)) % 188.18/188.25 [4940]~P95(x49401)+E(f334(f85(x49401),f84(x49401)),f334(f111(x49401),a104)) % 188.18/188.25 [4955]~P95(x49551)+P30(x49551,f334(f111(x49551),a89)) % 188.18/188.25 [4981]P38(x49811)+~P42(f334(f179(a1),x49811)) % 188.18/188.25 [5029]E(f334(f107(a1),f334(a112,x50291)),x50291)+P107(f334(a200,x50291)) % 188.18/188.25 [5097]~P116(x50971)+E(f253(x50971,f84(x50971),f87(x50971)),f252(x50971)) % 188.18/188.25 [5130]~P95(x51301)+~P30(x51301,f334(f111(x51301),a104)) % 188.18/188.25 [5277]E(f334(f81(a1),x52771),x52771)+P107(f334(f334(f243(a1),x52771),f2(a1))) % 188.18/188.25 [5295]~E(f334(a112,x52951),f2(a927))+P107(f334(f334(f242(a1),x52951),f2(a1))) % 188.18/188.25 [5359]~P107(f334(a200,x53591))+P107(f334(f334(f243(a1),x53591),f2(a1))) % 188.18/188.25 [5399]~P142(x53991)+P107(f334(f334(f336(x53991),f84(x53991)),f117(x53991))) % 188.18/188.25 [5400]~P147(x54001)+P107(f334(f334(f336(x54001),f84(x54001)),f193(x54001))) % 188.18/188.25 [5401]~P142(x54011)+P107(f334(f334(f336(x54011),f2(x54011)),f117(x54011))) % 188.18/188.25 [5402]~P147(x54021)+P107(f334(f334(f336(x54021),f2(x54021)),f193(x54021))) % 188.18/188.25 [5403]~P127(x54031)+P107(f334(f334(f242(x54031),f2(x54031)),f84(x54031))) % 188.18/188.25 [5404]~P127(x54041)+P107(f334(f334(f243(x54041),f2(x54041)),f84(x54041))) % 188.18/188.25 [5456]E(x54561,f2(a927))+~P107(f334(f334(f242(a927),x54561),f2(a927))) % 188.18/188.25 [5500]E(f334(a112,x55001),f2(a927))+~P107(f334(f334(f242(a1),x55001),f2(a1))) % 188.18/188.25 [5561]P107(f334(a200,x55611))+~P107(f334(f334(f243(a1),x55611),f2(a1))) % 188.18/188.25 [5568]~P109(x55681)+P18(x55681,f928(x55681),f155(x55681,x55681,f5(x55681))) % 188.18/188.25 [5586]P42(x55861)+~P107(f334(f334(f242(a1),f2(a1)),f832(x55861))) % 188.18/188.25 [5591]E(f334(f81(a1),x55911),f334(f85(a1),x55911))+~P107(f334(f334(f243(a1),x55911),f2(a1))) % 188.18/188.25 [5759]~P127(x57591)+~P107(f334(f334(f242(x57591),f84(x57591)),f2(x57591))) % 188.18/188.25 [5760]~P127(x57601)+~P107(f334(f334(f243(x57601),f84(x57601)),f2(x57601))) % 188.18/188.25 [5774]~E(x57741,f2(a927))+P107(f334(f334(f242(a1),f334(f107(a1),x57741)),f2(a1))) % 188.18/188.25 [5775]~E(x57751,f2(a1))+P107(f334(f334(f243(a1),f334(f81(a1),x57751)),f84(a1))) % 188.18/188.25 [5904]~P82(x59041)+E(f149(x59041,x59041,f86(x59041),f2(x59041)),f172(x59041)) % 188.18/188.25 [6080]~P97(x60801)+P27(a927,x60801,f107(x60801),f250(f935(a927,a922))) % 188.18/188.25 [6281]E(x62811,f2(a927))+~P107(f334(f334(f242(a1),f334(f107(a1),x62811)),f2(a1))) % 188.18/188.25 [6282]E(x62821,f2(a1))+~P107(f334(f334(f243(a1),f334(f81(a1),x62821)),f84(a1))) % 188.18/188.25 [8140]E(x81401,f334(a3,f2(a927)))+P107(f334(f334(f243(a927),f334(f334(f23(a927),f334(a20,x81401)),f334(a119,f2(a927)))),f334(a20,x81401))) % 188.18/188.25 [8983]~P107(f334(f334(f243(a1),x89831),f2(a1)))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x89831)),x89831)),f2(a1))) % 188.18/188.25 [9366]P107(f334(f334(f243(a1),x93661),f2(a1)))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93661)),x93661)),f2(a1))) % 188.18/188.25 [9823]~P107(f334(f334(f243(a1),x98231),f2(a1)))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98231)),x98231)),a104)),f2(a1))) % 188.18/188.25 [9992]P107(f334(f334(f243(a1),x99921),f2(a1)))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99921)),x99921)),a104)),f2(a1))) % 188.18/188.25 [4941]E(x49411,f2(a1))+E(f334(f334(f41(a1),x49411),x49411),f84(a1)) % 188.18/188.25 [5087]~P7(x50871)+E(f43(x50871,f195(f935(x50871,a922))),f250(x50871)) % 188.18/188.25 [5088]~P7(x50881)+E(f43(x50881,f250(f935(x50881,a922))),f195(x50881)) % 188.18/188.25 [5089]~P7(x50891)+E(f42(x50891,f195(f935(x50891,a922))),f195(x50891)) % 188.18/188.25 [5090]~P7(x50901)+E(f42(x50901,f250(f935(x50901,a922))),f250(x50901)) % 188.18/188.25 [5091]~P109(x50911)+E(f146(x50911,f195(f935(x50911,a922))),f120(x50911)) % 188.18/188.25 [5233]E(x52331,f2(a927))+P107(f334(f334(f243(a927),f2(a927)),x52331)) % 188.18/188.25 [5252]~P8(x52521)+P107(f334(f334(f242(a1),f2(a1)),x52521)) % 188.18/188.25 [5286]~E(f334(f111(a927),x52861),f2(a927))+P107(f334(f334(f242(a1),x52861),a89)) % 188.18/188.25 [5291]P42(x52911)+P107(f334(f334(f336(a1),f832(x52911)),x52911)) % 188.18/188.25 [5292]E(x52921,f334(a3,f2(a927)))+P107(f334(f334(f242(a106),f84(a106)),x52921)) % 188.18/188.25 [5332]P107(f334(a200,x53321))+P107(f334(f334(f242(a1),f2(a1)),x53321)) % 188.18/188.25 [5381]E(f334(f107(a1),f334(a112,x53811)),f2(a1))+P107(f334(f334(f242(a1),f2(a1)),x53811)) % 188.18/188.25 [5438]E(f334(f107(a1),f334(f111(a927),x54381)),f334(f111(a1),x54381))+P107(f334(a200,f334(f111(a1),x54381))) % 188.18/188.25 [5462]E(f334(f111(a927),x54621),f2(a927))+~P107(f334(a200,f334(f111(a1),x54621))) % 188.18/188.25 [5463]E(f334(f111(a927),x54631),f2(a927))+~P107(f334(f334(f242(a1),x54631),a89)) % 188.18/188.25 [5497]P8(x54971)+~P107(f334(f334(f242(a1),f2(a1)),x54971)) % 188.18/188.25 [5571]E(f334(a119,f834(x55711)),x55711)+~P107(f334(f334(f243(a927),f2(a927)),x55711)) % 188.18/188.25 [5580]E(f334(a119,f334(f111(a927),x55801)),f84(a927))+~P107(f334(a200,f334(f111(a1),x55801))) % 188.18/188.25 [5587]E(f334(f107(a1),f374(x55871)),x55871)+~P107(f334(f334(f243(a1),f2(a1)),x55871)) % 188.18/188.25 [5594]~E(x55941,f334(a3,f2(a927)))+~P107(f334(f334(f242(a106),f84(a106)),x55941)) % 188.18/188.25 [5601]E(f334(f107(a1),f334(f111(a927),x56011)),f2(a1))+~P107(f334(a200,f334(f111(a1),x56011))) % 188.18/188.25 [5626]E(f334(f172(a927),x56261),f2(a927))+P107(f334(f334(f336(a927),f580(x56261)),f334(f179(a927),x56261))) % 188.18/188.25 [5646]E(f334(f107(a1),f334(a112,x56461)),x56461)+~P107(f334(f334(f242(a1),f2(a1)),x56461)) % 188.18/188.25 [5654]~P107(f334(a200,x56541))+~P107(f334(f334(f242(a1),f2(a1)),x56541)) % 188.18/188.25 [5752]E(f334(f334(f86(a927),f84(a927)),f334(f111(a927),x57521)),f84(a927))+~P107(f334(f334(f243(a1),x57521),a89)) % 188.18/188.25 [5819]E(x58191,f2(a927))+~P107(f334(f334(f243(a927),x58191),f334(a119,f2(a927)))) % 188.18/188.25 [5863]E(f334(f334(f23(a927),f334(f111(a927),x58631)),f84(a927)),f2(a927))+~P107(f334(f334(f242(a1),x58631),a89)) % 188.18/188.25 [5864]E(f334(f334(f86(a927),f334(f111(a927),x58641)),f84(a927)),f84(a927))+~P107(f334(f334(f243(a1),x58641),a89)) % 188.18/188.25 [5876]~P42(x58761)+E(f334(f40(a927),f334(f317(a1,a927,a112),x58761)),f334(f40(a1),x58761)) % 188.18/188.25 [5905]~P109(x59051)+E(f245(x59051,f334(f7(x59051,x59051,a922),f242(x59051))),f246(x59051)) % 188.18/188.25 [5906]~P109(x59061)+E(f244(x59061,f334(f7(x59061,x59061,a922),f242(x59061))),f241(x59061)) % 188.18/188.25 [5916]E(f50(a927,f334(a119,f2(a927)),f334(f111(a927),x59161)),f334(a119,f2(a927)))+~P107(f334(a200,f334(f111(a1),x59161))) % 188.18/188.25 [5925]~P107(f334(f334(f243(a1),f2(a1)),x59251))+P107(f334(f334(f242(a1),f84(a1)),x59251)) % 188.18/188.25 [5926]P107(f334(f334(f243(a1),f2(a1)),x59261))+~P107(f334(f334(f242(a1),f84(a1)),x59261)) % 188.18/188.25 [5939]E(f334(a119,f334(f334(f23(a927),x59391),f84(a927))),x59391)+~P107(f334(f334(f243(a927),f2(a927)),x59391)) % 188.18/188.25 [5995]P107(f334(f334(f243(a927),f2(a927)),f374(x59951)))+~P107(f334(f334(f243(a1),f2(a1)),x59951)) % 188.18/188.25 [6056]E(f50(a1,f334(f111(a1),a104),x60561),f334(f334(f23(a1),x60561),f84(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x60561)) % 188.18/188.25 [6095]~P107(f334(f334(f243(a1),a89),x60951))+P107(f334(f334(f243(a927),f2(a927)),f334(f111(a927),x60951))) % 188.18/188.25 [6100]E(f334(a20,f824(x61001)),x61001)+~P107(f334(f334(f336(a927),x61001),f250(f935(a927,a922)))) % 188.18/188.25 [6150]P107(f334(f334(f243(a927),f2(a927)),f334(a112,x61501)))+~P107(f334(f334(f243(a1),f2(a1)),x61501)) % 188.18/188.25 [6198]~P107(f334(f334(f243(a927),f2(a927)),x61981))+P107(f334(f334(f243(a1),f2(a1)),f334(f107(a1),x61981))) % 188.18/188.25 [6234]~P107(f334(f334(f243(a927),f2(a927)),f334(a112,x62341)))+P107(f334(f334(f243(a1),f2(a1)),x62341)) % 188.18/188.25 [6248]~P42(x62481)+E(f334(f317(a927,a1,f107(a1)),f334(f317(a1,a927,a112),x62481)),x62481) % 188.18/188.25 [6262]P107(f334(f334(f243(a1),a89),x62621))+~P107(f334(f334(f243(a927),f2(a927)),f334(f111(a927),x62621))) % 188.18/188.25 [6317]P107(f334(f334(f243(a927),f2(a927)),x63171))+~P107(f334(f334(f243(a1),f2(a1)),f334(f107(a1),x63171))) % 188.18/188.25 [6428]E(f334(f317(a927,a1,f107(a1)),f334(f307(a927),f334(a112,x64281))),f334(f310(a1,f2(a1)),x64281))+~P107(f334(f334(f242(a1),f2(a1)),x64281)) % 188.18/188.25 [6444]~P127(x64441)+P107(f334(f334(f243(x64441),f2(x64441)),f334(f334(f86(x64441),f84(x64441)),f84(x64441)))) % 188.18/188.25 [6494]P107(f334(f334(f243(a927),f334(a119,f2(a927))),f334(a112,x64941)))+~P107(f334(f334(f243(a1),f84(a1)),x64941)) % 188.18/188.25 [6589]E(x65891,f2(a1))+P107(f334(f54(f2(a1),x65891),f334(f334(f260(a1,a1),f2(a1)),f2(a1)))) % 188.18/188.25 [6761]~P107(f334(f334(f243(a927),f334(a119,f2(a927))),f334(a112,x67611)))+P107(f334(f334(f243(a1),f84(a1)),x67611)) % 188.18/188.25 [7173]~P117(x71731)+P39(x71731,f334(f270(f934(x71731,x71731)),f334(f265(x71731,x71731,a922),f243(x71731)))) % 188.18/188.25 [5806]E(f334(f111(a927),f334(f334(f23(a1),x58061),a104)),f334(a119,f334(f111(a927),x58061)))+P107(f334(a200,f334(f111(a1),x58061))) % 188.18/188.25 [5822]~P38(x58221)+E(f334(f334(f161(a927,a1),f107(a1)),f334(f334(f161(a1,a927),a112),x58221)),x58221) % 188.18/188.25 [5945]E(f334(f85(a1),f334(f107(a1),f334(a119,f387(x59451)))),x59451)+~P107(f334(f334(f243(a1),x59451),f2(a1))) % 188.18/188.25 [5955]E(f334(f334(f86(a927),f84(a927)),f334(f111(a927),x59551)),f334(f111(a927),f334(f334(f23(a1),x59551),a104)))+P107(f334(f334(f243(a1),x59551),a89)) % 188.18/188.25 [5997]E(f334(f334(f41(a1),f334(f111(a1),a104)),x59971),f334(f111(a1),a104))+~P107(f334(f334(f243(a1),f2(a1)),x59971)) % 188.18/188.25 [6089]E(f334(f334(f23(a927),f334(f111(a927),x60891)),f84(a927)),f334(f111(a927),f334(f334(f86(a1),x60891),a104)))+P107(f334(f334(f242(a1),x60891),a89)) % 188.18/188.25 [6090]E(f334(f334(f86(a927),f334(f111(a927),x60901)),f84(a927)),f334(f111(a927),f334(f334(f23(a1),x60901),a104)))+P107(f334(f334(f243(a1),x60901),a89)) % 188.18/188.25 [6137]E(f334(a112,f334(f334(f86(a1),f84(a1)),x61371)),f334(a119,f334(a112,x61371)))+~P107(f334(f334(f242(a1),f2(a1)),x61371)) % 188.18/188.25 [6171]E(f334(a119,f334(f334(f23(a927),x61711),f334(a119,f2(a927)))),x61711)+~P107(f334(f334(f243(a927),f2(a927)),x61711)) % 188.18/188.25 [6381]E(f50(a927,f334(a119,f2(a927)),f334(f111(a927),x63811)),f334(a112,f50(a1,f84(a1),f334(f111(a1),x63811))))+P107(f334(a200,f334(f111(a1),x63811))) % 188.18/188.25 [6602]~P107(f334(f66(x66021),f250(f935(x66021,a922))))+P107(f334(f66(f931(x66021)),f250(f935(f931(x66021),a922)))) % 188.18/188.25 [6692]~P107(f334(f334(f242(a1),f2(a1)),x66921))+P107(f334(f334(f243(a1),f2(a1)),f334(f334(f86(a1),f84(a1)),x66921))) % 188.18/188.25 [6699]E(f334(f259(a1,a1),f52(f84(a1),f334(f111(a1),x66991))),f334(f334(f41(a1),f84(a1)),f334(f111(a1),x66991)))+~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x66991))) % 188.18/188.25 [6719]E(f334(f264(a1,a1),f52(f84(a1),f334(f111(a1),x67191))),f50(a1,f84(a1),f334(f111(a1),x67191)))+~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x67191))) % 188.18/188.25 [6731]P107(f334(f66(x67311),f250(f935(x67311,a922))))+~P107(f334(f66(f931(x67311)),f250(f935(f931(x67311),a922)))) % 188.18/188.25 [7067]~P107(f334(f66(x70671),f250(f935(x70671,a922))))+P107(f334(f334(f243(a927),f2(a927)),f334(f40(x70671),f250(f935(x70671,a922))))) % 188.18/188.25 [7640]P107(f334(f66(a927),x76401))+~P107(f334(f66(a1),f334(f317(a927,a1,f107(a1)),x76401))) % 188.18/188.25 [5839]~E(a104,x58391)+E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x58391)),x58391),a104) % 188.18/188.25 [5840]~E(x58401,a104)+E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x58401)),x58401),a104) % 188.18/188.25 [6392]E(x63921,a104)+~E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x63921)),x63921),a104) % 188.18/188.25 [6393]E(a104,x63931)+~E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x63931)),x63931),a104) % 188.18/188.25 [6658]~E(f334(f111(a927),x66581),f2(a927))+P107(f334(a200,f334(f111(a1),f334(f334(f86(a1),x66581),a104)))) % 188.18/188.25 [7317]E(f334(f111(a927),x73171),f2(a927))+~P107(f334(a200,f334(f111(a1),f334(f334(f86(a1),x73171),a104)))) % 188.18/188.25 [7912]E(f334(a115,f570(x79121)),x79121)+~P107(f334(f334(f336(f935(f934(a927,a927),a922)),x79121),a105)) % 188.18/188.25 [6775]~P95(x67751)+E(f334(f111(x67751),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f84(x67751)) % 188.18/188.25 [7191]~P107(f334(a200,f334(f111(a1),x71911)))+E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x71911)),x71911)),f2(a927)) % 188.18/188.25 [8090]~P107(f334(f334(f243(a1),f334(f111(a1),x80901)),f2(a1)))+E(f334(f259(a1,a1),f334(a56,f55(f334(f85(a1),f84(a1)),f334(f85(a1),f334(f111(a1),x80901))))),f334(f334(f41(a1),f84(a1)),f334(f111(a1),x80901))) % 188.18/188.25 [8099]~P107(f334(f334(f243(a1),f334(f111(a1),x80991)),f2(a1)))+E(f334(f264(a1,a1),f334(a56,f55(f334(f85(a1),f84(a1)),f334(f85(a1),f334(f111(a1),x80991))))),f50(a1,f84(a1),f334(f111(a1),x80991))) % 188.18/188.25 [8276]~P107(f334(f334(f242(a1),a89),x82761))+P107(f334(f334(f242(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x82761)),x82761))) % 188.18/188.25 [8277]~P107(f334(f334(f242(a1),a104),x82771))+P107(f334(f334(f242(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x82771)),x82771))) % 188.18/188.25 [8278]~P107(f334(f334(f242(a1),a89),x82781))+P107(f334(f334(f243(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x82781)),x82781))) % 188.18/188.25 [8279]~P107(f334(f334(f243(a1),a104),x82791))+P107(f334(f334(f243(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x82791)),x82791))) % 188.18/188.25 [8607]~P95(x86071)+~P30(x86071,f334(f111(x86071),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))) % 188.18/188.25 [8725]P107(f334(f334(f242(a1),a89),x87251))+~P107(f334(f334(f242(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x87251)),x87251))) % 188.18/188.25 [8726]P107(f334(f334(f242(a1),a89),x87261))+~P107(f334(f334(f243(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x87261)),x87261))) % 188.18/188.25 [8727]P107(f334(f334(f242(a1),a104),x87271))+~P107(f334(f334(f242(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x87271)),x87271))) % 188.18/188.25 [8728]P107(f334(f334(f243(a1),a104),x87281))+~P107(f334(f334(f243(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x87281)),x87281))) % 188.18/188.25 [8954]E(f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x89541)),x89541)),f334(f334(f94(a927,a927),f334(f111(a927),x89541)),f334(f334(f8(a927,a927,a927),a119),f334(f334(f18(a927,a927,a927),f86(a927)),f5(a927)))))+P107(f334(a200,f334(f111(a1),x89541))) % 188.18/188.25 [9796]E(x97961,f195(f935(f934(a927,a927),a922)))+P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x97961),f195(f935(f934(a927,a927),a922)))),a74)) % 188.18/188.25 [8001]~E(a89,x80011)+E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x80011)),x80011)),a104),a89) % 188.18/188.25 [8002]~E(x80021,a89)+E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x80021)),x80021)),a104),a89) % 188.18/188.25 [8622]E(x86221,a89)+~E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x86221)),x86221)),a104),a89) % 188.18/188.25 [8623]E(a89,x86231)+~E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x86231)),x86231)),a104),a89) % 188.18/188.25 [8969]~P107(f334(a200,f334(f111(a1),x89691)))+P107(f334(a200,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x89691)),x89691)))) % 188.18/188.25 [8970]~P107(f334(f334(f243(a1),x89701),a89))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x89701)),x89701)),a89)) % 188.18/188.25 [8971]~P107(f334(f334(f242(a1),x89711),a104))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x89711)),x89711)),a104)) % 188.18/188.25 [8972]~P107(f334(f334(f243(a1),x89721),a89))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x89721)),x89721)),a89)) % 188.18/188.25 [8973]~P107(f334(f334(f243(a1),x89731),a104))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x89731)),x89731)),a104)) % 188.18/188.25 [9056]~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x90561)))+P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x90561)),x90561)))) % 188.18/188.25 [9358]P107(f334(a200,f334(f111(a1),x93581)))+~P107(f334(a200,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93581)),x93581)))) % 188.18/188.25 [9359]P107(f334(f334(f242(a1),x93591),a104))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93591)),x93591)),a104)) % 188.18/188.25 [9360]P107(f334(f334(f243(a1),x93601),a89))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93601)),x93601)),a89)) % 188.18/188.25 [9361]P107(f334(f334(f243(a1),x93611),a89))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93611)),x93611)),a89)) % 188.18/188.25 [9362]P107(f334(f334(f243(a1),x93621),a104))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93621)),x93621)),a104)) % 188.18/188.25 [9846]~P107(f334(f66(f934(a927,a927)),x98461))+P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),f195(f935(f934(a927,a927),a922))),x98461)),a75)) % 188.18/188.25 [9518]~P107(f334(f334(f242(a1),a89),x95181))+P107(f334(f334(f242(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95181)),x95181)),a104))) % 188.18/188.25 [9519]~P107(f334(f334(f243(a1),a104),x95191))+P107(f334(f334(f242(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95191)),x95191)),a104))) % 188.18/188.25 [9520]~P107(f334(f334(f243(a1),a89),x95201))+P107(f334(f334(f243(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95201)),x95201)),a104))) % 188.18/188.25 [9521]~P107(f334(f334(f243(a1),a104),x95211))+P107(f334(f334(f243(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95211)),x95211)),a104))) % 188.18/188.25 [9737]P107(f334(f334(f242(a1),a89),x97371))+~P107(f334(f334(f242(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97371)),x97371)),a104))) % 188.18/188.25 [9738]P107(f334(f334(f243(a1),a89),x97381))+~P107(f334(f334(f243(a1),a89),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97381)),x97381)),a104))) % 188.18/188.25 [9739]P107(f334(f334(f243(a1),a104),x97391))+~P107(f334(f334(f242(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97391)),x97391)),a104))) % 188.18/188.25 [9740]P107(f334(f334(f243(a1),a104),x97401))+~P107(f334(f334(f243(a1),a104),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97401)),x97401)),a104))) % 188.18/188.25 [9818]~P107(f334(a200,f334(f111(a1),x98181)))+P107(f334(a200,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98181)),x98181)),a104)))) % 188.18/188.25 [9819]~P107(f334(f334(f242(a1),x98191),a89))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98191)),x98191)),a104)),a89)) % 188.18/188.25 [9820]~P107(f334(f334(f242(a1),x98201),a104))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98201)),x98201)),a104)),a104)) % 188.18/188.25 [9821]~P107(f334(f334(f243(a1),x98211),a89))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98211)),x98211)),a104)),a89)) % 188.18/188.25 [9822]~P107(f334(f334(f242(a1),x98221),a104))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98221)),x98221)),a104)),a104)) % 188.18/188.25 [9825]~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x98251)))+P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98251)),x98251)),a104)))) % 188.18/188.25 [9987]P107(f334(a200,f334(f111(a1),x99871)))+~P107(f334(a200,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99871)),x99871)),a104)))) % 188.18/188.25 [9988]P107(f334(f334(f242(a1),x99881),a89))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99881)),x99881)),a104)),a89)) % 188.18/188.25 [9989]P107(f334(f334(f242(a1),x99891),a104))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99891)),x99891)),a104)),a104)) % 188.18/188.25 [9990]P107(f334(f334(f242(a1),x99901),a104))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99901)),x99901)),a104)),a104)) % 188.18/188.25 [9991]P107(f334(f334(f243(a1),x99911),a89))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99911)),x99911)),a104)),a89)) % 188.18/188.25 [10090]~P95(x100901)+E(f334(f334(f86(x100901),f84(x100901)),f84(x100901)),f334(f111(x100901),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))) % 188.18/188.25 [10162]~P147(x101621)+E(f334(f334(f252(x101621),f84(x101621)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f84(x101621)) % 188.18/188.25 [10163]~P147(x101631)+E(f334(f334(f252(x101631),f2(x101631)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f2(x101631)) % 188.18/188.25 [10303]~P107(f334(f334(f243(a927),f84(a927)),x103031))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f41(a927),x103031),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.25 [10307]~P107(f334(f334(f243(a927),f2(a927)),x103071))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f41(a927),f334(f334(f86(a927),x103071),f84(a927))),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.25 [10331]~E(f50(a927,x103311,f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f84(a927))+P107(f334(f334(f243(a927),f2(a927)),f50(a927,x103311,f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.25 [10361]E(f50(a927,x103611,f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f84(a927))+~P107(f334(f334(f243(a927),f2(a927)),f50(a927,x103611,f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.25 [4857]~P9(x48571,x48572)+P45(x48571,x48572) % 188.18/188.25 [4858]~P39(x48581,x48582)+P61(x48581,x48582) % 188.18/188.25 [4859]~P46(x48591,x48592)+P61(x48591,x48592) % 188.18/188.25 [4861]~P9(x48611,x48612)+P52(x48611,x48612) % 188.18/188.25 [4863]~P17(x48631,x48632)+P52(x48631,x48632) % 188.18/188.25 [4865]~P9(x48651,x48652)+P53(x48651,x48652) % 188.18/188.25 [4867]~P17(x48671,x48672)+P53(x48671,x48672) % 188.18/188.25 [4868]~P9(x48681,x48682)+P17(x48681,x48682) % 188.18/188.25 [4813]E(x48131,x48132)+~E(f33(x48131),f33(x48132)) % 188.18/188.25 [4814]E(x48141,x48142)+~E(f34(x48141),f34(x48142)) % 188.18/188.25 [4818]~E(x48181,x48182)+E(f277(x48181,x48182),f84(a106)) % 188.18/188.25 [4821]E(f225(x48211,x48212),x48211)+~E(x48212,f2(a927)) % 188.18/188.25 [4828]~E(x48282,f120(x48281))+E(f159(x48281,x48282),f120(x48281)) % 188.18/188.25 [4847]~E(f159(x48472,x48471),f120(x48472))+E(x48471,f120(x48472)) % 188.18/188.25 [4872]~P1(x48722)+P1(f935(x48721,x48722)) % 188.18/188.25 [4873]~P2(x48732)+P2(f935(x48731,x48732)) % 188.18/188.25 [4874]~P108(x48742)+P108(f935(x48741,x48742)) % 188.18/188.25 [4875]~P110(x48752)+P110(f935(x48751,x48752)) % 188.18/188.25 [4876]~P111(x48762)+P111(f935(x48761,x48762)) % 188.18/188.25 [4877]~P112(x48772)+P112(f935(x48771,x48772)) % 188.18/188.25 [4878]~P83(x48782)+P83(f935(x48781,x48782)) % 188.18/188.25 [4879]~P91(x48792)+P91(f935(x48791,x48792)) % 188.18/188.25 [4880]~P99(x48802)+P98(f935(x48801,x48802)) % 188.18/188.25 [4881]~P99(x48812)+P99(f935(x48811,x48812)) % 188.18/188.25 [4882]~P102(x48822)+P100(f935(x48821,x48822)) % 188.18/188.25 [4883]~P102(x48832)+P101(f935(x48831,x48832)) % 188.18/188.25 [4884]~P103(x48842)+P103(f935(x48841,x48842)) % 188.18/188.25 [4885]~P7(x48852)+P7(f935(x48851,x48852)) % 188.18/188.25 [4886]~P99(x48862)+P104(f935(x48861,x48862)) % 188.18/188.25 [4887]~P102(x48872)+P102(f935(x48871,x48872)) % 188.18/188.25 [4900]E(x49001,x49002)+~E(f334(a119,x49001),f334(a119,x49002)) % 188.18/188.25 [4901]E(x49011,x49012)+~E(f334(a115,x49011),f334(a115,x49012)) % 188.18/188.25 [4902]E(x49021,x49022)+~E(f334(a3,x49021),f334(a3,x49022)) % 188.18/188.25 [4904]E(x49041,x49042)+~E(f334(a20,x49041),f334(a20,x49042)) % 188.18/188.25 [4957]P41(x49571,x49572)+~E(f719(x49572,x49571),f720(x49572,x49571)) % 188.18/188.25 [4987]~P61(x49871,x49872)+P41(x49871,f314(x49871,x49872)) % 188.18/188.25 [4988]~P54(x49881,x49882)+P54(x49881,f314(x49881,x49882)) % 188.18/188.25 [5001]~P5(x50011)+E(f50(x50011,x50012,x50012),f2(x50011)) % 188.18/188.25 [5028]~P119(x50281)+P59(x50281,x50282,f2(x50281)) % 188.18/188.25 [5036]~P39(x50361,x50362)+P39(f928(x50361),f153(x50361,x50362)) % 188.18/188.25 [5037]~P39(x50371,x50372)+P39(f928(x50371),f152(x50371,x50372)) % 188.18/188.25 [5038]~P40(x50381,x50382)+P40(f928(x50381),f154(x50381,x50382)) % 188.18/188.25 [5039]~P40(x50391,x50392)+P40(f928(x50391),f165(x50391,x50392)) % 188.18/188.25 [5040]~P54(x50401,x50402)+P54(f928(x50401),f165(x50401,x50402)) % 188.18/188.25 [5135]~P39(x51351,x51352)+P39(f935(x51351,a922),f327(x51351,x51352)) % 188.18/188.25 [5136]~P39(x51361,x51362)+P39(f935(x51361,a922),f325(x51361,x51362)) % 188.18/188.25 [5261]~P8(x52611)+P42(f311(a1,x52611,x52612)) % 188.18/188.25 [5362]~P39(x53621,x53622)+P63(x53621,f72(x53621,x53621,x53622)) % 188.18/188.25 [5870]~P79(x58701)+P27(x58701,x58701,f85(x58701),x58702) % 188.18/188.25 [4842]~E(x48422,f120(x48421))+E(f334(f174(x48421),x48422),f120(x48421)) % 188.18/188.25 [4843]~E(x48432,f120(x48431))+E(f334(f175(x48431),x48432),f120(x48431)) % 188.18/188.25 [4906]E(x49061,f334(a112,x49062))+~E(f334(f107(a1),x49061),x49062) % 188.18/188.25 [4909]E(x49091,f120(x49092))+~E(f334(f174(x49092),x49091),f120(x49092)) % 188.18/188.25 [4910]E(x49101,f120(x49102))+~E(f334(f175(x49102),x49101),f120(x49102)) % 188.18/188.25 [4928]~P95(x49281)+E(f334(f111(x49281),x49282),f334(f110(x49281),x49282)) % 188.18/188.25 [4934]~P4(x49341)+P107(f334(f66(x49341),x49342)) % 188.18/188.25 [4942]~E(f679(x49422,x49421),f120(x49421))+E(f186(x49421,x49422),f120(f928(x49421))) % 188.18/188.25 [4951]~E(x49512,f120(x49511))+E(f334(f179(x49511),x49512),f195(f935(x49511,a922))) % 188.18/188.25 [4952]~E(x49522,f120(x49521))+E(f195(f935(x49521,a922)),f334(f179(x49521),x49522)) % 188.18/188.25 [4954]E(x49541,x49542)+~E(f334(f107(a1),x49541),f334(f107(a1),x49542)) % 188.18/188.25 [4958]E(f223(x49581,x49582),f2(a927))+P107(f334(f66(x49581),x49582)) % 188.18/188.25 [4976]~P124(x49761)+E(f88(x49761,f88(x49761,x49762)),f88(x49761,x49762)) % 188.18/188.25 [4990]~P81(x49901)+E(f334(f334(f252(x49901),x49902),f84(a927)),x49902) % 188.18/188.25 [4991]~P119(x49911)+E(f334(f334(f252(x49911),x49912),f84(a927)),x49912) % 188.18/188.25 [4992]~P54(x49921,x49922)+E(f334(f293(x49921,x49921),x49922),x49922) % 188.18/188.25 [4996]E(x49961,x49962)+E(f277(x49961,x49962),f334(f334(f86(a106),x49962),f84(a106))) % 188.18/188.25 [4999]E(f334(f40(x49991),x49992),f2(a927))+P107(f334(f66(x49991),x49992)) % 188.18/188.25 [5002]~E(f159(x50021,x50022),x50022)+P107(f334(f144(x50021),x50022)) % 188.18/188.25 [5005]~P69(x50051)+E(f334(f334(f23(x50051),x50052),f2(x50051)),x50052) % 188.18/188.25 [5006]~P81(x50061)+E(f334(f334(f87(x50061),x50062),f84(x50061)),x50062) % 188.18/188.25 [5007]~P72(x50071)+E(f334(f334(f87(x50071),x50072),f84(x50071)),x50072) % 188.18/188.25 [5008]~P119(x50081)+E(f334(f334(f87(x50081),x50082),f84(x50081)),x50082) % 188.18/188.25 [5009]~P119(x50091)+E(f334(f334(f86(x50091),x50092),f2(x50091)),x50092) % 188.18/188.25 [5010]~P76(x50101)+E(f334(f334(f86(x50101),x50102),f2(x50101)),x50102) % 188.18/188.25 [5011]~P82(x50111)+E(f334(f334(f86(x50111),x50112),f2(x50111)),x50112) % 188.18/188.25 [5012]~P5(x50121)+E(f334(f334(f41(x50121),x50122),f84(x50121)),x50122) % 188.18/188.25 [5013]~P122(x50131)+E(f334(f334(f296(x50131),x50132),f84(x50131)),x50132) % 188.18/188.25 [5014]~P101(x50141)+E(f334(f334(f108(x50141),x50142),f195(x50141)),x50142) % 188.18/188.25 [5015]~P100(x50151)+E(f334(f334(f109(x50151),x50152),f250(x50151)),x50152) % 188.18/188.25 [5016]~P119(x50161)+E(f334(f334(f252(x50161),x50162),f2(a927)),f84(x50161)) % 188.18/188.25 [5017]~P116(x50171)+E(f334(f334(f252(x50171),x50172),f2(a927)),f84(x50171)) % 188.18/188.25 [5018]~E(x50182,f195(f935(x50181,a922)))+E(f334(f40(x50181),x50182),f2(a927)) % 188.18/188.25 [5030]~P5(x50301)+E(f50(x50301,x50302,f2(x50301)),x50302) % 188.18/188.25 [5041]~P119(x50411)+E(f334(f334(f87(x50411),x50412),f2(x50411)),f2(x50411)) % 188.18/188.25 [5042]~P134(x50421)+E(f334(f334(f87(x50421),x50422),f2(x50421)),f2(x50421)) % 188.18/188.25 [5043]~P5(x50431)+E(f334(f334(f41(x50431),x50432),f2(x50431)),f2(x50431)) % 188.18/188.25 [5044]~P123(x50441)+E(f334(f334(f296(x50441),x50442),f2(x50441)),f2(x50441)) % 188.18/188.25 [5045]~P100(x50451)+E(f334(f334(f108(x50451),x50452),f250(x50451)),f250(x50451)) % 188.18/188.25 [5046]~P101(x50461)+E(f334(f334(f109(x50461),x50462),f195(x50461)),f195(x50461)) % 188.18/188.25 [5048]~P5(x50481)+E(f50(x50481,x50482,f84(x50481)),f2(x50481)) % 188.18/188.25 [5049]~P5(x50491)+E(f50(x50491,f2(x50491),x50492),f2(x50491)) % 188.18/188.25 [5076]E(x50761,f2(a927))+E(f60(x50762,x50761,f120(x50762)),f120(f928(x50762))) % 188.18/188.25 [5099]P54(x50991,x50992)+~E(f334(f293(x50991,x50991),x50992),x50992) % 188.18/188.25 [5100]P39(x51001,x51002)+~E(f581(x51002,x51001),f195(f935(x51001,a922))) % 188.18/188.25 [5101]E(x51011,f120(x51012))+~E(f334(f179(x51012),x51011),f195(f935(x51012,a922))) % 188.18/188.25 [5102]E(x51021,f120(x51022))+~E(f195(f935(x51022,a922)),f334(f179(x51022),x51021)) % 188.18/188.25 [5105]~E(x51051,x51052)+P107(f334(f334(a331,x51051),x51052)) % 188.18/188.25 [5115]P107(x51151)+P107(f334(f334(a337,x51151),x51152)) % 188.18/188.25 [5116]E(x51161,f120(x51162))+E(f334(f334(f171(x51162),x51161),f2(a927)),f334(f148(x51162),x51161)) % 188.18/188.25 [5119]E(f159(x51191,x51192),x51192)+~P107(f334(f144(x51191),x51192)) % 188.18/188.25 [5126]~P107(x51262)+P107(f334(f334(a337,x51261),x51262)) % 188.18/188.25 [5127]~P107(x51272)+P107(f334(f334(a333,x51271),x51272)) % 188.18/188.25 [5128]~P107(x51281)+P107(f334(f334(a333,x51281),x51282)) % 188.18/188.25 [5138]~E(f680(x51382,x51381),f685(x51382,x51381))+P107(f334(f144(x51381),x51382)) % 188.18/188.25 [5145]E(f334(f270(x51451),x51452),f195(f935(x51451,a922)))+P107(f334(x51452,f340(x51452))) % 188.18/188.25 [5146]E(f195(f935(x51461,a922)),f334(f270(x51461),x51462))+P107(f334(x51462,f341(x51462))) % 188.18/188.25 [5215]~P124(x52151)+E(f334(f334(f87(x52151),x52152),f88(x52151,x52152)),f334(f81(x52151),x52152)) % 188.18/188.25 [5226]~E(x52261,f2(a1))+E(f51(x52261,x52262),f334(f334(f260(a1,a1),f2(a1)),f2(a1))) % 188.18/188.25 [5257]~P61(x52571,x52572)+P61(x52571,f334(f293(x52571,x52571),x52572)) % 188.18/188.25 [5258]~P40(x52581,x52582)+P40(x52581,f334(f293(x52581,x52581),x52582)) % 188.18/188.25 [5259]~P41(x52591,x52592)+P41(x52591,f334(f293(x52591,x52591),x52592)) % 188.18/188.25 [5260]~P54(x52601,x52602)+P54(x52601,f334(f293(x52601,x52601),x52602)) % 188.18/188.25 [5282]E(x52821,x52822)+~P107(f334(f334(a331,x52821),x52822)) % 188.18/188.25 [5293]P107(x52931)+~P107(f334(f334(a332,x52932),x52931)) % 188.18/188.25 [5294]P107(x52941)+~P107(f334(f334(a332,x52941),x52942)) % 188.18/188.25 [5299]~P112(x52991)+P107(f334(f334(f242(x52991),x52992),f250(x52991))) % 188.18/188.25 [5303]E(x53031,x53032)+~E(f334(x53031,f373(x53032,x53031)),f334(x53032,f373(x53032,x53031))) % 188.18/188.25 [5334]E(x53341,f2(a927))+E(f225(x53341,f50(a927,x53342,x53341)),f225(x53342,x53341)) % 188.18/188.25 [5339]~P109(x53391)+P15(x53391,f334(f334(f158(x53391),x53392),f120(x53391))) % 188.18/188.25 [5341]E(x53411,f2(a1))+P107(f334(f54(x53412,x53411),f51(x53412,x53411))) % 188.18/188.25 [5357]~P17(x53572,x53571)+P107(f334(f334(x53571,f817(x53571)),f817(x53571))) % 188.18/188.25 [5360]~E(x53601,x53602)+P107(f334(f334(f243(a927),x53601),f334(a119,x53602))) % 188.18/188.25 [5371]~E(x53711,f2(a927))+P107(f334(f334(f243(a927),x53711),f334(a119,x53712))) % 188.18/188.25 [5380]P107(f334(x53801,x53802))+P107(f334(f334(f242(a1),f2(a1)),f901(x53801))) % 188.18/188.25 [5443]P61(x54431,x54432)+~P61(x54431,f334(f293(x54431,x54431),x54432)) % 188.18/188.25 [5444]P40(x54441,x54442)+~P40(x54441,f334(f293(x54441,x54441),x54442)) % 188.18/188.25 [5445]P41(x54451,x54452)+~P41(x54451,f334(f293(x54451,x54451),x54452)) % 188.18/188.25 [5446]P54(x54461,x54462)+~P54(x54461,f334(f293(x54461,x54461),x54462)) % 188.18/188.25 [5449]~E(f50(a927,x54492,x54491),f2(a927))+E(f334(f334(f87(a927),x54491),f904(x54491,x54492)),x54492) % 188.18/188.25 [5450]~E(f50(a1,x54502,x54501),f2(a1))+E(f334(f334(f87(a1),x54501),f905(x54501,x54502)),x54502) % 188.18/188.25 [5478]~P107(f334(x54781,x54782))+P107(f334(f334(f242(a1),f2(a1)),f887(x54781))) % 188.18/188.25 [5489]E(f334(f334(f23(a927),f334(a112,x54891)),f334(a112,x54892)),f334(a112,x54891))+~P107(f334(a200,x54892)) % 188.18/188.25 [5518]E(f280(x55181,x55182),f84(a106))+~P107(f334(f334(f242(a106),x55181),f84(a106))) % 188.18/188.25 [5612]E(f334(f334(f171(x56121),x56122),f680(x56122,x56121)),f334(f334(f171(x56121),x56122),f685(x56122,x56121)))+P107(f334(f144(x56121),x56122)) % 188.18/188.25 [5655]~P107(f334(x56551,f96(x56552,x56551)))+P107(f334(x56551,f582(x56552,x56551))) % 188.18/188.25 [5719]P63(x57191,x57192)+~P107(f334(f322(x57191,x57192),f549(x57192,x57191))) % 188.18/188.25 [5867]~P17(x58672,x58671)+P107(f334(f334(x58671,f818(x58671,x58672)),f818(x58671,x58672))) % 188.18/188.25 [5868]~P17(x58682,x58681)+P107(f334(f334(x58681,f821(x58681,x58682)),f821(x58681,x58682))) % 188.18/188.25 [5877]~E(f334(a119,f50(a927,x58771,x58772)),x58772)+E(f50(a927,f334(a119,x58771),x58772),f2(a927)) % 188.18/188.25 [5934]P39(x59341,x59342)+P107(f334(f334(f336(x59341),f625(x59342,x59341)),f626(x59342,x59341))) % 188.18/188.25 [5941]~P95(x59411)+P107(f334(f334(f336(x59411),f334(f111(x59411),x59412)),f117(x59411))) % 188.18/188.25 [5942]~P142(x59421)+P107(f334(f334(f336(x59421),f334(f107(x59421),x59422)),f117(x59421))) % 188.18/188.25 [5943]~P147(x59431)+P107(f334(f334(f336(x59431),f334(f107(x59431),x59432)),f193(x59431))) % 188.18/188.25 [5944]~P142(x59441)+P107(f334(f334(f336(x59441),f334(f110(x59441),x59442)),f117(x59441))) % 188.18/188.25 [6078]~P40(x60781,x60782)+E(f334(f334(f295(x60781,x60781,x60781),x60782),f314(x60781,x60782)),x60782) % 188.18/188.25 [6094]E(f334(a119,f50(a927,x60941,x60942)),x60942)+E(f50(a927,f334(a119,x60941),x60942),f334(a119,f50(a927,x60941,x60942))) % 188.18/188.25 [6506]P39(x65061,x65062)+~P107(f334(f334(f336(x65061),f492(x65062,x65061)),f323(x65061,x65062))) % 188.18/188.25 [6542]~P127(x65421)+~P107(f334(f334(f243(x65421),f334(f107(x65421),x65422)),f2(x65421))) % 188.18/188.25 [6543]~P86(x65431)+~P107(f334(f334(f243(x65431),f334(f81(x65431),x65432)),f2(x65431))) % 188.18/188.25 [6632]P107(f334(f334(f243(a1),x66321),f50(a1,x66322,x66321)))+~P107(f334(f334(f243(a1),x66321),f2(a1))) % 188.18/188.25 [6733]E(f334(f334(f316(a927),f334(a119,x67331)),f311(a927,x67332,x67331)),f311(a927,x67332,f334(a119,x67331)))+~P107(f334(f334(f242(a927),x67332),f334(a119,x67331))) % 188.18/188.25 [6821]~P109(x68211)+P15(x68211,f157(x68211,x68211,f5(x68211),x68212)) % 188.18/188.25 [6948]E(f334(f174(x69481),x69482),x69482)+~P107(f334(f334(f242(a927),f334(f196(f928(x69481)),x69482)),f84(a927))) % 188.18/188.25 [6967]~P86(x69671)+P107(f334(f334(f242(x69671),f334(f85(x69671),f334(f81(x69671),x69672))),f2(x69671))) % 188.18/188.25 [7000]~P39(x70001,x70002)+P39(x70001,f334(f334(f295(x70001,x70001,x70001),x70002),f314(x70001,x70002))) % 188.18/188.25 [7001]~P54(x70011,x70012)+P54(x70011,f334(f334(f295(x70011,x70011,x70011),x70012),f314(x70011,x70012))) % 188.18/188.25 [7213]~P107(f334(f334(f243(a1),x72132),f2(a1)))+P107(f334(f334(f242(a1),f50(a1,x72131,x72132)),f2(a1))) % 188.18/188.25 [7599]~P147(x75991)+E(f197(x75991,f334(f334(f7(x75991,x75991,x75991),f86(x75991)),f84(x75991)),x75992,f2(x75991)),f334(f107(x75991),x75992)) % 188.18/188.25 [7626]~P128(x76261)+~P107(f334(f334(f243(x76261),f334(f334(f87(x76261),x76262),x76262)),f2(x76261))) % 188.18/188.25 [10399]~P124(x103991)+~P107(f334(f334(f243(x103991),f334(f334(f252(x103991),x103992),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f2(x103991))) % 188.18/188.25 [4907]~E(x49072,f120(x49071))+E(f334(f196(f928(x49071)),x49072),f2(a927)) % 188.18/188.25 [4943]~E(x49431,f2(a927))+E(f334(f334(f86(a927),x49431),x49432),x49432) % 188.18/188.25 [4944]~E(x49442,f2(a927))+E(f334(f334(f87(a927),x49441),x49442),f2(a927)) % 188.18/188.25 [4946]~E(x49461,f2(a927))+E(f334(f334(f87(a927),x49461),x49462),f2(a927)) % 188.18/188.25 [4947]~E(x49472,f2(a927))+E(f334(f334(f252(a927),x49471),x49472),f84(a927)) % 188.18/188.25 [4948]~E(x49482,f2(a1))+E(f334(f334(f41(a1),x49481),x49482),f2(a1)) % 188.18/188.25 [4959]E(x49591,f120(x49592))+~E(f334(f196(f928(x49592)),x49591),f2(a927)) % 188.18/188.25 [4961]~P96(x49611)+E(f334(f334(f87(x49611),x49612),x49612),x49612) % 188.18/188.25 [4963]~P109(x49631)+E(f334(f334(f246(x49631),x49632),x49632),x49632) % 188.18/188.25 [4965]~P109(x49651)+E(f334(f334(f241(x49651),x49652),x49652),x49652) % 188.18/188.25 [4967]~P98(x49671)+E(f334(f334(f108(x49671),x49672),x49672),x49672) % 188.18/188.25 [4968]~P99(x49681)+E(f334(f334(f108(x49681),x49682),x49682),x49682) % 188.18/188.25 [4969]~P99(x49691)+E(f334(f334(f109(x49691),x49692),x49692),x49692) % 188.18/188.25 [4971]~P104(x49711)+E(f334(f334(f109(x49711),x49712),x49712),x49712) % 188.18/188.25 [4989]~P69(x49891)+E(f334(f334(f23(x49891),x49892),x49892),f2(x49891)) % 188.18/188.25 [5003]~P69(x50031)+E(f334(f85(x50031),f334(f85(x50031),x50032)),x50032) % 188.18/188.25 [5004]~P91(x50041)+E(f334(f85(x50041),f334(f85(x50041),x50042)),x50042) % 188.18/188.25 [5021]~E(x50212,f2(a927))+E(f334(f334(f252(a927),x50211),x50212),f334(a119,f2(a927))) % 188.18/188.25 [5057]~P81(x50571)+E(f334(f334(f87(x50571),f84(x50571)),x50572),x50572) % 188.18/188.25 [5058]~P72(x50581)+E(f334(f334(f87(x50581),f84(x50581)),x50582),x50582) % 188.18/188.25 [5059]~P119(x50591)+E(f334(f334(f87(x50591),f84(x50591)),x50592),x50592) % 188.18/188.25 [5060]~P119(x50601)+E(f334(f334(f86(x50601),f2(x50601)),x50602),x50602) % 188.18/188.25 [5061]~P76(x50611)+E(f334(f334(f86(x50611),f2(x50611)),x50612),x50612) % 188.18/188.25 [5062]~P82(x50621)+E(f334(f334(f86(x50621),f2(x50621)),x50622),x50622) % 188.18/188.25 [5063]~P101(x50631)+E(f334(f334(f108(x50631),f195(x50631)),x50632),x50632) % 188.18/188.25 [5064]~P100(x50641)+E(f334(f334(f109(x50641),f250(x50641)),x50642),x50642) % 188.18/188.25 [5080]~P119(x50801)+E(f334(f334(f87(x50801),f2(x50801)),x50802),f2(x50801)) % 188.18/188.25 [5081]~P134(x50811)+E(f334(f334(f87(x50811),f2(x50811)),x50812),f2(x50811)) % 188.18/188.25 [5082]~P81(x50821)+E(f334(f334(f252(x50821),f84(x50821)),x50822),f84(x50821)) % 188.18/188.25 [5083]~P5(x50831)+E(f334(f334(f41(x50831),f2(x50831)),x50832),f2(x50831)) % 188.18/188.25 [5084]~P122(x50841)+E(f334(f334(f296(x50841),f2(x50841)),x50842),f2(x50841)) % 188.18/188.25 [5085]~P100(x50851)+E(f334(f334(f108(x50851),f250(x50851)),x50852),f250(x50851)) % 188.18/188.25 [5086]~P101(x50861)+E(f334(f334(f109(x50861),f195(x50861)),x50862),f195(x50861)) % 188.18/188.25 [5094]E(x50941,f120(x50942))+E(f151(x50942,f334(f175(x50942),x50941)),f334(f148(x50942),x50941)) % 188.18/188.25 [5095]E(x50951,f120(x50952))+E(f334(f148(x50952),f334(f175(x50952),x50951)),f151(x50952,x50951)) % 188.18/188.25 [5096]E(x50961,f2(a927))+~E(f334(f334(f86(a927),x50962),x50961),x50962) % 188.18/188.25 [5103]~P95(x51031)+E(f334(f110(x51031),f334(f111(a1),x51032)),f334(f111(x51031),x51032)) % 188.18/188.25 [5104]~P142(x51041)+E(f334(f110(x51041),f334(f107(a1),x51042)),f334(f107(x51041),x51042)) % 188.18/188.25 [5111]E(x51111,f84(a927))+~E(f334(f334(f87(a927),x51112),x51111),f84(a927)) % 188.18/188.25 [5112]E(x51121,f84(a927))+~E(f334(f334(f87(a927),x51121),x51122),f84(a927)) % 188.18/188.25 [5113]E(x51131,f2(a927))+~E(f334(f334(f86(a927),x51132),x51131),f2(a927)) % 188.18/188.25 [5114]E(x51141,f2(a927))+~E(f334(f334(f86(a927),x51141),x51142),f2(a927)) % 188.18/188.25 [5131]~P86(x51311)+E(f334(f81(x51311),f334(f85(x51311),x51312)),f334(f81(x51311),x51312)) % 188.18/188.25 [5132]~P124(x51321)+E(f334(f81(x51321),f334(f107(x51321),x51322)),f334(f107(x51321),x51322)) % 188.18/188.25 [5133]~P86(x51331)+E(f334(f81(x51331),f334(f81(x51331),x51332)),f334(f81(x51331),x51332)) % 188.18/188.25 [5134]~P76(x51341)+E(f334(f172(x51341),f334(f175(x51341),x51342)),f334(f172(x51341),x51342)) % 188.18/188.25 [5139]~E(x51391,f334(a119,f2(a927)))+E(f334(f334(f252(a927),x51391),x51392),f334(a119,f2(a927))) % 188.18/188.25 [5148]~P69(x51481)+E(f334(f334(f23(x51481),f2(x51481)),x51482),f334(f85(x51481),x51482)) % 188.18/188.25 [5149]~E(x51492,f2(a927))+E(f146(a927,f334(f310(a927,x51491),x51492)),f120(a927)) % 188.18/188.25 [5158]~P95(x51581)+E(f334(f334(f86(x51581),x51582),f334(f111(x51581),a89)),x51582) % 188.18/188.25 [5159]E(x51591,f2(a1))+E(f52(f334(f81(a1),x51592),f334(f81(a1),x51591)),f58(x51592,x51591)) % 188.18/188.25 [5175]~E(x51751,x51752)+P107(f334(f334(f242(a927),x51751),x51752)) % 188.18/188.25 [5182]~E(x51821,f2(a106))+E(f334(f334(f86(a927),f334(a20,x51821)),x51822),x51822) % 188.18/188.25 [5196]~P8(x51961)+P8(f334(f334(f252(a1),x51961),x51962)) % 188.18/188.25 [5197]~P69(x51971)+E(f334(f334(f86(x51971),x51972),f334(f85(x51971),x51972)),f2(x51971)) % 188.18/188.25 [5198]~P91(x51981)+E(f334(f334(f108(x51981),x51982),f334(f85(x51981),x51982)),f250(x51981)) % 188.18/188.25 [5199]~P91(x51991)+E(f334(f334(f109(x51991),x51992),f334(f85(x51991),x51992)),f195(x51991)) % 188.18/188.25 [5223]E(x52231,f2(a927))+~E(f334(f85(a1),f334(f107(a1),x52232)),f334(f107(a1),x52231)) % 188.18/188.25 [5224]E(x52241,f2(a927))+~E(f334(f85(a1),f334(f107(a1),x52241)),f334(f107(a1),x52242)) % 188.18/188.25 [5234]E(f201(x52341,x52342),f2(a1))+P107(f334(f334(f242(a1),x52342),x52341)) % 188.18/188.25 [5235]E(f185(x52351,x52352),f120(a1))+P107(f334(f334(f242(a1),x52351),x52352)) % 188.18/188.25 [5236]E(f249(x52361,x52362),f2(a106))+P107(f334(f334(f243(a106),x52361),x52362)) % 188.18/188.25 [5249]E(x52491,f334(a119,f2(a927)))+~E(f334(f334(f87(a927),x52492),x52491),f334(a119,f2(a927))) % 188.18/188.25 [5250]E(x52501,f334(a119,f2(a927)))+~E(f334(f334(f87(a927),x52501),x52502),f334(a119,f2(a927))) % 188.18/188.25 [5251]~P108(x52511)+P107(f334(f334(f242(x52511),x52512),x52512)) % 188.18/188.25 [5254]~P95(x52541)+E(f334(f334(f87(x52541),x52542),f334(f111(x52541),a104)),f334(f85(x52541),x52542)) % 188.18/188.25 [5274]~P95(x52741)+E(f334(f85(x52741),f334(f111(x52741),x52742)),f334(f111(x52741),f334(f85(a1),x52742))) % 188.18/188.25 [5275]~P142(x52751)+E(f334(f85(x52751),f334(f110(x52751),x52752)),f334(f110(x52751),f334(f85(a1),x52752))) % 188.18/188.25 [5304]~E(x53041,f334(a119,x53042))+P107(f334(f334(f243(a927),f2(a927)),x53041)) % 188.18/188.25 [5322]~P109(x53221)+E(f334(f85(f935(x53221,a922)),f334(f309(x53221),x53222)),f334(f308(x53221),x53222)) % 188.18/188.25 [5323]~P109(x53231)+E(f334(f85(f935(x53231,a922)),f334(f308(x53231),x53232)),f334(f309(x53231),x53232)) % 188.18/188.25 [5324]~P109(x53241)+E(f334(f85(f935(x53241,a922)),f334(f290(x53241),x53242)),f334(f307(x53241),x53242)) % 188.18/188.25 [5325]~P109(x53251)+E(f334(f85(f935(x53251,a922)),f334(f307(x53251),x53252)),f334(f290(x53251),x53252)) % 188.18/188.25 [5333]~E(f334(f107(a1),x53332),x53331)+P107(f334(f334(f242(a1),f2(a1)),x53331)) % 188.18/188.25 [5340]~E(x53402,f2(a1))+E(f58(x53401,x53402),f334(f334(f260(a1,a1),f2(a1)),f334(f81(a1),x53401))) % 188.18/188.25 [5342]~P1(x53421)+P107(f334(f334(f242(x53421),f195(x53421)),x53422)) % 188.18/188.25 [5379]~P107(f334(x53791,x53792))+P107(f334(x53791,f334(a112,f887(x53791)))) % 188.18/188.25 [5405]~P124(x54051)+E(f334(f334(f87(x54051),f88(x54051,x54052)),f334(f81(x54051),x54052)),x54052) % 188.18/188.25 [5412]~E(x54122,f2(a927))+E(f91(f934(a927,a927),f53(x54121,x54122)),f334(f334(f260(a927,a927),f2(a927)),x54121)) % 188.18/188.25 [5417]~E(x54171,x54172)+~P107(f334(f334(f243(a927),x54171),x54172)) % 188.18/188.25 [5418]~E(x54181,x54182)+~P107(f334(f334(f243(a1),x54181),x54182)) % 188.18/188.25 [5421]~P147(x54211)+E(f334(f334(f86(x54211),f84(x54211)),f334(f107(x54211),x54212)),f334(f107(x54211),f334(a119,x54212))) % 188.18/188.25 [5425]~E(x54251,f2(a927))+~P107(f334(f334(f243(a927),x54252),x54251)) % 188.18/188.25 [5439]E(f159(x54391,x54392),x54392)+~E(f334(f196(f928(x54391)),f159(x54391,x54392)),f334(f196(f928(x54391)),x54392)) % 188.18/188.25 [5440]E(f334(f40(x54401),f334(f179(x54401),x54402)),f334(f196(f928(x54401)),x54402))+~P107(f334(f144(x54401),x54402)) % 188.18/188.25 [5454]~P107(f334(x54541,f888(x54541)))+P107(f334(x54541,f334(f107(a1),x54542))) % 188.18/188.25 [5464]E(f249(x54641,x54642),x54642)+~P107(f334(f334(f243(a106),x54641),x54642)) % 188.18/188.25 [5468]E(f280(x54681,x54682),f84(a106))+~P107(f334(f334(f243(a106),x54682),x54681)) % 188.18/188.25 [5469]E(f185(x54691,x54692),f120(a1))+~P107(f334(f334(f243(a1),x54692),x54691)) % 188.18/188.25 [5470]E(f135(x54701,x54702),f122(a1))+~P107(f334(f334(f243(a1),x54701),x54702)) % 188.18/188.25 [5472]~P111(x54721)+E(f311(x54721,x54722,x54722),f334(f334(f316(x54721),x54722),f195(f935(x54721,a922)))) % 188.18/188.25 [5492]~E(f334(f334(f23(a927),x54921),x54922),f2(a927))+P107(f334(f334(f242(a927),x54921),x54922)) % 188.18/188.25 [5515]~E(x55152,f2(a927))+E(f60(x55151,x55152,f120(x55151)),f334(f334(f158(f928(x55151)),f120(x55151)),f120(f928(x55151)))) % 188.18/188.25 [5519]~P108(x55191)+~P107(f334(f334(f243(x55191),x55192),x55192)) % 188.18/188.25 [5521]~E(f50(a1,x55211,x55212),f2(a1))+E(f50(a1,x55211,f334(f85(a1),x55212)),f2(a1)) % 188.18/188.25 [5523]~E(f50(a1,x55231,x55232),f2(a1))+E(f50(a1,f334(f85(a1),x55231),x55232),f2(a1)) % 188.18/188.25 [5530]E(f334(f310(a927,x55301),f334(a119,x55302)),f195(f935(a927,a922)))+P107(f334(f334(f242(a927),x55301),x55302)) % 188.18/188.25 [5553]E(f146(a927,f334(f310(a927,x55531),x55532)),f120(a927))+P107(f334(f334(f243(a927),x55531),x55532)) % 188.18/188.25 [5558]~E(f334(f40(x55581),f334(f179(x55581),x55582)),f334(f196(f928(x55581)),x55582))+P107(f334(f144(x55581),x55582)) % 188.18/188.25 [5562]~P107(f334(f144(x55621),x55622))+P107(f334(f144(x55621),f334(f174(x55621),x55622))) % 188.18/188.25 [5563]~P107(f334(f144(x55631),x55632))+P107(f334(f144(x55631),f334(f178(x55631),x55632))) % 188.18/188.25 [5564]~P107(f334(f144(x55641),x55642))+P107(f334(f144(x55641),f334(f175(x55641),x55642))) % 188.18/188.25 [5572]P107(f334(x55721,x55722))+~P107(f334(x55721,f334(a112,f901(x55721)))) % 188.18/188.25 [5573]P107(f334(f334(f242(a927),x55732),x55731))+P107(f334(f334(f242(a927),x55731),x55732)) % 188.18/188.25 [5574]P107(f334(f334(f242(a1),x55742),x55741))+P107(f334(f334(f242(a1),x55741),x55742)) % 188.18/188.25 [5578]~P86(x55781)+P107(f334(f334(f242(x55781),x55782),f334(f81(x55781),x55782))) % 188.18/188.25 [5581]P107(f334(x55811,f895(x55811)))+~P107(f334(x55811,f334(f107(a1),x55812))) % 188.18/188.25 [5605]E(f334(f334(f23(a927),x56051),x56052),f2(a927))+~P107(f334(f334(f242(a927),x56051),x56052)) % 188.18/188.25 [5606]E(f334(f334(f41(a927),x56061),x56062),f2(a927))+~P107(f334(f334(f243(a927),x56061),x56062)) % 188.18/188.25 [5624]E(f50(a927,x56241,x56242),x56241)+~P107(f334(f334(f243(a927),x56241),x56242)) % 188.18/188.25 [5632]E(f50(a1,x56321,f334(f85(a1),x56322)),f297(x56321,x56322))+P107(f334(f334(f242(a1),f2(a1)),x56322)) % 188.18/188.25 [5644]E(f334(f334(f23(a1),x56441),x56442),f201(x56441,x56442))+~P107(f334(f334(f242(a1),x56442),x56441)) % 188.18/188.25 [5664]P107(f334(f334(f242(a1),f2(a1)),f888(x56641)))+P107(f334(x56641,f334(f107(a1),x56642))) % 188.18/188.25 [5677]~P127(x56771)+P107(f334(f334(f242(x56771),f2(x56771)),f334(f107(x56771),x56772))) % 188.18/188.25 [5678]~P86(x56781)+P107(f334(f334(f242(x56781),f2(x56781)),f334(f81(x56781),x56782))) % 188.18/188.25 [5705]E(f334(f334(f86(a927),x57051),f835(x57052,x57051)),x57052)+~P107(f334(f334(f242(a927),x57051),x57052)) % 188.18/188.25 [5720]E(f311(a1,x57201,x57202),f195(f935(a1,a922)))+~P107(f334(f334(f243(a1),x57202),x57201)) % 188.18/188.25 [5723]~P124(x57231)+E(f334(f334(f87(x57231),f334(f81(x57231),x57232)),f334(f81(x57231),x57232)),f334(f334(f87(x57231),x57232),x57232)) % 188.18/188.25 [5728]E(f146(a927,f334(f310(a927,x57281),f334(a119,x57282))),f120(a927))+P107(f334(f334(f242(a927),x57281),x57282)) % 188.18/188.25 [5730]E(f334(f334(f41(a1),x57301),x57302),f298(x57301,x57302))+~P107(f334(f334(f242(a1),f2(a1)),x57302)) % 188.18/188.25 [5750]P107(f334(f144(x57501),x57502))+~P107(f334(f144(x57501),f334(f174(x57501),x57502))) % 188.18/188.25 [5751]P107(f334(f144(x57511),x57512))+~P107(f334(f144(x57511),f334(f175(x57511),x57512))) % 188.18/188.25 [5776]P107(f334(f66(a927),x57761))+P107(f334(f334(f336(a927),f763(x57761,x57762)),x57761)) % 188.18/188.25 [5777]P107(f334(f66(a927),x57771))+P107(f334(f334(f336(a927),f794(x57771,x57772)),x57771)) % 188.18/188.25 [5780]P107(f334(f334(f243(a927),x57802),f334(a119,x57801)))+P107(f334(f334(f243(a927),x57801),x57802)) % 188.18/188.25 [5781]E(f50(a1,x57811,x57812),f297(x57811,x57812))+~P107(f334(f334(f242(a1),f2(a1)),x57812)) % 188.18/188.25 [5784]E(f146(a927,f334(f310(a927,x57841),x57842)),f120(a927))+~P107(f334(f334(f242(a927),x57842),x57841)) % 188.18/188.25 [5787]~P79(x57871)+E(f334(f317(x57871,x57871,f85(x57871)),f334(f309(x57871),x57872)),f334(f290(x57871),f334(f85(x57871),x57872))) % 188.18/188.25 [5788]~P79(x57881)+E(f334(f317(x57881,x57881,f85(x57881)),f334(f308(x57881),x57882)),f334(f307(x57881),f334(f85(x57881),x57882))) % 188.18/188.25 [5789]~P79(x57891)+E(f334(f317(x57891,x57891,f85(x57891)),f334(f290(x57891),x57892)),f334(f309(x57891),f334(f85(x57891),x57892))) % 188.18/188.25 [5790]~P79(x57901)+E(f334(f317(x57901,x57901,f85(x57901)),f334(f307(x57901),x57902)),f334(f308(x57901),f334(f85(x57901),x57902))) % 188.18/188.25 [5801]E(x58011,f195(f935(x58012,a922)))+P107(f334(f334(f336(x58012),f375(x58011,x58012)),x58011)) % 188.18/188.25 [5802]E(x58021,f195(f935(x58022,a922)))+P107(f334(f334(f336(x58022),f376(x58021,x58022)),x58021)) % 188.18/188.25 [5814]~P107(f334(f334(f243(a927),x58141),x58142))+P107(f334(f334(f242(a927),x58141),x58142)) % 188.18/188.25 [5815]~P107(f334(f334(f243(a1),x58151),x58152))+P107(f334(f334(f242(a1),x58151),x58152)) % 188.18/188.25 [5831]E(f52(x58311,x58312),f334(f334(f260(a1,a1),f2(a1)),x58311))+~P107(f334(f334(f243(a1),x58311),x58312)) % 188.18/188.25 [5834]E(f224(f334(f85(a1),x58341),f334(f85(a1),x58342)),f224(x58341,x58342))+~P107(f334(f334(f243(a1),x58342),f2(a1))) % 188.18/188.25 [5849]E(x58491,x58492)+~E(f334(a3,f334(a119,f334(a20,x58491))),f334(a3,f334(a119,f334(a20,x58492)))) % 188.18/188.25 [5854]E(f52(x58541,x58542),f334(f334(f260(a1,a1),f2(a1)),x58541))+~P107(f334(f334(f242(a1),x58542),f2(a1))) % 188.18/188.25 [5883]E(f50(a927,f334(f111(a927),x58831),f334(f111(a927),x58832)),f2(a927))+~P107(f334(a200,f334(f111(a1),x58831))) % 188.18/188.25 [5897]P107(f334(f334(f242(a1),f2(a1)),f895(x58971)))+~P107(f334(x58971,f334(f107(a1),x58972))) % 188.18/188.25 [5932]P42(f311(a1,x59321,x59322))+~P107(f334(f334(f242(a1),f2(a1)),x59321)) % 188.18/188.25 [5937]~P107(f334(f66(x59371),x59372))+P107(f334(f66(f935(x59371,a922)),f334(f315(x59371),x59372))) % 188.18/188.25 [5950]E(f334(f334(f86(a1),x59501),f334(f107(a1),f898(x59502,x59501))),x59502)+~P107(f334(f334(f242(a1),x59501),x59502)) % 188.18/188.25 [5958]P107(f334(f334(f242(a927),x59581),x59582))+P107(f334(f334(f242(a927),f334(a119,x59582)),x59581)) % 188.18/188.25 [6002]E(f334(f334(f41(a927),f334(f111(a927),x60021)),f334(f111(a927),x60022)),f2(a927))+~P107(f334(a200,f334(f111(a1),x60021))) % 188.18/188.25 [6003]E(f334(f334(f87(a927),f334(f111(a927),x60031)),f334(f111(a927),x60032)),f2(a927))+~P107(f334(f334(f243(a1),x60031),a89)) % 188.18/188.25 [6005]P107(f334(f334(f242(a927),x60051),f334(a119,x60052)))+~P107(f334(f334(f242(a927),x60051),x60052)) % 188.18/188.25 [6007]P107(f334(f334(f243(a927),x60071),f334(a119,x60072)))+~P107(f334(f334(f242(a927),x60071),x60072)) % 188.18/188.25 [6009]P107(f334(f334(f243(a927),x60091),f334(a119,x60092)))+~P107(f334(f334(f243(a927),x60091),x60092)) % 188.18/188.25 [6012]~E(x60121,x60122)+P107(f334(f334(f243(a1),x60121),f334(f334(f86(a1),x60122),f84(a1)))) % 188.18/188.25 [6015]E(f50(a1,x60151,x60152),f2(a1))+E(f334(f334(f23(a1),x60152),f50(a1,x60151,x60152)),f50(a1,f334(f85(a1),x60151),x60152)) % 188.18/188.25 [6024]E(x60241,f120(x60242))+P107(f334(f334(f336(x60242),f151(x60242,x60241)),f334(f179(x60242),x60241))) % 188.18/188.25 [6036]E(f91(f934(a927,a927),f53(x60361,x60362)),f334(f334(f260(a927,a927),f2(a927)),x60361))+~P107(f334(f334(f243(a927),x60361),x60362)) % 188.18/188.25 [6071]E(f334(f334(f23(a927),f334(f111(a927),x60711)),f334(f111(a927),x60712)),f334(f111(a927),x60711))+~P107(f334(f334(f243(a1),x60712),a89)) % 188.18/188.25 [6072]E(f334(f334(f86(a927),f334(f111(a927),x60721)),f334(f111(a927),x60722)),f334(f111(a927),x60722))+~P107(f334(f334(f243(a1),x60721),a89)) % 188.18/188.25 [6079]E(f334(a119,f334(f334(f86(a927),x60791),f836(x60792,x60791))),x60792)+~P107(f334(f334(f243(a927),x60791),x60792)) % 188.18/188.25 [6105]P107(f334(x61051,x61052))+~P107(f334(x61051,f334(a95,f568(x61052,x61051)))) % 188.18/188.25 [6106]P107(f334(x61061,x61062))+~P107(f334(x61061,f334(a3,f830(x61062,x61061)))) % 188.18/188.25 [6115]~P107(f334(f334(f243(a927),x61151),f334(a119,x61152)))+P107(f334(f334(f242(a927),x61151),x61152)) % 188.18/188.25 [6162]E(f334(f334(f316(a927),x61621),f334(f310(a927,x61622),x61621)),f334(f310(a927,x61622),f334(a119,x61621)))+~P107(f334(f334(f242(a927),x61622),x61621)) % 188.18/188.25 [6164]E(x61641,f120(x61642))+E(f334(f334(f141(x61642),f121(x61642,x61641)),f334(f334(f158(x61642),f151(x61642,x61641)),f120(x61642))),x61641) % 188.18/188.25 [6180]P107(f334(f66(x61801),x61802))+~P107(f334(f334(f243(a927),f2(a927)),f334(f40(x61801),x61802))) % 188.18/188.25 [6183]~E(x61831,f195(f935(x61832,a922)))+~P107(f334(f334(f243(a927),f2(a927)),f334(f40(x61832),x61831))) % 188.18/188.25 [6195]~P107(f334(f334(f243(a927),x61951),x61952))+P107(f334(f334(f242(a927),f334(a119,x61951)),x61952)) % 188.18/188.25 [6199]~P109(x61991)+E(f157(x61991,x61991,f5(x61991),f159(x61991,x61992)),f146(x61991,f334(f179(x61991),x61992))) % 188.18/188.25 [6202]E(x62021,f120(x62022))+P107(f334(f334(f336(x62022),f334(f148(x62022),x62021)),f334(f179(x62022),x62021))) % 188.18/188.25 [6208]~P127(x62081)+P107(f334(f334(f243(x62081),x62082),f334(f334(f86(x62081),x62082),f84(x62081)))) % 188.18/188.25 [6210]~P86(x62101)+P107(f334(f334(f242(x62101),f334(f85(x62101),x62102)),f334(f81(x62101),x62102))) % 188.18/188.25 [6241]P107(f334(f66(a927),x62411))+~P107(f334(f334(f242(a927),f763(x62411,x62412)),x62412)) % 188.18/188.25 [6242]P107(f334(f66(a927),x62421))+~P107(f334(f334(f243(a927),f794(x62421,x62422)),x62422)) % 188.18/188.25 [6245]~P107(f334(f66(f934(x62451,x62451)),x62452))+P107(f334(f66(x62451),f334(f289(x62451),x62452))) % 188.18/188.25 [6301]~P107(f334(f334(f243(a927),x63012),f334(a119,x63011)))+~P107(f334(f334(f243(a927),x63011),x63012)) % 188.18/188.25 [6302]~P111(x63021)+E(f334(f334(f109(f935(x63021,a922)),f334(f309(x63021),x63022)),f334(f290(x63021),x63022)),f334(f334(f316(x63021),x63022),f195(f935(x63021,a922)))) % 188.18/188.25 [6314]P107(f334(f66(x63141),x63142))+~P107(f334(f66(f935(x63141,a922)),f334(f315(x63141),x63142))) % 188.18/188.25 [6336]P107(f334(f334(f242(a927),f334(a119,x63361)),f334(a119,x63362)))+~P107(f334(f334(f242(a927),x63361),x63362)) % 188.18/188.25 [6337]P107(f334(f334(f242(a927),f334(a20,x63371)),f334(a20,x63372)))+~P107(f334(f334(f242(a106),x63371),x63372)) % 188.18/188.25 [6338]P107(f334(f334(f242(a106),f334(a3,x63381)),f334(a3,x63382)))+~P107(f334(f334(f242(a927),x63381),x63382)) % 188.18/188.25 [6340]P107(f334(f334(f243(a927),f334(a119,x63401)),f334(a119,x63402)))+~P107(f334(f334(f243(a927),x63401),x63402)) % 188.18/188.25 [6341]P107(f334(f334(f243(a927),f334(a20,x63411)),f334(a20,x63412)))+~P107(f334(f334(f243(a106),x63411),x63412)) % 188.18/188.25 [6342]P107(f334(f334(f243(a106),f334(a3,x63421)),f334(a3,x63422)))+~P107(f334(f334(f243(a927),x63421),x63422)) % 188.18/188.25 [6347]E(x63471,x63472)+~E(f334(f317(a927,a1,f107(a1)),x63471),f334(f317(a927,a1,f107(a1)),x63472)) % 188.18/188.25 [6363]P107(f334(f334(f242(a927),x63631),x63632))+~P107(f334(f334(f242(a927),f334(a119,x63631)),x63632)) % 188.18/188.25 [6366]P107(f334(f334(f243(a927),x63661),x63662))+~P107(f334(f334(f242(a927),f334(a119,x63661)),x63662)) % 188.18/188.25 [6367]P107(f334(f334(f243(a927),x63671),x63672))+~P107(f334(f334(f243(a927),f334(a119,x63671)),x63672)) % 188.18/188.25 [6384]E(f50(a1,x63841,x63842),f2(a1))+E(f334(f334(f23(a1),f50(a1,x63841,x63842)),x63842),f50(a1,x63841,f334(f85(a1),x63842))) % 188.18/188.25 [6447]E(f334(f40(f935(x64471,a922)),f334(f315(x64471),x64472)),f334(f334(f252(a927),f334(a119,f334(a119,f2(a927)))),f334(f40(x64471),x64472)))+~P107(f334(f66(x64471),x64472)) % 188.18/188.25 [6450]E(x64501,f120(x64502))+E(f334(f334(f171(x64502),x64501),f334(f334(f23(a927),f334(f196(f928(x64502)),x64501)),f84(a927))),f151(x64502,x64501)) % 188.18/188.25 [6472]E(x64721,f120(x64722))+E(f334(f334(f141(x64722),f334(f178(x64722),x64721)),f334(f334(f158(x64722),f334(f148(x64722),x64721)),f120(x64722))),f334(f174(x64722),x64721)) % 188.18/188.25 [6503]~P107(f334(f66(x65031),f42(f935(x65031,a922),x65032)))+P107(f334(f66(f935(x65031,a922)),x65032)) % 188.18/188.25 [6525]P107(f334(f334(f242(a927),f334(f111(a927),x65251)),f334(f111(a927),x65252)))+~P107(f334(f334(f242(a1),x65251),a89)) % 188.18/188.25 [6544]~P107(f334(f334(f243(a1),x65441),x65442))+P107(f334(f334(f242(a1),x65441),f334(f334(f23(a1),x65442),f84(a1)))) % 188.18/188.25 [6545]~P107(f334(f334(f242(a1),x65451),x65452))+P107(f334(f334(f243(a1),x65451),f334(f334(f86(a1),x65452),f84(a1)))) % 188.18/188.25 [6546]~P107(f334(f334(f243(a1),x65461),x65462))+P107(f334(f334(f243(a1),x65461),f334(f334(f86(a1),x65462),f84(a1)))) % 188.18/188.25 [6548]~P107(f334(f334(f242(a1),x65481),x65482))+P107(f334(f334(f242(a927),f334(f111(a927),x65481)),f334(f111(a927),x65482))) % 188.18/188.25 [6549]~P107(f334(f334(f242(a1),x65491),x65492))+P107(f334(f334(f242(a1),f334(f111(a1),x65491)),f334(f111(a1),x65492))) % 188.18/188.25 [6551]~P107(f334(f334(f242(a927),x65511),x65512))+P107(f334(f334(f242(a1),f334(f107(a1),x65511)),f334(f107(a1),x65512))) % 188.18/188.25 [6552]~P107(f334(f334(f243(a1),x65521),x65522))+P107(f334(f334(f243(a1),f334(f111(a1),x65521)),f334(f111(a1),x65522))) % 188.18/188.25 [6554]~P107(f334(f334(f243(a927),x65541),x65542))+P107(f334(f334(f243(a1),f334(f107(a1),x65541)),f334(f107(a1),x65542))) % 188.18/188.25 [6575]~P107(f334(f334(f242(a927),x65751),x65752))+~P107(f334(f334(f242(a927),f334(a119,x65752)),x65751)) % 188.18/188.25 [6615]~P107(f334(f334(f242(a927),f334(a119,x66151)),f334(a119,x66152)))+P107(f334(f334(f242(a927),x66151),x66152)) % 188.18/188.25 [6616]~P107(f334(f334(f242(a106),f334(a3,x66161)),f334(a3,x66162)))+P107(f334(f334(f242(a927),x66161),x66162)) % 188.18/188.25 [6617]~P107(f334(f334(f242(a927),f334(a20,x66171)),f334(a20,x66172)))+P107(f334(f334(f242(a106),x66171),x66172)) % 188.18/188.25 [6619]~P107(f334(f334(f243(a927),f334(a119,x66191)),f334(a119,x66192)))+P107(f334(f334(f243(a927),x66191),x66192)) % 188.18/188.25 [6620]~P107(f334(f334(f243(a106),f334(a3,x66201)),f334(a3,x66202)))+P107(f334(f334(f243(a927),x66201),x66202)) % 188.18/188.25 [6621]~P107(f334(f334(f243(a927),f334(a112,x66211)),f334(a112,x66212)))+P107(f334(f334(f243(a1),x66211),x66212)) % 188.18/188.25 [6622]~P107(f334(f334(f243(a927),f334(a20,x66221)),f334(a20,x66222)))+P107(f334(f334(f243(a106),x66221),x66222)) % 188.18/188.25 [6664]~P107(f334(f334(f243(a927),f334(a112,x66642)),f334(a112,x66641)))+P107(f334(f334(f243(a1),f2(a1)),x66641)) % 188.18/188.25 [6698]P107(f334(f334(f242(a1),f2(a1)),f50(a1,x66981,x66982)))+~P107(f334(f334(f243(a1),f2(a1)),x66982)) % 188.18/188.25 [6855]P39(x68551,x68552)+~E(f334(f334(f295(x68551,x68551,x68551),x68552),x68552),f195(f935(f934(x68551,x68551),a922))) % 188.18/188.25 [6867]~P39(x68671,x68672)+P39(x68671,f334(f334(f295(x68671,x68671,x68671),x68672),x68672)) % 188.18/188.25 [6878]P107(f334(f334(f242(a1),x68781),x68782))+~P107(f334(f334(f243(a1),x68781),f334(f334(f86(a1),x68782),f84(a1)))) % 188.18/188.25 [6879]P107(f334(f334(f243(a1),x68791),x68792))+~P107(f334(f334(f242(a1),x68791),f334(f334(f23(a1),x68792),f84(a1)))) % 188.18/188.25 [6882]P107(f334(f334(f242(a927),x68821),x68822))+~P107(f334(f334(f242(a1),f334(f107(a1),x68821)),f334(f107(a1),x68822))) % 188.18/188.25 [6883]P107(f334(f334(f242(a1),x68831),x68832))+~P107(f334(f334(f242(a1),f334(f111(a1),x68831)),f334(f111(a1),x68832))) % 188.18/188.25 [6885]P107(f334(f334(f243(a927),x68851),x68852))+~P107(f334(f334(f243(a1),f334(f107(a1),x68851)),f334(f107(a1),x68852))) % 188.18/188.25 [6886]P107(f334(f334(f243(a1),x68861),x68862))+~P107(f334(f334(f243(a927),f334(f111(a927),x68861)),f334(f111(a927),x68862))) % 188.18/188.25 [6887]P107(f334(f334(f243(a1),x68871),x68872))+~P107(f334(f334(f243(a1),f334(f111(a1),x68871)),f334(f111(a1),x68872))) % 188.18/188.25 [6982]~E(f710(x69822,x69821),f120(x69821))+E(f334(f149(f928(x69821),f928(x69821),f141(x69821),f120(x69821)),x69822),f120(x69821)) % 188.18/188.25 [6983]~E(f715(x69832,x69831),f120(x69831))+E(f334(f149(f928(x69831),f928(x69831),f141(x69831),f120(x69831)),x69832),f120(x69831)) % 188.18/188.25 [6987]~P7(x69871)+E(f334(f149(x69871,x69871,f109(x69871),f250(x69871)),x69872),f43(x69871,f334(f179(x69871),x69872))) % 188.18/188.25 [6988]~P7(x69881)+E(f334(f149(x69881,x69881,f108(x69881),f195(x69881)),x69882),f42(x69881,f334(f179(x69881),x69882))) % 188.18/188.25 [7002]E(x70021,f2(a106))+E(f334(f334(f86(a927),f334(a20,f334(f334(f23(a106),x70021),f84(a106)))),f334(a119,x70022)),f334(f334(f86(a927),f334(a20,x70021)),x70022)) % 188.18/188.25 [7047]P107(f334(f334(f243(a1),f334(f334(f23(a1),x70471),x70472)),f2(a1)))+~P107(f334(f334(f243(a1),x70471),x70472)) % 188.18/188.25 [7069]~P109(x70691)+E(f334(f334(f108(f935(x70691,a922)),f334(f334(f316(x70691),x70692),f195(f935(x70691,a922)))),f334(f308(x70691),x70692)),f334(f290(x70691),x70692)) % 188.18/188.25 [7143]~P63(x71431,x71432)+P39(x71431,f334(f270(f934(x71431,x71431)),f334(f265(x71431,x71431,a922),x71432))) % 188.18/188.25 [7144]~P63(x71441,x71442)+P61(x71441,f334(f270(f934(x71441,x71441)),f334(f265(x71441,x71441,a922),x71442))) % 188.18/188.25 [7145]~P52(x71451,x71452)+P40(x71451,f334(f270(f934(x71451,x71451)),f334(f265(x71451,x71451,a922),x71452))) % 188.18/188.25 [7146]~P53(x71461,x71462)+P54(x71461,f334(f270(f934(x71461,x71461)),f334(f265(x71461,x71461,a922),x71462))) % 188.18/188.25 [7147]E(x71471,f195(f935(x71472,a922)))+~P107(f334(f334(f242(f935(x71472,a922)),x71471),f195(f935(x71472,a922)))) % 188.18/188.25 [7228]~P107(f334(f334(f243(a927),f2(a927)),x72282))+P107(f334(f334(f242(a927),f50(a927,x72281,x72282)),x72282)) % 188.18/188.25 [7229]~P107(f334(f334(f242(a1),f2(a1)),x72291))+P107(f334(f334(f242(a1),f50(a1,x72291,x72292)),x72291)) % 188.18/188.25 [7230]~P107(f334(f334(f243(a927),f2(a927)),x72302))+P107(f334(f334(f243(a927),f50(a927,x72301,x72302)),x72302)) % 188.18/188.25 [7232]~P107(f334(f334(f243(a1),f2(a1)),x72322))+P107(f334(f334(f243(a1),f50(a1,x72321,x72322)),x72322)) % 188.18/188.25 [7308]~P111(x73081)+E(f334(f334(f23(f935(x73081,a922)),f334(f334(f316(x73081),x73082),f195(f935(x73081,a922)))),f334(f307(x73081),x73082)),f334(f334(f316(x73081),x73082),f195(f935(x73081,a922)))) % 188.18/188.25 [7380]~P45(x73801,x73802)+P55(x73801,f250(f935(x73801,a922)),f334(f270(f934(x73801,x73801)),f334(f265(x73801,x73801,a922),x73802))) % 188.18/188.25 [7381]P107(f334(x73811,x73812))+P107(f334(f334(f336(f935(f934(a927,a927),a922)),f568(x73812,x73811)),a105)) % 188.18/188.25 [7425]E(f334(f334(f141(a927),f146(a927,f334(f310(a927,x74251),x74252))),f334(f334(f158(a927),x74252),f120(a927))),f146(a927,f334(f310(a927,x74251),f334(a119,x74252))))+~P107(f334(f334(f242(a927),x74251),x74252)) % 188.18/188.25 [7567]E(x75671,f2(a927))+~E(f334(f149(a927,a927,f86(a927),x75671),x75672),f2(a927)) % 188.18/188.25 [7591]~P107(f334(f334(f243(a1),f334(f334(f23(a1),x75911),x75912)),f2(a1)))+P107(f334(f334(f243(a1),x75911),x75912)) % 188.18/188.25 [7617]P39(x76171,x76172)+~P39(x76171,f334(f334(f295(x76171,x76171,x76171),x76172),x76172)) % 188.18/188.25 [7643]~P107(f334(f334(f242(a927),f334(a119,x76431)),x76432))+P107(f192(a922,a247,f334(f242(a927),x76431),x76432)) % 188.18/188.25 [7794]P27(a927,a927,f334(f334(f7(a927,a927,a927),f23(a927)),x77941),x77942)+P107(f334(f334(f336(a927),f879(x77941,x77942)),x77942)) % 188.18/188.25 [7848]E(f334(f334(f334(f70(a927,x78481,f86(a927)),f334(f16(a927,x78481),f84(a927))),f2(a927)),x78482),f334(f40(x78481),x78482))+~P107(f334(f66(x78481),x78482)) % 188.18/188.25 [7889]P27(a927,a927,f334(f334(f7(a927,a927,a927),f23(a927)),x78891),x78892)+~P107(f334(f334(f242(a927),x78891),f879(x78891,x78892))) % 188.18/188.25 [7945]P39(x79451,x79452)+P107(f334(f334(f242(f935(x79451,a922)),f581(x79452,x79451)),f334(f292(x79451,x79451,x79452),f581(x79452,x79451)))) % 188.18/188.25 [7950]P63(x79501,x79502)+~P39(x79501,f334(f270(f934(x79501,x79501)),f334(f265(x79501,x79501,a922),x79502))) % 188.18/188.25 [7951]P52(x79511,x79512)+~P40(x79511,f334(f270(f934(x79511,x79511)),f334(f265(x79511,x79511,a922),x79512))) % 188.18/188.25 [7952]P53(x79521,x79522)+~P54(x79521,f334(f270(f934(x79521,x79521)),f334(f265(x79521,x79521,a922),x79522))) % 188.18/188.25 [8021]P107(f334(f334(f242(a927),f334(a119,x80211)),x80212))+~P107(f192(a922,a247,f334(f242(a927),x80211),x80212)) % 188.18/188.25 [8078]P107(f334(f334(f336(f934(a927,a927)),f334(f334(f260(a927,a927),x80781),x80782)),f314(a927,a324)))+~P107(f334(f334(f242(a927),x80781),x80782)) % 188.18/188.25 [8166]P45(x81661,x81662)+~P55(x81661,f250(f935(x81661,a922)),f334(f270(f934(x81661,x81661)),f334(f265(x81661,x81661,a922),x81662))) % 188.18/188.25 [8219]~P107(f334(f144(x82191),x82192))+P107(f334(f144(f935(x82191,a922)),f334(f334(f161(f928(x82191),f935(x82191,a922)),f179(x82191)),f59(x82191,x82192)))) % 188.18/188.25 [8419]~P39(x84191,f334(f293(x84191,x84191),x84192))+P39(x84191,f334(f293(x84191,x84191),f334(f334(f295(x84191,x84191,x84191),x84192),f314(x84191,x84192)))) % 188.18/188.25 [8516]P28(x85161,a927,f601(x85162,x85161),x85162,f334(f310(a927,f2(a927)),f334(f40(x85161),x85162)))+~P107(f334(f66(x85161),x85162)) % 188.18/188.25 [8517]P28(a927,x85171,f583(x85172,x85171),f334(f310(a927,f2(a927)),f334(f40(x85171),x85172)),x85172)+~P107(f334(f66(x85171),x85172)) % 188.18/188.25 [8534]P28(a927,x85341,f584(x85342,x85341),f311(a927,f84(a927),f334(f40(x85341),x85342)),x85342)+~P107(f334(f66(x85341),x85342)) % 188.18/188.25 [8543]P107(f334(f66(f934(x85431,x85431)),f334(f334(f295(x85431,x85431,x85431),x85432),f314(x85431,x85432))))+~P107(f334(f66(f934(x85431,x85431)),x85432)) % 188.18/188.25 [8567]E(x85671,f2(a1))+P107(f334(f54(x85672,x85671),f334(f334(f260(a1,a1),f334(f334(f41(a1),x85672),x85671)),f50(a1,x85672,x85671)))) % 188.18/188.25 [8581]~P107(f334(f334(f336(f934(a927,a927)),f334(f334(f260(a927,a927),x85811),x85812)),f314(a927,a324)))+P107(f334(f334(f242(a927),x85811),x85812)) % 188.18/188.25 [8596]~P82(x85961)+E(f334(f149(x85961,x85961,f334(f7(x85961,x85961,x85961),f86(x85961)),f2(x85961)),f334(f175(x85961),x85962)),f334(f149(x85961,x85961,f86(x85961),f2(x85961)),x85962)) % 188.18/188.25 [8768]~P109(x87681)+E(f334(f149(f928(x87681),x87681,f334(f7(x87681,f928(x87681),f928(x87681)),f155(x87681,x87681,f5(x87681))),f120(x87681)),x87682),f157(x87681,x87681,f5(x87681),x87682)) % 188.18/188.25 [8873]~P61(x88731,f334(f270(f934(x88731,x88731)),f334(f265(x88731,x88731,a922),x88732)))+P61(x88731,f334(f270(f934(x88731,x88731)),f334(f265(x88731,x88731,a922),f251(x88731,x88731,x88732)))) % 188.18/188.25 [8887]P107(f334(f334(f336(f934(a927,a927)),f334(f334(f260(a927,a927),x88871),x88872)),f334(f334(f295(a927,a927,a927),a324),f314(a927,a324))))+~P107(f334(f334(f243(a927),x88871),x88872)) % 188.18/188.25 [8931]~P107(f334(f66(f934(x89311,x89311)),f334(f334(f295(x89311,x89311,x89311),x89312),f314(x89311,x89312))))+P107(f334(f66(f934(x89311,x89311)),x89312)) % 188.18/188.25 [8988]~P61(x89881,f334(f270(f934(x89881,x89881)),f334(f265(x89881,x89881,a922),f251(x89881,x89881,x89882))))+P61(x89881,f334(f270(f934(x89881,x89881)),f334(f265(x89881,x89881,a922),x89882))) % 188.18/188.25 [9195]P61(x91951,x91952)+P107(f334(f334(f336(f934(x91951,x91951)),f334(f334(f260(x91951,x91951),f620(x91952,x91951)),f620(x91952,x91951))),f334(f334(f295(x91951,x91951,x91951),x91952),f314(x91951,x91952)))) % 188.18/188.25 [9196]P61(x91961,x91962)+P107(f334(f334(f336(f934(x91961,x91961)),f334(f334(f260(x91961,x91961),f630(x91962,x91961)),f630(x91962,x91961))),f334(f334(f295(x91961,x91961,x91961),x91962),f314(x91961,x91962)))) % 188.18/188.25 [9301]~P107(f334(f334(f336(f934(a927,a927)),f334(f334(f260(a927,a927),x93011),x93012)),f334(f334(f295(a927,a927,a927),a324),f314(a927,a324))))+P107(f334(f334(f243(a927),x93011),x93012)) % 188.18/188.25 [5318]~P95(x53181)+E(f334(f334(f86(x53181),f334(f111(x53181),a89)),x53182),x53182) % 188.18/188.25 [5347]~P3(x53471)+E(f334(f334(f86(x53471),f334(f85(x53471),x53472)),x53472),f2(x53471)) % 188.18/188.25 [5348]~P69(x53481)+E(f334(f334(f86(x53481),f334(f85(x53481),x53482)),x53482),f2(x53481)) % 188.18/188.25 [5349]~P91(x53491)+E(f334(f334(f108(x53491),f334(f85(x53491),x53492)),x53492),f250(x53491)) % 188.18/188.25 [5350]~P91(x53501)+E(f334(f334(f109(x53501),f334(f85(x53501),x53502)),x53502),f195(x53501)) % 188.18/188.25 [5383]~P95(x53831)+E(f334(f334(f87(x53831),f334(f111(x53831),a104)),x53832),f334(f85(x53831),x53832)) % 188.18/188.25 [5545]~P115(x55451)+E(f334(f334(f87(x55451),f334(f85(x55451),f84(x55451))),x55452),f334(f85(x55451),x55452)) % 188.18/188.25 [5590]E(f334(f81(a1),x55901),f84(a1))+~E(f334(f81(a1),f334(f334(f87(a1),x55901),x55902)),f84(a1)) % 188.18/188.25 [5680]~P95(x56801)+E(f334(f334(f86(x56801),f84(x56801)),f334(f111(x56801),x56802)),f334(f111(x56801),f334(f334(f23(a1),x56802),a104))) % 188.18/188.25 [5731]~P109(x57311)+E(f14(x57311,f334(f334(f316(x57311),x57312),f195(f935(x57311,a922)))),x57312) % 188.18/188.25 [5732]~P109(x57321)+E(f15(x57321,f334(f334(f316(x57321),x57322),f195(f935(x57321,a922)))),x57322) % 188.18/188.25 [5733]~P99(x57331)+E(f10(x57331,f334(f334(f316(x57331),x57332),f195(f935(x57331,a922)))),x57332) % 188.18/188.25 [5734]~P99(x57341)+E(f13(x57341,f334(f334(f316(x57341),x57342),f195(f935(x57341,a922)))),x57342) % 188.18/188.25 [5735]~P7(x57351)+E(f43(x57351,f334(f334(f316(x57351),x57352),f195(f935(x57351,a922)))),x57352) % 188.18/188.25 [5736]~P7(x57361)+E(f42(x57361,f334(f334(f316(x57361),x57362),f195(f935(x57361,a922)))),x57362) % 188.18/188.25 [5758]E(f334(f334(f86(a927),x57581),f334(f334(f23(a927),x57582),x57581)),x57582)+P107(f334(f334(f243(a927),x57582),x57581)) % 188.18/188.25 [5796]E(x57961,f120(x57962))+P107(f334(f334(f243(a927),f2(a927)),f334(f196(f928(x57962)),x57961))) % 188.18/188.25 [5927]~P109(x59271)+E(f11(x59271,f246(x59271),f334(f334(f316(x59271),x59272),f195(f935(x59271,a922)))),x59272) % 188.18/188.25 [5928]~P109(x59281)+E(f12(x59281,f241(x59281),f334(f334(f316(x59281),x59282),f195(f935(x59281,a922)))),x59282) % 188.18/188.25 [5991]E(f334(f334(f23(a927),x59911),f334(f334(f23(a927),x59911),x59912)),x59912)+~P107(f334(f334(f242(a927),x59912),x59911)) % 188.18/188.25 [5992]E(f334(f334(f86(a927),x59921),f334(f334(f23(a927),x59922),x59921)),x59922)+~P107(f334(f334(f242(a927),x59921),x59922)) % 188.18/188.25 [6014]E(f50(a927,f334(f334(f23(a927),x60141),x60142),x60142),f50(a927,x60141,x60142))+P107(f334(f334(f243(a927),x60141),x60142)) % 188.18/188.25 [6025]E(f334(f85(a1),f334(f334(f41(a1),x60251),f334(f85(a1),x60252))),f298(x60251,x60252))+P107(f334(f334(f242(a1),f2(a1)),x60252)) % 188.18/188.25 [6027]~E(x60272,f2(a927))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f252(a927),x60271),x60272))) % 188.18/188.25 [6081]~P95(x60811)+E(f334(f334(f86(x60811),f334(f85(x60811),f84(x60811))),f334(f111(x60811),x60812)),f334(f111(x60811),f334(f334(f86(a1),x60812),a104))) % 188.18/188.25 [6083]E(f334(f334(f252(a927),f334(f111(a927),x60831)),x60832),f334(f334(f252(a927),f2(a927)),x60832))+~P107(f334(a200,f334(f111(a1),x60831))) % 188.18/188.25 [6187]E(f334(f148(a927),f146(a927,f334(f310(a927,x61871),x61872))),x61871)+~P107(f334(f334(f243(a927),x61871),x61872)) % 188.18/188.25 [6203]E(f334(f334(f87(a927),f334(f111(a927),x62031)),f334(f111(a927),x62032)),f334(f111(a927),f334(f334(f87(a1),x62031),x62032)))+P107(f334(f334(f243(a1),x62031),a89)) % 188.18/188.25 [6209]~P128(x62091)+P107(f334(f334(f242(x62091),f2(x62091)),f334(f334(f87(x62091),x62092),x62092))) % 188.18/188.25 [6221]E(f334(f334(f23(a927),f334(a119,x62211)),x62212),f334(a119,f334(f334(f23(a927),x62211),x62212)))+~P107(f334(f334(f242(a927),x62212),x62211)) % 188.18/188.25 [6224]E(f50(a927,f334(f334(f23(a927),x62241),x62242),x62242),f50(a927,x62241,x62242))+~P107(f334(f334(f242(a927),x62242),x62241)) % 188.18/188.25 [6277]E(f334(f334(f252(a927),f334(a112,x62771)),x62772),f334(a112,f334(f334(f252(a1),x62771),x62772)))+~P107(f334(f334(f242(a1),f2(a1)),x62771)) % 188.18/188.25 [6295]P107(f334(f144(x62951),x62952))+P107(f334(f334(f243(a927),f680(x62952,x62951)),f334(f196(f928(x62951)),x62952))) % 188.18/188.25 [6296]P107(f334(f144(x62961),x62962))+P107(f334(f334(f243(a927),f685(x62962,x62961)),f334(f196(f928(x62961)),x62962))) % 188.18/188.25 [6308]~E(x63081,f120(x63082))+~P107(f334(f334(f243(a927),f2(a927)),f334(f196(f928(x63082)),x63081))) % 188.18/188.25 [6319]E(f151(a927,f146(a927,f334(f310(a927,x63191),x63192))),f334(f334(f23(a927),x63192),f84(a927)))+~P107(f334(f334(f243(a927),x63191),x63192)) % 188.18/188.25 [6322]E(f334(f334(f86(a1),x63221),f334(f107(a1),f334(a119,f899(x63222,x63221)))),x63222)+~P107(f334(f334(f243(a1),x63221),x63222)) % 188.18/188.25 [6329]E(x63291,f2(a927))+E(f334(f334(f87(a927),x63292),f334(f334(f252(a927),x63292),f334(f334(f23(a927),x63291),f84(a927)))),f334(f334(f252(a927),x63292),x63291)) % 188.18/188.25 [6357]E(f334(f334(f87(a927),f334(a112,x63571)),f334(a112,x63572)),f334(a112,f334(f334(f87(a1),x63571),x63572)))+~P107(f334(f334(f242(a1),f2(a1)),x63571)) % 188.18/188.25 [6358]E(f334(f334(f41(a927),f334(a112,x63581)),f334(a112,x63582)),f334(a112,f334(f334(f41(a1),x63581),x63582)))+~P107(f334(f334(f242(a1),f2(a1)),x63581)) % 188.18/188.25 [6372]~P119(x63721)+E(f334(f334(f86(x63721),x63722),x63722),f334(f334(f87(x63721),f334(f334(f86(x63721),f84(x63721)),f84(x63721))),x63722)) % 188.18/188.25 [6395]E(f334(f334(f23(a1),f334(f107(a1),x63951)),f334(f107(a1),x63952)),f334(f107(a1),f334(f334(f23(a927),x63951),x63952)))+~P107(f334(f334(f242(a927),x63952),x63951)) % 188.18/188.25 [6397]E(f334(f334(f260(a1,a1),f334(f111(a1),a104)),f334(f334(f86(a1),x63971),x63972)),f55(x63971,x63972))+~P107(f334(f334(f242(a1),x63972),f2(a1))) % 188.18/188.25 [6425]E(f186(x64251,x64252),f120(f928(x64251)))+P107(f334(f334(f336(f928(x64251)),f679(x64252,x64251)),f334(f179(f928(x64251)),x64252))) % 188.18/188.25 [6434]E(f123(a1,f334(f136(a1),x64341),f135(x64342,f334(f334(f86(a1),x64341),f84(a1)))),f135(x64342,x64341))+P107(f334(f334(f243(a1),x64342),x64341)) % 188.18/188.25 [6509]E(f334(f334(f158(a1),x65091),f185(f334(f334(f86(a1),x65091),f84(a1)),x65092)),f185(x65091,x65092))+~P107(f334(f334(f242(a1),x65091),x65092)) % 188.18/188.25 [6547]~P107(f334(f334(f243(a927),x65472),x65471))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f23(a927),x65471),x65472))) % 188.18/188.25 [6578]~P107(f334(f334(f243(a927),x65781),f334(a112,x65782)))+P107(f334(f334(f243(a1),f334(f107(a1),x65781)),x65782)) % 188.18/188.25 [6606]~P109(x66061)+E(f334(f334(f108(f935(x66061,a922)),f334(f307(x66061),x66062)),f334(f334(f316(x66061),x66062),f195(f935(x66061,a922)))),f334(f309(x66061),x66062)) % 188.18/188.25 [6607]~P107(f334(f334(f242(a1),f2(a1)),x66071))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f252(a1),x66071),x66072))) % 188.18/188.25 [6610]~P107(f334(f334(f243(a927),f2(a927)),x66101))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f252(a927),x66101),x66102))) % 188.18/188.25 [6640]~E(f334(x66401,f2(a927)),f2(a927))+E(f334(f334(f6(a927,a927),x66401),f311(a927,f334(a119,f2(a927)),x66402)),f334(f334(f6(a927,a927),x66401),f311(a927,f2(a927),x66402))) % 188.18/188.25 [6721]E(f334(f334(f316(a1),x67211),f311(a1,f334(f334(f86(a1),x67211),f84(a1)),x67212)),f311(a1,x67211,x67212))+P107(f334(f334(f243(a1),x67212),x67211)) % 188.18/188.25 [6722]P107(f334(f334(f243(a927),x67221),f334(a112,x67222)))+~P107(f334(f334(f243(a1),f334(f107(a1),x67221)),x67222)) % 188.18/188.25 [6824]E(f334(a112,f334(f334(f41(a1),f334(f111(a1),x68241)),f334(f111(a1),x68242))),f334(f334(f41(a927),f334(f111(a927),x68241)),f334(f111(a927),x68242)))+P107(f334(a200,f334(f111(a1),x68241))) % 188.18/188.25 [6880]P107(f334(f334(f243(a927),x68801),x68802))+~P107(f334(f334(f243(a927),f2(a927)),f334(f334(f23(a927),x68802),x68801))) % 188.18/188.25 [6924]P107(f334(f334(f243(a927),f2(a927)),x69241))+~P107(f334(f334(f243(a927),f2(a927)),f334(f334(f87(a927),x69242),x69241))) % 188.18/188.25 [6925]P107(f334(f334(f243(a927),f2(a927)),x69251))+~P107(f334(f334(f243(a927),f2(a927)),f334(f334(f87(a927),x69251),x69252))) % 188.18/188.25 [6943]~P107(f334(f334(f242(a1),x69431),f2(a1)))+E(f334(f334(f87(a927),f334(a112,f334(f85(a1),x69431))),f334(a112,f334(f85(a1),x69432))),f334(a112,f334(f334(f87(a1),x69431),x69432))) % 188.18/188.25 [6999]~E(x69992,f195(f935(x69991,a922)))+P107(f334(f334(f242(f935(x69991,a922)),x69992),f334(f85(f935(x69991,a922)),x69992))) % 188.18/188.25 [7108]~P107(f334(f334(f243(a1),x71081),x71082))+P107(f334(f334(f242(a1),f334(f334(f86(a1),x71081),f84(a1))),x71082)) % 188.18/188.25 [7174]E(x71741,f2(a927))+~P107(f334(f334(f242(a1),f334(f107(a1),x71742)),f334(f85(a1),f334(f107(a1),x71741)))) % 188.18/188.25 [7175]E(x71751,f2(a927))+~P107(f334(f334(f242(a1),f334(f107(a1),x71751)),f334(f85(a1),f334(f107(a1),x71752)))) % 188.18/188.25 [7276]E(f334(f334(f260(a1,a1),f334(f111(a1),a104)),f334(f334(f86(a1),x72761),x72762)),f55(x72761,x72762))+~P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),x72761),x72762))) % 188.18/188.25 [7319]~P29(x73191,x73192)+P39(x73191,f334(f259(f935(f934(x73191,x73191),a922),f935(f934(x73191,x73191),a922)),x73192)) % 188.18/188.25 [7338]~P107(f334(f334(f242(a927),f334(a119,f2(a927))),x73381))+P107(f334(f334(f242(a927),f334(a119,f2(a927))),f334(f334(f252(a927),x73381),x73382))) % 188.18/188.25 [7568]~P107(f334(f334(f243(a927),f2(a927)),x75681))+P107(f334(f334(f243(a927),f334(f334(f23(a927),x75681),f334(a119,x75682))),x75681)) % 188.18/188.25 [7600]P107(f334(f334(f242(a927),f334(a119,f2(a927))),x76001))+~P107(f334(f334(f242(a927),f334(a119,f2(a927))),f334(f334(f87(a927),x76002),x76001))) % 188.18/188.25 [7601]P107(f334(f334(f242(a927),f334(a119,f2(a927))),x76011))+~P107(f334(f334(f242(a927),f334(a119,f2(a927))),f334(f334(f87(a927),x76011),x76012))) % 188.18/188.25 [7604]P107(f334(f334(f242(a927),f334(f334(f171(a927),x76041),x76042)),f334(f172(a927),x76041)))+~P107(f334(f334(f243(a927),x76042),f334(f196(f928(a927)),x76041))) % 188.18/188.25 [7642]P107(f334(f334(f243(a1),x76421),x76422))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),x76421),f84(a1))),x76422)) % 188.18/188.25 [7684]P107(f334(f66(x76841),f250(f935(x76841,a922))))+~P107(f334(f66(f935(x76842,x76841)),f250(f935(f935(x76842,x76841),a922)))) % 188.18/188.25 [7685]P107(f334(f66(x76851),f250(f935(x76851,a922))))+~P107(f334(f66(f933(x76852,x76851)),f250(f935(f933(x76852,x76851),a922)))) % 188.18/188.25 [7686]P107(f334(f66(x76861),f250(f935(x76861,a922))))+~P107(f334(f66(f933(x76861,x76862)),f250(f935(f933(x76861,x76862),a922)))) % 188.18/188.25 [7724]E(x77241,f195(f935(x77242,a922)))+~P107(f334(f334(f242(f935(x77242,a922)),x77241),f334(f85(f935(x77242,a922)),x77241))) % 188.18/188.25 [7858]E(f334(f149(f928(x78581),f928(x78581),f141(x78581),f120(x78581)),x78582),f120(x78581))+P107(f334(f334(f336(f928(x78581)),f710(x78582,x78581)),f334(f179(f928(x78581)),x78582))) % 188.18/188.25 [7859]E(f334(f149(f928(x78591),f928(x78591),f141(x78591),f120(x78591)),x78592),f120(x78591))+P107(f334(f334(f336(f928(x78591)),f715(x78592,x78591)),f334(f179(f928(x78591)),x78592))) % 188.18/188.25 [8185]~P119(x81851)+E(f334(f334(f87(x81851),f334(f334(f86(x81851),f84(x81851)),f84(x81851))),f334(f334(f6(a927,x81851),f107(x81851)),f311(a927,f84(a927),x81852))),f334(f334(f87(x81851),f334(f107(x81851),x81852)),f334(f334(f86(x81851),f334(f107(x81851),x81852)),f84(x81851)))) % 188.18/188.25 [8233]P107(f334(f334(f336(a927),x82331),x82332))+~P107(f334(f334(f336(a1),f334(f107(a1),x82331)),f334(f317(a927,a1,f107(a1)),x82332))) % 188.18/188.25 [8390]~P107(f334(f66(x83901),x83902))+E(f334(f317(a927,x83901,f729(x83902,x83901)),f334(f270(a927),f334(f334(f7(a927,a927,a922),f243(a927)),f716(x83902,x83901)))),x83902) % 188.18/188.25 [8663]P56(x86631,x86632)+P107(f334(f334(f336(f934(x86631,x86631)),f334(f334(f260(x86631,x86631),f380(x86632,x86631)),f380(x86632,x86631))),x86632)) % 188.18/188.25 [8664]P40(x86641,x86642)+P107(f334(f334(f336(f934(x86641,x86641)),f334(f334(f260(x86641,x86641),f804(x86642,x86641)),f808(x86642,x86641))),x86642)) % 188.18/188.25 [8665]P40(x86651,x86652)+P107(f334(f334(f336(f934(x86651,x86651)),f334(f334(f260(x86651,x86651),f808(x86652,x86651)),f809(x86652,x86651))),x86652)) % 188.18/188.25 [8666]P41(x86661,x86662)+P107(f334(f334(f336(f934(x86661,x86661)),f334(f334(f260(x86661,x86661),f720(x86662,x86661)),f719(x86662,x86661))),x86662)) % 188.18/188.25 [8667]P41(x86671,x86672)+P107(f334(f334(f336(f934(x86671,x86671)),f334(f334(f260(x86671,x86671),f719(x86672,x86671)),f720(x86672,x86671))),x86672)) % 188.18/188.25 [8668]P54(x86681,x86682)+P107(f334(f334(f336(f934(x86681,x86681)),f334(f334(f260(x86681,x86681),f819(x86682,x86681)),f820(x86682,x86681))),x86682)) % 188.18/188.25 [8928]~P107(f334(f334(f243(f935(a927,a922)),x89281),x89282))+P107(f334(f334(f243(f935(a1,a922)),f334(f317(a927,a1,f107(a1)),x89281)),f334(f317(a927,a1,f107(a1)),x89282))) % 188.18/188.25 [8962]~P95(x89621)+E(f334(f334(f23(x89621),f84(x89621)),f334(f111(x89621),x89622)),f334(f111(x89621),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f334(f85(a1),x89622)))) % 188.18/188.25 [9038]~P107(f334(f334(f336(a927),x90381),f334(f179(a927),x90382)))+P107(f334(f334(f242(a927),x90381),f334(f149(a927,a927,f86(a927),f2(a927)),x90382))) % 188.18/188.25 [9136]P48(x91361,x91362)+~P107(f334(f334(f336(f934(x91361,x91361)),f334(f334(f260(x91361,x91361),f359(x91362,x91361)),f359(x91362,x91361))),x91362)) % 188.18/188.25 [9137]P40(x91371,x91372)+~P107(f334(f334(f336(f934(x91371,x91371)),f334(f334(f260(x91371,x91371),f804(x91372,x91371)),f809(x91372,x91371))),x91372)) % 188.18/188.25 [9138]P54(x91381,x91382)+~P107(f334(f334(f336(f934(x91381,x91381)),f334(f334(f260(x91381,x91381),f820(x91382,x91381)),f819(x91382,x91381))),x91382)) % 188.18/188.25 [9271]~P107(f334(f334(f242(f935(a1,a922)),f334(f317(a927,a1,f107(a1)),x92711)),f334(f317(a927,a1,f107(a1)),x92712)))+P107(f334(f334(f242(f935(a927,a922)),x92711),x92712)) % 188.18/188.25 [9272]~P107(f334(f334(f243(f935(a1,a922)),f334(f317(a927,a1,f107(a1)),x92721)),f334(f317(a927,a1,f107(a1)),x92722)))+P107(f334(f334(f243(f935(a927,a922)),x92721),x92722)) % 188.18/188.25 [10238]~P105(x102381)+E(f123(f928(x102381),f334(f136(f928(x102381)),f120(x102381)),f334(f334(f334(f103(f929(f928(x102381))),f334(f334(f243(a1),f2(a1)),x102382)),f334(f125(f934(x102381,f928(x102381)),f928(x102381),f138(x102381,f928(x102381),f139(x102381,f334(f334(f23(a1),x102382),f84(a1))),f139(f928(x102381),f334(f334(f23(a1),x102382),f84(a1))))),f334(f265(x102381,f928(x102381),f929(f928(x102381))),f334(f334(f8(f935(f928(x102381),f928(x102381)),f935(f928(x102381),f929(f928(x102381))),x102381),f334(f8(f928(x102381),f929(f928(x102381)),f928(x102381)),f136(f928(x102381)))),f158(x102381))))),f122(f928(x102381)))),f139(f928(x102381),x102382)) % 188.18/188.25 [10259]~P107(f334(f66(x102591),x102592))+E(f334(f196(f928(x102591)),f96(f928(x102591),f334(f334(f18(f928(x102591),a922,a922),f334(f334(f8(a922,f935(a922,a922),f928(x102591)),a332),f334(f334(f7(f928(x102591),f935(x102591,a922),a922),f334(f334(f8(f935(x102591,a922),f935(f935(x102591,a922),a922),f928(x102591)),a331),f179(x102591))),x102592))),f144(x102591)))),f223(x102591,x102592)) % 188.18/188.25 [6318]E(f334(f334(f86(a927),f334(f334(f23(a927),x63181),x63182)),x63182),x63181)+~P107(f334(f334(f242(a927),x63182),x63181)) % 188.18/188.25 [6389]E(f334(f334(f41(a927),f334(f334(f87(a927),x63891),x63892)),x63892),x63891)+~P107(f334(f334(f243(a927),f2(a927)),x63892)) % 188.18/188.25 [6390]E(f334(f334(f41(a927),f334(f334(f87(a927),x63901),x63902)),x63901),x63902)+~P107(f334(f334(f243(a927),f2(a927)),x63901)) % 188.18/188.25 [6396]~P76(x63961)+E(f334(f334(f6(a927,x63961),f334(f171(x63961),x63962)),f334(f310(a927,f2(a927)),f334(f196(f928(x63961)),x63962))),f334(f172(x63961),x63962)) % 188.18/188.25 [6501]E(f50(a927,f334(a119,f334(f334(f87(a927),x65011),x65012)),x65011),f84(a927))+~P107(f334(f334(f243(a927),f84(a927)),x65011)) % 188.18/188.25 [6507]E(f334(a119,f334(f334(f86(a927),f334(f111(a927),x65071)),x65072)),f334(f334(f86(a927),f84(a927)),x65072))+~P107(f334(a200,f334(f111(a1),x65071))) % 188.18/188.25 [6536]E(f334(a112,f334(f334(f252(a1),f334(f111(a1),x65361)),x65362)),f334(f334(f252(a927),f334(f111(a927),x65361)),x65362))+P107(f334(a200,f334(f111(a1),x65361))) % 188.18/188.25 [6773]E(f334(f334(f23(a927),x67731),f334(f111(a927),f334(f334(f86(a1),x67732),a104))),f334(f334(f23(a927),f334(a119,x67731)),f334(f111(a927),x67732)))+~P107(f334(f334(f243(a1),a89),x67732)) % 188.18/188.25 [6854]E(x68541,f2(a927))+E(f334(a119,f334(f334(f86(a927),f334(f334(f23(a927),x68541),f84(a927))),x68542)),f334(f334(f86(a927),x68541),x68542)) % 188.18/188.25 [6893]E(x68931,f2(a1))+P107(f334(f334(f243(a1),f2(a1)),f334(f334(f252(a1),f334(f81(a1),x68931)),x68932))) % 188.18/188.25 [6908]~E(x69082,f2(a927))+P107(f334(f334(f243(a1),f2(a1)),f334(f334(f252(a1),f334(f81(a1),x69081)),x69082))) % 188.18/188.25 [6946]E(x69461,f2(a927))+E(f334(f334(f86(a927),x69462),f334(f334(f87(a927),f334(f334(f23(a927),x69461),f84(a927))),x69462)),f334(f334(f87(a927),x69461),x69462)) % 188.18/188.25 [6992]~P107(f334(f334(f242(a1),x69921),x69922))+P107(f334(f334(f243(a1),f334(f334(f86(a1),x69921),a104)),x69922)) % 188.18/188.25 [7112]E(f334(f334(f158(a927),x71121),f146(a927,f334(f310(a927,f334(a119,x71121)),x71122))),f146(a927,f334(f310(a927,x71121),x71122)))+~P107(f334(f334(f243(a927),x71121),x71122)) % 188.18/188.25 [7313]E(x73131,f120(x73132))+E(f274(x73132,f334(f334(f161(x73132,f934(a106,x73132)),f334(f260(a106,x73132),f84(a106))),x73131)),f283(x73132,x73131)) % 188.18/188.25 [7544]P107(f334(f334(f242(a1),x75441),x75442))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),x75441),a104)),x75442)) % 188.18/188.25 [7545]E(x75451,x75452)+~E(f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x75451)),x75451),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x75452)),x75452)) % 188.18/188.25 [7999]~P107(f334(f334(f243(a927),x79991),x79992))+P107(f334(f334(f336(f934(a927,a927)),f334(f334(f260(a927,a927),x79991),x79992)),a248)) % 188.18/188.25 [8210]~P107(f334(f334(f243(a106),f2(a106)),x82101))+P107(f334(f334(f243(a106),f334(f259(a106,f934(a106,a106)),f334(f275(x82101),x82102))),x82101)) % 188.18/188.25 [8470]~P40(x84701,x84702)+P40(x84701,f334(f334(f108(f935(f934(x84701,x84701),a922)),x84702),f314(x84701,f195(f935(f934(x84701,x84701),a922))))) % 188.18/188.25 [8471]~P41(x84711,x84712)+P41(x84711,f334(f334(f108(f935(f934(x84711,x84711),a922)),x84712),f314(x84711,f195(f935(f934(x84711,x84711),a922))))) % 188.18/188.25 [8520]~P86(x85201)+P107(f334(f334(f242(x85201),f334(f81(x85201),f334(f172(x85201),x85202))),f334(f172(x85201),f334(f334(f161(x85201,x85201),f81(x85201)),x85202)))) % 188.18/188.25 [8545]P107(f334(f334(f243(a927),x85451),x85452))+~P107(f334(f334(f336(f934(a927,a927)),f334(f334(f260(a927,a927),x85451),x85452)),a248)) % 188.18/188.25 [8687]E(f334(f334(f260(x86871,x86871),f628(x86872,x86871)),f628(x86872,x86871)),x86872)+~P107(f334(f334(f336(f934(x86871,x86871)),x86872),f314(x86871,f195(f935(f934(x86871,x86871),a922))))) % 188.18/188.25 [8733]E(f334(f310(a927,x87331),f334(f334(f86(a927),x87331),f334(f40(a927),x87332))),x87332)+~P107(f334(f334(f242(f935(a927,a922)),x87332),f334(f310(a927,x87331),f334(f334(f86(a927),x87331),f334(f40(a927),x87332))))) % 188.18/188.25 [8956]P41(x89561,x89562)+~P41(x89561,f334(f334(f108(f935(f934(x89561,x89561),a922)),x89562),f314(x89561,f195(f935(f934(x89561,x89561),a922))))) % 188.18/188.25 [9180]~P40(x91801,x91802)+P107(f334(f334(f242(f935(f934(x91801,x91801),a922)),f334(f334(f295(x91801,x91801,x91801),x91802),x91802)),x91802)) % 188.18/188.25 [9206]E(f184(f928(x92061),f334(f334(f8(a922,a922,f928(x92061)),a329),f334(f334(f7(f928(x92061),f928(x92061),a922),a331),f120(x92061))),x92062),f186(x92061,f186(x92061,x92062)))+~P15(a927,f334(f175(a927),f334(f334(f161(f928(x92061),a927),f196(f928(x92061))),x92062))) % 188.18/188.25 [10070]P107(f334(a200,x100702))+E(f334(f334(f94(a1,a927),f334(f334(f23(a1),x100701),x100702)),f334(f334(f18(a1,a927,a927),f334(f334(f7(a1,a927,f935(a927,a927)),f334(f334(f8(a922,f935(a927,f935(a927,a927)),a1),f103(a927)),a200)),f2(a927))),a112)),f334(f334(f23(a927),f334(a112,x100701)),f334(a112,x100702))) % 188.18/188.25 [10082]E(f334(f334(f94(a1,a927),f334(f111(a1),f334(f334(f86(a1),x100821),f334(f85(a1),x100822)))),f334(f334(f18(a1,a927,a927),f334(f334(f7(a1,a927,f935(a927,a927)),f334(f334(f8(a922,f935(a927,f935(a927,a927)),a1),f103(a927)),a200)),f2(a927))),a112)),f334(f334(f23(a927),f334(f111(a927),x100821)),f334(f111(a927),x100822)))+P107(f334(f334(f243(a1),x100822),a89)) % 188.18/188.25 [10083]~P29(x100831,x100832)+P107(f334(f334(f242(f935(f934(x100831,x100831),a922)),f334(f334(f295(x100831,x100831,x100831),f334(f259(f935(f934(x100831,x100831),a922),f935(f934(x100831,x100831),a922)),x100832)),f334(f264(f935(f934(x100831,x100831),a922),f935(f934(x100831,x100831),a922)),x100832))),f334(f259(f935(f934(x100831,x100831),a922),f935(f934(x100831,x100831),a922)),x100832))) % 188.18/188.25 [10128]~E(f334(f40(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,f935(a927,a922),a922),f336(a927)),x101281))),f334(f334(f7(a927,a927,a922),f243(a927)),f334(a119,x101282))))),f2(a927))+~P107(f334(f334(f336(a927),f2(a927)),x101281)) % 188.18/188.25 [10227]~P7(x102271)+E(f42(x102271,f334(f270(x102271),f334(f334(f8(f935(x102271,a922),a922,x102271),f93(x102271)),f334(f334(f8(f935(x102271,a922),f935(x102271,a922),x102271),f334(f18(x102271,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102271),a337),f334(f334(f7(x102271,f935(x102271,a922),a922),f336(x102271)),x102272)))),f242(x102271))))),f43(x102271,x102272)) % 188.18/188.25 [10254]~P39(x102541,x102542)+P63(x102541,f334(f334(f7(x102541,f935(f934(x102541,x102541),a922),f935(x102541,a922)),f334(f334(f8(f935(x102541,f935(f935(f934(x102541,x102541),a922),a922)),f935(f935(f934(x102541,x102541),a922),f935(x102541,a922)),x102541),f7(x102541,f935(f934(x102541,x102541),a922),a922)),f334(f334(f8(f935(x102541,f934(x102541,x102541)),f935(x102541,f935(f935(f934(x102541,x102541),a922),a922)),x102541),f334(f8(f934(x102541,x102541),f935(f935(f934(x102541,x102541),a922),a922),x102541),f336(f934(x102541,x102541)))),f260(x102541,x102541)))),x102542)) % 188.18/188.25 [10255]~P10(x102551,f250(f935(x102551,a922)),x102552)+P9(x102551,f334(f334(f7(x102551,f935(f934(x102551,x102551),a922),f935(x102551,a922)),f334(f334(f8(f935(x102551,f935(f935(f934(x102551,x102551),a922),a922)),f935(f935(f934(x102551,x102551),a922),f935(x102551,a922)),x102551),f7(x102551,f935(f934(x102551,x102551),a922),a922)),f334(f334(f8(f935(x102551,f934(x102551,x102551)),f935(x102551,f935(f935(f934(x102551,x102551),a922),a922)),x102551),f334(f8(f934(x102551,x102551),f935(f935(f934(x102551,x102551),a922),a922),x102551),f336(f934(x102551,x102551)))),f260(x102551,x102551)))),x102552)) % 188.18/188.25 [10292]P39(x102921,x102922)+~P63(x102921,f334(f334(f7(x102921,f935(f934(x102921,x102921),a922),f935(x102921,a922)),f334(f334(f8(f935(x102921,f935(f935(f934(x102921,x102921),a922),a922)),f935(f935(f934(x102921,x102921),a922),f935(x102921,a922)),x102921),f7(x102921,f935(f934(x102921,x102921),a922),a922)),f334(f334(f8(f935(x102921,f934(x102921,x102921)),f935(x102921,f935(f935(f934(x102921,x102921),a922),a922)),x102921),f334(f8(f934(x102921,x102921),f935(f935(f934(x102921,x102921),a922),a922),x102921),f336(f934(x102921,x102921)))),f260(x102921,x102921)))),x102922)) % 188.18/188.25 [10293]P10(x102931,f250(f935(x102931,a922)),x102932)+~P9(x102931,f334(f334(f7(x102931,f935(f934(x102931,x102931),a922),f935(x102931,a922)),f334(f334(f8(f935(x102931,f935(f935(f934(x102931,x102931),a922),a922)),f935(f935(f934(x102931,x102931),a922),f935(x102931,a922)),x102931),f7(x102931,f935(f934(x102931,x102931),a922),a922)),f334(f334(f8(f935(x102931,f934(x102931,x102931)),f935(x102931,f935(f935(f934(x102931,x102931),a922),a922)),x102931),f334(f8(f934(x102931,x102931),f935(f935(f934(x102931,x102931),a922),a922),x102931),f336(f934(x102931,x102931)))),f260(x102931,x102931)))),x102932)) % 188.18/188.25 [7498]E(f334(f334(f86(a927),f334(f111(a927),f334(f334(f23(a1),x74981),a104))),x74982),f334(a119,f334(f334(f86(a927),f334(f111(a927),x74981)),x74982)))+P107(f334(a200,f334(f111(a1),x74981))) % 188.18/188.25 [7980]~P95(x79801)+E(f334(f334(f86(x79801),f334(f334(f86(x79801),f84(x79801)),f334(f111(x79801),x79802))),f334(f111(x79801),x79802)),f334(f111(x79801),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x79802)),x79802))) % 188.18/188.25 [9328]~P107(f334(f334(f242(a1),x93281),x93282))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93281)),x93281)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93282)),x93282))) % 188.18/188.25 [9330]~P107(f334(f334(f243(a1),x93301),x93302))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93301)),x93301)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93302)),x93302))) % 188.18/188.25 [9564]~P107(f334(f66(x95641),x95642))+P107(f334(f66(f935(x95641,a922)),f334(f270(f935(x95641,a922)),f334(f334(f7(f935(x95641,a922),f935(x95641,a922),a922),f242(f935(x95641,a922))),x95642)))) % 188.18/188.25 [9589]P107(f334(f334(f242(a1),x95891),x95892))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95891)),x95891)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95892)),x95892))) % 188.18/188.25 [9591]P107(f334(f334(f243(a1),x95911),x95912))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95911)),x95911)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95912)),x95912))) % 188.18/188.25 [9617]~E(f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),x96171),f195(f935(f934(a927,a927),a922)))),f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),x96172),f195(f935(f934(a927,a927),a922)))))+P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),x96171),x96172)),a116)) % 188.18/188.25 [9694]E(f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),x96941),f195(f935(f934(a927,a927),a922)))),f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),x96942),f195(f935(f934(a927,a927),a922)))))+~P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),x96941),x96942)),a116)) % 188.18/188.25 [9742]P107(f334(f334(f242(a1),f2(a1)),f651(x97421,x97422)))+E(f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x97421)),f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x97422))) % 188.18/188.25 [9857]~P107(f334(f334(f242(a1),x98571),x98572))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98571)),x98571)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98572)),x98572))) % 188.18/188.25 [9859]~P107(f334(f334(f242(a1),x98591),x98592))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98591)),x98591)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98592)),x98592))) % 188.18/188.25 [10012]P107(f334(f334(f242(a1),x100121),x100122))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100121)),x100121)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100122)),x100122))) % 188.18/188.25 [10014]P107(f334(f334(f242(a1),x100141),x100142))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100141)),x100141)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100142)),x100142))) % 188.18/188.25 [10235]~P7(x102351)+E(f43(x102351,f334(f270(x102351),f334(f334(f8(f935(x102351,a922),a922,x102351),f93(x102351)),f334(f334(f8(f935(x102351,a922),f935(x102351,a922),x102351),f334(f18(x102351,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102351),a337),f334(f334(f7(x102351,f935(x102351,a922),a922),f336(x102351)),x102352)))),f334(f7(x102351,x102351,a922),f242(x102351)))))),f42(x102351,x102352)) % 188.18/188.25 [10258]P107(f334(f334(f336(a927),f2(a927)),x102581))+E(f334(f40(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,f935(a927,a922),a922),f334(f334(f8(a927,f935(f935(a927,a922),a922),a927),f336(a927)),a119)),x102581))),f334(f334(f7(a927,a927,a922),f243(a927)),x102582)))),f334(f40(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,f935(a927,a922),a922),f336(a927)),x102581))),f334(f334(f7(a927,a927,a922),f243(a927)),f334(a119,x102582)))))) % 188.18/188.25 [8042]~P95(x80421)+E(f334(f334(f87(x80421),x80422),f334(f111(x80421),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),x80422) % 188.18/188.25 [8268]~P95(x82681)+E(f334(f334(f86(x82681),f334(f111(x82681),x82682)),f84(x82681)),f334(f111(x82681),f334(f334(f86(a1),x82682),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))) % 188.18/188.25 [8310]P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x83102)))+E(f334(f334(f252(a1),x83101),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x83102)),x83102))),f84(a1)) % 188.18/188.25 [9335]E(x93351,x93352)+~E(f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93351)),x93351)),a104),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x93352)),x93352)),a104)) % 188.18/188.25 [9600]~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x96002)))+E(f334(f334(f252(a1),x96001),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x96002)),x96002))),f334(f334(f94(a1,a1),f334(f334(f252(a1),x96001),f334(f111(a927),x96002))),f334(f334(f18(a1,a1,a1),f334(f334(f8(a1,f935(a1,a1),a1),f87(a1)),f334(f87(a1),x96001))),f5(a1)))) % 188.18/188.25 [9981]~P107(f334(f334(f242(a927),f663(x99812,x99811)),f334(x99811,f663(x99812,x99811))))+P107(f334(f66(a927),f334(f270(a927),f334(f334(f7(a927,a927,a922),f334(f334(f8(a927,f935(a927,a922),a927),f242(a927)),x99811)),x99812)))) % 188.18/188.25 [10119]~P107(f334(f334(f242(a927),f334(f111(a927),x101191)),f334(a119,x101192)))+P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x101191),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),f242(a927)),a112)),x101192)))) % 188.18/188.25 [10120]~P107(f334(f334(f243(a927),f334(f111(a927),x101201)),f334(a119,x101202)))+P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x101201),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),f243(a927)),a112)),x101202)))) % 188.18/188.25 [10155]P107(f334(f334(f242(a927),f334(f111(a927),x101551)),f334(a119,x101552)))+~P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x101551),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),f242(a927)),a112)),x101552)))) % 188.18/188.25 [10156]P107(f334(f334(f243(a927),f334(f111(a927),x101561)),f334(a119,x101562)))+~P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x101561),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),f243(a927)),a112)),x101562)))) % 188.18/188.25 [10185]~P107(f334(f334(f242(a927),f334(a119,x101852)),f334(f111(a927),x101851)))+P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x101851),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f8(a927,a922,a1),f334(f242(a927),x101852)),a112))))) % 188.18/188.25 [10186]~P107(f334(f334(f243(a927),f334(a119,x101862)),f334(f111(a927),x101861)))+P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x101861),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f8(a927,a922,a1),f334(f243(a927),x101862)),a112))))) % 188.18/188.25 [10225]P107(f334(f334(f242(a927),f334(a119,x102251)),f334(f111(a927),x102252)))+~P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x102252),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f8(a927,a922,a1),f334(f242(a927),x102251)),a112))))) % 188.18/188.25 [10226]P107(f334(f334(f243(a927),f334(a119,x102261)),f334(f111(a927),x102262)))+~P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x102262),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f8(a927,a922,a1),f334(f243(a927),x102261)),a112))))) % 188.18/188.25 [10311]~P107(f334(f334(f336(a927),f2(a927)),x103111))+E(f334(a119,f334(f40(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,f935(a927,a922),a922),f334(f334(f8(a927,f935(f935(a927,a922),a922),a927),f336(a927)),a119)),x103111))),f334(f334(f7(a927,a927,a922),f243(a927)),x103112))))),f334(f40(a927),f334(f270(a927),f334(f334(f18(a927,a922,a922),f334(f334(f8(a922,f935(a922,a922),a927),a332),f334(f334(f7(a927,f935(a927,a922),a922),f336(a927)),x103111))),f334(f334(f7(a927,a927,a922),f243(a927)),f334(a119,x103112)))))) % 188.18/188.25 [8893]~P95(x88931)+E(f334(f334(f87(x88931),f334(f111(x88931),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),x88932),x88932) % 188.18/188.25 [8937]~P95(x89371)+E(f334(f334(f86(x89371),f84(x89371)),f334(f111(x89371),x89372)),f334(f111(x89371),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),x89372))) % 188.18/188.25 [8977]~P95(x89771)+E(f334(f334(f23(x89771),f334(f111(x89771),x89772)),f84(x89771)),f334(f111(x89771),f334(f334(f86(a1),x89772),f334(f85(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))))) % 188.18/188.25 [9071]~P95(x90711)+E(f334(f334(f87(x90711),f334(f334(f86(x90711),f84(x90711)),f84(x90711))),f334(f111(x90711),x90712)),f334(f111(x90711),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x90712)),x90712)),a104))) % 188.18/188.25 [9102]~P107(f334(f334(f243(a927),f334(f111(a927),a89)),x91022))+E(f334(f334(f23(a927),x91021),f334(f334(f23(a927),x91022),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),f334(f334(f23(a927),f334(a119,x91021)),x91022)) % 188.18/188.25 [9125]~P95(x91251)+E(f334(f111(x91251),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x91252)),x91252)),a104)),f334(f334(f86(x91251),f334(f334(f86(x91251),f2(x91251)),f334(f111(x91251),x91252))),f334(f111(x91251),x91252))) % 188.18/188.25 [9709]~P107(f334(f334(f243(a1),x97091),x97092))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97091)),x97091)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97092)),x97092)),a104))) % 188.18/188.25 [9711]~P107(f334(f334(f243(a1),x97111),x97112))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97111)),x97111)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97112)),x97112)),a104))) % 188.18/188.25 [9872]P107(f334(f334(f243(a1),x98721),x98722))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98721)),x98721)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98722)),x98722)),a104))) % 188.18/188.25 [9874]P107(f334(f334(f243(a1),x98741),x98742))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98741)),x98741)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x98742)),x98742)),a104))) % 188.18/188.25 [9928]~P81(x99281)+E(f334(f334(f252(x99281),x99282),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)))),f334(f334(f87(x99281),f334(f334(f87(x99281),x99282),x99282)),x99282)) % 188.18/188.25 [9976]~P107(f334(f334(f242(a1),x99761),x99762))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99761)),x99761)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99762)),x99762)),a104))) % 188.18/188.25 [9978]~P107(f334(f334(f243(a1),x99781),x99782))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99781)),x99781)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x99782)),x99782)),a104))) % 188.18/188.25 [10079]P107(f334(f334(f242(a1),x100791),x100792))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100791)),x100791)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100792)),x100792)),a104))) % 188.18/188.25 [10081]P107(f334(f334(f243(a1),x100811),x100812))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100811)),x100811)),a104)),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x100812)),x100812)),a104))) % 188.18/188.25 [9726]~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x97262)))+E(f334(f334(f41(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97261)),x97261))),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97262)),x97262)),a104))),f334(f334(f41(a1),f334(f111(a1),x97261)),f334(f111(a1),x97262))) % 188.18/188.25 [9749]P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x97492)))+E(f334(f334(f41(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97491)),x97491))),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97492)),x97492)),a104))),f334(f334(f41(a1),f334(f334(f86(a1),f334(f111(a1),x97491)),f84(a1))),f334(f111(a1),x97492))) % 188.18/188.25 [10215]~E(f334(a119,x102152),f334(f111(a927),x102151))+P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x102151),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),a331),a112)),x102152))))) % 188.18/188.25 [10216]~E(f334(f111(a927),x102161),f334(a119,x102162))+P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x102161),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),a331),a112)),x102162))))) % 188.18/188.25 [10261]E(f334(a119,x102611),f334(f111(a927),x102612))+~P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x102612),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),a331),a112)),x102611))))) % 188.18/188.25 [10262]E(f334(f111(a927),x102621),f334(a119,x102622))+~P107(f334(f334(f94(a1,a922),f334(f111(a1),f334(f334(f86(a1),x102621),a104))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a337),f334(f334(f8(a922,a922,a1),a329),a200))),f334(f334(f7(a1,a927,a922),f334(f334(f8(a927,f935(a927,a922),a1),a331),a112)),x102622))))) % 188.18/188.25 [10312]~P17(x103121,x103122)+P107(f334(f334(f336(f935(x103121,a922)),f826(x103122,x103121)),f334(f334(f8(f935(x103121,a922),a922,f935(x103121,a922)),f92(x103121)),f334(f334(f8(f935(x103121,a922),f935(x103121,a922),f935(x103121,a922)),f334(f18(x103121,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103121),a332),f334(f334(f18(x103121,x103121,a922),x103122),f5(x103121))))),f334(f334(f7(f935(x103121,a922),f935(x103121,f935(x103121,a922)),f935(x103121,a922)),f334(f334(f8(f935(f935(x103121,a922),a922),f935(f935(x103121,f935(x103121,a922)),f935(x103121,a922)),f935(x103121,a922)),f8(f935(x103121,a922),a922,x103121)),a331)),x103122))))) % 188.18/188.25 [10383]~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x103832)))+E(f50(a1,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x103831)),x103831)),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x103832)),x103832)),a104))),f334(f334(f86(a1),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f50(a1,f334(f111(a1),x103831),f334(f111(a1),x103832)))),f84(a1))) % 188.18/188.25 [10385]P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x103852)))+E(f50(a1,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x103851)),x103851)),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x103852)),x103852)),a104))),f334(f334(f23(a1),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f50(a1,f334(f334(f86(a1),f334(f111(a1),x103851)),f84(a1)),f334(f111(a1),x103852)))),f84(a1))) % 188.18/188.25 [10165]~P119(x101651)+E(f334(f334(f87(x101651),x101652),x101652),f334(f334(f252(x101651),x101652),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.25 [10166]~P81(x101661)+E(f334(f334(f252(x101661),x101662),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f87(x101661),x101662),x101662)) % 188.18/188.25 [10167]~P95(x101671)+E(f334(f334(f87(x101671),x101672),f334(f111(x101671),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f86(x101671),x101672),x101672)) % 188.18/188.25 [10242]~P142(x102421)+E(f334(f334(f252(x102421),f334(f85(x102421),x102422)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f252(x102421),x102422),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.25 [10243]~P124(x102431)+E(f334(f334(f252(x102431),f334(f81(x102431),x102432)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f252(x102431),x102432),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.25 [10241]~P95(x102411)+E(f334(f334(f87(x102411),f334(f111(x102411),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x102412),f334(f334(f86(x102411),x102412),x102412)) % 188.18/188.25 [10282]~P124(x102821)+E(f334(f81(x102821),f334(f334(f252(x102821),x102822),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x102821),x102822),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.25 [10301]~P124(x103011)+P107(f334(f334(f242(x103011),f2(x103011)),f334(f334(f252(x103011),x103012),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.25 [10299]~P95(x102991)+E(f334(f334(f252(x102991),f334(f111(x102991),a104)),f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x102992)),f84(x102991)) % 188.18/188.25 [10300]~P142(x103001)+E(f334(f334(f252(x103001),f334(f85(x103001),f84(x103001))),f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103002)),f84(x103001)) % 188.18/188.25 [10410]~P107(f334(f334(f242(a1),f2(a1)),x104102))+E(f50(a1,f334(f334(f86(a1),f84(a1)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104101)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104102)),f334(f334(f86(a1),f84(a1)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f50(a1,x104101,x104102)))) % 188.18/188.25 [10423]~P107(f334(f334(f242(a1),f2(a1)),x104232))+E(f334(f334(f41(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104231))),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104232)),f334(f334(f41(a1),x104231),x104232)) % 188.18/188.25 [10424]~P107(f334(f334(f242(a1),x104242),f2(a1)))+E(f334(f334(f41(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104241))),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104242)),f334(f334(f41(a1),f334(f334(f86(a1),x104241),f84(a1))),x104242)) % 188.18/188.25 [10425]~P107(f334(f334(f242(a1),x104252),f2(a1)))+E(f50(a1,f334(f334(f86(a1),f84(a1)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104251)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104252)),f334(f334(f23(a1),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f50(a1,f334(f334(f86(a1),x104251),f84(a1)),x104252))),f84(a1))) % 188.18/188.25 [10366]~P95(x103661)+E(f334(f334(f252(x103661),f334(f111(x103661),a104)),f334(a119,f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103662))),f334(f111(x103661),a104)) % 188.18/188.25 [10368]~P142(x103681)+E(f334(f334(f252(x103681),f334(f85(x103681),f84(x103681))),f334(a119,f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103682))),f334(f85(x103681),f84(x103681))) % 188.18/188.25 [5185]P40(x51851,x51852)+~P10(x51851,x51853,x51852) % 188.18/188.25 [5187]P54(x51871,x51872)+~P10(x51871,x51873,x51872) % 188.18/188.25 [5356]~P10(x53561,x53562,x53563)+P55(x53561,x53562,x53563) % 188.18/188.25 [8248]~E(x82482,x82483)+P36(x82481,x82481,a331,x82482,x82483) % 188.18/188.25 [8789]E(x87891,x87892)+~P36(x87893,x87893,a331,x87891,x87892) % 188.18/188.25 [4994]E(f176(x49941,x49942,x49943),f120(x49941))+~E(x49942,f2(a927)) % 188.18/188.25 [5161]~E(f176(x51612,x51611,x51613),f120(x51612))+E(x51611,f2(a927)) % 188.18/188.25 [5361]~P39(x53611,x53613)+P39(x53611,f328(x53611,x53612,x53613)) % 188.18/188.25 [5471]~P31(x54711,x54712,x54713)+P33(a1,x54711,f185(x54712,x54713)) % 188.18/188.25 [5543]P31(x55431,x55432,x55433)+~P33(a1,x55431,f185(x55432,x55433)) % 188.18/188.25 [5613]~P10(x56131,x56132,x56133)+P10(f928(x56131),f168(x56131,x56132),f165(x56131,x56133)) % 188.18/188.25 [5614]~P55(x56141,x56142,x56143)+P55(f928(x56141),f168(x56141,x56142),f165(x56141,x56143)) % 188.18/188.25 [5725]P57(x57251,x57252,x57253)+~E(f597(x57253,x57252,x57251),f598(x57253,x57252,x57251)) % 188.18/188.25 [5726]P58(x57261,x57262,x57263)+~E(f623(x57263,x57262,x57261),f624(x57263,x57262,x57261)) % 188.18/188.25 [8254]~E(x82542,x82543)+P28(x82541,x82541,f32(x82541),x82542,x82543) % 188.18/188.25 [8797]E(x87971,x87972)+~P28(x87973,x87973,f32(x87973),x87971,x87972) % 188.18/188.25 [4949]~E(f334(f175(x49492),x49491),x49493)+E(x49491,f334(f175(x49492),x49493)) % 188.18/188.25 [4950]~E(x49502,f334(f175(x49501),x49503))+E(f334(f175(x49501),x49502),x49503) % 188.18/188.25 [5000]E(x50001,x50002)+~E(f334(f175(x50003),x50001),f334(f175(x50003),x50002)) % 188.18/188.25 [5211]~P9(x52113,x52111)+P107(f334(f334(x52111,x52112),x52112)) % 188.18/188.25 [5212]~P45(x52123,x52121)+P107(f334(f334(x52121,x52122),x52122)) % 188.18/188.25 [5214]~P63(x52141,x52142)+P107(f334(f322(x52141,x52142),x52143)) % 188.18/188.25 [5278]~P39(x52781,x52782)+P39(f928(x52781),f334(f150(x52781,x52782),x52783)) % 188.18/188.25 [5283]~P107(f334(x52832,x52833))+~E(f334(f270(x52831),x52832),f195(f935(x52831,a922))) % 188.18/188.25 [5284]~P107(f334(x52842,x52843))+~E(f195(f935(x52841,a922)),f334(f270(x52841),x52842)) % 188.18/188.25 [5296]E(x52961,f2(a927))+E(f151(x52962,f176(x52962,x52961,x52963)),x52963) % 188.18/188.25 [5314]~P107(f334(x53141,x53143))+P107(f334(x53141,f96(x53142,x53141))) % 188.18/188.25 [5315]~P107(f334(x53151,x53153))+P107(f334(x53151,f751(x53151,x53152))) % 188.18/188.25 [5327]E(x53271,f2(a927))+E(f334(f148(x53272),f176(x53272,x53271,x53273)),x53273) % 188.18/188.25 [5432]~E(x54322,x54323)+P107(f334(f334(f336(x54321),x54322),f334(a331,x54323))) % 188.18/188.25 [5447]~E(x54472,f2(a927))+E(f334(f179(x54471),f176(x54471,x54472,x54473)),f195(f935(x54471,a922))) % 188.18/188.25 [5493]E(f334(f175(x54931),x54932),f334(f334(f158(x54931),x54933),f120(x54931)))+~E(x54932,f334(f334(f158(x54931),x54933),f120(x54931))) % 188.18/188.25 [5494]~E(x54943,f334(f334(f158(x54941),x54942),f120(x54941)))+E(f334(f334(f158(x54941),x54942),f120(x54941)),f334(f175(x54941),x54943)) % 188.18/188.25 [5539]~P35(x55391,x55392,x55393)+P35(x55391,x55392,f334(f175(x55391),x55393)) % 188.18/188.25 [5540]~P33(x55401,x55402,x55403)+P33(x55401,x55402,f334(f175(x55401),x55403)) % 188.18/188.25 [5544]E(f334(f40(x55441),f833(x55442,x55443,x55441)),x55442)+~E(f334(f40(x55441),x55443),f334(a119,x55442)) % 188.18/188.25 [5551]~P39(x55511,x55513)+P107(f334(f334(f336(x55511),x55512),f323(x55511,x55513))) % 188.18/188.25 [5555]~E(f334(f175(x55552),x55551),f334(f334(f158(x55552),x55553),f120(x55552)))+E(x55551,f334(f334(f158(x55552),x55553),f120(x55552))) % 188.18/188.25 [5556]~E(f334(f334(f158(x55562),x55563),f120(x55562)),f334(f175(x55562),x55561))+E(x55561,f334(f334(f158(x55562),x55563),f120(x55562))) % 188.18/188.25 [5579]E(f91(f934(a927,a927),f53(x55791,x55792)),x55793)+~P107(f334(f53(x55791,x55792),x55793)) % 188.18/188.25 [5617]P35(x56171,x56172,x56173)+~P35(x56171,x56172,f334(f175(x56171),x56173)) % 188.18/188.25 [5618]P33(x56181,x56182,x56183)+~P33(x56181,x56182,f334(f175(x56181),x56183)) % 188.18/188.25 [5656]P107(f334(f334(x56561,x56562),x56562))+~P107(f334(f278(x56563,x56561),x56562)) % 188.18/188.25 [5657]~P107(f334(f334(x56572,x56573),x56573))+P107(f334(f278(x56571,x56572),x56573)) % 188.18/188.25 [5679]~E(x56792,f120(x56791))+P107(f334(f334(f336(f928(x56791)),x56792),f168(x56791,x56793))) % 188.18/188.25 [5688]~P55(x56881,x56882,x56883)+P55(x56881,x56882,f334(f293(x56881,x56881),x56883)) % 188.18/188.25 [5689]~P58(x56891,x56892,x56893)+P58(x56891,x56892,f334(f293(x56891,x56891),x56893)) % 188.18/188.25 [5706]~P5(x57061)+E(f50(x57061,f50(x57061,x57062,x57063),x57063),f50(x57061,x57062,x57063)) % 188.18/188.25 [5808]E(x58081,x58082)+~P107(f334(f334(f336(x58083),x58081),f334(a331,x58082))) % 188.18/188.25 [5859]~P147(x58591)+E(f197(x58591,x58592,f2(a927),x58593),x58593) % 188.18/188.25 [5881]P55(x58811,x58812,x58813)+~P55(x58811,x58812,f334(f293(x58811,x58811),x58813)) % 188.18/188.25 [5882]P58(x58821,x58822,x58823)+~P58(x58821,x58822,f334(f293(x58821,x58821),x58823)) % 188.18/188.25 [5886]~P109(x58862)+E(f157(x58861,x58862,x58863,f120(x58861)),f120(x58861)) % 188.18/188.25 [5898]E(f177(x58981,x58982,f159(x58981,x58983)),f159(x58981,f177(x58981,x58982,x58983)))+~P107(f334(f144(x58981),x58983)) % 188.18/188.25 [5999]~P107(f334(f334(x59993,x59992),x59992))+P107(f334(f334(f336(x59991),x59992),f278(x59991,x59993))) % 188.18/188.25 [6001]E(f334(f143(x60011,x60012),x60013),f120(x60011))+P107(f334(x60012,f686(x60013,x60012,x60011))) % 188.18/188.25 [6060]E(f73(x60601,x60602,x60603),x60602)+P107(f334(x60603,f752(x60602,x60601,x60603))) % 188.18/188.25 [6155]~P107(f334(f144(x61551),x61552))+P107(f334(f144(x61551),f183(x61551,x61552,x61553))) % 188.18/188.25 [6156]~P107(f334(f144(x61561),x61563))+P107(f334(f144(x61561),f177(x61561,x61562,x61563))) % 188.18/188.25 [6157]~P107(f334(f144(x61571),x61573))+P107(f334(f144(x61571),f184(x61571,x61572,x61573))) % 188.18/188.25 [6158]~P107(f334(f144(x61581),x61583))+P107(f334(f144(x61581),f147(x61581,x61582,x61583))) % 188.18/188.25 [6159]~P149(x61591,x61592,x61593)+P107(f334(x61591,f50(a1,x61592,x61593))) % 188.18/188.25 [6174]~P35(x61743,x61741,x61742)+P107(f334(x61741,f764(x61742,x61741,x61743))) % 188.18/188.25 [6175]~P37(x61753,x61751,x61752)+P107(f334(x61751,f770(x61752,x61751,x61753))) % 188.18/188.25 [6176]~P37(x61763,x61761,x61762)+P107(f334(x61761,f782(x61762,x61761,x61763))) % 188.18/188.25 [6177]~P35(x61773,x61771,x61772)+P107(f334(x61771,f810(x61772,x61771,x61773))) % 188.18/188.25 [6178]~P35(x61783,x61781,x61782)+P107(f334(x61781,f812(x61781,x61782,x61783))) % 188.18/188.25 [6182]P107(f334(f334(x61821,x61822),x61822))+~P107(f334(f334(f336(x61823),x61822),f278(x61823,x61821))) % 188.18/188.25 [6197]E(f334(f143(x61971,x61972),x61973),f184(x61971,x61972,x61973))+P107(f334(x61972,f735(x61973,x61972,x61971))) % 188.18/188.25 [6237]~P107(f334(f144(x62371),x62373))+P107(f334(f144(f928(x62371)),f60(x62371,x62372,x62373))) % 188.18/188.25 [6271]~P111(x62711)+E(f334(f334(f109(f935(x62711,a922)),f334(f309(x62711),x62712)),f313(x62711,x62712,x62713)),f195(f935(x62711,a922))) % 188.18/188.25 [6272]~P111(x62721)+E(f334(f334(f109(f935(x62721,a922)),f334(f309(x62721),x62722)),f312(x62721,x62722,x62723)),f195(f935(x62721,a922))) % 188.18/188.25 [6273]~P111(x62731)+E(f334(f334(f109(f935(x62731,a922)),f334(f307(x62731),x62732)),f311(x62731,x62732,x62733)),f195(f935(x62731,a922))) % 188.18/188.25 [6497]E(f334(f143(x64971,x64972),x64973),x64973)+~P107(f334(x64972,f687(x64973,x64972,x64971))) % 188.18/188.25 [6499]E(f334(f334(f316(x64991),f886(x64992,x64993,x64991)),f833(x64992,x64993,x64991)),x64993)+~E(f334(f40(x64991),x64993),f334(a119,x64992)) % 188.18/188.25 [6514]P149(x65141,x65142,x65143)+~P107(f334(x65141,f50(a1,x65142,x65143))) % 188.18/188.25 [6562]P33(x65621,x65622,x65623)+~P107(f334(x65622,f771(x65623,x65622,x65621))) % 188.18/188.25 [6563]P33(x65631,x65632,x65633)+~P107(f334(x65632,f780(x65632,x65633,x65631))) % 188.18/188.25 [6564]P33(x65641,x65642,x65643)+~P107(f334(x65642,f781(x65643,x65642,x65641))) % 188.18/188.25 [6565]P31(x65651,x65652,x65653)+~P107(f334(x65651,f797(x65653,x65652,x65651))) % 188.18/188.25 [6566]P32(x65661,x65662,x65663)+~P107(f334(x65661,f840(x65663,x65662,x65661))) % 188.18/188.25 [6569]E(f184(x65691,x65692,x65693),x65693)+~P107(f334(x65692,f731(x65693,x65692,x65691))) % 188.18/188.25 [6647]~P107(f334(x66472,f569(x66473,x66472,x66471)))+P107(f334(f256(x66471,x66472),x66473)) % 188.18/188.25 [6648]~P107(f334(x66482,f688(x66483,x66482,x66481)))+P107(f334(f167(x66481,x66482),x66483)) % 188.18/188.25 [6894]~P107(f334(f322(x68941,x68942),f363(x68943,x68942,x68941)))+P107(f334(f322(x68941,x68942),x68943)) % 188.18/188.25 [6895]~P107(f334(f322(x68951,x68952),f366(x68953,x68952,x68951)))+P107(f334(f322(x68951,x68952),x68953)) % 188.18/188.25 [7499]~P5(x74991)+E(f334(f334(f86(x74991),f334(f334(f87(x74991),x74992),f334(f334(f41(x74991),x74993),x74992))),f50(x74991,x74993,x74992)),x74993) % 188.18/188.25 [7524]P31(x75241,x75242,x75243)+P107(f334(f334(f336(a1),f797(x75243,x75242,x75241)),f311(a1,x75242,x75243))) % 188.18/188.25 [7936]E(f334(f334(f260(x79361,x79361),f397(x79362,x79363,x79361)),f397(x79362,x79363,x79361)),x79363)+~P107(f334(f334(f336(f934(x79361,x79361)),x79363),f271(x79361,x79362))) % 188.18/188.25 [8056]~P107(f334(f334(f336(x80561),f518(x80563,x80562,x80561)),f323(x80561,x80563)))+P107(f334(f334(f336(x80561),x80562),f323(x80561,x80563))) % 188.18/188.25 [8057]~P107(f334(f334(f336(x80571),f600(x80573,x80572,x80571)),f323(x80571,x80573)))+P107(f334(f334(f336(x80571),x80572),f323(x80571,x80573))) % 188.18/188.25 [8058]~P107(f334(f334(f336(x80581),f603(x80583,x80582,x80581)),f323(x80581,x80583)))+P107(f334(f334(f336(x80581),x80582),f323(x80581,x80583))) % 188.18/188.25 [8146]P35(a1,x81461,f185(x81462,x81463))+P31(f334(f78(a922,a922,a1,a329),x81461),x81462,x81463) % 188.18/188.25 [8229]~P5(x82291)+E(f334(f334(f86(x82291),f334(f334(f87(x82291),f334(f334(f41(x82291),x82292),x82293)),x82293)),f50(x82291,x82292,x82293)),x82292) % 188.18/188.25 [8280]~E(f334(f40(x82801),x82802),f334(a119,x82803))+~P107(f334(f334(f336(x82801),f886(x82803,x82802,x82801)),f833(x82803,x82802,x82801))) % 188.18/188.25 [8705]~P35(a1,x87051,f185(x87052,x87053))+~P31(f334(f78(a922,a922,a1,a329),x87051),x87052,x87053) % 188.18/188.25 [8888]P107(f334(f334(f242(f935(f934(x88881,x88881),a922)),f314(x88881,x88882)),f314(x88881,x88883)))+~P107(f334(f334(f242(f935(f934(x88881,x88881),a922)),x88882),f314(x88881,x88883))) % 188.18/188.25 [9176]E(x91761,f120(x91762))+~P107(f334(f334(f336(f934(f928(x91762),f928(x91762))),f334(f334(f260(f928(x91762),f928(x91762)),x91761),f120(x91762))),f165(x91762,x91763))) % 188.18/188.25 [9200]E(x92001,f120(x92002))+~P107(f334(f334(f336(f934(f928(x92002),f928(x92002))),f334(f334(f260(f928(x92002),f928(x92002)),f120(x92002)),x92001)),f165(x92002,x92003))) % 188.18/188.25 [9313]E(f334(f334(f158(x93131),f704(x93132,x93133,x93131)),f705(x93132,x93133,x93131)),x93133)+~P107(f334(f334(f336(f934(f928(x93131),f928(x93131))),f334(f334(f260(f928(x93131),f928(x93131)),f120(x93131)),x93133)),f154(x93131,x93132))) % 188.18/188.25 [9557]~P128(x95571)+~P107(f334(f334(f243(x95571),f334(f334(f86(x95571),f334(f334(f87(x95571),x95572),x95572)),f334(f334(f87(x95571),x95573),x95573))),f2(x95571))) % 188.18/188.25 [9610]P107(f334(f66(x96101),x96102))+~P107(f334(f334(f336(f934(f935(x96101,a922),f935(x96101,a922))),f334(f334(f260(f935(x96101,a922),f935(x96101,a922)),x96103),x96102)),f321(x96101))) % 188.18/188.25 [9919]~P49(x99191,x99192,x99193)+P107(f334(f334(f242(a1),f334(f334(f78(f934(a1,a1),a1,x99191,f259(a1,a1)),f221(x99191)),f239(x99191,x99192,f236(x99191,x99193)))),f2(a1))) % 188.18/188.25 [9920]~P50(x99201,x99202,x99203)+P107(f334(f334(f243(a1),f334(f334(f78(f934(a1,a1),a1,x99201,f259(a1,a1)),f221(x99201)),f239(x99201,x99202,f236(x99201,x99203)))),f2(a1))) % 188.18/188.25 [10052]P50(x100521,x100522,x100523)+~P107(f334(f334(f243(a1),f334(f334(f78(f934(a1,a1),a1,x100521,f259(a1,a1)),f221(x100521)),f239(x100521,x100522,f236(x100521,x100523)))),f2(a1))) % 188.18/188.25 [10053]P49(x100531,x100532,x100533)+~P107(f334(f334(f242(a1),f334(f334(f78(f934(a1,a1),a1,x100531,f259(a1,a1)),f221(x100531)),f239(x100531,x100532,f236(x100531,x100533)))),f2(a1))) % 188.18/188.25 [10467]~P124(x104671)+~P107(f334(f334(f243(x104671),f334(f334(f86(x104671),f334(f334(f252(x104671),x104672),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104671),x104673),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f2(x104671))) % 188.18/188.25 [4979]~E(x49793,f120(x49791))+E(f334(f334(f141(x49791),x49792),x49793),x49792) % 188.18/188.25 [4980]~E(x49802,f120(x49801))+E(f334(f334(f141(x49801),x49802),x49803),x49803) % 188.18/188.25 [4986]~E(x49862,f2(a927))+E(f334(f334(f182(x49861),x49862),x49863),f120(x49861)) % 188.18/188.25 [4995]~E(x49953,f120(x49951))+E(f334(f334(f182(x49951),x49952),x49953),f120(x49951)) % 188.18/188.25 [5035]~E(x50351,x50353)+E(x50351,f334(f334(f141(x50352),f120(x50352)),x50353)) % 188.18/188.25 [5124]~P1(x51242)+E(f334(f195(f935(x51241,x51242)),x51243),f195(x51242)) % 188.18/188.25 [5125]~P112(x51252)+E(f334(f250(f935(x51251,x51252)),x51253),f250(x51252)) % 188.18/188.25 [5143]E(x51431,f120(x51432))+~E(f334(f334(f141(x51432),x51433),x51431),x51433) % 188.18/188.25 [5144]E(x51441,f120(x51442))+~E(f334(f334(f141(x51442),x51441),x51443),x51443) % 188.18/188.25 [5152]E(x51521,f120(x51522))+~E(f334(f334(f141(x51522),x51523),x51521),f120(x51522)) % 188.18/188.25 [5153]E(x51531,f120(x51532))+~E(f334(f334(f141(x51532),x51531),x51533),f120(x51532)) % 188.18/188.25 [5178]~E(x51782,f2(a927))+E(f334(f334(f87(a927),x51781),x51782),f334(f334(f87(a927),x51783),x51782)) % 188.18/188.25 [5180]~E(x51801,f2(a927))+E(f334(f334(f87(a927),x51801),x51802),f334(f334(f87(a927),x51801),x51803)) % 188.18/188.25 [5237]~P119(x52371)+E(f334(f334(f87(x52371),x52372),x52373),f334(f334(f87(x52371),x52373),x52372)) % 188.18/188.25 [5238]~P119(x52381)+E(f334(f334(f86(x52381),x52382),x52383),f334(f334(f86(x52381),x52383),x52382)) % 188.18/188.25 [5240]~P109(x52401)+E(f334(f334(f246(x52401),x52402),x52403),f334(f334(f246(x52401),x52403),x52402)) % 188.18/188.25 [5242]~P109(x52421)+E(f334(f334(f241(x52421),x52422),x52423),f334(f334(f241(x52421),x52423),x52422)) % 188.18/188.25 [5244]~P98(x52441)+E(f334(f334(f108(x52441),x52442),x52443),f334(f334(f108(x52441),x52443),x52442)) % 188.18/188.25 [5245]~P99(x52451)+E(f334(f334(f108(x52451),x52452),x52453),f334(f334(f108(x52451),x52453),x52452)) % 188.18/188.25 [5246]~P99(x52461)+E(f334(f334(f109(x52461),x52462),x52463),f334(f334(f109(x52461),x52463),x52462)) % 188.18/188.25 [5248]~P104(x52481)+E(f334(f334(f109(x52481),x52482),x52483),f334(f334(f109(x52481),x52483),x52482)) % 188.18/188.25 [5309]E(f50(a927,x53091,x53092),f2(a927))+~E(x53091,f334(f334(f87(a927),x53092),x53093)) % 188.18/188.25 [5310]E(f50(a1,x53101,x53102),f2(a1))+~E(x53101,f334(f334(f87(a1),x53102),x53103)) % 188.18/188.25 [5374]E(x53741,x53742)+~E(f334(f334(f86(a927),x53743),x53741),f334(f334(f86(a927),x53743),x53742)) % 188.18/188.25 [5375]E(x53751,x53752)+~E(f334(f334(f86(a927),x53751),x53753),f334(f334(f86(a927),x53752),x53753)) % 188.18/188.25 [5384]~P3(x53841)+E(f334(f334(f86(x53841),x53842),f334(f85(x53841),x53843)),f334(f334(f23(x53841),x53842),x53843)) % 188.18/188.25 [5385]~P69(x53851)+E(f334(f334(f86(x53851),x53852),f334(f85(x53851),x53853)),f334(f334(f23(x53851),x53852),x53853)) % 188.18/188.25 [5386]~P115(x53861)+E(f334(f334(f86(x53861),x53862),f334(f85(x53861),x53863)),f334(f334(f23(x53861),x53862),x53863)) % 188.18/188.25 [5387]~P91(x53871)+E(f334(f334(f109(x53871),x53872),f334(f85(x53871),x53873)),f334(f334(f23(x53871),x53872),x53873)) % 188.18/188.25 [5388]~P69(x53881)+E(f334(f334(f23(x53881),x53882),f334(f85(x53881),x53883)),f334(f334(f86(x53881),x53882),x53883)) % 188.18/188.25 [5426]~P107(f334(x54263,x54262))+P107(f334(f334(f336(x54261),x54262),x54263)) % 188.18/188.25 [5428]~P72(x54282)+E(f334(f334(f9(x54281,x54282),x54283),f195(f935(x54281,a922))),f84(x54282)) % 188.18/188.25 [5430]~P76(x54302)+E(f334(f334(f6(x54301,x54302),x54303),f195(f935(x54301,a922))),f2(x54302)) % 188.18/188.25 [5465]~P119(x54651)+P59(x54651,x54652,f334(f334(f87(x54651),x54653),x54652)) % 188.18/188.25 [5466]~P119(x54661)+P59(x54661,x54662,f334(f334(f87(x54661),x54662),x54663)) % 188.18/188.25 [5483]~E(x54832,f334(f334(f86(a927),x54831),x54833))+P107(f334(f334(f242(a927),x54831),x54832)) % 188.18/188.25 [5486]~E(x54862,f195(f935(x54861,a922)))+E(f334(f334(f65(x54861),x54862),x54863),f195(f935(f935(x54861,a922),a922))) % 188.18/188.25 [5487]~E(x54872,f195(f935(x54871,a922)))+E(f195(f935(f935(x54871,a922),a922)),f334(f334(f65(x54871),x54872),x54873)) % 188.18/188.25 [5559]~E(f334(f291(x55592,x55593),x55591),f195(f935(x55593,a922)))+E(x55591,f195(f935(f934(x55592,x55593),a922))) % 188.18/188.25 [5560]~E(f334(f272(x55602,x55603),x55601),f195(f935(x55602,a922)))+E(x55601,f195(f935(f934(x55602,x55603),a922))) % 188.18/188.25 [5592]E(f334(f291(x55921,x55922),x55923),f195(f935(x55922,a922)))+~E(x55923,f195(f935(f934(x55921,x55922),a922))) % 188.18/188.25 [5593]E(f334(f272(x55931,x55932),x55933),f195(f935(x55931,a922)))+~E(x55933,f195(f935(f934(x55931,x55932),a922))) % 188.18/188.25 [5596]E(f282(x55961,x55962,x55963),f334(f334(f23(a106),x55962),x55963))+P107(f334(f334(f243(a106),x55962),x55963)) % 188.18/188.25 [5611]P107(f334(x56111,x56112))+~P107(f334(f334(f336(x56113),x56112),x56111)) % 188.18/188.25 [5649]E(x56491,x56492)+~E(f334(f85(f935(x56493,a922)),x56491),f334(f85(f935(x56493,a922)),x56492)) % 188.18/188.25 [5660]~E(x56601,f195(f935(x56602,a922)))+~P107(f334(f334(f336(x56602),x56603),x56601)) % 188.18/188.25 [5690]~E(x56902,f334(f334(f86(a1),x56901),f334(f107(a1),x56903)))+P107(f334(f334(f242(a1),x56901),x56902)) % 188.18/188.25 [5704]E(f334(f334(f316(x57041),x57042),x57043),x57043)+~P107(f334(f334(f336(x57041),x57042),x57043)) % 188.18/188.25 [5715]E(x57151,f195(f935(x57152,a922)))+~E(f334(f334(f65(x57152),x57151),x57153),f195(f935(f935(x57152,a922),a922))) % 188.18/188.25 [5716]E(x57161,f195(f935(x57162,a922)))+~E(f195(f935(f935(x57162,a922),a922)),f334(f334(f65(x57162),x57161),x57163)) % 188.18/188.25 [5722]~P113(x57221)+E(f334(f334(f87(x57221),f334(f85(x57221),x57222)),f334(f85(x57221),x57223)),f334(f334(f87(x57221),x57222),x57223)) % 188.18/188.25 [5724]~P65(x57241)+E(f334(f334(f296(x57241),f334(f85(x57241),x57242)),f334(f85(x57241),x57243)),f334(f334(f296(x57241),x57242),x57243)) % 188.18/188.25 [5754]~P107(f334(x57543,x57542))+P107(f334(f334(f336(x57541),x57542),f334(f270(x57541),x57543))) % 188.18/188.25 [5779]E(x57791,f2(a927))+E(f334(f179(x57792),f176(x57792,x57791,x57793)),f334(f334(f316(x57792),x57793),f195(f935(x57792,a922)))) % 188.18/188.25 [5800]E(f177(x58001,x58002,x58003),x58003)+P107(f334(f334(f336(x58001),x58002),f334(f179(x58001),x58003))) % 188.18/188.25 [5805]~E(x58051,f2(a927))+P59(a927,f334(f334(f87(a927),x58051),x58052),f334(f334(f87(a927),x58051),x58053)) % 188.18/188.25 [5890]~P107(f334(f144(x58901),x58903))+P107(f334(f144(x58901),f334(f143(x58901,x58902),x58903))) % 188.18/188.25 [5935]~P5(x59351)+E(f334(f334(f41(x59351),f50(x59351,x59352,x59353)),x59353),f2(x59351)) % 188.18/188.25 [5954]E(f183(x59541,f334(f334(f158(x59541),x59542),f120(x59541)),x59543),f120(x59541))+P107(f334(f334(f336(a927),f2(a927)),x59543)) % 188.18/188.25 [5960]E(x59601,f2(a927))+E(f334(f178(x59602),f176(x59602,x59601,x59603)),f176(x59602,f334(f334(f23(a927),x59601),f84(a927)),x59603)) % 188.18/188.25 [6011]E(f334(f334(f158(x60111),x60112),x60113),f147(x60111,x60112,x60113))+P107(f334(f334(f336(x60111),x60112),f334(f179(x60111),x60113))) % 188.18/188.25 [6020]E(x60201,x60202)+~E(f334(f334(f87(a927),f334(a119,x60203)),x60201),f334(f334(f87(a927),f334(a119,x60203)),x60202)) % 188.18/188.25 [6021]~E(x60212,f334(f334(f86(a1),x60211),f334(f107(a1),f334(a119,x60213))))+P107(f334(f334(f243(a1),x60211),x60212)) % 188.18/188.25 [6082]~P32(x60821,x60822,x60823)+P33(a927,x60821,f146(a927,f334(f310(a927,x60822),x60823))) % 188.18/188.25 [6130]~P59(a927,x61302,x61303)+P59(a927,f334(f334(f87(a927),x61301),x61302),f334(f334(f87(a927),x61301),x61303)) % 188.18/188.25 [6136]~E(x61363,f120(x61361))+E(f334(f334(f334(f190(f928(x61361),f928(x61361)),x61362),f174(x61361)),x61363),f120(x61361)) % 188.18/188.25 [6140]P107(f334(x61401,x61402))+~P107(f334(f334(f336(x61403),x61402),f334(f270(x61403),x61401))) % 188.18/188.25 [6170]E(x61701,x61702)+~E(f334(f334(f316(x61703),x61701),f195(f935(x61703,a922))),f334(f334(f316(x61703),x61702),f195(f935(x61703,a922)))) % 188.18/188.25 [6184]~P111(x61841)+E(f334(f334(f109(f935(x61841,a922)),f334(f307(x61841),x61842)),f334(f310(x61841,x61842),x61843)),f195(f935(x61841,a922))) % 188.18/188.25 [6223]E(f147(x62231,x62232,x62233),x62233)+~P107(f334(f334(f336(x62231),x62232),f334(f179(x62231),x62233))) % 188.18/188.25 [6244]~P79(x62441)+E(f334(f317(x62441,x62441,f85(x62441)),f334(f310(x62441,x62442),x62443)),f312(x62441,f334(f85(x62441),x62443),f334(f85(x62441),x62442))) % 188.18/188.25 [6258]E(f334(f196(f928(x62581)),f177(x62581,x62582,x62583)),f334(f196(f928(x62581)),x62583))+P107(f334(f334(f336(x62581),x62582),f334(f179(x62581),x62583))) % 188.18/188.25 [6307]~P111(x63071)+E(f334(f334(f109(f935(x63071,a922)),f334(f310(x63071,x63072),x63073)),f334(f290(x63071),x63073)),f195(f935(x63071,a922))) % 188.18/188.25 [6327]~P79(x63271)+E(f334(f317(x63271,x63271,f85(x63271)),f313(x63271,x63272,x63273)),f313(x63271,f334(f85(x63271),x63273),f334(f85(x63271),x63272))) % 188.18/188.25 [6328]~P79(x63281)+E(f334(f317(x63281,x63281,f85(x63281)),f311(x63281,x63282,x63283)),f311(x63281,f334(f85(x63281),x63283),f334(f85(x63281),x63282))) % 188.18/188.25 [6391]E(f183(x63911,f334(f334(f158(x63911),x63912),f120(x63911)),x63913),f334(f334(f158(x63911),x63912),f120(x63911)))+~P107(f334(f334(f336(a927),f2(a927)),x63913)) % 188.18/188.25 [6398]P32(x63981,x63982,x63983)+~P33(a927,x63981,f146(a927,f334(f310(a927,x63982),x63983))) % 188.18/188.25 [6401]~P79(x64011)+E(f334(f317(x64011,x64011,f85(x64011)),f312(x64011,x64012,x64013)),f334(f310(x64011,f334(f85(x64011),x64013)),f334(f85(x64011),x64012))) % 188.18/188.25 [6421]~P6(x64211)+E(f50(x64211,f334(f85(x64211),f50(x64211,x64212,x64213)),x64213),f50(x64211,f334(f85(x64211),x64212),x64213)) % 188.18/188.25 [6512]~P107(f334(f66(f934(x65122,x65121)),x65123))+P107(f334(f66(x65121),f334(f291(x65122,x65121),x65123))) % 188.18/188.25 [6513]~P107(f334(f66(f934(x65131,x65132)),x65133))+P107(f334(f66(x65131),f334(f272(x65131,x65132),x65133))) % 188.18/188.25 [6518]~P111(x65181)+E(f334(f334(f109(f935(x65181,a922)),f313(x65181,x65182,x65183)),f334(f290(x65181),x65183)),f195(f935(x65181,a922))) % 188.18/188.25 [6519]~P111(x65191)+E(f334(f334(f109(f935(x65191,a922)),f312(x65191,x65192,x65193)),f334(f308(x65191),x65193)),f195(f935(x65191,a922))) % 188.18/188.25 [6520]~P111(x65201)+E(f334(f334(f109(f935(x65201,a922)),f311(x65201,x65202,x65203)),f334(f308(x65201),x65203)),f195(f935(x65201,a922))) % 188.18/188.25 [6587]E(f334(f334(f171(x65871),x65872),f647(x65872,x65873,x65871)),x65873)+~P107(f334(f334(f336(x65871),x65873),f334(f179(x65871),x65872))) % 188.18/188.25 [6732]E(x67321,f120(x67322))+~E(f334(f334(f334(f190(f928(x67322),f928(x67322)),x67323),f174(x67322)),x67321),f120(x67322)) % 188.18/188.25 [6834]~P107(f334(f66(f934(x68342,x68341)),x68343))+P107(f334(f66(f934(x68341,x68342)),f334(f293(x68342,x68341),x68343))) % 188.18/188.25 [6984]P58(x69841,x69842,x69843)+P107(f334(f334(f336(x69841),f624(x69843,x69842,x69841)),x69842)) % 188.18/188.25 [6985]P58(x69851,x69852,x69853)+P107(f334(f334(f336(x69851),f623(x69853,x69852,x69851)),x69852)) % 188.18/188.25 [6995]P107(f334(f322(x69951,x69952),x69953))+P107(f334(f334(x69952,f363(x69953,x69952,x69951)),x69953)) % 188.18/188.25 [6996]P107(f334(f322(x69961,x69962),x69963))+P107(f334(f334(x69962,f366(x69963,x69962,x69961)),x69963)) % 188.18/188.25 [7022]E(f334(f196(f928(x70221)),f177(x70221,x70222,x70223)),f334(f334(f23(a927),f334(f196(f928(x70221)),x70223)),f84(a927)))+~P107(f334(f334(f336(x70221),x70222),f334(f179(x70221),x70223))) % 188.18/188.25 [7060]P107(f334(f256(x70601,x70602),x70603))+P107(f334(f334(f336(x70601),f569(x70603,x70602,x70601)),x70603)) % 188.18/188.25 [7068]~P107(f334(f66(f934(x70682,x70681)),f334(f293(x70681,x70682),x70683)))+P107(f334(f66(f934(x70681,x70682)),x70683)) % 188.18/188.25 [7125]~P107(f334(f334(f336(x71251),x71252),f334(f179(x71251),f121(x71251,x71253))))+P107(f334(f334(f336(x71251),x71252),f334(f179(x71251),x71253))) % 188.18/188.25 [7158]E(f334(f143(x71581,x71582),x71583),x71583)+P107(f334(f334(f336(x71581),f687(x71583,x71582,x71581)),f334(f179(x71581),x71583))) % 188.18/188.25 [7172]E(f334(f143(x71721,x71722),x71723),f120(x71721))+P107(f334(f334(f336(x71721),f686(x71723,x71722,x71721)),f334(f179(x71721),x71723))) % 188.18/188.25 [7197]P33(x71971,x71972,x71973)+P107(f334(f334(f336(x71971),f771(x71973,x71972,x71971)),f334(f179(x71971),x71973))) % 188.18/188.25 [7198]P33(x71981,x71982,x71983)+P107(f334(f334(f336(x71981),f781(x71983,x71982,x71981)),f334(f179(x71981),x71983))) % 188.18/188.25 [7199]P33(x71991,x71992,x71993)+P107(f334(f334(f336(x71991),f780(x71992,x71993,x71991)),f334(f179(x71991),x71993))) % 188.18/188.25 [7202]E(f184(x72021,x72022,x72023),x72023)+P107(f334(f334(f336(x72021),f731(x72023,x72022,x72021)),f334(f179(x72021),x72023))) % 188.18/188.25 [7277]P107(f334(f167(x72771,x72772),x72773))+P107(f334(f334(f336(x72771),f688(x72773,x72772,x72771)),f334(f179(x72771),x72773))) % 188.18/188.25 [7286]~P35(x72861,x72863,x72862)+P107(f334(f334(f336(x72861),f764(x72862,x72863,x72861)),f334(f179(x72861),x72862))) % 188.18/188.25 [7287]~P37(x72871,x72873,x72872)+P107(f334(f334(f336(x72871),f770(x72872,x72873,x72871)),f334(f179(x72871),x72872))) % 188.18/188.25 [7288]~P37(x72881,x72883,x72882)+P107(f334(f334(f336(x72881),f782(x72882,x72883,x72881)),f334(f179(x72881),x72882))) % 188.18/188.25 [7289]~P35(x72891,x72893,x72892)+P107(f334(f334(f336(x72891),f810(x72892,x72893,x72891)),f334(f179(x72891),x72892))) % 188.18/188.25 [7290]~P35(x72901,x72902,x72903)+P107(f334(f334(f336(x72901),f812(x72902,x72903,x72901)),f334(f179(x72901),x72903))) % 188.18/188.25 [7323]P107(f334(f334(f336(x73231),x73232),f649(x73233,x73232,x73231)))+~P107(f334(f334(f336(x73231),x73232),f42(f935(x73231,a922),x73233))) % 188.18/188.25 [7324]~P76(x73241)+E(f334(f334(f86(x73241),f334(f334(f6(a927,x73241),x73242),f334(f307(a927),x73243))),f334(x73242,x73243)),f334(f334(f6(a927,x73241),x73242),f334(f307(a927),f334(a119,x73243)))) % 188.18/188.25 [7336]P32(x73361,x73362,x73363)+P107(f334(f334(f336(a927),f840(x73363,x73362,x73361)),f334(f310(a927,x73362),x73363))) % 188.18/188.25 [7414]~P35(x74142,x74141,x74143)+P107(f334(x74141,f334(f334(f171(x74142),x74143),f767(x74143,x74141,x74142)))) % 188.18/188.25 [7426]~P107(f334(f334(f336(x74261),x74262),f609(x74262,x74263,x74261)))+P107(f334(f334(f336(x74261),x74262),f43(f935(x74261,a922),x74263))) % 188.18/188.25 [7459]~P76(x74591)+E(f334(f334(f86(x74591),f334(f334(f6(a927,x74591),x74592),f334(f309(a927),x74593))),f334(x74592,f334(a119,x74593))),f334(f334(f6(a927,x74591),x74592),f334(f309(a927),f334(a119,x74593)))) % 188.18/188.25 [7589]P107(f334(f334(f336(f928(x75891)),x75892),f168(x75891,x75893)))+P107(f334(f334(f336(x75891),f671(x75893,x75892,x75891)),f334(f179(x75891),x75892))) % 188.18/188.25 [7602]~P107(f334(f334(f336(f928(x76021)),x76022),f168(x76021,f323(x76021,x76023))))+P107(f334(f334(f336(f928(x76021)),x76022),f323(f928(x76021),f164(x76021,x76023)))) % 188.18/188.25 [7627]~P107(f334(f334(f336(f928(x76271)),x76272),f323(f928(x76271),f164(x76271,x76273))))+P107(f334(f334(f336(f928(x76271)),x76272),f168(x76271,f323(x76271,x76273)))) % 188.18/188.25 [7660]E(f334(f334(f334(f190(f928(x76601),f928(x76601)),x76602),f174(x76601)),x76603),x76603)+~P107(f334(f334(f242(a927),f334(f196(f928(x76601)),x76603)),f84(a927))) % 188.18/188.25 [7693]E(f334(f334(f141(x76931),f768(x76932,x76933,x76931)),f334(f334(f158(x76931),x76933),f769(x76932,x76933,x76931))),x76932)+~P107(f334(f334(f336(x76931),x76933),f334(f179(x76931),x76932))) % 188.18/188.25 [7694]E(f334(f334(f141(x76941),f774(x76942,x76943,x76941)),f334(f334(f158(x76941),x76943),f775(x76942,x76943,x76941))),x76942)+~P107(f334(f334(f336(x76941),x76943),f334(f179(x76941),x76942))) % 188.18/188.25 [7695]E(f334(f334(f141(x76951),f776(x76952,x76953,x76951)),f334(f334(f158(x76951),x76953),f777(x76952,x76953,x76951))),x76952)+~P107(f334(f334(f336(x76951),x76953),f334(f179(x76951),x76952))) % 188.18/188.25 [7716]~P27(x77161,x77162,x77163,f250(f935(x77161,a922)))+P27(f928(x77161),f928(x77162),f334(f161(x77161,x77162),x77163),f250(f935(f928(x77161),a922))) % 188.18/188.25 [7860]E(x78601,f334(f334(f86(a927),f334(f334(f87(a927),f334(f259(a927,a927),x78602)),x78603)),f334(f264(a927,a927),x78602)))+~P107(f334(f53(x78601,x78603),x78602)) % 188.18/188.25 [7868]P27(x78681,x78682,x78683,f250(f935(x78681,a922)))+~P27(f928(x78681),f928(x78682),f334(f161(x78681,x78682),x78683),f250(f935(f928(x78681),a922))) % 188.18/188.25 [7911]P107(f334(f334(f336(f935(x79111,a922)),f609(x79112,x79113,x79111)),x79113))+P107(f334(f334(f336(x79111),x79112),f43(f935(x79111,a922),x79113))) % 188.18/188.25 [8004]P107(f334(f334(f336(f928(x80041)),x80042),f168(x80041,x80043)))+~P107(f334(f334(f336(x80041),f671(x80043,x80042,x80041)),x80043)) % 188.18/188.25 [8101]P33(x81011,x81012,x81013)+~P107(f334(x81012,f334(f334(f171(x81011),x81013),f773(x81013,x81012,x81011)))) % 188.18/188.25 [8125]E(x81251,x81252)+~E(f334(f334(f7(x81253,f935(x81253,a922),a922),f336(x81253)),x81251),f334(f334(f7(x81253,f935(x81253,a922),a922),f336(x81253)),x81252)) % 188.18/188.25 [8133]~P107(f334(f334(f336(f934(x81331,x81331)),x81333),f271(x81331,x81332)))+P107(f334(f334(f336(x81331),f397(x81332,x81333,x81331)),x81332)) % 188.18/188.25 [8135]~P107(f334(f334(f336(x81351),x81353),f42(f935(x81351,a922),x81352)))+P107(f334(f334(f336(f935(x81351,a922)),f649(x81352,x81353,x81351)),x81352)) % 188.18/188.25 [8249]P27(x82491,x82492,f97(x82492,x82491,f250(f935(x82492,a922)),x82493),f250(f935(x82491,a922)))+~E(f334(f317(x82492,x82491,x82493),f250(f935(x82492,a922))),f250(f935(x82491,a922))) % 188.18/188.25 [8305]~P107(f334(f334(f336(x83051),x83052),f334(f179(x83051),f774(x83053,x83052,x83051))))+~P107(f334(f334(f336(x83051),x83052),f334(f179(x83051),x83053))) % 188.18/188.25 [8306]~P107(f334(f334(f336(x83061),x83062),f334(f179(x83061),f777(x83063,x83062,x83061))))+~P107(f334(f334(f336(x83061),x83062),f334(f179(x83061),x83063))) % 188.18/188.25 [8330]P32(f334(f78(a922,a922,a927,a329),x83301),x83302,x83303)+P35(a927,x83301,f146(a927,f334(f310(a927,x83302),x83303))) % 188.18/188.25 [8491]E(x84911,f120(x84912))+P107(f334(f334(f336(x84912),f334(f259(x84912,f934(a106,a106)),f334(f283(x84912,x84911),x84913))),f334(f179(x84912),x84911))) % 188.18/188.25 [8586]~P71(x85861)+E(f334(f149(x85861,x85861,f334(f7(x85861,x85861,x85861),f86(x85861)),x85862),f334(f175(x85861),x85863)),f334(f149(x85861,x85861,f86(x85861),x85862),x85863)) % 188.18/188.25 [8777]~P27(x87772,x87771,x87773,f250(f935(x87772,a922)))+E(f334(f317(x87771,x87772,f97(x87772,x87771,f250(f935(x87772,a922)),x87773)),f250(f935(x87771,a922))),f250(f935(x87772,a922))) % 188.18/188.25 [8847]~P32(f334(f78(a922,a922,a927,a329),x88471),x88472,x88473)+~P35(a927,x88471,f146(a927,f334(f310(a927,x88472),x88473))) % 188.18/188.25 [9091]~P109(x90911)+E(f334(f179(x90911),f156(x90911,x90911,f5(x90911),x90912,x90913)),f334(f334(f316(x90911),x90912),f334(f179(x90911),x90913))) % 188.18/188.25 [9103]~E(f334(x91033,f334(f97(x91031,x91032,f250(f935(x91031,a922)),x91033),f585(x91033,x91032,x91031))),f585(x91033,x91032,x91031))+E(f334(f317(x91031,x91032,x91033),f250(f935(x91031,a922))),f250(f935(x91032,a922))) % 188.18/188.25 [9105]P107(f334(f334(f243(a927),f2(a927)),f632(x91051,x91052,x91053)))+~P107(f334(f334(f336(f934(x91053,x91053)),x91052),f334(f334(f295(x91053,x91053,x91053),x91051),f314(x91053,x91051)))) % 188.18/188.25 [9377]~P61(x93771,x93772)+~P107(f334(f334(f336(f934(x93771,x93771)),f334(f334(f260(x93771,x93771),x93773),x93773)),f334(f334(f295(x93771,x93771,x93771),x93772),f314(x93771,x93772)))) % 188.18/188.25 [9512]~E(f334(f334(f109(f935(f934(x95121,x95121),a922)),f334(f293(x95121,x95121),x95122)),f314(x95121,x95122)),f195(f935(f934(x95121,x95121),a922)))+~P107(f334(f334(f336(f934(x95121,x95121)),f334(f334(f260(x95121,x95121),x95123),x95123)),f334(f334(f295(x95121,x95121,x95121),x95122),f314(x95121,x95122)))) % 188.18/188.25 [9687]~P107(f334(f66(x96871),x96872))+P107(f334(f334(f242(a927),f334(f40(x96871),f334(f334(f23(f935(x96871,a922)),x96872),f334(f334(f316(x96871),x96873),f195(f935(x96871,a922)))))),f334(f40(x96871),x96872))) % 188.18/188.25 [5298]~E(x52983,f120(x52981))+E(f151(x52981,f334(f334(f158(x52981),x52982),x52983)),x52982) % 188.18/188.25 [5306]~E(x53063,f120(x53061))+E(f121(x53061,f334(f334(f158(x53061),x53062),x53063)),f120(x53061)) % 188.18/188.25 [5336]E(x53361,f120(x53362))+E(f151(x53362,f334(f334(f158(x53362),x53363),x53361)),f151(x53362,x53361)) % 188.18/188.25 [5338]E(x53381,f120(x53382))+E(f151(x53382,f334(f334(f141(x53382),x53383),x53381)),f151(x53382,x53381)) % 188.18/188.25 [5343]~E(x53433,f120(x53431))+E(f121(x53431,f334(f334(f141(x53431),x53432),x53433)),f121(x53431,x53432)) % 188.18/188.25 [5345]~E(x53453,f120(x53451))+E(f151(x53451,f334(f334(f141(x53451),x53452),x53453)),f151(x53451,x53452)) % 188.18/188.25 [5378]E(x53781,f120(x53782))+E(f334(f148(x53782),f334(f334(f141(x53782),x53781),x53783)),f334(f148(x53782),x53781)) % 188.18/188.25 [5406]~E(x54062,f120(x54061))+E(f334(f148(x54061),f334(f334(f141(x54061),x54062),x54063)),f334(f148(x54061),x54063)) % 188.18/188.25 [5457]~P109(x54571)+E(f334(f334(f246(x54571),x54572),f334(f334(f241(x54571),x54572),x54573)),x54572) % 188.18/188.25 [5458]~P109(x54581)+E(f334(f334(f241(x54581),x54582),f334(f334(f246(x54581),x54582),x54583)),x54582) % 188.18/188.25 [5459]~P99(x54591)+E(f334(f334(f108(x54591),x54592),f334(f334(f109(x54591),x54592),x54593)),x54592) % 188.18/188.25 [5460]~P99(x54601)+E(f334(f334(f109(x54601),x54602),f334(f334(f108(x54601),x54602),x54603)),x54602) % 188.18/188.25 [5481]~P5(x54811)+E(f50(x54811,f334(f334(f87(x54811),x54812),x54813),x54813),f2(x54811)) % 188.18/188.25 [5482]~P5(x54821)+E(f50(x54821,f334(f334(f87(x54821),x54822),x54823),x54822),f2(x54821)) % 188.18/188.25 [5554]~P3(x55541)+E(f334(f85(x55541),f334(f334(f23(x55541),x55542),x55543)),f334(f334(f23(x55541),x55543),x55542)) % 188.18/188.25 [5615]E(x56151,f120(x56152))+E(f121(x56152,f334(f334(f158(x56152),x56153),x56151)),f334(f334(f158(x56152),x56153),f121(x56152,x56151))) % 188.18/188.25 [5616]E(x56161,f120(x56162))+E(f121(x56162,f334(f334(f141(x56162),x56163),x56161)),f334(f334(f141(x56162),x56163),f121(x56162,x56161))) % 188.18/188.25 [5619]~P7(x56191)+E(f43(x56191,f334(f334(f316(x56191),x56192),x56193)),f334(f334(f109(x56191),x56192),f43(x56191,x56193))) % 188.18/188.25 [5620]~P7(x56201)+E(f42(x56201,f334(f334(f316(x56201),x56202),x56203)),f334(f334(f108(x56201),x56202),f42(x56201,x56203))) % 188.18/188.25 [5665]~P96(x56651)+E(f334(f334(f87(x56651),x56652),f334(f334(f87(x56651),x56652),x56653)),f334(f334(f87(x56651),x56652),x56653)) % 188.18/188.25 [5667]~P109(x56671)+E(f334(f334(f246(x56671),x56672),f334(f334(f246(x56671),x56672),x56673)),f334(f334(f246(x56671),x56672),x56673)) % 188.18/188.25 [5669]~P109(x56691)+E(f334(f334(f241(x56691),x56692),f334(f334(f241(x56691),x56692),x56693)),f334(f334(f241(x56691),x56692),x56693)) % 188.18/188.25 [5671]~P98(x56711)+E(f334(f334(f108(x56711),x56712),f334(f334(f108(x56711),x56712),x56713)),f334(f334(f108(x56711),x56712),x56713)) % 188.18/188.25 [5672]~P99(x56721)+E(f334(f334(f108(x56721),x56722),f334(f334(f108(x56721),x56722),x56723)),f334(f334(f108(x56721),x56722),x56723)) % 188.18/188.25 [5673]~P99(x56731)+E(f334(f334(f109(x56731),x56732),f334(f334(f109(x56731),x56732),x56733)),f334(f334(f109(x56731),x56732),x56733)) % 188.18/188.25 [5675]~P104(x56751)+E(f334(f334(f109(x56751),x56752),f334(f334(f109(x56751),x56752),x56753)),f334(f334(f109(x56751),x56752),x56753)) % 188.18/188.25 [5682]~P5(x56821)+E(f50(x56821,f334(f334(f86(x56821),x56822),x56823),x56823),f50(x56821,x56822,x56823)) % 188.18/188.25 [5683]~P5(x56831)+E(f50(x56831,f334(f334(f86(x56831),x56832),x56833),x56832),f50(x56831,x56833,x56832)) % 188.18/188.25 [5691]~P113(x56911)+E(f334(f334(f87(x56911),x56912),f334(f85(x56911),x56913)),f334(f85(x56911),f334(f334(f87(x56911),x56912),x56913))) % 188.18/188.25 [5692]~P65(x56921)+E(f334(f334(f296(x56921),x56922),f334(f85(x56921),x56923)),f334(f85(x56921),f334(f334(f296(x56921),x56922),x56923))) % 188.18/188.25 [5693]~P82(x56931)+E(f334(f334(f86(x56931),x56932),f334(f172(x56931),x56933)),f334(f172(x56931),f334(f334(f158(x56931),x56932),x56933))) % 188.18/188.25 [5721]~P113(x57211)+E(f334(f334(f87(x57211),f334(f85(x57211),x57212)),x57213),f334(f334(f87(x57211),x57212),f334(f85(x57211),x57213))) % 188.18/188.25 [5727]~P10(x57271,x57272,x57273)+E(f42(f935(x57271,a922),f334(f334(f65(x57271),x57272),x57273)),x57272) % 188.18/188.25 [5792]~P116(x57921)+E(f334(f334(f87(x57921),x57922),f334(f334(f252(x57921),x57922),x57923)),f334(f334(f252(x57921),x57922),f334(a119,x57923))) % 188.18/188.25 [5793]~P119(x57931)+E(f334(f334(f87(x57931),x57932),f334(f334(f252(x57931),x57932),x57933)),f334(f334(f252(x57931),x57932),f334(a119,x57933))) % 188.18/188.25 [5803]~P69(x58031)+E(f334(f334(f86(x58031),f334(f85(x58031),x58032)),f334(f334(f86(x58031),x58032),x58033)),x58033) % 188.18/188.25 [5827]~P147(x58271)+E(f334(f334(f252(x58271),f334(f107(x58271),x58272)),x58273),f334(f107(x58271),f334(f334(f252(a927),x58272),x58273))) % 188.18/188.25 [5828]~P142(x58281)+E(f334(f334(f252(x58281),f334(f110(x58281),x58282)),x58283),f334(f110(x58281),f334(f334(f252(a1),x58282),x58283))) % 188.18/188.25 [5837]~P86(x58371)+E(f334(f81(x58371),f334(f334(f23(x58371),x58372),x58373)),f334(f81(x58371),f334(f334(f23(x58371),x58373),x58372))) % 188.18/188.25 [5841]~P124(x58411)+E(f334(f334(f87(x58411),f88(x58411,x58412)),f88(x58411,x58413)),f88(x58411,f334(f334(f87(x58411),x58412),x58413))) % 188.18/188.25 [5845]E(x58451,f120(x58452))+E(f334(f334(f141(x58452),f334(f178(x58452),x58451)),x58453),f334(f178(x58452),f334(f334(f141(x58452),x58451),x58453))) % 188.18/188.25 [5850]~E(x58502,f334(a119,f334(f334(f86(a927),x58501),x58503)))+P107(f334(f334(f243(a927),x58501),x58502)) % 188.18/188.25 [5851]~P113(x58511)+E(f334(f334(f87(x58511),f334(f85(x58511),x58512)),x58513),f334(f85(x58511),f334(f334(f87(x58511),x58512),x58513))) % 188.18/188.25 [5852]~P122(x58521)+E(f334(f334(f296(x58521),f334(f85(x58521),x58522)),x58523),f334(f85(x58521),f334(f334(f296(x58521),x58522),x58523))) % 188.18/188.25 [5853]~P124(x58531)+E(f334(f334(f252(x58531),f334(f81(x58531),x58532)),x58533),f334(f81(x58531),f334(f334(f252(x58531),x58532),x58533))) % 188.18/188.25 [5953]E(f463(x59531,x59532,x59533),f472(x59531,x59532,x59533))+E(f334(f334(f109(f935(x59533,a922)),x59532),x59531),f195(f935(x59533,a922))) % 188.18/188.25 [5968]~P72(x59682)+E(f334(f334(f9(x59681,x59682),f334(f16(x59682,x59681),f84(x59682))),x59683),f84(x59682)) % 188.18/188.25 [5969]~P76(x59692)+E(f334(f334(f6(x59691,x59692),f334(f16(x59692,x59691),f2(x59692))),x59693),f2(x59692)) % 188.18/188.25 [5971]~P95(x59711)+E(f334(f334(f23(x59711),f334(f111(x59711),x59712)),f334(f111(x59711),x59713)),f334(f111(x59711),f334(f334(f23(a1),x59712),x59713))) % 188.18/188.25 [5974]~P147(x59741)+E(f334(f334(f87(x59741),f334(f107(x59741),x59742)),f334(f107(x59741),x59743)),f334(f107(x59741),f334(f334(f87(a927),x59742),x59743))) % 188.18/188.25 [5975]~P147(x59751)+E(f334(f334(f86(x59751),f334(f107(x59751),x59752)),f334(f107(x59751),x59753)),f334(f107(x59751),f334(f334(f86(a927),x59752),x59753))) % 188.18/188.25 [5976]~P142(x59761)+E(f334(f334(f23(x59761),f334(f110(x59761),x59762)),f334(f110(x59761),x59763)),f334(f110(x59761),f334(f334(f23(a1),x59762),x59763))) % 188.18/188.25 [5977]~P142(x59771)+E(f334(f334(f87(x59771),f334(f110(x59771),x59772)),f334(f110(x59771),x59773)),f334(f110(x59771),f334(f334(f87(a1),x59772),x59773))) % 188.18/188.25 [5978]~P142(x59781)+E(f334(f334(f86(x59781),f334(f110(x59781),x59782)),f334(f110(x59781),x59783)),f334(f110(x59781),f334(f334(f86(a1),x59782),x59783))) % 188.18/188.25 [5979]~P95(x59791)+E(f334(f334(f87(x59791),f334(f111(x59791),x59792)),f334(f111(x59791),x59793)),f334(f111(x59791),f334(f334(f87(a1),x59792),x59793))) % 188.18/188.25 [5980]~P95(x59801)+E(f334(f334(f86(x59801),f334(f111(x59801),x59802)),f334(f111(x59801),x59803)),f334(f111(x59801),f334(f334(f86(a1),x59802),x59803))) % 188.18/188.25 [6028]~E(x60283,x60282)+P107(f334(f334(f242(f935(x60281,a922)),x60282),x60283)) % 188.18/188.25 [6034]~E(x60342,x60343)+P107(f334(f334(f242(f935(x60341,a922)),x60342),x60343)) % 188.18/188.25 [6039]~P69(x60391)+E(f334(f334(f86(x60391),f334(f85(x60391),x60392)),f334(f85(x60391),x60393)),f334(f85(x60391),f334(f334(f86(x60391),x60393),x60392))) % 188.18/188.25 [6040]~P3(x60401)+E(f334(f334(f86(x60401),f334(f85(x60401),x60402)),f334(f85(x60401),x60403)),f334(f85(x60401),f334(f334(f86(x60401),x60402),x60403))) % 188.18/188.25 [6041]~P77(x60411)+E(f334(f334(f241(x60411),f334(f85(x60411),x60412)),f334(f85(x60411),x60413)),f334(f85(x60411),f334(f334(f246(x60411),x60412),x60413))) % 188.18/188.25 [6042]~P77(x60421)+E(f334(f334(f246(x60421),f334(f85(x60421),x60422)),f334(f85(x60421),x60423)),f334(f85(x60421),f334(f334(f241(x60421),x60422),x60423))) % 188.18/188.25 [6043]~P91(x60431)+E(f334(f334(f109(x60431),f334(f85(x60431),x60432)),f334(f85(x60431),x60433)),f334(f85(x60431),f334(f334(f108(x60431),x60432),x60433))) % 188.18/188.25 [6044]~P91(x60441)+E(f334(f334(f108(x60441),f334(f85(x60441),x60442)),f334(f85(x60441),x60443)),f334(f85(x60441),f334(f334(f109(x60441),x60442),x60443))) % 188.18/188.25 [6045]~P124(x60451)+E(f334(f334(f87(x60451),f334(f81(x60451),x60452)),f334(f81(x60451),x60453)),f334(f81(x60451),f334(f334(f87(x60451),x60452),x60453))) % 188.18/188.25 [6046]~P67(x60461)+E(f334(f334(f296(x60461),f334(f81(x60461),x60462)),f334(f81(x60461),x60463)),f334(f81(x60461),f334(f334(f296(x60461),x60462),x60463))) % 188.18/188.25 [6047]~P82(x60471)+E(f334(f334(f86(x60471),f334(f172(x60471),x60472)),f334(f172(x60471),x60473)),f334(f172(x60471),f334(f334(f141(x60471),x60472),x60473))) % 188.18/188.25 [6048]E(x60481,f195(f935(x60482,a922)))+~E(f334(f334(f108(f935(x60482,a922)),x60483),x60481),f195(f935(x60482,a922))) % 188.18/188.25 [6049]E(x60491,f195(f935(x60492,a922)))+~E(f334(f334(f108(f935(x60492,a922)),x60491),x60493),f195(f935(x60492,a922))) % 188.18/188.25 [6050]~P150(x60501,x60502,x60503)+P107(f334(x60501,f334(f334(f41(a1),x60502),x60503))) % 188.18/188.25 [6108]~P107(f334(f66(x61081),x61083))+P107(f334(f66(x61081),f334(f334(f316(x61081),x61082),x61083))) % 188.18/188.25 [6109]~P107(f334(f144(x61091),x61093))+P107(f334(f144(x61091),f334(f334(f182(x61091),x61092),x61093))) % 188.18/188.25 [6110]~P107(f334(f144(x61101),x61103))+P107(f334(f144(x61101),f334(f334(f145(x61101),x61102),x61103))) % 188.18/188.25 [6141]~P109(x61411)+P107(f334(f334(f242(x61411),x61412),f334(f334(f241(x61411),x61413),x61412))) % 188.18/188.25 [6142]~P109(x61421)+P107(f334(f334(f242(x61421),x61422),f334(f334(f241(x61421),x61422),x61423))) % 188.18/188.25 [6143]~P98(x61431)+P107(f334(f334(f242(x61431),x61432),f334(f334(f108(x61431),x61433),x61432))) % 188.18/188.25 [6144]~P99(x61441)+P107(f334(f334(f242(x61441),x61442),f334(f334(f108(x61441),x61443),x61442))) % 188.18/188.25 [6145]~P98(x61451)+P107(f334(f334(f242(x61451),x61452),f334(f334(f108(x61451),x61452),x61453))) % 188.18/188.25 [6146]~P99(x61461)+P107(f334(f334(f242(x61461),x61462),f334(f334(f108(x61461),x61462),x61463))) % 188.18/188.25 [6160]~E(x61601,f2(a927))+E(f334(f334(f41(a927),f334(f334(f87(a927),x61601),x61602)),f334(f334(f87(a927),x61601),x61603)),f2(a927)) % 188.18/188.25 [6239]~P95(x62391)+E(f334(f334(f23(x62391),f334(f111(x62391),x62392)),f334(f111(x62391),x62393)),f334(f111(x62391),f334(f334(f86(a1),x62392),f334(f85(a1),x62393)))) % 188.18/188.25 [6297]E(x62971,f2(a927))+E(f334(f334(f41(a927),f334(f334(f87(a927),x62971),x62972)),f334(f334(f87(a927),x62971),x62973)),f334(f334(f41(a927),x62972),x62973)) % 188.18/188.25 [6325]E(f159(x63251,f334(f334(f158(x63251),x63252),x63253)),f334(f334(f158(x63251),x63252),f159(x63251,x63253)))+P107(f334(f334(f336(x63251),x63252),f334(f179(x63251),x63253))) % 188.18/188.25 [6361]P150(x63611,x63612,x63613)+~P107(f334(x63611,f334(f334(f41(a1),x63612),x63613))) % 188.18/188.25 [6430]E(x64301,f120(x64302))+E(f334(f334(f158(x64302),f334(f148(x64302),x64301)),f334(f334(f182(x64302),x64303),f334(f178(x64302),x64301))),f334(f334(f182(x64302),f334(a119,x64303)),x64301)) % 188.18/188.25 [6437]E(f334(f334(f23(f935(x64371,a922)),x64372),x64373),x64372)+~E(f334(f334(f109(f935(x64371,a922)),x64372),x64373),f195(f935(x64371,a922))) % 188.18/188.25 [6451]E(f159(x64511,f334(f334(f158(x64511),x64512),x64513)),f159(x64511,x64513))+~P107(f334(f334(f336(x64511),x64512),f334(f179(x64511),x64513))) % 188.18/188.25 [6481]~P107(f334(f334(f242(a927),x64811),x64813))+P107(f334(f334(f242(a927),x64811),f334(f334(f86(a927),x64812),x64813))) % 188.18/188.25 [6483]~P107(f334(f334(f242(a927),x64831),x64832))+P107(f334(f334(f242(a927),x64831),f334(f334(f86(a927),x64832),x64833))) % 188.18/188.25 [6485]~P107(f334(f334(f243(a927),x64851),x64853))+P107(f334(f334(f243(a927),x64851),f334(f334(f86(a927),x64852),x64853))) % 188.18/188.25 [6487]~P107(f334(f334(f243(a927),x64871),x64872))+P107(f334(f334(f243(a927),x64871),f334(f334(f86(a927),x64872),x64873))) % 188.18/188.25 [6526]P107(f334(f66(x65261),x65262))+~P107(f334(f66(x65261),f334(f334(f316(x65261),x65263),x65262))) % 188.18/188.25 [6527]P107(f334(f144(x65271),x65272))+~P107(f334(f144(x65271),f334(f334(f158(x65271),x65273),x65272))) % 188.18/188.25 [6528]P107(f334(f144(x65281),x65282))+~P107(f334(f144(x65281),f334(f334(f141(x65281),x65283),x65282))) % 188.18/188.25 [6529]P107(f334(f144(x65291),x65292))+~P107(f334(f144(x65291),f334(f334(f141(x65291),x65292),x65293))) % 188.18/188.25 [6577]~P119(x65771)+E(f334(f334(f86(x65771),x65772),f334(f334(f87(x65771),x65773),x65772)),f334(f334(f87(x65771),f334(f334(f86(x65771),x65773),f84(x65771))),x65772)) % 188.18/188.25 [6623]~E(x66231,x66232)+~P107(f334(f334(f243(f935(x66233,a922)),x66231),x66232)) % 188.18/188.25 [6670]P107(f334(f334(f336(x66701),x66702),x66703))+P107(f334(f334(f336(x66701),x66702),f334(f85(f935(x66701,a922)),x66703))) % 188.18/188.25 [6678]E(f151(x66781,f334(f334(f145(x66781),x66782),x66783)),f151(x66781,x66783))+~P107(f334(f334(f243(a927),x66782),f334(f196(f928(x66781)),x66783))) % 188.18/188.25 [6679]E(f334(f334(f182(x66791),x66792),f121(x66791,x66793)),f334(f334(f182(x66791),x66792),x66793))+~P107(f334(f334(f243(a927),x66792),f334(f196(f928(x66791)),x66793))) % 188.18/188.25 [6734]E(f334(f334(f334(f190(f928(x67341),f928(x67341)),x67342),f174(x67341)),x67343),x67343)+~E(f50(a927,x67342,f334(f196(f928(x67341)),x67343)),f2(a927)) % 188.18/188.25 [6741]~P10(x67411,x67413,x67412)+E(f334(f334(f295(x67411,x67411,x67411),f334(f293(x67411,x67411),x67412)),x67412),x67412) % 188.18/188.25 [6782]~E(f334(f334(f108(f935(x67821,a922)),x67822),x67823),x67823)+P107(f334(f334(f242(f935(x67821,a922)),x67822),x67823)) % 188.18/188.25 [6787]~P57(x67871,x67871,x67873)+P57(x67871,x67871,f334(f334(f190(f934(x67871,x67871),a922),x67872),x67873)) % 188.18/188.25 [6791]~P107(f334(f334(f336(x67911),x67913),f334(f179(x67911),x67912)))+P107(f334(f334(f243(a927),f2(a927)),f334(f196(f928(x67911)),x67912))) % 188.18/188.25 [6817]~P86(x68171)+E(f334(f81(x68171),f334(f334(f86(x68171),f334(f81(x68171),x68172)),f334(f81(x68171),x68173))),f334(f334(f86(x68171),f334(f81(x68171),x68172)),f334(f81(x68171),x68173))) % 188.18/188.25 [6827]E(f334(f334(f41(a927),f334(f334(f87(a927),x68271),x68272)),f334(f334(f87(a927),x68271),x68273)),f334(f334(f41(a927),x68272),x68273))+~P107(f334(f334(f243(a927),f2(a927)),x68271)) % 188.18/188.25 [6963]~P107(f334(f66(x69631),x69633))+E(f334(f334(f69(x69631,f935(x69631,a922),f316(x69631)),x69632),x69633),f334(f334(f108(f935(x69631,a922)),x69633),x69632)) % 188.18/188.25 [7015]E(f334(f334(f108(f935(x70151,a922)),x70152),x70153),x70152)+~P107(f334(f334(f242(f935(x70151,a922)),x70153),x70152)) % 188.18/188.25 [7017]E(f334(f334(f108(f935(x70171,a922)),x70172),x70173),x70173)+~P107(f334(f334(f242(f935(x70171,a922)),x70172),x70173)) % 188.18/188.25 [7018]E(f334(f334(f109(f935(x70181,a922)),x70182),x70183),x70183)+~P107(f334(f334(f242(f935(x70181,a922)),x70183),x70182)) % 188.18/188.25 [7019]E(f334(f334(f109(f935(x70191,a922)),x70192),x70193),x70192)+~P107(f334(f334(f242(f935(x70191,a922)),x70192),x70193)) % 188.18/188.25 [7066]~P107(f334(f144(x70661),x70662))+E(f334(f334(f23(f935(x70661,a922)),f334(f179(x70661),x70662)),f334(f334(f316(x70661),x70663),f195(f935(x70661,a922)))),f334(f179(x70661),f177(x70661,x70663,x70662))) % 188.18/188.25 [7120]P39(x71201,x71202)+~P39(x71201,f334(f334(f190(f934(x71201,x71201),a922),x71203),x71202)) % 188.18/188.25 [7184]P107(f334(f54(x71841,x71842),f334(a56,x71843)))+~P107(f334(f54(f334(f85(a1),x71841),f334(f85(a1),x71842)),x71843)) % 188.18/188.25 [7189]E(f334(f334(f23(f935(x71891,a922)),f334(f334(f316(x71891),x71892),x71893)),f334(f334(f316(x71891),x71892),f195(f935(x71891,a922)))),x71893)+P107(f334(f334(f336(x71891),x71892),x71893)) % 188.18/188.25 [7211]E(f334(f334(f109(f935(x72111,a922)),f334(f179(x72111),x72112)),f334(f179(x72111),x72113)),f195(f935(x72111,a922)))+~P107(f334(f144(x72111),f334(f334(f141(x72111),x72112),x72113))) % 188.18/188.25 [7226]~P107(f334(f334(f336(x72261),x72262),f334(f179(x72261),x72263)))+~P107(f334(f144(x72261),f334(f334(f158(x72261),x72262),x72263))) % 188.18/188.25 [7296]P33(x72961,x72962,x72963)+P107(f334(f334(f243(a927),f773(x72963,x72962,x72961)),f334(f196(f928(x72961)),x72963))) % 188.18/188.25 [7306]E(f334(f334(f109(f935(x73061,a922)),x73062),x73063),f195(f935(x73061,a922)))+P107(f334(f334(f336(x73061),f463(x73063,x73062,x73061)),x73062)) % 188.18/188.25 [7307]E(f334(f334(f109(f935(x73071,a922)),x73072),x73073),f195(f935(x73071,a922)))+P107(f334(f334(f336(x73071),f472(x73073,x73072,x73071)),x73073)) % 188.18/188.25 [7310]E(f121(x73101,f334(f334(f182(x73101),x73102),x73103)),f334(f334(f182(x73101),f334(f334(f23(a927),x73102),f84(a927))),x73103))+~P107(f334(f334(f242(a927),x73102),f334(f196(f928(x73101)),x73103))) % 188.18/188.25 [7369]~P35(x73693,x73692,x73691)+P107(f334(f334(f243(a927),f767(x73691,x73692,x73693)),f334(f196(f928(x73693)),x73691))) % 188.18/188.25 [7387]P107(f334(f334(f243(a927),f2(a927)),x73871))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x73872),x73871)),f334(f334(f87(a927),x73873),x73871))) % 188.18/188.25 [7388]P107(f334(f334(f243(a927),f2(a927)),x73881))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x73881),x73882)),f334(f334(f87(a927),x73881),x73883))) % 188.18/188.25 [7391]~P107(f334(f334(f336(x73911),x73912),x73913))+~P107(f334(f334(f336(x73911),x73912),f334(f85(f935(x73911,a922)),x73913))) % 188.18/188.25 [7397]~P107(f334(f334(f243(f935(x73971,a922)),x73972),x73973))+P107(f334(f334(f242(f935(x73971,a922)),x73972),x73973)) % 188.18/188.25 [7507]~P107(f334(f334(f242(a927),x75073),x75072))+P107(f334(f334(f242(a927),f334(f334(f23(a927),x75071),x75072)),f334(f334(f23(a927),x75071),x75073))) % 188.18/188.25 [7508]~P107(f334(f334(f242(a927),x75081),x75083))+P107(f334(f334(f242(a927),f334(f334(f23(a927),x75081),x75082)),f334(f334(f23(a927),x75083),x75082))) % 188.18/188.25 [7510]~P107(f334(f334(f242(a927),x75102),x75103))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x75101),x75102)),f334(f334(f87(a927),x75101),x75103))) % 188.18/188.25 [7512]~P107(f334(f334(f242(a927),x75121),x75123))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x75121),x75122)),f334(f334(f87(a927),x75123),x75122))) % 188.18/188.25 [7513]~P107(f334(f334(f242(a927),x75132),x75133))+P107(f334(f334(f242(a927),f334(f334(f86(a927),x75131),x75132)),f334(f334(f86(a927),x75131),x75133))) % 188.18/188.25 [7514]~P107(f334(f334(f242(a927),x75141),x75143))+P107(f334(f334(f242(a927),f334(f334(f86(a927),x75141),x75142)),f334(f334(f86(a927),x75143),x75142))) % 188.18/188.25 [7515]~P107(f334(f334(f242(a927),x75151),x75153))+P107(f334(f334(f242(a927),f334(f334(f41(a927),x75151),x75152)),f334(f334(f41(a927),x75153),x75152))) % 188.18/188.25 [7516]~P107(f334(f334(f242(a1),x75162),x75163))+P107(f334(f334(f242(a1),f334(f334(f86(a1),x75161),x75162)),f334(f334(f86(a1),x75161),x75163))) % 188.18/188.25 [7517]~P107(f334(f334(f243(a927),x75172),x75173))+P107(f334(f334(f243(a927),f334(f334(f86(a927),x75171),x75172)),f334(f334(f86(a927),x75171),x75173))) % 188.18/188.25 [7518]~P107(f334(f334(f243(a927),x75181),x75183))+P107(f334(f334(f243(a927),f334(f334(f86(a927),x75181),x75182)),f334(f334(f86(a927),x75183),x75182))) % 188.18/188.25 [7519]~P107(f334(f334(f243(a1),x75191),x75193))+P107(f334(f334(f243(a1),f334(f334(f86(a1),x75191),x75192)),f334(f334(f86(a1),x75193),x75192))) % 188.18/188.25 [7588]E(x75881,x75882)+~P107(f334(f334(f336(x75883),x75881),f334(f334(f316(x75883),x75882),f195(f935(x75883,a922))))) % 188.18/188.25 [7590]~E(f334(f334(f109(f935(x75901,a922)),x75902),x75903),f195(f935(x75901,a922)))+P107(f334(f334(f242(f935(x75901,a922)),x75902),f334(f85(f935(x75901,a922)),x75903))) % 188.18/188.25 [7595]P107(f334(f334(f336(f935(x75951,a922)),x75952),f334(f315(x75951),x75953)))+~P107(f334(f334(f242(f935(x75951,a922)),x75952),x75953)) % 188.18/188.25 [7644]E(f334(f334(f158(x76441),f334(f334(f171(x76441),x76442),x76443)),f334(f334(f145(x76441),f334(a119,x76443)),x76442)),f334(f334(f145(x76441),x76443),x76442))+~P107(f334(f334(f243(a927),x76443),f334(f196(f928(x76441)),x76442))) % 188.18/188.25 [7670]P107(f334(f334(f336(f934(x76701,x76701)),x76702),f314(x76701,x76703)))+~P107(f334(f334(f336(f934(x76701,x76701)),x76702),x76703)) % 188.18/188.25 [7679]~P107(f334(f334(f336(f935(x76791,a922)),x76792),f334(f315(x76791),x76793)))+P107(f334(f334(f242(f935(x76791,a922)),x76792),x76793)) % 188.18/188.25 [7722]P107(f334(f334(f242(f935(x77221,a922)),x77222),f42(f935(x77221,a922),x77223)))+~P107(f334(f334(f336(f935(x77221,a922)),x77222),x77223)) % 188.18/188.25 [7744]~P142(x77441)+E(f334(f334(f87(x77441),f334(f334(f252(x77441),f334(f85(x77441),f84(x77441))),x77442)),f334(f334(f252(x77441),x77443),x77442)),f334(f334(f252(x77441),f334(f85(x77441),x77443)),x77442)) % 188.18/188.25 [7767]E(f334(f334(f171(x77671),x77672),f334(f334(f23(a927),f334(f196(f928(x77671)),x77672)),f334(a119,x77673))),f334(f334(f171(x77671),f334(f175(x77671),x77672)),x77673))+~P107(f334(f334(f243(a927),x77673),f334(f196(f928(x77671)),x77672))) % 188.18/188.25 [7784]~E(f334(f334(f109(f935(x77841,a922)),f526(x77843,x77842,x77841)),x77843),f195(f935(x77841,a922)))+E(f334(f334(f109(f935(x77841,a922)),f42(f935(x77841,a922),x77842)),x77843),f195(f935(x77841,a922))) % 188.18/188.25 [7843]~P107(f334(f334(f336(x78433),x78432),f334(f179(x78433),x78431)))+P107(f334(f334(f243(a927),f647(x78431,x78432,x78433)),f334(f196(f928(x78433)),x78431))) % 188.18/188.25 [7851]P107(f334(f334(f336(x78511),f334(f334(f171(x78511),x78512),x78513)),f334(f179(x78511),x78512)))+~P107(f334(f334(f243(a927),x78513),f334(f196(f928(x78511)),x78512))) % 188.18/188.25 [7948]~P107(f334(x79482,f732(x79483,x79482,x79481)))+E(f334(f334(f145(x79481),f334(f196(f928(x79481)),f184(x79481,x79482,x79483))),x79483),f120(x79481)) % 188.18/188.25 [7961]P107(f334(f334(f242(f935(f928(x79611),a922)),f168(x79611,x79612)),f168(x79611,x79613)))+~P107(f334(f334(f242(f935(x79611,a922)),x79612),x79613)) % 188.18/188.25 [7962]P107(f334(f334(f242(f935(f928(x79621),a922)),f167(x79621,x79622)),f167(x79621,x79623)))+~P107(f334(f334(f242(f935(x79621,a922)),x79622),x79623)) % 188.18/188.25 [7989]E(f334(f334(f109(f935(x79891,a922)),f42(f935(x79891,a922),x79892)),x79893),f195(f935(x79891,a922)))+P107(f334(f334(f336(f935(x79891,a922)),f526(x79893,x79892,x79891)),x79892)) % 188.18/188.25 [7991]~P107(f334(f334(f336(f935(x79911,a922)),x79913),x79912))+P107(f334(f334(f242(f935(x79911,a922)),f43(f935(x79911,a922),x79912)),x79913)) % 188.18/188.25 [7993]E(f334(f334(f109(f935(x79931,a922)),x79932),x79933),f195(f935(x79931,a922)))+~P107(f334(f334(f242(f935(x79931,a922)),x79932),f334(f85(f935(x79931,a922)),x79933))) % 188.18/188.25 [8041]E(f334(f334(f23(a927),f334(f334(f86(a927),f334(f172(a927),x80411)),x80412)),f334(f334(f171(a927),x80411),x80413)),f334(f172(a927),f334(f334(f166(a927,x80411),x80413),x80412)))+~P107(f334(f334(f243(a927),x80413),f334(f196(f928(a927)),x80411))) % 188.18/188.25 [8094]P107(f334(f334(f242(a927),x80941),x80942))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),x80943),x80941)),f334(f334(f86(a927),x80943),x80942))) % 188.18/188.25 [8095]P107(f334(f334(f243(a927),x80951),x80952))+~P107(f334(f334(f243(a927),f334(f334(f86(a927),x80953),x80951)),f334(f334(f86(a927),x80953),x80952))) % 188.18/188.25 [8096]P107(f334(f334(f243(a927),x80961),x80962))+~P107(f334(f334(f243(a927),f334(f334(f87(a927),x80963),x80961)),f334(f334(f87(a927),x80963),x80962))) % 188.18/188.25 [8097]P107(f334(f334(f243(a927),x80971),x80972))+~P107(f334(f334(f243(a927),f334(f334(f87(a927),x80971),x80973)),f334(f334(f87(a927),x80972),x80973))) % 188.18/188.25 [8123]P107(f334(f334(f243(a927),f2(a927)),x81231))+~P107(f334(f334(f243(a927),f334(f334(f87(a927),x81232),x81231)),f334(f334(f87(a927),x81233),x81231))) % 188.18/188.25 [8124]P107(f334(f334(f243(a927),f2(a927)),x81241))+~P107(f334(f334(f243(a927),f334(f334(f87(a927),x81241),x81242)),f334(f334(f87(a927),x81241),x81243))) % 188.18/188.25 [8193]E(f255(x81931,x81932,x81933),x81932)+~P107(f334(f334(f242(f935(x81931,a922)),x81933),f334(f334(f316(x81931),x81932),f195(f935(x81931,a922))))) % 188.18/188.25 [8242]~P107(f334(f144(x82421),x82423))+E(f334(f143(x82421,f334(f334(f8(a922,a922,x82421),a329),f334(a331,x82422))),x82423),f177(x82421,x82422,x82423)) % 188.18/188.25 [8267]E(f334(f334(f145(x82671),f334(f196(f928(x82671)),f184(x82671,x82672,x82673))),x82673),f120(x82671))+P107(f334(f334(f336(x82671),f732(x82673,x82672,x82671)),f334(f179(x82671),x82673))) % 188.18/188.25 [8272]E(f334(f334(f141(x82721),f334(f334(f182(x82721),x82722),x82723)),f334(f334(f158(x82721),f334(f334(f171(x82721),x82723),x82722)),f120(x82721))),f334(f334(f182(x82721),f334(a119,x82722)),x82723))+~P107(f334(f334(f243(a927),x82722),f334(f196(f928(x82721)),x82723))) % 188.18/188.25 [8336]E(f334(f143(x83361,f334(f334(f8(a922,a922,x83361),a329),f334(a331,x83362))),x83363),x83363)+P107(f334(f334(f336(x83361),x83362),f334(f179(x83361),x83363))) % 188.18/188.25 [8342]P107(f334(f334(f242(f935(f935(x83421,a922),a922)),f256(x83421,x83422)),f256(x83421,x83423)))+~P107(f334(f334(f242(f935(x83421,a922)),x83422),x83423)) % 188.18/188.25 [8381]~P107(f334(f144(x83811),x83813))+P107(f334(f144(x83811),f334(f334(f334(f190(f928(x83811),f928(x83811)),x83812),f174(x83811)),x83813))) % 188.18/188.25 [8387]~P107(f334(f334(f243(a927),x83872),x83873))+P107(f334(f334(f243(a927),f334(f334(f87(a927),f334(a119,x83871)),x83872)),f334(f334(f87(a927),f334(a119,x83871)),x83873))) % 188.18/188.25 [8407]P107(f334(f334(f242(f935(f935(x84071,a922),a922)),f334(f315(x84071),x84072)),f334(f315(x84071),x84073)))+~P107(f334(f334(f242(f935(x84071,a922)),x84072),x84073)) % 188.18/188.25 [8475]~E(f334(f317(x84751,x84752,x84753),f250(f935(x84751,a922))),f250(f935(x84752,a922)))+E(f334(f78(x84751,x84752,x84752,x84753),f97(x84751,x84752,f250(f935(x84751,a922)),x84753)),f32(x84752)) % 188.18/188.25 [8566]~P107(f334(f334(f242(f935(x85661,a922)),x85663),x85662))+P107(f334(f334(f242(f935(x85661,a922)),f334(f85(f935(x85661,a922)),x85662)),f334(f85(f935(x85661,a922)),x85663))) % 188.18/188.25 [8599]E(f334(f317(a927,a927,f334(f334(f7(a927,a927,a927),f23(a927)),x85991)),f334(f310(a927,x85992),x85993)),f334(f310(a927,f334(f334(f23(a927),x85992),x85991)),f334(f334(f23(a927),x85993),x85991)))+~P107(f334(f334(f243(a927),x85991),x85993)) % 188.18/188.25 [8621]~P82(x86211)+E(f334(f334(f86(x86211),x86212),f334(f149(x86211,x86211,f86(x86211),f2(x86211)),x86213)),f334(f149(x86211,x86211,f86(x86211),x86212),x86213)) % 188.18/188.25 [8699]~P86(x86991)+P107(f334(f334(f242(x86991),f334(f81(x86991),f334(f334(f23(x86991),x86992),x86993))),f334(f334(f86(x86991),f334(f81(x86991),x86992)),f334(f81(x86991),x86993)))) % 188.18/188.25 [8700]~P86(x87001)+P107(f334(f334(f242(x87001),f334(f81(x87001),f334(f334(f86(x87001),x87002),x87003))),f334(f334(f86(x87001),f334(f81(x87001),x87002)),f334(f81(x87001),x87003)))) % 188.18/188.25 [8711]E(f334(f334(f86(a1),f334(f334(f87(a1),x87111),f50(a1,f334(f334(f41(a1),x87112),x87111),x87113))),f50(a1,x87112,x87111)),f50(a1,x87112,f334(f334(f87(a1),x87111),x87113)))+~P107(f334(f334(f243(a1),f2(a1)),x87113)) % 188.18/188.25 [8716]E(f334(f334(f141(x87161),f334(f334(f182(x87161),x87162),x87163)),f334(f334(f158(x87161),f334(f148(x87161),f334(f334(f145(x87161),x87162),x87163))),f120(x87161))),f334(f334(f182(x87161),f334(a119,x87162)),x87163))+~P107(f334(f334(f243(a927),x87162),f334(f196(f928(x87161)),x87163))) % 188.18/188.25 [8740]E(f334(f276(x87401,f334(f334(f161(x87401,f934(a106,x87401)),f334(f260(a106,x87401),f84(a106))),x87402)),f334(a3,x87403)),f334(f334(f171(x87401),x87402),x87403))+~P107(f334(f334(f243(a927),x87403),f334(f196(f928(x87401)),x87402))) % 188.18/188.25 [8807]P107(f334(f334(f336(f934(x88071,x88071)),x88072),f334(f334(f295(x88071,x88071,x88071),x88073),f314(x88071,x88073))))+~P107(f334(f334(f336(f934(x88071,x88071)),x88072),x88073)) % 188.18/188.25 [8817]E(f334(f317(x88171,x88172,x88173),f250(f935(x88171,a922))),f250(f935(x88172,a922)))+~E(f334(f78(x88171,x88172,x88172,x88173),f97(x88171,x88172,f250(f935(x88171,a922)),x88173)),f32(x88172)) % 188.18/188.25 [8828]P107(f334(f334(f242(a927),x88281),x88282))+~P107(f334(f334(f242(a927),f334(f334(f87(a927),f334(a119,x88283)),x88281)),f334(f334(f87(a927),f334(a119,x88283)),x88282))) % 188.18/188.25 [8843]P107(f334(f334(f242(f935(x88431,a922)),x88432),x88433))+~P107(f334(f334(f242(f935(x88431,a922)),f334(f85(f935(x88431,a922)),x88433)),f334(f85(f935(x88431,a922)),x88432))) % 188.18/188.25 [8866]P107(f334(f144(x88661),x88662))+~P107(f334(f144(x88661),f334(f334(f334(f190(f928(x88661),f928(x88661)),x88663),f174(x88661)),x88662))) % 188.18/188.25 [8932]E(f334(f292(x89321,x89321,f314(x89321,x89322)),x89323),x89323)+~P107(f334(f334(f242(f935(x89321,a922)),f334(f292(x89321,x89321,x89322),x89323)),x89323)) % 188.18/188.25 [8979]~P109(x89791)+P15(x89791,f334(f143(x89791,f334(f334(f7(x89791,x89791,a922),a331),f334(x89792,x89793))),x89793)) % 188.18/188.25 [8986]~P107(f334(f334(f242(a927),x89861),x89862))+P107(f334(f334(f242(a927),x89861),f334(f149(a927,a927,f86(a927),x89862),x89863))) % 188.18/188.25 [9078]~P107(f334(f334(f336(f934(x90781,x90781)),x90782),f314(x90781,x90783)))+P107(f334(f334(f336(f934(x90781,x90781)),x90782),f334(f334(f190(f934(x90781,x90781),a922),f629(x90783,x90782,x90781)),x90783))) % 188.18/188.25 [9163]~P82(x91631)+E(f334(f334(f86(x91631),x91632),f334(f149(x91631,x91631,f334(f7(x91631,x91631,x91631),f86(x91631)),f2(x91631)),f334(f175(x91631),x91633))),f334(f149(x91631,x91631,f86(x91631),x91632),x91633)) % 188.18/188.25 [9273]~P28(x92732,x92731,x92733,f250(f935(x92732,a922)),f250(f935(x92731,a922)))+E(f97(x92731,x92732,f250(f935(x92731,a922)),f97(x92732,x92731,f250(f935(x92732,a922)),x92733)),x92733) % 188.18/188.25 [9427]P57(x94271,x94272,x94273)+P107(f334(f334(f336(f934(x94271,x94272)),f334(f334(f260(x94271,x94272),f621(x94273,x94272,x94271)),f598(x94273,x94272,x94271))),x94273)) % 188.18/188.25 [9428]P57(x94281,x94282,x94283)+P107(f334(f334(f336(f934(x94281,x94282)),f334(f334(f260(x94281,x94282),f621(x94283,x94282,x94281)),f597(x94283,x94282,x94281))),x94283)) % 188.18/188.25 [9494]~P107(f334(f334(f336(f934(x94941,x94941)),x94942),f334(f334(f295(x94941,x94941,x94941),x94943),f314(x94941,x94943))))+P107(f334(f334(f336(f934(x94941,x94941)),x94942),f334(f334(f190(f934(x94941,x94941),a922),f632(x94943,x94942,x94941)),x94943))) % 188.18/188.25 [9495]~P107(f334(x94951,f334(f334(f171(x94952),x94953),f334(f196(f928(x94952)),f184(x94952,x94951,x94953)))))+~P107(f334(f334(f243(a927),f334(f196(f928(x94952)),f184(x94952,x94951,x94953))),f334(f196(f928(x94952)),x94953))) % 188.18/188.25 [9587]~P107(f334(f334(f242(f935(x95871,a922)),x95872),x95873))+P107(f334(f334(f242(f935(x95871,a922)),f334(f334(f7(x95871,f935(x95871,a922),a922),f336(x95871)),x95872)),f334(f334(f7(x95871,f935(x95871,a922),a922),f336(x95871)),x95873))) % 188.18/188.25 [9641]~P107(f334(f334(f336(f934(f935(x96411,a922),f935(x96411,a922))),f334(f334(f260(f935(x96411,a922),f935(x96411,a922)),x96412),x96413)),f321(x96411)))+P107(f334(f334(f243(f935(x96411,a922)),x96412),x96413)) % 188.18/188.25 [9665]P58(x96651,x96652,x96653)+~P107(f334(f334(f336(f934(x96651,x96651)),f334(f334(f260(x96651,x96651),f624(x96653,x96652,x96651)),f623(x96653,x96652,x96651))),x96653)) % 188.18/188.25 [9666]P58(x96661,x96662,x96663)+~P107(f334(f334(f336(f934(x96661,x96661)),f334(f334(f260(x96661,x96661),f623(x96663,x96662,x96661)),f624(x96663,x96662,x96661))),x96663)) % 188.18/188.25 [9701]~P107(f334(f334(f336(f934(f928(x97011),f928(x97011))),f334(f334(f260(f928(x97011),f928(x97011)),x97012),x97012)),f154(x97011,x97013)))+P107(f334(f334(f336(f934(x97011,x97011)),f334(f334(f260(x97011,x97011),f662(x97012,x97013,x97011)),f662(x97012,x97013,x97011))),x97013)) % 188.18/188.25 [9764]P107(f334(f334(f242(f935(x97641,a922)),x97642),x97643))+~P107(f334(f334(f242(f935(x97641,a922)),f334(f334(f7(x97641,f935(x97641,a922),a922),f336(x97641)),x97642)),f334(f334(f7(x97641,f935(x97641,a922),a922),f336(x97641)),x97643))) % 188.18/188.25 [9850]E(f334(f334(f23(a927),f334(f334(f6(a927,a927),x98501),f334(f307(a927),x98502))),f334(f334(f6(a927,a927),x98503),f334(f307(a927),x98502))),f334(f334(f6(a927,a927),f334(f334(f18(a927,a927,a927),f334(f334(f8(a927,f935(a927,a927),a927),f23(a927)),x98501)),x98503)),f334(f307(a927),x98502)))+~P107(f334(f334(f242(a927),f334(x98503,f499(x98502,x98501,x98503))),f334(x98501,f499(x98502,x98501,x98503)))) % 188.18/188.25 [5887]~P69(x58871)+E(f334(f334(f23(x58871),f334(f334(f86(x58871),x58872),x58873)),x58873),x58872) % 188.18/188.25 [5888]~P69(x58881)+E(f334(f334(f86(x58881),f334(f334(f23(x58881),x58882),x58883)),x58883),x58882) % 188.18/188.25 [6117]~P69(x61171)+E(f334(f334(f86(x61171),x61172),f334(f334(f86(x61171),f334(f85(x61171),x61172)),x61173)),x61173) % 188.18/188.25 [6200]~P81(x62001)+E(f334(f334(f87(x62001),f334(f334(f252(x62001),x62002),x62003)),x62002),f334(f334(f252(x62001),x62002),f334(a119,x62003))) % 188.18/188.25 [6201]~P119(x62011)+E(f334(f334(f87(x62011),f334(f334(f252(x62011),x62012),x62013)),x62012),f334(f334(f252(x62011),x62012),f334(a119,x62013))) % 188.18/188.25 [6418]~P124(x64181)+E(f334(f81(x64181),f334(f334(f252(x64181),f334(f85(x64181),x64182)),x64183)),f334(f81(x64181),f334(f334(f252(x64181),x64182),x64183))) % 188.18/188.25 [6457]~P81(x64571)+E(f334(f334(f87(x64571),f334(f334(f252(x64571),x64572),x64573)),x64572),f334(f334(f87(x64571),x64572),f334(f334(f252(x64571),x64572),x64573))) % 188.18/188.25 [6517]E(f334(f334(f23(a106),f334(f334(f86(a106),x65171),x65172)),x65173),f282(x65171,x65172,x65173))+~P107(f334(f334(f243(a106),x65172),x65173)) % 188.18/188.25 [6539]~E(f334(f334(f145(x65391),x65393),x65392),f120(x65391))+P107(f334(f334(f242(a927),f334(f196(f928(x65391)),x65392)),x65393)) % 188.18/188.25 [6675]E(f334(f334(f87(a927),f334(f111(a927),x66751)),f334(f334(f87(a927),f334(f111(a927),x66752)),x66753)),f2(a927))+~P107(f334(f334(f243(a1),x66751),a89)) % 188.18/188.25 [6693]~P65(x66931)+E(f334(f334(f252(x66931),f334(f334(f296(x66931),f84(x66931)),x66932)),x66933),f334(f334(f296(x66931),f84(x66931)),f334(f334(f252(x66931),x66932),x66933))) % 188.18/188.25 [6767]E(f334(f334(f23(a927),f334(f334(f86(a927),x67671),x67672)),x67673),f334(f334(f23(a927),x67671),f334(f334(f23(a927),x67673),x67672)))+~P107(f334(f334(f242(a927),x67672),x67673)) % 188.18/188.25 [6769]E(f334(f334(f23(a927),f334(f334(f86(a927),x67691),x67692)),x67693),f334(f334(f86(a927),x67691),f334(f334(f23(a927),x67692),x67693)))+~P107(f334(f334(f242(a927),x67693),x67692)) % 188.18/188.25 [6808]~P109(x68081)+P107(f334(f334(f242(x68081),f334(f334(f246(x68081),x68082),x68083)),x68083)) % 188.18/188.25 [6809]~P109(x68091)+P107(f334(f334(f242(x68091),f334(f334(f246(x68091),x68092),x68093)),x68092)) % 188.18/188.25 [6810]~P99(x68101)+P107(f334(f334(f242(x68101),f334(f334(f109(x68101),x68102),x68103)),x68103)) % 188.18/188.25 [6811]~P104(x68111)+P107(f334(f334(f242(x68111),f334(f334(f109(x68111),x68112),x68113)),x68113)) % 188.18/188.25 [6812]~P99(x68121)+P107(f334(f334(f242(x68121),f334(f334(f109(x68121),x68122),x68123)),x68122)) % 188.18/188.25 [6813]~P104(x68131)+P107(f334(f334(f242(x68131),f334(f334(f109(x68131),x68132),x68133)),x68132)) % 188.18/188.25 [6826]E(f334(f334(f41(a1),f334(f334(f41(a1),x68261),x68262)),x68263),f334(f334(f41(a1),x68261),f334(f334(f87(a1),x68262),x68263)))+~P107(f334(f334(f243(a1),f2(a1)),x68263)) % 188.18/188.25 [6876]~P119(x68761)+E(f334(f334(f86(x68761),f334(f334(f87(x68761),x68762),x68763)),x68763),f334(f334(f87(x68761),f334(f334(f86(x68761),x68762),f84(x68761))),x68763)) % 188.18/188.25 [6877]~P95(x68771)+E(f334(f334(f87(x68771),f334(f85(x68771),f334(f111(x68771),x68772))),x68773),f334(f334(f87(x68771),f334(f111(x68771),f334(f85(a1),x68772))),x68773)) % 188.18/188.25 [6949]~P82(x69491)+E(f334(f172(x69491),f334(f334(f161(x69492,x69491),f334(f16(x69491,x69492),f2(x69491))),x69493)),f2(x69491)) % 188.18/188.25 [6964]E(f334(f334(f86(a927),f334(f111(a927),x69641)),f334(f334(f86(a927),f334(f111(a927),x69642)),x69643)),f334(f334(f86(a927),f334(f111(a927),x69642)),x69643))+~P107(f334(a200,f334(f111(a1),x69641))) % 188.18/188.25 [6978]~P7(x69781)+E(f43(x69781,f334(f334(f316(x69781),x69782),f334(f334(f316(x69781),x69783),f195(f935(x69781,a922))))),f334(f334(f109(x69781),x69782),x69783)) % 188.18/188.25 [6979]~P7(x69791)+E(f42(x69791,f334(f334(f316(x69791),x69792),f334(f334(f316(x69791),x69793),f195(f935(x69791,a922))))),f334(f334(f108(x69791),x69792),x69793)) % 188.18/188.25 [7003]E(f334(f334(f182(x70031),x70032),x70033),x70033)+~P107(f334(f334(f242(a927),f334(f196(f928(x70031)),x70033)),x70032)) % 188.18/188.25 [7010]E(f334(f334(f145(x70101),x70102),x70103),f120(x70101))+~P107(f334(f334(f242(a927),f334(f196(f928(x70101)),x70103)),x70102)) % 188.18/188.25 [7021]E(f334(f334(f86(a927),f334(f334(f23(a927),x70211),x70212)),x70213),f334(f334(f23(a927),f334(f334(f86(a927),x70211),x70213)),x70212))+~P107(f334(f334(f242(a927),x70212),x70211)) % 188.18/188.25 [7035]~P107(f334(f334(f243(a927),x70351),x70353))+P107(f334(f334(f243(a927),f334(f334(f23(a927),x70351),x70352)),x70353)) % 188.18/188.25 [7061]~P109(x70611)+E(f177(x70611,x70612,f334(f334(f155(x70611,x70611,f5(x70611)),x70612),x70613)),x70613) % 188.18/188.25 [7148]E(f334(f334(f23(a927),f334(f334(f86(a927),x71481),x71482)),f334(a119,x71483)),f334(f334(f23(a927),x71481),f334(a119,f334(f334(f23(a927),x71483),x71482))))+~P107(f334(f334(f242(a927),x71482),x71483)) % 188.18/188.25 [7149]~P124(x71491)+P107(f334(f334(f242(x71491),f2(x71491)),f334(f334(f252(x71491),f334(f81(x71491),x71492)),x71493))) % 188.18/188.25 [7195]P26(x71951,x71952,x71953)+~P107(f334(f334(f242(f935(f926(x71951),a922)),x71953),x71952)) % 188.18/188.25 [7237]~P107(f334(f66(x72371),x72372))+P107(f334(f66(x72371),f334(f334(f23(f935(x72371,a922)),x72372),x72373))) % 188.18/188.25 [7238]~P107(f334(f66(x72381),x72383))+P107(f334(f66(x72381),f334(f334(f109(f935(x72381,a922)),x72382),x72383))) % 188.18/188.25 [7239]~P107(f334(f66(x72391),x72392))+P107(f334(f66(x72391),f334(f334(f109(f935(x72391,a922)),x72392),x72393))) % 188.18/188.25 [7377]~P39(x73771,x73773)+P39(x73771,f334(f334(f109(f935(f934(x73771,x73771),a922)),x73772),x73773)) % 188.18/188.25 [7378]~P39(x73781,x73782)+P39(x73781,f334(f334(f109(f935(f934(x73781,x73781),a922)),x73782),x73783)) % 188.18/188.25 [7503]~P109(x75031)+E(f14(x75031,f334(f179(x75031),f334(f334(f158(x75031),x75032),x75033))),f334(f149(x75031,x75031,f246(x75031),x75032),x75033)) % 188.18/188.25 [7504]~P109(x75041)+E(f15(x75041,f334(f179(x75041),f334(f334(f158(x75041),x75042),x75043))),f334(f149(x75041,x75041,f241(x75041),x75042),x75043)) % 188.18/188.25 [7505]~P99(x75051)+E(f10(x75051,f334(f179(x75051),f334(f334(f158(x75051),x75052),x75053))),f334(f149(x75051,x75051,f109(x75051),x75052),x75053)) % 188.18/188.25 [7506]~P99(x75061)+E(f13(x75061,f334(f179(x75061),f334(f334(f158(x75061),x75062),x75063))),f334(f149(x75061,x75061,f108(x75061),x75062),x75063)) % 188.18/188.25 [7563]~P107(f334(f66(x75631),x75632))+P107(f334(f334(f242(a927),f334(f40(x75631),x75632)),f334(f40(x75631),f334(f334(f316(x75631),x75633),x75632)))) % 188.18/188.25 [7564]E(f334(f334(f108(f935(a927,a922)),f334(f310(a927,x75641),x75642)),f334(f310(a927,x75642),f334(f334(f86(a927),x75642),x75643))),f334(f310(a927,x75641),f334(f334(f86(a927),x75642),x75643)))+~P107(f334(f334(f242(a927),x75641),x75642)) % 188.18/188.25 [7573]P107(f334(f334(f242(a927),x75731),x75732))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),x75733),x75731)),x75732)) % 188.18/188.25 [7574]P107(f334(f334(f242(a927),x75741),x75742))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),x75741),x75743)),x75742)) % 188.18/188.25 [7575]P107(f334(f334(f243(a927),x75751),x75752))+~P107(f334(f334(f243(a927),f334(f334(f86(a927),x75751),x75753)),x75752)) % 188.18/188.25 [7611]~P109(x76111)+E(f11(x76111,f246(x76111),f334(f179(x76111),f334(f334(f158(x76111),x76112),x76113))),f334(f149(x76111,x76111,f246(x76111),x76112),x76113)) % 188.18/188.25 [7612]~P109(x76121)+E(f12(x76121,f241(x76121),f334(f179(x76121),f334(f334(f158(x76121),x76122),x76123))),f334(f149(x76121,x76121,f241(x76121),x76122),x76123)) % 188.18/188.25 [7616]~E(x76162,f195(f935(f934(x76161,x76161),a922)))+P107(f334(f334(f242(f935(f934(x76161,x76161),a922)),x76162),x76163)) % 188.18/188.25 [7717]E(f334(f334(f108(f935(x77171,a922)),x77172),f334(f334(f23(f935(x77171,a922)),x77173),x77172)),x77173)+~P107(f334(f334(f242(f935(x77171,a922)),x77172),x77173)) % 188.18/188.25 [7718]~P107(f334(f334(f242(a927),x77181),f334(f334(f86(a927),x77183),x77182)))+P107(f334(f334(f242(a927),f334(f334(f23(a927),x77181),x77182)),x77183)) % 188.18/188.25 [7719]~P107(f334(f334(f243(a927),x77191),f334(f334(f23(a927),x77193),x77192)))+P107(f334(f334(f243(a927),f334(f334(f86(a927),x77191),x77192)),x77193)) % 188.18/188.25 [7774]E(x77741,f120(x77742))+E(f334(f148(x77742),f334(f334(f334(f190(f928(x77742),f928(x77742)),x77743),f174(x77742)),x77741)),f334(f334(f171(x77742),x77741),f50(a927,x77743,f334(f196(f928(x77742)),x77741)))) % 188.18/188.25 [7783]E(f334(f334(f316(x77831),x77832),f334(f334(f23(f935(x77831,a922)),x77833),f334(f334(f316(x77831),x77832),f195(f935(x77831,a922))))),x77833)+~P107(f334(f334(f336(x77831),x77832),x77833)) % 188.18/188.25 [7938]P107(f334(f334(f242(a927),x79381),f334(f334(f86(a927),x79382),x79383)))+~P107(f334(f334(f242(a927),f334(f334(f23(a927),x79381),x79383)),x79382)) % 188.18/188.25 [7939]P107(f334(f334(f243(a927),x79391),f334(f334(f23(a927),x79392),x79393)))+~P107(f334(f334(f243(a927),f334(f334(f86(a927),x79391),x79393)),x79392)) % 188.18/188.25 [7965]P107(f334(f66(x79651),x79652))+~P107(f334(f66(x79651),f334(f334(f108(f935(x79651,a922)),x79653),x79652))) % 188.18/188.25 [7966]P107(f334(f66(x79661),x79662))+~P107(f334(f66(x79661),f334(f334(f108(f935(x79661,a922)),x79662),x79663))) % 188.18/188.25 [8040]~P48(x80401,x80403)+P107(f334(f334(f336(f934(x80401,x80401)),f334(f334(f260(x80401,x80401),x80402),x80402)),x80403)) % 188.18/188.25 [8167]E(f334(f334(f171(a927),f146(a927,f334(f310(a927,x81671),x81672))),x81673),f334(f334(f86(a927),x81671),x81673))+~P107(f334(f334(f243(a927),f334(f334(f86(a927),x81671),x81673)),x81672)) % 188.18/188.25 [8231]E(f334(f334(f182(a927),x82311),f146(a927,f334(f310(a927,x82312),x82313))),f146(a927,f334(f310(a927,x82312),f334(f334(f86(a927),x82312),x82311))))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),x82312),x82311)),x82313)) % 188.18/188.25 [8546]E(f334(f334(f141(x85461),f334(f334(f182(x85461),x85462),x85463)),f334(f334(f158(x85461),f334(f334(f171(x85461),x85463),x85462)),f334(f334(f145(x85461),f334(a119,x85462)),x85463))),x85463)+~P107(f334(f334(f243(a927),x85462),f334(f196(f928(x85461)),x85463))) % 188.18/188.25 [8554]P107(f334(f334(f242(f935(x85541,a922)),f322(x85541,x85542)),f322(x85541,x85543)))+~P107(f334(f334(f242(f935(x85541,f935(x85541,a922))),x85543),x85542)) % 188.18/188.25 [8555]~P58(x85551,x85552,x85553)+P58(x85551,x85552,f334(f334(f23(f935(f934(x85551,x85551),a922)),x85553),f314(x85551,f195(f935(f934(x85551,x85551),a922))))) % 188.18/188.25 [8574]P107(f334(f334(f242(f935(x85741,a922)),f323(x85741,x85742)),f323(x85741,x85743)))+~P107(f334(f334(f242(f935(f934(x85741,x85741),a922)),x85743),x85742)) % 188.18/188.25 [8580]~P107(f334(f334(f243(f935(x85801,a922)),x85803),x85802))+P107(f334(f334(f336(x85801),f553(x85802,x85803,x85801)),f334(f334(f23(f935(x85801,a922)),x85802),x85803))) % 188.18/188.25 [8582]~P128(x85821)+P107(f334(f334(f242(x85821),f2(x85821)),f334(f334(f86(x85821),f334(f334(f87(x85821),x85822),x85822)),f334(f334(f87(x85821),x85823),x85823)))) % 188.18/188.25 [8614]P107(f334(f334(f242(f935(x86141,a922)),f334(f289(x86141),x86142)),f334(f289(x86141),x86143)))+~P107(f334(f334(f242(f935(f934(x86141,x86141),a922)),x86142),x86143)) % 188.18/188.25 [8641]~P56(x86411,x86412)+~P107(f334(f334(f336(f934(x86411,x86411)),f334(f334(f260(x86411,x86411),x86413),x86413)),x86412)) % 188.18/188.25 [8643]~P39(x86431,x86432)+~P107(f334(f334(f336(f934(x86431,x86431)),f334(f334(f260(x86431,x86431),x86433),x86433)),x86432)) % 188.18/188.25 [8701]P107(f334(f334(f242(f935(x87011,a922)),f43(f935(x87011,a922),x87012)),f43(f935(x87011,a922),x87013)))+~P107(f334(f334(f242(f935(f935(x87011,a922),a922)),x87013),x87012)) % 188.18/188.25 [8702]P107(f334(f334(f242(f935(x87021,a922)),f42(f935(x87021,a922),x87022)),f42(f935(x87021,a922),x87023)))+~P107(f334(f334(f242(f935(f935(x87021,a922),a922)),x87022),x87023)) % 188.18/188.25 [8759]~P10(x87591,x87593,x87592)+P107(f334(f334(f242(f935(f934(x87591,x87591),a922)),x87592),f334(f334(f262(x87591,x87591),x87593),f334(f16(f935(x87591,a922),x87591),x87593)))) % 188.18/188.25 [8760]~P55(x87601,x87603,x87602)+P107(f334(f334(f242(f935(f934(x87601,x87601),a922)),x87602),f334(f334(f262(x87601,x87601),x87603),f334(f16(f935(x87601,a922),x87601),x87603)))) % 188.18/188.25 [8808]~P86(x88081)+P107(f334(f334(f242(x88081),f334(f334(f23(x88081),f334(f81(x88081),x88082)),f334(f81(x88081),x88083))),f334(f81(x88081),f334(f334(f23(x88081),x88083),x88082)))) % 188.18/188.25 [8809]~P86(x88091)+P107(f334(f334(f242(x88091),f334(f334(f23(x88091),f334(f81(x88091),x88092)),f334(f81(x88091),x88093))),f334(f81(x88091),f334(f334(f23(x88091),x88092),x88093)))) % 188.18/188.25 [8841]P107(f334(f334(f242(f935(f934(x88411,x88411),a922)),f314(x88411,x88412)),f314(x88411,x88413)))+~P107(f334(f334(f242(f935(f934(x88411,x88411),a922)),x88412),x88413)) % 188.18/188.25 [8945]~P27(x89452,x89451,x89453,f250(f935(x89452,a922)))+E(f334(f78(x89451,x89452,x89452,f97(x89452,x89451,f250(f935(x89452,a922)),x89453)),x89453),f32(x89452)) % 188.18/188.25 [9004]P58(x90041,x90042,x90043)+~P58(x90041,x90042,f334(f334(f23(f935(f934(x90041,x90041),a922)),x90043),f314(x90041,f195(f935(f934(x90041,x90041),a922))))) % 188.18/188.25 [9024]P107(f334(f334(f242(f935(f934(f928(x90241),f928(x90241)),a922)),f164(x90241,x90242)),f164(x90241,x90243)))+~P107(f334(f334(f242(f935(f934(x90241,x90241),a922)),x90242),x90243)) % 188.18/188.25 [9025]P107(f334(f334(f242(f935(f934(f928(x90251),f928(x90251)),a922)),f165(x90251,x90252)),f165(x90251,x90253)))+~P107(f334(f334(f242(f935(f934(x90251,x90251),a922)),x90252),x90253)) % 188.18/188.25 [9048]~P55(x90481,x90483,x90482)+P107(f334(f334(f242(f935(f934(x90481,x90481),a922)),x90482),f334(f334(f295(x90481,x90481,x90481),f334(f293(x90481,x90481),x90482)),x90482))) % 188.18/188.25 [9106]~P107(f334(f144(x91061),x91062))+E(f334(f143(x91061,f334(f334(f7(x91061,f935(x91061,a922),a922),f336(x91061)),f334(f179(x91061),f183(x91061,x91062,x91063)))),x91062),f183(x91061,x91062,x91063)) % 188.18/188.25 [9161]E(x91611,x91612)+~P107(f334(f334(f336(f934(x91613,x91613)),f334(f334(f260(x91613,x91613),x91611),x91612)),f314(x91613,f195(f935(f934(x91613,x91613),a922))))) % 188.18/188.25 [9242]P107(f334(f334(f336(x92421),x92422),f323(x92421,x92423)))+P107(f334(f334(f336(f934(x92421,x92421)),f334(f334(f260(x92421,x92421),f518(x92423,x92422,x92421)),x92422)),x92423)) % 188.18/188.25 [9243]P107(f334(f334(f336(x92431),x92432),f323(x92431,x92433)))+P107(f334(f334(f336(f934(x92431,x92431)),f334(f334(f260(x92431,x92431),f600(x92433,x92432,x92431)),x92432)),x92433)) % 188.18/188.25 [9244]P107(f334(f334(f336(x92441),x92442),f323(x92441,x92443)))+P107(f334(f334(f336(f934(x92441,x92441)),f334(f334(f260(x92441,x92441),f603(x92443,x92442,x92441)),x92442)),x92443)) % 188.18/188.25 [9274]P27(x92741,x92742,x92743,f250(f935(x92741,a922)))+~E(f334(f78(x92742,x92741,x92741,f97(x92741,x92742,f250(f935(x92741,a922)),x92743)),x92743),f32(x92741)) % 188.18/188.25 [9322]~P107(f334(f334(f336(f928(x93221)),x93223),f168(x93221,x93222)))+P107(f334(f167(x93221,f334(f334(f7(x93221,f935(x93221,a922),a922),f336(x93221)),x93222)),x93223)) % 188.18/188.25 [9350]P107(f334(x93503,x93502))+E(f334(f270(x93501),f334(f334(f18(x93501,a922,a922),f334(f334(f8(a922,f935(a922,a922),x93501),a332),f334(a331,x93502))),x93503)),f195(f935(x93501,a922))) % 188.18/188.25 [9368]~P86(x93681)+P107(f334(f334(f242(x93681),f334(f81(x93681),f334(f334(f23(x93681),f334(f81(x93681),x93682)),f334(f81(x93681),x93683)))),f334(f81(x93681),f334(f334(f23(x93681),x93682),x93683)))) % 188.18/188.25 [9384]~P107(f334(x93843,x93842))+E(f334(f270(x93841),f334(f334(f18(x93841,a922,a922),f334(f334(f8(a922,f935(a922,a922),x93841),a332),f334(a331,x93842))),x93843)),f334(f334(f316(x93841),x93842),f195(f935(x93841,a922)))) % 188.18/188.25 [9391]~P107(f334(f334(f336(f935(x93911,a922)),x93913),f334(f315(x93911),x93912)))+P107(f334(f256(x93911,f334(f334(f7(x93911,f935(x93911,a922),a922),f336(x93911)),x93912)),x93913)) % 188.18/188.25 [9426]P39(x94261,x94262)+P107(f334(f334(f336(f934(x94261,x94261)),f334(f334(f260(x94261,x94261),f334(f530(x94262,x94261),f334(a119,x94263))),f334(f530(x94262,x94261),x94263))),x94262)) % 188.18/188.25 [9566]P107(f334(f334(f336(f928(x95661)),x95662),f168(x95661,x95663)))+~P107(f334(f167(x95661,f334(f334(f7(x95661,f935(x95661,a922),a922),f336(x95661)),x95663)),x95662)) % 188.18/188.25 [9579]P107(f334(f334(f336(f935(x95791,a922)),x95792),f334(f315(x95791),x95793)))+~P107(f334(f256(x95791,f334(f334(f7(x95791,f935(x95791,a922),a922),f336(x95791)),x95793)),x95792)) % 188.18/188.25 [9636]P107(f334(f334(f336(x96361),f334(f276(x96361,x96362),x96363)),f334(f179(x96361),f334(f334(f161(f934(a106,x96361),x96361),f264(a106,x96361)),x96362))))+~P107(f334(f334(f243(a106),x96363),f334(f172(a106),f334(f334(f161(f934(a106,x96361),a106),f259(a106,x96361)),x96362)))) % 188.18/188.25 [9680]P107(f334(f334(f242(f935(f934(f928(x96801),f928(x96801)),a922)),f165(x96801,x96802)),f334(f334(f262(f928(x96801),f928(x96801)),f168(x96801,x96803)),f334(f16(f935(f928(x96801),a922),f928(x96801)),f168(x96801,x96803)))))+~P107(f334(f334(f242(f935(f934(x96801,x96801),a922)),x96802),f334(f334(f262(x96801,x96801),x96803),f334(f16(f935(x96801,a922),x96801),x96803)))) % 188.18/188.25 [9704]P107(f334(f334(f336(x97041),f334(f259(x97041,f934(a106,a106)),f334(f274(x97041,x97042),x97043))),f334(f179(x97041),f334(f334(f161(f934(a106,x97041),x97041),f264(a106,x97041)),x97042))))+~P107(f334(f334(f243(a106),f2(a106)),f334(f172(a106),f334(f334(f161(f934(a106,x97041),a106),f259(a106,x97041)),x97042)))) % 188.18/188.25 [9727]~P107(f334(f334(f242(f935(f934(x97271,x97271),a922)),x97272),f334(f334(f262(x97271,x97271),x97273),f334(f16(f935(x97271,a922),x97271),x97273))))+P107(f334(f334(f242(f935(f934(x97271,x97271),a922)),f334(f334(f295(x97271,x97271,x97271),x97272),f314(x97271,x97272))),f334(f334(f262(x97271,x97271),x97273),f334(f16(f935(x97271,a922),x97271),x97273)))) % 188.18/188.25 [10055]~P39(x100551,x100552)+~P107(f334(f334(f336(f934(x100551,x100551)),f334(f334(f260(x100551,x100551),f334(x100553,f334(a119,f531(x100552,x100551,x100553)))),f334(x100553,f531(x100552,x100551,x100553)))),x100552)) % 188.18/188.25 [10056]~P39(x100561,x100562)+~P107(f334(f334(f336(f934(x100561,x100561)),f334(f334(f260(x100561,x100561),f334(x100563,f334(a119,f617(x100563,x100562,x100561)))),f334(x100563,f617(x100563,x100562,x100561)))),x100562)) % 188.18/188.25 [10272]P107(f334(f334(f242(f935(f934(f935(x102721,a922),f935(x102721,a922)),a922)),f334(f334(f295(f935(x102721,a922),f935(x102721,a922),f935(x102721,a922)),f327(x102721,x102722)),f334(f334(f108(f935(f934(f935(x102721,a922),f935(x102721,a922)),a922)),f327(x102721,x102723)),f334(f334(f316(f934(f935(x102721,a922),f935(x102721,a922))),f334(f334(f260(f935(x102721,a922),f935(x102721,a922)),f195(f935(x102721,a922))),f195(f935(x102721,a922)))),f195(f935(f934(f935(x102721,a922),f935(x102721,a922)),a922)))))),f327(x102721,x102722)))+~P107(f334(f334(f242(f935(f934(x102721,x102721),a922)),f334(f334(f295(x102721,x102721,x102721),x102722),x102723)),x102722)) % 188.18/188.25 [10273]P107(f334(f334(f242(f935(f934(f935(x102731,a922),f935(x102731,a922)),a922)),f334(f334(f295(f935(x102731,a922),f935(x102731,a922),f935(x102731,a922)),f325(x102731,x102732)),f334(f334(f108(f935(f934(f935(x102731,a922),f935(x102731,a922)),a922)),f325(x102731,x102733)),f334(f334(f316(f934(f935(x102731,a922),f935(x102731,a922))),f334(f334(f260(f935(x102731,a922),f935(x102731,a922)),f195(f935(x102731,a922))),f195(f935(x102731,a922)))),f195(f935(f934(f935(x102731,a922),f935(x102731,a922)),a922)))))),f325(x102731,x102732)))+~P107(f334(f334(f242(f935(f934(x102731,x102731),a922)),f334(f334(f295(x102731,x102731,x102731),x102732),x102733)),x102732)) % 188.18/188.25 [7502]~P107(f334(f334(f242(a927),x75022),x75021))+E(f334(f334(f23(a927),f334(a119,f334(f334(f23(a927),x75021),x75022))),x75023),f334(f334(f23(a927),f334(a119,x75021)),f334(f334(f86(a927),x75022),x75023))) % 188.18/188.25 [7537]~P5(x75371)+E(f334(f334(f86(x75371),f50(x75371,x75372,x75373)),f334(f334(f87(x75371),f334(f334(f41(x75371),x75372),x75373)),x75373)),x75372) % 188.18/188.25 [7723]E(f334(f334(f87(a927),f334(f111(a927),x77231)),f334(f334(f87(a927),f334(f111(a927),x77232)),x77233)),f334(f334(f87(a927),f334(f111(a927),f334(f334(f87(a1),x77231),x77232))),x77233))+P107(f334(f334(f243(a1),x77231),a89)) % 188.18/188.25 [8176]~P107(f334(f334(f242(a927),x81763),x81762))+P107(f334(f334(f242(a927),x81761),f334(f334(f23(a927),f334(f334(f86(a927),x81762),x81761)),x81763))) % 188.18/188.25 [8372]~P107(f334(f334(f242(a927),x83721),x83722))+E(f334(f334(f141(a927),f146(a927,f334(f310(a927,x83721),x83722))),f146(a927,f334(f310(a927,x83722),f334(f334(f86(a927),x83722),x83723)))),f146(a927,f334(f310(a927,x83721),f334(f334(f86(a927),x83722),x83723)))) % 188.18/188.25 [8618]~P107(f334(f66(x86181),x86182))+E(f334(a119,f334(f40(x86181),f334(f334(f23(f935(x86181,a922)),x86182),f334(f334(f316(x86181),x86183),f195(f935(x86181,a922)))))),f334(f40(x86181),f334(f334(f316(x86181),x86183),x86182))) % 188.18/188.25 [8660]~P107(f334(f66(x86601),x86602))+E(f334(f334(f86(a927),f84(a927)),f334(f40(x86601),f334(f334(f23(f935(x86601,a922)),x86602),f334(f334(f316(x86601),x86603),f195(f935(x86601,a922)))))),f334(f40(x86601),f334(f334(f316(x86601),x86603),x86602))) % 188.18/188.25 [8850]E(f334(f334(f23(a927),f334(f40(x88501),x88502)),f334(f40(x88501),f334(f334(f109(f935(x88501,a922)),x88502),x88503))),f334(f40(x88501),f334(f334(f23(f935(x88501,a922)),x88502),x88503)))+~P107(f334(f66(x88501),f334(f334(f109(f935(x88501,a922)),x88502),x88503))) % 188.18/188.25 [9100]~P8(f334(x91002,f352(x91002,x91003,x91001)))+E(f334(f107(a1),f334(f334(f9(x91001,a927),f334(f334(f8(a1,a927,x91001),a112),x91002)),x91003)),f334(f334(f9(x91001,a1),x91002),x91003)) % 188.18/188.25 [9101]~P8(f334(x91012,f459(x91012,x91013,x91011)))+E(f334(f107(a1),f334(f334(f6(x91011,a927),f334(f334(f8(a1,a927,x91011),a112),x91012)),x91013)),f334(f334(f6(x91011,a1),x91012),x91013)) % 188.18/188.25 [9144]~P107(f334(f66(x91441),x91443))+P107(f334(f334(f242(a927),f334(f334(f23(a927),f334(f40(x91441),x91442)),f334(f40(x91441),x91443))),f334(f40(x91441),f334(f334(f23(f935(x91441,a922)),x91442),x91443)))) % 188.18/188.25 [9171]P107(f334(f334(f336(x91711),f352(x91712,x91713,x91711)),x91713))+E(f334(f107(a1),f334(f334(f9(x91711,a927),f334(f334(f8(a1,a927,x91711),a112),x91712)),x91713)),f334(f334(f9(x91711,a1),x91712),x91713)) % 188.18/188.25 [9172]P107(f334(f334(f336(x91721),f459(x91722,x91723,x91721)),x91723))+E(f334(f107(a1),f334(f334(f6(x91721,a927),f334(f334(f8(a1,a927,x91721),a112),x91722)),x91723)),f334(f334(f6(x91721,a1),x91722),x91723)) % 188.18/188.25 [9234]E(f91(x92341,f334(f334(f7(x92341,f935(x92341,a922),a922),f336(x92341)),f334(f334(f23(f935(x92341,a922)),x92342),f334(f334(f316(x92341),x92343),f195(f935(x92341,a922)))))),f255(x92341,x92343,x92342))+P107(f334(f334(f242(f935(x92341,a922)),x92342),f334(f334(f316(x92341),x92343),f195(f935(x92341,a922))))) % 188.18/188.25 [9580]E(f334(f334(f161(f928(x95801),x95801),f334(f334(f7(f928(x95801),a927,x95801),f171(x95801)),x95802)),f334(f143(f928(x95801),f334(f334(f8(a927,a922,f928(x95801)),f334(f243(a927),x95802)),f196(f928(x95801)))),x95803)),f334(f334(f171(f928(x95801)),f186(x95801,x95803)),x95802))+~P107(f334(f334(f243(a927),x95802),f334(f196(f928(f928(x95801))),f186(x95801,x95803)))) % 188.18/188.25 [9654]E(f334(f143(x96541,x96542),x96543),f184(x96541,x96542,x96543))+P107(f334(f334(f336(x96541),f735(x96543,x96542,x96541)),f334(f179(x96541),f334(f334(f145(x96541),f334(f196(f928(x96541)),f184(x96541,x96542,x96543))),x96543)))) % 188.18/188.25 [9803]E(f334(f334(f145(x98031),f334(f196(f928(x98031)),f184(x98031,x98032,x98033))),x98033),f120(x98031))+~P107(f334(x98032,f334(f148(x98031),f334(f334(f145(x98031),f334(f196(f928(x98031)),f184(x98031,x98032,x98033))),x98033)))) % 188.18/188.25 [9908]~P107(f334(f334(f336(f934(x99081,x99081)),x99082),f314(x99081,x99083)))+P107(f334(f334(f336(f934(x99081,x99081)),x99082),f334(f334(f44(a927,f935(f934(x99081,x99081),a922)),f250(f935(a927,a922))),f334(f334(f7(a927,f935(f934(x99081,x99081),a922),f935(f934(x99081,x99081),a922)),f190(f934(x99081,x99081),a922)),x99083)))) % 188.18/188.25 [9970]~P107(f334(f334(f242(f935(x99701,a922)),f334(f334(f44(a927,f935(x99701,a922)),f334(f310(a927,f2(a927)),f454(x99703,x99702,x99701))),x99702)),x99703))+P107(f334(f334(f242(f935(x99701,a922)),f334(f334(f44(a927,f935(x99701,a922)),f250(f935(a927,a922))),x99702)),x99703)) % 188.18/188.25 [10029]~P107(f334(f334(f243(a1),f2(a1)),x100293))+P107(f334(f334(f243(a1),x100291),f334(f334(f86(a1),x100292),f334(f334(f87(a1),f334(f334(f86(a1),f334(f81(a1),f334(f334(f23(a1),x100292),x100291))),f84(a1))),x100293)))) % 188.18/188.25 [10041]~P39(x100411,f334(f334(f108(f935(f934(x100411,x100411),a922)),x100412),x100413))+P39(x100411,f334(f334(f108(f935(f934(x100411,x100411),a922)),f334(f334(f108(f935(f934(x100411,x100411),a922)),f334(f334(f295(x100411,x100411,x100411),x100412),x100412)),f334(f334(f295(x100411,x100411,x100411),x100413),x100412))),x100413)) % 188.18/188.25 [10113]P39(x101131,f334(f334(f108(f935(f934(x101131,x101131),a922)),x101132),x101133))+~P39(x101131,f334(f334(f108(f935(f934(x101131,x101131),a922)),f334(f334(f108(f935(f934(x101131,x101131),a922)),f334(f334(f295(x101131,x101131,x101131),x101132),x101132)),f334(f334(f295(x101131,x101131,x101131),x101133),x101132))),x101133)) % 188.18/188.25 [9659]~P142(x96591)+E(f334(f110(x96591),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x96592),x96593)),f195(f935(f934(a927,a927),a922)))))),f334(f334(f23(x96591),f334(f107(x96591),x96592)),f334(f107(x96591),x96593))) % 188.18/188.25 [9752]P107(f334(x97523,x97522))+E(f334(f270(x97521),f334(f334(f18(x97521,a922,a922),f334(f334(f8(a922,f935(a922,a922),x97521),a332),f334(f334(f7(x97521,x97521,a922),a331),x97522))),x97523)),f195(f935(x97521,a922))) % 188.18/188.25 [9754]~P107(f334(x97543,x97542))+E(f334(f270(x97541),f334(f334(f18(x97541,a922,a922),f334(f334(f8(a922,f935(a922,a922),x97541),a332),f334(f334(f7(x97541,x97541,a922),a331),x97542))),x97543)),f334(f334(f316(x97541),x97542),f195(f935(x97541,a922)))) % 188.18/188.25 [10006]E(x100061,x100062)+P107(f334(f334(f251(x100063,x100063,f334(f334(f8(f935(x100063,a922),f935(x100063,a922),x100063),f334(f8(a922,a922,x100063),a329)),a331)),x100061),x100062)) % 188.18/188.25 [10092]~E(x100921,x100922)+~P107(f334(f334(f251(x100923,x100923,f334(f334(f8(f935(x100923,a922),f935(x100923,a922),x100923),f334(f8(a922,a922,x100923),a329)),a331)),x100921),x100922)) % 188.18/188.25 [10105]~P107(f334(f66(x101051),x101053))+E(f334(f334(f69(x101051,f935(x101051,a922),f334(f334(f8(f935(x101051,a922),f935(f935(x101051,a922),f935(x101051,a922)),x101051),f334(f7(f935(x101051,a922),f935(x101051,a922),f935(x101051,a922)),f23(f935(x101051,a922)))),f334(f334(f7(x101051,f935(x101051,a922),f935(x101051,a922)),f316(x101051)),f195(f935(x101051,a922))))),x101052),x101053),f334(f334(f23(f935(x101051,a922)),x101052),x101053)) % 188.18/188.25 [10132]~P107(f334(f334(f243(a1),f2(a1)),x101323))+P107(f334(f334(f243(a1),f334(f334(f23(a1),x101321),f334(f334(f87(a1),f334(f334(f86(a1),f334(f81(a1),f334(f334(f23(a1),x101321),x101322))),f84(a1))),x101323))),x101322)) % 188.18/188.25 [10389]~P107(f334(f334(f336(x103891),x103893),f323(x103891,x103892)))+P107(f334(f322(x103891,f334(f334(f7(x103891,f935(f934(x103891,x103891),a922),f935(x103891,a922)),f334(f334(f8(f935(x103891,f935(f935(f934(x103891,x103891),a922),a922)),f935(f935(f934(x103891,x103891),a922),f935(x103891,a922)),x103891),f7(x103891,f935(f934(x103891,x103891),a922),a922)),f334(f334(f8(f935(x103891,f934(x103891,x103891)),f935(x103891,f935(f935(f934(x103891,x103891),a922),a922)),x103891),f334(f8(f934(x103891,x103891),f935(f935(f934(x103891,x103891),a922),a922),x103891),f336(f934(x103891,x103891)))),f260(x103891,x103891)))),x103892)),x103893)) % 188.18/188.25 [10405]P107(f334(f334(f336(x104051),x104052),f323(x104051,x104053)))+~P107(f334(f322(x104051,f334(f334(f7(x104051,f935(f934(x104051,x104051),a922),f935(x104051,a922)),f334(f334(f8(f935(x104051,f935(f935(f934(x104051,x104051),a922),a922)),f935(f935(f934(x104051,x104051),a922),f935(x104051,a922)),x104051),f7(x104051,f935(f934(x104051,x104051),a922),a922)),f334(f334(f8(f935(x104051,f934(x104051,x104051)),f935(x104051,f935(f935(f934(x104051,x104051),a922),a922)),x104051),f334(f8(f934(x104051,x104051),f935(f935(f934(x104051,x104051),a922),a922),x104051),f336(f934(x104051,x104051)))),f260(x104051,x104051)))),x104053)),x104052)) % 188.18/188.25 [9968]~P107(f334(f66(x99681),f334(f270(x99681),x99683)))+P107(f334(f66(x99681),f334(f270(x99681),f334(f334(f18(x99681,a922,a922),f334(f334(f8(a922,f935(a922,a922),x99681),a332),x99682)),x99683)))) % 188.18/188.25 [9969]~P107(f334(f66(x99691),f334(f270(x99691),x99692)))+P107(f334(f66(x99691),f334(f270(x99691),f334(f334(f18(x99691,a922,a922),f334(f334(f8(a922,f935(a922,a922),x99691),a332),x99692)),x99693)))) % 188.18/188.25 [10076]P107(f334(f66(x100761),f334(f270(x100761),x100762)))+~P107(f334(f66(x100761),f334(f270(x100761),f334(f334(f18(x100761,a922,a922),f334(f334(f8(a922,f935(a922,a922),x100761),a333),x100763)),x100762)))) % 188.18/188.25 [10077]P107(f334(f66(x100771),f334(f270(x100771),x100772)))+~P107(f334(f66(x100771),f334(f270(x100771),f334(f334(f18(x100771,a922,a922),f334(f334(f8(a922,f935(a922,a922),x100771),a333),x100772)),x100773)))) % 188.18/188.25 [10343]~P107(f334(f66(x103431),x103432))+P107(f334(f66(f928(x103431)),f334(f270(f928(x103431)),f334(f334(f18(f928(x103431),a922,a922),f334(f334(f8(a922,f935(a922,a922),f928(x103431)),a332),f334(f334(f7(f928(x103431),f935(x103431,a922),a922),f334(f334(f8(f935(x103431,a922),f935(f935(x103431,a922),a922),f928(x103431)),f242(f935(x103431,a922))),f179(x103431))),x103432))),f334(f334(f7(f928(x103431),a927,a922),f334(f334(f8(a927,f935(a927,a922),f928(x103431)),a331),f196(f928(x103431)))),x103433))))) % 188.18/188.25 [10344]~P107(f334(f66(x103441),x103442))+P107(f334(f66(f928(x103441)),f334(f270(f928(x103441)),f334(f334(f18(f928(x103441),a922,a922),f334(f334(f8(a922,f935(a922,a922),f928(x103441)),a332),f334(f334(f7(f928(x103441),f935(x103441,a922),a922),f334(f334(f8(f935(x103441,a922),f935(f935(x103441,a922),a922),f928(x103441)),f242(f935(x103441,a922))),f179(x103441))),x103442))),f334(f334(f7(f928(x103441),a927,a922),f334(f334(f8(a927,f935(a927,a922),f928(x103441)),f242(a927)),f196(f928(x103441)))),x103443))))) % 188.18/188.25 [9621]~P95(x96211)+E(f334(f334(f252(x96211),x96212),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x96213)),x96213)),a104))),f334(f334(f94(x96211,x96211),f334(f334(f252(x96211),x96212),f334(f111(a927),x96213))),f334(f334(f18(x96211,x96211,x96211),f87(x96211)),f5(x96211)))) % 188.18/188.25 [10304]~P119(x103041)+E(f334(f334(f252(x103041),x103042),f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103043)),f334(f334(f87(x103041),f334(f334(f252(x103041),x103042),x103043)),f334(f334(f252(x103041),x103042),x103043))) % 188.18/188.25 [10320]~P81(x103201)+E(f334(f334(f252(x103201),f334(f334(f252(x103201),x103202),x103203)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f252(x103201),x103202),f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103203))) % 188.18/188.25 [10367]~P142(x103671)+E(f334(f334(f252(x103671),f334(f85(x103671),x103672)),f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103673)),f334(f334(f252(x103671),x103672),f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103673))) % 188.18/188.25 [10429]~P124(x104291)+P107(f334(f334(f242(x104291),f2(x104291)),f334(f334(f86(x104291),f334(f334(f252(x104291),x104292),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104291),x104293),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))))) % 188.18/188.25 [10375]~P119(x103751)+E(f334(f334(f252(x103751),x103752),f334(a119,f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103753))),f334(f334(f87(x103751),x103752),f334(f334(f87(x103751),f334(f334(f252(x103751),x103752),x103753)),f334(f334(f252(x103751),x103752),x103753)))) % 188.18/188.25 [10395]~P81(x103951)+E(f334(f334(f87(x103951),x103952),f334(f334(f252(x103951),f334(f334(f252(x103951),x103952),x103953)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x103951),x103952),f334(a119,f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103953)))) % 188.18/188.25 [10409]~P124(x104091)+P107(f334(f334(f242(x104091),f2(x104091)),f334(f334(f252(x104091),x104092),f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104093)))) % 188.18/188.25 [10448]~P95(x104481)+E(f334(f334(f23(x104481),f334(f334(f86(x104481),f334(f334(f252(x104481),x104482),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104481),x104483),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f334(f334(f87(x104481),f334(f334(f87(x104481),f334(f111(x104481),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104482)),x104483)),f334(f334(f252(x104481),f334(f334(f23(x104481),x104482),x104483)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.25 [10449]~P95(x104491)+E(f334(f334(f86(x104491),f334(f334(f86(x104491),f334(f334(f252(x104491),x104492),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104491),x104493),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f334(f334(f87(x104491),f334(f334(f87(x104491),f334(f111(x104491),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104492)),x104493)),f334(f334(f252(x104491),f334(f334(f86(x104491),x104492),x104493)),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.25 [4922]E(x49221,x49222)+~E(f31(x49223,x49221),f31(x49224,x49222)) % 188.18/188.25 [4923]E(x49231,x49232)+~E(f31(x49231,x49233),f31(x49232,x49234)) % 188.18/188.25 [4924]E(x49241,x49242)+~E(f26(x49243,x49241),f26(x49244,x49242)) % 188.18/188.25 [4925]E(x49251,x49252)+~E(f26(x49251,x49253),f26(x49252,x49254)) % 188.18/188.25 [4926]E(x49261,x49262)+~E(f30(x49263,x49261),f30(x49264,x49262)) % 188.18/188.25 [4927]E(x49271,x49272)+~E(f30(x49271,x49273),f30(x49272,x49274)) % 188.18/188.25 [7983]P27(x79831,x79832,x79833,x79834)+~E(f426(x79834,x79833,x79832,x79831),f449(x79834,x79833,x79832,x79831)) % 188.18/188.25 [8265]P36(x82651,x82652,x82653,x82654,f120(x82652))+~E(x82654,f120(x82651)) % 188.18/188.25 [8266]P36(x82661,x82662,x82663,f120(x82661),x82664)+~E(x82664,f120(x82662)) % 188.18/188.25 [8798]~P36(x87982,x87983,x87984,x87981,f120(x87983))+E(x87981,f120(x87982)) % 188.18/188.25 [8799]~P36(x87993,x87992,x87994,f120(x87993),x87991)+E(x87991,f120(x87992)) % 188.18/188.25 [5302]~P19(x53023,x53021,x53024)+E(f334(f334(x53021,x53022),x53022),x53022) % 188.18/188.25 [5552]P107(f334(x55522,x55524))+E(f334(f143(x55521,x55522),f176(x55521,x55523,x55524)),f120(x55521)) % 188.18/188.25 [5589]~E(x55894,f195(f935(x55891,a922)))+E(f334(f317(x55891,x55892,x55893),x55894),f195(f935(x55892,a922))) % 188.18/188.25 [5833]~P107(f334(x58332,x58334))+E(f334(f143(x58331,x58332),f176(x58331,x58333,x58334)),f176(x58331,x58333,x58334)) % 188.18/188.25 [5866]~E(f334(f317(x58662,x58663,x58664),x58661),f195(f935(x58663,a922)))+E(x58661,f195(f935(x58662,a922))) % 188.18/188.25 [6055]~P9(x60551,x60553)+E(f279(x60551,x60552,f278(x60551,x60553),x60554),x60554) % 188.18/188.25 [6161]~P109(x61612)+E(f334(f334(f155(x61611,x61612,x61613),x61614),f120(x61611)),f334(f334(f158(x61611),x61614),f120(x61611))) % 188.18/188.25 [6511]~E(x65111,f195(f935(x65112,a922)))+~P107(f334(f67(x65112,x65113,x65111),x65114)) % 188.18/188.25 [6533]~P62(x65331,x65333,x65334,x65332)+P107(f334(f66(x65331),x65332)) % 188.18/188.25 [6535]~P62(x65351,x65353,x65352,x65354)+P107(f334(f66(x65351),x65352)) % 188.18/188.25 [6541]~P62(x65412,x65413,x65414,x65411)+~E(x65411,f195(f935(x65412,a922))) % 188.18/188.25 [6574]~P111(x65741)+E(f334(f334(f109(f935(x65741,a922)),f334(f310(x65741,x65742),x65743)),f311(x65741,x65743,x65744)),f195(f935(x65741,a922))) % 188.18/188.25 [6598]~P107(f334(f334(x65983,x65984),x65982))+P107(f334(f334(f336(x65981),x65982),f299(x65981,x65983,x65984))) % 188.18/188.25 [6599]~P107(f334(f334(x65993,x65994),x65992))+P107(f334(f334(f336(x65991),x65992),f300(x65991,x65993,x65994))) % 188.18/188.25 [6600]~P107(f334(f334(x66003,x66002),x66004))+P107(f334(f334(f336(x66001),x66002),f304(x66001,x66003,x66004))) % 188.18/188.25 [6601]~P107(f334(f334(x66013,x66012),x66014))+P107(f334(f334(f336(x66011),x66012),f301(x66011,x66013,x66014))) % 188.18/188.25 [6666]~P51(x66664,x66661,x66662,x66663)+P107(f334(f334(x66661,x66662),x66663)) % 188.18/188.25 [6745]~P111(x67451)+E(f334(f334(f109(f935(x67451,a922)),f313(x67451,x67452,x67453)),f311(x67451,x67453,x67454)),f195(f935(x67451,a922))) % 188.18/188.25 [6746]~P111(x67461)+E(f334(f334(f109(f935(x67461,a922)),f312(x67461,x67462,x67463)),f313(x67461,x67463,x67464)),f195(f935(x67461,a922))) % 188.18/188.25 [6747]~P111(x67471)+E(f334(f334(f109(f935(x67471,a922)),f312(x67471,x67472,x67473)),f312(x67471,x67473,x67474)),f195(f935(x67471,a922))) % 188.18/188.25 [6748]~P111(x67481)+E(f334(f334(f109(f935(x67481,a922)),f311(x67481,x67482,x67483)),f313(x67481,x67483,x67484)),f195(f935(x67481,a922))) % 188.18/188.25 [6749]~P111(x67491)+E(f334(f334(f109(f935(x67491,a922)),f311(x67491,x67492,x67493)),f312(x67491,x67493,x67494)),f195(f935(x67491,a922))) % 188.18/188.25 [6785]P107(f334(f334(x67851,x67852),f528(x67852,x67851)))+~P107(f334(f257(x67853,x67854,x67851),x67852)) % 188.18/188.25 [6789]~P51(x67891,x67892,x67893,x67894)+~P107(f334(f334(x67892,x67894),x67893)) % 188.18/188.25 [6863]~P109(x68632)+E(f334(f179(x68631),f157(x68631,x68632,x68633,x68634)),f334(f179(x68631),x68634)) % 188.18/188.25 [6913]~P147(x69131)+E(f197(x69131,x69132,f334(a119,x69133),x69134),f197(x69131,x69132,x69133,f334(x69132,x69134))) % 188.18/188.25 [6973]~P107(f334(f334(f336(x69734),x69733),f299(x69734,x69731,x69732)))+P107(f334(f334(x69731,x69732),x69733)) % 188.18/188.25 [6974]~P107(f334(f334(f336(x69744),x69743),f300(x69744,x69741,x69742)))+P107(f334(f334(x69741,x69742),x69743)) % 188.18/188.25 [6975]~P107(f334(f334(f336(x69754),x69752),f304(x69754,x69751,x69753)))+P107(f334(f334(x69751,x69752),x69753)) % 188.18/188.25 [6976]~P107(f334(f334(f336(x69764),x69762),f301(x69764,x69761,x69763)))+P107(f334(f334(x69761,x69762),x69763)) % 188.18/188.25 [7048]E(f334(f40(f933(x70481,x70482)),f320(x70481,x70482,x70483,x70484)),f2(a927))+P107(f334(f66(x70482),x70484)) % 188.18/188.25 [7049]E(f334(f40(f933(x70491,x70492)),f320(x70491,x70492,x70493,x70494)),f2(a927))+P107(f334(f66(x70491),x70493)) % 188.18/188.25 [7245]~P16(x72454,x72451,x72452)+E(f334(f78(x72451,x72451,x72451,f334(x72452,x72453)),f334(x72452,x72453)),f334(x72452,x72453)) % 188.18/188.25 [7484]E(f285(x74841,x74842,x74843,x74844),f334(f260(f935(a106,f935(a922,f931(f929(x74841)))),f934(a106,a106)),f46(x74841)))+~P107(f334(f334(f242(a106),x74843),f2(a106))) % 188.18/188.25 [8102]~E(x81022,x81023)+P107(f334(f334(f336(f934(x81021,x81021)),f334(f334(f260(x81021,x81021),x81022),x81023)),f314(x81021,x81024))) % 188.18/188.25 [8131]~P27(x81311,x81312,x81313,f250(f935(x81311,a922)))+E(f334(f83(x81311,x81312,f250(f935(x81311,a922)),x81313),f334(x81313,x81314)),x81314) % 188.18/188.25 [8132]~P27(x81321,x81322,x81323,f250(f935(x81321,a922)))+E(f334(f97(x81321,x81322,f250(f935(x81321,a922)),x81323),f334(x81323,x81324)),x81324) % 188.18/188.25 [8214]~P107(f334(f334(f336(f928(x82141)),f334(f334(f158(x82141),x82144),x82142)),f168(x82141,x82143)))+P107(f334(f334(f336(f928(x82141)),x82142),f168(x82141,x82143))) % 188.18/188.25 [8215]~P107(f334(f334(f336(f928(x82151)),f334(f334(f141(x82151),x82154),x82152)),f168(x82151,x82153)))+P107(f334(f334(f336(f928(x82151)),x82152),f168(x82151,x82153))) % 188.18/188.25 [8216]~P107(f334(f334(f336(f928(x82161)),f334(f334(f141(x82161),x82162),x82164)),f168(x82161,x82163)))+P107(f334(f334(f336(f928(x82161)),x82162),f168(x82161,x82163))) % 188.18/188.25 [8227]~P109(x82271)+P15(x82271,f334(f334(f161(x82272,x82271),x82273),f157(x82272,x82271,x82273,x82274))) % 188.18/188.25 [8329]P27(x83294,x83293,x83291,x83292)+E(f334(x83291,f426(x83292,x83291,x83293,x83294)),f334(x83291,f449(x83292,x83291,x83293,x83294))) % 188.18/188.25 [8436]~P27(x84362,x84361,x84364,x84363)+P27(x84361,x84362,f83(x84362,x84361,x84363,x84364),f334(f317(x84362,x84361,x84364),x84363)) % 188.18/188.25 [8572]P39(f934(x85722,x85724),f288(x85722,x85724,x85721,x85723))+P107(f334(x85721,f542(x85722,x85723,x85724,x85721))) % 188.18/188.25 [8685]E(x86851,x86852)+~P107(f334(f334(f336(f934(x86853,x86853)),f334(f334(f260(x86853,x86853),x86851),x86852)),f271(x86853,x86854))) % 188.18/188.25 [8751]~P107(f334(f66(f933(x87513,x87511)),f320(x87513,x87511,x87514,x87512)))+P107(f334(f66(x87511),x87512)) % 188.18/188.25 [8752]~P107(f334(f66(f933(x87521,x87523)),f320(x87521,x87523,x87522,x87524)))+P107(f334(f66(x87521),x87522)) % 188.18/188.25 [8761]~P27(x87611,x87612,x87613,x87614)+P28(x87611,x87612,x87613,x87614,f334(f317(x87611,x87612,x87613),x87614)) % 188.18/188.25 [8762]P13(x87621,x87622,x87623,x87624)+~E(f334(x87624,f841(x87622,x87624,x87623,x87621)),f334(x87624,f842(x87622,x87624,x87623,x87621))) % 188.18/188.25 [8851]~P28(x88512,x88513,x88514,x88511,f195(f935(x88513,a922)))+E(x88511,f195(f935(x88512,a922))) % 188.18/188.25 [8852]~P28(x88523,x88522,x88524,f195(f935(x88523,a922)),x88521)+E(x88521,f195(f935(x88522,a922))) % 188.18/188.25 [8936]P39(f934(x89361,x89362),f288(x89361,x89362,x89363,x89364))+~P39(x89362,f334(x89364,f542(x89361,x89364,x89362,x89363))) % 188.18/188.25 [9499]E(f334(f334(f166(x94991,x94992),f684(x94993,x94994,x94992,x94991)),f683(x94993,x94994,x94992,x94991)),x94994)+~P107(f334(f334(f336(f934(f928(x94991),f928(x94991))),f334(f334(f260(f928(x94991),f928(x94991)),x94992),x94994)),f164(x94991,x94993))) % 188.18/188.25 [9507]~P107(f334(f334(f336(f934(f928(x95071),f928(x95071))),f334(f334(f260(f928(x95071),f928(x95071)),x95072),x95073)),f152(x95071,x95074)))+P107(f334(f334(f336(f934(f928(x95071),f928(x95071))),f334(f334(f260(f928(x95071),f928(x95071)),x95072),x95073)),f154(x95071,x95074))) % 188.18/188.25 [9618]P107(f334(f66(x96181),x96182))+~P107(f334(f334(f336(f934(f935(x96181,a922),f935(x96181,a922))),f334(f334(f260(f935(x96181,a922),f935(x96181,a922)),x96183),x96182)),f325(x96181,x96184))) % 188.18/188.25 [9619]P107(f334(f66(x96191),x96192))+~P107(f334(f334(f336(f934(f935(x96191,a922),f935(x96191,a922))),f334(f334(f260(f935(x96191,a922),f935(x96191,a922)),x96192),x96193)),f325(x96191,x96194))) % 188.18/188.25 [9620]~E(x96201,f195(f935(x96202,a922)))+~P107(f334(f334(f336(f934(f935(x96202,a922),f935(x96202,a922))),f334(f334(f260(f935(x96202,a922),f935(x96202,a922)),x96203),x96201)),f325(x96202,x96204))) % 188.18/188.25 [10253]P13(x102531,x102532,x102533,x102534)+~P107(f334(f334(f265(x102531,x102531,a922),f334(f334(f7(x102531,f935(x102531,x102532),f935(x102531,a922)),f334(f334(f8(f935(x102532,a922),f935(f935(x102531,x102532),f935(x102531,a922)),x102531),f8(x102532,a922,x102531)),f334(f334(f8(x102532,f935(x102532,a922),x102531),a331),x102534))),x102534)),f578(x102534,x102533,x102532,x102531))) % 188.18/188.25 [5203]~E(x52032,f120(x52031))+E(f334(f334(f166(x52031,x52032),x52033),x52034),f120(x52031)) % 188.18/188.25 [5204]~E(x52044,f120(x52041))+E(f334(f334(f161(x52041,x52042),x52043),x52044),f120(x52042)) % 188.18/188.25 [5434]E(x54341,f120(x54342))+~E(f334(f334(f161(x54342,x54343),x54344),x54341),f120(x54343)) % 188.18/188.25 [5435]E(x54351,f120(x54352))+~E(f334(f334(f166(x54352,x54351),x54353),x54354),f120(x54352)) % 188.18/188.25 [5473]E(x54731,x54732)+~E(f334(f334(f141(x54733),x54734),x54731),f334(f334(f141(x54733),x54734),x54732)) % 188.18/188.25 [5474]E(x54741,x54742)+~E(f334(f334(f141(x54743),x54741),x54744),f334(f334(f141(x54743),x54742),x54744)) % 188.18/188.25 [5625]P107(f334(x56253,x56252))+E(f177(x56251,x56252,f334(f143(x56251,x56253),x56254)),f334(f143(x56251,x56253),x56254)) % 188.18/188.25 [5627]~P107(f334(x56272,x56273))+P35(x56271,x56272,f334(f334(f158(x56271),x56273),x56274)) % 188.18/188.25 [5636]E(x56361,x56362)+~E(f146(a927,f334(f310(a927,x56361),x56363)),f334(f334(f158(a927),x56362),x56364)) % 188.18/188.25 [5684]~P29(x56842,x56843)+P29(x56841,f334(f334(f79(x56842,x56841),x56843),x56844)) % 188.18/188.25 [5685]~P39(x56852,x56853)+P39(x56851,f334(f334(f294(x56852,x56851),x56853),x56854)) % 188.18/188.25 [5686]~P40(x56862,x56863)+P40(x56861,f334(f334(f294(x56862,x56861),x56863),x56864)) % 188.18/188.25 [5687]~P54(x56872,x56873)+P54(x56871,f334(f334(f294(x56872,x56871),x56873),x56874)) % 188.18/188.25 [5816]~P35(x58161,x58162,x58164)+P35(x58161,x58162,f334(f334(f158(x58161),x58163),x58164)) % 188.18/188.25 [5817]~P35(x58171,x58172,x58174)+P35(x58171,x58172,f334(f334(f141(x58171),x58173),x58174)) % 188.18/188.25 [5818]~P35(x58181,x58182,x58183)+P35(x58181,x58182,f334(f334(f141(x58181),x58183),x58184)) % 188.18/188.25 [5909]~E(x59091,f120(x59092))+~E(f334(f334(f141(x59092),x59093),f334(f334(f158(x59092),x59094),f120(x59092))),x59091) % 188.18/188.25 [5936]~P33(x59363,x59361,f334(f334(f158(x59363),x59362),x59364))+P107(f334(x59361,x59362)) % 188.18/188.25 [5946]E(f121(x59461,x59462),x59463)+~E(f334(f334(f141(x59461),x59463),f334(f334(f158(x59461),x59464),f120(x59461))),x59462) % 188.18/188.25 [5947]E(f151(x59471,x59472),x59473)+~E(f334(f334(f141(x59471),x59474),f334(f334(f158(x59471),x59473),f120(x59471))),x59472) % 188.18/188.25 [6057]~E(f146(a927,f334(f310(a927,x60571),x60572)),f334(f334(f158(a927),x60573),x60574))+P107(f334(f334(f243(a927),x60571),x60572)) % 188.18/188.25 [6066]P33(x60661,x60662,x60663)+~P33(x60661,x60662,f334(f334(f158(x60661),x60664),x60663)) % 188.18/188.25 [6067]P33(x60671,x60672,x60673)+~P33(x60671,x60672,f334(f334(f141(x60671),x60674),x60673)) % 188.18/188.25 [6068]P33(x60681,x60682,x60683)+~P33(x60681,x60682,f334(f334(f141(x60681),x60683),x60684)) % 188.18/188.25 [6263]E(x62631,f334(f334(f141(x62632),f334(f175(x62632),x62633)),f334(f334(f158(x62632),x62634),f120(x62632))))+~E(f334(f175(x62632),x62631),f334(f334(f158(x62632),x62634),x62633)) % 188.18/188.25 [6432]~P111(x64321)+E(f334(f334(f109(f935(x64321,a922)),f334(f310(x64321,x64322),x64323)),f334(f310(x64321,x64323),x64324)),f195(f935(x64321,a922))) % 188.18/188.25 [6443]E(f334(f334(f171(x64431),f176(x64431,x64432,x64433)),x64434),x64433)+~P107(f334(f334(f243(a927),x64434),x64432)) % 188.18/188.25 [6470]~P76(x64701)+E(f334(f172(x64701),f334(f334(f161(a1,x64701),x64702),f185(x64703,x64704))),f334(f334(f6(a1,x64701),x64702),f334(f179(a1),f185(x64703,x64704)))) % 188.18/188.25 [6471]~P76(x64711)+E(f334(f334(f6(a1,x64711),x64712),f334(f179(a1),f185(x64713,x64714))),f334(f172(x64711),f334(f334(f161(a1,x64711),x64712),f185(x64713,x64714)))) % 188.18/188.25 [6611]~E(x66112,f334(f334(f141(x66111),f334(f175(x66111),x66114)),f334(f334(f158(x66111),x66113),f120(x66111))))+E(f334(f175(x66111),x66112),f334(f334(f158(x66111),x66113),x66114)) % 188.18/188.25 [6629]~P21(x66292,x66293,x66294,x66291)+E(f334(x66291,f195(f935(x66292,a922))),f32(x66293)) % 188.18/188.25 [6655]~P111(x66551)+E(f334(f334(f109(f935(x66551,a922)),f313(x66551,x66552,x66553)),f334(f310(x66551,x66553),x66554)),f195(f935(x66551,a922))) % 188.18/188.25 [6864]E(x68641,f195(f935(x68642,a922)))+~E(f320(x68643,x68642,x68644,x68641),f195(f935(f933(x68643,x68642),a922))) % 188.18/188.25 [6865]E(x68651,f195(f935(x68652,a922)))+~E(f320(x68652,x68653,x68651,x68654),f195(f935(f933(x68652,x68653),a922))) % 188.18/188.25 [6934]~P109(x69342)+E(f334(f196(f928(x69341)),f157(x69341,x69342,x69343,x69344)),f334(f196(f928(x69341)),x69344)) % 188.18/188.25 [6945]~P107(f334(f258(x69453,x69454,x69451),x69452))+P107(f334(f334(x69451,f534(x69452,x69451)),x69452)) % 188.18/188.25 [6986]~P107(f334(f66(x69862),x69864))+P107(f334(f66(x69861),f334(f317(x69862,x69861,x69863),x69864))) % 188.18/188.25 [7207]~P27(x72072,x72071,x72073,x72074)+E(f334(f40(x72071),f334(f317(x72072,x72071,x72073),x72074)),f334(f40(x72072),x72074)) % 188.18/188.25 [7225]E(f334(f317(x72251,x72252,x72253),f334(f318(x72251,x72252,x72253),x72254)),x72254)+~E(f334(f317(x72251,x72252,x72253),f250(f935(x72251,a922))),f250(f935(x72252,a922))) % 188.18/188.25 [7625]~P27(x76251,x76252,x76253,f250(f935(x76251,a922)))+E(f334(f318(x76251,x76252,x76253),f334(f317(x76251,x76252,x76253),x76254)),x76254) % 188.18/188.25 [7899]E(x78991,x78992)+~P107(f334(f334(f336(x78993),x78991),f334(f179(x78993),f176(x78993,x78994,x78992)))) % 188.18/188.25 [7908]~E(x79081,f2(a927))+~P107(f334(f334(f336(x79082),x79083),f334(f179(x79082),f176(x79082,x79081,x79084)))) % 188.18/188.25 [7941]P107(f334(x79411,x79412))+~P107(f334(f334(f336(x79413),x79412),f334(f179(x79413),f184(x79413,x79411,x79414)))) % 188.18/188.25 [8053]~P107(f334(f334(f336(f928(x80531)),f334(f334(f158(x80531),x80532),x80534)),f168(x80531,x80533)))+P107(f334(f334(f336(x80531),x80532),x80533)) % 188.18/188.25 [8173]~P107(f334(f334(f336(x81731),x81732),f334(f179(x81731),f183(x81731,x81733,x81734))))+P107(f334(f334(f336(x81731),x81732),f334(f179(x81731),x81733))) % 188.18/188.25 [8174]~P107(f334(f334(f336(x81741),x81742),f334(f179(x81741),f177(x81741,x81744,x81743))))+P107(f334(f334(f336(x81741),x81742),f334(f179(x81741),x81743))) % 188.18/188.25 [8175]~P107(f334(f334(f336(x81751),x81752),f334(f179(x81751),f184(x81751,x81754,x81753))))+P107(f334(f334(f336(x81751),x81752),f334(f179(x81751),x81753))) % 188.18/188.25 [8184]E(f334(f196(f928(x81841)),x81842),x81843)+~P107(f334(f334(f336(f928(x81841)),x81842),f334(f179(f928(x81841)),f60(x81841,x81843,x81844)))) % 188.18/188.25 [8283]P107(f334(x82833,x82832))+E(f334(f143(x82831,f334(f334(f8(a922,a922,x82831),a329),f334(a331,x82832))),f334(f143(x82831,x82833),x82834)),f334(f143(x82831,x82833),x82834)) % 188.18/188.25 [8388]E(f334(f334(f171(x83881),f184(x83881,x83882,x83883)),x83884),f334(f334(f171(x83881),x83883),x83884))+~P107(f334(f334(f243(a927),x83884),f334(f196(f928(x83881)),f184(x83881,x83882,x83883)))) % 188.18/188.25 [8473]~P76(x84731)+E(f334(f334(f6(a927,x84731),f334(f334(f8(a927,x84731,a927),x84732),a119)),f334(f310(a927,x84733),x84734)),f334(f334(f6(a927,x84731),x84732),f334(f310(a927,f334(a119,x84733)),f334(a119,x84734)))) % 188.18/188.25 [8483]~P76(x84831)+E(f334(f334(f6(a927,x84831),f334(f334(f8(a927,x84831,a927),x84832),a119)),f311(a927,x84833,x84834)),f334(f334(f6(a927,x84831),x84832),f311(a927,f334(a119,x84833),f334(a119,x84834)))) % 188.18/188.25 [8608]~P27(x86081,x86083,x86084,f250(f935(x86081,a922)))+P27(x86081,f935(x86082,x86083),f334(f334(f8(x86083,f935(x86082,x86083),x86081),f16(x86083,x86082)),x86084),f250(f935(x86081,a922))) % 188.18/188.25 [8690]~P27(x86902,x86901,x86904,x86903)+E(f334(f317(x86901,x86902,f83(x86902,x86901,x86903,x86904)),f334(f317(x86902,x86901,x86904),x86903)),x86903) % 188.18/188.25 [8753]~P107(f334(f334(f336(f934(x87531,x87531)),f334(f334(f260(x87531,x87531),x87532),x87534)),f271(x87531,x87533)))+P107(f334(f334(f336(x87531),x87532),x87533)) % 188.18/188.25 [8870]~P27(x88702,x88701,x88703,f250(f935(x88702,a922)))+E(f334(f317(x88701,x88702,f97(x88702,x88701,f250(f935(x88702,a922)),x88703)),f334(f317(x88702,x88701,x88703),x88704)),x88704) % 188.18/188.25 [8943]~P28(x89431,x89432,x89433,x89434,f250(f935(x89432,a922)))+E(f334(f317(x89431,x89432,x89433),f250(f935(x89431,a922))),f250(f935(x89432,a922))) % 188.18/188.25 [8974]~E(f334(f334(f6(x89741,a927),x89744),x89743),f334(a119,x89742))+P107(f334(f334(f336(x89741),f590(x89742,x89743,x89744,x89741)),x89743)) % 188.18/188.25 [8996]~E(f334(f334(f6(x89964,a927),x89961),x89963),f334(a119,x89962))+P107(f334(f334(f243(a927),f2(a927)),f334(x89961,f590(x89962,x89963,x89961,x89964)))) % 188.18/188.25 [9007]~P107(f334(f66(x90072),x90074))+P107(f334(f334(f242(a927),f334(f40(x90071),f334(f317(x90072,x90071,x90073),x90074))),f334(f40(x90072),x90074))) % 188.18/188.25 [9008]E(f334(f334(f260(x90081,x90082),f654(x90083,x90084,x90082,x90081)),f655(x90083,x90084,x90082,x90081)),x90084)+~P107(f334(f334(f336(f934(x90081,x90082)),x90084),f334(f293(x90082,x90081),x90083))) % 188.18/188.25 [9016]P27(x90161,x90162,x90163,x90164)+P107(f334(f334(f336(x90161),f426(x90164,x90163,x90162,x90161)),x90164)) % 188.18/188.25 [9017]P27(x90171,x90172,x90173,x90174)+P107(f334(f334(f336(x90171),f449(x90174,x90173,x90172,x90171)),x90174)) % 188.18/188.25 [9090]P13(x90901,x90902,x90903,x90904)+P107(f334(f334(f336(f934(x90901,x90901)),f578(x90904,x90903,x90902,x90901)),x90903)) % 188.18/188.25 [9149]P107(f334(x91491,x91492))+~P107(f334(x91491,f334(f334(f260(x91493,x91494),f360(x91494,x91493,x91491)),f361(x91494,x91493,x91491)))) % 188.18/188.25 [9166]E(f334(f196(f928(x91661)),x91662),f334(f196(f928(x91661)),x91663))+~P107(f334(f334(f336(f934(f928(x91661),f928(x91661))),f334(f334(f260(f928(x91661),f928(x91661)),x91662),x91663)),f152(x91661,x91664))) % 188.18/188.25 [9167]E(f334(f196(f928(x91671)),x91672),f334(f196(f928(x91671)),x91673))+~P107(f334(f334(f336(f934(f928(x91671),f928(x91671))),f334(f334(f260(f928(x91671),f928(x91671)),x91672),x91673)),f164(x91671,x91674))) % 188.18/188.25 [9170]E(f334(f196(f928(x91701)),x91702),f334(f196(f928(x91701)),x91703))+~P107(f334(f334(f336(f934(f928(x91701),f928(x91701))),f334(f334(f260(f928(x91701),f928(x91701)),x91702),x91703)),f165(x91701,x91704))) % 188.18/188.25 [9238]P107(f334(f334(f242(a927),f162(x92381,x92382,x92383)),f162(x92381,x92384,x92383)))+P107(f334(f334(f336(x92381),f682(x92384,x92382,x92383,x92381)),f334(f179(x92381),x92383))) % 188.18/188.25 [9241]E(f334(f196(f928(x92411)),x92412),f334(f196(f928(x92411)),x92413))+~P107(f334(f334(f336(f934(f928(x92411),f928(x92411))),f334(f334(f260(f928(x92411),f928(x92411)),x92412),x92413)),f314(f928(x92411),f164(x92411,x92414)))) % 188.18/188.25 [9470]~P27(x94701,x94702,x94703,x94704)+~P107(f334(f334(f243(a927),f334(f40(x94702),f334(f317(x94701,x94702,x94703),x94704))),f334(f40(x94701),x94704))) % 188.18/188.25 [9524]~P107(f334(f334(f336(f934(f928(x95241),f928(x95241))),f334(f334(f260(f928(x95241),f928(x95241)),x95242),x95243)),f164(x95241,x95244)))+P107(f334(f334(f336(f934(f928(x95241),f928(x95241))),f334(f334(f260(f928(x95241),f928(x95241)),x95242),x95243)),f165(x95241,f314(x95241,x95244)))) % 188.18/188.25 [9528]~P107(f334(f334(f336(f934(f928(x95281),f928(x95281))),f334(f334(f260(f928(x95281),f928(x95281)),x95282),x95283)),f165(x95281,x95284)))+P107(f334(f334(f336(f934(f928(x95281),f928(x95281))),f334(f334(f260(f928(x95281),f928(x95281)),x95282),x95283)),f314(f928(x95281),f164(x95281,x95284)))) % 188.18/188.25 [9540]P107(f334(f334(f336(f934(x95401,x95401)),f334(f334(f260(x95401,x95401),x95402),x95403)),f314(x95401,x95404)))+~P107(f334(f334(f336(f934(x95401,x95401)),f334(f334(f260(x95401,x95401),x95402),x95403)),f334(f334(f295(x95401,x95401,x95401),x95404),f314(x95401,x95404)))) % 188.18/188.25 [9728]E(f334(f334(f141(x97281),f698(x97282,x97283,x97284,x97281)),f334(f334(f158(x97281),f699(x97282,x97283,x97284,x97281)),f701(x97282,x97283,x97284,x97281))),x97284)+~P107(f334(f334(f336(f934(f928(x97281),f928(x97281))),f334(f334(f260(f928(x97281),f928(x97281)),x97284),x97283)),f164(x97281,x97282))) % 188.18/188.25 [9729]E(f334(f334(f141(x97291),f698(x97292,x97293,x97294,x97291)),f334(f334(f158(x97291),f700(x97292,x97293,x97294,x97291)),f701(x97292,x97293,x97294,x97291))),x97293)+~P107(f334(f334(f336(f934(f928(x97291),f928(x97291))),f334(f334(f260(f928(x97291),f928(x97291)),x97294),x97293)),f164(x97291,x97292))) % 188.18/188.25 [9810]P107(f334(f334(f336(f934(x98101,x98101)),f334(f334(f260(x98101,x98101),x98102),f646(x98103,x98104,x98102,x98101))),f314(x98101,x98103)))+~P107(f334(f334(f336(f934(x98101,x98101)),f334(f334(f260(x98101,x98101),x98102),x98104)),f334(f334(f295(x98101,x98101,x98101),x98103),f314(x98101,x98103)))) % 188.18/188.25 [9893]P107(f334(f334(f242(a927),f162(x98931,x98932,x98933)),f162(x98931,x98934,x98933)))+~P107(f334(f334(f243(a927),f334(x98932,f682(x98934,x98932,x98933,x98931))),f334(x98934,f682(x98934,x98932,x98933,x98931)))) % 188.18/188.25 [9964]P107(f334(f334(f336(f934(x99641,x99641)),f334(f334(f260(x99641,x99641),f642(x99642,x99643,x99644,x99641)),x99643)),f314(x99641,x99642)))+~P107(f334(f334(f336(f934(x99641,x99641)),f334(f334(f260(x99641,x99641),x99644),x99643)),f334(f334(f295(x99641,x99641,x99641),x99642),f314(x99641,x99642)))) % 188.18/188.25 [5453]~E(x54532,x54533)+E(f177(x54531,x54532,f334(f334(f158(x54531),x54533),x54534)),x54534) % 188.18/188.25 [5582]P107(f334(x55822,x55823))+E(f184(x55821,x55822,f334(f334(f158(x55821),x55823),x55824)),f120(x55821)) % 188.18/188.25 [5648]~P83(x56482)+E(f334(f334(f85(f935(x56481,x56482)),x56483),x56484),f334(f85(x56482),f334(x56483,x56484))) % 188.18/188.25 [5661]~E(x56612,f2(a927))+E(f334(f334(f145(x56611),x56612),f334(f334(f158(x56611),x56613),x56614)),f334(f334(f158(x56611),x56613),x56614)) % 188.18/188.25 [5662]P107(f334(x56622,x56623))+E(f334(f143(x56621,x56622),f334(f334(f158(x56621),x56623),x56624)),f334(f143(x56621,x56622),x56624)) % 188.18/188.25 [5798]~E(x57982,x57984)+P107(f334(f334(f334(f316(x57981),x57982),x57983),x57984)) % 188.18/188.25 [5807]E(x58071,f120(x58072))+E(f151(x58073,f334(f334(f161(x58072,x58073),x58074),x58071)),f334(x58074,f151(x58072,x58071))) % 188.18/188.25 [5821]~E(x58211,f68(x58212,x58214))+E(f334(x58211,f334(f334(f316(x58212),x58213),f195(f935(x58212,a922)))),x58213) % 188.18/188.25 [5861]E(x58611,f120(x58612))+E(f334(f148(x58613),f334(f334(f161(x58612,x58613),x58614),x58611)),f334(x58614,f334(f148(x58612),x58611))) % 188.18/188.25 [5966]~P107(f334(x59663,x59664))+P107(f334(f334(f334(f316(x59661),x59662),x59663),x59664)) % 188.18/188.25 [6085]~P20(x60852,x60854,x60851)+E(f334(x60851,f334(f334(f316(x60852),x60853),f195(f935(x60852,a922)))),x60853) % 188.18/188.25 [6113]~E(x61132,x61133)+P107(f334(f334(f336(x61131),x61132),f334(f334(f316(x61131),x61133),x61134))) % 188.18/188.25 [6118]~P119(x61181)+E(f334(f334(f87(x61181),x61182),f334(f334(f87(x61181),x61183),x61184)),f334(f334(f87(x61181),x61183),f334(f334(f87(x61181),x61182),x61184))) % 188.18/188.25 [6119]~P119(x61191)+E(f334(f334(f86(x61191),x61192),f334(f334(f86(x61191),x61193),x61194)),f334(f334(f86(x61191),x61193),f334(f334(f86(x61191),x61192),x61194))) % 188.18/188.25 [6121]~P109(x61211)+E(f334(f334(f246(x61211),x61212),f334(f334(f246(x61211),x61213),x61214)),f334(f334(f246(x61211),x61213),f334(f334(f246(x61211),x61212),x61214))) % 188.18/188.25 [6123]~P109(x61231)+E(f334(f334(f241(x61231),x61232),f334(f334(f241(x61231),x61233),x61234)),f334(f334(f241(x61231),x61233),f334(f334(f241(x61231),x61232),x61234))) % 188.18/188.25 [6125]~P98(x61251)+E(f334(f334(f108(x61251),x61252),f334(f334(f108(x61251),x61253),x61254)),f334(f334(f108(x61251),x61253),f334(f334(f108(x61251),x61252),x61254))) % 188.18/188.25 [6126]~P99(x61261)+E(f334(f334(f108(x61261),x61262),f334(f334(f108(x61261),x61263),x61264)),f334(f334(f108(x61261),x61263),f334(f334(f108(x61261),x61262),x61264))) % 188.18/188.25 [6127]~P99(x61271)+E(f334(f334(f109(x61271),x61272),f334(f334(f109(x61271),x61273),x61274)),f334(f334(f109(x61271),x61273),f334(f334(f109(x61271),x61272),x61274))) % 188.18/188.25 [6129]~P104(x61291)+E(f334(f334(f109(x61291),x61292),f334(f334(f109(x61291),x61293),x61294)),f334(f334(f109(x61291),x61293),f334(f334(f109(x61291),x61292),x61294))) % 188.18/188.25 [6135]E(x61351,x61352)+E(f177(x61353,x61351,f334(f334(f158(x61353),x61352),x61354)),f334(f334(f158(x61353),x61352),f177(x61353,x61351,x61354))) % 188.18/188.25 [6148]~P107(f334(x61482,x61483))+E(f334(f143(x61481,x61482),f334(f334(f158(x61481),x61483),x61484)),f334(f334(f158(x61481),x61483),f334(f143(x61481,x61482),x61484))) % 188.18/188.25 [6283]~P107(f334(x62832,x62833))+E(f184(x62831,x62832,f334(f334(f158(x62831),x62833),x62834)),f334(f334(f158(x62831),x62833),f184(x62831,x62832,x62834))) % 188.18/188.25 [6345]E(x63451,f195(f935(x63452,a922)))+E(f334(f334(f44(x63452,f935(x63453,a922)),x63451),f334(f16(f935(x63453,a922),x63452),x63454)),x63454) % 188.18/188.25 [6346]E(x63461,f195(f935(x63462,a922)))+E(f334(f334(f45(x63462,f935(x63463,a922)),x63461),f334(f16(f935(x63463,a922),x63462),x63464)),x63464) % 188.18/188.25 [6355]~E(x63554,f195(f935(x63552,a922)))+E(f334(f334(f262(x63551,x63552),x63553),f334(f16(f935(x63552,a922),x63551),x63554)),f195(f935(f934(x63551,x63552),a922))) % 188.18/188.25 [6356]~E(x63563,f195(f935(x63561,a922)))+E(f334(f334(f262(x63561,x63562),x63563),f334(f16(f935(x63562,a922),x63561),x63564)),f195(f935(f934(x63561,x63562),a922))) % 188.18/188.25 [6409]E(x64091,f2(a927))+E(f334(f334(f145(x64092),x64091),f334(f334(f158(x64092),x64093),x64094)),f334(f334(f145(x64092),f334(f334(f23(a927),x64091),f84(a927))),x64094)) % 188.18/188.25 [6426]E(x64261,f195(f935(x64262,a922)))+E(f334(f317(x64262,x64263,f334(f16(x64263,x64262),x64264)),x64261),f334(f334(f316(x64263),x64264),f195(f935(x64263,a922)))) % 188.18/188.25 [6429]E(f334(f318(x64291,x64292,f334(f16(x64292,x64291),x64293)),x64294),f195(f935(x64291,a922)))+P107(f334(f334(f336(x64292),x64293),x64294)) % 188.18/188.25 [6495]~E(x64953,f195(f935(x64951,a922)))+E(f334(f334(f44(x64951,f935(x64952,a922)),x64953),f334(f16(f935(x64952,a922),x64951),x64954)),f195(f935(x64952,a922))) % 188.18/188.25 [6496]~E(x64963,f195(f935(x64961,a922)))+E(f334(f334(f45(x64961,f935(x64962,a922)),x64963),f334(f16(f935(x64962,a922),x64961),x64964)),f250(f935(x64962,a922))) % 188.18/188.25 [6498]~P5(x64981)+E(f50(x64981,f334(f334(f87(x64981),x64982),x64983),f334(f334(f87(x64981),x64982),x64984)),f334(f334(f87(x64981),x64982),f50(x64981,x64983,x64984))) % 188.18/188.25 [6665]E(f334(f318(x66651,x66652,f334(f16(x66652,x66651),x66653)),x66654),f250(f935(x66651,a922)))+~P107(f334(f334(f336(x66652),x66653),x66654)) % 188.18/188.25 [6691]~P107(f334(f334(f336(x66911),x66912),x66914))+P107(f334(f334(f336(x66911),x66912),f334(f334(f316(x66911),x66913),x66914))) % 188.18/188.25 [6696]P107(f334(x66961,x66962))+~P107(f334(f167(x66963,x66961),f334(f334(f158(x66963),x66962),x66964))) % 188.18/188.25 [6706]~E(x67063,f334(f334(f23(a927),f334(f196(f928(x67061)),x67062)),f84(a927)))+E(f121(x67061,f334(f334(f166(x67061,x67062),x67063),x67064)),f121(x67061,x67062)) % 188.18/188.25 [6723]~P109(x67231)+E(f334(f334(f109(f935(x67231,a922)),f334(f309(x67231),x67232)),f311(x67231,x67233,x67234)),f311(x67231,x67233,f334(f334(f246(x67231),x67232),x67234))) % 188.18/188.25 [6724]~P109(x67241)+E(f334(f334(f109(f935(x67241,a922)),f334(f290(x67241),x67242)),f311(x67241,x67243,x67244)),f311(x67241,f334(f334(f241(x67241),x67242),x67243),x67244)) % 188.18/188.25 [6740]E(f334(f334(f109(f935(x67401,a922)),x67402),f334(f334(f316(x67401),x67403),x67404)),f334(f334(f109(f935(x67401,a922)),x67402),x67404))+P107(f334(f334(f336(x67401),x67403),x67402)) % 188.18/188.25 [6752]E(f177(x67521,x67522,f334(f334(f141(x67521),x67523),x67524)),f334(f334(f141(x67521),x67523),f177(x67521,x67522,x67524)))+P107(f334(f334(f336(x67521),x67522),f334(f179(x67521),x67523))) % 188.18/188.25 [6758]~P81(x67581)+E(f334(f334(f87(x67581),f334(f334(f252(x67581),x67582),x67583)),f334(f334(f252(x67581),x67582),x67584)),f334(f334(f252(x67581),x67582),f334(f334(f86(a927),x67583),x67584))) % 188.18/188.25 [6759]~P119(x67591)+E(f334(f334(f87(x67591),f334(f334(f252(x67591),x67592),x67593)),f334(f334(f252(x67591),x67592),x67594)),f334(f334(f252(x67591),x67592),f334(f334(f86(a927),x67593),x67594))) % 188.18/188.25 [6794]~P119(x67941)+E(f334(f334(f86(x67941),f334(f334(f87(x67941),x67942),x67943)),f334(f334(f87(x67941),x67942),x67944)),f334(f334(f87(x67941),x67942),f334(f334(f86(x67941),x67943),x67944))) % 188.18/188.25 [6795]~P109(x67951)+E(f334(f334(f241(x67951),f334(f334(f246(x67951),x67952),x67953)),f334(f334(f246(x67951),x67952),x67954)),f334(f334(f246(x67951),x67952),f334(f334(f241(x67951),x67953),x67954))) % 188.18/188.25 [6796]~P109(x67961)+E(f334(f334(f246(x67961),f334(f334(f241(x67961),x67962),x67963)),f334(f334(f241(x67961),x67962),x67964)),f334(f334(f241(x67961),x67962),f334(f334(f246(x67961),x67963),x67964))) % 188.18/188.25 [6797]~P103(x67971)+E(f334(f334(f109(x67971),f334(f334(f108(x67971),x67972),x67973)),f334(f334(f108(x67971),x67972),x67974)),f334(f334(f108(x67971),x67972),f334(f334(f109(x67971),x67973),x67974))) % 188.18/188.25 [6798]~P103(x67981)+E(f334(f334(f108(x67981),f334(f334(f109(x67981),x67982),x67983)),f334(f334(f109(x67981),x67982),x67984)),f334(f334(f109(x67981),x67982),f334(f334(f108(x67981),x67983),x67984))) % 188.18/188.25 [6829]~P5(x68291)+E(f50(x68291,f334(f334(f87(x68291),x68292),x68293),f334(f334(f87(x68291),x68294),x68293)),f334(f334(f87(x68291),f50(x68291,x68292,x68294)),x68293)) % 188.18/188.25 [6832]~E(f334(f196(f928(x68321)),x68323),f334(f196(f928(x68322)),x68324))+E(f334(f334(f161(f934(x68321,x68322),x68322),f264(x68321,x68322)),f334(f334(f188(x68321,x68322),x68323),x68324)),x68324) % 188.18/188.25 [6833]~E(f334(f196(f928(x68331)),x68333),f334(f196(f928(x68332)),x68334))+E(f334(f334(f161(f934(x68331,x68332),x68331),f259(x68331,x68332)),f334(f334(f188(x68331,x68332),x68333),x68334)),x68333) % 188.18/188.25 [6838]P107(f334(f167(x68381,x68382),x68383))+~P107(f334(f167(x68381,x68382),f334(f334(f158(x68381),x68384),x68383))) % 188.18/188.25 [6839]P107(f334(f167(x68391,x68392),x68393))+~P107(f334(f167(x68391,x68392),f334(f334(f141(x68391),x68394),x68393))) % 188.18/188.25 [6840]P107(f334(f167(x68401,x68402),x68403))+~P107(f334(f167(x68401,x68402),f334(f334(f141(x68401),x68403),x68404))) % 188.18/188.25 [6845]~P6(x68451)+E(f50(x68451,f334(f334(f23(x68451),x68452),f50(x68451,x68453,x68454)),x68454),f50(x68451,f334(f334(f23(x68451),x68452),x68453),x68454)) % 188.18/188.25 [6846]~P5(x68461)+E(f50(x68461,f334(f334(f87(x68461),x68462),f50(x68461,x68463,x68464)),x68464),f50(x68461,f334(f334(f87(x68461),x68462),x68463),x68464)) % 188.18/188.25 [6848]~P5(x68481)+E(f50(x68481,f334(f334(f86(x68481),x68482),f50(x68481,x68483,x68484)),x68484),f50(x68481,f334(f334(f86(x68481),x68482),x68483),x68484)) % 188.18/188.25 [6927]~P109(x69271)+E(f334(f334(f109(f935(x69271,a922)),f311(x69271,x69272,x69273)),f334(f309(x69271),x69274)),f311(x69271,x69272,f334(f334(f246(x69271),x69273),x69274))) % 188.18/188.25 [6928]~P109(x69281)+E(f334(f334(f109(f935(x69281,a922)),f311(x69281,x69282,x69283)),f334(f290(x69281),x69284)),f311(x69281,f334(f334(f241(x69281),x69282),x69284),x69283)) % 188.18/188.25 [6931]~E(f334(f196(f928(x69311)),x69313),f334(f196(f928(x69312)),x69314))+E(f334(f334(f188(x69311,x69312),f334(f175(x69311),x69313)),f334(f175(x69312),x69314)),f334(f175(f934(x69311,x69312)),f334(f334(f188(x69311,x69312),x69313),x69314))) % 188.18/188.25 [6942]E(x69421,f334(f334(f23(a927),f334(f196(f928(x69422)),x69423)),f84(a927)))+E(f121(x69422,f334(f334(f166(x69422,x69423),x69421),x69424)),f334(f334(f166(x69422,f121(x69422,x69423)),x69421),x69424)) % 188.18/188.25 [6956]~P107(f334(f144(x69562),x69564))+P107(f334(f144(f934(x69561,x69562)),f334(f334(f188(x69561,x69562),x69563),x69564))) % 188.18/188.25 [6957]~P107(f334(f144(x69571),x69573))+P107(f334(f144(f934(x69571,x69572)),f334(f334(f188(x69571,x69572),x69573),x69574))) % 188.18/188.25 [7210]E(f334(f334(f41(a927),x72101),x72102),x72103)+~P107(f334(f53(x72101,x72102),f334(f334(f260(a927,a927),x72103),x72104))) % 188.18/188.25 [7233]E(f50(a927,x72331,x72332),x72333)+~P107(f334(f53(x72331,x72332),f334(f334(f260(a927,a927),x72334),x72333))) % 188.18/188.25 [7236]P107(f334(f144(x72361),x72362))+~P107(f334(f144(x72363),f334(f334(f161(x72361,x72363),x72364),x72362))) % 188.18/188.25 [7318]E(f177(x73181,x73182,f334(f334(f141(x73181),x73183),x73184)),f334(f334(f141(x73181),f177(x73181,x73182,x73183)),x73184))+~P107(f334(f334(f336(x73181),x73182),f334(f179(x73181),x73183))) % 188.18/188.25 [7409]~P6(x74091)+E(f50(x74091,f334(f334(f23(x74091),f50(x74091,x74092,x74093)),x74094),x74093),f50(x74091,f334(f334(f23(x74091),x74092),x74094),x74093)) % 188.18/188.25 [7412]~P5(x74121)+E(f50(x74121,f334(f334(f87(x74121),f50(x74121,x74122,x74123)),x74124),x74123),f50(x74121,f334(f334(f87(x74121),x74122),x74124),x74123)) % 188.18/188.25 [7413]~P5(x74131)+E(f50(x74131,f334(f334(f86(x74131),f50(x74131,x74132,x74133)),x74134),x74133),f50(x74131,f334(f334(f86(x74131),x74132),x74134),x74133)) % 188.18/188.25 [7597]~E(x75971,f334(f334(f158(x75972),x75973),x75974))+~P107(f334(f334(f242(a927),f334(f196(f928(x75972)),x75971)),f334(f196(f928(x75972)),x75974))) % 188.18/188.25 [7795]P27(x77951,x77952,x77953,f334(f179(x77951),x77954))+~P107(f334(f144(x77952),f334(f334(f161(x77951,x77952),x77953),x77954))) % 188.18/188.25 [7866]~P107(f334(f334(f242(f935(x78661,a922)),x78662),x78664))+P107(f334(f334(f242(f935(x78661,a922)),x78662),f334(f334(f316(x78661),x78663),x78664))) % 188.18/188.25 [7900]~P6(x79001)+E(f50(x79001,f334(f334(f23(x79001),f50(x79001,x79002,x79003)),f50(x79001,x79004,x79003)),x79003),f50(x79001,f334(f334(f23(x79001),x79002),x79004),x79003)) % 188.18/188.25 [7901]~P5(x79011)+E(f50(x79011,f334(f334(f87(x79011),f50(x79011,x79012,x79013)),f50(x79011,x79014,x79013)),x79013),f50(x79011,f334(f334(f87(x79011),x79012),x79014),x79013)) % 188.18/188.25 [7902]~P5(x79021)+E(f50(x79021,f334(f334(f86(x79021),f50(x79021,x79022,x79023)),f50(x79021,x79024,x79023)),x79023),f50(x79021,f334(f334(f86(x79021),x79022),x79024),x79023)) % 188.18/188.25 [8008]~E(f334(x80084,f398(x80084,x80083,x80081,x80082)),f195(f935(x80082,a922)))+E(f334(f334(f44(x80081,f935(x80082,a922)),x80083),x80084),f195(f935(x80082,a922))) % 188.18/188.25 [8009]~E(f334(x80094,f495(x80094,x80093,x80091,x80092)),f250(f935(x80092,a922)))+E(f334(f334(f45(x80091,f935(x80092,a922)),x80093),x80094),f250(f935(x80092,a922))) % 188.18/188.25 [8010]~E(f334(x80104,f399(x80104,x80103,x80102,x80101)),f195(f935(x80102,a922)))+E(f334(f334(f44(x80101,f935(x80102,a922)),x80103),x80104),f195(f935(x80102,a922))) % 188.18/188.25 [8011]~E(f334(x80114,f496(x80114,x80113,x80112,x80111)),f250(f935(x80112,a922)))+E(f334(f334(f45(x80111,f935(x80112,a922)),x80113),x80114),f250(f935(x80112,a922))) % 188.18/188.25 [8389]P107(f334(x83891,x83892))+~P107(f334(f334(f336(x83893),x83892),f334(f334(f109(f935(x83893,a922)),x83894),f334(f270(x83893),x83891)))) % 188.18/188.25 [8425]~P107(f334(f334(f242(f935(x84251,a922)),x84253),x84254))+P107(f334(f334(f242(f935(x84251,a922)),f334(f334(f316(x84251),x84252),x84253)),f334(f334(f316(x84251),x84252),x84254))) % 188.18/188.25 [8435]E(f334(x84351,f540(x84351,x84352,x84353)),x84353)+~P107(f334(f334(f336(x84354),x84353),f334(f317(x84352,x84354,x84351),f250(f935(x84352,a922))))) % 188.18/188.25 [8600]P107(f334(x86002,x86003))+E(f334(f334(f145(x86001),f334(f196(f928(x86001)),f184(x86001,x86002,f334(f334(f158(x86001),x86003),x86004)))),f334(f334(f158(x86001),x86003),x86004)),f334(f334(f158(x86001),x86003),x86004)) % 188.18/188.25 [8704]~P107(f334(f334(f243(a927),f334(x87044,x87042)),f334(x87044,x87043)))+P107(f334(f334(f336(f934(x87041,x87041)),f334(f334(f260(x87041,x87041),x87042),x87043)),f334(f334(f294(a927,x87041),a248),x87044))) % 188.18/188.25 [8802]~P107(f334(x88022,f754(x88024,x88022,x88023,x88021)))+E(f184(x88021,x88022,f334(f334(f141(x88021),x88023),x88024)),f334(f334(f141(x88021),x88023),f184(x88021,x88022,x88024))) % 188.18/188.25 [8874]P27(f928(x88741),f928(x88742),f334(f161(x88741,x88742),x88743),x88744)+~P27(x88741,x88742,x88743,f42(f935(x88741,a922),f334(f317(f928(x88741),f935(x88741,a922),f179(x88741)),x88744))) % 188.18/188.25 [8947]~P107(f334(x89472,x89473))+E(f334(f334(f145(x89471),f334(f196(f928(x89471)),f184(x89471,x89472,f334(f334(f158(x89471),x89473),x89474)))),f334(f334(f158(x89471),x89473),x89474)),f334(f334(f145(x89471),f334(f196(f928(x89471)),f184(x89471,x89472,x89474))),x89474)) % 188.18/188.25 [8987]~E(x89872,x89873)+E(f334(f143(x89871,f334(f334(f8(a922,a922,x89871),a329),f334(a331,x89872))),f334(f334(f158(x89871),x89873),x89874)),f334(f143(x89871,f334(f334(f8(a922,a922,x89871),a329),f334(a331,x89872))),x89874)) % 188.18/188.25 [8997]E(f334(f334(f44(x89971,f935(x89972,a922)),x89973),x89974),f195(f935(x89972,a922)))+P107(f334(f334(f336(x89971),f398(x89974,x89973,x89971,x89972)),x89973)) % 188.18/188.25 [8998]E(f334(f334(f45(x89981,f935(x89982,a922)),x89983),x89984),f250(f935(x89982,a922)))+P107(f334(f334(f336(x89981),f495(x89984,x89983,x89981,x89982)),x89983)) % 188.18/188.25 [8999]E(f334(f334(f44(x89991,f935(x89992,a922)),x89993),x89994),f195(f935(x89992,a922)))+P107(f334(f334(f336(x89991),f399(x89994,x89993,x89992,x89991)),x89993)) % 188.18/188.25 [9000]E(f334(f334(f45(x90001,f935(x90002,a922)),x90003),x90004),f250(f935(x90002,a922)))+P107(f334(f334(f336(x90001),f496(x90004,x90003,x90002,x90001)),x90003)) % 188.18/188.25 [9040]P107(f334(f334(f243(a927),f334(x90401,x90402)),f334(x90401,x90403)))+~P107(f334(f334(f336(f934(x90404,x90404)),f334(f334(f260(x90404,x90404),x90402),x90403)),f334(f334(f294(a927,x90404),a248),x90401))) % 188.18/188.25 [9069]E(f184(x90691,x90692,f334(f334(f141(x90691),x90693),x90694)),f334(f334(f141(x90691),x90693),f184(x90691,x90692,x90694)))+P107(f334(f334(f336(x90691),f754(x90694,x90692,x90693,x90691)),f334(f179(x90691),x90693))) % 188.18/188.25 [9126]~P28(x91261,x91262,x91263,f250(f935(x91261,a922)),f250(f935(x91262,a922)))+E(f334(f317(x91261,x91262,x91263),f334(f85(f935(x91261,a922)),x91264)),f334(f85(f935(x91262,a922)),f334(f317(x91261,x91262,x91263),x91264))) % 188.18/188.25 [9227]P107(f334(f334(f336(x92271),f464(x92272,x92273,x92274,x92271)),x92273))+~P107(f334(f334(f336(f935(x92271,a922)),x92274),f334(f334(f65(x92271),x92273),x92272))) % 188.18/188.25 [9230]E(x92301,x92302)+~P107(f334(f334(f336(f934(x92303,x92303)),f334(f334(f260(x92303,x92303),x92301),x92302)),f334(f334(f190(f934(x92303,x92303),a922),f2(a927)),x92304))) % 188.18/188.25 [9300]E(f334(f292(x93001,x93001,x93002),f334(f334(f316(x93001),f464(x93002,x93003,x93004,x93001)),f195(f935(x93001,a922)))),x93004)+~P107(f334(f334(f336(f935(x93001,a922)),x93004),f334(f334(f65(x93001),x93003),x93002))) % 188.18/188.25 [9305]~P107(f334(f334(f336(f934(x93051,x93051)),f334(f334(f260(x93051,x93051),x93053),x93052)),f314(x93051,x93054)))+P107(f334(f334(f336(f934(x93051,x93051)),f334(f334(f260(x93051,x93051),x93052),x93053)),f314(x93051,f334(f293(x93051,x93051),x93054)))) % 188.18/188.25 [9318]~P5(x93181)+E(f334(f334(f86(x93181),f334(f334(f86(x93181),f334(f334(f87(x93181),x93182),f334(f334(f41(x93181),x93183),x93182))),f50(x93181,x93183,x93182))),x93184),f334(f334(f86(x93181),x93183),x93184)) % 188.18/188.25 [9333]~P107(f334(f334(f336(x93331),x93333),x93334))+P107(f334(f334(f336(f935(x93331,a922)),f334(f292(x93331,x93331,x93332),f334(f334(f316(x93331),x93333),f195(f935(x93331,a922))))),f334(f334(f65(x93331),x93334),x93332))) % 188.18/188.25 [9346]P107(f334(f334(f336(f934(x93461,x93461)),f334(f334(f260(x93461,x93461),x93462),x93463)),f314(x93461,x93464)))+~P107(f334(f334(f336(f934(x93461,x93461)),f334(f334(f260(x93461,x93461),x93463),x93462)),f314(x93461,f334(f293(x93461,x93461),x93464)))) % 188.18/188.25 [9431]E(f334(f334(f166(x94311,f334(f175(x94311),x94312)),f334(f334(f23(a927),f334(f334(f23(a927),f334(f196(f928(x94311)),x94312)),x94313)),f84(a927))),x94314),f334(f175(x94311),f334(f334(f166(x94311,x94312),x94313),x94314)))+~P107(f334(f334(f243(a927),x94313),f334(f196(f928(x94311)),x94312))) % 188.18/188.25 [9434]~P107(f334(x94342,f749(x94344,x94342,x94343,x94341)))+E(f334(f334(f145(x94341),f334(f196(f928(x94341)),f184(x94341,x94342,f334(f334(f141(x94341),x94343),x94344)))),f334(f334(f141(x94341),x94343),x94344)),f334(f334(f145(x94341),f334(f196(f928(x94341)),f184(x94341,x94342,x94344))),x94344)) % 188.18/188.25 [9478]~P27(x94782,x94781,x94783,f250(f935(x94782,a922)))+P107(f334(f334(f242(f935(x94781,a922)),f334(f317(x94782,x94781,x94783),f334(f85(f935(x94782,a922)),x94784))),f334(f85(f935(x94781,a922)),f334(f317(x94782,x94781,x94783),x94784)))) % 188.18/188.25 [9490]~P7(x94901)+E(f334(f149(x94901,x94902,f334(f7(x94902,x94901,x94901),f334(f334(f8(x94901,f935(x94901,x94901),x94902),f108(x94901)),x94903)),f195(x94901)),x94904),f334(f334(f44(x94902,x94901),f334(f179(x94902),x94904)),x94903)) % 188.18/188.25 [9491]~P7(x94911)+E(f334(f149(x94911,x94912,f334(f7(x94912,x94911,x94911),f334(f334(f8(x94911,f935(x94911,x94911),x94912),f109(x94911)),x94913)),f250(x94911)),x94914),f334(f334(f45(x94912,x94911),f334(f179(x94912),x94914)),x94913)) % 188.18/188.25 [9503]E(f334(f334(f145(x95031),f334(f196(f928(x95031)),f184(x95031,x95032,f334(f334(f141(x95031),x95033),x95034)))),f334(f334(f141(x95031),x95033),x95034)),f334(f334(f145(x95031),f334(f196(f928(x95031)),f184(x95031,x95032,x95034))),x95034))+P107(f334(f334(f336(x95031),f749(x95034,x95032,x95033,x95031)),f334(f179(x95031),x95033))) % 188.18/188.25 [9574]~P107(f334(f334(f336(f934(f928(x95744),f928(x95744))),f334(f334(f260(f928(x95744),f928(x95744)),x95743),x95742)),f164(x95744,x95741)))+P107(f334(f334(f243(a927),f684(x95741,x95742,x95743,x95744)),f334(f196(f928(x95744)),x95743))) % 188.18/188.25 [9575]~P5(x95751)+E(f334(f334(f86(x95751),f334(f334(f86(x95751),f334(f334(f87(x95751),f334(f334(f41(x95751),x95752),x95753)),x95753)),f50(x95751,x95752,x95753))),x95754),f334(f334(f86(x95751),x95752),x95754)) % 188.18/188.25 [9606]~P107(f334(f334(f336(f934(f928(x96061),f928(x96061))),f334(f334(f260(f928(x96061),f928(x96061)),x96062),x96063)),f334(f293(f928(x96061),f928(x96061)),f164(x96061,x96064))))+P107(f334(f334(f336(f934(f928(x96061),f928(x96061))),f334(f334(f260(f928(x96061),f928(x96061)),x96062),x96063)),f164(x96061,f334(f293(x96061,x96061),x96064)))) % 188.18/188.25 [9607]P107(f334(f334(f336(f934(f928(x96071),f928(x96071))),f334(f334(f260(f928(x96071),f928(x96071)),x96072),x96073)),f334(f293(f928(x96071),f928(x96071)),f164(x96071,x96074))))+~P107(f334(f334(f336(f934(f928(x96071),f928(x96071))),f334(f334(f260(f928(x96071),f928(x96071)),x96072),x96073)),f164(x96071,f334(f293(x96071,x96071),x96074)))) % 188.18/188.25 [9639]~P107(f334(f334(f336(x96391),x96393),f334(f272(x96391,x96392),x96394)))+P107(f334(f334(f336(f934(x96391,x96392)),f334(f334(f260(x96391,x96392),x96393),f546(x96394,x96392,x96393,x96391))),x96394)) % 188.18/188.25 [9640]~P107(f334(f334(f336(x96401),x96403),f334(f272(x96401,x96402),x96404)))+P107(f334(f334(f336(f934(x96401,x96402)),f334(f334(f260(x96401,x96402),x96403),f547(x96404,x96402,x96403,x96401))),x96404)) % 188.18/188.25 [9805]~P107(f334(f334(f336(f934(x98051,x98051)),f334(f334(f260(x98051,x98051),x98052),x98054)),f334(f334(f295(x98051,x98051,x98051),x98053),f314(x98051,x98053))))+P107(f334(f334(f336(f934(x98051,x98051)),f334(f334(f260(x98051,x98051),x98052),f642(x98053,x98054,x98052,x98051))),x98053)) % 188.18/188.25 [9982]P13(x99821,x99822,x99823,x99824)+P107(f334(f334(f336(f934(x99821,x99821)),f334(f334(f260(x99821,x99821),f842(x99822,x99824,x99823,x99821)),f841(x99822,x99824,x99823,x99821))),x99823)) % 188.18/188.25 [9995]~P107(f334(f334(f336(f934(x99952,x99951)),x99954),f334(f293(x99951,x99952),x99953)))+P107(f334(f334(f336(f934(x99951,x99952)),f334(f334(f260(x99951,x99952),f655(x99953,x99954,x99951,x99952)),f654(x99953,x99954,x99951,x99952))),x99953)) % 188.18/188.25 [10023]~P107(f334(f334(f336(f934(f928(x100231),f928(x100231))),f334(f334(f260(f928(x100231),f928(x100231)),x100234),x100233)),f164(x100231,x100232)))+P107(f334(f334(f336(f934(x100231,x100231)),f334(f334(f260(x100231,x100231),f699(x100232,x100233,x100234,x100231)),f700(x100232,x100233,x100234,x100231))),x100232)) % 188.18/188.25 [10107]~P107(f334(f334(f336(f934(f928(x101071),f928(x101071))),f334(f334(f260(f928(x101071),f928(x101071)),x101072),x101074)),f164(x101071,x101073)))+P107(f334(f334(f336(f934(x101071,x101071)),f334(f334(f260(x101071,x101071),f334(f334(f171(x101071),x101072),f684(x101073,x101074,x101072,x101071))),f683(x101073,x101074,x101072,x101071))),x101073)) % 188.18/188.25 [10126]~P107(f334(f66(x101262),x101264))+E(f334(f334(f334(f70(f935(x101261,a922),x101262,f108(f935(x101261,a922))),f334(f334(f7(x101262,f935(x101261,a922),f935(x101261,a922)),f334(f334(f8(x101261,f935(f935(x101261,a922),f935(x101261,a922)),x101262),f316(x101261)),x101263)),f195(f935(x101261,a922)))),f195(f935(x101261,a922))),x101264),f334(f317(x101262,x101261,x101263),x101264)) % 188.18/188.25 [10204]~P27(x102041,x102042,x102043,f250(f935(x102041,a922)))+P107(f334(f334(f242(f935(x102041,a922)),f334(f318(x102041,x102042,x102043),f334(f334(f316(x102042),x102044),f195(f935(x102042,a922))))),f334(f334(f316(x102041),f91(x102041,f334(f334(f7(x102041,x102042,a922),f334(f334(f8(x102042,f935(x102042,a922),x102041),a331),x102043)),x102044))),f195(f935(x102041,a922))))) % 188.18/188.25 [5872]~E(f334(f334(f141(x58721),x58722),x58724),x58723)+E(f334(f334(f182(x58721),f334(f196(f928(x58721)),x58722)),x58723),x58722) % 188.18/188.25 [5873]~E(f334(f334(f141(x58732),x58733),x58731),x58734)+E(x58731,f334(f334(f145(x58732),f334(f196(f928(x58732)),x58733)),x58734)) % 188.18/188.25 [5884]~E(x58844,f2(a927))+E(f334(f334(f171(x58841),f334(f334(f158(x58841),x58842),x58843)),x58844),x58842) % 188.18/188.25 [6422]~P119(x64221)+E(f334(f334(f252(x64221),f334(f334(f252(x64221),x64222),x64223)),x64224),f334(f334(f252(x64221),x64222),f334(f334(f87(a927),x64223),x64224))) % 188.18/188.25 [6423]~P81(x64231)+E(f334(f334(f252(x64231),f334(f334(f252(x64231),x64232),x64233)),x64234),f334(f334(f252(x64231),x64232),f334(f334(f87(a927),x64233),x64234))) % 188.18/188.25 [6427]E(x64271,f2(a927))+E(f334(f334(f171(x64272),f334(f334(f158(x64272),x64273),x64274)),x64271),f334(f334(f171(x64272),x64274),f334(f334(f23(a927),x64271),f84(a927)))) % 188.18/188.25 [6453]~P122(x64531)+E(f334(f334(f296(x64531),f334(f334(f87(x64531),x64532),x64533)),x64534),f334(f334(f87(x64531),x64532),f334(f334(f296(x64531),x64533),x64534))) % 188.18/188.25 [6455]~P70(x64551)+E(f334(f334(f87(x64551),f334(f334(f87(x64551),x64552),x64553)),x64554),f334(f334(f87(x64551),x64552),f334(f334(f87(x64551),x64553),x64554))) % 188.18/188.25 [6456]~P119(x64561)+E(f334(f334(f87(x64561),f334(f334(f87(x64561),x64562),x64563)),x64564),f334(f334(f87(x64561),x64562),f334(f334(f87(x64561),x64563),x64564))) % 188.18/188.25 [6458]~P119(x64581)+E(f334(f334(f86(x64581),f334(f334(f86(x64581),x64582),x64583)),x64584),f334(f334(f86(x64581),x64582),f334(f334(f86(x64581),x64583),x64584))) % 188.18/188.25 [6459]~P71(x64591)+E(f334(f334(f86(x64591),f334(f334(f86(x64591),x64592),x64593)),x64594),f334(f334(f86(x64591),x64592),f334(f334(f86(x64591),x64593),x64594))) % 188.18/188.25 [6461]~P109(x64611)+E(f334(f334(f246(x64611),f334(f334(f246(x64611),x64612),x64613)),x64614),f334(f334(f246(x64611),x64612),f334(f334(f246(x64611),x64613),x64614))) % 188.18/188.25 [6463]~P109(x64631)+E(f334(f334(f241(x64631),f334(f334(f241(x64631),x64632),x64633)),x64634),f334(f334(f241(x64631),x64632),f334(f334(f241(x64631),x64633),x64634))) % 188.18/188.25 [6465]~P98(x64651)+E(f334(f334(f108(x64651),f334(f334(f108(x64651),x64652),x64653)),x64654),f334(f334(f108(x64651),x64652),f334(f334(f108(x64651),x64653),x64654))) % 188.18/188.25 [6466]~P99(x64661)+E(f334(f334(f108(x64661),f334(f334(f108(x64661),x64662),x64663)),x64664),f334(f334(f108(x64661),x64662),f334(f334(f108(x64661),x64663),x64664))) % 188.18/188.25 [6467]~P99(x64671)+E(f334(f334(f109(x64671),f334(f334(f109(x64671),x64672),x64673)),x64674),f334(f334(f109(x64671),x64672),f334(f334(f109(x64671),x64673),x64674))) % 188.18/188.25 [6469]~P104(x64691)+E(f334(f334(f109(x64691),f334(f334(f109(x64691),x64692),x64693)),x64694),f334(f334(f109(x64691),x64692),f334(f334(f109(x64691),x64693),x64694))) % 188.18/188.25 [6478]~P5(x64781)+E(f50(x64781,f334(f334(f86(x64781),x64782),f334(f334(f87(x64781),x64783),x64784)),x64784),f50(x64781,x64782,x64784)) % 188.18/188.25 [6479]~P5(x64791)+E(f50(x64791,f334(f334(f86(x64791),x64792),f334(f334(f87(x64791),x64793),x64794)),x64793),f50(x64791,x64792,x64793)) % 188.18/188.25 [6612]E(f334(f334(f171(x66121),f334(f334(f182(x66121),x66122),x66123)),x66124),f334(f334(f171(x66121),x66123),x66124))+~P107(f334(f334(f243(a927),x66124),x66122)) % 188.18/188.25 [6790]~E(x67902,x67904)+P107(f334(f334(f179(x67901),f334(f334(f158(x67901),x67902),x67903)),x67904)) % 188.18/188.25 [6792]~P119(x67921)+E(f334(f334(f87(x67921),f334(f334(f87(x67921),x67922),x67923)),x67924),f334(f334(f87(x67921),f334(f334(f87(x67921),x67922),x67924)),x67923)) % 188.18/188.25 [6793]~P119(x67931)+E(f334(f334(f86(x67931),f334(f334(f86(x67931),x67932),x67933)),x67934),f334(f334(f86(x67931),f334(f334(f86(x67931),x67932),x67934)),x67933)) % 188.18/188.25 [6851]~P147(x68512)+E(f334(f334(f6(x68511,x68512),f334(f16(x68512,x68511),x68513)),x68514),f334(f334(f87(x68512),f334(f107(x68512),f334(f40(x68511),x68514))),x68513)) % 188.18/188.25 [7013]E(f334(f334(f109(f935(x70131,a922)),f334(f334(f316(x70131),x70132),x70133)),x70134),f334(f334(f109(f935(x70131,a922)),x70133),x70134))+P107(f334(f334(f336(x70131),x70132),x70134)) % 188.18/188.25 [7078]~P79(x70781)+E(f334(f334(f246(x70781),f334(f334(f23(x70781),x70782),x70783)),f334(f334(f23(x70781),x70784),x70783)),f334(f334(f23(x70781),f334(f334(f246(x70781),x70782),x70784)),x70783)) % 188.18/188.25 [7079]~P79(x70791)+E(f334(f334(f241(x70791),f334(f334(f23(x70791),x70792),x70793)),f334(f334(f23(x70791),x70794),x70793)),f334(f334(f23(x70791),f334(f334(f241(x70791),x70792),x70794)),x70793)) % 188.18/188.25 [7081]~P120(x70811)+E(f334(f334(f86(x70811),f334(f334(f87(x70811),x70812),x70813)),f334(f334(f87(x70811),x70814),x70813)),f334(f334(f87(x70811),f334(f334(f86(x70811),x70812),x70814)),x70813)) % 188.18/188.25 [7082]~P84(x70821)+E(f334(f334(f246(x70821),f334(f334(f86(x70821),x70822),x70823)),f334(f334(f86(x70821),x70824),x70823)),f334(f334(f86(x70821),f334(f334(f246(x70821),x70822),x70824)),x70823)) % 188.18/188.25 [7083]~P84(x70831)+E(f334(f334(f241(x70831),f334(f334(f86(x70831),x70832),x70833)),f334(f334(f86(x70831),x70834),x70833)),f334(f334(f86(x70831),f334(f334(f241(x70831),x70832),x70834)),x70833)) % 188.18/188.25 [7084]~P72(x70841)+E(f334(f334(f87(x70841),f334(f334(f252(x70841),x70842),x70843)),f334(f334(f252(x70841),x70844),x70843)),f334(f334(f252(x70841),f334(f334(f87(x70841),x70842),x70844)),x70843)) % 188.18/188.25 [7085]~P119(x70851)+E(f334(f334(f87(x70851),f334(f334(f252(x70851),x70852),x70853)),f334(f334(f252(x70851),x70854),x70853)),f334(f334(f252(x70851),f334(f334(f87(x70851),x70852),x70854)),x70853)) % 188.18/188.25 [7086]~P65(x70861)+E(f334(f334(f296(x70861),f334(f334(f252(x70861),x70862),x70863)),f334(f334(f252(x70861),x70864),x70863)),f334(f334(f252(x70861),f334(f334(f296(x70861),x70862),x70864)),x70863)) % 188.18/188.25 [7087]~P109(x70871)+E(f334(f334(f241(x70871),f334(f334(f246(x70871),x70872),x70873)),f334(f334(f246(x70871),x70874),x70873)),f334(f334(f246(x70871),f334(f334(f241(x70871),x70872),x70874)),x70873)) % 188.18/188.25 [7088]~P109(x70881)+E(f334(f334(f246(x70881),f334(f334(f241(x70881),x70882),x70883)),f334(f334(f241(x70881),x70884),x70883)),f334(f334(f241(x70881),f334(f334(f246(x70881),x70882),x70884)),x70883)) % 188.18/188.25 [7089]~P122(x70891)+E(f334(f334(f23(x70891),f334(f334(f296(x70891),x70892),x70893)),f334(f334(f296(x70891),x70894),x70893)),f334(f334(f296(x70891),f334(f334(f23(x70891),x70892),x70894)),x70893)) % 188.18/188.25 [7090]~P122(x70901)+E(f334(f334(f86(x70901),f334(f334(f296(x70901),x70902),x70903)),f334(f334(f296(x70901),x70904),x70903)),f334(f334(f296(x70901),f334(f334(f86(x70901),x70902),x70904)),x70903)) % 188.18/188.25 [7091]~P103(x70911)+E(f334(f334(f109(x70911),f334(f334(f108(x70911),x70912),x70913)),f334(f334(f108(x70911),x70914),x70913)),f334(f334(f108(x70911),f334(f334(f109(x70911),x70912),x70914)),x70913)) % 188.18/188.25 [7092]~P103(x70921)+E(f334(f334(f108(x70921),f334(f334(f109(x70921),x70922),x70923)),f334(f334(f109(x70921),x70924),x70923)),f334(f334(f109(x70921),f334(f334(f108(x70921),x70922),x70924)),x70923)) % 188.18/188.25 [7093]~P119(x70931)+E(f334(f334(f86(x70931),f334(f334(f87(x70931),x70932),x70933)),f334(f334(f87(x70931),x70934),x70933)),f334(f334(f87(x70931),f334(f334(f86(x70931),x70932),x70934)),x70933)) % 188.18/188.25 [7126]E(f334(f334(f166(x71261,x71262),x71263),x71264),x71262)+~P107(f334(f334(f242(a927),f334(f196(f928(x71261)),x71262)),x71263)) % 188.18/188.25 [7151]~P107(f334(x71513,x71514))+P107(f334(f334(f334(f108(f935(x71511,a922)),x71512),x71513),x71514)) % 188.18/188.25 [7153]~P107(f334(x71532,x71534))+P107(f334(f334(f334(f108(f935(x71531,a922)),x71532),x71533),x71534)) % 188.18/188.25 [7171]E(f334(f334(f171(x71711),f334(f334(f141(x71711),x71712),x71713)),x71714),f334(f334(f171(x71711),x71712),x71714))+~P107(f334(f334(f243(a927),x71714),f334(f196(f928(x71711)),x71712))) % 188.18/188.25 [7182]E(f334(f334(f23(f935(x71821,a922)),f334(f334(f316(x71821),x71822),x71823)),x71824),f334(f334(f23(f935(x71821,a922)),x71823),x71824))+~P107(f334(f334(f336(x71821),x71822),x71824)) % 188.18/188.25 [7223]~E(f146(a927,f334(f310(a927,x72231),x72232)),f334(f334(f158(a927),x72234),x72233))+E(f146(a927,f334(f310(a927,f334(f334(f86(a927),x72231),f84(a927))),x72232)),x72233) % 188.18/188.25 [7244]~P107(f334(f334(f179(x72441),x72443),x72444))+P107(f334(f334(f179(x72441),f334(f334(f158(x72441),x72442),x72443)),x72444)) % 188.18/188.25 [7294]E(x72941,f2(a927))+E(f334(f334(f158(x72942),x72943),f334(f334(f182(x72942),f334(f334(f23(a927),x72941),f84(a927))),x72944)),f334(f334(f182(x72942),x72941),f334(f334(f158(x72942),x72943),x72944))) % 188.18/188.25 [7393]E(f334(f334(f171(x73931),x73932),f334(f334(f23(a927),x73933),f334(f196(f928(x73931)),x73934))),f334(f334(f171(x73931),f334(f334(f141(x73931),x73934),x73932)),x73933))+P107(f334(f334(f243(a927),x73933),f334(f196(f928(x73931)),x73934))) % 188.18/188.25 [7422]E(f334(f334(f109(f935(x74221,a922)),x74222),f334(f334(f316(x74221),x74223),x74224)),f334(f334(f316(x74221),x74223),f334(f334(f109(f935(x74221,a922)),x74222),x74224)))+~P107(f334(f334(f336(x74221),x74223),x74222)) % 188.18/188.25 [7460]E(f334(f334(f171(x74601),f334(f334(f166(x74601,x74602),x74603),x74604)),x74603),x74604)+~P107(f334(f334(f243(a927),x74603),f334(f196(f928(x74601)),x74602))) % 188.18/188.25 [7482]E(x74821,f195(f935(x74822,a922)))+E(f334(f317(f934(x74823,x74822),x74823,f259(x74823,x74822)),f334(f334(f262(x74823,x74822),x74824),f334(f16(f935(x74822,a922),x74823),x74821))),x74824) % 188.18/188.25 [7483]E(x74831,f195(f935(x74832,a922)))+E(f334(f317(f934(x74832,x74833),x74833,f264(x74832,x74833)),f334(f334(f262(x74832,x74833),x74831),f334(f16(f935(x74833,a922),x74832),x74834))),x74834) % 188.18/188.25 [7554]E(f334(f334(f23(f935(x75541,a922)),f334(f334(f316(x75541),x75542),x75543)),x75544),f334(f334(f316(x75541),x75542),f334(f334(f23(f935(x75541,a922)),x75543),x75544)))+P107(f334(f334(f336(x75541),x75542),x75544)) % 188.18/188.25 [7583]~E(x75834,f195(f935(x75832,a922)))+E(f334(f317(f934(x75831,x75832),x75831,f259(x75831,x75832)),f334(f334(f262(x75831,x75832),x75833),f334(f16(f935(x75832,a922),x75831),x75834))),f195(f935(x75831,a922))) % 188.18/188.25 [7584]~E(x75843,f195(f935(x75841,a922)))+E(f334(f317(f934(x75841,x75842),x75842,f264(x75841,x75842)),f334(f334(f262(x75841,x75842),x75843),f334(f16(f935(x75842,a922),x75841),x75844))),f195(f935(x75842,a922))) % 188.18/188.25 [7634]~P107(f334(f334(f336(x76341),x76342),x76344))+P107(f334(f334(f336(x76341),x76342),f334(f334(f108(f935(x76341,a922)),x76343),x76344))) % 188.18/188.25 [7637]~P107(f334(f334(f336(x76371),x76372),x76373))+P107(f334(f334(f336(x76371),x76372),f334(f334(f108(f935(x76371,a922)),x76373),x76374))) % 188.18/188.25 [7655]E(f334(f334(f109(f935(x76551,a922)),f334(f334(f316(x76551),x76552),x76553)),x76554),f334(f334(f316(x76551),x76552),f334(f334(f109(f935(x76551,a922)),x76553),x76554)))+~P107(f334(f334(f336(x76551),x76552),x76554)) % 188.18/188.25 [7921]P107(f334(x79211,x79212))+~P107(f334(f334(f334(f109(f935(x79213,a922)),x79214),x79211),x79212)) % 188.18/188.25 [7922]P107(f334(x79221,x79222))+~P107(f334(f334(f334(f109(f935(x79223,a922)),x79221),x79224),x79222)) % 188.18/188.25 [7923]E(f334(f334(f6(x79231,a927),x79232),f334(f334(f23(f935(x79231,a922)),x79233),f334(f334(f316(x79231),x79234),f195(f935(x79231,a922))))),f334(f334(f6(x79231,a927),x79232),x79233))+P107(f334(f334(f336(x79231),x79234),x79233)) % 188.18/188.25 [7928]~P76(x79281)+E(f334(f172(x79281),f334(f334(f161(a927,x79281),x79282),f146(a927,f334(f310(a927,x79283),x79284)))),f334(f334(f6(a927,x79281),x79282),f334(f179(a927),f146(a927,f334(f310(a927,x79283),x79284))))) % 188.18/188.25 [7929]~P76(x79291)+E(f334(f334(f6(a927,x79291),x79292),f334(f179(a927),f146(a927,f334(f310(a927,x79293),x79294)))),f334(f172(x79291),f334(f334(f161(a927,x79291),x79292),f146(a927,f334(f310(a927,x79293),x79294))))) % 188.18/188.25 [8045]~E(x80453,x80454)+P107(f334(f67(x80451,x80452,f334(f334(f316(x80451),x80453),f195(f935(x80451,a922)))),x80454)) % 188.18/188.25 [8138]P107(f334(f334(f336(x81381),x81382),f334(f179(x81381),x81383)))+~P107(f334(f334(f336(x81381),x81382),f334(f179(x81381),f334(f334(f182(x81381),x81384),x81383)))) % 188.18/188.25 [8139]P107(f334(f334(f336(x81391),x81392),f334(f179(x81391),x81393)))+~P107(f334(f334(f336(x81391),x81392),f334(f179(x81391),f334(f334(f145(x81391),x81394),x81393)))) % 188.18/188.25 [8204]P107(f334(f334(f336(x82041),x82042),x82043))+~P107(f334(f334(f336(x82041),x82042),f334(f334(f23(f935(x82041,a922)),x82043),x82044))) % 188.18/188.25 [8206]P107(f334(f334(f336(x82061),x82062),x82063))+~P107(f334(f334(f336(x82061),x82062),f334(f334(f109(f935(x82061,a922)),x82064),x82063))) % 188.18/188.25 [8209]P107(f334(f334(f336(x82091),x82092),x82093))+~P107(f334(f334(f336(x82091),x82092),f334(f334(f109(f935(x82091,a922)),x82093),x82094))) % 188.18/188.25 [8224]E(f334(f334(f141(x82241),f334(f334(f182(x82241),x82242),x82243)),f334(f334(f158(x82241),x82244),f334(f334(f145(x82241),f334(a119,x82242)),x82243))),f334(f334(f166(x82241,x82243),x82242),x82244))+~P107(f334(f334(f243(a927),x82242),f334(f196(f928(x82241)),x82243))) % 188.18/188.25 [8247]P107(f334(f334(f336(x82471),x82472),x82473))+~P107(f334(f334(f242(f935(x82471,a922)),f334(f334(f316(x82471),x82472),x82474)),x82473)) % 188.18/188.25 [8288]~P107(f334(f334(f336(x82881),x82882),x82883))+~P107(f334(f334(f336(x82881),x82882),f334(f334(f23(f935(x82881,a922)),x82884),x82883))) % 188.18/188.25 [8317]~P107(f334(f334(f243(a927),x83174),f334(f196(f928(x83171)),x83173)))+P107(f334(f334(f336(x83171),x83172),f334(f179(x83171),f334(f334(f166(x83171,x83173),x83174),x83172)))) % 188.18/188.25 [8368]E(f334(f334(f171(x83681),f334(f334(f145(x83681),x83682),x83683)),x83684),f334(f334(f171(x83681),x83683),f334(f334(f86(a927),x83682),x83684)))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),x83682),x83684)),f334(f196(f928(x83681)),x83683))) % 188.18/188.25 [8377]~P147(x83772)+E(f334(f334(f6(x83771,x83772),f334(f334(f8(a927,x83772,x83771),f107(x83772)),x83773)),x83774),f334(f107(x83772),f334(f334(f6(x83771,a927),x83773),x83774))) % 188.18/188.25 [8378]~P142(x83782)+E(f334(f334(f6(x83781,x83782),f334(f334(f8(a1,x83782,x83781),f110(x83782)),x83783)),x83784),f334(f110(x83782),f334(f334(f6(x83781,a1),x83783),x83784))) % 188.18/188.25 [8427]~P68(x84272)+E(f334(f334(f9(x84271,x84272),f334(f334(f8(x84272,x84272,x84271),f81(x84272)),x84273)),x84274),f334(f81(x84272),f334(f334(f9(x84271,x84272),x84273),x84274))) % 188.18/188.25 [8428]~P3(x84282)+E(f334(f334(f6(x84281,x84282),f334(f334(f8(x84282,x84282,x84281),f85(x84282)),x84283)),x84284),f334(f85(x84282),f334(f334(f6(x84281,x84282),x84283),x84284))) % 188.18/188.25 [8430]E(f334(f334(f6(x84301,a927),x84302),f334(f334(f23(f935(x84301,a922)),x84303),f334(f334(f316(x84301),x84304),f195(f935(x84301,a922))))),f334(f334(f23(a927),f334(f334(f6(x84301,a927),x84302),x84303)),f334(x84302,x84304)))+~P107(f334(f334(f336(x84301),x84304),x84303)) % 188.18/188.25 [8449]P107(f334(f334(f242(f935(x84491,a922)),x84492),x84493))+~P107(f334(f334(f242(f935(x84491,a922)),f334(f334(f316(x84491),x84494),x84492)),x84493)) % 188.18/188.25 [8570]~E(f334(f317(x85702,x85703,x85701),f250(f935(x85702,a922))),f250(f935(x85703,a922)))+E(f334(x85701,f334(f97(x85702,x85703,f250(f935(x85702,a922)),x85701),x85704)),x85704) % 188.18/188.25 [8651]P39(x86511,x86512)+~P39(x86511,f334(f334(f316(f934(x86511,x86511)),f334(f334(f260(x86511,x86511),x86513),x86514)),x86512)) % 188.18/188.25 [8652]P61(x86521,x86522)+~P61(x86521,f334(f334(f316(f934(x86521,x86521)),f334(f334(f260(x86521,x86521),x86523),x86524)),x86522)) % 188.18/188.25 [8657]~P109(x86571)+E(f334(f334(f155(x86571,x86571,f5(x86571)),x86572),f334(f334(f155(x86571,x86571,f5(x86571)),x86573),x86574)),f334(f334(f155(x86571,x86571,f5(x86571)),x86573),f334(f334(f155(x86571,x86571,f5(x86571)),x86572),x86574))) % 188.18/188.25 [8672]E(x86721,x86722)+~P107(f334(f67(x86723,x86724,f334(f334(f316(x86723),x86721),f195(f935(x86723,a922)))),x86722)) % 188.18/188.25 [8681]E(f334(f334(f141(x86811),f334(f334(f182(x86811),x86812),x86813)),f334(f334(f182(x86811),x86814),f334(f334(f145(x86811),x86812),x86813))),f334(f334(f182(x86811),f334(f334(f86(a927),x86812),x86814)),x86813))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),x86812),x86814)),f334(f196(f928(x86811)),x86813))) % 188.18/188.25 [8719]P107(f334(f66(x87191),x87192))+~E(x87192,f334(f317(a927,x87191,x87193),f334(f270(a927),f334(f334(f7(a927,a927,a922),f243(a927)),x87194)))) % 188.18/188.25 [8743]~P90(x87431)+E(f334(f149(x87431,x87431,f86(x87431),f334(f334(f86(x87431),x87432),x87433)),x87434),f334(f334(f86(x87431),x87432),f334(f149(x87431,x87431,f86(x87431),x87433),x87434))) % 188.18/188.25 [8778]P107(f334(f334(f242(f935(x87781,a922)),f334(f272(x87781,x87782),x87783)),f334(f272(x87781,x87782),x87784)))+~P107(f334(f334(f242(f935(f934(x87781,x87782),a922)),x87783),x87784)) % 188.18/188.25 [8790]~P107(f334(f334(f242(a927),x87902),x87904))+P107(f334(f334(f242(f935(x87901,a922)),f334(f179(x87901),f334(f334(f182(x87901),x87902),x87903))),f334(f179(x87901),f334(f334(f182(x87901),x87904),x87903)))) % 188.18/188.25 [8791]~P107(f334(f334(f242(a927),x87914),x87912))+P107(f334(f334(f242(f935(x87911,a922)),f334(f179(x87911),f334(f334(f145(x87911),x87912),x87913))),f334(f179(x87911),f334(f334(f145(x87911),x87914),x87913)))) % 188.18/188.25 [8848]~P107(f334(f66(x88481),f334(f334(f23(f935(x88481,a922)),x88482),x88484)))+P107(f334(f66(x88481),f334(f334(f23(f935(x88481,a922)),x88482),f334(f334(f316(x88481),x88483),x88484)))) % 188.18/188.25 [8885]P107(f334(f334(f336(f934(x88851,x88851)),x88852),f314(x88851,x88853)))+~P107(f334(f334(f336(f934(x88851,x88851)),x88852),f334(f334(f190(f934(x88851,x88851),a922),x88854),x88853))) % 188.18/188.25 [8963]~P107(f334(f66(x89631),f334(f334(f23(f935(x89631,a922)),x89632),f334(f334(f316(x89631),x89634),x89633))))+P107(f334(f66(x89631),f334(f334(f23(f935(x89631,a922)),x89632),x89633))) % 188.18/188.25 [9189]~P109(x91891)+P107(f334(f334(f242(x91891),f334(f334(f241(x91891),x91892),f334(f334(f246(x91891),x91893),x91894))),f334(f334(f246(x91891),f334(f334(f241(x91891),x91892),x91893)),f334(f334(f241(x91891),x91892),x91894)))) % 188.18/188.25 [9190]~P99(x91901)+P107(f334(f334(f242(x91901),f334(f334(f108(x91901),x91902),f334(f334(f109(x91901),x91903),x91904))),f334(f334(f109(x91901),f334(f334(f108(x91901),x91902),x91903)),f334(f334(f108(x91901),x91902),x91904)))) % 188.18/188.25 [9325]E(x93251,x93252)+~P107(f334(f334(f336(f934(x93253,x93253)),f334(f334(f260(x93253,x93253),x93251),x93252)),f334(f179(f934(x93253,x93253)),f334(f334(f188(x93253,x93253),x93254),x93254)))) % 188.18/188.25 [9356]~P107(f334(f334(f336(f934(x93561,x93561)),f334(f334(f260(x93561,x93561),x93563),x93562)),f314(x93561,x93564)))+~P39(x93561,f334(f334(f316(f934(x93561,x93561)),f334(f334(f260(x93561,x93561),x93562),x93563)),x93564)) % 188.18/188.25 [9357]~P107(f334(f334(f336(f934(x93571,x93571)),f334(f334(f260(x93571,x93571),x93573),x93572)),f314(x93571,x93574)))+~P61(x93571,f334(f334(f316(f934(x93571,x93571)),f334(f334(f260(x93571,x93571),x93572),x93573)),x93574)) % 188.18/188.25 [9367]E(x93671,x93672)+E(f334(f143(x93673,f334(f334(f8(a922,a922,x93673),a329),f334(a331,x93671))),f334(f334(f158(x93673),x93672),x93674)),f334(f334(f158(x93673),x93672),f334(f143(x93673,f334(f334(f8(a922,a922,x93673),a329),f334(a331,x93671))),x93674))) % 188.18/188.25 [9397]~P28(x93972,x93971,x93973,f250(f935(x93972,a922)),f250(f935(x93971,a922)))+E(f334(f317(x93971,x93972,f97(x93972,x93971,f250(f935(x93972,a922)),x93973)),x93974),f334(f318(x93972,x93971,x93973),x93974)) % 188.18/188.25 [9412]~P109(x94121)+P107(f334(f334(f242(x94121),f334(f334(f241(x94121),f334(f334(f246(x94121),x94122),x94123)),f334(f334(f246(x94121),x94122),x94124))),f334(f334(f246(x94121),x94122),f334(f334(f241(x94121),x94123),x94124)))) % 188.18/188.25 [9413]~P99(x94131)+P107(f334(f334(f242(x94131),f334(f334(f108(x94131),f334(f334(f109(x94131),x94132),x94133)),f334(f334(f109(x94131),x94132),x94134))),f334(f334(f109(x94131),x94132),f334(f334(f108(x94131),x94133),x94134)))) % 188.18/188.25 [9472]~P28(x94722,x94721,x94724,f250(f935(x94722,a922)),f250(f935(x94721,a922)))+E(f334(f270(x94721),f334(f334(f8(x94722,a922,x94721),x94723),f97(x94722,x94721,f250(f935(x94722,a922)),x94724))),f334(f317(x94722,x94721,x94724),f334(f270(x94722),x94723))) % 188.18/188.25 [9486]~E(f334(f317(x94862,x94861,x94863),f250(f935(x94862,a922))),f250(f935(x94861,a922)))+P107(f334(f334(f242(f935(x94861,a922)),f334(f85(f935(x94861,a922)),f334(f317(x94862,x94861,x94863),x94864))),f334(f317(x94862,x94861,x94863),f334(f85(f935(x94862,a922)),x94864)))) % 188.18/188.25 [9824]P107(f334(f334(f336(f934(x98241,x98241)),f334(f334(f260(x98241,x98241),x98242),x98243)),f334(f293(x98241,x98241),f334(f334(f295(x98241,x98241,x98241),x98244),f314(x98241,x98244)))))+~P107(f334(f334(f336(f934(x98241,x98241)),f334(f334(f260(x98241,x98241),x98242),x98243)),f334(f334(f295(x98241,x98241,x98241),f334(f293(x98241,x98241),x98244)),f314(x98241,f334(f293(x98241,x98241),x98244))))) % 188.18/188.25 [9826]~P107(f334(f334(f336(f934(x98261,x98261)),f334(f334(f260(x98261,x98261),x98262),x98263)),f334(f293(x98261,x98261),f334(f334(f295(x98261,x98261,x98261),x98264),f314(x98261,x98264)))))+P107(f334(f334(f336(f934(x98261,x98261)),f334(f334(f260(x98261,x98261),x98262),x98263)),f334(f334(f295(x98261,x98261,x98261),f334(f293(x98261,x98261),x98264)),f314(x98261,f334(f293(x98261,x98261),x98264))))) % 188.18/188.25 [9847]~P107(f334(f334(f336(x98472),x98474),f334(f291(x98471,x98472),x98473)))+P107(f334(f334(f336(f934(x98471,x98472)),f334(f334(f260(x98471,x98472),f544(x98473,x98471,x98474,x98472)),x98474)),x98473)) % 188.18/188.25 [9848]~P107(f334(f334(f336(x98482),x98484),f334(f291(x98481,x98482),x98483)))+P107(f334(f334(f336(f934(x98481,x98482)),f334(f334(f260(x98481,x98482),f545(x98483,x98481,x98484,x98482)),x98484)),x98483)) % 188.18/188.25 [9882]~P107(f334(f334(f336(x98821),x98824),f334(f334(f108(f935(x98821,a922)),x98822),x98823)))+P107(f334(f334(f334(f108(f935(x98821,a922)),f334(f334(f7(x98821,f935(x98821,a922),a922),f336(x98821)),x98822)),f334(f334(f7(x98821,f935(x98821,a922),a922),f336(x98821)),x98823)),x98824)) % 188.18/188.25 [9883]~P107(f334(f334(f336(x98831),x98834),f334(f334(f109(f935(x98831,a922)),x98832),x98833)))+P107(f334(f334(f334(f109(f935(x98831,a922)),f334(f334(f7(x98831,f935(x98831,a922),a922),f336(x98831)),x98832)),f334(f334(f7(x98831,f935(x98831,a922),a922),f336(x98831)),x98833)),x98834)) % 188.18/188.25 [9962]~P107(f334(f334(f336(f934(x99621,x99621)),f334(f334(f260(x99621,x99621),x99624),x99623)),f334(f334(f295(x99621,x99621,x99621),x99622),f314(x99621,x99622))))+P107(f334(f334(f336(f934(x99621,x99621)),f334(f334(f260(x99621,x99621),f646(x99622,x99623,x99624,x99621)),x99623)),x99622)) % 188.18/188.25 [10007]P107(f334(f334(f336(x100071),x100072),f334(f334(f108(f935(x100071,a922)),x100073),x100074)))+~P107(f334(f334(f334(f108(f935(x100071,a922)),f334(f334(f7(x100071,f935(x100071,a922),a922),f336(x100071)),x100073)),f334(f334(f7(x100071,f935(x100071,a922),a922),f336(x100071)),x100074)),x100072)) % 188.18/188.25 [10008]P107(f334(f334(f336(x100081),x100082),f334(f334(f109(f935(x100081,a922)),x100083),x100084)))+~P107(f334(f334(f334(f109(f935(x100081,a922)),f334(f334(f7(x100081,f935(x100081,a922),a922),f336(x100081)),x100083)),f334(f334(f7(x100081,f935(x100081,a922),a922),f336(x100081)),x100084)),x100082)) % 188.18/188.25 [10256]P34(x102561,f334(f334(f7(x102561,f935(f934(x102561,x102561),a922),f935(x102561,a922)),f334(f334(f8(f935(x102561,f935(f935(f934(x102561,x102561),a922),a922)),f935(f935(f934(x102561,x102561),a922),f935(x102561,a922)),x102561),f7(x102561,f935(f934(x102561,x102561),a922),a922)),f334(f334(f8(f935(x102561,f934(x102561,x102561)),f935(x102561,f935(f935(f934(x102561,x102561),a922),a922)),x102561),f334(f8(f934(x102561,x102561),f935(f935(f934(x102561,x102561),a922),a922),x102561),f336(f934(x102561,x102561)))),f260(x102561,x102561)))),x102562),x102563,x102564)+~P107(f334(f334(f336(f934(f928(x102561),f928(x102561))),f334(f334(f260(f928(x102561),f928(x102561)),x102563),x102564)),f165(x102561,x102562))) % 188.18/188.25 [10260]P62(x102601,f334(f334(f7(x102601,f935(f934(x102601,x102601),a922),f935(x102601,a922)),f334(f334(f8(f935(x102601,f935(f935(f934(x102601,x102601),a922),a922)),f935(f935(f934(x102601,x102601),a922),f935(x102601,a922)),x102601),f7(x102601,f935(f934(x102601,x102601),a922),a922)),f334(f334(f8(f935(x102601,f934(x102601,x102601)),f935(x102601,f935(f935(f934(x102601,x102601),a922),a922)),x102601),f334(f8(f934(x102601,x102601),f935(f935(f934(x102601,x102601),a922),a922),x102601),f336(f934(x102601,x102601)))),f260(x102601,x102601)))),x102602),x102603,x102604)+~P107(f334(f334(f336(f934(f935(x102601,a922),f935(x102601,a922))),f334(f334(f260(f935(x102601,a922),f935(x102601,a922)),x102603),x102604)),f325(x102601,x102602))) % 188.18/188.25 [10291]E(x102911,x102912)+~E(f334(f334(f7(x102913,f935(f934(x102913,x102914),a922),f935(x102914,a922)),f334(f334(f8(f935(x102914,f935(f935(f934(x102913,x102914),a922),a922)),f935(f935(f934(x102913,x102914),a922),f935(x102914,a922)),x102913),f7(x102914,f935(f934(x102913,x102914),a922),a922)),f334(f334(f8(f935(x102914,f934(x102913,x102914)),f935(x102914,f935(f935(f934(x102913,x102914),a922),a922)),x102913),f334(f8(f934(x102913,x102914),f935(f935(f934(x102913,x102914),a922),a922),x102914),f336(f934(x102913,x102914)))),f260(x102913,x102914)))),x102911),f334(f334(f7(x102913,f935(f934(x102913,x102914),a922),f935(x102914,a922)),f334(f334(f8(f935(x102914,f935(f935(f934(x102913,x102914),a922),a922)),f935(f935(f934(x102913,x102914),a922),f935(x102914,a922)),x102913),f7(x102914,f935(f934(x102913,x102914),a922),a922)),f334(f334(f8(f935(x102914,f934(x102913,x102914)),f935(x102914,f935(f935(f934(x102913,x102914),a922),a922)),x102913),f334(f8(f934(x102913,x102914),f935(f935(f934(x102913,x102914),a922),a922),x102914),f336(f934(x102913,x102914)))),f260(x102913,x102914)))),x102912)) % 188.18/188.25 [10294]~P34(x102941,f334(f334(f7(x102941,f935(f934(x102941,x102941),a922),f935(x102941,a922)),f334(f334(f8(f935(x102941,f935(f935(f934(x102941,x102941),a922),a922)),f935(f935(f934(x102941,x102941),a922),f935(x102941,a922)),x102941),f7(x102941,f935(f934(x102941,x102941),a922),a922)),f334(f334(f8(f935(x102941,f934(x102941,x102941)),f935(x102941,f935(f935(f934(x102941,x102941),a922),a922)),x102941),f334(f8(f934(x102941,x102941),f935(f935(f934(x102941,x102941),a922),a922),x102941),f336(f934(x102941,x102941)))),f260(x102941,x102941)))),x102944),x102942,x102943)+P107(f334(f334(f336(f934(f928(x102941),f928(x102941))),f334(f334(f260(f928(x102941),f928(x102941)),x102942),x102943)),f165(x102941,x102944))) % 188.18/188.25 [10295]~P62(x102951,f334(f334(f7(x102951,f935(f934(x102951,x102951),a922),f935(x102951,a922)),f334(f334(f8(f935(x102951,f935(f935(f934(x102951,x102951),a922),a922)),f935(f935(f934(x102951,x102951),a922),f935(x102951,a922)),x102951),f7(x102951,f935(f934(x102951,x102951),a922),a922)),f334(f334(f8(f935(x102951,f934(x102951,x102951)),f935(x102951,f935(f935(f934(x102951,x102951),a922),a922)),x102951),f334(f8(f934(x102951,x102951),f935(f935(f934(x102951,x102951),a922),a922),x102951),f336(f934(x102951,x102951)))),f260(x102951,x102951)))),x102954),x102952,x102953)+P107(f334(f334(f336(f934(f935(x102951,a922),f935(x102951,a922))),f334(f334(f260(f935(x102951,a922),f935(x102951,a922)),x102952),x102953)),f325(x102951,x102954))) % 188.18/188.25 [7704]~P95(x77041)+E(f334(f334(f87(x77041),f334(f111(x77041),x77042)),f334(f334(f87(x77041),f334(f111(x77041),x77043)),x77044)),f334(f334(f87(x77041),f334(f111(x77041),f334(f334(f87(a1),x77042),x77043))),x77044)) % 188.18/188.25 [7705]~P95(x77051)+E(f334(f334(f86(x77051),f334(f111(x77051),x77052)),f334(f334(f23(x77051),f334(f111(x77051),x77053)),x77054)),f334(f334(f23(x77051),f334(f111(x77051),f334(f334(f86(a1),x77052),x77053))),x77054)) % 188.18/188.25 [7706]~P95(x77061)+E(f334(f334(f86(x77061),f334(f111(x77061),x77062)),f334(f334(f86(x77061),f334(f111(x77061),x77063)),x77064)),f334(f334(f86(x77061),f334(f111(x77061),f334(f334(f86(a1),x77062),x77063))),x77064)) % 188.18/188.25 [7746]~P147(x77461)+E(f334(f172(x77461),f334(f334(f161(x77462,x77461),f334(f16(x77461,x77462),x77463)),x77464)),f334(f334(f87(x77461),f334(f107(x77461),f334(f196(f928(x77462)),x77464))),x77463)) % 188.18/188.25 [7979]E(f334(f276(x79791,f334(f334(f158(f934(a106,x79791)),x79792),x79793)),x79794),f334(f264(a106,x79791),x79792))+~P107(f334(f334(f243(a106),x79794),f334(f259(a106,x79791),x79792))) % 188.18/188.25 [8022]~P95(x80221)+E(f334(f334(f86(x80221),f334(f111(x80221),x80222)),f334(f334(f23(x80221),x80223),f334(f111(x80221),x80224))),f334(f334(f86(x80221),f334(f111(x80221),f334(f334(f86(a1),x80222),f334(f85(a1),x80224)))),x80223)) % 188.18/188.25 [8147]E(f334(f276(x81471,x81472),f334(f334(f23(a106),x81473),f334(f259(a106,x81471),x81474))),f334(f276(x81471,f334(f334(f158(f934(a106,x81471)),x81474),x81472)),x81473))+P107(f334(f334(f243(a106),x81473),f334(f259(a106,x81471),x81474))) % 188.18/188.25 [8576]~P107(f334(f334(f336(x85761),x85762),f334(f179(x85761),f121(x85761,x85764))))+P107(f334(f334(f336(x85761),x85762),f334(f179(x85761),f121(x85761,f334(f334(f141(x85761),x85763),x85764))))) % 188.18/188.25 [8577]~P107(f334(f334(f336(x85771),x85772),f334(f179(x85771),f121(x85771,x85773))))+P107(f334(f334(f336(x85771),x85772),f334(f179(x85771),f121(x85771,f334(f334(f141(x85771),x85773),x85774))))) % 188.18/188.25 [8595]E(f334(f334(f108(f935(x85951,a922)),f334(f334(f109(f935(x85951,a922)),x85952),x85953)),x85954),f334(f334(f109(f935(x85951,a922)),x85952),f334(f334(f108(f935(x85951,a922)),x85953),x85954)))+~P107(f334(f334(f242(f935(x85951,a922)),x85954),x85952)) % 188.18/188.25 [8897]~E(f334(f334(f108(f935(x88971,a922)),f334(f334(f109(f935(x88971,a922)),x88973),x88974)),x88972),f334(f334(f109(f935(x88971,a922)),x88973),f334(f334(f108(f935(x88971,a922)),x88974),x88972)))+P107(f334(f334(f242(f935(x88971,a922)),x88972),x88973)) % 188.18/188.25 [9194]~P107(f334(f334(f242(f935(x91941,a922)),x91942),f334(f334(f108(f935(x91941,a922)),x91943),x91944)))+P107(f334(f334(f242(f935(x91941,a922)),f334(f334(f23(f935(x91941,a922)),x91942),x91943)),x91944)) % 188.18/188.25 [9298]~E(f334(f317(x92981,x92982,x92983),f250(f935(x92981,a922))),f250(f935(x92982,a922)))+E(f334(f317(x92981,x92982,x92983),f334(f317(x92982,x92981,f97(x92981,x92982,f250(f935(x92981,a922)),x92983)),x92984)),x92984) % 188.18/188.25 [9302]P107(f334(f334(f242(f935(x93021,a922)),x93022),f334(f334(f108(f935(x93021,a922)),x93023),x93024)))+~P107(f334(f334(f242(f935(x93021,a922)),f334(f334(f23(f935(x93021,a922)),x93022),x93023)),x93024)) % 188.18/188.25 [9393]~P86(x93931)+E(f334(f81(x93931),f334(f334(f6(x93932,x93931),f334(f334(f8(x93931,x93931,x93932),f81(x93931)),x93933)),x93934)),f334(f334(f6(x93932,x93931),f334(f334(f8(x93931,x93931,x93932),f81(x93931)),x93933)),x93934)) % 188.18/188.25 [9565]~P86(x95651)+P107(f334(f334(f242(x95651),f2(x95651)),f334(f334(f6(x95652,x95651),f334(f334(f8(x95651,x95651,x95652),f81(x95651)),x95653)),x95654))) % 188.18/188.25 [9569]~P3(x95691)+E(f334(f172(x95691),f334(f334(f161(x95692,x95691),f334(f78(x95691,x95691,x95692,f85(x95691)),x95693)),x95694)),f334(f85(x95691),f334(f172(x95691),f334(f334(f161(x95692,x95691),x95693),x95694)))) % 188.18/188.25 [9703]~P86(x97031)+P107(f334(f334(f242(x97031),f334(f81(x97031),f334(f334(f6(x97032,x97031),x97033),x97034))),f334(f334(f6(x97032,x97031),f334(f334(f8(x97031,x97031,x97032),f81(x97031)),x97033)),x97034))) % 188.18/188.25 [9744]~E(f334(f334(f86(a927),x97441),x97444),f334(f334(f86(a927),x97443),x97442))+P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),f334(f334(f260(a927,a927),x97441),x97442)),f334(f334(f260(a927,a927),x97443),x97444))),a116)) % 188.18/188.25 [9745]~P107(f334(f334(f243(a927),x97451),x97453))+P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),f334(f334(f260(a927,a927),x97451),x97452)),f334(f334(f260(a927,a927),x97453),x97454))),a38)) % 188.18/188.25 [9746]~P107(f334(f334(f243(a927),x97461),x97463))+P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),f334(f334(f260(a927,a927),x97461),x97462)),f334(f334(f260(a927,a927),x97463),x97464))),a76)) % 188.18/188.25 [9904]E(f334(f334(f86(a927),x99041),x99042),f334(f334(f86(a927),x99043),x99044))+~P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),f334(f334(f260(a927,a927),x99041),x99044)),f334(f334(f260(a927,a927),x99043),x99042))),a116)) % 188.18/188.25 [9937]E(f334(f334(f171(x99371),f334(f334(f145(x99371),f334(f196(f928(x99371)),f184(x99371,x99372,x99373))),x99373)),x99374),f334(f334(f171(x99371),x99373),f334(f334(f86(a927),x99374),f334(f196(f928(x99371)),f184(x99371,x99372,x99373)))))+~P107(f334(f334(f243(a927),x99374),f334(f196(f928(x99371)),f334(f334(f145(x99371),f334(f196(f928(x99371)),f184(x99371,x99372,x99373))),x99373)))) % 188.18/188.25 [9953]~P107(f334(f334(f336(x99532),x99534),f334(f334(f44(x99531,f935(x99532,a922)),f250(f935(x99531,a922))),x99533)))+P107(f334(f334(f334(f44(x99531,f935(x99532,a922)),f250(f935(x99531,a922))),f334(f334(f8(f935(x99532,a922),f935(x99532,a922),x99531),f334(f7(x99532,f935(x99532,a922),a922),f336(x99532))),x99533)),x99534)) % 188.18/188.25 [9954]~P107(f334(f334(f336(x99542),x99544),f334(f334(f45(x99541,f935(x99542,a922)),f250(f935(x99541,a922))),x99543)))+P107(f334(f334(f334(f45(x99541,f935(x99542,a922)),f250(f935(x99541,a922))),f334(f334(f8(f935(x99542,a922),f935(x99542,a922),x99541),f334(f7(x99542,f935(x99542,a922),a922),f336(x99542))),x99543)),x99544)) % 188.18/188.25 [10035]~P107(f334(f54(x100351,x100352),f334(f334(f260(a1,a1),x100354),x100353)))+P107(f334(f54(f334(f85(a1),x100351),x100352),f334(f334(f260(a1,a1),f334(f334(f334(f103(a1),f334(f334(a331,x100353),f2(a1))),f334(f85(a1),x100354)),f334(f334(f23(a1),f334(f85(a1),x100354)),f84(a1)))),f334(f334(f334(f103(a1),f334(f334(a331,x100353),f2(a1))),f2(a1)),f334(f334(f23(a1),x100352),x100353))))) % 188.18/188.25 [10047]P107(f334(f334(f336(x100471),x100472),f334(f334(f44(x100473,f935(x100471,a922)),f250(f935(x100473,a922))),x100474)))+~P107(f334(f334(f334(f44(x100473,f935(x100471,a922)),f250(f935(x100473,a922))),f334(f334(f8(f935(x100471,a922),f935(x100471,a922),x100473),f334(f7(x100471,f935(x100471,a922),a922),f336(x100471))),x100474)),x100472)) % 188.18/188.25 [10048]P107(f334(f334(f336(x100481),x100482),f334(f334(f45(x100483,f935(x100481,a922)),f250(f935(x100483,a922))),x100484)))+~P107(f334(f334(f334(f45(x100483,f935(x100481,a922)),f250(f935(x100483,a922))),f334(f334(f8(f935(x100481,a922),f935(x100481,a922),x100483),f334(f7(x100481,f935(x100481,a922),a922),f336(x100481))),x100484)),x100482)) % 188.18/188.25 [10060]E(f334(f334(f44(a927,f935(x100601,a922)),f250(f935(a927,a922))),x100602),f334(f334(f44(a927,f935(x100601,a922)),f250(f935(a927,a922))),x100603))+~E(f334(f334(f44(a927,f935(x100601,a922)),f334(f310(a927,f2(a927)),f455(x100602,x100604,x100603,x100601))),x100603),f334(f334(f44(a927,f935(x100601,a922)),f334(f310(a927,f2(a927)),f334(f334(f86(a927),f455(x100602,x100604,x100603,x100601)),x100604))),x100602)) % 188.18/188.25 [10403]~P107(f334(f334(f242(f935(f934(x104031,x104032),a922)),x104033),x104034))+P107(f334(f334(f242(f935(x104031,f935(x104032,a922))),f334(f334(f7(x104031,f935(f934(x104031,x104032),a922),f935(x104032,a922)),f334(f334(f8(f935(x104032,f935(f935(f934(x104031,x104032),a922),a922)),f935(f935(f934(x104031,x104032),a922),f935(x104032,a922)),x104031),f7(x104032,f935(f934(x104031,x104032),a922),a922)),f334(f334(f8(f935(x104032,f934(x104031,x104032)),f935(x104032,f935(f935(f934(x104031,x104032),a922),a922)),x104031),f334(f8(f934(x104031,x104032),f935(f935(f934(x104031,x104032),a922),a922),x104032),f336(f934(x104031,x104032)))),f260(x104031,x104032)))),x104033)),f334(f334(f7(x104031,f935(f934(x104031,x104032),a922),f935(x104032,a922)),f334(f334(f8(f935(x104032,f935(f935(f934(x104031,x104032),a922),a922)),f935(f935(f934(x104031,x104032),a922),f935(x104032,a922)),x104031),f7(x104032,f935(f934(x104031,x104032),a922),a922)),f334(f334(f8(f935(x104032,f934(x104031,x104032)),f935(x104032,f935(f935(f934(x104031,x104032),a922),a922)),x104031),f334(f8(f934(x104031,x104032),f935(f935(f934(x104031,x104032),a922),a922),x104032),f336(f934(x104031,x104032)))),f260(x104031,x104032)))),x104034))) % 188.18/188.25 [10426]P107(f334(f334(f242(f935(f934(x104261,x104262),a922)),x104263),x104264))+~P107(f334(f334(f242(f935(x104261,f935(x104262,a922))),f334(f334(f7(x104261,f935(f934(x104261,x104262),a922),f935(x104262,a922)),f334(f334(f8(f935(x104262,f935(f935(f934(x104261,x104262),a922),a922)),f935(f935(f934(x104261,x104262),a922),f935(x104262,a922)),x104261),f7(x104262,f935(f934(x104261,x104262),a922),a922)),f334(f334(f8(f935(x104262,f934(x104261,x104262)),f935(x104262,f935(f935(f934(x104261,x104262),a922),a922)),x104261),f334(f8(f934(x104261,x104262),f935(f935(f934(x104261,x104262),a922),a922),x104262),f336(f934(x104261,x104262)))),f260(x104261,x104262)))),x104263)),f334(f334(f7(x104261,f935(f934(x104261,x104262),a922),f935(x104262,a922)),f334(f334(f8(f935(x104262,f935(f935(f934(x104261,x104262),a922),a922)),f935(f935(f934(x104261,x104262),a922),f935(x104262,a922)),x104261),f7(x104262,f935(f934(x104261,x104262),a922),a922)),f334(f334(f8(f935(x104262,f934(x104261,x104262)),f935(x104262,f935(f935(f934(x104261,x104262),a922),a922)),x104261),f334(f8(f934(x104261,x104262),f935(f935(f934(x104261,x104262),a922),a922),x104262),f336(f934(x104261,x104262)))),f260(x104261,x104262)))),x104264))) % 188.18/188.25 [9437]~P107(f334(f334(f336(f934(x94371,x94371)),x94372),f314(x94371,x94374)))+P107(f334(f334(f336(f934(x94371,x94371)),x94372),f314(x94371,f334(f334(f108(f935(f934(x94371,x94371),a922)),x94373),x94374)))) % 188.18/188.25 [9438]~P107(f334(f334(f336(f934(x94381,x94381)),x94382),f314(x94381,x94383)))+P107(f334(f334(f336(f934(x94381,x94381)),x94382),f314(x94381,f334(f334(f108(f935(f934(x94381,x94381),a922)),x94383),x94384)))) % 188.18/188.25 [10137]~P107(f334(f334(f242(a927),f334(f334(f86(a927),x101371),x101374)),f334(f334(f86(a927),x101373),x101372)))+P107(f334(f334(f242(a1),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x101371),x101372)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x101373),x101374)),f195(f935(f934(a927,a927),a922))))))) % 188.18/188.25 [10138]~P107(f334(f334(f243(a927),f334(f334(f86(a927),x101381),x101384)),f334(f334(f86(a927),x101383),x101382)))+P107(f334(f334(f243(a1),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x101381),x101382)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x101383),x101384)),f195(f935(f934(a927,a927),a922))))))) % 188.18/188.25 [10202]P107(f334(f334(f242(a927),f334(f334(f86(a927),x102021),x102022)),f334(f334(f86(a927),x102023),x102024)))+~P107(f334(f334(f242(a1),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x102021),x102024)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x102023),x102022)),f195(f935(f934(a927,a927),a922))))))) % 188.18/188.25 [10203]P107(f334(f334(f243(a927),f334(f334(f86(a927),x102031),x102032)),f334(f334(f86(a927),x102033),x102034)))+~P107(f334(f334(f243(a1),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x102031),x102034)),f195(f935(f934(a927,a927),a922)))))),f334(a95,f334(f292(f934(a927,a927),f934(a927,a927),a116),f334(f334(f316(f934(a927,a927)),f334(f334(f260(a927,a927),x102033),x102032)),f195(f935(f934(a927,a927),a922))))))) % 188.18/188.25 [10244]P107(f334(f334(f242(f935(x102441,a922)),f334(f334(f44(a927,f935(x102441,a922)),f250(f935(a927,a922))),x102442)),f334(f334(f44(a927,f935(x102441,a922)),f250(f935(a927,a922))),x102443)))+~P107(f334(f334(f242(f935(x102441,a922)),f334(f334(f44(a927,f935(x102441,a922)),f334(f310(a927,f2(a927)),f450(x102443,x102444,x102442,x102441))),x102442)),f334(f334(f44(a927,f935(x102441,a922)),f334(f310(a927,f2(a927)),f334(f334(f86(a927),f450(x102443,x102444,x102442,x102441)),x102444))),x102443))) % 188.18/188.25 [10298]P107(f334(f334(f242(a106),x102984),f2(a106)))+E(f334(f334(f267(f934(a106,a106),f934(x102981,f935(a930,a330)),f934(a106,a106),f934(f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106))),f334(x102982,x102983)),f334(f334(f8(f935(f935(a106,f935(a922,f931(f929(x102981)))),f935(f934(a106,a106),f934(f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106)))),f935(f934(a106,a106),f934(f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106))),f934(x102981,f935(a930,a330))),f334(f267(f934(a106,a106),f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106),f934(f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106))),f285(x102981,x102982,f334(f334(f23(a106),x102984),f84(a106)),x102983))),f334(f334(f8(f935(f935(a106,f935(a922,f931(f929(x102981)))),f935(a106,f935(a922,f931(f929(x102981))))),f935(f935(a106,f935(a922,f931(f929(x102981)))),f935(f934(a106,a106),f934(f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106)))),f934(x102981,f935(a930,a330))),f334(f8(f935(a106,f935(a922,f931(f929(x102981)))),f935(f934(a106,a106),f934(f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106))),f935(a106,f935(a922,f931(f929(x102981))))),f260(f935(a106,f935(a922,f931(f929(x102981)))),f934(a106,a106)))),f334(f334(f8(f935(a106,f935(a922,f931(f929(x102981)))),f935(f935(a106,f935(a922,f931(f929(x102981)))),f935(a106,f935(a922,f931(f929(x102981))))),f934(x102981,f935(a930,a330))),f49(x102981)),f334(f334(f8(x102981,f935(a106,f935(a922,f931(f929(x102981)))),f934(x102981,f935(a930,a330))),f47(x102981)),f259(x102981,f935(a930,a330))))))),f285(x102981,x102982,x102984,x102983)) % 188.18/188.25 [10390]~P107(f334(f334(f336(x103902),x103904),f334(f291(x103901,x103902),x103903)))+P107(f334(f258(x103901,x103902,f334(f334(f7(x103901,f935(f934(x103901,x103902),a922),f935(x103902,a922)),f334(f334(f8(f935(x103902,f935(f935(f934(x103901,x103902),a922),a922)),f935(f935(f934(x103901,x103902),a922),f935(x103902,a922)),x103901),f7(x103902,f935(f934(x103901,x103902),a922),a922)),f334(f334(f8(f935(x103902,f934(x103901,x103902)),f935(x103902,f935(f935(f934(x103901,x103902),a922),a922)),x103901),f334(f8(f934(x103901,x103902),f935(f935(f934(x103901,x103902),a922),a922),x103902),f336(f934(x103901,x103902)))),f260(x103901,x103902)))),x103903)),x103904)) % 188.18/188.25 [10391]~P107(f334(f334(f336(x103911),x103914),f334(f272(x103911,x103912),x103913)))+P107(f334(f257(x103911,x103912,f334(f334(f7(x103911,f935(f934(x103911,x103912),a922),f935(x103912,a922)),f334(f334(f8(f935(x103912,f935(f935(f934(x103911,x103912),a922),a922)),f935(f935(f934(x103911,x103912),a922),f935(x103912,a922)),x103911),f7(x103912,f935(f934(x103911,x103912),a922),a922)),f334(f334(f8(f935(x103912,f934(x103911,x103912)),f935(x103912,f935(f935(f934(x103911,x103912),a922),a922)),x103911),f334(f8(f934(x103911,x103912),f935(f935(f934(x103911,x103912),a922),a922),x103912),f336(f934(x103911,x103912)))),f260(x103911,x103912)))),x103913)),x103914)) % 188.18/188.25 [10406]P107(f334(f334(f336(x104061),x104062),f334(f291(x104063,x104061),x104064)))+~P107(f334(f258(x104063,x104061,f334(f334(f7(x104063,f935(f934(x104063,x104061),a922),f935(x104061,a922)),f334(f334(f8(f935(x104061,f935(f935(f934(x104063,x104061),a922),a922)),f935(f935(f934(x104063,x104061),a922),f935(x104061,a922)),x104063),f7(x104061,f935(f934(x104063,x104061),a922),a922)),f334(f334(f8(f935(x104061,f934(x104063,x104061)),f935(x104061,f935(f935(f934(x104063,x104061),a922),a922)),x104063),f334(f8(f934(x104063,x104061),f935(f935(f934(x104063,x104061),a922),a922),x104061),f336(f934(x104063,x104061)))),f260(x104063,x104061)))),x104064)),x104062)) % 188.18/188.25 [10407]P107(f334(f334(f336(x104071),x104072),f334(f272(x104071,x104073),x104074)))+~P107(f334(f257(x104071,x104073,f334(f334(f7(x104071,f935(f934(x104071,x104073),a922),f935(x104073,a922)),f334(f334(f8(f935(x104073,f935(f935(f934(x104071,x104073),a922),a922)),f935(f935(f934(x104071,x104073),a922),f935(x104073,a922)),x104071),f7(x104073,f935(f934(x104071,x104073),a922),a922)),f334(f334(f8(f935(x104073,f934(x104071,x104073)),f935(x104073,f935(f935(f934(x104071,x104073),a922),a922)),x104071),f334(f8(f934(x104071,x104073),f935(f935(f934(x104071,x104073),a922),a922),x104073),f336(f934(x104071,x104073)))),f260(x104071,x104073)))),x104074)),x104072)) % 188.18/188.25 [10071]P107(f334(f167(x100711,x100712),x100713))+~P107(f334(f167(x100711,f334(f334(f18(x100711,a922,a922),f334(f334(f8(a922,f935(a922,a922),x100711),a332),x100714)),x100712)),x100713)) % 188.18/188.25 [10072]P107(f334(f167(x100721,x100722),x100723))+~P107(f334(f167(x100721,f334(f334(f18(x100721,a922,a922),f334(f334(f8(a922,f935(a922,a922),x100721),a332),x100722)),x100724)),x100723)) % 188.18/188.25 [10139]~P119(x101391)+E(f334(f334(f87(x101391),f334(f334(f86(x101391),f84(x101391)),f84(x101391))),f334(f334(f6(a927,x101391),f334(f334(f8(x101391,x101391,a927),f334(f86(x101391),x101392)),f334(f334(f7(a927,x101391,x101391),f334(f334(f8(x101391,f935(x101391,x101391),a927),f87(x101391)),f107(x101391))),x101393))),f334(f307(a927),x101394))),f334(f334(f87(x101391),f334(f107(x101391),x101394)),f334(f334(f86(x101391),x101392),f334(f334(f86(x101391),x101392),f334(f334(f87(x101391),f334(f107(x101391),f334(f334(f23(a927),x101394),f84(a927)))),x101393))))) % 188.18/188.25 [10263]P107(f334(x102631,f533(x102632,x102633,x102634,x102631)))+P39(x102632,f334(f270(f934(x102632,x102632)),f334(f265(x102632,x102632,a922),f334(f334(f8(f935(x102632,a922),f935(x102632,a922),x102632),f334(f18(x102632,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102632),a332),x102631))),f334(f334(f7(x102632,f935(x102632,x102632),f935(x102632,a922)),f334(f334(f8(f935(x102632,a922),f935(f935(x102632,x102632),f935(x102632,a922)),x102632),f8(x102632,a922,x102632)),a331)),x102633))))) % 188.18/188.25 [10274]~P107(f334(f334(f243(a927),f334(x102744,f334(x102743,f533(x102741,x102743,x102744,x102742)))),f334(x102744,f533(x102741,x102743,x102744,x102742))))+P39(x102741,f334(f270(f934(x102741,x102741)),f334(f265(x102741,x102741,a922),f334(f334(f8(f935(x102741,a922),f935(x102741,a922),x102741),f334(f18(x102741,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102741),a332),x102742))),f334(f334(f7(x102741,f935(x102741,x102741),f935(x102741,a922)),f334(f334(f8(f935(x102741,a922),f935(f935(x102741,x102741),f935(x102741,a922)),x102741),f8(x102741,a922,x102741)),a331)),x102743))))) % 188.18/188.25 [10355]~P7(x103551)+E(f43(x103551,f334(f270(x103551),f334(f334(f8(f935(f935(x103552,x103551),a922),a922,x103551),f92(f935(x103552,x103551))),f334(f334(f8(f935(f935(x103552,x103551),a922),f935(f935(x103552,x103551),a922),x103551),f334(f18(f935(x103552,x103551),a922,a922),f334(f334(f8(a922,f935(a922,a922),f935(x103552,x103551)),a332),f334(f334(f7(f935(x103552,x103551),f935(f935(x103552,x103551),a922),a922),f336(f935(x103552,x103551))),x103553)))),f334(f334(f7(x103551,f935(f935(x103552,x103551),x103551),f935(f935(x103552,x103551),a922)),f334(f334(f8(f935(x103551,a922),f935(f935(f935(x103552,x103551),x103551),f935(f935(x103552,x103551),a922)),x103551),f8(x103551,a922,f935(x103552,x103551))),a331)),f334(f334(f7(f935(x103552,x103551),x103552,x103551),f5(f935(x103552,x103551))),x103554)))))),f334(f43(f935(x103552,x103551),x103553),x103554)) % 188.18/188.25 [10356]~P7(x103561)+E(f43(x103561,f334(f270(x103561),f334(f334(f8(f935(f935(x103562,x103561),a922),a922,x103561),f92(f935(x103562,x103561))),f334(f334(f8(f935(f935(x103562,x103561),a922),f935(f935(x103562,x103561),a922),x103561),f334(f18(f935(x103562,x103561),a922,a922),f334(f334(f8(a922,f935(a922,a922),f935(x103562,x103561)),a332),f334(f334(f7(f935(x103562,x103561),f935(f935(x103562,x103561),a922),a922),f336(f935(x103562,x103561))),x103563)))),f334(f334(f7(x103561,f935(f935(x103562,x103561),x103561),f935(f935(x103562,x103561),a922)),f334(f334(f8(f935(x103561,a922),f935(f935(f935(x103562,x103561),x103561),f935(f935(x103562,x103561),a922)),x103561),f8(x103561,a922,f935(x103562,x103561))),a331)),f334(f334(f7(f935(x103562,x103561),x103562,x103561),f5(f935(x103562,x103561))),x103564)))))),f334(f43(f935(x103562,x103561),x103563),x103564)) % 188.18/188.25 [10357]~P7(x103571)+E(f42(x103571,f334(f270(x103571),f334(f334(f8(f935(f935(x103572,x103571),a922),a922,x103571),f92(f935(x103572,x103571))),f334(f334(f8(f935(f935(x103572,x103571),a922),f935(f935(x103572,x103571),a922),x103571),f334(f18(f935(x103572,x103571),a922,a922),f334(f334(f8(a922,f935(a922,a922),f935(x103572,x103571)),a332),f334(f334(f7(f935(x103572,x103571),f935(f935(x103572,x103571),a922),a922),f336(f935(x103572,x103571))),x103573)))),f334(f334(f7(x103571,f935(f935(x103572,x103571),x103571),f935(f935(x103572,x103571),a922)),f334(f334(f8(f935(x103571,a922),f935(f935(f935(x103572,x103571),x103571),f935(f935(x103572,x103571),a922)),x103571),f8(x103571,a922,f935(x103572,x103571))),a331)),f334(f334(f7(f935(x103572,x103571),x103572,x103571),f5(f935(x103572,x103571))),x103574)))))),f334(f42(f935(x103572,x103571),x103573),x103574)) % 188.18/188.25 [10358]~P7(x103581)+E(f42(x103581,f334(f270(x103581),f334(f334(f8(f935(f935(x103582,x103581),a922),a922,x103581),f92(f935(x103582,x103581))),f334(f334(f8(f935(f935(x103582,x103581),a922),f935(f935(x103582,x103581),a922),x103581),f334(f18(f935(x103582,x103581),a922,a922),f334(f334(f8(a922,f935(a922,a922),f935(x103582,x103581)),a332),f334(f334(f7(f935(x103582,x103581),f935(f935(x103582,x103581),a922),a922),f336(f935(x103582,x103581))),x103583)))),f334(f334(f7(x103581,f935(f935(x103582,x103581),x103581),f935(f935(x103582,x103581),a922)),f334(f334(f8(f935(x103581,a922),f935(f935(f935(x103582,x103581),x103581),f935(f935(x103582,x103581),a922)),x103581),f8(x103581,a922,f935(x103582,x103581))),a331)),f334(f334(f7(f935(x103582,x103581),x103582,x103581),f5(f935(x103582,x103581))),x103584)))))),f334(f42(f935(x103582,x103581),x103583),x103584)) % 188.18/188.25 [10443]~P107(f334(f334(f336(f934(x104431,x104431)),f334(f334(f260(x104431,x104431),x104433),x104434)),f334(f334(f108(f935(f934(x104431,x104431),a922)),x104432),f314(x104431,f195(f935(f934(x104431,x104431),a922))))))+P107(f334(f334(f334(f334(f108(f935(x104431,f935(x104431,a922))),f334(f334(f7(x104431,f935(f934(x104431,x104431),a922),f935(x104431,a922)),f334(f334(f8(f935(x104431,f935(f935(f934(x104431,x104431),a922),a922)),f935(f935(f934(x104431,x104431),a922),f935(x104431,a922)),x104431),f7(x104431,f935(f934(x104431,x104431),a922),a922)),f334(f334(f8(f935(x104431,f934(x104431,x104431)),f935(x104431,f935(f935(f934(x104431,x104431),a922),a922)),x104431),f334(f8(f934(x104431,x104431),f935(f935(f934(x104431,x104431),a922),a922),x104431),f336(f934(x104431,x104431)))),f260(x104431,x104431)))),x104432)),a331),x104433),x104434)) % 188.18/188.25 [10458]P107(f334(f334(f336(f934(x104581,x104581)),f334(f334(f260(x104581,x104581),x104582),x104583)),f334(f334(f108(f935(f934(x104581,x104581),a922)),x104584),f314(x104581,f195(f935(f934(x104581,x104581),a922))))))+~P107(f334(f334(f334(f334(f108(f935(x104581,f935(x104581,a922))),f334(f334(f7(x104581,f935(f934(x104581,x104581),a922),f935(x104581,a922)),f334(f334(f8(f935(x104581,f935(f935(f934(x104581,x104581),a922),a922)),f935(f935(f934(x104581,x104581),a922),f935(x104581,a922)),x104581),f7(x104581,f935(f934(x104581,x104581),a922),a922)),f334(f334(f8(f935(x104581,f934(x104581,x104581)),f935(x104581,f935(f935(f934(x104581,x104581),a922),a922)),x104581),f334(f8(f934(x104581,x104581),f935(f935(f934(x104581,x104581),a922),a922),x104581),f336(f934(x104581,x104581)))),f260(x104581,x104581)))),x104584)),a331),x104582),x104583)) % 188.18/188.25 [10386]E(f334(f334(f158(f928(x103861)),f334(f334(f158(x103861),x103862),f334(f149(f928(x103861),f928(x103861),f141(x103861),f120(x103861)),f334(f334(f161(f928(x103861),f928(x103861)),f163(f928(x103861),x103861,f120(x103861),f334(f334(f8(f928(x103861),f935(f928(x103861),f928(x103861)),x103861),f16(f928(x103861),f928(x103861))),f334(f334(f7(x103861,f928(x103861),f928(x103861)),f158(x103861)),f120(x103861))))),x103863)))),f186(x103861,f334(f334(f158(f928(x103861)),x103864),f334(f149(f928(f928(x103861)),f928(f928(x103861)),f141(f928(x103861)),f120(f928(x103861))),f334(f334(f161(f928(x103861),f928(f928(x103861))),f163(f928(f928(x103861)),x103861,f120(f928(x103861)),f334(f16(f935(f928(x103861),f928(f928(x103861))),x103861),f334(f334(f7(f928(x103861),f928(f928(x103861)),f928(f928(x103861))),f158(f928(x103861))),f120(f928(x103861)))))),x103863))))),f186(x103861,f334(f334(f158(f928(x103861)),f334(f334(f158(x103861),x103862),x103864)),x103863)))+~P107(f334(f322(f928(f928(x103861)),f187(x103861)),f334(f334(f158(f928(x103861)),f334(f334(f158(x103861),x103862),x103864)),x103863))) % 188.18/188.25 [10442]~P107(f334(f66(x104422),f334(f270(x104422),x104424)))+P107(f334(f66(x104421),f334(f270(x104421),f334(f334(f8(f935(x104422,a922),a922,x104421),f92(x104422)),f334(f334(f7(x104421,f935(x104422,a922),f935(x104422,a922)),f334(f334(f8(f935(x104422,f935(a922,a922)),f935(f935(x104422,a922),f935(x104422,a922)),x104421),f18(x104422,a922,a922)),f334(f334(f8(f935(x104422,a922),f935(x104422,f935(a922,a922)),x104421),f334(f8(a922,f935(a922,a922),x104422),a332)),f334(f334(f7(x104421,f935(x104422,x104421),f935(x104422,a922)),f334(f334(f8(f935(x104421,a922),f935(f935(x104422,x104421),f935(x104422,a922)),x104421),f8(x104421,a922,x104422)),a331)),x104423)))),x104424))))) % 188.18/188.25 [8934]P27(x89341,x89342,x89343,x89344)+~P28(x89341,x89342,x89343,x89344,x89345) % 188.18/188.25 [5507]E(x55071,x55072)+~E(f176(x55073,x55071,x55074),f176(x55073,x55072,x55075)) % 188.18/188.25 [5508]E(x55081,x55082)+~E(f133(x55083,x55084,x55081),f133(x55083,x55085,x55082)) % 188.18/188.25 [5509]E(x55091,x55092)+~E(f133(x55093,x55091,x55094),f133(x55093,x55092,x55095)) % 188.18/188.25 [8282]~E(f334(x82823,x82824),x82825)+E(f80(x82821,x82822,x82823,x82824,x82825),x82823) % 188.18/188.25 [8800]~E(f80(x88004,x88005,x88001,x88002,x88003),x88001)+E(f334(x88001,x88002),x88003) % 188.18/188.25 [9410]~P28(x94102,x94101,x94104,x94103,x94105)+P28(x94101,x94102,f83(x94102,x94101,x94103,x94104),x94105,x94103) % 188.18/188.25 [9411]~P28(x94112,x94111,x94114,x94113,x94115)+P28(x94111,x94112,f97(x94112,x94111,x94113,x94114),x94115,x94113) % 188.18/188.25 [6311]P107(f334(f258(x63111,x63112,x63113),x63114))+~P107(f334(f334(x63113,x63115),x63114)) % 188.18/188.25 [6313]P107(f334(f257(x63131,x63132,x63133),x63134))+~P107(f334(f334(x63133,x63134),x63135)) % 188.18/188.25 [6780]~E(x67805,f2(a106))+E(f334(f205(x67801,x67802,x67803,x67804),x67805),f131(x67802)) % 188.18/188.25 [6781]~E(x67815,f2(a106))+E(f334(f207(x67811,x67812,x67813,x67814),x67815),f122(x67812)) % 188.18/188.25 [6915]~E(x69153,f2(a106))+E(f334(f281(x69151,x69152,x69153,x69154),x69155),f334(f260(x69151,x69152),x69155)) % 188.18/188.25 [7934]~P22(x79344,x79341,x79342,x79345)+E(f334(f78(x79341,x79341,x79341,f334(x79342,x79343)),f334(x79342,x79343)),f334(x79342,x79343)) % 188.18/188.25 [8318]~P18(x83185,x83181,x83182)+E(f334(f78(x83181,x83181,x83181,f334(x83182,x83183)),f334(x83182,x83184)),f334(f78(x83181,x83181,x83181,f334(x83182,x83184)),f334(x83182,x83183))) % 188.18/188.25 [8633]P107(f334(f334(f336(f934(x86331,x86331)),f334(f334(f260(x86331,x86331),x86332),x86333)),f328(x86331,x86334,x86335)))+~P107(f334(f334(f243(a927),f334(x86334,x86332)),f334(x86334,x86333))) % 188.18/188.25 [8729]~P107(f334(f334(f336(x87294),x87293),f305(x87294,x87291,x87292,x87295)))+P107(f334(f334(x87291,x87292),x87293)) % 188.18/188.25 [8730]~P107(f334(f334(f336(x87304),x87303),f302(x87304,x87301,x87302,x87305)))+P107(f334(f334(x87301,x87302),x87303)) % 188.18/188.25 [8731]~P107(f334(f334(f336(x87314),x87312),f305(x87314,x87311,x87315,x87313)))+P107(f334(f334(x87311,x87312),x87313)) % 188.18/188.25 [8732]~P107(f334(f334(f336(x87324),x87322),f302(x87324,x87321,x87325,x87323)))+P107(f334(f334(x87321,x87322),x87323)) % 188.18/188.25 [8811]~P28(x88111,x88113,x88115,x88112,x88114)+E(f334(f40(x88111),x88112),f334(f40(x88113),x88114)) % 188.18/188.25 [8860]~P28(x88601,x88602,x88603,x88604,x88605)+E(f334(f317(x88601,x88602,x88603),x88604),x88605) % 188.18/188.25 [8875]~P60(x88752,x88751,x88755,x88753,x88754)+E(f334(f317(x88751,x88752,x88753),x88754),f250(f935(x88752,a922))) % 188.18/188.25 [9314]~P36(x93141,x93142,x93143,x93144,x93145)+P36(x93141,x93142,x93143,f334(f175(x93141),x93144),f334(f175(x93142),x93145)) % 188.18/188.25 [9316]~P36(x93161,x93162,x93163,f334(f175(x93161),x93164),x93165)+P36(x93161,x93162,x93163,x93164,f334(f175(x93162),x93165)) % 188.18/188.25 [9317]~P36(x93171,x93172,x93173,x93174,f334(f175(x93172),x93175))+P36(x93171,x93172,x93173,f334(f175(x93171),x93174),x93175) % 188.18/188.25 [9323]P36(x93231,x93232,x93233,x93234,x93235)+~P36(x93231,x93232,x93233,f334(f175(x93231),x93234),f334(f175(x93232),x93235)) % 188.18/188.25 [9730]P107(f334(f334(f336(f934(f928(x97301),f928(x97301))),f334(f334(f260(f928(x97301),f928(x97301)),f334(f334(f158(x97301),x97302),x97303)),f334(f334(f158(x97301),x97302),x97304))),f164(x97301,x97305)))+~P107(f334(f334(f336(f934(f928(x97301),f928(x97301))),f334(f334(f260(f928(x97301),f928(x97301)),x97303),x97304)),f164(x97301,x97305))) % 188.18/188.25 [9731]P107(f334(f334(f336(f934(f928(x97311),f928(x97311))),f334(f334(f260(f928(x97311),f928(x97311)),f334(f334(f141(x97311),x97312),x97313)),f334(f334(f141(x97311),x97312),x97314))),f154(x97311,x97315)))+~P107(f334(f334(f336(f934(f928(x97311),f928(x97311))),f334(f334(f260(f928(x97311),f928(x97311)),x97313),x97314)),f154(x97311,x97315))) % 188.18/188.25 [9944]E(f334(f334(f158(x99441),f665(x99442,x99443,x99444,x99445,x99441)),f666(x99442,x99443,x99444,x99445,x99441)),x99445)+~P107(f334(f334(f336(f934(f928(x99441),f928(x99441))),f334(f334(f260(f928(x99441),f928(x99441)),x99445),f334(f334(f158(x99441),x99444),x99443))),f165(x99441,x99442))) % 188.18/188.25 [9965]E(f334(f334(f158(x99651),f667(x99652,x99653,x99654,x99655,x99651)),f668(x99652,x99653,x99654,x99655,x99651)),x99653)+~P107(f334(f334(f336(f934(f928(x99651),f928(x99651))),f334(f334(f260(f928(x99651),f928(x99651)),f334(f334(f158(x99651),x99655),x99654)),x99653)),f165(x99651,x99652))) % 188.18/188.25 [10116]~P107(f334(f334(f336(f934(f928(x101161),f928(x101161))),f334(f334(f260(f928(x101161),f928(x101161)),f334(f334(f158(x101161),x101165),x101162)),x101164)),f165(x101161,x101163)))+P107(f334(f334(f336(f934(f928(x101161),f928(x101161))),f334(f334(f260(f928(x101161),f928(x101161)),x101162),f668(x101163,x101164,x101162,x101165,x101161))),f165(x101161,x101163))) % 188.18/188.25 [10174]~P107(f334(f334(f336(f934(f928(x101741),f928(x101741))),f334(f334(f260(f928(x101741),f928(x101741)),x101745),f334(f334(f158(x101741),x101744),x101743))),f165(x101741,x101742)))+P107(f334(f334(f336(f934(f928(x101741),f928(x101741))),f334(f334(f260(f928(x101741),f928(x101741)),f666(x101742,x101743,x101744,x101745,x101741)),x101743)),f165(x101741,x101742))) % 188.18/188.25 [10359]P107(f334(f334(f336(f934(x103591,x103591)),f334(f334(f260(x103591,x103591),f334(x103592,f334(f334(f86(a927),x103593),x103594))),f334(x103592,x103593))),f314(x103591,x103595)))+~P107(f334(f334(f336(f934(x103591,x103591)),f334(f334(f260(x103591,x103591),f334(x103592,f334(a119,f622(x103594,x103593,x103595,x103592,x103591)))),f334(x103592,f622(x103594,x103593,x103595,x103592,x103591)))),f314(x103591,x103595))) % 188.18/188.25 [5475]E(x54751,x54752)+~E(f334(f334(f158(x54753),x54754),x54751),f334(f334(f158(x54753),x54755),x54752)) % 188.18/188.25 [5476]E(x54761,x54762)+~E(f334(f334(f158(x54763),x54761),x54764),f334(f334(f158(x54763),x54762),x54765)) % 188.18/188.25 [5524]P107(f334(x55241,x55242))+~E(f334(f143(x55243,x55241),x55244),f334(f334(f158(x55243),x55242),x55245)) % 188.18/188.25 [5525]P107(f334(x55251,x55252))+~E(f334(f334(f158(x55253),x55252),x55254),f334(f143(x55253,x55251),x55255)) % 188.18/188.25 [5681]~E(f334(f334(f145(x56811),x56813),x56812),f334(f334(f158(x56811),x56814),x56815))+E(f334(f334(f171(x56811),x56812),x56813),x56814) % 188.18/188.25 [5820]~P16(x58204,x58205,x58201)+E(f334(f334(x58201,x58202),f334(f334(x58201,x58202),x58203)),f334(f334(x58201,x58202),x58203)) % 188.18/188.25 [6369]~E(x63694,f2(a106))+E(f334(f334(f124(x63691,x63692,x63693),x63694),x63695),f334(f334(f260(f928(x63692),x63691),f120(x63692)),x63695)) % 188.18/188.25 [6436]~P109(x64362)+~E(f334(f334(f155(x64361,x64362,x64363),x64364),x64365),f120(x64361)) % 188.18/188.25 [6819]E(x68191,x68192)+~E(f334(f334(f141(x68193),x68194),f334(f334(f158(x68193),x68191),f120(x68193))),f334(f334(f141(x68193),x68195),f334(f334(f158(x68193),x68192),f120(x68193)))) % 188.18/188.25 [6820]E(x68201,x68202)+~E(f334(f334(f141(x68203),x68201),f334(f334(f158(x68203),x68204),f120(x68203))),f334(f334(f141(x68203),x68202),f334(f334(f158(x68203),x68205),f120(x68203)))) % 188.18/188.25 [7124]E(f334(f334(f316(x71241),f334(x71242,x71243)),f334(f317(x71244,x71241,x71242),x71245)),f334(f317(x71244,x71241,x71242),x71245))+~P107(f334(f334(f336(x71244),x71243),x71245)) % 188.18/188.25 [7130]~P107(f334(x71304,f334(x71303,x71305)))+P107(f334(f334(f318(x71301,x71302,x71303),x71304),x71305)) % 188.18/188.25 [7133]~P107(f334(f334(x71333,x71335),x71334))+P107(f334(f334(f251(x71331,x71332,x71333),x71334),x71335)) % 188.18/188.25 [7227]~E(f334(f317(x72271,x72272,x72273),x72274),x72275)+E(f334(f317(f935(x72271,a922),f935(x72272,a922),f317(x72271,x72272,x72273)),f334(f315(x72271),x72274)),f334(f315(x72272),x72275)) % 188.18/188.25 [7254]E(f334(f279(x72541,x72542,x72543,x72544),x72545),f334(x72544,x72545))+~P107(f334(f334(f336(x72541),x72545),x72543)) % 188.18/188.25 [7562]P27(x75621,x75622,x75623,x75624)+~P27(x75621,x75622,x75623,f334(f334(f316(x75621),x75625),x75624)) % 188.18/188.25 [7618]P107(f334(x76181,x76182))+~P107(f334(f334(f99(x76183,x76184,x76181),x76185),x76182)) % 188.18/188.25 [7659]~P107(f334(f334(f336(x76594),x76593),x76595))+P107(f334(f334(f336(x76591),f334(x76592,x76593)),f334(f317(x76594,x76591,x76592),x76595))) % 188.18/188.25 [7680]~P109(x76802)+E(f157(x76801,x76802,x76803,f334(f143(x76801,x76804),x76805)),f334(f143(x76801,x76804),f157(x76801,x76802,x76803,x76805))) % 188.18/188.25 [7710]P107(f334(x77101,f334(x77102,x77103)))+~P107(f334(f334(f318(x77104,x77105,x77102),x77101),x77103)) % 188.18/188.25 [7713]P107(f334(f334(x77131,x77132),x77133))+~P107(f334(f334(f251(x77134,x77135,x77131),x77133),x77132)) % 188.18/188.25 [7714]P107(f334(f334(x77141,x77142),x77143))+~P107(f334(f334(f99(x77144,x77141,x77145),x77142),x77143)) % 188.18/188.25 [7776]~P107(f334(f334(f336(x77763),f334(x77764,x77762)),x77765))+P107(f334(f334(f336(x77761),x77762),f334(f318(x77761,x77763,x77764),x77765))) % 188.18/188.25 [8161]~P107(f334(f334(f336(x81615),x81613),f334(f318(x81615,x81611,x81612),x81614)))+P107(f334(f334(f336(x81611),f334(x81612,x81613)),x81614)) % 188.18/188.25 [8454]~P18(x84542,x84541,x84543)+E(f334(f149(x84541,x84542,f334(f7(x84542,x84541,x84541),x84543),x84544),f159(x84542,x84545)),f334(f334(f69(x84542,x84541,x84543),x84544),f334(f179(x84542),x84545))) % 188.18/188.25 [8476]E(f334(x84761,f404(x84762,x84761,x84763,x84764)),x84764)+~P107(f334(f334(f336(x84765),x84764),f334(f317(x84763,x84765,x84761),x84762))) % 188.18/188.25 [8477]E(f334(x84771,f413(x84772,x84771,x84773,x84774)),x84774)+~P107(f334(f334(f336(x84775),x84774),f334(f317(x84773,x84775,x84771),x84772))) % 188.18/188.25 [8776]~E(x87762,f334(f334(f158(x87761),x87764),x87765))+P107(f334(f334(f336(f934(f928(x87761),f928(x87761))),f334(f334(f260(f928(x87761),f928(x87761)),f120(x87761)),x87762)),f154(x87761,x87763))) % 188.18/188.25 [8820]E(f334(x88201,f334(f97(x88202,x88203,x88204,x88201),x88205)),x88205)+~P107(f334(f334(f336(x88203),x88205),f334(f317(x88202,x88203,x88201),x88204))) % 188.18/188.25 [8823]P27(x88231,x88232,f97(x88232,x88231,x88233,x88234),x88235)+~P107(f334(f334(f242(f935(x88231,a922)),x88235),f334(f317(x88232,x88231,x88234),x88233))) % 188.18/188.25 [8832]~P36(x88321,x88323,x88325,x88322,x88324)+E(f334(f196(f928(x88321)),x88322),f334(f196(f928(x88323)),x88324)) % 188.18/188.25 [8842]P107(f334(f334(f242(f935(x88421,a922)),f334(f334(f45(x88422,f935(x88421,a922)),x88423),x88424)),f334(x88424,x88425)))+~P107(f334(f334(f336(x88422),x88425),x88423)) % 188.18/188.25 [8890]~P60(x88901,x88902,x88903,x88905,x88904)+E(f334(f317(x88901,x88902,x88903),f250(f935(x88901,a922))),x88904) % 188.18/188.25 [9121]E(f334(f143(x91211,x91212),f755(x91213,x91214,x91215,x91212,x91211)),x91213)+~E(f334(f143(x91211,x91212),x91215),f334(f334(f158(x91211),x91214),x91213)) % 188.18/188.25 [9122]E(f334(f143(x91221,x91222),f758(x91223,x91222,x91224,x91225,x91221)),x91224)+~E(f334(f334(f158(x91221),x91225),x91224),f334(f143(x91221,x91222),x91223)) % 188.18/188.25 [9214]E(f334(f196(f928(x92141)),x92142),x92143)+~P107(f334(f334(f336(f934(f928(x92141),f928(x92141))),f334(f334(f260(f928(x92141),f928(x92141)),x92144),x92142)),f334(f150(x92141,x92145),x92143))) % 188.18/188.25 [9215]E(f334(f196(f928(x92151)),x92152),x92153)+~P107(f334(f334(f336(f934(f928(x92151),f928(x92151))),f334(f334(f260(f928(x92151),f928(x92151)),x92152),x92154)),f334(f150(x92151,x92155),x92153))) % 188.18/188.25 [9278]P107(f334(f334(f336(x92781),f404(x92782,x92783,x92781,x92784)),x92782))+~P107(f334(f334(f336(x92785),x92784),f334(f317(x92781,x92785,x92783),x92782))) % 188.18/188.25 [9279]P107(f334(f334(f336(x92791),f413(x92792,x92793,x92791,x92794)),x92792))+~P107(f334(f334(f336(x92795),x92794),f334(f317(x92791,x92795,x92793),x92792))) % 188.18/188.25 [9435]E(f334(f317(x94351,x94352,x94353),f481(x94354,x94353,x94351,x94355,x94352)),x94355)+~P107(f334(f334(f242(f935(x94352,a922)),x94355),f334(f317(x94351,x94352,x94353),x94354))) % 188.18/188.25 [9753]P107(f334(f334(f336(f934(f928(x97531),f928(x97531))),f334(f334(f260(f928(x97531),f928(x97531)),f334(f334(f158(x97531),x97532),x97533)),f334(f334(f158(x97531),x97532),x97534))),f314(f928(x97531),f164(x97531,x97535))))+~P107(f334(f334(f336(f934(f928(x97531),f928(x97531))),f334(f334(f260(f928(x97531),f928(x97531)),x97533),x97534)),f314(f928(x97531),f164(x97531,x97535)))) % 188.18/188.25 [9784]~E(f334(x97843,f708(x97845,x97844,x97843,x97842,x97841)),f334(x97845,f708(x97845,x97844,x97843,x97842,x97841)))+E(f334(f334(f161(x97841,x97842),x97843),x97844),f334(f334(f161(x97841,x97842),x97845),x97844)) % 188.18/188.25 [9869]~E(f334(f143(x98691,x98695),x98694),f334(f334(f158(x98691),x98693),x98692))+E(f334(f334(f141(x98691),f756(x98692,x98693,x98694,x98695,x98691)),f334(f334(f158(x98691),x98693),f755(x98692,x98693,x98694,x98695,x98691))),x98694) % 188.18/188.25 [9870]~E(f334(f334(f158(x98701),x98705),x98704),f334(f143(x98701,x98703),x98702))+E(f334(f334(f141(x98701),f759(x98702,x98703,x98704,x98705,x98701)),f334(f334(f158(x98701),x98705),f758(x98702,x98703,x98704,x98705,x98701))),x98702) % 188.18/188.25 [9878]E(f334(f334(f161(x98781,x98782),x98783),x98784),f334(f334(f161(x98781,x98782),x98785),x98784))+P107(f334(f334(f336(x98781),f708(x98783,x98784,x98785,x98782,x98781)),f334(f179(x98781),x98784))) % 188.18/188.25 [9905]~P107(f334(f334(f336(x99055),x99054),f334(f292(x99051,x99055,x99053),x99052)))+P107(f334(f334(f336(x99051),f453(x99052,x99053,x99051,x99054,x99055)),x99052)) % 188.18/188.25 [9906]~P107(f334(f334(f336(x99065),x99064),f334(f292(x99061,x99065,x99063),x99062)))+P107(f334(f334(f336(x99061),f506(x99062,x99063,x99061,x99064,x99065)),x99062)) % 188.18/188.25 [9938]~P107(f334(f334(f242(f935(x99385,a922)),x99384),f334(f317(x99381,x99385,x99383),x99382)))+P107(f334(f334(f242(f935(x99381,a922)),f481(x99382,x99383,x99381,x99384,x99385)),x99382)) % 188.18/188.25 [10362]E(x103621,f2(a106))+E(f232(f934(f928(x103622),x103623),f934(x103622,x103623),f334(f334(f260(f928(x103622),x103623),f120(x103622)),x103624),f334(f265(x103622,x103623,f934(f928(x103622),x103623)),f334(f334(f7(x103622,f935(x103623,f934(f928(x103622),x103623)),f935(x103623,f934(f928(x103622),x103623))),f334(f334(f8(f935(f934(f928(x103622),x103623),f934(f928(x103622),x103623)),f935(f935(x103623,f934(f928(x103622),x103623)),f935(x103623,f934(f928(x103622),x103623))),x103622),f8(f934(f928(x103622),x103623),f934(f928(x103622),x103623),x103623)),f334(f334(f8(f935(f928(x103622),f935(x103623,f934(f928(x103622),x103623))),f935(f934(f928(x103622),x103623),f934(f928(x103622),x103623)),x103622),f265(f928(x103622),x103623,f934(f928(x103622),x103623))),f334(f334(f8(f935(f928(x103622),f928(x103622)),f935(f928(x103622),f935(x103623,f934(f928(x103622),x103623))),x103622),f334(f8(f928(x103622),f935(x103623,f934(f928(x103622),x103623)),f928(x103622)),f260(f928(x103622),x103623))),f158(x103622))))),f334(f124(x103623,x103622,x103625),f334(f334(f23(a106),x103621),f84(a106))))),f334(x103625,x103624)),f334(f334(f124(x103623,x103622,x103625),x103621),x103624)) % 188.18/188.25 [6252]E(x62521,x62522)+~E(f334(f264(x62523,x62524),f334(f334(f260(x62523,x62524),x62525),x62521)),x62522) % 188.18/188.25 [6253]E(x62531,x62532)+~E(f334(f259(x62533,x62534),f334(f334(f260(x62533,x62534),x62531),x62535)),x62532) % 188.18/188.25 [6510]~E(x65103,f334(f334(f141(x65101),x65104),f334(f334(f158(x65101),x65102),x65105)))+P107(f334(f334(f336(x65101),x65102),f334(f179(x65101),x65103))) % 188.18/188.25 [6902]E(f334(f317(x69021,x69022,f334(f16(x69022,x69021),x69023)),x69024),f334(f334(f316(x69022),x69023),f195(f935(x69022,a922))))+~P107(f334(f334(f336(x69021),x69025),x69024)) % 188.18/188.25 [6972]E(f334(f334(f108(f935(x69721,a922)),f334(f179(x69721),x69722)),f334(f179(x69721),x69723)),f334(f179(x69721),x69724))+~E(f173(x69721,x69725,x69724),f334(f334(f260(f928(x69721),f928(x69721)),x69722),x69723)) % 188.18/188.25 [7065]~P109(x70652)+E(f334(f196(f928(x70651)),f334(f334(f155(x70651,x70652,x70653),x70654),x70655)),f334(a119,f334(f196(f928(x70651)),x70655))) % 188.18/188.25 [7077]~P109(x70772)+E(f334(f179(x70771),f334(f334(f155(x70771,x70772,x70773),x70774),x70775)),f334(f334(f316(x70771),x70774),f334(f179(x70771),x70775))) % 188.18/188.25 [7347]~P119(x73471)+E(f334(f334(f87(x73471),f334(f334(f87(x73471),x73472),x73473)),f334(f334(f87(x73471),x73474),x73475)),f334(f334(f87(x73471),f334(f334(f87(x73471),x73472),x73474)),f334(f334(f87(x73471),x73473),x73475))) % 188.18/188.25 [7348]~P119(x73481)+E(f334(f334(f86(x73481),f334(f334(f86(x73481),x73482),x73483)),f334(f334(f86(x73481),x73484),x73485)),f334(f334(f86(x73481),f334(f334(f86(x73481),x73482),x73484)),f334(f334(f86(x73481),x73483),x73485))) % 188.18/188.25 [7349]~P65(x73491)+E(f334(f334(f296(x73491),f334(f334(f87(x73491),x73492),x73493)),f334(f334(f87(x73491),x73494),x73495)),f334(f334(f87(x73491),f334(f334(f296(x73491),x73492),x73494)),f334(f334(f296(x73491),x73493),x73495))) % 188.18/188.25 [7363]~P109(x73631)+E(f313(x73631,f334(f334(f241(x73631),x73632),x73633),f334(f334(f246(x73631),x73634),x73635)),f334(f334(f109(f935(x73631,a922)),f313(x73631,x73632,x73634)),f313(x73631,x73633,x73635))) % 188.18/188.25 [7364]~P109(x73641)+E(f312(x73641,f334(f334(f241(x73641),x73642),x73643),f334(f334(f246(x73641),x73644),x73645)),f334(f334(f109(f935(x73641,a922)),f312(x73641,x73642,x73644)),f312(x73641,x73643,x73645))) % 188.18/188.25 [7365]~P109(x73651)+E(f311(x73651,f334(f334(f241(x73651),x73652),x73653),f334(f334(f246(x73651),x73654),x73655)),f334(f334(f109(f935(x73651,a922)),f311(x73651,x73652,x73654)),f311(x73651,x73653,x73655))) % 188.18/188.25 [7366]~P109(x73661)+E(f334(f334(f109(f935(x73661,a922)),f334(f310(x73661,x73662),x73663)),f334(f310(x73661,x73664),x73665)),f334(f310(x73661,f334(f334(f241(x73661),x73662),x73664)),f334(f334(f246(x73661),x73663),x73665))) % 188.18/188.25 [7485]~P107(f334(x74851,f349(x74853,x74852,x74851)))+P107(f334(x74851,f334(f334(f260(x74852,x74853),x74854),x74855))) % 188.18/188.26 [7586]~E(x75862,f334(x75864,x75865))+P107(f334(f334(f336(x75861),x75862),f334(f317(x75863,x75861,x75864),f250(f935(x75863,a922))))) % 188.18/188.26 [7656]~P16(x76563,x76562,x76564)+P16(x76561,x76562,f334(f334(f8(x76563,f935(x76562,x76562),x76561),x76564),x76565)) % 188.18/188.26 [7657]~P18(x76573,x76572,x76574)+P18(x76571,x76572,f334(f334(f8(x76573,f935(x76572,x76572),x76571),x76574),x76575)) % 188.18/188.26 [7792]~P27(x77921,x77922,x77923,x77924)+P27(x77921,x77922,x77923,f334(f334(f23(f935(x77921,a922)),x77924),x77925)) % 188.18/188.26 [7943]~P107(f334(f334(x79433,x79434),x79435))+P107(f334(f334(f265(x79431,x79432,a922),x79433),f334(f334(f260(x79431,x79432),x79434),x79435))) % 188.18/188.26 [8059]~P107(f334(x80592,x80594))+~E(f334(f334(f145(x80591),f334(f196(f928(x80591)),f184(x80591,x80592,x80593))),x80593),f334(f334(f158(x80591),x80594),x80595)) % 188.18/188.26 [8079]P27(x80791,x80792,x80793,x80794)+~P27(x80791,x80792,x80793,f334(f334(f108(f935(x80791,a922)),x80795),x80794)) % 188.18/188.26 [8080]P27(x80801,x80802,x80803,x80804)+~P27(x80801,x80802,x80803,f334(f334(f108(f935(x80801,a922)),x80804),x80805)) % 188.18/188.26 [8122]~P109(x81222)+E(f334(f334(f155(x81221,x81222,x81223),x81224),f157(x81221,x81222,x81223,x81225)),f157(x81221,x81222,x81223,f334(f334(f158(x81221),x81224),x81225))) % 188.18/188.26 [8431]~P16(x84312,x84311,x84313)+E(f334(f149(x84311,x84312,f334(f7(x84312,x84311,x84311),x84313),x84314),x84315),f334(f334(f69(x84312,x84311,x84313),x84314),f334(f179(x84312),x84315))) % 188.18/188.26 [8459]~E(f334(f334(f145(x84591),f334(f196(f928(x84591)),f184(x84591,x84592,x84593))),x84593),f334(f334(f158(x84591),x84594),x84595))+E(f334(f334(f141(x84591),f184(x84591,x84592,x84593)),f334(f334(f158(x84591),x84594),x84595)),x84593) % 188.18/188.26 [8487]P107(f334(f334(x84871,x84872),x84873))+~P107(f334(f334(f265(x84874,x84875,a922),x84871),f334(f334(f260(x84874,x84875),x84872),x84873))) % 188.18/188.26 [8952]P107(f334(f334(f242(f935(x89521,a922)),f334(f317(x89522,x89521,x89523),x89524)),f334(f317(x89522,x89521,x89523),x89525)))+~P107(f334(f334(f242(f935(x89522,a922)),x89524),x89525)) % 188.18/188.26 [8953]P107(f334(f334(f242(f935(x89531,a922)),f334(f318(x89531,x89532,x89533),x89534)),f334(f318(x89531,x89532,x89533),x89535)))+~P107(f334(f334(f242(f935(x89532,a922)),x89534),x89535)) % 188.18/188.26 [9033]E(x90331,f2(a106))+E(f334(f334(f267(x90332,x90333,x90332,f934(x90333,x90332)),f334(x90334,x90335)),f281(x90333,x90332,f334(f334(f23(a106),x90331),f84(a106)),x90334)),f334(f281(x90333,x90332,x90331,x90334),x90335)) % 188.18/188.26 [9148]P107(f334(f334(f263(x91481,x91482,a922,x91483),x91484),x91485))+~P107(f334(x91483,f334(f334(f260(x91481,x91482),x91484),x91485))) % 188.18/188.26 [9416]~P107(f334(f334(f263(x94162,x94163,a922,x94161),x94164),x94165))+P107(f334(x94161,f334(f334(f260(x94162,x94163),x94164),x94165))) % 188.18/188.26 [9601]~P107(f334(f334(f336(x96012),x96015),f334(f317(x96011,x96012,x96014),x96013)))+P107(f334(f334(f336(x96011),f334(f97(x96011,x96012,x96013,x96014),x96015)),x96013)) % 188.18/188.26 [9682]~P107(f334(f66(x96823),f334(f317(x96822,x96823,x96825),f250(f935(x96822,a922)))))+P107(f334(f66(x96821),f334(f317(x96822,x96821,f334(f334(f8(x96823,x96821,x96822),x96824),x96825)),f250(f935(x96822,a922))))) % 188.18/188.26 [9707]P107(f334(f334(f242(f935(f935(x97071,a922),a922)),f334(f317(f935(x97072,a922),f935(x97071,a922),f317(x97072,x97071,x97073)),f334(f315(x97072),x97074))),f334(f315(x97071),x97075)))+~P107(f334(f334(f242(f935(x97071,a922)),f334(f317(x97072,x97071,x97073),x97074)),x97075)) % 188.18/188.26 [9792]E(x97921,x97922)+~P107(f334(f71(x97923,x97924,x97925,x97921,f195(f935(x97923,a922))),x97922)) % 188.18/188.26 [9806]E(f334(f334(f260(x98061,x98062),f559(x98063,x98064,x98065,x98062,x98061)),f560(x98063,x98064,x98065,x98062,x98061)),x98065)+~P107(f334(f334(f336(f934(x98061,x98062)),x98065),f334(f334(f262(x98061,x98062),x98064),x98063))) % 188.18/188.26 [9911]P107(f334(f334(f336(x99111),f559(x99112,x99113,x99114,x99115,x99111)),x99113))+~P107(f334(f334(f336(f934(x99111,x99115)),x99114),f334(f334(f262(x99111,x99115),x99113),x99112))) % 188.18/188.26 [9921]P107(f334(f334(f336(x99211),f574(x99212,x99213,x99214,x99215,x99211)),x99215))+P107(f334(f334(f242(f935(x99214,a922)),f334(f317(x99211,x99214,x99213),x99215)),x99212)) % 188.18/188.26 [10044]P26(x100445,x100444,f334(f334(f316(f926(x100445)),f98(x100445,x100441,x100443,x100442)),f195(f935(f926(x100445),a922))))+P107(f334(f334(x100441,f564(x100442,x100443,x100444,x100445,x100441)),f675(x100442,x100443,x100444,x100445,x100441))) % 188.18/188.26 [10084]P107(f334(f334(f336(x100841),f560(x100842,x100843,x100844,x100841,x100845)),f334(x100842,f559(x100842,x100843,x100844,x100841,x100845))))+~P107(f334(f334(f336(f934(x100845,x100841)),x100844),f334(f334(f262(x100845,x100841),x100843),x100842))) % 188.18/188.26 [10095]P107(f334(f334(f336(f934(x100951,x100951)),f334(f334(f260(x100951,x100951),x100952),f643(x100953,x100954,x100955,x100952,x100951))),x100953))+~P107(f334(f334(f336(f934(x100951,x100951)),f334(f334(f260(x100951,x100951),x100952),x100955)),f334(f334(f190(f934(x100951,x100951),a922),f334(a119,x100954)),x100953))) % 188.18/188.26 [10096]P107(f334(f334(f336(f934(x100961,x100961)),f334(f334(f260(x100961,x100961),x100962),f644(x100963,x100964,x100965,x100962,x100961))),x100963))+~P107(f334(f334(f336(f934(x100961,x100961)),f334(f334(f260(x100961,x100961),x100962),x100965)),f334(f334(f190(f934(x100961,x100961),a922),f334(a119,x100964)),x100963))) % 188.18/188.26 [10102]~P26(x101021,x101022,f334(f334(f316(f926(x101021)),f98(x101021,f99(x101021,x101023,x101024),x101025,x101023)),f195(f935(f926(x101021),a922))))+P26(x101021,x101022,f334(f334(f316(f926(x101021)),f98(x101021,x101023,f30(x101024,x101025),f99(x101021,x101023,f334(f78(a922,a922,a923,a329),x101024)))),f195(f935(f926(x101021),a922)))) % 188.18/188.26 [10114]~P107(f334(f334(f336(f934(f928(x101141),f928(x101141))),f334(f334(f260(f928(x101141),f928(x101141)),f334(f334(f158(x101141),x101142),x101145)),x101144)),f165(x101141,x101143)))+P107(f334(f334(f336(f934(x101141,x101141)),f334(f334(f260(x101141,x101141),x101142),f667(x101143,x101144,x101145,x101142,x101141))),x101143)) % 188.18/188.26 [10133]~P107(f334(f334(f336(x101331),f334(x101333,f574(x101335,x101333,x101331,x101334,x101332))),x101335))+P107(f334(f334(f242(f935(x101331,a922)),f334(f317(x101332,x101331,x101333),x101334)),x101335)) % 188.18/188.26 [10348]P26(x103481,x103482,f334(f334(f316(f926(x103481)),f98(x103481,x103483,x103484,x103485)),f195(f935(f926(x103481),a922))))+~P26(x103481,x103482,f334(f334(f316(f926(x103481)),f98(x103481,f334(f16(f935(a923,a922),x103481),f334(f334(f7(a923,a923,a922),a331),f675(x103485,x103484,x103482,x103481,x103483))),x103484,f334(f16(f935(a923,a922),x103481),f334(x103485,f564(x103485,x103484,x103482,x103481,x103483))))),f195(f935(f926(x103481),a922)))) % 188.18/188.26 [6584]P107(f334(x65842,x65844))+E(f184(x65841,x65842,f334(f334(f141(x65841),x65843),f334(f334(f158(x65841),x65844),x65845))),f184(x65841,x65842,x65843)) % 188.18/188.26 [6635]~P2(x66352)+E(f334(f334(f334(f23(f935(x66351,x66352)),x66353),x66354),x66355),f334(f334(f23(x66352),f334(x66353,x66355)),f334(x66354,x66355))) % 188.18/188.26 [6637]~P99(x66372)+E(f334(f334(f334(f108(f935(x66371,x66372)),x66373),x66374),x66375),f334(f334(f108(x66372),f334(x66373,x66375)),f334(x66374,x66375))) % 188.18/188.26 [6639]~P99(x66392)+E(f334(f334(f334(f109(f935(x66391,x66392)),x66393),x66394),x66395),f334(f334(f109(x66392),f334(x66393,x66395)),f334(x66394,x66395))) % 188.18/188.26 [6656]E(x66561,x66562)+E(f334(f334(f171(x66563),f334(f334(f166(x66563,x66564),x66561),x66565)),x66562),f334(f334(f171(x66563),x66564),x66562)) % 188.18/188.26 [6921]~E(x69214,f195(f935(x69213,a922)))+E(f334(f334(f23(f935(x69211,a922)),x69212),f334(f334(f44(x69213,f935(x69211,a922)),x69214),x69215)),x69212) % 188.18/188.26 [6922]~E(x69224,f195(f935(x69223,a922)))+E(f334(f334(f108(f935(x69221,a922)),x69222),f334(f334(f44(x69223,f935(x69221,a922)),x69224),x69225)),x69222) % 188.18/188.26 [6923]~E(x69234,f195(f935(x69233,a922)))+E(f334(f334(f109(f935(x69231,a922)),x69232),f334(f334(f45(x69233,f935(x69231,a922)),x69234),x69235)),x69232) % 188.18/188.26 [6938]~E(x69384,f195(f935(x69383,a922)))+E(f334(f334(f316(x69381),x69382),f334(f334(f44(x69383,f935(x69381,a922)),x69384),x69385)),f334(f334(f316(x69381),x69382),f195(f935(x69381,a922)))) % 188.18/188.26 [7702]E(f334(f334(f171(x77021),f334(f334(f161(x77022,x77021),x77023),x77024)),x77025),f334(x77023,f334(f334(f171(x77022),x77024),x77025)))+~P107(f334(f334(f243(a927),x77025),f334(f196(f928(x77022)),x77024))) % 188.18/188.26 [7764]E(f334(f334(f108(f935(x77641,a922)),f334(x77642,x77643)),f334(f334(f44(x77644,f935(x77641,a922)),x77645),x77642)),f334(f334(f44(x77644,f935(x77641,a922)),x77645),x77642))+~P107(f334(f334(f336(x77644),x77643),x77645)) % 188.18/188.26 [7765]E(f334(f334(f109(f935(x77651,a922)),f334(x77652,x77653)),f334(f334(f45(x77654,f935(x77651,a922)),x77655),x77652)),f334(f334(f45(x77654,f935(x77651,a922)),x77655),x77652))+~P107(f334(f334(f336(x77654),x77653),x77655)) % 188.18/188.26 [8355]~E(x83553,f195(f935(x83551,a922)))+E(f334(f334(f44(x83551,f935(x83552,a922)),x83553),f334(f334(f8(f935(x83552,a922),f935(x83552,a922),x83551),f334(f316(x83552),x83554)),x83555)),f195(f935(x83552,a922))) % 188.18/188.26 [8360]~P107(f334(f334(f336(x83604),x83603),x83605))+P107(f334(f334(f242(f935(x83601,a922)),f334(x83602,x83603)),f334(f334(f44(x83604,f935(x83601,a922)),x83605),x83602))) % 188.18/188.26 [8486]~E(f334(x84864,x84862),x84865)+P107(f334(f334(f336(x84861),x84862),f334(f318(x84861,x84863,x84864),f334(f334(f316(x84863),x84865),f195(f935(x84863,a922)))))) % 188.18/188.26 [8533]~P57(x85331,x85332,f334(f293(x85332,x85331),x85333))+E(f334(f334(f109(f935(x85331,a922)),f334(f292(x85332,x85331,x85333),x85334)),f334(f292(x85332,x85331,x85333),x85335)),f334(f292(x85332,x85331,x85333),f334(f334(f109(f935(x85332,a922)),x85334),x85335))) % 188.18/188.26 [8604]E(x86041,f2(a106))+E(f334(f125(x86042,x86043,f334(x86044,f334(f334(f23(a106),x86041),f84(a106)))),f334(f334(f7(x86042,a106,f929(x86043)),x86045),x86041)),f334(f207(x86042,x86043,x86044,x86045),x86041)) % 188.18/188.26 [8640]E(x86401,f195(f935(x86402,a922)))+E(f334(f334(f44(x86402,f935(x86403,a922)),x86401),f334(f334(f8(f935(x86403,a922),f935(x86403,a922),x86402),f334(f316(x86403),x86404)),x86405)),f334(f334(f316(x86403),x86404),f334(f334(f44(x86402,f935(x86403,a922)),x86401),x86405))) % 188.18/188.26 [8691]~P27(x86912,x86911,x86913,f250(f935(x86912,a922)))+E(f334(f334(f23(f935(x86911,a922)),f334(f317(x86912,x86911,x86913),x86914)),f334(f317(x86912,x86911,x86913),x86915)),f334(f317(x86912,x86911,x86913),f334(f334(f23(f935(x86912,a922)),x86914),x86915))) % 188.18/188.26 [8692]~P27(x86922,x86921,x86923,f250(f935(x86922,a922)))+E(f334(f334(f109(f935(x86921,a922)),f334(f317(x86922,x86921,x86923),x86924)),f334(f317(x86922,x86921,x86923),x86925)),f334(f317(x86922,x86921,x86923),f334(f334(f109(f935(x86922,a922)),x86924),x86925))) % 188.18/188.26 [8763]~P107(f334(f334(f72(x87631,x87632,x87635),x87633),x87634))+P107(f334(f334(f336(f934(x87631,x87632)),f334(f334(f260(x87631,x87632),x87633),x87634)),x87635)) % 188.18/188.26 [8794]P107(f334(f334(f336(x87941),x87942),f334(f291(x87943,x87941),x87944)))+~P107(f334(f334(f336(f934(x87943,x87941)),f334(f334(f260(x87943,x87941),x87945),x87942)),x87944)) % 188.18/188.26 [8796]P107(f334(f334(f336(x87961),x87962),f334(f272(x87961,x87963),x87964)))+~P107(f334(f334(f336(f934(x87961,x87963)),f334(f334(f260(x87961,x87963),x87962),x87965)),x87964)) % 188.18/188.26 [8935]P107(f334(f334(f72(x89351,x89352,x89353),x89354),x89355))+~P107(f334(f334(f336(f934(x89351,x89352)),f334(f334(f260(x89351,x89352),x89354),x89355)),x89353)) % 188.18/188.26 [8968]E(f334(x89681,x89682),x89683)+~P107(f334(f334(f336(x89684),x89682),f334(f318(x89684,x89685,x89681),f334(f334(f316(x89685),x89683),f195(f935(x89685,a922)))))) % 188.18/188.26 [9211]P107(f334(f334(f336(f934(x92111,x92112)),f334(f334(f260(x92111,x92112),x92113),x92114)),f334(f293(x92112,x92111),x92115)))+~P107(f334(f334(f336(f934(x92112,x92111)),f334(f334(f260(x92112,x92111),x92114),x92113)),x92115)) % 188.18/188.26 [9229]~P107(f334(f334(x92291,x92295),x92294))+P107(f334(f334(x92291,f334(f264(x92292,x92293),f334(f334(f260(x92292,x92293),x92294),x92295))),f334(f259(x92292,x92293),f334(f334(f260(x92292,x92293),x92294),x92295)))) % 188.18/188.26 [9259]~P107(f334(f334(f336(f934(x92592,x92591)),f334(f334(f260(x92592,x92591),x92594),x92593)),f334(f293(x92591,x92592),x92595)))+P107(f334(f334(f336(f934(x92591,x92592)),f334(f334(f260(x92591,x92592),x92593),x92594)),x92595)) % 188.18/188.26 [9286]~P107(f334(f334(f336(f934(x92863,x92861)),f334(f334(f260(x92863,x92861),x92865),x92862)),x92864))+P107(f334(f334(f336(x92861),x92862),f334(f292(x92863,x92861,x92864),f334(f334(f316(x92863),x92865),f195(f935(x92863,a922)))))) % 188.18/188.26 [9331]P107(f334(f334(f336(f934(x93311,x93312)),f334(f334(f260(x93311,x93312),x93313),x93314)),x93315))+~P107(f334(f334(f336(x93312),x93314),f334(f292(x93311,x93312,x93315),f334(f334(f316(x93311),x93313),f195(f935(x93311,a922)))))) % 188.18/188.26 [9423]~P76(x94231)+E(f334(f334(f6(a927,x94231),x94232),f311(a927,f334(f334(f86(a927),x94233),x94234),f334(f334(f86(a927),x94235),x94234))),f334(f334(f6(a927,x94231),f334(f334(f8(a927,x94231,a927),x94232),f334(f334(f7(a927,a927,a927),f86(a927)),x94234))),f311(a927,x94233,x94235))) % 188.18/188.26 [9440]~P76(x94401)+E(f334(f334(f6(a927,x94401),x94402),f334(f310(a927,f334(f334(f86(a927),x94403),x94404)),f334(f334(f86(a927),x94405),x94404))),f334(f334(f6(a927,x94401),f334(f334(f8(a927,x94401,a927),x94402),f334(f334(f7(a927,a927,a927),f86(a927)),x94404))),f334(f310(a927,x94403),x94405))) % 188.18/188.26 [9496]~P27(x94961,x94962,x94963,f250(f935(x94961,a922)))+E(f334(f334(f161(x94961,x94962),x94963),f334(f143(x94961,f334(f334(f8(a922,a922,x94961),a329),f334(a331,x94964))),x94965)),f334(f143(x94962,f334(f334(f8(a922,a922,x94962),a329),f334(a331,f334(x94963,x94964)))),f334(f334(f161(x94961,x94962),x94963),x94965))) % 188.18/188.26 [9517]~P27(x95171,x95172,x95173,f334(f334(f316(x95171),x95174),f334(f179(x95171),x95175)))+E(f334(f334(f161(x95171,x95172),x95173),f334(f143(x95171,f334(f334(f8(a922,a922,x95171),a329),f334(a331,x95174))),x95175)),f334(f143(x95172,f334(f334(f8(a922,a922,x95172),a329),f334(a331,f334(x95173,x95174)))),f334(f334(f161(x95171,x95172),x95173),x95175))) % 188.18/188.26 [9670]P107(f334(f334(f336(f934(f928(x96701),f928(x96701))),f334(f334(f260(f928(x96701),f928(x96701)),f334(f334(f158(x96701),x96702),x96703)),f334(f334(f158(x96701),x96704),x96703))),f164(x96701,x96705)))+~P107(f334(f334(f336(f934(x96701,x96701)),f334(f334(f260(x96701,x96701),x96702),x96704)),x96705)) % 188.18/188.26 [9801]E(f334(f334(f316(x98011),f608(x98012,x98013,x98014,x98015,x98011)),f616(x98012,x98013,x98014,x98015,x98011)),f334(f334(f316(x98011),x98014),x98013))+~P107(f334(f67(x98011,x98015,f334(f334(f316(x98011),x98014),x98013)),x98012)) % 188.18/188.26 [9802]E(f334(f334(f316(x98021),f631(x98022,x98023,x98024,x98025,x98021)),f637(x98022,x98023,x98024,x98025,x98021)),f334(f334(f316(x98021),x98024),x98023))+~P107(f334(f67(x98021,x98025,f334(f334(f316(x98021),x98024),x98023)),x98022)) % 188.18/188.26 [9896]P107(f334(f334(f336(x98961),f509(x98962,x98963,x98964,x98965,x98961)),x98964))+P107(f334(f334(f334(f45(x98961,f935(x98965,a922)),x98964),x98963),x98962)) % 188.18/188.26 [9901]P107(f334(f334(f336(x99011),f500(x99012,x99013,x99011,x99014,x99015)),x99013))+P107(f334(f334(f336(x99015),x99014),f334(f334(f45(x99011,f935(x99015,a922)),x99013),x99012))) % 188.18/188.26 [9909]P107(f334(f334(f336(x99091),f503(x99092,x99093,x99091,x99094,x99095)),x99093))+P107(f334(f334(f242(f935(x99095,a922)),x99094),f334(f334(f45(x99091,f935(x99095,a922)),x99093),x99092))) % 188.18/188.26 [9910]P107(f334(f334(f336(x99101),f847(x99102,x99103,x99104,x99105,x99101)),x99105))+P107(f334(f334(f242(f935(x99104,a922)),x99103),f334(f334(f45(x99101,f935(x99104,a922)),x99105),x99102))) % 188.18/188.26 [9912]P107(f334(f334(x99121,f395(x99122,x99121,x99123,x99124,x99125)),x99122))+~P107(f334(f334(f334(f44(x99125,f935(x99124,a922)),x99123),x99121),x99122)) % 188.18/188.26 [9916]P107(f334(f334(f336(x99161),f395(x99162,x99163,x99164,x99165,x99161)),x99164))+~P107(f334(f334(f334(f44(x99161,f935(x99165,a922)),x99164),x99163),x99162)) % 188.18/188.26 [9917]P55(x99174,f334(f334(f45(x99171,f935(x99174,a922)),x99175),x99173),f334(f334(f45(x99171,f935(f934(x99174,x99174),a922)),x99175),x99172))+P107(f334(f334(f336(x99171),f791(x99172,x99173,x99174,x99175,x99171)),x99175)) % 188.18/188.26 [9918]P55(x99184,f334(f334(f44(x99181,f935(x99184,a922)),x99185),x99183),f334(f334(f44(x99181,f935(f934(x99184,x99184),a922)),x99185),x99182))+P107(f334(f334(f336(x99181),f839(x99182,x99183,x99184,x99185,x99181)),x99185)) % 188.18/188.26 [9930]P107(f334(f334(f336(x99301),f403(x99302,x99303,x99301,x99304,x99305)),x99303))+~P107(f334(f334(f336(x99305),x99304),f334(f334(f44(x99301,f935(x99305,a922)),x99303),x99302))) % 188.18/188.26 [9936]P107(f334(f334(f336(x99361),x99362),f334(x99363,f403(x99363,x99364,x99365,x99362,x99361))))+~P107(f334(f334(f336(x99361),x99362),f334(f334(f44(x99365,f935(x99361,a922)),x99364),x99363))) % 188.18/188.26 [10030]~P107(f334(f334(x100304,f509(x100305,x100304,x100303,x100302,x100301)),x100305))+P107(f334(f334(f334(f45(x100301,f935(x100302,a922)),x100303),x100304),x100305)) % 188.18/188.26 [10033]~P107(f334(f334(f336(x100331),x100332),f334(x100335,f500(x100335,x100334,x100333,x100332,x100331))))+P107(f334(f334(f336(x100331),x100332),f334(f334(f45(x100333,f935(x100331,a922)),x100334),x100335))) % 188.18/188.26 [10036]~P55(x100361,f334(x100364,f839(x100365,x100364,x100361,x100363,x100362)),f334(x100365,f839(x100365,x100364,x100361,x100363,x100362)))+P55(x100361,f334(f334(f44(x100362,f935(x100361,a922)),x100363),x100364),f334(f334(f44(x100362,f935(f934(x100361,x100361),a922)),x100363),x100365)) % 188.18/188.26 [10037]~P55(x100371,f334(x100374,f791(x100375,x100374,x100371,x100373,x100372)),f334(x100375,f791(x100375,x100374,x100371,x100373,x100372)))+P55(x100371,f334(f334(f45(x100372,f935(x100371,a922)),x100373),x100374),f334(f334(f45(x100372,f935(f934(x100371,x100371),a922)),x100373),x100375)) % 188.18/188.26 [10038]~P107(f334(f334(f242(f935(x100381,a922)),x100382),f334(x100385,f503(x100385,x100384,x100383,x100382,x100381))))+P107(f334(f334(f242(f935(x100381,a922)),x100382),f334(f334(f45(x100383,f935(x100381,a922)),x100384),x100385))) % 188.18/188.26 [10039]~P107(f334(f334(f242(f935(x100391,a922)),x100392),f334(x100395,f847(x100395,x100392,x100391,x100394,x100393))))+P107(f334(f334(f242(f935(x100391,a922)),x100392),f334(f334(f45(x100393,f935(x100391,a922)),x100394),x100395))) % 188.18/188.26 [10099]~P107(f334(f334(f336(x100991),f608(x100995,x100994,x100993,x100992,x100991)),f616(x100995,x100994,x100993,x100992,x100991)))+~P107(f334(f67(x100991,x100992,f334(f334(f316(x100991),x100993),x100994)),x100995)) % 188.18/188.26 [10100]~P107(f334(f334(f336(x101001),f631(x101005,x101004,x101003,x101002,x101001)),f637(x101005,x101004,x101003,x101002,x101001)))+~P107(f334(f67(x101001,x101002,f334(f334(f316(x101001),x101003),x101004)),x101005)) % 188.18/188.26 [10101]~P107(f334(f334(f336(f934(x101011,x101011)),f334(f334(f260(x101011,x101011),x101012),x101015)),f334(f334(f190(f934(x101011,x101011),a922),f334(a119,x101014)),x101013)))+P107(f334(f334(f336(f934(x101011,x101011)),f334(f334(f260(x101011,x101011),x101012),f645(x101013,x101014,x101015,x101012,x101011))),f334(f334(f190(f934(x101011,x101011),a922),x101014),x101013))) % 188.18/188.26 [10108]P107(f334(f71(x101081,x101081,x101082,f608(x101083,x101084,x101085,x101082,x101081),f616(x101083,x101084,x101085,x101082,x101081)),x101083))+~P107(f334(f67(x101081,x101082,f334(f334(f316(x101081),x101085),x101084)),x101083)) % 188.18/188.26 [10109]P107(f334(f71(x101091,x101091,x101092,f631(x101093,x101094,x101095,x101092,x101091),f637(x101093,x101094,x101095,x101092,x101091)),x101093))+~P107(f334(f67(x101091,x101092,f334(f334(f316(x101091),x101095),x101094)),x101093)) % 188.18/188.26 [10118]~P109(x101181)+P15(x101181,f334(f334(f161(x101182,x101181),x101183),f334(f143(x101182,f334(f334(f7(x101182,x101181,a922),f334(f334(f8(x101181,f935(x101181,a922),x101182),a331),x101183)),f334(x101184,x101185))),x101185))) % 188.18/188.26 [10153]~P107(f334(f334(f336(x101532),x101535),f334(f292(x101531,x101532,x101534),x101533)))+P107(f334(f334(f336(f934(x101531,x101532)),f334(f334(f260(x101531,x101532),f453(x101533,x101534,x101531,x101535,x101532)),x101535)),x101534)) % 188.18/188.26 [10154]~P107(f334(f334(f336(x101542),x101545),f334(f292(x101541,x101542,x101544),x101543)))+P107(f334(f334(f336(f934(x101541,x101542)),f334(f334(f260(x101541,x101542),f506(x101543,x101544,x101541,x101545,x101542)),x101545)),x101544)) % 188.18/188.26 [10159]~P107(f334(f334(f336(f934(x101591,x101591)),f334(f334(f260(x101591,x101591),x101595),x101594)),f334(f334(f190(f934(x101591,x101591),a922),f334(a119,x101593)),x101592)))+P107(f334(f334(f336(f934(x101591,x101591)),f334(f334(f260(x101591,x101591),f645(x101592,x101593,x101594,x101595,x101591)),x101594)),x101592)) % 188.18/188.26 [10171]~P107(f334(f334(f336(f934(x101711,x101711)),f334(f334(f260(x101711,x101711),x101715),x101714)),f334(f334(f190(f934(x101711,x101711),a922),f334(a119,x101713)),x101712)))+P107(f334(f334(f336(f934(x101711,x101711)),f334(f334(f260(x101711,x101711),f643(x101712,x101713,x101714,x101715,x101711)),x101714)),f334(f334(f190(f934(x101711,x101711),a922),x101713),x101712))) % 188.18/188.26 [10172]~P107(f334(f334(f336(f934(x101721,x101721)),f334(f334(f260(x101721,x101721),x101725),x101724)),f334(f334(f190(f934(x101721,x101721),a922),f334(a119,x101723)),x101722)))+P107(f334(f334(f336(f934(x101721,x101721)),f334(f334(f260(x101721,x101721),f644(x101722,x101723,x101724,x101725,x101721)),x101724)),f334(f334(f190(f934(x101721,x101721),a922),x101723),x101722))) % 188.18/188.26 [10173]~P107(f334(f334(f336(f934(f928(x101731),f928(x101731))),f334(f334(f260(f928(x101731),f928(x101731)),x101735),f334(f334(f158(x101731),x101734),x101733))),f165(x101731,x101732)))+P107(f334(f334(f336(f934(x101731,x101731)),f334(f334(f260(x101731,x101731),f665(x101732,x101733,x101734,x101735,x101731)),x101734)),x101732)) % 188.18/188.26 [7785]~E(x77853,f195(f935(x77852,a922)))+E(f334(f334(f108(f935(x77851,a922)),f334(f334(f44(x77852,f935(x77851,a922)),x77853),x77854)),x77855),x77855) % 188.18/188.26 [7786]~E(x77863,f195(f935(x77862,a922)))+E(f334(f334(f109(f935(x77861,a922)),f334(f334(f45(x77862,f935(x77861,a922)),x77863),x77864)),x77865),x77865) % 188.18/188.26 [8198]~E(x81983,f195(f935(x81982,a922)))+E(f334(f334(f23(f935(x81981,a922)),f334(f334(f45(x81982,f935(x81981,a922)),x81983),x81984)),x81985),f334(f334(f23(f935(x81981,a922)),f250(f935(x81981,a922))),x81985)) % 188.18/188.26 [8328]E(f334(f334(f166(x83281,f334(f334(f141(x83281),x83282),x83283)),x83284),x83285),f334(f334(f141(x83281),f334(f334(f166(x83281,x83282),x83284),x83285)),x83283))+~P107(f334(f334(f243(a927),x83284),f334(f196(f928(x83281)),x83282))) % 188.18/188.26 [8594]E(f334(f334(f171(x85941),f334(f334(f161(a927,x85941),x85942),f146(a927,f334(f310(a927,x85943),x85944)))),x85945),f334(x85942,f334(f334(f86(a927),x85943),x85945)))+~P107(f334(f334(f243(a927),x85945),f334(f334(f23(a927),x85944),x85943))) % 188.18/188.26 [8609]E(x86091,f2(a106))+E(f129(x86092,x86093,f334(x86094,f334(f334(f23(a106),x86091),f84(a106))),f334(f334(f7(x86092,a106,f929(f931(x86093))),x86095),x86091)),f334(f205(x86092,x86093,x86094,x86095),x86091)) % 188.18/188.26 [8630]~E(x86303,f195(f935(x86301,a922)))+E(f334(f334(f44(x86301,f935(x86302,a922)),x86303),f334(f334(f8(f935(x86302,a922),f935(x86302,a922),x86301),f334(f108(f935(x86302,a922)),x86304)),x86305)),f195(f935(x86302,a922))) % 188.18/188.26 [8631]~E(x86313,f195(f935(x86311,a922)))+E(f334(f334(f45(x86311,f935(x86312,a922)),x86313),f334(f334(f8(f935(x86312,a922),f935(x86312,a922),x86311),f334(f23(f935(x86312,a922)),x86314)),x86315)),f250(f935(x86312,a922))) % 188.18/188.26 [8632]~E(x86323,f195(f935(x86321,a922)))+E(f334(f334(f45(x86321,f935(x86322,a922)),x86323),f334(f334(f8(f935(x86322,a922),f935(x86322,a922),x86321),f334(f109(f935(x86322,a922)),x86324)),x86325)),f250(f935(x86322,a922))) % 188.18/188.26 [8634]~P148(x86342)+E(f334(f334(f6(x86341,x86342),f334(f334(f8(x86342,x86342,x86341),f334(f87(x86342),x86343)),x86344)),x86345),f334(f334(f87(x86342),x86343),f334(f334(f6(x86341,x86342),x86344),x86345))) % 188.18/188.26 [8920]E(x89201,f195(f935(x89202,a922)))+E(f334(f334(f44(x89202,f935(x89203,a922)),x89201),f334(f334(f8(f935(x89203,a922),f935(x89203,a922),x89202),f334(f108(f935(x89203,a922)),x89204)),x89205)),f334(f334(f108(f935(x89203,a922)),x89204),f334(f334(f44(x89202,f935(x89203,a922)),x89201),x89205))) % 188.18/188.26 [8921]E(x89211,f195(f935(x89212,a922)))+E(f334(f334(f45(x89212,f935(x89213,a922)),x89211),f334(f334(f8(f935(x89213,a922),f935(x89213,a922),x89212),f334(f23(f935(x89213,a922)),x89214)),x89215)),f334(f334(f23(f935(x89213,a922)),x89214),f334(f334(f44(x89212,f935(x89213,a922)),x89211),x89215))) % 188.18/188.26 [8922]E(x89221,f195(f935(x89222,a922)))+E(f334(f334(f45(x89222,f935(x89223,a922)),x89221),f334(f334(f8(f935(x89223,a922),f935(x89223,a922),x89222),f334(f109(f935(x89223,a922)),x89224)),x89225)),f334(f334(f109(f935(x89223,a922)),x89224),f334(f334(f45(x89222,f935(x89223,a922)),x89221),x89225))) % 188.18/188.26 [9131]~P107(f334(f334(f243(a927),f334(x91314,x91312)),f334(x91314,x91313)))+P107(f334(f334(f336(f934(x91311,x91311)),f334(f334(f260(x91311,x91311),x91312),x91313)),f160(x91311,f334(f334(f158(f935(x91311,a927)),x91314),x91315)))) % 188.18/188.26 [9389]~P27(x93892,x93891,x93893,f334(f334(f108(f935(x93892,a922)),x93894),x93895))+E(f334(f334(f109(f935(x93891,a922)),f334(f317(x93892,x93891,x93893),f334(f334(f23(f935(x93892,a922)),x93894),x93895))),f334(f317(x93892,x93891,x93893),f334(f334(f23(f935(x93892,a922)),x93895),x93894))),f195(f935(x93891,a922))) % 188.18/188.26 [9638]~P27(x96383,x96381,x96385,f250(f935(x96383,a922)))+E(f334(f78(x96381,x96382,x96383,f334(f78(x96383,x96382,x96381,x96384),f97(x96383,x96381,f250(f935(x96383,a922)),x96385))),x96385),x96384) % 188.18/188.26 [9668]~P107(f334(f334(f242(f935(x96683,a922)),f334(f292(x96681,x96683,x96684),x96682)),x96685))+P107(f334(f334(f242(f935(x96681,a922)),x96682),f334(f85(f935(x96681,a922)),f334(f292(x96683,x96681,f334(f293(x96681,x96683),x96684)),f334(f85(f935(x96683,a922)),x96685))))) % 188.18/188.26 [9691]~P27(x96911,x96912,x96913,f334(f334(f316(x96911),x96914),x96915))+~P107(f334(f334(f336(x96912),f334(x96913,x96914)),f334(f317(x96911,x96912,x96913),f334(f334(f23(f935(x96911,a922)),x96915),f334(f334(f316(x96911),x96914),f195(f935(x96911,a922))))))) % 188.18/188.26 [9757]P107(f334(f334(f242(f935(x97571,a922)),f334(f292(x97572,x97571,x97573),x97574)),x97575))+~P107(f334(f334(f242(f935(x97572,a922)),x97574),f334(f85(f935(x97572,a922)),f334(f292(x97571,x97572,f334(f293(x97572,x97571),x97573)),f334(f85(f935(x97571,a922)),x97575))))) % 188.18/188.26 [9835]~P86(x98351)+P107(f334(f334(f242(x98351),f334(f81(x98351),f334(f334(f23(x98351),f334(f334(f86(x98351),x98352),x98353)),f334(f334(f86(x98351),x98354),x98355)))),f334(f334(f86(x98351),f334(f81(x98351),f334(f334(f23(x98351),x98352),x98354))),f334(f81(x98351),f334(f334(f23(x98351),x98353),x98355))))) % 188.18/188.26 [9951]P107(f334(f334(f336(x99511),f408(x99512,x99513,x99514,x99511,x99515)),x99514))+P107(f334(f334(f242(f935(x99515,a922)),f334(f334(f44(x99511,f935(x99515,a922)),x99514),x99513)),x99512)) % 188.18/188.26 [10135]~P107(f334(f334(f242(f935(x101351,a922)),f334(x101354,f408(x101355,x101354,x101353,x101352,x101351))),x101355))+P107(f334(f334(f242(f935(x101351,a922)),f334(f334(f44(x101352,f935(x101351,a922)),x101353),x101354)),x101355)) % 188.18/188.26 [8742]E(f334(f334(f141(x87421),x87422),f334(f334(f166(x87421,x87423),f334(f334(f23(a927),x87424),f334(f196(f928(x87421)),x87422))),x87425)),f334(f334(f166(x87421,f334(f334(f141(x87421),x87422),x87423)),x87424),x87425))+P107(f334(f334(f243(a927),x87424),f334(f196(f928(x87421)),x87422))) % 188.18/188.26 [8770]~P144(x87701)+E(f334(f334(f86(x87701),f334(f334(f87(x87701),x87702),x87703)),f334(f334(f86(x87701),f334(f334(f87(x87701),x87704),x87703)),x87705)),f334(f334(f86(x87701),f334(f334(f87(x87701),f334(f334(f86(x87701),x87702),x87704)),x87703)),x87705)) % 188.18/188.26 [9341]~P148(x93411)+E(f334(f172(x93411),f334(f334(f161(x93412,x93411),f334(f334(f8(x93411,x93411,x93412),f334(f87(x93411),x93413)),x93414)),x93415)),f334(f334(f87(x93411),x93413),f334(f172(x93411),f334(f334(f161(x93412,x93411),x93414),x93415)))) % 188.18/188.26 [9516]E(f334(f196(f928(x95161)),f334(f334(f182(x95161),f334(f334(f246(a927),f334(f196(f928(x95161)),x95162)),f334(f196(f928(x95163)),x95164))),x95162)),f334(f196(f928(x95163)),f334(f334(f182(x95163),f334(f334(f246(a927),f334(f196(f928(x95161)),x95162)),f334(f196(f928(x95163)),x95164))),x95164)))+P107(f334(x95165,f334(f334(f188(x95161,x95163),x95162),x95164))) % 188.18/188.26 [9767]~P148(x97672)+E(f334(f334(f6(x97671,x97672),f334(f334(f7(x97671,x97672,x97672),f334(f334(f8(x97672,f935(x97672,x97672),x97671),f87(x97672)),x97673)),x97674)),x97675),f334(f334(f87(x97672),f334(f334(f6(x97671,x97672),x97673),x97675)),x97674)) % 188.18/188.26 [9768]~P66(x97682)+E(f334(f334(f6(x97681,x97682),f334(f334(f7(x97681,x97682,x97682),f334(f334(f8(x97682,f935(x97682,x97682),x97681),f296(x97682)),x97683)),x97684)),x97685),f334(f334(f296(x97682),f334(f334(f6(x97681,x97682),x97683),x97685)),x97684)) % 188.18/188.26 [9775]~P72(x97752)+E(f334(f334(f9(x97751,x97752),f334(f334(f18(x97751,x97752,x97752),f334(f334(f8(x97752,f935(x97752,x97752),x97751),f87(x97752)),x97753)),x97754)),x97755),f334(f334(f87(x97752),f334(f334(f9(x97751,x97752),x97753),x97755)),f334(f334(f9(x97751,x97752),x97754),x97755))) % 188.18/188.26 [9776]~P3(x97762)+E(f334(f334(f6(x97761,x97762),f334(f334(f18(x97761,x97762,x97762),f334(f334(f8(x97762,f935(x97762,x97762),x97761),f23(x97762)),x97763)),x97764)),x97765),f334(f334(f23(x97762),f334(f334(f6(x97761,x97762),x97763),x97765)),f334(f334(f6(x97761,x97762),x97764),x97765))) % 188.18/188.26 [9777]~P76(x97772)+E(f334(f334(f6(x97771,x97772),f334(f334(f18(x97771,x97772,x97772),f334(f334(f8(x97772,f935(x97772,x97772),x97771),f86(x97772)),x97773)),x97774)),x97775),f334(f334(f86(x97772),f334(f334(f6(x97771,x97772),x97773),x97775)),f334(f334(f6(x97771,x97772),x97774),x97775))) % 188.18/188.26 [9813]~E(x98133,f195(f935(x98131,a922)))+E(f334(f334(f44(x98131,f935(x98132,a922)),x98133),f334(f334(f7(x98131,f935(x98132,a922),f935(x98132,a922)),f334(f334(f8(f935(x98132,a922),f935(f935(x98132,a922),f935(x98132,a922)),x98131),f108(f935(x98132,a922))),x98134)),x98135)),f195(f935(x98132,a922))) % 188.18/188.26 [9814]~E(x98143,f195(f935(x98141,a922)))+E(f334(f334(f45(x98141,f935(x98142,a922)),x98143),f334(f334(f7(x98141,f935(x98142,a922),f935(x98142,a922)),f334(f334(f8(f935(x98142,a922),f935(f935(x98142,a922),f935(x98142,a922)),x98141),f23(f935(x98142,a922))),x98144)),x98145)),f250(f935(x98142,a922))) % 188.18/188.26 [9815]~E(x98153,f195(f935(x98151,a922)))+E(f334(f334(f45(x98151,f935(x98152,a922)),x98153),f334(f334(f7(x98151,f935(x98152,a922),f935(x98152,a922)),f334(f334(f8(f935(x98152,a922),f935(f935(x98152,a922),f935(x98152,a922)),x98151),f109(f935(x98152,a922))),x98154)),x98155)),f250(f935(x98152,a922))) % 188.18/188.26 [9843]E(x98431,f195(f935(x98432,a922)))+E(f334(f334(f44(x98432,f935(x98433,a922)),x98431),f334(f334(f7(x98432,f935(x98433,a922),f935(x98433,a922)),f334(f334(f8(f935(x98433,a922),f935(f935(x98433,a922),f935(x98433,a922)),x98432),f108(f935(x98433,a922))),x98434)),x98435)),f334(f334(f108(f935(x98433,a922)),f334(f334(f44(x98432,f935(x98433,a922)),x98431),x98434)),x98435)) % 188.18/188.26 [9844]E(x98441,f195(f935(x98442,a922)))+E(f334(f334(f45(x98442,f935(x98443,a922)),x98441),f334(f334(f7(x98442,f935(x98443,a922),f935(x98443,a922)),f334(f334(f8(f935(x98443,a922),f935(f935(x98443,a922),f935(x98443,a922)),x98442),f23(f935(x98443,a922))),x98444)),x98445)),f334(f334(f23(f935(x98443,a922)),f334(f334(f45(x98442,f935(x98443,a922)),x98441),x98444)),x98445)) % 188.18/188.26 [9845]E(x98451,f195(f935(x98452,a922)))+E(f334(f334(f45(x98452,f935(x98453,a922)),x98451),f334(f334(f7(x98452,f935(x98453,a922),f935(x98453,a922)),f334(f334(f8(f935(x98453,a922),f935(f935(x98453,a922),f935(x98453,a922)),x98452),f109(f935(x98453,a922))),x98454)),x98455)),f334(f334(f109(f935(x98453,a922)),f334(f334(f45(x98452,f935(x98453,a922)),x98451),x98454)),x98455)) % 188.18/188.26 [9394]~P107(f334(f334(f242(a927),x93941),x93944))+E(f334(f334(f23(a927),f334(f334(f86(a927),f334(f334(f87(a927),x93941),x93942)),x93943)),f334(f334(f86(a927),f334(f334(f87(a927),x93944),x93942)),x93945)),f334(f334(f23(a927),x93943),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x93944),x93941)),x93942)),x93945))) % 188.18/188.26 [10010]~P148(x100101)+E(f334(f172(x100101),f334(f334(f161(x100102,x100101),f334(f334(f7(x100102,x100101,x100101),f334(f334(f8(x100101,f935(x100101,x100101),x100102),f87(x100101)),x100103)),x100104)),x100105)),f334(f334(f87(x100101),f334(f172(x100101),f334(f334(f161(x100102,x100101),x100103),x100105))),x100104)) % 188.18/188.26 [10020]~P3(x100201)+E(f334(f172(x100201),f334(f334(f161(x100202,x100201),f334(f334(f18(x100202,x100201,x100201),f334(f334(f8(x100201,f935(x100201,x100201),x100202),f23(x100201)),x100203)),x100204)),x100205)),f334(f334(f23(x100201),f334(f172(x100201),f334(f334(f161(x100202,x100201),x100203),x100205))),f334(f172(x100201),f334(f334(f161(x100202,x100201),x100204),x100205)))) % 188.18/188.26 [10021]~P76(x100211)+E(f334(f172(x100211),f334(f334(f161(x100212,x100211),f334(f334(f18(x100212,x100211,x100211),f334(f334(f8(x100211,f935(x100211,x100211),x100212),f86(x100211)),x100213)),x100214)),x100215)),f334(f334(f86(x100211),f334(f172(x100211),f334(f334(f161(x100212,x100211),x100213),x100215))),f334(f172(x100211),f334(f334(f161(x100212,x100211),x100214),x100215)))) % 188.18/188.26 [10146]P107(f334(x101461,f334(f334(f188(x101462,x101463),x101464),x101465)))+~P107(f334(x101461,f334(f334(f188(x101462,x101463),f334(f334(f182(x101462),f334(f334(f246(a927),f334(f196(f928(x101462)),x101464)),f334(f196(f928(x101463)),x101465))),x101464)),f334(f334(f182(x101463),f334(f334(f246(a927),f334(f196(f928(x101462)),x101464)),f334(f196(f928(x101463)),x101465))),x101465)))) % 188.18/188.26 [10420]~P107(f334(f334(f336(f934(x104202,x104201)),f334(f334(f260(x104202,x104201),x104204),x104205)),f334(f293(x104201,x104202),x104203)))+P107(f334(f334(f251(x104201,x104202,f334(f334(f7(x104201,f935(f934(x104201,x104202),a922),f935(x104202,a922)),f334(f334(f8(f935(x104202,f935(f935(f934(x104201,x104202),a922),a922)),f935(f935(f934(x104201,x104202),a922),f935(x104202,a922)),x104201),f7(x104202,f935(f934(x104201,x104202),a922),a922)),f334(f334(f8(f935(x104202,f934(x104201,x104202)),f935(x104202,f935(f935(f934(x104201,x104202),a922),a922)),x104201),f334(f8(f934(x104201,x104202),f935(f935(f934(x104201,x104202),a922),a922),x104202),f336(f934(x104201,x104202)))),f260(x104201,x104202)))),x104203)),x104204),x104205)) % 188.18/188.26 [10439]P107(f334(f334(f336(f934(x104391,x104392)),f334(f334(f260(x104391,x104392),x104393),x104394)),f334(f293(x104392,x104391),x104395)))+~P107(f334(f334(f251(x104392,x104391,f334(f334(f7(x104392,f935(f934(x104392,x104391),a922),f935(x104391,a922)),f334(f334(f8(f935(x104391,f935(f935(f934(x104392,x104391),a922),a922)),f935(f935(f934(x104392,x104391),a922),f935(x104391,a922)),x104392),f7(x104391,f935(f934(x104392,x104391),a922),a922)),f334(f334(f8(f935(x104391,f934(x104392,x104391)),f935(x104391,f935(f935(f934(x104392,x104391),a922),a922)),x104392),f334(f8(f934(x104392,x104391),f935(f935(f934(x104392,x104391),a922),a922),x104391),f336(f934(x104392,x104391)))),f260(x104392,x104391)))),x104395)),x104393),x104394)) % 188.18/188.26 [9637]~P107(f334(f334(f242(a927),x96374),x96371))+E(f334(f334(f23(a927),f334(f334(f86(a927),f334(f334(f87(a927),x96371),x96372)),x96373)),f334(f334(f86(a927),f334(f334(f87(a927),x96374),x96372)),x96375)),f334(f334(f23(a927),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x96371),x96374)),x96372)),x96373)),x96375)) % 188.18/188.26 [5501]E(x55011,x55012)+~E(f28(x55013,x55014,x55011),f28(x55015,x55016,x55012)) % 188.18/188.26 [5502]E(x55021,x55022)+~E(f28(x55023,x55021,x55024),f28(x55025,x55022,x55026)) % 188.18/188.26 [5503]E(x55031,x55032)+~E(f28(x55031,x55033,x55034),f28(x55032,x55035,x55036)) % 188.18/188.26 [5504]E(x55041,x55042)+~E(f27(x55043,x55044,x55041),f27(x55045,x55046,x55042)) % 188.18/188.26 [5505]E(x55051,x55052)+~E(f27(x55053,x55051,x55054),f27(x55055,x55052,x55056)) % 188.18/188.26 [5506]E(x55061,x55062)+~E(f27(x55061,x55063,x55064),f27(x55062,x55065,x55066)) % 188.18/188.26 [7496]E(x74961,x74962)+~E(f229(x74963,x74964,x74965,x74961),f229(x74963,x74964,x74966,x74962)) % 188.18/188.26 [7497]E(x74971,x74972)+~E(f229(x74973,x74974,x74971,x74975),f229(x74973,x74974,x74972,x74976)) % 188.18/188.26 [8579]~P21(x85795,x85791,x85792,x85796)+E(f334(f78(x85791,x85791,x85791,f334(x85792,x85793)),f334(x85792,x85794)),f334(f78(x85791,x85791,x85791,f334(x85792,x85794)),f334(x85792,x85793))) % 188.18/188.26 [8812]~P60(x88124,x88125,x88122,x88121,x88126)+E(f334(x88121,f334(x88122,x88123)),x88123) % 188.18/188.26 [8967]P27(x89671,x89672,x89673,x89674)+~P27(x89671,x89675,f334(f78(x89672,x89675,x89671,x89676),x89673),x89674) % 188.18/188.26 [9047]~E(x90476,x90474)+E(f334(f80(x90471,x90472,x90473,x90474,x90475),x90476),x90475) % 188.18/188.26 [9055]E(x90551,x90552)+E(f334(f80(x90553,x90554,x90555,x90552,x90556),x90551),f334(x90555,x90551)) % 188.18/188.26 [9068]~P27(x90684,x90682,f334(f78(x90681,x90682,x90684,x90683),x90685),x90686)+P27(x90681,x90682,x90683,f334(f317(x90684,x90681,x90685),x90686)) % 188.18/188.26 [9778]P107(f334(f66(x97781),x97782))+~P107(f334(f71(x97781,x97783,x97784,x97785,x97782),x97786)) % 188.18/188.26 [9787]~P107(f334(f334(f336(x97874),x97873),f306(x97874,x97875,x97871,x97872,x97876)))+P107(f334(f334(x97871,x97872),x97873)) % 188.18/188.26 [9788]~P107(f334(f334(f336(x97884),x97883),f303(x97884,x97881,x97885,x97882,x97886)))+P107(f334(f334(x97881,x97882),x97883)) % 188.18/188.26 [9789]~P107(f334(f334(f336(x97894),x97892),f306(x97894,x97891,x97895,x97896,x97893)))+P107(f334(f334(x97891,x97892),x97893)) % 188.18/188.26 [9790]~P107(f334(f334(f336(x97904),x97902),f303(x97904,x97905,x97901,x97906,x97903)))+P107(f334(f334(x97901,x97902),x97903)) % 188.18/188.26 [10275]P14(x102751,x102752,x102753,x102754,x102755,x102756)+~E(f334(f334(x102756,f862(x102753,x102756,x102755,x102752,x102754,x102751)),f864(x102753,x102756,x102755,x102752,x102754,x102751)),f334(f334(x102756,f863(x102753,x102756,x102755,x102752,x102754,x102751)),f865(x102753,x102756,x102755,x102752,x102754,x102751))) % 188.18/188.26 [6017]E(x60171,x60172)+~E(f334(f334(f260(x60173,x60174),x60175),x60171),f334(f334(f260(x60173,x60174),x60176),x60172)) % 188.18/188.26 [6019]E(x60191,x60192)+~E(f334(f334(f260(x60193,x60194),x60191),x60195),f334(f334(f260(x60193,x60194),x60192),x60196)) % 188.18/188.26 [6154]~P18(x61545,x61546,x61541)+E(f334(f334(x61541,x61542),f334(f334(x61541,x61543),x61544)),f334(f334(x61541,x61543),f334(f334(x61541,x61542),x61544))) % 188.18/188.26 [7556]~P34(x75564,x75561,f334(f334(f158(x75564),x75562),x75565),f334(f334(f158(x75564),x75563),x75566))+P107(f334(f334(x75561,x75562),x75563)) % 188.18/188.26 [7896]P34(x78961,x78962,x78963,x78964)+~P34(x78961,x78962,f334(f334(f158(x78961),x78965),x78963),f334(f334(f158(x78961),x78966),x78964)) % 188.18/188.26 [8910]~P60(x89105,x89101,x89102,x89106,x89104)+P107(f334(f334(f336(x89101),f334(x89102,x89103)),x89104)) % 188.18/188.26 [9096]E(f334(f82(x90961,x90962,x90963,x90964,x90965),x90966),f334(x90963,x90966))+P107(f334(f334(f336(x90961),x90966),x90965)) % 188.18/188.26 [9119]~E(x91193,f334(f334(f158(x91191),x91195),x91196))+P107(f334(f334(f336(f934(f928(x91191),f928(x91191))),f334(f334(f260(f928(x91191),f928(x91191)),x91192),f334(f334(f141(x91191),x91192),x91193))),f154(x91191,x91194))) % 188.18/188.26 [9124]E(f334(f82(x91241,x91242,x91243,x91244,x91245),x91246),f334(x91244,x91246))+~P107(f334(f334(f336(x91241),x91246),x91245)) % 188.18/188.26 [9347]~P36(x93471,x93472,x93473,x93475,x93476)+P36(x93471,x93472,x93473,f334(f334(f182(x93471),x93474),x93475),f334(f334(f182(x93472),x93474),x93476)) % 188.18/188.26 [9348]~P36(x93481,x93482,x93483,x93485,x93486)+P36(x93481,x93482,x93483,f334(f334(f145(x93481),x93484),x93485),f334(f334(f145(x93482),x93484),x93486)) % 188.18/188.26 [9611]E(f334(f317(x96111,x96112,f80(x96111,x96112,x96113,x96114,x96115)),x96116),f334(f317(x96111,x96112,x96113),x96116))+P107(f334(f334(f336(x96111),x96114),x96116)) % 188.18/188.26 [9614]E(f334(f334(f161(x96141,x96142),f80(x96141,x96142,x96143,x96144,x96145)),x96146),f334(f334(f161(x96141,x96142),x96143),x96146))+P107(f334(f334(f336(x96141),x96144),f334(f179(x96141),x96146))) % 188.18/188.26 [9855]~P25(x98554,x98552,x98555,x98553,x98556,x98551)+E(f334(x98551,f195(f935(x98552,a922))),x98553) % 188.18/188.26 [10103]~E(f334(x101034,f334(f259(x101031,x101033),x101035)),f334(x101036,f334(f259(x101031,x101033),x101035)))+E(f334(f266(x101031,x101032,x101033,x101033,x101034,f32(x101033)),x101035),f334(f266(x101031,x101032,x101033,x101033,x101036,f32(x101033)),x101035)) % 188.18/188.26 [10104]~E(f334(x101044,f334(f264(x101041,x101042),x101045)),f334(x101046,f334(f264(x101041,x101042),x101045)))+E(f334(f266(x101041,x101041,x101042,x101043,f32(x101041),x101044),x101045),f334(f266(x101041,x101041,x101042,x101043,f32(x101041),x101046),x101045)) % 188.18/188.26 [10142]~E(f334(f266(x101422,x101426,x101423,x101423,x101421,f32(x101423)),x101424),f334(f266(x101422,x101426,x101423,x101423,x101425,f32(x101423)),x101424))+E(f334(x101421,f334(f259(x101422,x101423),x101424)),f334(x101425,f334(f259(x101422,x101423),x101424))) % 188.18/188.26 [10143]~E(f334(f266(x101432,x101432,x101433,x101436,f32(x101432),x101431),x101434),f334(f266(x101432,x101432,x101433,x101436,f32(x101432),x101435),x101434))+E(f334(x101431,f334(f264(x101432,x101433),x101434)),f334(x101435,f334(f264(x101432,x101433),x101434))) % 188.18/188.26 [9012]P107(f334(f334(f336(x90121),x90122),x90123))+~P107(f334(f334(f336(f934(x90121,x90124)),f334(f334(f260(x90121,x90124),x90122),x90125)),f334(f334(f262(x90121,x90124),x90123),x90126))) % 188.18/188.26 [9028]P107(f334(f334(f336(x90281),x90282),f334(x90283,x90284)))+~P107(f334(f334(f336(f934(x90285,x90281)),f334(f334(f260(x90285,x90281),x90284),x90282)),f334(f334(f262(x90285,x90281),x90286),x90283))) % 188.18/188.26 [9463]P107(f334(f334(f336(f934(x94631,x94631)),f334(f334(f260(x94631,x94631),f334(x94632,x94633)),f334(x94632,x94634))),x94635))+~P107(f334(f334(f336(f934(x94636,x94636)),f334(f334(f260(x94636,x94636),x94633),x94634)),f334(f334(f294(x94631,x94636),x94635),x94632))) % 188.18/188.26 [9483]~P107(f334(f334(f336(f934(x94834,x94834)),f334(f334(f260(x94834,x94834),f334(x94836,x94832)),f334(x94836,x94833))),x94835))+P107(f334(f334(f336(f934(x94831,x94831)),f334(f334(f260(x94831,x94831),x94832),x94833)),f334(f334(f294(x94834,x94831),x94835),x94836))) % 188.18/188.26 [10144]E(f334(f334(f260(x101441,x101442),f657(x101443,x101444,x101445,x101446,x101442,x101441)),f658(x101443,x101444,x101445,x101446,x101442,x101441)),x101446)+~P107(f334(f334(f336(f934(x101441,x101442)),x101446),f334(f334(f295(x101441,x101445,x101442),x101444),x101443))) % 188.18/188.26 [10351]~P107(f334(f334(f336(f934(x103511,x103516)),x103515),f334(f334(f295(x103511,x103512,x103516),x103514),x103513)))+P107(f334(f334(f336(f934(x103511,x103512)),f334(f334(f260(x103511,x103512),f657(x103513,x103514,x103512,x103515,x103516,x103511)),f659(x103513,x103514,x103512,x103515,x103516,x103511))),x103514)) % 188.18/188.26 [10352]~P107(f334(f334(f336(f934(x103526,x103522)),x103525),f334(f334(f295(x103526,x103521,x103522),x103524),x103523)))+P107(f334(f334(f336(f934(x103521,x103522)),f334(f334(f260(x103521,x103522),f659(x103523,x103524,x103521,x103525,x103522,x103526)),f658(x103523,x103524,x103521,x103525,x103522,x103526))),x103523)) % 188.18/188.26 [10353]P14(x103531,x103532,x103533,x103534,x103535,x103536)+P107(f334(f334(f336(f934(x103532,x103532)),f334(f334(f260(x103532,x103532),f865(x103533,x103536,x103535,x103532,x103534,x103531)),f864(x103533,x103536,x103535,x103532,x103534,x103531))),x103535)) % 188.18/188.26 [10354]P14(x103541,x103542,x103543,x103544,x103545,x103546)+P107(f334(f334(f336(f934(x103541,x103541)),f334(f334(f260(x103541,x103541),f863(x103543,x103546,x103545,x103542,x103544,x103541)),f862(x103543,x103546,x103545,x103542,x103544,x103541))),x103544)) % 188.18/188.26 [7967]~P7(x79672)+E(f334(f334(f44(x79671,x79672),x79673),f334(f334(f7(x79671,x79674,x79672),x79675),x79676)),f334(f334(f334(f44(x79671,f935(x79674,x79672)),x79673),x79675),x79676)) % 188.18/188.26 [7968]~P7(x79682)+E(f334(f334(f45(x79681,x79682),x79683),f334(f334(f7(x79681,x79684,x79682),x79685),x79686)),f334(f334(f334(f45(x79681,f935(x79684,x79682)),x79683),x79685),x79686)) % 188.18/188.26 [8720]E(f334(f334(f44(x87201,f935(x87202,a922)),x87203),f334(f334(f8(f935(x87202,a922),f935(x87202,a922),x87201),f334(f316(x87202),x87204)),x87205)),f334(f334(f316(x87202),x87204),f334(f334(f44(x87201,f935(x87202,a922)),x87203),x87205)))+~P107(f334(f334(f336(x87201),x87206),x87203)) % 188.18/188.26 [9174]~P7(x91742)+E(f334(f334(f44(x91741,x91742),x91743),f334(f334(f8(f935(x91744,x91742),x91742,x91741),f334(f44(x91744,x91742),x91745)),f334(f7(x91744,x91741,x91742),x91746))),f334(f334(f44(x91744,x91742),x91745),f334(f334(f8(f935(x91741,x91742),x91742,x91744),f334(f44(x91741,x91742),x91743)),x91746))) % 188.18/188.26 [9175]~P7(x91752)+E(f334(f334(f45(x91751,x91752),x91753),f334(f334(f8(f935(x91754,x91752),x91752,x91751),f334(f45(x91754,x91752),x91755)),f334(f7(x91754,x91751,x91752),x91756))),f334(f334(f45(x91754,x91752),x91755),f334(f334(f8(f935(x91751,x91752),x91752,x91754),f334(f45(x91751,x91752),x91753)),x91756))) % 188.18/188.26 [9374]P107(f334(f334(f336(x93741),x93742),f334(f179(x93741),x93743)))+~P107(f334(f334(f336(f934(x93744,x93741)),f334(f334(f260(x93744,x93741),x93745),x93742)),f334(f179(f934(x93744,x93741)),f334(f334(f188(x93744,x93741),x93746),x93743)))) % 188.18/188.26 [9375]P107(f334(f334(f336(x93751),x93752),f334(f179(x93751),x93753)))+~P107(f334(f334(f336(f934(x93751,x93754)),f334(f334(f260(x93751,x93754),x93752),x93755)),f334(f179(f934(x93751,x93754)),f334(f334(f188(x93751,x93754),x93753),x93756)))) % 188.18/188.26 [9479]P107(f334(f334(f242(f935(x94791,a922)),f334(f292(x94792,x94791,x94793),x94794)),x94795))+~P107(f334(f334(f242(f935(f934(x94792,x94791),a922)),x94793),f334(f334(f262(x94792,x94791),x94796),f334(f16(f935(x94791,a922),x94792),x94795)))) % 188.18/188.26 [9484]~P28(x94844,x94842,x94845,f250(f935(x94844,a922)),f250(f935(x94842,a922)))+E(f334(f334(f45(x94841,f935(x94842,a922)),x94843),f334(f334(f8(f935(x94844,a922),f935(x94842,a922),x94841),f317(x94844,x94842,x94845)),x94846)),f334(f317(x94844,x94842,x94845),f334(f334(f45(x94841,f935(x94844,a922)),x94843),x94846))) % 188.18/188.26 [9669]P107(f334(f334(f336(f934(f928(x96691),f928(x96691))),f334(f334(f260(f928(x96691),f928(x96691)),f334(f334(f158(x96691),x96692),x96693)),f334(f334(f158(x96691),x96694),x96695))),f154(x96691,x96696)))+~P107(f334(f334(f336(f934(x96691,x96691)),f334(f334(f260(x96691,x96691),x96692),x96694)),x96696)) % 188.18/188.26 [10141]E(f334(f334(f260(x101411,x101412),f591(x101413,x101414,x101415,x101412,x101411,x101416)),f592(x101413,x101414,x101415,x101412,x101411,x101416)),x101416)+P107(f334(f334(f336(x101415),x101414),f334(f334(f265(x101411,x101412,f935(x101415,a922)),x101413),x101416))) % 188.18/188.26 [10147]E(f334(f334(f260(x101471,x101472),f593(x101473,x101474,x101472,x101471,x101475,x101476)),f594(x101473,x101474,x101472,x101471,x101475,x101476)),x101473)+~P107(f334(f334(f336(x101476),x101475),f334(f334(f265(x101471,x101472,f935(x101476,a922)),x101474),x101473))) % 188.18/188.26 [10289]P107(f334(f334(f336(x102891),x102892),f334(f334(x102893,f593(x102894,x102893,x102895,x102896,x102892,x102891)),f594(x102894,x102893,x102895,x102896,x102892,x102891))))+~P107(f334(f334(f336(x102891),x102892),f334(f334(f265(x102896,x102895,f935(x102891,a922)),x102893),x102894))) % 188.18/188.26 [10321]~P107(f334(f334(f336(x103211),x103212),f334(f334(x103215,f591(x103215,x103212,x103211,x103214,x103213,x103216)),f592(x103215,x103212,x103211,x103214,x103213,x103216))))+P107(f334(f334(f336(x103211),x103212),f334(f334(f265(x103213,x103214,f935(x103211,a922)),x103215),x103216))) % 188.18/188.26 [8620]E(x86201,x86202)+E(f334(f334(f166(x86203,f334(f334(f166(x86203,x86204),x86201),x86205)),x86202),x86206),f334(f334(f166(x86203,f334(f334(f166(x86203,x86204),x86202),x86206)),x86201),x86205)) % 188.18/188.26 [9741]~P107(f334(f334(f336(x97413),x97416),x97415))+E(f334(f334(f316(x97411),x97412),f334(f317(x97413,x97411,x97414),f334(f334(f23(f935(x97413,a922)),x97415),f334(f334(f316(x97413),x97416),f195(f935(x97413,a922)))))),f334(f317(x97413,x97411,f80(x97413,x97411,x97414,x97416,x97412)),x97415)) % 188.18/188.26 [9252]~P107(f334(f334(x92524,x92525),x92526))+P107(f334(f334(f334(f334(f108(f935(x92521,f935(x92522,a922))),x92523),x92524),x92525),x92526)) % 188.18/188.26 [9254]~P107(f334(f334(x92543,x92545),x92546))+P107(f334(f334(f334(f334(f108(f935(x92541,f935(x92542,a922))),x92543),x92544),x92545),x92546)) % 188.18/188.26 [9537]P107(f334(f334(x95371,x95372),x95373))+~P107(f334(f334(f334(f334(f109(f935(x95374,f935(x95375,a922))),x95376),x95371),x95372),x95373)) % 188.18/188.26 [9538]P107(f334(f334(x95381,x95382),x95383))+~P107(f334(f334(f334(f334(f109(f935(x95384,f935(x95385,a922))),x95381),x95386),x95382),x95383)) % 188.18/188.26 [9998]~P72(x99982)+E(f334(f334(f9(x99981,x99982),f334(f334(f7(x99981,f935(x99983,a922),x99982),f334(f334(f8(f935(x99983,x99982),f935(f935(x99983,a922),x99982),x99981),f9(x99983,x99982)),x99984)),x99985)),x99986),f334(f334(f9(f934(x99981,x99983),x99982),f334(f265(x99981,x99983,x99982),x99984)),f334(f334(f262(x99981,x99983),x99986),f334(f16(f935(x99983,a922),x99981),x99985)))) % 188.18/188.26 [9999]~P76(x99992)+E(f334(f334(f6(x99991,x99992),f334(f334(f7(x99991,f935(x99993,a922),x99992),f334(f334(f8(f935(x99993,x99992),f935(f935(x99993,a922),x99992),x99991),f6(x99993,x99992)),x99994)),x99995)),x99996),f334(f334(f6(f934(x99991,x99993),x99992),f334(f265(x99991,x99993,x99992),x99994)),f334(f334(f262(x99991,x99993),x99996),f334(f16(f935(x99993,a922),x99991),x99995)))) % 188.18/188.26 [10127]~P76(x101272)+E(f334(f334(f6(x101271,x101272),f334(f334(f7(x101271,f935(x101273,a922),x101272),f334(f334(f8(f935(x101273,x101272),f935(f935(x101273,a922),x101272),x101271),f6(x101273,x101272)),f334(f7(x101273,x101271,x101272),x101274))),x101275)),x101276),f334(f334(f6(x101273,x101272),f334(f334(f7(x101273,f935(x101271,a922),x101272),f334(f334(f8(f935(x101271,x101272),f935(f935(x101271,a922),x101272),x101273),f6(x101271,x101272)),x101274)),x101276)),x101275)) % 188.18/188.26 [10456]~P107(f334(f334(f336(f934(x104561,x104562)),f334(f334(f260(x104561,x104562),x104565),x104566)),f334(f334(f108(f935(f934(x104561,x104562),a922)),x104563),x104564)))+P107(f334(f334(f334(f334(f108(f935(x104561,f935(x104562,a922))),f334(f334(f7(x104561,f935(f934(x104561,x104562),a922),f935(x104562,a922)),f334(f334(f8(f935(x104562,f935(f935(f934(x104561,x104562),a922),a922)),f935(f935(f934(x104561,x104562),a922),f935(x104562,a922)),x104561),f7(x104562,f935(f934(x104561,x104562),a922),a922)),f334(f334(f8(f935(x104562,f934(x104561,x104562)),f935(x104562,f935(f935(f934(x104561,x104562),a922),a922)),x104561),f334(f8(f934(x104561,x104562),f935(f935(f934(x104561,x104562),a922),a922),x104562),f336(f934(x104561,x104562)))),f260(x104561,x104562)))),x104563)),f334(f334(f7(x104561,f935(f934(x104561,x104562),a922),f935(x104562,a922)),f334(f334(f8(f935(x104562,f935(f935(f934(x104561,x104562),a922),a922)),f935(f935(f934(x104561,x104562),a922),f935(x104562,a922)),x104561),f7(x104562,f935(f934(x104561,x104562),a922),a922)),f334(f334(f8(f935(x104562,f934(x104561,x104562)),f935(x104562,f935(f935(f934(x104561,x104562),a922),a922)),x104561),f334(f8(f934(x104561,x104562),f935(f935(f934(x104561,x104562),a922),a922),x104562),f336(f934(x104561,x104562)))),f260(x104561,x104562)))),x104564)),x104565),x104566)) % 188.18/188.26 [10457]~P107(f334(f334(f336(f934(x104571,x104572)),f334(f334(f260(x104571,x104572),x104575),x104576)),f334(f334(f109(f935(f934(x104571,x104572),a922)),x104573),x104574)))+P107(f334(f334(f334(f334(f109(f935(x104571,f935(x104572,a922))),f334(f334(f7(x104571,f935(f934(x104571,x104572),a922),f935(x104572,a922)),f334(f334(f8(f935(x104572,f935(f935(f934(x104571,x104572),a922),a922)),f935(f935(f934(x104571,x104572),a922),f935(x104572,a922)),x104571),f7(x104572,f935(f934(x104571,x104572),a922),a922)),f334(f334(f8(f935(x104572,f934(x104571,x104572)),f935(x104572,f935(f935(f934(x104571,x104572),a922),a922)),x104571),f334(f8(f934(x104571,x104572),f935(f935(f934(x104571,x104572),a922),a922),x104572),f336(f934(x104571,x104572)))),f260(x104571,x104572)))),x104573)),f334(f334(f7(x104571,f935(f934(x104571,x104572),a922),f935(x104572,a922)),f334(f334(f8(f935(x104572,f935(f935(f934(x104571,x104572),a922),a922)),f935(f935(f934(x104571,x104572),a922),f935(x104572,a922)),x104571),f7(x104572,f935(f934(x104571,x104572),a922),a922)),f334(f334(f8(f935(x104572,f934(x104571,x104572)),f935(x104572,f935(f935(f934(x104571,x104572),a922),a922)),x104571),f334(f8(f934(x104571,x104572),f935(f935(f934(x104571,x104572),a922),a922),x104572),f336(f934(x104571,x104572)))),f260(x104571,x104572)))),x104574)),x104575),x104576)) % 188.18/188.26 [10470]P107(f334(f334(f336(f934(x104701,x104702)),f334(f334(f260(x104701,x104702),x104703),x104704)),f334(f334(f108(f935(f934(x104701,x104702),a922)),x104705),x104706)))+~P107(f334(f334(f334(f334(f108(f935(x104701,f935(x104702,a922))),f334(f334(f7(x104701,f935(f934(x104701,x104702),a922),f935(x104702,a922)),f334(f334(f8(f935(x104702,f935(f935(f934(x104701,x104702),a922),a922)),f935(f935(f934(x104701,x104702),a922),f935(x104702,a922)),x104701),f7(x104702,f935(f934(x104701,x104702),a922),a922)),f334(f334(f8(f935(x104702,f934(x104701,x104702)),f935(x104702,f935(f935(f934(x104701,x104702),a922),a922)),x104701),f334(f8(f934(x104701,x104702),f935(f935(f934(x104701,x104702),a922),a922),x104702),f336(f934(x104701,x104702)))),f260(x104701,x104702)))),x104705)),f334(f334(f7(x104701,f935(f934(x104701,x104702),a922),f935(x104702,a922)),f334(f334(f8(f935(x104702,f935(f935(f934(x104701,x104702),a922),a922)),f935(f935(f934(x104701,x104702),a922),f935(x104702,a922)),x104701),f7(x104702,f935(f934(x104701,x104702),a922),a922)),f334(f334(f8(f935(x104702,f934(x104701,x104702)),f935(x104702,f935(f935(f934(x104701,x104702),a922),a922)),x104701),f334(f8(f934(x104701,x104702),f935(f935(f934(x104701,x104702),a922),a922),x104702),f336(f934(x104701,x104702)))),f260(x104701,x104702)))),x104706)),x104703),x104704)) % 188.18/188.26 [10471]P107(f334(f334(f336(f934(x104711,x104712)),f334(f334(f260(x104711,x104712),x104713),x104714)),f334(f334(f109(f935(f934(x104711,x104712),a922)),x104715),x104716)))+~P107(f334(f334(f334(f334(f109(f935(x104711,f935(x104712,a922))),f334(f334(f7(x104711,f935(f934(x104711,x104712),a922),f935(x104712,a922)),f334(f334(f8(f935(x104712,f935(f935(f934(x104711,x104712),a922),a922)),f935(f935(f934(x104711,x104712),a922),f935(x104712,a922)),x104711),f7(x104712,f935(f934(x104711,x104712),a922),a922)),f334(f334(f8(f935(x104712,f934(x104711,x104712)),f935(x104712,f935(f935(f934(x104711,x104712),a922),a922)),x104711),f334(f8(f934(x104711,x104712),f935(f935(f934(x104711,x104712),a922),a922),x104712),f336(f934(x104711,x104712)))),f260(x104711,x104712)))),x104715)),f334(f334(f7(x104711,f935(f934(x104711,x104712),a922),f935(x104712,a922)),f334(f334(f8(f935(x104712,f935(f935(f934(x104711,x104712),a922),a922)),f935(f935(f934(x104711,x104712),a922),f935(x104712,a922)),x104711),f7(x104712,f935(f934(x104711,x104712),a922),a922)),f334(f334(f8(f935(x104712,f934(x104711,x104712)),f935(x104712,f935(f935(f934(x104711,x104712),a922),a922)),x104711),f334(f8(f934(x104711,x104712),f935(f935(f934(x104711,x104712),a922),a922),x104712),f336(f934(x104711,x104712)))),f260(x104711,x104712)))),x104716)),x104713),x104714)) % 188.18/188.26 [10445]~P107(f334(f334(f336(f934(x104452,x104453)),f334(f334(f260(x104452,x104453),x104455),x104456)),f334(f334(f44(x104451,f935(f934(x104452,x104453),a922)),f250(f935(x104451,a922))),x104454)))+P107(f334(f334(f334(f334(f44(x104451,f935(x104452,f935(x104453,a922))),f250(f935(x104451,a922))),f334(f334(f8(f935(f934(x104452,x104453),a922),f935(x104452,f935(x104453,a922)),x104451),f334(f7(x104452,f935(f934(x104452,x104453),a922),f935(x104453,a922)),f334(f334(f8(f935(x104453,f935(f935(f934(x104452,x104453),a922),a922)),f935(f935(f934(x104452,x104453),a922),f935(x104453,a922)),x104452),f7(x104453,f935(f934(x104452,x104453),a922),a922)),f334(f334(f8(f935(x104453,f934(x104452,x104453)),f935(x104453,f935(f935(f934(x104452,x104453),a922),a922)),x104452),f334(f8(f934(x104452,x104453),f935(f935(f934(x104452,x104453),a922),a922),x104453),f336(f934(x104452,x104453)))),f260(x104452,x104453))))),x104454)),x104455),x104456)) % 188.18/188.26 [10446]~P107(f334(f334(f336(f934(x104462,x104463)),f334(f334(f260(x104462,x104463),x104465),x104466)),f334(f334(f45(x104461,f935(f934(x104462,x104463),a922)),f250(f935(x104461,a922))),x104464)))+P107(f334(f334(f334(f334(f45(x104461,f935(x104462,f935(x104463,a922))),f250(f935(x104461,a922))),f334(f334(f8(f935(f934(x104462,x104463),a922),f935(x104462,f935(x104463,a922)),x104461),f334(f7(x104462,f935(f934(x104462,x104463),a922),f935(x104463,a922)),f334(f334(f8(f935(x104463,f935(f935(f934(x104462,x104463),a922),a922)),f935(f935(f934(x104462,x104463),a922),f935(x104463,a922)),x104462),f7(x104463,f935(f934(x104462,x104463),a922),a922)),f334(f334(f8(f935(x104463,f934(x104462,x104463)),f935(x104463,f935(f935(f934(x104462,x104463),a922),a922)),x104462),f334(f8(f934(x104462,x104463),f935(f935(f934(x104462,x104463),a922),a922),x104463),f336(f934(x104462,x104463)))),f260(x104462,x104463))))),x104464)),x104465),x104466)) % 188.18/188.26 [10460]P107(f334(f334(f336(f934(x104601,x104602)),f334(f334(f260(x104601,x104602),x104603),x104604)),f334(f334(f44(x104605,f935(f934(x104601,x104602),a922)),f250(f935(x104605,a922))),x104606)))+~P107(f334(f334(f334(f334(f44(x104605,f935(x104601,f935(x104602,a922))),f250(f935(x104605,a922))),f334(f334(f8(f935(f934(x104601,x104602),a922),f935(x104601,f935(x104602,a922)),x104605),f334(f7(x104601,f935(f934(x104601,x104602),a922),f935(x104602,a922)),f334(f334(f8(f935(x104602,f935(f935(f934(x104601,x104602),a922),a922)),f935(f935(f934(x104601,x104602),a922),f935(x104602,a922)),x104601),f7(x104602,f935(f934(x104601,x104602),a922),a922)),f334(f334(f8(f935(x104602,f934(x104601,x104602)),f935(x104602,f935(f935(f934(x104601,x104602),a922),a922)),x104601),f334(f8(f934(x104601,x104602),f935(f935(f934(x104601,x104602),a922),a922),x104602),f336(f934(x104601,x104602)))),f260(x104601,x104602))))),x104606)),x104603),x104604)) % 188.18/188.26 [10461]P107(f334(f334(f336(f934(x104611,x104612)),f334(f334(f260(x104611,x104612),x104613),x104614)),f334(f334(f45(x104615,f935(f934(x104611,x104612),a922)),f250(f935(x104615,a922))),x104616)))+~P107(f334(f334(f334(f334(f45(x104615,f935(x104611,f935(x104612,a922))),f250(f935(x104615,a922))),f334(f334(f8(f935(f934(x104611,x104612),a922),f935(x104611,f935(x104612,a922)),x104615),f334(f7(x104611,f935(f934(x104611,x104612),a922),f935(x104612,a922)),f334(f334(f8(f935(x104612,f935(f935(f934(x104611,x104612),a922),a922)),f935(f935(f934(x104611,x104612),a922),f935(x104612,a922)),x104611),f7(x104612,f935(f934(x104611,x104612),a922),a922)),f334(f334(f8(f935(x104612,f934(x104611,x104612)),f935(x104612,f935(f935(f934(x104611,x104612),a922),a922)),x104611),f334(f8(f934(x104611,x104612),f935(f935(f934(x104611,x104612),a922),a922),x104612),f336(f934(x104611,x104612)))),f260(x104611,x104612))))),x104616)),x104613),x104614)) % 188.18/188.26 [7493]E(x74931,x74932)+~E(f98(x74933,x74934,x74935,x74931),f98(x74933,x74936,x74937,x74932)) % 188.18/188.26 [7494]E(x74941,x74942)+~E(f98(x74943,x74944,x74941,x74945),f98(x74943,x74946,x74942,x74947)) % 188.18/188.26 [7495]E(x74951,x74952)+~E(f98(x74953,x74951,x74954,x74955),f98(x74953,x74952,x74956,x74957)) % 188.18/188.26 [7652]E(f334(x76521,f334(x76522,x76523)),f334(x76524,x76523))+~E(f334(f78(x76525,x76526,x76527,x76521),x76522),x76524) % 188.18/188.26 [9758]E(x97581,x97582)+E(f80(x97583,x97584,f80(x97583,x97584,x97585,x97581,x97586),x97582,x97587),f80(x97583,x97584,f80(x97583,x97584,x97585,x97582,x97587),x97581,x97586)) % 188.18/188.26 [9854]~P24(x98543,x98544,x98541,x98545,x98546,x98547)+E(f334(f334(x98541,x98542),x98542),x98542) % 188.18/188.26 [6256]~E(f334(f334(f161(x62561,x62565),x62566),x62562),f334(f334(f161(x62563,x62565),x62567),x62564))+E(f334(f196(f928(x62561)),x62562),f334(f196(f928(x62563)),x62564)) % 188.18/188.26 [8654]E(f334(x86541,f334(x86542,x86543)),f334(x86544,x86543))+~E(f334(f78(x86545,x86546,x86547,x86541),x86542),f334(f78(x86546,x86546,x86547,f32(x86546)),x86544)) % 188.18/188.26 [9001]~P36(x90014,x90015,x90011,f334(f334(f158(x90014),x90012),x90016),f334(f334(f158(x90015),x90013),x90017))+P107(f334(f334(x90011,x90012),x90013)) % 188.18/188.26 [9383]P36(x93831,x93832,x93833,x93834,x93835)+~P36(x93831,x93832,x93833,f334(f334(f158(x93831),x93836),x93834),f334(f334(f158(x93832),x93837),x93835)) % 188.18/188.26 [10034]P107(f334(f334(x100341,x100342),f525(x100343,x100342,x100344,x100341)))+~P107(f334(f334(f261(x100345,x100346,x100347,x100341,x100344),x100342),x100343)) % 188.18/188.26 [10057]P107(f334(f334(x100571,f525(x100572,x100573,x100571,x100574)),x100572))+~P107(f334(f334(f261(x100575,x100576,x100577,x100574,x100571),x100573),x100572)) % 188.18/188.26 [9129]~P22(x91296,x91291,x91293,x91297)+E(f334(f78(x91291,x91291,x91292,f334(x91293,x91294)),f334(f78(x91291,x91291,x91292,f334(x91293,x91294)),x91295)),f334(f78(x91291,x91291,x91292,f334(x91293,x91294)),x91295)) % 188.18/188.26 [9487]~P36(x94873,x94872,x94874,f334(f334(f161(x94871,x94873),x94875),x94876),x94877)+P36(x94871,x94872,f334(f334(f8(x94873,f935(x94872,a922),x94871),x94874),x94875),x94876,x94877) % 188.18/188.26 [9513]P36(x95131,x95132,x95133,f334(f334(f161(x95134,x95131),x95135),x95136),x95137)+~P36(x95134,x95132,f334(f334(f8(x95131,f935(x95132,a922),x95134),x95133),x95135),x95136,x95137) % 188.18/188.26 [9128]~P107(f334(f334(f336(x91281),x91282),f334(f334(x91285,x91286),x91287)))+P107(f334(f334(f336(x91281),x91282),f334(f334(f265(x91283,x91284,f935(x91281,a922)),x91285),f334(f334(f260(x91283,x91284),x91286),x91287)))) % 188.18/188.26 [9406]P107(f334(f334(f334(x94061,x94062),x94063),x94064))+~P107(f334(f334(f334(f265(x94065,x94066,f935(x94067,a922)),x94061),f334(f334(f260(x94065,x94066),x94062),x94063)),x94064)) % 188.18/188.26 [9552]P107(f334(f334(f336(x95521),f334(f334(x95522,x95523),x95524)),f334(f317(f934(x95525,x95526),x95521,f334(f265(x95525,x95526,x95521),x95522)),x95527)))+~P107(f334(f334(f336(f934(x95525,x95526)),f334(f334(f260(x95525,x95526),x95523),x95524)),x95527)) % 188.18/188.26 [9907]P107(f334(f334(f336(f934(f928(x99071),f928(x99071))),f334(f334(f260(f928(x99071),f928(x99071)),f334(f334(f141(x99071),x99072),f334(f334(f158(x99071),x99073),x99074))),f334(f334(f141(x99071),x99072),f334(f334(f158(x99071),x99075),x99076)))),f154(x99071,x99077)))+~P107(f334(f334(f336(f934(x99071,x99071)),f334(f334(f260(x99071,x99071),x99073),x99075)),x99077)) % 188.18/188.26 [9973]~P36(x99731,x99733,x99734,x99736,f334(f334(f161(x99732,x99733),x99735),x99737))+P36(x99731,x99732,f334(f334(f7(x99731,f935(x99732,x99733),f935(x99732,a922)),f334(f334(f8(f935(x99733,a922),f935(f935(x99732,x99733),f935(x99732,a922)),x99731),f8(x99733,a922,x99732)),x99734)),x99735),x99736,x99737) % 188.18/188.26 [10061]P36(x100611,x100612,x100613,x100614,f334(f334(f161(x100615,x100612),x100616),x100617))+~P36(x100611,x100615,f334(f334(f7(x100611,f935(x100615,x100612),f935(x100615,a922)),f334(f334(f8(f935(x100612,a922),f935(f935(x100615,x100612),f935(x100615,a922)),x100611),f8(x100612,a922,x100615)),x100613)),x100616),x100614,x100617) % 188.18/188.26 [10336]P107(f334(f334(f336(x103361),f510(x103362,x103363,x103364,x103365,x103366,x103367,x103361)),x103365))+P107(f334(f334(f334(f334(f45(x103361,f935(x103367,f935(x103366,a922))),x103365),x103364),x103363),x103362)) % 188.18/188.26 [10337]P107(f334(f334(f336(x103371),f802(x103372,x103373,x103374,x103375,x103376,x103377,x103371)),x103377))+P107(f334(f334(f334(f334(f45(x103371,f935(x103373,f935(x103372,a922))),x103377),x103376),x103375),x103374)) % 188.18/188.26 [10338]P107(f334(f334(f336(x103381),f396(x103382,x103383,x103384,x103385,x103386,x103387,x103381)),x103385))+~P107(f334(f334(f334(f334(f44(x103381,f935(x103387,f935(x103386,a922))),x103385),x103384),x103383),x103382)) % 188.18/188.26 [10339]P107(f334(f334(f336(x103391),f803(x103392,x103393,x103394,x103395,x103396,x103397,x103391)),x103395))+~P107(f334(f334(f334(f334(f44(x103391,f935(x103397,f935(x103396,a922))),x103395),x103394),x103393),x103392)) % 188.18/188.26 [10397]P107(f334(f334(f334(x103971,f396(x103972,x103973,x103971,x103974,x103975,x103976,x103977)),x103973),x103972))+~P107(f334(f334(f334(f334(f44(x103977,f935(x103976,f935(x103975,a922))),x103974),x103971),x103973),x103972)) % 188.18/188.26 [10398]P107(f334(f334(f334(x103981,f803(x103982,x103983,x103981,x103984,x103985,x103986,x103987)),x103983),x103982))+~P107(f334(f334(f334(f334(f44(x103987,f935(x103986,f935(x103985,a922))),x103984),x103981),x103983),x103982)) % 188.18/188.26 [10417]~P107(f334(f334(f334(x104175,f510(x104177,x104176,x104175,x104174,x104173,x104172,x104171)),x104176),x104177))+P107(f334(f334(f334(f334(f45(x104171,f935(x104172,f935(x104173,a922))),x104174),x104175),x104176),x104177)) % 188.18/188.26 [10418]~P107(f334(f334(f334(x104185,f802(x104183,x104182,x104187,x104186,x104185,x104184,x104181)),x104186),x104187))+P107(f334(f334(f334(f334(f45(x104181,f935(x104182,f935(x104183,a922))),x104184),x104185),x104186),x104187)) % 188.18/188.26 [10444]~P107(f334(f334(f336(f934(x104441,x104443)),f334(f334(f260(x104441,x104443),x104446),x104447)),f334(f334(f295(x104441,x104442,x104443),x104444),x104445)))+P107(f334(f334(f261(x104441,x104442,x104443,f334(f334(f7(x104441,f935(f934(x104441,x104442),a922),f935(x104442,a922)),f334(f334(f8(f935(x104442,f935(f935(f934(x104441,x104442),a922),a922)),f935(f935(f934(x104441,x104442),a922),f935(x104442,a922)),x104441),f7(x104442,f935(f934(x104441,x104442),a922),a922)),f334(f334(f8(f935(x104442,f934(x104441,x104442)),f935(x104442,f935(f935(f934(x104441,x104442),a922),a922)),x104441),f334(f8(f934(x104441,x104442),f935(f935(f934(x104441,x104442),a922),a922),x104442),f336(f934(x104441,x104442)))),f260(x104441,x104442)))),x104444),f334(f334(f7(x104442,f935(f934(x104442,x104443),a922),f935(x104443,a922)),f334(f334(f8(f935(x104443,f935(f935(f934(x104442,x104443),a922),a922)),f935(f935(f934(x104442,x104443),a922),f935(x104443,a922)),x104442),f7(x104443,f935(f934(x104442,x104443),a922),a922)),f334(f334(f8(f935(x104443,f934(x104442,x104443)),f935(x104443,f935(f935(f934(x104442,x104443),a922),a922)),x104442),f334(f8(f934(x104442,x104443),f935(f935(f934(x104442,x104443),a922),a922),x104443),f336(f934(x104442,x104443)))),f260(x104442,x104443)))),x104445)),x104446),x104447)) % 188.18/188.26 [10459]P107(f334(f334(f336(f934(x104591,x104592)),f334(f334(f260(x104591,x104592),x104593),x104594)),f334(f334(f295(x104591,x104595,x104592),x104596),x104597)))+~P107(f334(f334(f261(x104591,x104595,x104592,f334(f334(f7(x104591,f935(f934(x104591,x104595),a922),f935(x104595,a922)),f334(f334(f8(f935(x104595,f935(f935(f934(x104591,x104595),a922),a922)),f935(f935(f934(x104591,x104595),a922),f935(x104595,a922)),x104591),f7(x104595,f935(f934(x104591,x104595),a922),a922)),f334(f334(f8(f935(x104595,f934(x104591,x104595)),f935(x104595,f935(f935(f934(x104591,x104595),a922),a922)),x104591),f334(f8(f934(x104591,x104595),f935(f935(f934(x104591,x104595),a922),a922),x104595),f336(f934(x104591,x104595)))),f260(x104591,x104595)))),x104596),f334(f334(f7(x104595,f935(f934(x104595,x104592),a922),f935(x104592,a922)),f334(f334(f8(f935(x104592,f935(f935(f934(x104595,x104592),a922),a922)),f935(f935(f934(x104595,x104592),a922),f935(x104592,a922)),x104595),f7(x104592,f935(f934(x104595,x104592),a922),a922)),f334(f334(f8(f935(x104592,f934(x104595,x104592)),f935(x104592,f935(f935(f934(x104595,x104592),a922),a922)),x104595),f334(f8(f934(x104595,x104592),f935(f935(f934(x104595,x104592),a922),a922),x104592),f336(f934(x104595,x104592)))),f260(x104595,x104592)))),x104597)),x104593),x104594)) % 188.18/188.26 [10347]~P148(x103472)+E(f334(f334(f6(x103471,x103472),f334(f334(f7(x103471,f935(x103473,a922),x103472),f334(f334(f8(f935(x103473,x103472),f935(f935(x103473,a922),x103472),x103471),f6(x103473,x103472)),f334(f334(f7(x103471,f935(x103473,x103472),f935(x103473,x103472)),f334(f334(f8(f935(x103472,x103472),f935(f935(x103473,x103472),f935(x103473,x103472)),x103471),f8(x103472,x103472,x103473)),f334(f334(f8(x103472,f935(x103472,x103472),x103471),f87(x103472)),x103474))),x103475))),x103476)),x103477),f334(f334(f87(x103472),f334(f334(f6(x103471,x103472),x103474),x103477)),f334(f334(f6(x103473,x103472),x103475),x103476))) % 188.18/188.26 [9436]~P21(x94367,x94361,x94363,x94368)+E(f334(f78(x94361,x94361,x94362,f334(x94363,x94364)),f334(f78(x94361,x94361,x94362,f334(x94363,x94365)),x94366)),f334(f78(x94361,x94361,x94362,f334(x94363,x94365)),f334(f78(x94361,x94361,x94362,f334(x94363,x94364)),x94366))) % 188.18/188.26 [10396]P26(x103961,x103962,f334(f334(f316(f926(x103961)),f98(x103961,f334(f334(f8(f935(a923,a922),f935(a923,a922),x103961),f334(f18(a923,a922,a922),f334(f334(f8(a922,f935(a922,a922),a923),a332),f334(a331,x103963)))),f334(f334(f7(x103961,f935(a923,a923),f935(a923,a922)),f334(f334(f8(f935(a923,a922),f935(f935(a923,a923),f935(a923,a922)),x103961),f8(a923,a922,a923)),x103964)),f334(f334(f18(a923,a927,a923),f334(f334(f7(a923,a925,f935(a927,a923)),a203),f33(x103965))),x103966))),f27(x103965,x103966,x103967),x103968)),f195(f935(f926(x103961),a922))))+~P26(x103961,x103962,f334(f334(f316(f926(x103961)),f98(x103961,x103964,x103967,f334(f334(f7(x103961,f935(a923,a923),f935(a923,a922)),f334(f334(f8(f935(a923,a922),f935(f935(a923,a923),f935(a923,a922)),x103961),f8(a923,a922,a923)),x103968)),f334(f334(f7(a923,a927,a923),f334(f334(f7(a923,a925,f935(a927,a923)),a203),f33(x103965))),f204(x103963,x103965))))),f195(f935(f926(x103961),a922)))) % 188.18/188.26 [10452]E(f334(f334(f260(x104521,x104522),f334(x104523,f561(x104524,x104525,x104523,x104526,x104527,x104528,x104522,x104521))),f334(x104525,f562(x104524,x104525,x104523,x104526,x104527,x104528,x104522,x104521))),x104528)+~P107(f334(f334(f336(f934(x104521,x104522)),x104528),f334(f317(f934(x104527,x104526),f934(x104521,x104522),f266(x104527,x104521,x104526,x104522,x104523,x104525)),x104524))) % 188.18/188.26 [10476]~P107(f334(f334(f336(f934(x104768,x104767)),x104766),f334(f317(f934(x104761,x104762),f934(x104768,x104767),f266(x104761,x104768,x104762,x104767,x104765,x104764)),x104763)))+P107(f334(f334(f336(f934(x104761,x104762)),f334(f334(f260(x104761,x104762),f561(x104763,x104764,x104765,x104762,x104761,x104766,x104767,x104768)),f562(x104763,x104764,x104765,x104762,x104761,x104766,x104767,x104768))),x104763)) % 188.18/188.26 [9897]P107(f334(f334(f336(f934(f934(x98971,x98972),f934(x98971,x98972))),f334(f334(f260(f934(x98971,x98972),f934(x98971,x98972)),f334(f334(f260(x98971,x98972),x98973),x98974)),f334(f334(f260(x98971,x98972),x98975),x98976))),f326(x98971,x98972,x98977,x98978)))+~P107(f334(f334(f336(f934(x98971,x98971)),f334(f334(f260(x98971,x98971),x98973),x98975)),x98977)) % 188.18/188.26 [10438]E(f334(f149(x104381,x104382,f334(f7(x104382,x104381,x104381),x104383),f334(x104384,x104385)),x104386),f334(x104384,f334(f149(x104387,x104382,f334(f7(x104382,x104387,x104387),x104388),x104385),x104386)))+P107(f334(f334(f336(x104382),f746(x104385,x104388,x104384,x104383,x104387,x104381,x104386,x104382)),f334(f179(x104382),x104386))) % 188.18/188.26 [10463]~E(f334(f78(x104631,x104631,x104637,f334(x104633,f746(x104635,x104638,x104634,x104633,x104637,x104631,x104636,x104632))),x104634),f334(f78(x104637,x104631,x104637,x104634),f334(x104638,f746(x104635,x104638,x104634,x104633,x104637,x104631,x104636,x104632))))+E(f334(f149(x104631,x104632,f334(f7(x104632,x104631,x104631),x104633),f334(x104634,x104635)),x104636),f334(x104634,f334(f149(x104637,x104632,f334(f7(x104632,x104637,x104637),x104638),x104635),x104636))) % 188.18/188.26 [8659]E(f334(x86591,f334(x86592,x86593)),f334(x86594,f334(x86595,x86593)))+~E(f334(f78(x86596,x86597,x86598,x86591),x86592),f334(f78(x86599,x86597,x86598,x86594),x86595)) % 188.18/188.26 [10257]P107(f334(f334(f336(f934(x102571,x102572)),f334(f334(f260(x102571,x102572),f334(x102573,x102574)),f334(x102575,x102576))),f334(f317(f934(x102577,x102578),f934(x102571,x102572),f266(x102577,x102571,x102578,x102572,x102573,x102575)),x102579)))+~P107(f334(f334(f336(f934(x102577,x102578)),f334(f334(f260(x102577,x102578),x102574),x102576)),x102579)) % 188.18/188.26 [8948]~E(f334(x89484,f334(x89485,x89486)),f334(x89489,f334(x894810,x894811)))+E(f334(f334(f78(x89481,x89482,x89483,x89484),x89485),x89486),f334(f334(f78(x89487,x89482,x89488,x89489),x894810),x894811)) % 188.18/188.26 [4824]~P109(x48241)+~P98(x48241)+E(f241(x48241),f108(x48241)) % 188.18/188.26 [4825]~P109(x48251)+~P104(x48251)+E(f246(x48251),f109(x48251)) % 188.18/188.26 [5075]~P124(x50751)+~P95(x50751)+E(f334(f81(x50751),f334(f111(x50751),a104)),f84(x50751)) % 188.18/188.26 [5358]E(x53581,f2(a1))+E(f88(a1,x53581),f334(f85(a1),f84(a1)))+P107(f334(f334(f243(a1),f2(a1)),x53581)) % 188.18/188.26 [5567]E(x55671,f2(a1))+E(f88(a1,x55671),f84(a1))+~P107(f334(f334(f243(a1),f2(a1)),x55671)) % 188.18/188.26 [7560]~P42(x75601)+P107(f334(f66(a1),x75601))+~P107(f334(f66(a927),f334(f317(a1,a927,a112),x75601))) % 188.18/188.26 [9853]E(x98531,f195(f935(f934(a927,a927),a922)))+~P107(f334(f66(f934(a927,a927)),x98531))+P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),f195(f935(f934(a927,a927),a922))),x98531)),a39)) % 188.18/188.26 [10285]E(x102851,f2(a927))+E(x102851,f334(a119,f2(a927)))+~P107(f334(f334(f243(a927),x102851),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.26 [10432]E(x104321,f2(a106))+E(f334(f334(f86(a1),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(a22,f334(f334(f41(a106),x104321),f334(f111(a106),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))))),f84(a1)),f334(a22,x104321))+E(f50(a106,x104321,f334(f111(a106),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f2(a106)) % 188.18/188.26 [10363]E(x103631,f2(a106))+~E(f50(a106,x103631,f334(f111(a106),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f2(a106))+E(f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(a22,f334(f334(f41(a106),x103631),f334(f111(a106),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f334(a22,x103631)) % 188.18/188.26 [4905]~P61(x49051,x49052)+P46(x49051,x49052)+~P47(a922) % 188.18/188.26 [4834]~P147(x48341)+P30(x48341,x48342)+~E(x48342,f2(x48341)) % 188.18/188.26 [4835]~P109(x48351)+P15(x48351,x48352)+~E(x48352,f120(x48351)) % 188.18/188.26 [4844]~P124(x48441)+~E(x48442,f2(x48441))+E(f88(x48441,x48442),f2(x48441)) % 188.18/188.26 [4845]~P89(x48451)+~E(x48452,f2(x48451))+E(f88(x48451,x48452),f2(x48451)) % 188.18/188.26 [4853]~P147(x48532)+~P30(x48532,x48531)+E(x48531,f2(x48532)) % 188.18/188.26 [4898]~P124(x48982)+~E(f88(x48982,x48981),f2(x48982))+E(x48981,f2(x48982)) % 188.18/188.26 [4912]~P4(x49122)+~P4(x49121)+P4(f935(x49121,x49122)) % 188.18/188.26 [4913]~P4(x49132)+~P4(x49131)+P4(f933(x49131,x49132)) % 188.18/188.26 [4914]~P4(x49142)+~P4(x49141)+P4(f934(x49141,x49142)) % 188.18/188.26 [4915]~P8(x49152)+~P8(x49151)+P8(f201(x49151,x49152)) % 188.18/188.26 [4916]~P64(x49162)+~P64(x49161)+P64(f935(x49161,x49162)) % 188.18/188.26 [4917]~P64(x49172)+~P64(x49171)+P64(f933(x49171,x49172)) % 188.18/188.26 [4918]~P64(x49182)+~P64(x49181)+P64(f934(x49181,x49182)) % 188.18/188.26 [4919]~P105(x49192)+~P105(x49191)+P105(f934(x49191,x49192)) % 188.18/188.26 [5047]~P109(x50471)+~P15(x50471,x50472)+P15(x50471,f159(x50471,x50472)) % 188.18/188.26 [5287]~P8(x52872)+~P8(x52871)+P8(f50(a1,x52871,x52872)) % 188.18/188.26 [4855]~P77(x48551)+~E(x48552,f2(x48551))+E(f334(f85(x48551),x48552),x48552) % 188.18/188.26 [4870]~P93(x48701)+~E(x48702,f2(a1))+E(f334(f110(x48701),x48702),f2(x48701)) % 188.18/188.26 [4871]~P142(x48711)+~E(x48712,f2(a1))+E(f334(f110(x48711),x48712),f2(x48711)) % 188.18/188.26 [4895]~P69(x48951)+~E(f2(x48951),x48952)+E(f334(f85(x48951),x48952),f2(x48951)) % 188.18/188.26 [4896]~P69(x48961)+~E(x48962,f2(x48961))+E(f334(f85(x48961),x48962),f2(x48961)) % 188.18/188.26 [4897]~P86(x48971)+~E(x48972,f2(x48971))+E(f334(f81(x48971),x48972),f2(x48971)) % 188.18/188.26 [4921]~P77(x49212)+E(x49211,f2(x49212))+~E(f334(f85(x49212),x49211),x49211) % 188.18/188.26 [4929]E(x49291,f334(a112,x49292))+~E(x49291,f2(a927))+~E(x49292,f334(f107(a1),x49291)) % 188.18/188.26 [4930]E(f334(a112,x49301),x49302)+~E(x49302,f2(a927))+~E(x49301,f334(f107(a1),x49302)) % 188.18/188.26 [4932]~P93(x49322)+E(x49321,f2(a1))+~E(f334(f110(x49322),x49321),f2(x49322)) % 188.18/188.26 [4936]~P69(x49362)+E(x49361,f2(x49362))+~E(f334(f85(x49362),x49361),f2(x49362)) % 188.18/188.26 [4937]~P86(x49372)+E(x49371,f2(x49372))+~E(f334(f81(x49372),x49371),f2(x49372)) % 188.18/188.26 [4938]~P69(x49381)+E(f2(x49381),x49382)+~E(f334(f85(x49381),x49382),f2(x49381)) % 188.18/188.26 [5120]~P109(x51201)+~P15(x51201,x51202)+P15(x51201,f334(f178(x51201),x51202)) % 188.18/188.26 [5147]~P107(x51472)+~P107(x51471)+P107(f334(f334(a332,x51471),x51472)) % 188.18/188.26 [5181]~E(f84(a927),f2(a927))+E(f334(f40(x51811),x51812),f2(a927))+~P107(f334(f66(x51811),x51812)) % 188.18/188.26 [5217]~P116(x52171)+~P148(x52171)+E(f334(f334(f252(x52171),f2(x52171)),f334(a119,x52172)),f2(x52171)) % 188.18/188.26 [5255]~P109(x52551)+P15(x52551,f146(x52551,x52552))+~P107(f334(f66(x52551),x52552)) % 188.18/188.26 [5256]~P109(x52561)+P15(x52561,f738(x52562,x52561))+~P107(f334(f66(x52561),x52562)) % 188.18/188.26 [5279]~P109(x52791)+E(f334(f179(x52791),f146(x52791,x52792)),x52792)+~P107(f334(f66(x52791),x52792)) % 188.18/188.26 [5280]~P109(x52801)+E(f334(f179(x52801),f738(x52802,x52801)),x52802)+~P107(f334(f66(x52801),x52802)) % 188.18/188.26 [5308]P107(x53081)+P107(x53082)+~P107(f334(f334(a333,x53082),x53081)) % 188.18/188.26 [5321]E(x53211,f195(f935(x53212,a922)))+~E(f334(f40(x53212),x53211),f2(a927))+~P107(f334(f66(x53212),x53211)) % 188.18/188.26 [5326]P107(x53261)+~P107(x53262)+~P107(f334(f334(a337,x53262),x53261)) % 188.18/188.26 [5376]~P75(x53761)+E(f334(f81(x53761),x53762),x53762)+P107(f334(f334(f243(x53761),x53762),f2(x53761))) % 188.18/188.26 [5436]~P64(x54362)+~P107(f334(f61(x54362),x54361))+P107(f334(x54361,f739(x54361,x54362))) % 188.18/188.26 [5437]~P64(x54372)+~P107(f334(f61(x54372),x54371))+P107(f334(x54371,f747(x54371,x54372))) % 188.18/188.26 [5479]E(x54791,f120(x54792))+P107(f334(f144(x54792),f121(x54792,x54791)))+~P107(f334(f144(x54792),x54791)) % 188.18/188.26 [5484]~P109(x54841)+~P107(f334(f66(x54841),x54842))+P107(f334(f144(x54841),f146(x54841,x54842))) % 188.18/188.26 [5485]~P109(x54851)+~P107(f334(f66(x54851),x54852))+P107(f334(f144(x54851),f738(x54852,x54851))) % 188.18/188.26 [5490]~P142(x54901)+E(f334(f107(x54901),f334(a112,x54902)),f334(f110(x54901),x54902))+P107(f334(f334(f243(a1),x54902),f2(a1))) % 188.18/188.26 [5517]P9(x55172,x55171)+E(f334(x55171,f462(x55171)),f334(x55171,f491(x55171)))+P107(f334(f334(x55171,f462(x55171)),f491(x55171))) % 188.18/188.26 [5529]E(f334(f107(a1),f906(x55291,x55292)),x55291)+P107(f334(x55292,f334(a112,x55291)))+~P107(f334(x55292,f2(a927))) % 188.18/188.26 [5541]~P64(x55411)+~P107(f334(x55412,f753(x55412,x55411)))+P107(f334(f62(x55411),x55412)) % 188.18/188.26 [5542]~P64(x55421)+~P107(f334(x55422,f762(x55422,x55421)))+P107(f334(f62(x55421),x55422)) % 188.18/188.26 [5577]~P124(x55771)+~E(f88(x55771,x55772),f334(f85(x55771),f84(x55771)))+P107(f334(f334(f243(x55771),x55772),f2(x55771))) % 188.18/188.26 [5650]~E(x56502,f2(a1))+E(f224(x56501,x56502),f334(f334(f260(a1,a1),f2(a1)),f84(a1)))+P107(f334(f334(f243(a1),x56502),f2(a1))) % 188.18/188.26 [5651]~E(x56511,f2(a1))+E(f224(x56511,x56512),f334(f334(f260(a1,a1),f2(a1)),f84(a1)))+P107(f334(f334(f243(a1),x56512),f2(a1))) % 188.18/188.26 [5703]E(f334(f107(a1),f906(x57031,x57032)),x57031)+P107(f334(x57032,f334(a112,x57031)))+P107(f334(f334(f243(a1),x57031),f2(a1))) % 188.18/188.26 [5768]~P124(x57681)+E(f88(x57681,x57682),f334(f85(x57681),f84(x57681)))+~P107(f334(f334(f243(x57681),x57682),f2(x57681))) % 188.18/188.26 [5769]~P86(x57691)+E(f334(f81(x57691),x57692),f334(f85(x57691),x57692))+~P107(f334(f334(f242(x57691),x57692),f2(x57691))) % 188.18/188.26 [5770]~P86(x57701)+E(f334(f81(x57701),x57702),f334(f85(x57701),x57702))+~P107(f334(f334(f243(x57701),x57702),f2(x57701))) % 188.18/188.26 [5771]~P75(x57711)+E(f334(f81(x57711),x57712),f334(f85(x57711),x57712))+~P107(f334(f334(f243(x57711),x57712),f2(x57711))) % 188.18/188.26 [5878]~P107(f334(x58781,f906(x58782,x58781)))+P107(f334(x58781,f334(a112,x58782)))+~P107(f334(x58781,f2(a927))) % 188.18/188.26 [5885]E(x58851,f2(a927))+E(f334(a119,f883(x58852,x58851)),x58851)+~P107(f334(f334(f243(a927),x58851),f334(a119,x58852))) % 188.18/188.26 [5889]P9(x58891,x58892)+~E(f334(x58892,f462(x58892)),f334(x58892,f491(x58892)))+~P107(f334(f334(x58892,f462(x58892)),f491(x58892))) % 188.18/188.26 [5907]~P109(x59071)+P15(x59071,x59072)+P107(f334(f334(f242(a927),f722(x59072,x59071)),f723(x59072,x59071))) % 188.18/188.26 [5908]~P109(x59081)+P15(x59081,x59082)+P107(f334(f334(f242(a927),f730(x59082,x59081)),f734(x59082,x59081))) % 188.18/188.26 [5996]~P86(x59961)+~E(x59962,f2(x59961))+P107(f334(f334(f242(x59961),f334(f81(x59961),x59962)),f2(x59961))) % 188.18/188.26 [6084]~P107(f334(x60841,f906(x60842,x60841)))+P107(f334(x60841,f334(a112,x60842)))+P107(f334(f334(f243(a1),x60842),f2(a1))) % 188.18/188.26 [6111]~P107(f334(x61111,f334(a112,x61112)))+P107(f334(x61111,f2(a927)))+~P107(f334(f334(f243(a1),x61112),f2(a1))) % 188.18/188.26 [6446]~P124(x64461)+~P107(f334(f334(f243(x64461),x64462),f2(x64461)))+P107(f334(f334(f243(x64461),f88(x64461,x64462)),f2(x64461))) % 188.18/188.26 [6559]~P124(x65591)+P107(f334(f334(f242(x65591),f334(f110(x65591),x65592)),f2(x65591)))+~P107(f334(f334(f242(a1),x65592),f2(a1))) % 188.18/188.26 [6560]~P124(x65601)+P107(f334(f334(f243(x65601),f334(f110(x65601),x65602)),f2(x65601)))+~P107(f334(f334(f243(a1),x65602),f2(a1))) % 188.18/188.26 [6570]~P86(x65702)+E(x65701,f2(x65702))+~P107(f334(f334(f242(x65702),f334(f81(x65702),x65701)),f2(x65702))) % 188.18/188.26 [6645]~P142(x66451)+~P107(f334(f334(f336(x66451),x66452),f117(x66451)))+P107(f334(f334(f336(x66451),f334(f85(x66451),x66452)),f117(x66451))) % 188.18/188.26 [6680]~P124(x66801)+~P107(f334(f334(f243(x66801),f88(x66801,x66802)),f2(x66801)))+P107(f334(f334(f243(x66801),x66802),f2(x66801))) % 188.18/188.26 [6849]~P124(x68492)+~P107(f334(f334(f242(x68492),f334(f110(x68492),x68491)),f2(x68492)))+P107(f334(f334(f242(a1),x68491),f2(a1))) % 188.18/188.26 [6850]~P124(x68502)+~P107(f334(f334(f243(x68502),f334(f110(x68502),x68501)),f2(x68502)))+P107(f334(f334(f243(a1),x68501),f2(a1))) % 188.18/188.26 [7340]~P77(x73401)+~P107(f334(f334(f242(x73401),x73402),f2(x73401)))+P107(f334(f334(f242(x73401),f334(f334(f86(x73401),x73402),x73402)),f2(x73401))) % 188.18/188.26 [7341]~P124(x73411)+~P107(f334(f334(f243(x73411),x73412),f2(x73411)))+P107(f334(f334(f243(x73411),f334(f334(f86(x73411),x73412),x73412)),f2(x73411))) % 188.18/188.26 [7342]~P77(x73421)+~P107(f334(f334(f243(x73421),x73422),f2(x73421)))+P107(f334(f334(f243(x73421),f334(f334(f86(x73421),x73422),x73422)),f2(x73421))) % 188.18/188.26 [7890]~P77(x78901)+~P107(f334(f334(f242(x78901),f334(f334(f86(x78901),x78902),x78902)),f2(x78901)))+P107(f334(f334(f242(x78901),x78902),f2(x78901))) % 188.18/188.26 [7891]~P124(x78911)+~P107(f334(f334(f243(x78911),f334(f334(f86(x78911),x78912),x78912)),f2(x78911)))+P107(f334(f334(f243(x78911),x78912),f2(x78911))) % 188.18/188.26 [7892]~P77(x78921)+~P107(f334(f334(f243(x78921),f334(f334(f86(x78921),x78922),x78922)),f2(x78921)))+P107(f334(f334(f243(x78921),x78922),f2(x78921))) % 188.18/188.26 [4973]~E(x49732,f84(a927))+~E(x49731,f84(a927))+E(f334(f334(f87(a927),x49731),x49732),f84(a927)) % 188.18/188.26 [4974]~E(x49742,f84(a1))+~E(x49741,f84(a1))+E(f334(f334(f87(a1),x49741),x49742),f84(a1)) % 188.18/188.26 [4975]~E(x49752,f2(a927))+~E(x49751,f2(a927))+E(f334(f334(f86(a927),x49751),x49752),f2(a927)) % 188.18/188.26 [5031]~P5(x50312)+E(x50311,f2(x50312))+E(f334(f334(f41(x50312),x50311),x50311),f84(x50312)) % 188.18/188.26 [5032]~P122(x50322)+E(x50321,f2(x50322))+E(f334(f334(f296(x50322),x50321),x50321),f84(x50322)) % 188.18/188.26 [5033]~P123(x50332)+E(x50331,f2(x50332))+E(f334(f334(f296(x50332),x50331),x50331),f84(x50332)) % 188.18/188.26 [5053]~P141(x50531)+~E(x50532,f84(x50531))+E(f334(f334(f87(x50531),x50532),x50532),f84(x50531)) % 188.18/188.26 [5054]~P77(x50541)+~E(x50542,f2(x50541))+E(f334(f334(f86(x50541),x50542),x50542),f2(x50541)) % 188.18/188.26 [5055]~P123(x50551)+~E(x50552,f2(x50551))+E(f334(f334(f296(x50551),x50552),x50552),f2(x50551)) % 188.18/188.26 [5098]~E(x50982,f2(a927))+~E(x50981,f2(a927))+E(f334(f85(a1),f334(f107(a1),x50981)),f334(f107(a1),x50982)) % 188.18/188.26 [5117]E(x51171,f84(a927))+E(x51172,f2(a927))+~E(f334(f334(f87(a927),x51172),x51171),x51172) % 188.18/188.26 [5129]E(x51291,f2(a927))+E(x51292,f2(a927))+~E(f334(f334(f87(a927),x51292),x51291),f2(a927)) % 188.18/188.26 [5156]~E(x51562,f2(a927))+~E(x51561,f334(a119,f2(a927)))+E(f334(f334(f86(a927),x51561),x51562),f334(a119,f2(a927))) % 188.18/188.26 [5157]~E(x51571,f2(a927))+~E(x51572,f334(a119,f2(a927)))+E(f334(f334(f86(a927),x51571),x51572),f334(a119,f2(a927))) % 188.18/188.26 [5164]E(x51641,f84(a1))+E(x51642,f334(f111(a1),a104))+~E(f334(f334(f87(a1),x51641),x51642),f84(a1)) % 188.18/188.26 [5165]E(x51651,f84(a1))+E(x51652,f334(f111(a1),a104))+~E(f334(f334(f87(a1),x51652),x51651),f84(a1)) % 188.18/188.26 [5166]E(x51661,f84(a1))+E(x51661,f334(f111(a1),a104))+~E(f334(f334(f87(a1),x51662),x51661),f84(a1)) % 188.18/188.26 [5168]E(x51681,f84(a1))+E(x51681,f334(f111(a1),a104))+~E(f334(f334(f87(a1),x51681),x51682),f84(a1)) % 188.18/188.26 [5189]~P77(x51892)+E(x51891,f2(x51892))+~E(f334(f334(f86(x51892),x51891),x51891),f2(x51892)) % 188.18/188.26 [5195]~E(x51951,f334(f111(a1),a104))+~E(x51952,f334(f111(a1),a104))+E(f334(f334(f87(a1),x51951),x51952),f84(a1)) % 188.18/188.26 [5206]E(x52061,f2(a927))+E(x52062,f2(a927))+~E(f334(f334(f86(a927),x52062),x52061),f334(a119,f2(a927))) % 188.18/188.26 [5216]~P95(x52161)+~P65(x52161)+E(f334(f334(f296(x52161),x52162),f334(f111(x52161),a89)),f2(x52161)) % 188.18/188.26 [5222]~P141(x52221)+~E(x52222,f334(f85(x52221),f84(x52221)))+E(f334(f334(f87(x52221),x52222),x52222),f84(x52221)) % 188.18/188.26 [5227]~P8(x52272)+~P8(x52271)+P8(f334(f334(f87(a1),x52271),x52272)) % 188.18/188.26 [5228]~P8(x52282)+~P8(x52281)+P8(f334(f334(f86(a1),x52281),x52282)) % 188.18/188.26 [5229]~P8(x52292)+~P8(x52291)+P8(f334(f334(f41(a1),x52291),x52292)) % 188.18/188.26 [5231]~E(x52312,f2(a1))+E(x52311,f2(a1))+E(f51(x52311,x52312),f334(f334(f260(a1,a1),f2(a1)),x52311)) % 188.18/188.26 [5253]~E(x52532,f334(a119,f2(a927)))+~E(x52531,f334(a119,f2(a927)))+E(f334(f334(f87(a927),x52531),x52532),f334(a119,f2(a927))) % 188.18/188.26 [5270]E(x52701,f2(a927))+E(x52702,f334(a119,f2(a927)))+~E(f334(f334(f252(a927),x52702),x52701),f334(a119,f2(a927))) % 188.18/188.26 [5271]E(x52711,f2(a927))+E(x52711,f334(a119,f2(a927)))+~E(f334(f334(f86(a927),x52712),x52711),f334(a119,f2(a927))) % 188.18/188.26 [5272]E(x52721,f2(a927))+E(x52721,f334(a119,f2(a927)))+~E(f334(f334(f86(a927),x52721),x52722),f334(a119,f2(a927))) % 188.18/188.26 [5281]~P95(x52811)+~P65(x52811)+E(f334(f334(f296(x52811),x52812),f334(f111(x52811),a104)),f334(f85(x52811),x52812)) % 188.18/188.26 [5300]E(x53001,f334(a112,x53002))+~E(x53001,f2(a927))+P107(f334(f334(f242(a1),f2(a1)),x53002)) % 188.18/188.26 [5301]E(f334(a112,x53011),x53012)+~E(x53012,f2(a927))+P107(f334(f334(f242(a1),f2(a1)),x53011)) % 188.18/188.26 [5317]E(x53171,f334(a119,f2(a927)))+E(x53172,f334(a119,f2(a927)))+~E(f334(f334(f86(a927),x53171),x53172),f334(a119,f2(a927))) % 188.18/188.26 [5328]~E(x53281,f334(a112,x53282))+E(x53281,f2(a927))+P107(f334(f334(f242(a1),f2(a1)),x53282)) % 188.18/188.26 [5329]~E(f334(a112,x53292),x53291)+E(x53291,f2(a927))+P107(f334(f334(f242(a1),f2(a1)),x53292)) % 188.18/188.26 [5351]~P109(x53511)+E(f334(f68(x53511,f246(x53511)),x53512),f14(x53511,x53512))+~P107(f334(f66(x53511),x53512)) % 188.18/188.26 [5352]~P109(x53521)+E(f334(f68(x53521,f241(x53521)),x53522),f15(x53521,x53522))+~P107(f334(f66(x53521),x53522)) % 188.18/188.26 [5353]~P99(x53531)+E(f334(f68(x53531,f109(x53531)),x53532),f10(x53531,x53532))+~P107(f334(f66(x53531),x53532)) % 188.18/188.26 [5354]~P99(x53541)+E(f334(f68(x53541,f108(x53541)),x53542),f13(x53541,x53542))+~P107(f334(f66(x53541),x53542)) % 188.18/188.26 [5431]E(x54311,x54312)+~E(f334(f334(f23(a927),x54312),x54311),f2(a927))+~E(f334(f334(f23(a927),x54311),x54312),f2(a927)) % 188.18/188.26 [5448]P8(x54481)+~P42(x54482)+~P107(f334(f334(f336(a1),x54481),x54482)) % 188.18/188.26 [5480]~P124(x54801)+~E(f88(x54801,x54802),f84(x54801))+P107(f334(f334(f243(x54801),f2(x54801)),x54802)) % 188.18/188.26 [5491]~P95(x54911)+E(f334(f107(x54911),f334(f111(a927),x54912)),f334(f111(x54911),x54912))+P107(f334(a200,f334(f111(a1),x54912))) % 188.18/188.26 [5496]~P46(x54961,x54962)+P47(a922)+P107(f334(f66(f934(x54961,x54961)),x54962)) % 188.18/188.26 [5569]~P109(x55691)+E(f334(f68(x55691,f246(x55691)),x55692),f11(x55691,f246(x55691),x55692))+~P107(f334(f66(x55691),x55692)) % 188.18/188.26 [5570]~P109(x55701)+E(f334(f68(x55701,f241(x55701)),x55702),f12(x55701,f241(x55701),x55702))+~P107(f334(f66(x55701),x55702)) % 188.18/188.26 [5584]E(x55841,x55842)+P107(f334(f334(f243(a927),x55842),x55841))+P107(f334(f334(f243(a927),x55841),x55842)) % 188.18/188.26 [5585]E(x55851,x55852)+P107(f334(f334(f243(a1),x55852),x55851))+P107(f334(f334(f243(a1),x55851),x55852)) % 188.18/188.26 [5637]~P95(x56371)+E(f334(f107(x56371),f334(f111(a927),x56372)),f2(x56371))+~P107(f334(a200,f334(f111(a1),x56372))) % 188.18/188.26 [5640]~E(x56402,f334(a112,x56401))+E(x56401,f334(f107(a1),x56402))+~P107(f334(f334(f242(a1),f2(a1)),x56401)) % 188.18/188.26 [5641]~E(f334(a112,x56411),x56412)+E(x56411,f334(f107(a1),x56412))+~P107(f334(f334(f242(a1),f2(a1)),x56411)) % 188.18/188.26 [5642]~E(x56421,f334(a112,x56422))+E(f334(f107(a1),x56421),x56422)+~P107(f334(f334(f242(a1),f2(a1)),x56422)) % 188.18/188.26 [5652]E(x56521,f334(a112,x56522))+~E(x56522,f334(f107(a1),x56521))+~P107(f334(f334(f242(a1),f2(a1)),x56522)) % 188.18/188.26 [5653]E(f334(a112,x56531),x56532)+~E(x56531,f334(f107(a1),x56532))+~P107(f334(f334(f242(a1),f2(a1)),x56531)) % 188.18/188.26 [5694]~P86(x56942)+E(x56941,f2(x56942))+P107(f334(f334(f243(x56942),f2(x56942)),f334(f81(x56942),x56941))) % 188.18/188.26 [5757]~P124(x57571)+E(f88(x57571,x57572),f84(x57571))+~P107(f334(f334(f243(x57571),f2(x57571)),x57572)) % 188.18/188.26 [5761]~P95(x57611)+E(f334(f107(x57611),f334(f111(a927),x57612)),f2(x57611))+P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x57612))) % 188.18/188.26 [5772]~P86(x57721)+E(f334(f81(x57721),x57722),x57722)+~P107(f334(f334(f242(x57721),f2(x57721)),x57722)) % 188.18/188.26 [5773]~P86(x57731)+E(f334(f81(x57731),x57732),x57732)+~P107(f334(f334(f243(x57731),f2(x57731)),x57732)) % 188.18/188.26 [5782]E(x57821,f2(a927))+~E(f146(a927,f334(f310(a927,x57822),x57821)),f120(a927))+P107(f334(f334(f242(a927),x57821),x57822)) % 188.18/188.26 [5794]~P76(x57941)+E(f334(f334(f6(x57941,x57941),f5(x57941)),f334(f179(x57941),x57942)),f334(f172(x57941),x57942))+~P107(f334(f144(x57941),x57942)) % 188.18/188.26 [5797]~P142(x57971)+E(f334(f107(x57971),f334(a112,x57972)),f334(f110(x57971),x57972))+~P107(f334(f334(f242(a1),f2(a1)),x57972)) % 188.18/188.26 [5825]E(x58251,x58252)+P107(f334(f334(f243(a927),x58251),x58252))+~P107(f334(f334(f242(a927),x58251),x58252)) % 188.18/188.26 [5826]E(x58261,x58262)+P107(f334(f334(f243(a1),x58261),x58262))+~P107(f334(f334(f242(a1),x58261),x58262)) % 188.18/188.26 [5829]E(x58291,f84(a1))+~E(f334(f334(f87(a1),x58292),x58291),f84(a1))+~P107(f334(f334(f243(a1),f2(a1)),x58292)) % 188.18/188.26 [5830]E(x58301,f84(a1))+~E(f334(f334(f87(a1),x58301),x58302),f84(a1))+~P107(f334(f334(f243(a1),f2(a1)),x58301)) % 188.18/188.26 [5875]~P42(x58752)+P107(f334(f334(f242(a1),f2(a1)),x58751))+~P107(f334(f334(f336(a1),x58751),x58752)) % 188.18/188.26 [5894]~P61(x58941,x58942)+P39(x58941,x58942)+~P107(f334(f66(f934(x58941,x58941)),x58942)) % 188.18/188.26 [5896]~P61(x58961,x58962)+P46(x58961,x58962)+~P107(f334(f66(f934(x58961,x58961)),x58962)) % 188.18/188.26 [5940]E(x59401,f195(f935(x59402,a922)))+~P107(f334(f66(x59402),x59401))+P107(f334(f334(f243(a927),f2(a927)),f334(f40(x59402),x59401))) % 188.18/188.26 [5967]~P107(f334(x59671,x59672))+P107(f334(x59671,f2(a927)))+P107(f334(f334(f243(a927),f889(x59672,x59671)),x59672)) % 188.18/188.26 [5990]E(x59901,f2(a927))+~E(f334(f172(a927),x59902),f2(a927))+~P107(f334(f334(f336(a927),x59901),f334(f179(a927),x59902))) % 188.18/188.26 [6058]E(x60581,x60582)+~P107(f334(f334(f242(a927),x60582),x60581))+~P107(f334(f334(f242(a927),x60581),x60582)) % 188.18/188.26 [6059]E(x60591,x60592)+~P107(f334(f334(f242(a1),x60592),x60591))+~P107(f334(f334(f242(a1),x60591),x60592)) % 188.18/188.26 [6061]E(f334(f40(x60611),x60612),f2(a927))+~P107(f334(f66(x60611),x60612))+P107(f334(f334(f336(x60611),f890(x60612,x60611)),x60612)) % 188.18/188.26 [6070]E(f55(x60701,x60702),f51(x60701,x60702))+P107(f334(f334(f242(a1),f2(a1)),x60701))+~P107(f334(f334(f243(a1),f2(a1)),x60702)) % 188.18/188.26 [6098]~P107(f334(x60981,f902(x60981)))+P107(f334(x60981,f334(a112,x60982)))+~P107(f334(f334(f242(a1),f2(a1)),x60982)) % 188.18/188.26 [6101]P107(f334(f334(f242(a927),x61011),f748(x61012)))+~P107(f334(f66(a927),x61012))+~P107(f334(f334(f336(a927),x61011),x61012)) % 188.18/188.26 [6102]P107(f334(f334(f243(a927),x61021),f795(x61022)))+~P107(f334(f66(a927),x61022))+~P107(f334(f334(f336(a927),x61021),x61022)) % 188.18/188.26 [6134]E(x61341,x61342)+~P107(f334(f334(f243(a927),x61341),f334(a119,x61342)))+P107(f334(f334(f243(a927),x61341),x61342)) % 188.18/188.26 [6166]E(x61661,f334(a119,x61662))+~P107(f334(f334(f242(a927),x61661),f334(a119,x61662)))+P107(f334(f334(f242(a927),x61661),x61662)) % 188.18/188.26 [6181]P107(f334(x61811,f903(x61811)))+~P107(f334(x61811,f334(a112,x61812)))+~P107(f334(f334(f242(a1),f2(a1)),x61812)) % 188.18/188.26 [6196]~P107(f334(x61961,x61962))+~P107(f334(f334(f242(a1),f2(a1)),x61962))+P107(f334(x61961,f334(f107(a1),f896(x61961)))) % 188.18/188.26 [6207]~P86(x62072)+~E(x62071,f2(x62072))+~P107(f334(f334(f243(x62072),f2(x62072)),f334(f81(x62072),x62071))) % 188.18/188.26 [6231]~P61(x62311,x62312)+P39(x62311,f334(f293(x62311,x62311),x62312))+~P107(f334(f66(f934(x62311,x62311)),x62312)) % 188.18/188.26 [6232]~P59(a927,x62321,x62322)+~P107(f334(f334(f243(a927),f2(a927)),x62322))+P107(f334(f334(f242(a927),x62321),x62322)) % 188.18/188.26 [6240]~P95(x62401)+E(f334(f107(x62401),f334(f111(a927),x62402)),f334(f111(x62401),x62402))+~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x62402))) % 188.18/188.26 [6243]E(f334(a119,x62431),x62432)+~P107(f334(f334(f243(a927),x62431),x62432))+P107(f334(f334(f243(a927),f334(a119,x62431)),x62432)) % 188.18/188.26 [6260]E(f334(f334(f41(a1),x62601),x62602),f2(a1))+~P107(f334(f334(f242(a1),x62601),f2(a1)))+~P107(f334(f334(f243(a1),x62602),x62601)) % 188.18/188.26 [6270]E(f50(a1,x62701,x62702),x62701)+~P107(f334(f334(f242(a1),x62701),f2(a1)))+~P107(f334(f334(f243(a1),x62702),x62701)) % 188.18/188.26 [6284]E(f52(x62841,x62842),f51(x62841,x62842))+~P107(f334(f334(f242(a1),f2(a1)),x62841))+~P107(f334(f334(f242(a1),f2(a1)),x62842)) % 188.18/188.26 [6294]E(f334(f334(f41(a1),x62941),x62942),f2(a1))+~P107(f334(f334(f242(a1),f2(a1)),x62941))+~P107(f334(f334(f243(a1),x62941),x62942)) % 188.18/188.26 [6303]E(f50(a927,f334(f111(a927),x63031),f334(f111(a927),x63032)),f334(f111(a927),x63031))+P107(f334(a200,f334(f111(a1),x63031)))+~P107(f334(a200,f334(f111(a1),x63032))) % 188.18/188.26 [6305]E(f50(a1,x63051,x63052),x63051)+~P107(f334(f334(f242(a1),f2(a1)),x63051))+~P107(f334(f334(f243(a1),x63051),x63052)) % 188.18/188.26 [6306]E(x63061,x63062)+~P107(f334(f334(f243(a927),x63061),f334(a119,x63062)))+~P107(f334(f334(f242(a927),x63062),x63061)) % 188.18/188.26 [6320]~P77(x63201)+~P107(f334(f334(f242(x63201),x63202),f2(x63201)))+P107(f334(f334(f242(x63201),x63202),f334(f85(x63201),x63202))) % 188.18/188.26 [6321]~P124(x63211)+~P107(f334(f334(f243(x63211),x63212),f2(x63211)))+P107(f334(f334(f243(x63211),x63212),f334(f85(x63211),x63212))) % 188.18/188.26 [6330]~P7(x63301)+E(f334(f334(f69(x63301,x63301,f109(x63301)),f250(x63301)),x63302),f43(x63301,x63302))+~P107(f334(f66(x63301),x63302)) % 188.18/188.26 [6331]~P7(x63311)+E(f334(f334(f69(x63311,x63311,f108(x63311)),f195(x63311)),x63312),f42(x63311,x63312))+~P107(f334(f66(x63311),x63312)) % 188.18/188.26 [6348]~P124(x63481)+~P107(f334(f334(f242(a1),f2(a1)),x63482))+P107(f334(f334(f242(x63481),f2(x63481)),f334(f110(x63481),x63482))) % 188.18/188.26 [6349]~P127(x63491)+~P107(f334(f334(f243(a927),f2(a927)),x63492))+P107(f334(f334(f243(x63491),f2(x63491)),f334(f107(x63491),x63492))) % 188.18/188.26 [6350]~P124(x63501)+~P107(f334(f334(f243(a1),f2(a1)),x63502))+P107(f334(f334(f243(x63501),f2(x63501)),f334(f110(x63501),x63502))) % 188.18/188.26 [6353]~P8(x63532)+~P8(x63531)+E(f334(f317(a927,a1,f107(a1)),f311(a927,f334(a112,x63531),f334(a112,x63532))),f311(a1,x63531,x63532)) % 188.18/188.26 [6359]P107(f334(x63591,x63592))+~P107(f334(f334(f242(a1),f2(a1)),x63592))+~P107(f334(x63591,f334(f107(a1),f897(x63591)))) % 188.18/188.26 [6388]E(f334(f334(f86(a927),f334(f111(a927),x63881)),f334(f111(a927),x63882)),f334(f111(a927),x63881))+P107(f334(f334(f243(a1),x63881),a89))+~P107(f334(f334(f243(a1),x63882),a89)) % 188.18/188.26 [6394]~P124(x63941)+P107(f334(f334(f243(x63941),f2(x63941)),f88(x63941,x63942)))+~P107(f334(f334(f243(x63941),f2(x63941)),x63942)) % 188.18/188.26 [6406]~P79(x64061)+~P107(f334(f334(f242(x64061),x64062),f2(x64061)))+P107(f334(f334(f242(x64061),f2(x64061)),f334(f85(x64061),x64062))) % 188.18/188.26 [6407]~P79(x64071)+~P107(f334(f334(f243(x64071),x64072),f2(x64071)))+P107(f334(f334(f243(x64071),f2(x64071)),f334(f85(x64071),x64072))) % 188.18/188.26 [6410]E(x64101,f250(f935(x64102,a922)))+~E(f334(f40(x64102),x64101),f334(f40(x64102),f250(f935(x64102,a922))))+~P107(f334(f66(x64102),f250(f935(x64102,a922)))) % 188.18/188.26 [6438]~P77(x64381)+P107(f334(f334(f242(x64381),x64382),f2(x64381)))+~P107(f334(f334(f242(x64381),x64382),f334(f85(x64381),x64382))) % 188.18/188.26 [6439]~P124(x64391)+P107(f334(f334(f243(x64391),x64392),f2(x64391)))+~P107(f334(f334(f243(x64391),x64392),f334(f85(x64391),x64392))) % 188.18/188.26 [6448]~P95(x64481)+P107(f334(f334(f336(x64481),f334(f111(x64481),x64482)),f193(x64481)))+~P107(f334(f334(f242(a1),a89),x64482)) % 188.18/188.26 [6477]E(x64771,f2(a927))+~P107(f334(f334(f243(a927),x64771),f334(a119,x64772)))+P107(f334(f334(f243(a927),f883(x64772,x64771)),x64772)) % 188.18/188.26 [6500]~P124(x65001)+~P107(f334(f334(f243(x65001),f2(x65001)),f88(x65001,x65002)))+P107(f334(f334(f243(x65001),f2(x65001)),x65002)) % 188.18/188.26 [6502]~E(f334(f111(a927),x65022),f334(f111(a927),x65021))+P107(f334(f334(f242(a1),f334(f111(a1),x65021)),f2(a1)))+~P107(f334(a200,f334(f111(a1),x65022))) % 188.18/188.26 [6531]E(f334(f259(a1,a1),f55(x65311,x65312)),f334(f334(f41(a1),x65311),x65312))+~P107(f334(f334(f243(a1),x65311),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x65312)) % 188.18/188.26 [6567]E(f334(f264(a1,a1),f55(x65671,x65672)),f50(a1,x65671,x65672))+~P107(f334(f334(f243(a1),x65671),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x65672)) % 188.18/188.26 [6571]~P124(x65712)+~P107(f334(f334(f242(x65712),f2(x65712)),f334(f110(x65712),x65711)))+P107(f334(f334(f242(a1),f2(a1)),x65711)) % 188.18/188.26 [6572]~P127(x65722)+~P107(f334(f334(f243(x65722),f2(x65722)),f334(f107(x65722),x65721)))+P107(f334(f334(f243(a927),f2(a927)),x65721)) % 188.18/188.26 [6573]~P124(x65732)+~P107(f334(f334(f243(x65732),f2(x65732)),f334(f110(x65732),x65731)))+P107(f334(f334(f243(a1),f2(a1)),x65731)) % 188.18/188.26 [6576]E(f334(f259(a1,a1),f52(x65761,x65762)),f334(f334(f41(a1),x65761),x65762))+~P107(f334(f334(f242(a1),f2(a1)),x65762))+~P107(f334(f334(f243(a1),f2(a1)),x65761)) % 188.18/188.26 [6588]E(f334(f264(a1,a1),f52(x65881,x65882)),f50(a1,x65881,x65882))+~P107(f334(f334(f242(a1),f2(a1)),x65882))+~P107(f334(f334(f243(a1),f2(a1)),x65881)) % 188.18/188.26 [6603]~P79(x66031)+P107(f334(f334(f242(x66031),x66032),f2(x66031)))+~P107(f334(f334(f242(x66031),f2(x66031)),f334(f85(x66031),x66032))) % 188.18/188.26 [6604]~P79(x66041)+P107(f334(f334(f243(x66041),x66042),f2(x66041)))+~P107(f334(f334(f243(x66041),f2(x66041)),f334(f85(x66041),x66042))) % 188.18/188.26 [6633]P107(f334(f54(x66331,x66332),f55(x66331,x66332)))+~P107(f334(f334(f243(a1),x66331),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x66332)) % 188.18/188.26 [6657]P107(f334(f54(x66571,x66572),f52(x66571,x66572)))+~P107(f334(f334(f242(a1),f2(a1)),x66571))+~P107(f334(f334(f243(a1),f2(a1)),x66572)) % 188.18/188.26 [6703]~P79(x67031)+P107(f334(f334(f242(x67031),f334(f85(x67031),x67032)),f2(x67031)))+~P107(f334(f334(f242(x67031),f2(x67031)),x67032)) % 188.18/188.26 [6704]~P79(x67041)+P107(f334(f334(f243(x67041),f334(f85(x67041),x67042)),f2(x67041)))+~P107(f334(f334(f243(x67041),f2(x67041)),x67042)) % 188.18/188.26 [6720]E(f334(f334(f23(a927),f334(a112,x67201)),f334(a112,x67202)),f334(a112,f201(x67201,x67202)))+~P107(f334(f334(f242(a1),f2(a1)),x67202))+~P107(f334(f334(f242(a1),f2(a1)),x67201)) % 188.18/188.26 [6738]P107(f334(f334(f242(a1),f2(a1)),f201(x67381,x67382)))+~P107(f334(f334(f242(a1),f2(a1)),x67382))+~P107(f334(f334(f242(a1),f2(a1)),x67381)) % 188.18/188.26 [6772]~P107(f334(x67721,x67722))+P107(f334(x67721,f2(a927)))+P107(f334(x67721,f334(f334(f86(a927),f889(x67722,x67721)),f84(a927)))) % 188.18/188.26 [6856]E(f334(f111(a927),x68561),f334(f111(a927),x68562))+~P107(f334(f334(f242(a1),f334(f111(a1),x68562)),f2(a1)))+~P107(f334(a200,f334(f111(a1),x68561))) % 188.18/188.26 [6866]~E(x68661,f2(a927))+~E(f689(x68662,x68661),f2(a927))+E(f334(f149(a927,a927,f86(a927),x68661),x68662),f2(a927)) % 188.18/188.26 [6890]~P107(f334(f66(x68901),f529(x68902,x68901)))+~P107(f334(f66(f935(x68901,a922)),x68902))+P107(f334(f66(x68901),f42(f935(x68901,a922),x68902))) % 188.18/188.26 [6896]E(x68961,x68962)+P107(f334(f334(f243(a1),x68961),x68962))+~P107(f334(f334(f243(a1),x68961),f334(f334(f86(a1),x68962),f84(a1)))) % 188.18/188.26 [6897]P107(f334(f334(f242(a927),f334(a112,x68971)),f334(a112,x68972)))+~P107(f334(f334(f242(a1),f2(a1)),x68972))+~P107(f334(f334(f242(a1),x68971),x68972)) % 188.18/188.26 [6898]P107(f334(f334(f242(a927),f334(a112,x68981)),f334(a112,x68982)))+~P107(f334(f334(f243(a1),f2(a1)),x68981))+~P107(f334(f334(f242(a1),x68981),x68982)) % 188.18/188.26 [6900]P107(f334(f334(f243(a927),f334(a112,x69001)),f334(a112,x69002)))+~P107(f334(f334(f242(a1),f2(a1)),x69001))+~P107(f334(f334(f243(a1),x69001),x69002)) % 188.18/188.26 [6901]P107(f334(f334(f243(a927),f334(a112,x69011)),f334(a112,x69012)))+~P107(f334(f334(f243(a1),f2(a1)),x69012))+~P107(f334(f334(f243(a1),x69011),x69012)) % 188.18/188.26 [6912]E(f50(a927,f334(a112,x69121),f334(a112,x69122)),f334(a112,f50(a1,x69121,x69122)))+~P107(f334(f334(f242(a1),f2(a1)),x69122))+~P107(f334(f334(f242(a1),f2(a1)),x69121)) % 188.18/188.26 [6936]~P79(x69361)+~P107(f334(f334(f242(x69361),f334(f85(x69361),x69362)),f2(x69361)))+P107(f334(f334(f242(x69361),f2(x69361)),x69362)) % 188.18/188.26 [6937]~P79(x69371)+~P107(f334(f334(f243(x69371),f334(f85(x69371),x69372)),f2(x69371)))+P107(f334(f334(f243(x69371),f2(x69371)),x69372)) % 188.18/188.26 [6951]~P107(f334(f334(f243(a1),a89),x69512))+~P107(f334(f334(f243(a1),x69511),x69512))+P107(f334(f334(f243(a927),f334(f111(a927),x69511)),f334(f111(a927),x69512))) % 188.18/188.26 [7036]~P107(f334(f334(f242(a1),f2(a1)),x70361))+P107(f334(f334(f243(a927),f334(a112,x70361)),x70362))+~P107(f334(f334(f243(a1),x70361),f334(f107(a1),x70362))) % 188.18/188.26 [7041]P107(f334(x70411,x70412))+~P107(f334(x70411,f334(a20,f831(x70411,x70412))))+~P107(f334(f334(f336(a927),x70412),f250(f935(a927,a922)))) % 188.18/188.26 [7052]E(x70521,f2(a1))+E(f50(a1,x70522,x70521),f2(a1))+E(f334(f334(f23(a1),f334(f85(a1),f334(f334(f41(a1),x70522),x70521))),f84(a1)),f334(f334(f41(a1),x70522),f334(f85(a1),x70521))) % 188.18/188.26 [7064]~P107(f334(f334(f242(a1),f2(a1)),x70641))+~P107(f334(f334(f243(a927),f334(a112,x70641)),x70642))+P107(f334(f334(f243(a1),x70641),f334(f107(a1),x70642))) % 188.18/188.26 [7098]~P107(f334(f334(f242(a927),f334(a112,x70981)),f334(a112,x70982)))+~P107(f334(f334(f242(a1),f2(a1)),x70982))+P107(f334(f334(f242(a1),x70981),x70982)) % 188.18/188.26 [7099]~P107(f334(f334(f242(a927),f334(a112,x70991)),f334(a112,x70992)))+~P107(f334(f334(f243(a1),f2(a1)),x70991))+P107(f334(f334(f242(a1),x70991),x70992)) % 188.18/188.26 [7129]P107(f334(f334(f242(a1),x71291),x71292))+~P107(f334(f334(f242(a927),f334(f111(a927),x71291)),f334(f111(a927),x71292)))+P107(f334(f334(f242(a1),x71291),a89)) % 188.18/188.26 [7154]P107(f334(f334(f242(a1),f2(a1)),f50(a1,x71541,x71542)))+~P107(f334(f334(f242(a1),f2(a1)),x71542))+~P107(f334(f334(f242(a1),f2(a1)),x71541)) % 188.18/188.26 [7250]P107(f334(f334(f243(a1),a89),x72501))+~P107(f334(f334(f243(a1),x72502),x72501))+~P107(f334(f334(f243(a927),f334(f111(a927),x72502)),f334(f111(a927),x72501))) % 188.18/188.26 [7303]E(f334(f334(f260(a1,a1),f334(f334(f41(a1),x73031),x73032)),f50(a1,x73031,x73032)),f55(x73031,x73032))+~P107(f334(f334(f243(a1),x73031),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x73032)) % 188.18/188.26 [7322]E(f334(f334(f260(a1,a1),f334(f334(f41(a1),x73221),x73222)),f50(a1,x73221,x73222)),f52(x73221,x73222))+~P107(f334(f334(f242(a1),f2(a1)),x73222))+~P107(f334(f334(f242(a1),f2(a1)),x73221)) % 188.18/188.26 [7374]~P96(x73742)+E(x73741,f120(x73742))+E(f334(f149(x73742,x73742,f87(x73742),f334(f148(x73742),x73741)),f334(f178(x73742),x73741)),f334(f68(x73742,f87(x73742)),f334(f179(x73742),x73741))) % 188.18/188.26 [7490]~E(x74901,f2(a927))+E(f334(f149(a927,a927,f86(a927),x74901),x74902),f2(a927))+P107(f334(f334(f336(a927),f689(x74902,x74901)),f334(f179(a927),x74902))) % 188.18/188.26 [7539]~P107(f334(f334(f242(a1),x75391),f2(a1)))+P107(f334(f334(f242(a1),f334(f334(f41(a1),x75391),x75392)),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x75392)) % 188.18/188.26 [7540]~P107(f334(f334(f243(a1),x75402),f2(a1)))+P107(f334(f334(f242(a1),f334(f334(f41(a1),x75401),x75402)),f2(a1)))+~P107(f334(f334(f242(a1),f2(a1)),x75401)) % 188.18/188.26 [7541]~P107(f334(f334(f243(a1),x75412),f2(a1)))+P107(f334(f334(f243(a1),f334(f334(f41(a1),x75411),x75412)),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x75411)) % 188.18/188.26 [7543]~P107(f334(f334(f243(a1),x75431),f2(a1)))+P107(f334(f334(f243(a1),f334(f334(f41(a1),x75431),x75432)),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x75432)) % 188.18/188.26 [7550]P107(f334(f334(f336(f935(x75501,a922)),f529(x75502,x75501)),x75502))+~P107(f334(f66(f935(x75501,a922)),x75502))+P107(f334(f66(x75501),f42(f935(x75501,a922),x75502))) % 188.18/188.26 [7631]P27(x76311,x76311,x76312,f250(f935(x76311,a922)))+~E(f334(f317(x76311,x76311,x76312),f250(f935(x76311,a922))),f250(f935(x76311,a922)))+~P107(f334(f66(x76311),f250(f935(x76311,a922)))) % 188.18/188.26 [7750]~P27(x77501,x77501,x77502,f250(f935(x77501,a922)))+E(f334(f317(x77501,x77501,x77502),f250(f935(x77501,a922))),f250(f935(x77501,a922)))+~P107(f334(f66(x77501),f250(f935(x77501,a922)))) % 188.18/188.26 [7884]E(f334(f334(f41(a1),x78841),x78842),f334(f111(a1),a104))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),x78841),x78842)),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x78841)) % 188.18/188.26 [7940]~P107(f334(f334(f243(a1),x79402),f2(a1)))+~P107(f334(f334(f243(a1),f334(f334(f41(a1),x79401),x79402)),f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x79401)) % 188.18/188.26 [7946]E(f334(f334(f86(a1),x79461),x79462),f50(a1,x79461,x79462))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),x79461),x79462)),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x79461)) % 188.18/188.26 [7949]P107(f334(f334(f243(a1),x79491),f2(a1)))+~P107(f334(f334(f243(a1),f334(f334(f41(a1),x79491),x79492)),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x79492)) % 188.18/188.26 [8627]~P109(x86271)+P15(x86271,x86272)+~P107(f334(f334(f242(x86271),f334(f334(f171(x86271),x86272),f722(x86272,x86271))),f334(f334(f171(x86271),x86272),f723(x86272,x86271)))) % 188.18/188.26 [8628]~P109(x86281)+P15(x86281,x86282)+~P107(f334(f334(f242(x86281),f334(f334(f171(x86281),x86282),f730(x86282,x86281))),f334(f334(f171(x86281),x86282),f734(x86282,x86281)))) % 188.18/188.26 [5933]E(x59331,f2(a1))+~E(f50(a1,x59332,x59331),f2(a1))+E(f334(f334(f41(a1),x59332),f334(f85(a1),x59331)),f334(f85(a1),f334(f334(f41(a1),x59332),x59331))) % 188.18/188.26 [5951]~P42(x59512)+~P42(x59511)+P42(f334(f334(f108(f935(a1,a922)),x59511),x59512)) % 188.18/188.26 [5952]~P42(x59522)+~P42(x59521)+P42(f334(f334(f109(f935(a1,a922)),x59521),x59522)) % 188.18/188.26 [5970]~P95(x59701)+~P65(x59701)+E(f334(f85(x59701),f334(f334(f296(x59701),f84(x59701)),x59702)),f334(f334(f296(x59701),f334(f111(x59701),a104)),x59702)) % 188.18/188.26 [6088]E(x60881,f2(a1))+~E(f50(a1,x60882,x60881),f2(a1))+E(f334(f334(f41(a1),f334(f85(a1),x60882)),x60881),f334(f85(a1),f334(f334(f41(a1),x60882),x60881))) % 188.18/188.26 [6225]~P109(x62251)+P15(x62251,x62252)+P107(f334(f334(f243(a927),f723(x62252,x62251)),f334(f196(f928(x62251)),x62252))) % 188.18/188.26 [6226]~P109(x62261)+P15(x62261,x62262)+P107(f334(f334(f243(a927),f734(x62262,x62261)),f334(f196(f928(x62261)),x62262))) % 188.18/188.26 [6382]~P95(x63821)+~E(f334(f111(x63821),x63822),f2(x63821))+P30(x63821,f334(f111(x63821),f334(f334(f86(a1),x63822),f334(f85(a1),a89)))) % 188.18/188.26 [6383]~P95(x63831)+~E(f334(f111(x63831),x63832),f2(x63831))+P30(x63831,f334(f111(x63831),f334(f334(f86(a1),a89),f334(f85(a1),x63832)))) % 188.18/188.26 [6385]E(f334(a56,f52(f334(f85(a1),x63851),f334(f85(a1),x63852))),f51(x63851,x63852))+P107(f334(f334(f242(a1),f2(a1)),x63851))+P107(f334(f334(f243(a1),f2(a1)),x63852)) % 188.18/188.26 [6508]~E(x65082,f2(a927))+~E(x65081,f2(a927))+P107(f334(f334(f242(a1),f334(f107(a1),x65081)),f334(f85(a1),f334(f107(a1),x65082)))) % 188.18/188.26 [6537]E(f334(f334(f86(a927),f334(f111(a927),x65371)),f334(f111(a927),x65372)),f334(f111(a927),f334(f334(f86(a1),x65371),x65372)))+P107(f334(f334(f243(a1),x65371),a89))+P107(f334(f334(f243(a1),x65372),a89)) % 188.18/188.26 [6667]~P77(x66671)+~P107(f334(f334(f242(x66671),f2(x66671)),x66672))+P107(f334(f334(f242(x66671),f334(f85(x66671),x66672)),x66672)) % 188.18/188.26 [6668]~P77(x66681)+~P107(f334(f334(f243(x66681),f2(x66681)),x66682))+P107(f334(f334(f243(x66681),f334(f85(x66681),x66682)),x66682)) % 188.18/188.26 [6842]E(f334(f334(f23(a927),f334(a112,x68421)),f334(a112,x68422)),f334(a112,f334(f334(f23(a1),x68421),x68422)))+~P107(f334(f334(f242(a1),f2(a1)),x68422))+~P107(f334(f334(f242(a1),x68422),x68421)) % 188.18/188.26 [6874]E(f334(a112,f50(a1,f334(f111(a1),x68741),f334(f111(a1),x68742))),f50(a927,f334(f111(a927),x68741),f334(f111(a927),x68742)))+P107(f334(a200,f334(f111(a1),x68741)))+P107(f334(a200,f334(f111(a1),x68742))) % 188.18/188.26 [6891]~P77(x68911)+P107(f334(f334(f242(x68911),f2(x68911)),x68912))+~P107(f334(f334(f242(x68911),f334(f85(x68911),x68912)),x68912)) % 188.18/188.26 [6892]~P77(x68921)+P107(f334(f334(f243(x68921),f2(x68921)),x68922))+~P107(f334(f334(f243(x68921),f334(f85(x68921),x68922)),x68922)) % 188.18/188.26 [6904]~P77(x69041)+~P107(f334(f334(f242(x69041),f2(x69041)),x69042))+P107(f334(f334(f242(x69041),f2(x69041)),f334(f334(f86(x69041),x69042),x69042))) % 188.18/188.26 [6906]~P77(x69061)+~P107(f334(f334(f243(x69061),f2(x69061)),x69062))+P107(f334(f334(f243(x69061),f2(x69061)),f334(f334(f86(x69061),x69062),x69062))) % 188.18/188.26 [6919]E(f334(f334(f86(a927),f334(a112,x69191)),f334(a112,x69192)),f334(a112,f334(f334(f86(a1),x69191),x69192)))+~P107(f334(f334(f242(a1),f2(a1)),x69192))+~P107(f334(f334(f242(a1),f2(a1)),x69191)) % 188.18/188.26 [6930]E(x69301,f2(a927))+P107(f334(f334(f243(a927),f2(a927)),x69302))+~P107(f334(f334(f243(a927),f2(a927)),f334(f334(f252(a927),x69302),x69301))) % 188.18/188.26 [6961]~P95(x69611)+E(f334(f111(x69611),x69612),f2(x69611))+~P30(x69611,f334(f111(x69611),f334(f334(f86(a1),a89),f334(f85(a1),x69612)))) % 188.18/188.26 [6962]~P95(x69621)+E(f334(f111(x69621),x69622),f2(x69621))+~P30(x69621,f334(f111(x69621),f334(f334(f86(a1),x69622),f334(f85(a1),a89)))) % 188.18/188.26 [7014]~P107(f334(f66(x70141),x70142))+~P107(f334(f66(x70141),f250(f935(x70141,a922))))+P107(f334(f66(x70141),f334(f85(f935(x70141,a922)),x70142))) % 188.18/188.26 [7037]~P107(f334(f334(f243(a1),f2(a1)),x70372))+~P107(f334(f334(f242(a1),x70372),x70371))+P107(f334(f334(f243(a1),f2(a1)),f334(f334(f41(a1),x70371),x70372))) % 188.18/188.26 [7038]~P107(f334(f334(f242(a1),x70381),f2(a1)))+~P107(f334(f334(f243(a1),x70382),f2(a1)))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f41(a1),x70381),x70382))) % 188.18/188.26 [7072]~P107(f334(f334(f242(a1),f2(a1)),x70722))+~P107(f334(f334(f242(a1),f2(a1)),x70721))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f87(a1),x70721),x70722))) % 188.18/188.26 [7073]~P107(f334(f334(f242(a1),f2(a1)),x70732))+~P107(f334(f334(f242(a1),f2(a1)),x70731))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),x70731),x70732))) % 188.18/188.26 [7074]~P107(f334(f334(f242(a1),f2(a1)),x70742))+~P107(f334(f334(f242(a1),f2(a1)),x70741))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f41(a1),x70741),x70742))) % 188.18/188.26 [7075]~P107(f334(f334(f242(a1),f2(a1)),x70751))+~P107(f334(f334(f243(a1),f2(a1)),x70752))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f41(a1),x70751),x70752))) % 188.18/188.26 [7076]~P107(f334(f334(f243(a927),f2(a927)),x70762))+~P107(f334(f334(f243(a927),f2(a927)),x70761))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f87(a927),x70761),x70762))) % 188.18/188.26 [7141]E(x71411,f2(a1))+E(f50(a1,x71412,x71411),f2(a1))+E(f334(f334(f23(a1),f334(f85(a1),f334(f334(f41(a1),x71412),x71411))),f84(a1)),f334(f334(f41(a1),f334(f85(a1),x71412)),x71411)) % 188.18/188.26 [7196]P107(f334(f334(f243(a927),f2(a927)),x71961))+P107(f334(f334(f243(a927),f2(a927)),x71962))+~P107(f334(f334(f243(a927),f2(a927)),f334(f334(f86(a927),x71962),x71961))) % 188.18/188.26 [7200]~P77(x72001)+P107(f334(f334(f242(x72001),f2(x72001)),x72002))+~P107(f334(f334(f242(x72001),f2(x72001)),f334(f334(f86(x72001),x72002),x72002))) % 188.18/188.26 [7201]~P77(x72011)+P107(f334(f334(f243(x72011),f2(x72011)),x72012))+~P107(f334(f334(f243(x72011),f2(x72011)),f334(f334(f86(x72011),x72012),x72012))) % 188.18/188.26 [7251]~P107(f334(f66(x72511),x72512))+P107(f334(f66(x72511),f250(f935(x72511,a922))))+~P107(f334(f66(x72511),f334(f85(f935(x72511,a922)),x72512))) % 188.18/188.26 [7314]P107(f334(f334(f242(a1),x73141),f2(a1)))+~P107(f334(f334(f243(a1),x73142),f2(a1)))+~P107(f334(f334(f242(a1),f2(a1)),f334(f334(f41(a1),x73141),x73142))) % 188.18/188.26 [7320]~P107(f334(f334(f243(a1),f2(a1)),x73201))+P107(f334(f334(f242(a1),x73201),x73202))+~P107(f334(f334(f243(a1),f2(a1)),f334(f334(f41(a1),x73202),x73201))) % 188.18/188.26 [7321]~P107(f334(f334(f242(a1),f2(a1)),x73212))+P107(f334(f334(f242(a1),x73211),x73212))+~P107(f334(f334(f243(a1),f2(a1)),f334(f334(f41(a1),x73212),x73211))) % 188.18/188.26 [7351]P107(f334(f334(f242(a1),f2(a1)),x73511))+~P107(f334(f334(f243(a1),f2(a1)),x73512))+~P107(f334(f334(f242(a1),f2(a1)),f334(f334(f41(a1),x73511),x73512))) % 188.18/188.26 [7352]P107(f334(f334(f243(a1),f2(a1)),x73521))+~P107(f334(f334(f242(a1),f2(a1)),x73522))+~P107(f334(f334(f243(a1),f2(a1)),f334(f334(f41(a1),x73522),x73521))) % 188.18/188.26 [7781]~P107(f334(f66(x77812),f250(f935(x77812,a922))))+~P107(f334(f66(x77811),f250(f935(x77811,a922))))+P107(f334(f66(f933(x77811,x77812)),f250(f935(f933(x77811,x77812),a922)))) % 188.18/188.26 [7782]~P107(f334(f66(x77822),f250(f935(x77822,a922))))+~P107(f334(f66(x77821),f250(f935(x77821,a922))))+P107(f334(f66(f934(x77821,x77822)),f250(f935(f934(x77821,x77822),a922)))) % 188.18/188.26 [7849]~P107(f334(f334(f243(a927),f334(a119,f2(a927))),x78491))+~P107(f334(f334(f243(a927),f334(a119,f2(a927))),x78492))+P107(f334(f334(f243(a927),x78491),f334(f334(f87(a927),x78492),x78491))) % 188.18/188.26 [7850]~P107(f334(f334(f243(a927),f334(a119,f2(a927))),x78501))+~P107(f334(f334(f243(a927),f334(a119,f2(a927))),x78502))+P107(f334(f334(f243(a927),x78501),f334(f334(f87(a927),x78501),x78502))) % 188.18/188.26 [7883]E(f334(f40(x78831),f250(f935(x78831,a922))),f334(a119,f2(a927)))+P107(f334(f66(x78832),f250(f935(x78832,a922))))+~P107(f334(f66(f935(x78832,x78831)),f250(f935(f935(x78832,x78831),a922)))) % 188.18/188.26 [8012]~P107(f334(f334(f242(a927),f334(a119,f2(a927))),x80121))+~P107(f334(f334(f242(a927),f334(a119,f2(a927))),x80122))+P107(f334(f334(f242(a927),f334(a119,f2(a927))),f334(f334(f87(a927),x80121),x80122))) % 188.18/188.26 [8013]~P107(f334(f334(f243(a927),f334(a119,f2(a927))),x80132))+~P107(f334(f334(f243(a927),f334(a119,f2(a927))),x80131))+P107(f334(f334(f243(a927),f334(a119,f2(a927))),f334(f334(f87(a927),x80131),x80132))) % 188.18/188.26 [8675]E(x86751,f120(x86752))+~P107(f334(f144(x86752),x86751))+E(f184(x86752,f334(f334(f8(a922,a922,x86752),a329),f334(f334(f7(x86752,x86752,a922),a331),f151(x86752,x86751))),x86751),f121(x86752,x86751)) % 188.18/188.26 [8772]~P42(x87722)+~P42(x87721)+E(f334(f317(a927,a1,f107(a1)),f334(f334(f108(f935(a927,a922)),f334(f317(a1,a927,a112),x87721)),f334(f317(a1,a927,a112),x87722))),f334(f334(f108(f935(a1,a922)),x87721),x87722)) % 188.18/188.26 [8773]~P42(x87732)+~P42(x87731)+E(f334(f317(a927,a1,f107(a1)),f334(f334(f109(f935(a927,a922)),f334(f317(a1,a927,a112),x87731)),f334(f317(a1,a927,a112),x87732))),f334(f334(f109(f935(a1,a922)),x87731),x87732)) % 188.18/188.26 [9502]~P95(x95021)+~E(f334(f111(x95021),x95022),f84(x95021))+P30(x95021,f334(f111(x95021),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f334(f85(a1),x95022)))) % 188.18/188.26 [9723]~P95(x97231)+E(f334(f111(x97231),x97232),f84(x97231))+~P30(x97231,f334(f111(x97231),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),f334(f85(a1),x97232)))) % 188.18/188.26 [10473]E(x104731,f2(a1))+E(x104732,f2(a1))+E(f334(f266(a1,a1,a1,a1,f32(a1),f334(f87(a1),f88(a1,x104732))),f334(f334(f334(f103(f934(a1,a1)),f334(f334(a331,f88(a1,x104731)),f88(a1,x104732))),f58(x104731,x104732)),f334(f334(f265(a1,a1,f934(a1,a1)),f334(f334(f18(a1,f935(a1,f934(a1,a1)),f935(a1,f934(a1,a1))),f334(f334(f8(f935(a1,f935(f934(a1,a1),f934(a1,a1))),f935(f935(a1,f934(a1,a1)),f935(a1,f934(a1,a1))),a1),f18(a1,f934(a1,a1),f934(a1,a1))),f334(f334(f8(f934(a1,a1),f935(a1,f935(f934(a1,a1),f934(a1,a1))),a1),f334(f7(a1,f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),f334(f334(f8(a922,f935(f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),a1),f103(f934(a1,a1))),f334(f334(f7(a1,a1,a922),a331),f2(a1))))),f334(f334(f7(a1,a1,f934(a1,a1)),f334(f334(f8(a1,f935(a1,f934(a1,a1)),a1),f260(a1,a1)),f85(a1))),f2(a1))))),f334(f334(f7(a1,f935(a1,a1),f935(a1,f934(a1,a1))),f334(f334(f8(f935(a1,f934(a1,a1)),f935(f935(a1,a1),f935(a1,f934(a1,a1))),a1),f8(a1,f934(a1,a1),a1)),f334(f334(f8(a1,f935(a1,f934(a1,a1)),a1),f260(a1,a1)),f334(f334(f7(a1,a1,a1),f334(f334(f8(a1,f935(a1,a1),a1),f23(a1)),f85(a1))),f84(a1))))),f334(f23(a1),f334(f81(a1),x104732))))),f58(x104731,x104732)))),f51(x104731,x104732)) % 188.18/188.26 [10474]E(x104741,f2(a1))+E(x104742,f2(a1))+E(f334(f266(a1,a1,a1,a1,f32(a1),f334(f87(a1),f88(a1,x104742))),f334(f334(f334(f103(f934(a1,a1)),f334(f334(a333,f334(f334(a332,f334(f334(f243(a1),f2(a1)),x104742)),f334(f334(f242(a1),f2(a1)),x104741))),f334(f334(a332,f334(f334(f243(a1),x104742),f2(a1))),f334(f334(f243(a1),x104741),f2(a1))))),f58(x104741,x104742)),f334(f334(f265(a1,a1,f934(a1,a1)),f334(f334(f18(a1,f935(a1,f934(a1,a1)),f935(a1,f934(a1,a1))),f334(f334(f8(f935(a1,f935(f934(a1,a1),f934(a1,a1))),f935(f935(a1,f934(a1,a1)),f935(a1,f934(a1,a1))),a1),f18(a1,f934(a1,a1),f934(a1,a1))),f334(f334(f8(f934(a1,a1),f935(a1,f935(f934(a1,a1),f934(a1,a1))),a1),f334(f7(a1,f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),f334(f334(f8(a922,f935(f934(a1,a1),f935(f934(a1,a1),f934(a1,a1))),a1),f103(f934(a1,a1))),f334(f334(f7(a1,a1,a922),a331),f2(a1))))),f334(f334(f7(a1,a1,f934(a1,a1)),f334(f334(f8(a1,f935(a1,f934(a1,a1)),a1),f260(a1,a1)),f85(a1))),f2(a1))))),f334(f334(f7(a1,f935(a1,a1),f935(a1,f934(a1,a1))),f334(f334(f8(f935(a1,f934(a1,a1)),f935(f935(a1,a1),f935(a1,f934(a1,a1))),a1),f8(a1,f934(a1,a1),a1)),f334(f334(f8(a1,f935(a1,f934(a1,a1)),a1),f260(a1,a1)),f334(f334(f7(a1,a1,a1),f334(f334(f8(a1,f935(a1,a1),a1),f23(a1)),f85(a1))),f84(a1))))),f334(f23(a1),f334(f81(a1),x104742))))),f58(x104741,x104742)))),f51(x104741,x104742)) % 188.18/188.26 [5959]~P124(x59591)+~P95(x59591)+E(f334(f81(x59591),f334(f334(f252(x59591),f334(f111(x59591),a104)),x59592)),f84(x59591)) % 188.18/188.26 [6449]~P142(x64491)+~P107(f334(f334(f243(a1),x64492),f2(a1)))+E(f334(f85(x64491),f334(f107(x64491),f334(a112,f334(f85(a1),x64492)))),f334(f110(x64491),x64492)) % 188.18/188.26 [6650]P107(f334(f334(f242(a106),x66501),f84(a106)))+E(f334(f334(f86(a106),f84(a106)),f280(x66501,f334(f334(f41(a106),x66502),x66501))),f280(x66501,x66502))+P107(f334(f334(f243(a106),x66502),x66501)) % 188.18/188.26 [7240]~P93(x72401)+~P107(f334(f334(f336(x72401),x72402),f117(x72401)))+~E(f334(f334(f86(x72401),f334(f334(f86(x72401),f84(x72401)),x72402)),x72402),f2(x72401)) % 188.18/188.26 [7353]~P107(f334(f334(f242(a1),x73532),f2(a1)))+~P107(f334(f334(f243(a1),x73531),f2(a1)))+E(f334(f259(a1,a1),f334(a56,f52(f334(f85(a1),x73531),f334(f85(a1),x73532)))),f334(f334(f41(a1),x73531),x73532)) % 188.18/188.26 [7370]~P107(f334(f334(f242(a1),x73702),f2(a1)))+~P107(f334(f334(f243(a1),x73701),f2(a1)))+E(f334(f264(a1,a1),f334(a56,f52(f334(f85(a1),x73701),f334(f85(a1),x73702)))),f50(a1,x73701,x73702)) % 188.18/188.26 [7376]~P107(f334(f334(f243(a1),x73762),f2(a1)))+E(f334(f259(a1,a1),f334(a56,f55(f334(f85(a1),x73761),f334(f85(a1),x73762)))),f334(f334(f41(a1),x73761),x73762))+~P107(f334(f334(f243(a1),f2(a1)),x73761)) % 188.18/188.26 [7394]~P107(f334(f334(f243(a1),x73942),f2(a1)))+E(f334(f264(a1,a1),f334(a56,f55(f334(f85(a1),x73941),f334(f85(a1),x73942)))),f50(a1,x73941,x73942))+~P107(f334(f334(f243(a1),f2(a1)),x73941)) % 188.18/188.26 [7446]E(f334(f334(f41(a1),f334(f334(f252(a1),x74461),x74462)),x74461),f334(f334(f252(a1),x74461),f334(f334(f23(a927),x74462),f334(a119,f2(a927)))))+~P107(f334(f334(f243(a927),f2(a927)),x74462))+~P107(f334(f334(f243(a1),f2(a1)),x74461)) % 188.18/188.26 [7547]~P107(f334(f334(f243(a927),f2(a927)),x75471))+~P107(f334(f334(f243(a927),f2(a927)),x75472))+P107(f334(f334(f243(a927),f334(f334(f23(a927),x75471),x75472)),x75471)) % 188.18/188.26 [7548]~P107(f334(f334(f243(a927),f2(a927)),x75481))+~P107(f334(f334(f243(a927),f84(a927)),x75482))+P107(f334(f334(f243(a927),f334(f334(f41(a927),x75481),x75482)),x75481)) % 188.18/188.26 [7549]~P107(f334(f334(f243(a1),f2(a1)),x75491))+~P107(f334(f334(f243(a1),f84(a1)),x75492))+P107(f334(f334(f243(a1),f334(f334(f41(a1),x75491),x75492)),x75491)) % 188.18/188.26 [7677]E(x76771,f2(a927))+~E(x76772,f2(a1))+~P107(f334(f334(f243(a1),f2(a1)),f334(f334(f252(a1),f334(f81(a1),x76772)),x76771))) % 188.18/188.26 [8091]~E(x80912,f120(f928(x80911)))+E(f334(f196(f928(f928(x80911))),f186(x80911,x80912)),f2(a927))+~P15(a927,f334(f175(a927),f334(f334(f161(f928(x80911),a927),f196(f928(x80911))),x80912))) % 188.18/188.26 [8331]P107(f334(x83311,x83312))+~P107(f334(x83311,f334(a115,f571(x83311,x83312))))+~P107(f334(f334(f336(f935(f934(a927,a927),a922)),x83312),a105)) % 188.18/188.26 [8348]E(x83481,f120(f928(x83482)))+E(f334(f196(f928(x83482)),f334(f334(f171(f928(x83482)),x83481),f2(a927))),f334(f196(f928(f928(x83482))),f186(x83482,x83481)))+~P15(a927,f334(f175(a927),f334(f334(f161(f928(x83482),a927),f196(f928(x83482))),x83481))) % 188.18/188.26 [8488]~P40(x84881,x84882)+~P41(x84881,x84882)+P40(x84881,f334(f334(f23(f935(f934(x84881,x84881),a922)),x84882),f314(x84881,f195(f935(f934(x84881,x84881),a922))))) % 188.18/188.26 [9052]~P107(f334(f66(x90521),f334(f270(x90521),x90522)))+~P107(f334(f66(x90521),f250(f935(x90521,a922))))+P107(f334(f66(x90521),f334(f270(x90521),f334(f334(f8(a922,a922,x90521),a329),x90522)))) % 188.18/188.26 [9120]E(f334(f334(f260(a927,a927),f334(a119,f334(f334(f41(a927),f334(f334(f23(a927),x91201),x91202)),x91202))),f50(a927,f334(f334(f23(a927),x91201),x91202),x91202)),f91(f934(a927,a927),f53(x91201,x91202)))+~P107(f334(f334(f243(a927),f2(a927)),x91202))+~P107(f334(f334(f242(a927),x91202),x91201)) % 188.18/188.26 [9398]~P107(f334(f66(x93981),f334(f270(x93981),x93982)))+P107(f334(f66(x93981),f250(f935(x93981,a922))))+~P107(f334(f66(x93981),f334(f270(x93981),f334(f334(f8(a922,a922,x93981),a329),x93982)))) % 188.18/188.26 [10136]P29(x101361,x101362)+~P39(x101361,f334(f259(f935(f934(x101361,x101361),a922),f935(f934(x101361,x101361),a922)),x101362))+~P107(f334(f334(f242(f935(f934(x101361,x101361),a922)),f334(f334(f295(x101361,x101361,x101361),f334(f259(f935(f934(x101361,x101361),a922),f935(f934(x101361,x101361),a922)),x101362)),f334(f264(f935(f934(x101361,x101361),a922),f935(f934(x101361,x101361),a922)),x101362))),f334(f259(f935(f934(x101361,x101361),a922),f935(f934(x101361,x101361),a922)),x101362))) % 188.18/188.26 [7476]~P107(f334(f334(f243(a927),f2(a927)),x74762))+P107(f334(f334(f243(a927),x74761),x74762))+E(f334(a119,f334(f334(f41(a927),f334(f334(f23(a927),x74761),x74762)),x74762)),f334(f334(f41(a927),x74761),x74762)) % 188.18/188.26 [7603]~P107(f334(f334(f243(a927),f2(a927)),x76032))+~P107(f334(f334(f242(a927),x76032),x76031))+E(f334(a119,f334(f334(f41(a927),f334(f334(f23(a927),x76031),x76032)),x76032)),f334(f334(f41(a927),x76031),x76032)) % 188.18/188.26 [8650]~P95(x86501)+~P93(x86501)+~P30(x86501,f334(f111(x86501),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x86502)),x86502))) % 188.18/188.26 [9299]E(x92991,f2(a927))+E(f334(f334(f265(a927,a927,f934(a927,a927)),f334(f334(f8(a927,f935(a927,f934(a927,a927)),a927),f260(a927,a927)),a119)),f91(f934(a927,a927),f53(f334(f334(f23(a927),x92992),x92991),x92991))),f91(f934(a927,a927),f53(x92992,x92991)))+P107(f334(f334(f243(a927),x92992),x92991)) % 188.18/188.26 [9482]~P40(x94821,x94822)+~P54(x94821,x94822)+P107(f334(f334(f242(f935(f934(x94821,x94821),a922)),f334(f334(f295(x94821,x94821,x94821),f334(f293(x94821,x94821),x94822)),x94822)),x94822)) % 188.18/188.26 [9743]P107(f334(x97432,f651(x97432,x97431)))+P107(f334(x97431,f651(x97432,x97431)))+E(f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x97431)),f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x97432))) % 188.18/188.26 [9747]~P107(f334(x97472,f651(x97472,x97471)))+~P107(f334(x97471,f651(x97472,x97471)))+E(f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x97471)),f334(f270(a1),f334(f334(f18(a1,a922,a922),f334(f334(f8(a922,f935(a922,a922),a1),a332),f334(f242(a1),f2(a1)))),x97472))) % 188.18/188.26 [8048]~P95(x80481)+~P66(x80481)+E(f334(f334(f296(x80481),x80482),f334(f111(x80481),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),x80482) % 188.18/188.26 [9501]~P95(x95011)+~E(f334(f111(x95011),x95012),f84(x95011))+P30(x95011,f334(f111(x95011),f334(f334(f86(a1),x95012),f334(f85(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))))) % 188.18/188.26 [9724]~P95(x97241)+E(f334(f111(x97241),x97242),f84(x97241))+~P30(x97241,f334(f111(x97241),f334(f334(f86(a1),x97242),f334(f85(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))))) % 188.18/188.26 [10160]~P141(x101601)+~E(x101602,f84(x101601))+E(f334(f334(f252(x101601),x101602),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f84(x101601)) % 188.18/188.26 [10161]~P141(x101611)+~E(x101612,f2(x101611))+E(f334(f334(f252(x101611),x101612),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f2(x101611)) % 188.18/188.26 [10164]~P141(x101641)+~E(x101642,f334(f85(x101641),f84(x101641)))+E(f334(f334(f252(x101641),x101642),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f84(x101641)) % 188.18/188.26 [10302]~P124(x103022)+E(x103021,f2(x103022))+P107(f334(f334(f243(x103022),f2(x103022)),f334(f334(f252(x103022),x103021),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.26 [10349]~P124(x103492)+~E(x103491,f2(x103492))+~P107(f334(f334(f243(x103492),f2(x103492)),f334(f334(f252(x103492),x103491),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.26 [10369]P107(f334(f334(f242(a1),x103691),f2(a1)))+P107(f334(f334(f243(a1),x103692),x103691))+E(f334(f48(x103691),f52(x103692,f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103691))),f52(x103692,x103691)) % 188.18/188.26 [10370]~P107(f334(f334(f243(a1),f2(a1)),x103701))+P107(f334(f334(f243(a1),x103702),x103701))+E(f334(f48(x103701),f52(x103702,f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103701))),f52(x103702,x103701)) % 188.18/188.26 [10371]P107(f334(f334(f242(a1),x103711),f2(a1)))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),x103712),x103711)))+E(f334(f48(x103711),f55(x103712,f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103711))),f55(x103712,x103711)) % 188.18/188.26 [10372]~P107(f334(f334(f243(a1),f2(a1)),x103721))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),x103722),x103721)))+E(f334(f48(x103721),f55(x103722,f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103721))),f55(x103722,x103721)) % 188.18/188.26 [10373]~P147(x103731)+~P107(f334(f334(f242(a1),f2(a1)),x103732))+E(f334(f107(x103731),f334(a112,f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x103732))),f334(f334(f86(x103731),f334(f107(x103731),f334(a112,x103732))),f334(f107(x103731),f334(a112,x103732)))) % 188.18/188.26 [5288]~P149(x52881,x52882,x52883)+~E(x52883,f2(a1))+P107(f334(x52881,x52882)) % 188.18/188.26 [5410]~P109(x54101)+~P15(x54101,x54103)+P15(x54101,f177(x54101,x54102,x54103)) % 188.18/188.26 [5411]~P109(x54111)+~P15(x54111,x54113)+P15(x54111,f184(x54111,x54112,x54113)) % 188.18/188.26 [4983]~P69(x49832)+~E(x49833,f334(f85(x49832),x49831))+E(x49831,f334(f85(x49832),x49833)) % 188.18/188.26 [4985]~P69(x49851)+~E(f334(f85(x49851),x49853),x49852)+E(f334(f85(x49851),x49852),x49853) % 188.18/188.26 [5065]~P69(x50653)+E(x50651,x50652)+~E(f334(f85(x50653),x50651),f334(f85(x50653),x50652)) % 188.18/188.26 [5066]~P91(x50663)+E(x50661,x50662)+~E(f334(f85(x50663),x50661),f334(f85(x50663),x50662)) % 188.18/188.26 [5067]~P97(x50673)+E(x50671,x50672)+~E(f334(f107(x50673),x50671),f334(f107(x50673),x50672)) % 188.18/188.26 [5068]~P93(x50683)+E(x50681,x50682)+~E(f334(f110(x50683),x50681),f334(f110(x50683),x50682)) % 188.18/188.26 [5069]~P109(x50693)+E(x50691,x50692)+~E(f334(f309(x50693),x50691),f334(f309(x50693),x50692)) % 188.18/188.26 [5070]~P109(x50703)+E(x50701,x50702)+~E(f334(f308(x50703),x50701),f334(f308(x50703),x50702)) % 188.18/188.26 [5071]~P109(x50713)+E(x50711,x50712)+~E(f334(f290(x50713),x50711),f334(f290(x50713),x50712)) % 188.18/188.26 [5072]~P109(x50723)+E(x50721,x50722)+~E(f334(f307(x50723),x50721),f334(f307(x50723),x50722)) % 188.18/188.26 [5172]~P64(x51721)+~P107(f334(x51722,x51723))+P107(f334(f61(x51721),x51722)) % 188.18/188.26 [5208]~P64(x52083)+P107(f334(x52081,x52082))+~P107(f334(f62(x52083),x52081)) % 188.18/188.26 [5307]~P150(x53071,x53073,x53072)+~E(x53072,f2(a1))+P107(f334(x53071,f2(a1))) % 188.18/188.26 [5346]~E(x53461,f2(a927))+E(f833(x53461,x53462,x53463),f195(f935(x53463,a922)))+~E(f334(f40(x53463),x53462),f334(a119,x53461)) % 188.18/188.26 [5495]~E(x54952,f2(a927))+E(f334(f259(a927,a927),x54951),f2(a927))+~P107(f334(f53(x54953,x54952),x54951)) % 188.18/188.26 [5538]P107(f334(x55381,x55382))+~E(x55383,f334(f107(a1),x55382))+~P107(f334(x55381,f334(a112,x55383))) % 188.18/188.26 [6023]~E(x60233,f2(a927))+~P107(f334(x60231,x60232))+P107(f334(x60231,f50(a927,x60232,x60233))) % 188.18/188.26 [6257]~P105(x62572)+~P105(x62571)+E(f138(x62571,x62572,f139(x62571,x62573),f139(x62572,x62573)),f139(f934(x62571,x62572),x62573)) % 188.18/188.26 [6431]~E(x64313,f2(a927))+P107(f334(x64311,x64312))+~P107(f334(x64311,f50(a927,x64312,x64313))) % 188.18/188.26 [6916]E(x69161,f195(f935(x69162,a922)))+~P107(f334(f66(x69162),x69161))+P107(f334(f67(x69162,x69163,x69161),f869(x69163,x69161,x69162))) % 188.18/188.26 [7097]E(x70971,f2(a927))+~P107(f334(x70972,f914(x70971,x70973,x70972)))+P107(f334(x70972,f50(a927,x70973,x70971))) % 188.18/188.26 [7206]~P7(x72061)+~P107(f334(f334(f242(x72061),x72062),f514(x72063,x72062,x72061)))+P107(f334(f334(f242(x72061),x72062),f43(x72061,x72063))) % 188.18/188.26 [7208]~P107(f334(x72081,x72082))+~P107(f334(x72081,f914(x72083,x72082,x72081)))+P107(f334(x72081,f50(a927,x72082,x72083))) % 188.18/188.26 [7309]E(x73091,f120(x73092))+E(f334(f334(f158(x73092),f703(x73093,x73091,x73092)),f706(x73093,x73091,x73092)),x73091)+~P107(f334(f334(f336(f928(x73092)),x73091),f168(x73092,x73093))) % 188.18/188.26 [7339]~P142(x73391)+~P107(f334(f334(f336(x73391),x73392),f117(x73391)))+P107(f334(f334(f336(x73391),f334(f334(f252(x73391),x73392),x73393)),f117(x73391))) % 188.18/188.26 [7649]P39(x76491,x76492)+~P107(f334(f334(f336(x76491),x76493),f626(x76492,x76491)))+P107(f334(f334(f336(x76491),f650(x76492,x76491,x76493)),f626(x76492,x76491))) % 188.18/188.26 [7910]E(x79101,f120(x79102))+~P107(f334(f334(f336(f928(x79102)),x79101),f168(x79102,x79103)))+P107(f334(f334(f336(f928(x79102)),f706(x79103,x79101,x79102)),f168(x79102,x79103))) % 188.18/188.26 [7963]E(x79631,f2(a927))+E(f334(f334(f86(a927),f334(f334(f87(a927),x79631),f916(x79631,x79632,x79633))),f914(x79631,x79632,x79633)),x79632)+P107(f334(x79633,f50(a927,x79632,x79631))) % 188.18/188.26 [8007]~P107(f334(x80073,x80072))+E(f334(f334(f86(a927),f334(f334(f87(a927),x80071),f916(x80071,x80072,x80073))),f914(x80071,x80072,x80073)),x80072)+P107(f334(x80073,f50(a927,x80072,x80071))) % 188.18/188.26 [8142]P107(f334(f334(f243(a1),x81421),f907(x81422,x81423,x81421)))+P107(f334(f334(x81423,f334(f334(f41(a1),x81422),x81421)),f50(a1,x81422,x81421)))+~P107(f334(f334(f243(a1),x81421),f2(a1))) % 188.18/188.26 [8403]P107(f334(f334(x84032,f334(f334(f41(a1),x84031),x84033)),f50(a1,x84031,x84033)))+~P107(f334(f334(f243(a1),x84033),f2(a1)))+P107(f334(f334(f242(a1),f907(x84031,x84032,x84033)),f2(a1))) % 188.18/188.26 [8583]E(f334(f334(f86(a1),f334(f334(f87(a1),x85831),f910(x85832,x85833,x85831))),f907(x85832,x85833,x85831)),x85832)+P107(f334(f334(x85833,f334(f334(f41(a1),x85832),x85831)),f50(a1,x85832,x85831)))+~P107(f334(f334(f243(a1),x85831),f2(a1))) % 188.18/188.26 [8818]~P107(f334(f334(x88181,f910(x88182,x88181,x88183)),f907(x88182,x88181,x88183)))+P107(f334(f334(x88181,f334(f334(f41(a1),x88182),x88183)),f50(a1,x88182,x88183)))+~P107(f334(f334(f243(a1),x88183),f2(a1))) % 188.18/188.26 [9066]~P109(x90661)+~P15(x90661,x90663)+P15(x90661,f156(x90661,x90661,f5(x90661),x90662,x90663)) % 188.18/188.26 [9562]~P129(x95622)+E(x95621,f2(x95622))+~P107(f334(f334(f242(x95622),f334(f334(f86(x95622),f334(f334(f87(x95622),x95623),x95623)),f334(f334(f87(x95622),x95621),x95621))),f2(x95622))) % 188.18/188.26 [9563]~P129(x95632)+E(x95631,f2(x95632))+~P107(f334(f334(f242(x95632),f334(f334(f86(x95632),f334(f334(f87(x95632),x95631),x95631)),f334(f334(f87(x95632),x95633),x95633))),f2(x95632))) % 188.18/188.26 [10462]~P124(x104621)+~P107(f334(f334(f243(x104621),x104622),f2(x104621)))+P107(f334(f334(f243(x104621),f334(f334(f252(x104621),x104622),f334(a119,f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104623)))),f2(x104621))) % 188.18/188.26 [10468]~P124(x104682)+E(x104681,f2(x104682))+~P107(f334(f334(f242(x104682),f334(f334(f86(x104682),f334(f334(f252(x104682),x104683),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104682),x104681),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f2(x104682))) % 188.18/188.26 [10469]~P124(x104692)+E(x104691,f2(x104692))+~P107(f334(f334(f242(x104692),f334(f334(f86(x104692),f334(f334(f252(x104692),x104691),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104692),x104693),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f2(x104692))) % 188.18/188.26 [5019]~E(x50192,x50193)+~P3(x50191)+E(f334(f334(f23(x50191),x50192),x50193),f2(x50191)) % 188.18/188.26 [5020]~E(x50202,x50203)+~P69(x50201)+E(f334(f334(f23(x50201),x50202),x50203),f2(x50201)) % 188.18/188.26 [5034]~P143(x50341)+~E(x50343,f2(x50341))+E(f334(f334(f86(x50341),x50342),x50343),x50342) % 188.18/188.26 [5051]~P145(x50511)+~E(x50513,f2(x50511))+E(f334(f334(f87(x50511),x50512),x50513),f2(x50511)) % 188.18/188.26 [5052]~P145(x50521)+~E(x50522,f2(x50521))+E(f334(f334(f87(x50521),x50522),x50523),f2(x50521)) % 188.18/188.26 [5074]~E(x50743,f120(x50741))+~E(x50742,f120(x50741))+E(f334(f334(f141(x50741),x50742),x50743),f120(x50741)) % 188.18/188.26 [5162]~P143(x51622)+E(x51621,f2(x51622))+~E(f334(f334(f86(x51622),x51623),x51621),x51623) % 188.18/188.26 [5163]~P69(x51631)+~E(x51632,f334(f85(x51631),x51633))+E(f334(f334(f86(x51631),x51632),x51633),f2(x51631)) % 188.18/188.26 [5170]E(x51701,f120(x51702))+E(x51703,f2(a927))+~E(f334(f334(f182(x51702),x51703),x51701),f120(x51702)) % 188.18/188.26 [5176]~P3(x51763)+E(x51761,x51762)+~E(f334(f334(f23(x51763),x51761),x51762),f2(x51763)) % 188.18/188.26 [5177]~P69(x51773)+E(x51771,x51772)+~E(f334(f334(f23(x51773),x51771),x51772),f2(x51773)) % 188.18/188.26 [5190]~P141(x51902)+E(x51901,f2(x51902))+~E(f334(f334(f252(x51902),x51901),x51903),f2(x51902)) % 188.18/188.26 [5191]~P101(x51912)+E(x51911,f195(x51912))+~E(f334(f334(f108(x51912),x51913),x51911),f195(x51912)) % 188.18/188.26 [5192]~P101(x51922)+E(x51921,f195(x51922))+~E(f334(f334(f108(x51922),x51921),x51923),f195(x51922)) % 188.18/188.26 [5193]~P100(x51932)+E(x51931,f250(x51932))+~E(f334(f334(f109(x51932),x51933),x51931),f250(x51932)) % 188.18/188.26 [5194]~P100(x51942)+E(x51941,f250(x51942))+~E(f334(f334(f109(x51942),x51941),x51943),f250(x51942)) % 188.18/188.26 [5262]~P69(x52622)+E(x52621,f334(f85(x52622),x52623))+~E(f334(f334(f86(x52622),x52621),x52623),f2(x52622)) % 188.18/188.26 [5263]~P69(x52631)+E(f334(f85(x52631),x52632),x52633)+~E(f334(f334(f86(x52631),x52632),x52633),f2(x52631)) % 188.18/188.26 [5265]~E(x52652,x52653)+~P108(x52651)+P107(f334(f334(f242(x52651),x52652),x52653)) % 188.18/188.26 [5267]~E(x52672,x52673)+~P111(x52671)+P107(f334(f334(f242(x52671),x52672),x52673)) % 188.18/188.26 [5363]~P114(x53631)+~E(x53632,f334(f85(x53631),x53633))+E(f334(f334(f87(x53631),x53632),x53632),f334(f334(f87(x53631),x53633),x53633)) % 188.18/188.26 [5372]~P109(x53721)+~P15(x53721,x53723)+P15(x53721,f334(f334(f182(x53721),x53722),x53723)) % 188.18/188.26 [5373]~P109(x53731)+~P15(x53731,x53733)+P15(x53731,f334(f334(f145(x53731),x53732),x53733)) % 188.18/188.26 [5408]E(x54081,x54082)+E(x54083,f2(a927))+~E(f334(f334(f87(a927),x54083),x54081),f334(f334(f87(a927),x54083),x54082)) % 188.18/188.26 [5409]E(x54091,x54092)+E(x54093,f2(a927))+~E(f334(f334(f87(a927),x54091),x54093),f334(f334(f87(a927),x54092),x54093)) % 188.18/188.26 [5488]~E(x54882,x54883)+~P111(x54881)+E(f311(x54881,x54882,x54883),f334(f334(f316(x54881),x54882),f195(f935(x54881,a922)))) % 188.18/188.26 [5536]~E(x55361,x55362)+~P109(x55363)+~P107(f334(f334(f243(x55363),x55361),x55362)) % 188.18/188.26 [5537]~E(x55371,x55372)+~P111(x55373)+~P107(f334(f334(f243(x55373),x55371),x55372)) % 188.18/188.26 [5549]~P111(x55491)+E(f334(f310(x55491,x55492),x55493),f195(f935(x55491,a922)))+P107(f334(f334(f243(x55491),x55492),x55493)) % 188.18/188.26 [5597]~P111(x55971)+E(f312(x55971,x55972,x55973),f195(f935(x55971,a922)))+P107(f334(f334(f243(x55971),x55972),x55973)) % 188.18/188.26 [5598]~P111(x55981)+E(f311(x55981,x55982,x55983),f195(f935(x55981,a922)))+P107(f334(f334(f242(x55981),x55982),x55983)) % 188.18/188.26 [5599]~P111(x55991)+E(f195(f935(x55991,a922)),f312(x55991,x55992,x55993))+P107(f334(f334(f243(x55991),x55992),x55993)) % 188.18/188.26 [5600]~P111(x56001)+E(f195(f935(x56001,a922)),f311(x56001,x56002,x56003))+P107(f334(f334(f242(x56001),x56002),x56003)) % 188.18/188.26 [5607]~P109(x56071)+~E(f334(f334(f246(x56071),x56072),x56073),x56072)+P107(f334(f334(f242(x56071),x56072),x56073)) % 188.18/188.26 [5608]~P109(x56081)+~E(f334(f334(f241(x56081),x56082),x56083),x56083)+P107(f334(f334(f242(x56081),x56082),x56083)) % 188.18/188.26 [5609]~P98(x56091)+~E(f334(f334(f108(x56091),x56092),x56093),x56093)+P107(f334(f334(f242(x56091),x56092),x56093)) % 188.18/188.26 [5610]~P104(x56101)+~E(f334(f334(f109(x56101),x56102),x56103),x56102)+P107(f334(f334(f242(x56101),x56102),x56103)) % 188.18/188.26 [5629]~P109(x56291)+P15(x56291,x56292)+~P15(x56291,f334(f334(f158(x56291),x56293),x56292)) % 188.18/188.26 [5630]~P109(x56301)+P15(x56301,x56302)+~P15(x56301,f334(f334(f141(x56301),x56303),x56302)) % 188.18/188.26 [5631]~P109(x56311)+P15(x56311,x56312)+~P15(x56311,f334(f334(f141(x56311),x56312),x56313)) % 188.18/188.26 [5696]~P109(x56961)+P107(f334(f334(f242(x56961),x56963),x56962))+P107(f334(f334(f242(x56961),x56962),x56963)) % 188.18/188.26 [5701]~P109(x57011)+P107(f334(f334(f243(x57011),x57013),x57012))+P107(f334(f334(f242(x57011),x57012),x57013)) % 188.18/188.26 [5737]~P109(x57371)+E(f334(f334(f246(x57371),x57372),x57373),x57373)+~P107(f334(f334(f242(x57371),x57373),x57372)) % 188.18/188.26 [5739]~P109(x57391)+E(f334(f334(f246(x57391),x57392),x57393),x57392)+~P107(f334(f334(f242(x57391),x57392),x57393)) % 188.18/188.26 [5740]~P109(x57401)+E(f334(f334(f241(x57401),x57402),x57403),x57402)+~P107(f334(f334(f242(x57401),x57403),x57402)) % 188.18/188.26 [5742]~P109(x57421)+E(f334(f334(f241(x57421),x57422),x57423),x57423)+~P107(f334(f334(f242(x57421),x57422),x57423)) % 188.18/188.26 [5743]~P98(x57431)+E(f334(f334(f108(x57431),x57432),x57433),x57432)+~P107(f334(f334(f242(x57431),x57433),x57432)) % 188.18/188.26 [5745]~P98(x57451)+E(f334(f334(f108(x57451),x57452),x57453),x57453)+~P107(f334(f334(f242(x57451),x57452),x57453)) % 188.18/188.26 [5746]~P104(x57461)+E(f334(f334(f109(x57461),x57462),x57463),x57463)+~P107(f334(f334(f242(x57461),x57463),x57462)) % 188.18/188.26 [5748]~P104(x57481)+E(f334(f334(f109(x57481),x57482),x57483),x57482)+~P107(f334(f334(f242(x57481),x57482),x57483)) % 188.18/188.26 [5755]~P122(x57552)+E(x57551,f2(x57552))+E(f334(f334(f296(x57552),f334(f85(x57552),x57553)),f334(f85(x57552),x57551)),f334(f334(f296(x57552),x57553),x57551)) % 188.18/188.26 [5809]~P111(x58091)+E(f334(f310(x58091,x58092),x58093),f195(f935(x58091,a922)))+~P107(f334(f334(f242(x58091),x58093),x58092)) % 188.18/188.26 [5846]~P111(x58461)+E(f313(x58461,x58462,x58463),f195(f935(x58461,a922)))+~P107(f334(f334(f242(x58461),x58463),x58462)) % 188.18/188.26 [5847]~P111(x58471)+E(f312(x58471,x58472,x58473),f195(f935(x58471,a922)))+~P107(f334(f334(f242(x58471),x58473),x58472)) % 188.18/188.26 [5848]~P111(x58481)+E(f311(x58481,x58482,x58483),f195(f935(x58481,a922)))+~P107(f334(f334(f243(x58481),x58483),x58482)) % 188.18/188.26 [5900]~E(f334(f334(f23(a927),x59001),x59003),x59002)+E(x59001,f334(f334(f86(a927),x59002),x59003))+~P107(f334(f334(f242(a927),x59003),x59001)) % 188.18/188.26 [5901]~E(x59011,f334(f334(f86(a927),x59013),x59012))+E(f334(f334(f23(a927),x59011),x59012),x59013)+~P107(f334(f334(f242(a927),x59012),x59011)) % 188.18/188.26 [5948]~P107(f334(x59481,x59483))+P107(f334(x59481,f410(x59481,x59482)))+~P107(f334(f334(f242(a927),x59483),x59482)) % 188.18/188.26 [5949]~P107(f334(x59491,x59493))+P107(f334(x59491,f422(x59491,x59492)))+~P107(f334(f334(f243(a927),x59493),x59492)) % 188.18/188.26 [5957]~P111(x59571)+~E(f334(f310(x59571,x59572),x59573),f195(f935(x59571,a922)))+~P107(f334(f334(f243(x59571),x59572),x59573)) % 188.18/188.26 [5962]~P108(x59621)+~P107(f334(f334(f243(x59621),x59622),x59623))+P107(f334(f334(f242(x59621),x59622),x59623)) % 188.18/188.26 [5964]~P111(x59641)+~P107(f334(f334(f243(x59641),x59642),x59643))+P107(f334(f334(f242(x59641),x59642),x59643)) % 188.18/188.26 [6073]~P111(x60731)+~E(f312(x60731,x60732,x60733),f195(f935(x60731,a922)))+~P107(f334(f334(f243(x60731),x60732),x60733)) % 188.18/188.26 [6074]~P111(x60741)+~E(f311(x60741,x60742,x60743),f195(f935(x60741,a922)))+~P107(f334(f334(f242(x60741),x60742),x60743)) % 188.18/188.26 [6075]~P111(x60751)+~E(f195(f935(x60751,a922)),f312(x60751,x60752,x60753))+~P107(f334(f334(f243(x60751),x60752),x60753)) % 188.18/188.26 [6076]~P111(x60761)+~E(f195(f935(x60761,a922)),f311(x60761,x60762,x60763))+~P107(f334(f334(f242(x60761),x60762),x60763)) % 188.18/188.26 [6086]P107(f334(x60861,x60862))+~P107(f334(x60861,f411(x60861,x60863)))+~P107(f334(f334(f242(a927),x60862),x60863)) % 188.18/188.26 [6087]P107(f334(x60871,x60872))+~P107(f334(x60871,f423(x60871,x60873)))+~P107(f334(f334(f243(a927),x60872),x60873)) % 188.18/188.26 [6097]~E(x60971,f334(a119,x60973))+P107(f334(f334(f243(a927),x60971),f334(a119,x60972)))+~P107(f334(f334(f243(a927),x60973),x60972)) % 188.18/188.26 [6116]E(x61161,x61162)+~E(f334(f334(f87(a927),x61163),x61161),f334(f334(f87(a927),x61163),x61162))+~P107(f334(f334(f243(a927),f2(a927)),x61163)) % 188.18/188.26 [6173]E(f334(x61731,f451(x61731,x61732,x61733)),f84(a927))+~E(f334(f334(f6(x61733,a927),x61731),x61732),f84(a927))+~P107(f334(f66(x61733),x61732)) % 188.18/188.26 [6188]~P7(x61881)+P107(f334(f334(f242(x61881),x61882),f42(x61881,x61883)))+~P107(f334(f334(f336(x61881),x61882),x61883)) % 188.18/188.26 [6211]~P108(x62111)+~P107(f334(f334(f243(x62111),x62113),x62112))+~P107(f334(f334(f242(x62111),x62112),x62113)) % 188.18/188.26 [6215]~P108(x62151)+~P107(f334(f334(f243(x62151),x62153),x62152))+~P107(f334(f334(f243(x62151),x62152),x62153)) % 188.18/188.26 [6218]~P109(x62181)+~P107(f334(f334(f243(x62181),x62183),x62182))+~P107(f334(f334(f242(x62181),x62182),x62183)) % 188.18/188.26 [6219]~P109(x62191)+~P107(f334(f334(f243(x62191),x62193),x62192))+~P107(f334(f334(f243(x62191),x62192),x62193)) % 188.18/188.26 [6220]~P111(x62201)+~P107(f334(f334(f243(x62201),x62203),x62202))+~P107(f334(f334(f243(x62201),x62202),x62203)) % 188.18/188.26 [6246]~E(f334(x62462,f342(x62462,x62463,x62461)),f84(a927))+E(f334(f334(f9(x62461,a927),x62462),x62463),f84(a927))+~P107(f334(f66(x62461),x62463)) % 188.18/188.26 [6247]~E(f334(x62472,f452(x62472,x62473,x62471)),f2(a927))+E(f334(f334(f6(x62471,a927),x62472),x62473),f2(a927))+~P107(f334(f66(x62471),x62473)) % 188.18/188.26 [6264]~P110(x62641)+~P107(f334(f334(f243(x62641),x62643),x62642))+P107(f334(f334(f336(x62641),x62642),f334(f308(x62641),x62643))) % 188.18/188.26 [6265]~P110(x62651)+~P107(f334(f334(f242(x62651),x62653),x62652))+P107(f334(f334(f336(x62651),x62652),f334(f290(x62651),x62653))) % 188.18/188.26 [6266]~P110(x62661)+~P107(f334(f334(f242(x62661),x62662),x62663))+P107(f334(f334(f336(x62661),x62662),f334(f309(x62661),x62663))) % 188.18/188.26 [6267]~P110(x62671)+~P107(f334(f334(f243(x62671),x62672),x62673))+P107(f334(f334(f336(x62671),x62672),f334(f307(x62671),x62673))) % 188.18/188.26 [6279]E(f334(x62791,f456(x62791,x62792,x62793)),f334(a119,f2(a927)))+~E(f334(f334(f6(x62793,a927),x62791),x62792),f334(a119,f2(a927)))+~P107(f334(f66(x62793),x62792)) % 188.18/188.26 [6360]~P7(x63601)+~P107(f334(f334(f336(x63601),x63603),x63602))+P107(f334(f334(f242(x63601),f43(x63601,x63602)),x63603)) % 188.18/188.26 [6379]~P107(f334(f334(f242(a927),x63791),x63793))+P107(f334(f334(f242(a927),x63791),x63792))+~P107(f334(f334(f242(a927),x63793),x63792)) % 188.18/188.26 [6380]~P107(f334(f334(f242(a1),x63801),x63803))+P107(f334(f334(f242(a1),x63801),x63802))+~P107(f334(f334(f242(a1),x63803),x63802)) % 188.18/188.26 [6402]~P110(x64021)+~P107(f334(f334(f336(x64021),x64023),f334(f290(x64021),x64022)))+P107(f334(f334(f242(x64021),x64022),x64023)) % 188.18/188.26 [6403]~P110(x64031)+~P107(f334(f334(f336(x64031),x64032),f334(f309(x64031),x64033)))+P107(f334(f334(f242(x64031),x64032),x64033)) % 188.18/188.26 [6404]~P110(x64041)+~P107(f334(f334(f336(x64041),x64043),f334(f308(x64041),x64042)))+P107(f334(f334(f243(x64041),x64042),x64043)) % 188.18/188.26 [6405]~P110(x64051)+~P107(f334(f334(f336(x64051),x64052),f334(f307(x64051),x64053)))+P107(f334(f334(f243(x64051),x64052),x64053)) % 188.18/188.26 [6474]~P107(f334(x64741,x64742))+P107(f334(x64741,f807(x64741)))+~P107(f334(f334(f336(x64743),x64742),f250(f935(x64743,a922)))) % 188.18/188.26 [6493]P59(a927,x64932,x64933)+E(x64931,f2(a927))+~P59(a927,f334(f334(f87(a927),x64931),x64932),f334(f334(f87(a927),x64931),x64933)) % 188.18/188.26 [6613]~P67(x66131)+P107(f334(f334(f243(x66131),f2(x66131)),f493(x66133,x66132,x66131)))+P107(f334(f334(f242(x66131),x66132),x66133)) % 188.18/188.26 [6614]~P68(x66141)+P107(f334(f334(f243(x66141),f2(x66141)),f783(x66143,x66142,x66141)))+P107(f334(f334(f242(x66141),x66142),x66143)) % 188.18/188.26 [6686]~P79(x66861)+~P107(f334(f334(f242(x66861),x66863),f334(f85(x66861),x66862)))+P107(f334(f334(f242(x66861),x66862),f334(f85(x66861),x66863))) % 188.18/188.26 [6688]~P79(x66881)+~P107(f334(f334(f243(x66881),x66883),f334(f85(x66881),x66882)))+P107(f334(f334(f243(x66881),x66882),f334(f85(x66881),x66883))) % 188.18/188.26 [6700]~P107(f334(f334(f243(a927),x67001),x67003))+~P107(f334(f334(f243(a927),x67003),x67002))+P107(f334(f334(f243(a927),f334(a119,x67001)),x67002)) % 188.18/188.26 [6726]~P127(x67261)+P107(f334(f334(f242(x67261),f334(f107(x67261),x67262)),f334(f107(x67261),x67263)))+~P107(f334(f334(f242(a927),x67262),x67263)) % 188.18/188.26 [6727]~P124(x67271)+P107(f334(f334(f242(x67271),f334(f110(x67271),x67272)),f334(f110(x67271),x67273)))+~P107(f334(f334(f242(a1),x67272),x67273)) % 188.18/188.26 [6729]~P124(x67291)+P107(f334(f334(f243(x67291),f334(f110(x67291),x67292)),f334(f110(x67291),x67293)))+~P107(f334(f334(f243(a1),x67292),x67293)) % 188.18/188.26 [6730]~P127(x67301)+P107(f334(f334(f243(x67301),f334(f107(x67301),x67302)),f334(f107(x67301),x67303)))+~P107(f334(f334(f243(a927),x67302),x67303)) % 188.18/188.26 [6736]~P109(x67361)+E(f334(f334(f108(f935(x67361,a922)),f334(f307(x67361),x67362)),f334(f310(x67361,x67362),x67363)),f334(f307(x67361),x67363))+~P107(f334(f334(f242(x67361),x67362),x67363)) % 188.18/188.26 [6763]~P79(x67631)+~P107(f334(f334(f242(x67631),x67633),x67632))+P107(f334(f334(f242(x67631),f334(f85(x67631),x67632)),f334(f85(x67631),x67633))) % 188.18/188.26 [6765]~P91(x67651)+~P107(f334(f334(f242(x67651),x67653),x67652))+P107(f334(f334(f242(x67651),f334(f85(x67651),x67652)),f334(f85(x67651),x67653))) % 188.18/188.26 [6766]~P79(x67661)+~P107(f334(f334(f243(x67661),x67663),x67662))+P107(f334(f334(f243(x67661),f334(f85(x67661),x67662)),f334(f85(x67661),x67663))) % 188.18/188.26 [6802]~P109(x68021)+E(f334(f334(f108(f935(x68021,a922)),f334(f309(x68021),x68022)),f313(x68021,x68022,x68023)),f334(f307(x68021),x68023))+~P107(f334(f334(f243(x68021),x68022),x68023)) % 188.18/188.26 [6803]~P109(x68031)+E(f334(f334(f108(f935(x68031,a922)),f334(f309(x68031),x68032)),f312(x68031,x68032,x68033)),f334(f309(x68031),x68033))+~P107(f334(f334(f242(x68031),x68032),x68033)) % 188.18/188.26 [6804]~P109(x68041)+E(f334(f334(f108(f935(x68041,a922)),f334(f307(x68041),x68042)),f311(x68041,x68042,x68043)),f334(f309(x68041),x68043))+~P107(f334(f334(f242(x68041),x68042),x68043)) % 188.18/188.26 [6837]~P109(x68371)+E(f334(f334(f108(f935(x68371,a922)),f334(f310(x68371,x68372),x68373)),f334(f290(x68371),x68373)),f334(f290(x68371),x68372))+~P107(f334(f334(f242(x68371),x68372),x68373)) % 188.18/188.26 [6981]P59(a927,x69811,x69812)+~P59(a927,f334(f334(f87(a927),x69813),x69811),f334(f334(f87(a927),x69813),x69812))+~P107(f334(f334(f243(a927),f2(a927)),x69813)) % 188.18/188.26 [6989]~P109(x69891)+E(f334(f334(f108(f935(x69891,a922)),f313(x69891,x69892,x69893)),f334(f290(x69891),x69893)),f334(f308(x69891),x69892))+~P107(f334(f334(f243(x69891),x69892),x69893)) % 188.18/188.26 [6990]~P109(x69901)+E(f334(f334(f108(f935(x69901,a922)),f312(x69901,x69902,x69903)),f334(f308(x69901),x69903)),f334(f308(x69901),x69902))+~P107(f334(f334(f242(x69901),x69902),x69903)) % 188.18/188.26 [6991]~P109(x69911)+E(f334(f334(f108(f935(x69911,a922)),f311(x69911,x69912,x69913)),f334(f308(x69911),x69913)),f334(f290(x69911),x69912))+~P107(f334(f334(f242(x69911),x69912),x69913)) % 188.18/188.26 [7005]P107(f334(x70051,x70052))+~P107(f334(f334(f242(a927),x70052),x70053))+P107(f334(f334(f336(a927),f411(x70051,x70053)),f311(a927,f2(a927),x70053))) % 188.18/188.26 [7039]E(x70391,x70392)+~E(f334(f334(f171(x70393),x70391),f648(x70393,x70392,x70391)),f334(f334(f171(x70393),x70392),f648(x70393,x70392,x70391)))+~E(f334(f196(f928(x70393)),x70391),f334(f196(f928(x70393)),x70392)) % 188.18/188.26 [7045]~E(x70453,f334(f334(f41(a927),x70451),x70452))+~P107(f334(f334(f243(a927),f2(a927)),x70452))+P107(f334(f334(f243(a927),x70451),f334(f334(f87(a927),x70452),f334(a119,x70453)))) % 188.18/188.26 [7059]~P107(f334(x70591,x70593))+~P107(f334(f334(f242(a927),x70593),x70592))+P107(f334(f334(f336(a927),f410(x70591,x70592)),f311(a927,f2(a927),x70592))) % 188.18/188.26 [7095]~P107(f334(x70951,x70953))+P107(f334(x70951,f425(x70951,x70952)))+~P107(f334(f334(f336(a927),x70953),f311(a927,f2(a927),x70952))) % 188.18/188.26 [7114]~P127(x71143)+~P107(f334(f334(f242(x71143),f334(f107(x71143),x71141)),f334(f107(x71143),x71142)))+P107(f334(f334(f242(a927),x71141),x71142)) % 188.18/188.26 [7115]~P124(x71153)+~P107(f334(f334(f242(x71153),f334(f110(x71153),x71151)),f334(f110(x71153),x71152)))+P107(f334(f334(f242(a1),x71151),x71152)) % 188.18/188.26 [7117]~P127(x71173)+~P107(f334(f334(f243(x71173),f334(f107(x71173),x71171)),f334(f107(x71173),x71172)))+P107(f334(f334(f243(a927),x71171),x71172)) % 188.18/188.26 [7118]~P124(x71183)+~P107(f334(f334(f243(x71183),f334(f110(x71183),x71181)),f334(f110(x71183),x71182)))+P107(f334(f334(f243(a1),x71181),x71182)) % 188.18/188.26 [7119]~P59(a927,f334(f334(f252(a927),x71193),x71191),f334(f334(f252(a927),x71193),x71192))+P107(f334(f334(f242(a927),x71191),x71192))+~P107(f334(f334(f243(a927),f84(a927)),x71193)) % 188.18/188.26 [7135]~P127(x71351)+~P107(f334(f334(f243(x71351),f84(x71351)),x71352))+P107(f334(f334(f243(x71351),f84(x71351)),f334(f334(f252(x71351),x71352),f334(a119,x71353)))) % 188.18/188.26 [7137]~P79(x71371)+~P107(f334(f334(f242(x71371),f334(f85(x71371),x71373)),f334(f85(x71371),x71372)))+P107(f334(f334(f242(x71371),x71372),x71373)) % 188.18/188.26 [7138]~P91(x71381)+~P107(f334(f334(f242(x71381),f334(f85(x71381),x71383)),f334(f85(x71381),x71382)))+P107(f334(f334(f242(x71381),x71382),x71383)) % 188.18/188.26 [7139]~P79(x71391)+~P107(f334(f334(f243(x71391),f334(f85(x71391),x71393)),f334(f85(x71391),x71392)))+P107(f334(f334(f243(x71391),x71392),x71393)) % 188.18/188.26 [7163]P107(f334(x71631,x71632))+~P107(f334(x71631,f412(x71631,x71633)))+~P107(f334(f334(f336(a927),x71632),f311(a927,f2(a927),x71633))) % 188.18/188.26 [7183]~P67(x71831)+P107(f334(f334(f243(x71831),f493(x71833,x71832,x71831)),f84(x71831)))+P107(f334(f334(f242(x71831),x71832),x71833)) % 188.18/188.26 [7203]~E(f50(a927,x72033,x72032),f50(a927,x72031,x72032))+E(f334(f334(f86(a927),x72031),f334(f334(f87(a927),x72032),f596(x72031,x72032,x72033))),x72033)+~P107(f334(f334(f242(a927),x72031),x72033)) % 188.18/188.26 [7257]E(f334(f334(f9(x72571,a927),x72572),x72573),f84(a927))+~P107(f334(f66(x72571),x72573))+P107(f334(f334(f336(x72571),f342(x72572,x72573,x72571)),x72573)) % 188.18/188.26 [7258]E(f334(f334(f6(x72581,a927),x72582),x72583),f2(a927))+~P107(f334(f66(x72581),x72583))+P107(f334(f334(f336(x72581),f452(x72582,x72583,x72581)),x72583)) % 188.18/188.26 [7280]~P111(x72801)+~P107(f334(f334(f242(x72801),x72802),x72803))+P107(f334(f334(f242(f935(x72801,a922)),f334(f309(x72801),x72802)),f334(f309(x72801),x72803))) % 188.18/188.26 [7281]~P109(x72811)+~P107(f334(f334(f242(x72811),x72813),x72812))+P107(f334(f334(f242(f935(x72811,a922)),f334(f308(x72811),x72812)),f334(f308(x72811),x72813))) % 188.18/188.26 [7282]~P111(x72821)+~P107(f334(f334(f242(x72821),x72823),x72822))+P107(f334(f334(f242(f935(x72821,a922)),f334(f290(x72821),x72822)),f334(f290(x72821),x72823))) % 188.18/188.26 [7283]~P109(x72831)+~P107(f334(f334(f242(x72831),x72832),x72833))+P107(f334(f334(f242(f935(x72831,a922)),f334(f307(x72831),x72832)),f334(f307(x72831),x72833))) % 188.18/188.26 [7284]~P109(x72841)+~P107(f334(f334(f243(x72841),x72842),x72843))+P107(f334(f334(f243(f935(x72841,a922)),f334(f307(x72841),x72842)),f334(f307(x72841),x72843))) % 188.18/188.26 [7295]~P7(x72951)+P107(f334(f334(f242(x72951),x72952),f43(x72951,x72953)))+P107(f334(f334(f336(x72951),f514(x72953,x72952,x72951)),x72953)) % 188.18/188.26 [7301]~P79(x73011)+P107(f334(f334(f242(x73011),f334(f334(f23(x73011),x73012),x73013)),f2(x73011)))+~P107(f334(f334(f242(x73011),x73012),x73013)) % 188.18/188.26 [7302]~P79(x73021)+P107(f334(f334(f243(x73021),f334(f334(f23(x73021),x73022),x73023)),f2(x73021)))+~P107(f334(f334(f243(x73021),x73022),x73023)) % 188.18/188.26 [7343]P107(f334(x73431,x73432))+P107(f334(f334(f242(a927),f412(x73431,x73433)),x73433))+~P107(f334(f334(f336(a927),x73432),f311(a927,f2(a927),x73433))) % 188.18/188.26 [7383]~E(f334(f334(f6(x73831,a927),x73832),x73833),f84(a927))+~P107(f334(f66(x73831),x73833))+P107(f334(f334(f336(x73831),f451(x73832,x73833,x73831)),x73833)) % 188.18/188.26 [7384]~P107(f334(x73841,x73843))+P107(f334(f334(f242(a927),f425(x73841,x73842)),x73842))+~P107(f334(f334(f336(a927),x73843),f311(a927,f2(a927),x73842))) % 188.18/188.26 [7423]~P7(x74231)+P107(f334(f334(f336(x74231),f517(x74233,x74232,x74231)),x74232))+P107(f334(f334(f242(x74231),f42(x74231,x74232)),x74233)) % 188.18/188.26 [7457]~E(f334(f334(f6(x74571,a927),x74572),x74573),f334(a119,f2(a927)))+~P107(f334(f66(x74571),x74573))+P107(f334(f334(f336(x74571),f456(x74572,x74573,x74571)),x74573)) % 188.18/188.26 [7468]E(x74681,f2(a927))+P107(f334(x74682,f50(a927,x74683,x74681)))+P107(f334(f334(f243(a927),f914(x74681,x74683,x74682)),x74681)) % 188.18/188.26 [7570]~P107(f334(x75701,x75702))+P107(f334(x75701,f50(a927,x75702,x75703)))+P107(f334(f334(f243(a927),f914(x75703,x75702,x75701)),x75703)) % 188.18/188.26 [7681]E(x76811,f120(x76812))+~P107(f334(f334(f336(f928(x76812)),x76811),f168(x76812,x76813)))+P107(f334(f334(f336(x76812),f703(x76813,x76811,x76812)),x76813)) % 188.18/188.26 [7703]~P109(x77031)+E(f334(f334(f108(f935(x77031,a922)),f334(f334(f316(x77031),x77032),f195(f935(x77031,a922)))),f313(x77031,x77032,x77033)),f334(f310(x77031,x77032),x77033))+~P107(f334(f334(f243(x77031),x77032),x77033)) % 188.18/188.26 [7725]~P109(x77251)+E(f334(f334(f108(f935(x77251,a922)),f334(f334(f316(x77251),x77252),f195(f935(x77251,a922)))),f312(x77251,x77252,x77253)),f311(x77251,x77252,x77253))+~P107(f334(f334(f242(x77251),x77252),x77253)) % 188.18/188.26 [7829]~P109(x78291)+P107(f334(f334(f242(x78291),x78292),x78293))+~P107(f334(f334(f242(f935(x78291,a922)),f334(f308(x78291),x78293)),f334(f308(x78291),x78292))) % 188.18/188.26 [7830]~P111(x78301)+P107(f334(f334(f242(x78301),x78302),x78303))+~P107(f334(f334(f242(f935(x78301,a922)),f334(f290(x78301),x78303)),f334(f290(x78301),x78302))) % 188.18/188.26 [7831]~P109(x78311)+P107(f334(f334(f242(x78311),x78312),x78313))+~P107(f334(f334(f242(f935(x78311,a922)),f334(f307(x78311),x78312)),f334(f307(x78311),x78313))) % 188.18/188.26 [7832]~P111(x78321)+P107(f334(f334(f242(x78321),x78322),x78323))+~P107(f334(f334(f242(f935(x78321,a922)),f334(f309(x78321),x78322)),f334(f309(x78321),x78323))) % 188.18/188.26 [7833]~P109(x78331)+P107(f334(f334(f243(x78331),x78332),x78333))+~P107(f334(f334(f243(f935(x78331,a922)),f334(f307(x78331),x78332)),f334(f307(x78331),x78333))) % 188.18/188.26 [7856]~P79(x78561)+~P107(f334(f334(f242(x78561),f334(f334(f23(x78561),x78562),x78563)),f2(x78561)))+P107(f334(f334(f242(x78561),x78562),x78563)) % 188.18/188.26 [7857]~P79(x78571)+~P107(f334(f334(f243(x78571),f334(f334(f23(x78571),x78572),x78573)),f2(x78571)))+P107(f334(f334(f243(x78571),x78572),x78573)) % 188.18/188.26 [8014]E(x80141,f2(a927))+~E(f334(f149(a927,a927,f86(a927),x80142),x80143),f2(a927))+~P107(f334(f334(f336(a927),x80141),f334(f179(a927),x80143))) % 188.18/188.26 [8018]~P7(x80181)+~P107(f334(f334(f242(x80181),f517(x80183,x80182,x80181)),x80183))+P107(f334(f334(f242(x80181),f42(x80181,x80182)),x80183)) % 188.18/188.26 [8164]P107(f334(f334(f242(a1),f2(a1)),f908(x81641,x81642,x81643)))+P107(f334(f334(x81642,f334(f334(f41(a1),x81641),x81643)),f50(a1,x81641,x81643)))+~P107(f334(f334(f243(a1),f2(a1)),x81643)) % 188.18/188.26 [8250]E(x82501,x82502)+~E(f334(f196(f928(x82503)),x82501),f334(f196(f928(x82503)),x82502))+~P107(f334(f334(f265(x82503,x82503,a922),a331),f677(x82503,x82501,x82502))) % 188.18/188.26 [8321]~P39(x83212,x83213)+E(x83211,f195(f935(x83212,a922)))+~P107(f334(f334(f242(f935(x83212,a922)),x83211),f334(f292(x83212,x83212,x83213),x83211))) % 188.18/188.26 [8350]~P68(x83501)+~P107(f334(f334(f242(x83501),x83502),f334(f334(f86(x83501),x83503),f783(x83503,x83502,x83501))))+P107(f334(f334(f242(x83501),x83502),x83503)) % 188.18/188.26 [8385]P55(x83851,x83852,x83853)+P107(f334(f334(f336(x83851),f572(x83853,x83852,x83851)),x83852))+P107(f334(f334(f336(f934(x83851,x83851)),f573(x83853,x83852,x83851)),x83853)) % 188.18/188.26 [8406]P107(f334(f334(x84062,f334(f334(f41(a1),x84061),x84063)),f50(a1,x84061,x84063)))+~P107(f334(f334(f243(a1),f2(a1)),x84063))+P107(f334(f334(f243(a1),f908(x84061,x84062,x84063)),x84063)) % 188.18/188.26 [8429]E(f334(f317(a927,a927,f334(f334(f7(a927,a927,a927),f23(a927)),x84291)),f334(f310(a927,x84292),x84293)),f195(f935(a927,a922)))+P107(f334(f334(f243(a927),x84291),x84293))+P107(f334(f334(f243(a927),x84292),x84293)) % 188.18/188.26 [8540]E(f334(f317(a927,a927,f334(f334(f7(a927,a927,a927),f23(a927)),x85401)),f334(f310(a927,x85402),x85403)),f334(f334(f316(a927),f2(a927)),f195(f935(a927,a922))))+P107(f334(f334(f243(a927),x85401),x85403))+~P107(f334(f334(f243(a927),x85402),x85403)) % 188.18/188.26 [8551]~P109(x85511)+E(f156(x85511,x85511,f5(x85511),x85512,x85513),x85513)+~P107(f334(f334(f336(x85511),x85512),f334(f179(x85511),x85513))) % 188.18/188.26 [8564]P27(x85641,x85641,x85642,x85643)+~P107(f334(f66(x85641),x85643))+~P107(f334(f334(f242(f935(x85641,a922)),x85643),f334(f317(x85641,x85641,x85642),x85643))) % 188.18/188.26 [8590]E(f334(f334(f86(a1),f334(f334(f87(a1),x85901),f909(x85902,x85903,x85901))),f908(x85902,x85903,x85901)),x85902)+P107(f334(f334(x85903,f334(f334(f41(a1),x85902),x85901)),f50(a1,x85902,x85901)))+~P107(f334(f334(f243(a1),f2(a1)),x85901)) % 188.18/188.26 [8825]~P107(f334(f334(x88251,f909(x88252,x88251,x88253)),f908(x88252,x88251,x88253)))+P107(f334(f334(x88251,f334(f334(f41(a1),x88252),x88253)),f50(a1,x88252,x88253)))+~P107(f334(f334(f243(a1),f2(a1)),x88253)) % 188.18/188.26 [9699]~P107(f334(f66(x96991),x96992))+~P107(f334(f334(f336(x96991),x96993),x96992))+P107(f334(f334(f243(a927),f334(f40(x96991),f334(f334(f23(f935(x96991,a922)),x96992),f334(f334(f316(x96991),x96993),f195(f935(x96991,a922)))))),f334(f40(x96991),x96992))) % 188.18/188.26 [10297]P55(x102971,x102972,x102973)+~P107(f334(f334(f265(x102971,x102971,a922),f334(f334(f7(x102971,f935(x102971,a922),f935(x102971,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x102971,a922),f935(x102971,a922)),x102971),f8(a922,a922,x102971)),f334(f334(f8(a922,f935(a922,a922),x102971),a332),f334(f334(f7(x102971,f935(x102971,a922),a922),f336(x102971)),x102972)))),f334(f334(f7(x102971,f935(x102971,a922),a922),f336(x102971)),x102972))),f573(x102973,x102972,x102971)))+P107(f334(f334(f336(x102971),f572(x102973,x102972,x102971)),x102972)) % 188.18/188.26 [5718]~P122(x57182)+E(x57181,f2(x57182))+E(f334(f334(f296(x57182),x57183),f334(f85(x57182),x57181)),f334(f85(x57182),f334(f334(f296(x57182),x57183),x57181))) % 188.18/188.26 [5832]~P5(x58321)+~P59(x58321,x58322,x58323)+E(f334(f334(f87(x58321),x58322),f334(f334(f41(x58321),x58323),x58322)),x58323) % 188.18/188.26 [5862]~E(x58623,f195(f935(x58621,a922)))+~E(x58622,f195(f935(x58621,a922)))+E(f334(f334(f108(f935(x58621,a922)),x58622),x58623),f195(f935(x58621,a922))) % 188.18/188.26 [5920]~E(x59203,f2(a927))+~P107(f334(x59201,f2(a927)))+P107(f334(x59201,f334(f334(f41(a927),x59202),x59203))) % 188.18/188.26 [6065]~P68(x60652)+E(x60651,f2(x60652))+E(f334(f334(f296(x60652),f334(f81(x60652),x60653)),f334(f81(x60652),x60651)),f334(f81(x60652),f334(f334(f296(x60652),x60653),x60651))) % 188.18/188.26 [6236]~P107(f334(f66(x62361),x62363))+E(f334(f40(x62361),f334(f334(f316(x62361),x62362),x62363)),f334(a119,f334(f40(x62361),x62363)))+P107(f334(f334(f336(x62361),x62362),x62363)) % 188.18/188.26 [6309]~E(x63092,f2(a927))+P107(f334(x63091,f2(a927)))+~P107(f334(x63091,f334(f334(f41(a927),x63093),x63092))) % 188.18/188.26 [6326]~P107(f334(f66(x63261),x63263))+E(f334(f40(x63261),f334(f334(f316(x63261),x63262),x63263)),f334(f40(x63261),x63263))+~P107(f334(f334(f336(x63261),x63262),x63263)) % 188.18/188.26 [6362]~P107(f334(f66(x63621),x63623))+E(f334(f40(x63621),f334(f334(f316(x63621),x63622),x63623)),f334(f334(f86(a927),f84(a927)),f334(f40(x63621),x63623)))+P107(f334(f334(f336(x63621),x63622),x63623)) % 188.18/188.26 [6475]E(f334(f334(f86(a927),x64751),f884(x64751,x64752,x64753)),x64752)+~P107(f334(x64753,f2(a927)))+P107(f334(x64753,f334(f334(f23(a927),x64752),x64751))) % 188.18/188.26 [6476]E(f334(f334(f86(a927),x64761),f885(x64761,x64762,x64763)),x64762)+~P107(f334(x64763,f2(a927)))+P107(f334(x64763,f334(f334(f23(a927),x64762),x64761))) % 188.18/188.26 [6523]~P7(x65231)+~P107(f334(f66(x65231),x65233))+E(f334(f334(f69(x65231,x65231,f108(x65231)),x65232),x65233),f334(f334(f108(x65231),x65232),f42(x65231,x65233))) % 188.18/188.26 [6524]~P7(x65241)+~P107(f334(f66(x65241),x65243))+E(f334(f334(f69(x65241,x65241,f109(x65241)),x65242),x65243),f334(f334(f109(x65241),x65242),f43(x65241,x65243))) % 188.18/188.26 [6530]~P95(x65301)+~E(f334(f111(x65301),x65302),f334(f111(x65301),x65303))+P30(x65301,f334(f111(x65301),f334(f334(f86(a1),x65302),f334(f85(a1),x65303)))) % 188.18/188.26 [6538]~P142(x65381)+E(f334(f334(f23(x65381),f334(f107(x65381),x65382)),f334(f107(x65381),x65383)),f334(f107(x65381),f334(f334(f23(a927),x65382),x65383)))+~P107(f334(f334(f242(a927),x65383),x65382)) % 188.18/188.26 [6624]E(f334(f334(f86(a927),x66241),f884(x66241,x66242,x66243)),x66242)+P107(f334(f334(f243(a927),x66242),x66241))+P107(f334(x66243,f334(f334(f23(a927),x66242),x66241))) % 188.18/188.26 [6625]E(f334(f334(f86(a927),x66251),f885(x66251,x66252,x66253)),x66252)+P107(f334(f334(f243(a927),x66252),x66251))+P107(f334(x66253,f334(f334(f23(a927),x66252),x66251))) % 188.18/188.26 [6642]~P124(x66421)+E(f334(f334(f87(x66421),f334(f81(x66421),x66422)),x66423),f334(f81(x66421),f334(f334(f87(x66421),x66422),x66423)))+~P107(f334(f334(f242(x66421),f2(x66421)),x66423)) % 188.18/188.26 [6643]~P67(x66431)+E(f334(f334(f296(x66431),f334(f81(x66431),x66432)),x66433),f334(f81(x66431),f334(f334(f296(x66431),x66432),x66433)))+~P107(f334(f334(f243(x66431),f2(x66431)),x66433)) % 188.18/188.26 [6651]~P109(x66511)+~P107(f334(f66(x66511),x66513))+E(f334(f334(f69(x66511,x66511,f246(x66511)),x66512),x66513),f14(x66511,f334(f334(f316(x66511),x66512),x66513))) % 188.18/188.26 [6652]~P109(x66521)+~P107(f334(f66(x66521),x66523))+E(f334(f334(f69(x66521,x66521,f241(x66521)),x66522),x66523),f15(x66521,f334(f334(f316(x66521),x66522),x66523))) % 188.18/188.26 [6653]~P99(x66531)+~P107(f334(f66(x66531),x66533))+E(f334(f334(f69(x66531,x66531,f109(x66531)),x66532),x66533),f10(x66531,f334(f334(f316(x66531),x66532),x66533))) % 188.18/188.26 [6654]~P99(x66541)+~P107(f334(f66(x66541),x66543))+E(f334(f334(f69(x66541,x66541,f108(x66541)),x66542),x66543),f13(x66541,f334(f334(f316(x66541),x66542),x66543))) % 188.18/188.26 [6702]E(x67021,f120(x67022))+~E(f186(x67022,x67023),f120(f928(x67022)))+~P107(f334(f334(f336(f928(x67022)),x67021),f334(f179(f928(x67022)),x67023))) % 188.18/188.26 [6744]~P107(f334(f144(x67441),x67443))+P107(f334(f334(f336(x67441),x67442),f334(f179(x67441),x67443)))+P107(f334(f144(x67441),f334(f334(f158(x67441),x67442),x67443))) % 188.18/188.26 [6756]~P96(x67561)+~P107(f334(f66(x67561),x67563))+E(f334(f68(x67561,f87(x67561)),f334(f334(f316(x67561),x67562),x67563)),f334(f334(f69(x67561,x67561,f87(x67561)),x67562),x67563)) % 188.18/188.26 [6776]~P109(x67761)+~P107(f334(f66(x67761),x67763))+E(f11(x67761,f246(x67761),f334(f334(f316(x67761),x67762),x67763)),f334(f334(f69(x67761,x67761,f246(x67761)),x67762),x67763)) % 188.18/188.26 [6777]~P109(x67771)+~P107(f334(f66(x67771),x67773))+E(f12(x67771,f241(x67771),f334(f334(f316(x67771),x67772),x67773)),f334(f334(f69(x67771,x67771,f241(x67771)),x67772),x67773)) % 188.18/188.26 [6779]P107(f334(x67791,f2(a927)))+~P107(f334(f334(f243(a927),x67792),x67793))+~P107(f334(x67791,f334(f334(f23(a927),x67792),x67793))) % 188.18/188.26 [6800]~P86(x68001)+P107(f334(f334(f242(x68001),x68002),x68003))+~P107(f334(f334(f242(x68001),f334(f81(x68001),x68002)),x68003)) % 188.18/188.26 [6801]~P124(x68011)+P107(f334(f334(f243(x68011),x68012),x68013))+~P107(f334(f334(f243(x68011),f334(f81(x68011),x68012)),x68013)) % 188.18/188.26 [6818]E(x68181,f120(x68182))+E(f334(f148(x68182),f334(f334(f145(x68182),x68183),x68181)),f334(f334(f171(x68182),x68181),x68183))+~P107(f334(f334(f243(a927),x68183),f334(f196(f928(x68182)),x68181))) % 188.18/188.26 [6868]~P107(f334(x68681,x68683))+P107(f334(x68681,f448(x68681,x68682)))+~P107(f334(f334(f336(a927),x68683),f334(f310(a927,f2(a927)),x68682))) % 188.18/188.26 [6888]P107(f334(x68881,x68882))+~P107(f334(f334(f243(a927),x68882),x68883))+P107(f334(f334(f336(a927),f423(x68881,x68883)),f334(f310(a927,f2(a927)),x68883))) % 188.18/188.26 [6903]~P127(x69031)+~P107(f334(f334(f242(x69031),f84(x69031)),x69032))+P107(f334(f334(f242(x69031),f84(x69031)),f334(f334(f252(x69031),x69032),x69033))) % 188.18/188.26 [6905]~P127(x69051)+~P107(f334(f334(f242(x69051),f2(x69051)),x69052))+P107(f334(f334(f242(x69051),f2(x69051)),f334(f334(f252(x69051),x69052),x69053))) % 188.18/188.26 [6907]~P127(x69071)+~P107(f334(f334(f243(x69071),f2(x69071)),x69072))+P107(f334(f334(f243(x69071),f2(x69071)),f334(f334(f252(x69071),x69072),x69073))) % 188.18/188.26 [6932]~P107(f334(x69321,x69323))+~P107(f334(f334(f243(a927),x69323),x69322))+P107(f334(f334(f336(a927),f422(x69321,x69322)),f334(f310(a927,f2(a927)),x69322))) % 188.18/188.26 [6940]P107(f334(f66(x69401),x69402))+~P107(f334(f66(x69401),x69403))+~P107(f334(f334(f242(f935(x69401,a922)),x69402),x69403)) % 188.18/188.26 [6947]P107(f334(x69471,x69472))+~P107(f334(x69471,f424(x69471,x69473)))+~P107(f334(f334(f336(a927),x69472),f334(f310(a927,f2(a927)),x69473))) % 188.18/188.26 [6958]E(x69581,f2(a927))+P107(f334(x69582,f912(x69581,x69583,x69582)))+~P107(f334(x69582,f334(f334(f41(a927),x69583),x69581))) % 188.18/188.26 [6965]~P129(x69652)+E(x69651,f2(x69652))+~E(f334(f334(f86(x69652),f334(f334(f87(x69652),x69653),x69653)),f334(f334(f87(x69652),x69651),x69651)),f2(x69652)) % 188.18/188.26 [6966]~P129(x69662)+E(x69661,f2(x69662))+~E(f334(f334(f86(x69662),f334(f334(f87(x69662),x69661),x69661)),f334(f334(f87(x69662),x69663),x69663)),f2(x69662)) % 188.18/188.26 [7006]E(x70061,f2(a927))+~P107(f334(x70062,f913(x70061,x70063,x70062)))+P107(f334(x70062,f334(f334(f41(a927),x70063),x70061))) % 188.18/188.26 [7011]~P109(x70111)+~P15(x70111,x70113)+P15(x70111,f334(f334(f155(x70111,x70111,f5(x70111)),x70112),x70113)) % 188.18/188.26 [7053]P107(f334(x70531,f912(x70532,x70533,x70531)))+P107(f334(x70531,f2(a927)))+~P107(f334(x70531,f334(f334(f41(a927),x70533),x70532))) % 188.18/188.26 [7058]~P95(x70581)+E(f334(f111(x70581),x70582),f334(f111(x70581),x70583))+~P30(x70581,f334(f111(x70581),f334(f334(f86(a1),x70582),f334(f85(a1),x70583)))) % 188.18/188.26 [7122]E(x71221,f2(a1))+E(x71222,f2(a1))+~P107(f334(f54(x71222,x71222),f334(f334(f260(a1,a1),x71223),x71221))) % 188.18/188.26 [7123]E(x71231,f84(a1))+E(x71232,f2(a1))+~P107(f334(f54(x71232,x71232),f334(f334(f260(a1,a1),x71231),x71233))) % 188.18/188.26 [7136]P107(f334(x71361,x71362))+P107(f334(f334(f243(a927),f424(x71361,x71363)),x71363))+~P107(f334(f334(f336(a927),x71362),f334(f310(a927,f2(a927)),x71363))) % 188.18/188.26 [7159]~P107(f334(x71591,f884(x71593,x71592,x71591)))+~P107(f334(x71591,f2(a927)))+P107(f334(x71591,f334(f334(f23(a927),x71592),x71593))) % 188.18/188.26 [7160]~P107(f334(x71601,f885(x71603,x71602,x71601)))+~P107(f334(x71601,f2(a927)))+P107(f334(x71601,f334(f334(f23(a927),x71602),x71603))) % 188.18/188.26 [7161]~P107(f334(x71611,f913(x71613,x71612,x71611)))+~P107(f334(x71611,f2(a927)))+P107(f334(x71611,f334(f334(f41(a927),x71612),x71613))) % 188.18/188.26 [7179]~P107(f334(x71791,x71793))+P107(f334(f334(f243(a927),f448(x71791,x71792)),x71792))+~P107(f334(f334(f336(a927),x71793),f334(f310(a927,f2(a927)),x71792))) % 188.18/188.26 [7180]E(f334(f334(f23(a927),f334(f334(f23(a927),x71801),x71802)),f334(f334(f23(a927),x71803),x71802)),f334(f334(f23(a927),x71801),x71803))+~P107(f334(f334(f242(a927),x71802),x71801))+~P107(f334(f334(f242(a927),x71802),x71803)) % 188.18/188.26 [7216]~P79(x72161)+~P107(f334(f334(f242(x72161),f334(f85(x72161),x72163)),x72162))+P107(f334(f334(f242(x72161),f334(f85(x72161),x72162)),x72163)) % 188.18/188.26 [7218]~P86(x72181)+~P107(f334(f334(f242(x72181),f334(f81(x72181),x72182)),x72183))+P107(f334(f334(f242(x72181),f334(f85(x72181),x72182)),x72183)) % 188.18/188.26 [7220]~P79(x72201)+~P107(f334(f334(f243(x72201),f334(f85(x72201),x72203)),x72202))+P107(f334(f334(f243(x72201),f334(f85(x72201),x72202)),x72203)) % 188.18/188.26 [7221]~P124(x72211)+~P107(f334(f334(f243(x72211),f334(f81(x72211),x72212)),x72213))+P107(f334(f334(f243(x72211),f334(f85(x72211),x72212)),x72213)) % 188.18/188.26 [7252]~P107(f334(x72523,f884(x72522,x72521,x72523)))+P107(f334(f334(f243(a927),x72521),x72522))+P107(f334(x72523,f334(f334(f23(a927),x72521),x72522))) % 188.18/188.26 [7253]~P107(f334(x72533,f885(x72532,x72531,x72533)))+P107(f334(f334(f243(a927),x72531),x72532))+P107(f334(x72533,f334(f334(f23(a927),x72531),x72532))) % 188.18/188.26 [7305]~E(f535(x73053,x73052,x73051),f536(x73053,x73052,x73051))+E(f334(f334(f109(f935(x73051,a922)),x73052),f42(f935(x73051,a922),x73053)),f195(f935(x73051,a922)))+P107(f334(f334(f336(f935(x73051,a922)),x73052),x73053)) % 188.18/188.26 [7312]~P107(f334(f66(x73121),x73123))+P107(f334(f66(x73121),f43(f935(x73121,a922),x73122)))+~P107(f334(f334(f336(f935(x73121,a922)),x73123),x73122)) % 188.18/188.26 [7372]~P109(x73721)+E(f334(f334(f108(f935(x73721,a922)),f334(f310(x73721,x73722),x73723)),f334(f334(f316(x73721),x73723),f195(f935(x73721,a922)))),f311(x73721,x73722,x73723))+~P107(f334(f334(f242(x73721),x73722),x73723)) % 188.18/188.26 [7373]E(x73731,f2(a927))+P107(f334(f334(f243(a927),f915(x73731,x73733,x73732)),x73731))+P107(f334(x73732,f334(f334(f41(a927),x73733),x73731))) % 188.18/188.26 [7402]P107(f334(f334(f243(a927),f334(f196(f928(x74021)),x74022)),f798(x74023,x74021)))+~P107(f334(f66(f928(x74021)),x74023))+~P107(f334(f334(f336(f928(x74021)),x74022),x74023)) % 188.18/188.26 [7408]E(x74081,x74082)+~P107(f334(f334(f242(f935(x74083,a922)),x74081),x74082))+P107(f334(f334(f243(f935(x74083,a922)),x74081),x74082)) % 188.18/188.26 [7420]E(x74201,x74202)+~E(f334(f196(f928(x74203)),x74201),f334(f196(f928(x74203)),x74202))+P107(f334(f334(f243(a927),f648(x74203,x74201,x74202)),f334(f196(f928(x74203)),x74202))) % 188.18/188.26 [7469]P10(x74691,x74692,x74693)+~E(f334(f272(x74691,x74691),x74693),x74692)+~E(f334(f334(f295(x74691,x74691,x74691),f334(f293(x74691,x74691),x74693)),x74693),x74693) % 188.18/188.26 [7546]~P107(f334(x75461,f2(a927)))+P107(f334(f334(f243(a927),f915(x75463,x75462,x75461)),x75463))+P107(f334(x75461,f334(f334(f41(a927),x75462),x75463))) % 188.18/188.26 [7555]~P109(x75551)+E(f334(f334(f108(f935(x75551,a922)),f313(x75551,x75552,x75553)),f334(f334(f316(x75551),x75553),f195(f935(x75551,a922)))),f312(x75551,x75552,x75553))+~P107(f334(f334(f243(x75551),x75552),x75553)) % 188.18/188.26 [7638]~P107(f334(f66(x76381),x76383))+P107(f334(f334(f242(a927),f334(f40(x76381),x76382)),f334(f40(x76381),x76383)))+~P107(f334(f334(f242(f935(x76381,a922)),x76382),x76383)) % 188.18/188.26 [7639]~P107(f334(f66(x76391),x76393))+P107(f334(f334(f243(a927),f334(f40(x76391),x76392)),f334(f40(x76391),x76393)))+~P107(f334(f334(f243(f935(x76391,a922)),x76392),x76393)) % 188.18/188.26 [7769]E(x77691,x77692)+~P107(f334(f334(f242(f935(x77693,a922)),x77692),x77691))+~P107(f334(f334(f242(f935(x77693,a922)),x77691),x77692)) % 188.18/188.26 [7772]~P109(x77721)+P15(x77721,x77722)+~P15(x77721,f334(f334(f155(x77721,x77721,f5(x77721)),x77723),x77722)) % 188.18/188.26 [7838]~P107(f334(f334(f243(a927),x78383),x78382))+~P107(f334(f334(f243(a927),x78383),x78381))+P107(f334(f334(f243(a927),f334(f334(f23(a927),x78381),x78382)),f334(f334(f23(a927),x78381),x78383))) % 188.18/188.26 [7839]~P107(f334(f334(f242(a927),x78392),x78391))+~P107(f334(f334(f243(a927),x78391),x78393))+P107(f334(f334(f243(a927),f334(f334(f23(a927),x78391),x78392)),f334(f334(f23(a927),x78393),x78392))) % 188.18/188.26 [7854]~P107(f334(f334(f243(a1),x78542),f2(a1)))+~P107(f334(f334(f242(a1),x78543),x78541))+P107(f334(f334(f242(a1),f334(f334(f41(a1),x78541),x78542)),f334(f334(f41(a1),x78543),x78542))) % 188.18/188.26 [7871]~P107(f334(f334(f243(a927),f2(a927)),x78713))+~P107(f334(f334(f242(a927),x78713),x78712))+P107(f334(f334(f242(a927),f334(f334(f41(a927),x78711),x78712)),f334(f334(f41(a927),x78711),x78713))) % 188.18/188.26 [7872]~P107(f334(f334(f243(a1),f2(a1)),x78722))+~P107(f334(f334(f242(a1),x78721),x78723))+P107(f334(f334(f242(a1),f334(f334(f41(a1),x78721),x78722)),f334(f334(f41(a1),x78723),x78722))) % 188.18/188.26 [7876]~P107(f334(f334(f243(a927),f2(a927)),x78762))+~P107(f334(f334(f243(a927),x78761),x78763))+P107(f334(f334(f243(a927),f334(f334(f87(a927),x78761),x78762)),f334(f334(f87(a927),x78763),x78762))) % 188.18/188.26 [7877]~P107(f334(f334(f243(a927),f2(a927)),x78771))+~P107(f334(f334(f243(a927),x78772),x78773))+P107(f334(f334(f243(a927),f334(f334(f87(a927),x78771),x78772)),f334(f334(f87(a927),x78771),x78773))) % 188.18/188.26 [7878]~P107(f334(f334(f243(a1),f2(a1)),x78781))+~P107(f334(f334(f243(a1),x78782),x78783))+P107(f334(f334(f243(a1),f334(f334(f87(a1),x78781),x78782)),f334(f334(f87(a1),x78781),x78783))) % 188.18/188.26 [7924]E(x79241,f2(a927))+E(f334(f334(f86(a927),f334(f334(f87(a927),x79241),f913(x79241,x79242,x79243))),f915(x79241,x79242,x79243)),x79242)+P107(f334(x79243,f334(f334(f41(a927),x79242),x79241))) % 188.18/188.26 [7986]E(f334(f334(f86(a927),f334(f334(f87(a927),x79861),f913(x79861,x79862,x79863))),f915(x79861,x79862,x79863)),x79862)+~P107(f334(x79863,f2(a927)))+P107(f334(x79863,f334(f334(f41(a927),x79862),x79861))) % 188.18/188.26 [8005]~P107(f334(f66(x80051),x80053))+P107(f334(f334(f336(x80051),f350(x80052,x80053,x80051)),x80053))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f9(x80051,a927),x80052),x80053))) % 188.18/188.26 [8006]~P107(f334(f66(x80061),x80063))+P107(f334(f334(f336(x80061),f550(x80062,x80063,x80061)),x80063))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f9(x80061,a927),x80062),x80063))) % 188.18/188.26 [8290]E(x82901,f195(f935(x82902,a922)))+E(x82901,f334(f334(f316(x82902),x82903),f195(f935(x82902,a922))))+~P107(f334(f334(f242(f935(x82902,a922)),x82901),f334(f334(f316(x82902),x82903),f195(f935(x82902,a922))))) % 188.18/188.26 [8323]~P107(f334(f334(f243(a927),f2(a927)),x83233))+P107(f334(f334(f242(a927),x83231),x83232))+~P107(f334(f334(f242(a927),f334(f334(f87(a927),x83233),x83231)),f334(f334(f87(a927),x83233),x83232))) % 188.18/188.26 [8324]~P107(f334(f334(f243(a927),f2(a927)),x83243))+P107(f334(f334(f242(a927),x83241),x83242))+~P107(f334(f334(f242(a927),f334(f334(f87(a927),x83241),x83243)),f334(f334(f87(a927),x83242),x83243))) % 188.18/188.26 [8326]~P107(f334(f334(f243(a927),f2(a927)),x83263))+P107(f334(f334(f243(a927),x83261),x83262))+~P107(f334(f334(f243(a927),f334(f334(f252(a927),x83263),x83261)),f334(f334(f252(a927),x83263),x83262))) % 188.18/188.26 [8366]~E(f334(f334(f109(f935(x83661,a922)),f536(x83663,x83662,x83661)),f535(x83663,x83662,x83661)),f195(f935(x83661,a922)))+E(f334(f334(f109(f935(x83661,a922)),x83662),f42(f935(x83661,a922),x83663)),f195(f935(x83661,a922)))+P107(f334(f334(f336(f935(x83661,a922)),x83662),x83663)) % 188.18/188.26 [8380]E(x83801,f120(x83802))+~E(f334(f149(f928(x83802),f928(x83802),f141(x83802),f120(x83802)),x83803),f120(x83802))+~P107(f334(f334(f336(f928(x83802)),x83801),f334(f179(f928(x83802)),x83803))) % 188.18/188.26 [8434]E(x84341,f195(f935(f935(x84342,a922),a922)))+P107(f334(f334(f336(f935(x84342,a922)),f541(x84343,x84341,x84342)),x84341))+P107(f334(f334(f242(f935(x84342,a922)),f43(f935(x84342,a922),x84341)),x84343)) % 188.18/188.26 [8440]~P72(x84401)+~P76(x84401)+E(f334(f334(f9(a1,x84401),f334(f334(f8(a927,x84401,a1),x84402),a112)),f334(f317(a927,a1,f107(a1)),x84403)),f334(f334(f9(a927,x84401),x84402),x84403)) % 188.18/188.26 [8441]~P72(x84411)+~P76(x84411)+E(f334(f334(f6(a1,x84411),f334(f334(f8(a927,x84411,a1),x84412),a112)),f334(f317(a927,a1,f107(a1)),x84413)),f334(f334(f6(a927,x84411),x84412),x84413)) % 188.18/188.26 [8484]~P107(f334(f66(x84841),x84843))+~P107(f334(f334(f243(a927),f2(a927)),f334(x84842,f350(x84842,x84843,x84841))))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f9(x84841,a927),x84842),x84843))) % 188.18/188.26 [8485]~P107(f334(f66(x84851),x84853))+~P107(f334(f334(f243(a927),f2(a927)),f334(x84852,f550(x84852,x84853,x84851))))+P107(f334(f334(f243(a927),f2(a927)),f334(f334(f9(x84851,a927),x84852),x84853))) % 188.18/188.26 [8521]~P66(x85212)+E(x85211,f84(x85212))+E(f334(f334(f296(x85212),f334(f334(f23(x85212),f334(f334(f252(x85212),x85211),x85213)),f84(x85212))),f334(f334(f23(x85212),x85211),f84(x85212))),f334(f334(f6(a927,x85212),f334(f252(x85212),x85211)),f334(f310(a927,f2(a927)),x85213))) % 188.18/188.26 [8575]E(x85751,f2(a927))+~P107(f334(x85753,f334(f334(f41(a927),x85752),x85751)))+P107(f334(f334(f243(a927),x85752),f334(f334(f87(a927),x85751),f334(a119,f912(x85751,x85752,x85753))))) % 188.18/188.26 [8593]P107(f334(x85931,f2(a927)))+~P107(f334(x85931,f334(f334(f41(a927),x85932),x85933)))+P107(f334(f334(f243(a927),x85932),f334(f334(f87(a927),x85933),f334(a119,f912(x85933,x85932,x85931))))) % 188.18/188.26 [8629]E(x86291,f2(a927))+~P107(f334(x86293,f334(f334(f41(a927),x86292),x86291)))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x86291),f912(x86291,x86292,x86293))),x86292)) % 188.18/188.26 [8661]P107(f334(x86611,f2(a927)))+~P107(f334(x86611,f334(f334(f41(a927),x86613),x86612)))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x86612),f912(x86612,x86613,x86611))),x86613)) % 188.18/188.26 [8669]~P109(x86691)+E(f334(f334(f155(x86691,x86691,f5(x86691)),x86692),x86693),f156(x86691,x86691,f5(x86691),x86692,x86693))+P107(f334(f334(f336(x86691),x86692),f334(f179(x86691),x86693))) % 188.18/188.26 [8703]~E(f334(x87033,f587(x87032,x87033,x87031)),f334(x87033,f589(x87032,x87033,x87031)))+~P63(x87031,f334(x87033,f588(x87032,x87033,x87031)))+P63(x87031,f334(f334(f44(x87032,f935(x87031,f935(x87031,a922))),f250(f935(x87032,a922))),x87033)) % 188.18/188.26 [8712]E(x87121,f195(f935(f935(x87122,a922),a922)))+~P107(f334(f334(f242(f935(x87122,a922)),f541(x87123,x87121,x87122)),x87123))+P107(f334(f334(f242(f935(x87122,a922)),f43(f935(x87122,a922),x87121)),x87123)) % 188.18/188.26 [8775]~P68(x87751)+~P107(f334(f334(f243(x87751),x87752),x87753))+P107(f334(f334(f243(x87751),x87752),f334(f334(f296(x87751),f334(f334(f86(x87751),x87752),x87753)),f334(f334(f86(x87751),f84(x87751)),f84(x87751))))) % 188.18/188.26 [8833]~P107(f334(f334(x88331,f358(x88331,x88333,x88332)),f362(x88331,x88333,x88332)))+P107(f334(f334(x88331,x88332),x88333))+~P107(f334(f322(f934(a1,a1),a57),f334(f334(f260(a1,a1),x88332),x88333))) % 188.18/188.26 [8834]~P107(f334(f334(x88341,f364(x88341,x88343,x88342)),f365(x88341,x88343,x88342)))+P107(f334(f334(x88341,x88342),x88343))+~P107(f334(f322(f934(a1,a1),a63),f334(f334(f260(a1,a1),x88342),x88343))) % 188.18/188.26 [8835]~P107(f334(f334(x88351,f367(x88351,x88353,x88352)),f368(x88351,x88353,x88352)))+P107(f334(f334(x88351,x88352),x88353))+~P107(f334(f322(f934(a1,a1),a230),f334(f334(f260(a1,a1),x88352),x88353))) % 188.18/188.26 [8836]~P107(f334(f334(x88361,f521(x88361,x88363,x88362)),f522(x88361,x88363,x88362)))+P107(f334(f334(x88361,x88362),x88363))+~P107(f334(f322(f934(a927,a927),a228),f334(f334(f260(a927,a927),x88362),x88363))) % 188.18/188.26 [8837]~P107(f334(f334(x88371,f690(x88371,x88373,x88372)),f692(x88371,x88373,x88372)))+P107(f334(f334(x88371,x88372),x88373))+~P107(f334(f322(f934(a1,a1),a189),f334(f334(f260(a1,a1),x88372),x88373))) % 188.18/188.26 [8838]~P107(f334(f334(x88381,f789(x88381,x88383,x88382)),f790(x88381,x88383,x88382)))+P107(f334(f334(x88381,x88382),x88383))+~P107(f334(f322(f934(a1,a1),a140),f334(f334(f260(a1,a1),x88382),x88383))) % 188.18/188.26 [9110]P107(f334(f334(x91101,x91102),x91103))+P107(f334(f322(f934(a927,a927),a228),f334(f334(f260(a927,a927),f521(x91101,x91103,x91102)),f522(x91101,x91103,x91102))))+~P107(f334(f322(f934(a927,a927),a228),f334(f334(f260(a927,a927),x91102),x91103))) % 188.18/188.26 [9111]P107(f334(f334(x91111,x91112),x91113))+P107(f334(f322(f934(a1,a1),a57),f334(f334(f260(a1,a1),f358(x91111,x91113,x91112)),f362(x91111,x91113,x91112))))+~P107(f334(f322(f934(a1,a1),a57),f334(f334(f260(a1,a1),x91112),x91113))) % 188.18/188.26 [9112]P107(f334(f334(x91121,x91122),x91123))+P107(f334(f322(f934(a1,a1),a63),f334(f334(f260(a1,a1),f364(x91121,x91123,x91122)),f365(x91121,x91123,x91122))))+~P107(f334(f322(f934(a1,a1),a63),f334(f334(f260(a1,a1),x91122),x91123))) % 188.18/188.26 [9113]P107(f334(f334(x91131,x91132),x91133))+P107(f334(f322(f934(a1,a1),a230),f334(f334(f260(a1,a1),f367(x91131,x91133,x91132)),f368(x91131,x91133,x91132))))+~P107(f334(f322(f934(a1,a1),a230),f334(f334(f260(a1,a1),x91132),x91133))) % 188.18/188.26 [9114]P107(f334(f334(x91141,x91142),x91143))+P107(f334(f322(f934(a1,a1),a189),f334(f334(f260(a1,a1),f690(x91141,x91143,x91142)),f692(x91141,x91143,x91142))))+~P107(f334(f322(f934(a1,a1),a189),f334(f334(f260(a1,a1),x91142),x91143))) % 188.18/188.26 [9115]P107(f334(f334(x91151,x91152),x91153))+P107(f334(f322(f934(a1,a1),a140),f334(f334(f260(a1,a1),f789(x91151,x91153,x91152)),f790(x91151,x91153,x91152))))+~P107(f334(f322(f934(a1,a1),a140),f334(f334(f260(a1,a1),x91152),x91153))) % 188.18/188.26 [9442]~P107(f334(f66(x94421),x94423))+P107(f334(f334(f336(f934(f935(x94421,a922),f935(x94421,a922))),f334(f334(f260(f935(x94421,a922),f935(x94421,a922)),x94422),x94423)),f321(x94421)))+~P107(f334(f334(f243(f935(x94421,a922)),x94422),x94423)) % 188.18/188.26 [9522]~P63(x95221,f334(x95223,f588(x95222,x95223,x95221)))+P63(x95221,f334(f334(f44(x95222,f935(x95221,f935(x95221,a922))),f250(f935(x95222,a922))),x95223))+~E(f334(f334(f109(f935(x95221,a922)),f257(x95221,x95221,f334(x95223,f587(x95222,x95223,x95221)))),f258(x95221,x95221,f334(x95223,f589(x95222,x95223,x95221)))),f195(f935(x95221,a922))) % 188.18/188.26 [9715]P55(x97151,x97152,x97153)+P107(f334(f334(f336(f934(x97151,x97151)),f573(x97153,x97152,x97151)),x97153))+~P107(f334(f334(f336(f934(x97151,x97151)),f334(f334(f260(x97151,x97151),f572(x97153,x97152,x97151)),f572(x97153,x97152,x97151))),x97153)) % 188.18/188.26 [10309]P55(x103091,x103092,x103093)+~P107(f334(f334(f265(x103091,x103091,a922),f334(f334(f7(x103091,f935(x103091,a922),f935(x103091,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x103091,a922),f935(x103091,a922)),x103091),f8(a922,a922,x103091)),f334(f334(f8(a922,f935(a922,a922),x103091),a332),f334(f334(f7(x103091,f935(x103091,a922),a922),f336(x103091)),x103092)))),f334(f334(f7(x103091,f935(x103091,a922),a922),f336(x103091)),x103092))),f573(x103093,x103092,x103091)))+~P107(f334(f334(f336(f934(x103091,x103091)),f334(f334(f260(x103091,x103091),f572(x103093,x103092,x103091)),f572(x103093,x103092,x103091))),x103093)) % 188.18/188.26 [5902]~P5(x59022)+E(x59021,f2(x59022))+E(f334(f334(f41(x59022),f334(f334(f87(x59022),x59023),x59021)),x59021),x59023) % 188.18/188.26 [5903]~P5(x59032)+E(x59031,f2(x59032))+E(f334(f334(f41(x59032),f334(f334(f87(x59032),x59031),x59033)),x59031),x59033) % 188.18/188.26 [6251]~P5(x62511)+~P59(x62511,x62513,x62512)+E(f334(f334(f87(x62511),f334(f334(f41(x62511),x62512),x62513)),x62513),x62512) % 188.18/188.26 [6701]~P76(x67011)+~E(f334(x67012,f2(a927)),f2(x67011))+E(f334(f334(f6(a927,x67011),x67012),f334(f310(a927,f334(a119,f2(a927))),x67013)),f334(f334(f6(a927,x67011),x67012),f334(f310(a927,f2(a927)),x67013))) % 188.18/188.26 [6830]~P5(x68302)+E(x68301,f2(x68302))+E(f334(f334(f41(x68302),f334(f334(f86(x68302),x68303),x68301)),x68301),f334(f334(f86(x68302),f334(f334(f41(x68302),x68303),x68301)),f84(x68302))) % 188.18/188.26 [6831]~P5(x68312)+E(x68311,f2(x68312))+E(f334(f334(f41(x68312),f334(f334(f86(x68312),x68311),x68313)),x68311),f334(f334(f86(x68312),f334(f334(f41(x68312),x68313),x68311)),f84(x68312))) % 188.18/188.26 [7042]~P107(f334(x70423,f2(a1)))+P107(f334(f334(f242(a927),x70421),x70422))+P107(f334(x70423,f334(f107(a1),f334(f334(f23(a927),x70422),x70421)))) % 188.18/188.26 [7142]P107(f334(f334(f243(a927),x71422),x71421))+P107(f334(f334(f242(a927),x71421),x71422))+P107(f334(x71423,f334(f107(a1),f334(f334(f23(a927),x71422),x71421)))) % 188.18/188.26 [7214]E(f334(f334(f86(a927),f334(f111(a927),x72141)),f334(f334(f86(a927),f334(f111(a927),x72142)),x72143)),f334(f334(f86(a927),f334(f111(a927),x72141)),x72143))+P107(f334(a200,f334(f111(a1),x72141)))+~P107(f334(a200,f334(f111(a1),x72142))) % 188.18/188.26 [7292]~E(x72922,f334(f334(f41(a927),x72923),x72921))+~P107(f334(f334(f243(a927),f2(a927)),x72921))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x72921),x72922)),x72923)) % 188.18/188.26 [7406]~P107(f334(f66(x74061),x74063))+~P107(f334(f66(x74061),x74062))+P107(f334(f66(x74061),f334(f334(f108(f935(x74061,a922)),x74062),x74063))) % 188.18/188.26 [7454]~P40(x74541,x74543)+~P40(x74541,x74542)+P40(x74541,f334(f334(f109(f935(f934(x74541,x74541),a922)),x74542),x74543)) % 188.18/188.26 [7455]~P54(x74551,x74553)+~P54(x74551,x74552)+P54(x74551,f334(f334(f108(f935(f934(x74551,x74551),a922)),x74552),x74553)) % 188.18/188.26 [7456]~P54(x74561,x74563)+~P54(x74561,x74562)+P54(x74561,f334(f334(f109(f935(f934(x74561,x74561),a922)),x74562),x74563)) % 188.18/188.26 [7687]~P109(x76871)+~P107(f334(f66(x76871),x76872))+E(f146(x76871,f334(f334(f23(f935(x76871,a922)),x76872),f334(f334(f316(x76871),x76873),f195(f935(x76871,a922))))),f177(x76871,x76873,f146(x76871,x76872))) % 188.18/188.26 [7748]P107(f334(x77481,f2(a1)))+~P107(f334(f334(f243(a927),x77482),x77483))+~P107(f334(x77481,f334(f107(a1),f334(f334(f23(a927),x77482),x77483)))) % 188.18/188.26 [7766]~P107(f334(f66(x77661),x77662))+E(f334(f40(x77661),f334(f334(f23(f935(x77661,a922)),x77662),f334(f334(f316(x77661),x77663),f195(f935(x77661,a922))))),f334(f40(x77661),x77662))+P107(f334(f334(f336(x77661),x77663),x77662)) % 188.18/188.26 [7893]~P127(x78931)+~P107(f334(f334(f243(x78931),f84(x78931)),x78932))+P107(f334(f334(f243(x78931),f84(x78931)),f334(f334(f87(x78931),x78932),f334(f334(f252(x78931),x78932),x78933)))) % 188.18/188.26 [7935]~P107(f334(f66(x79351),x79353))+E(f334(f334(f23(a927),f334(f40(x79351),x79352)),f334(f40(x79351),x79353)),f334(f40(x79351),f334(f334(f23(f935(x79351,a922)),x79352),x79353)))+~P107(f334(f334(f242(f935(x79351,a922)),x79353),x79352)) % 188.18/188.26 [7994]~P107(f334(f334(f242(a927),x79942),x79943))+~P107(f334(f334(f242(a927),x79941),f334(f334(f23(a927),x79943),x79942)))+P107(f334(f334(f242(a927),f334(f334(f86(a927),x79941),x79942)),x79943)) % 188.18/188.26 [8049]P107(f334(f66(x80491),x80492))+~P107(f334(f66(x80491),x80493))+~P107(f334(f66(x80491),f334(f334(f23(f935(x80491,a922)),x80492),x80493))) % 188.18/188.26 [8055]~P107(f334(f66(x80551),x80552))+E(f334(f40(x80551),f334(f334(f23(f935(x80551,a922)),x80552),f334(f334(f316(x80551),x80553),f195(f935(x80551,a922))))),f334(f334(f23(a927),f334(f40(x80551),x80552)),f84(a927)))+~P107(f334(f334(f336(x80551),x80553),x80552)) % 188.18/188.26 [8126]P63(x81261,x81262)+~P63(x81261,x81263)+~P107(f334(f334(f242(f935(x81261,f935(x81261,a922))),x81262),x81263)) % 188.18/188.26 [8163]~P107(f334(f334(f242(a927),x81633),x81632))+P107(f334(f334(f242(a927),x81631),f334(f334(f23(a927),x81632),x81633)))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),x81631),x81633)),x81632)) % 188.18/188.26 [8181]P39(x81811,x81812)+~P39(x81811,x81813)+~P107(f334(f334(f242(f935(f934(x81811,x81811),a922)),x81812),x81813)) % 188.18/188.26 [8182]P61(x81821,x81822)+~P61(x81821,x81823)+~P107(f334(f334(f242(f935(f934(x81821,x81821),a922)),x81822),x81823)) % 188.18/188.26 [8183]P41(x81831,x81832)+~P41(x81831,x81833)+~P107(f334(f334(f242(f935(f934(x81831,x81831),a922)),x81832),x81833)) % 188.18/188.26 [8414]~P127(x84141)+~P107(f334(f334(f243(x84141),f84(x84141)),x84142))+P107(f334(f334(f243(x84141),f334(f334(f252(x84141),x84142),x84143)),f334(f334(f87(x84141),x84142),f334(f334(f252(x84141),x84142),x84143)))) % 188.18/188.26 [8503]~P107(f334(x85031,f2(a1)))+~P107(f334(x85031,f334(f334(f23(a1),f334(f107(a1),x85032)),f334(f107(a1),x85033))))+P107(f334(x85031,f334(f107(a1),f334(f334(f23(a927),x85032),x85033)))) % 188.18/188.26 [8518]~P107(f334(f334(f242(a927),x85183),x85182))+P107(f334(x85181,f334(f334(f23(a1),f334(f107(a1),x85182)),f334(f107(a1),x85183))))+~P107(f334(x85181,f334(f107(a1),f334(f334(f23(a927),x85182),x85183)))) % 188.18/188.26 [8537]P107(f334(f334(f243(a927),x85371),x85372))+~P107(f334(x85373,f334(f334(f23(a1),f334(f107(a1),x85371)),f334(f107(a1),x85372))))+P107(f334(x85373,f334(f107(a1),f334(f334(f23(a927),x85371),x85372)))) % 188.18/188.26 [8587]~P129(x85872)+E(x85871,f2(x85872))+P107(f334(f334(f243(x85872),f2(x85872)),f334(f334(f86(x85872),f334(f334(f87(x85872),x85873),x85873)),f334(f334(f87(x85872),x85871),x85871)))) % 188.18/188.26 [8588]~P129(x85882)+E(x85881,f2(x85882))+P107(f334(f334(f243(x85882),f2(x85882)),f334(f334(f86(x85882),f334(f334(f87(x85882),x85881),x85881)),f334(f334(f87(x85882),x85883),x85883)))) % 188.18/188.26 [8686]~P107(f334(f334(f243(a927),f2(a927)),x86861))+~P107(f334(f334(f243(a1),x86862),x86863))+P107(f334(f334(f243(a1),f334(f334(f87(a1),f334(f107(a1),x86861)),x86862)),f334(f334(f87(a1),f334(f107(a1),x86861)),x86863))) % 188.18/188.26 [8744]E(f334(f334(f109(f935(x87441,a922)),x87442),f42(f935(x87441,a922),x87443)),f195(f935(x87441,a922)))+P107(f334(f334(f336(f935(x87441,a922)),x87442),x87443))+P107(f334(f334(f336(f935(x87441,a922)),f536(x87443,x87442,x87441)),f334(f334(f316(f935(x87441,a922)),x87442),x87443))) % 188.18/188.26 [8745]E(f334(f334(f109(f935(x87451,a922)),x87452),f42(f935(x87451,a922),x87453)),f195(f935(x87451,a922)))+P107(f334(f334(f336(f935(x87451,a922)),x87452),x87453))+P107(f334(f334(f336(f935(x87451,a922)),f535(x87453,x87452,x87451)),f334(f334(f316(f935(x87451,a922)),x87452),x87453))) % 188.18/188.26 [8774]E(x87741,x87742)+~E(f334(f196(f928(x87743)),x87741),f334(f196(f928(x87743)),x87742))+P107(f334(f334(f336(f934(x87743,x87743)),f677(x87743,x87741,x87742)),f334(f179(f934(x87743,x87743)),f334(f334(f188(x87743,x87743),x87742),x87741)))) % 188.18/188.26 [9015]E(f314(x90151,x90152),f314(x90151,x90153))+~P107(f334(f334(f242(f935(f934(x90151,x90151),a922)),x90153),f314(x90151,x90152)))+~P107(f334(f334(f242(f935(f934(x90151,x90151),a922)),x90152),x90153)) % 188.18/188.26 [9087]~P55(x90871,f250(f935(x90871,a922)),x90873)+P107(f334(f334(f242(f935(f934(f928(x90871),f928(x90871)),a922)),f164(x90871,x90872)),f165(x90871,x90873)))+~P107(f334(f334(f242(f935(f934(x90871,x90871),a922)),x90872),x90873)) % 188.18/188.26 [9281]P39(x92811,x92812)+~P107(f334(f334(f336(x92811),x92813),f626(x92812,x92811)))+P107(f334(f334(f336(f934(x92811,x92811)),f334(f334(f260(x92811,x92811),f650(x92812,x92811,x92813)),x92813)),x92812)) % 188.18/188.26 [9310]~P107(f334(f66(x93101),x93102))+P107(f334(f66(f935(x93101,a922)),f334(f334(f65(x93101),x93102),x93103)))+~P107(f334(f334(f242(f935(f934(x93101,x93101),a922)),x93103),f334(f334(f262(x93101,x93101),x93102),f334(f16(f935(x93101,a922),x93101),x93102)))) % 188.18/188.26 [9351]P55(x93511,x93512,x93513)+P107(f334(f334(f336(x93511),f563(x93513,x93512,x93511)),x93512))+~P107(f334(f334(f242(f935(f934(x93511,x93511),a922)),x93513),f334(f334(f262(x93511,x93511),x93512),f334(f16(f935(x93511,a922),x93511),x93512)))) % 188.18/188.26 [9352]P55(x93521,x93522,x93523)+P107(f334(f334(f336(x93521),f567(x93522,x93523,x93521)),x93522))+~P107(f334(f334(f242(f935(f934(x93521,x93521),a922)),x93523),f334(f334(f262(x93521,x93521),x93522),f334(f16(f935(x93521,a922),x93521),x93522)))) % 188.18/188.26 [9388]~P68(x93881)+~P107(f334(f334(f243(x93881),x93882),x93883))+P107(f334(f334(f243(x93881),f334(f334(f296(x93881),f334(f334(f86(x93881),x93882),x93883)),f334(f334(f86(x93881),f84(x93881)),f84(x93881)))),x93883)) % 188.18/188.26 [9417]~P67(x94171)+P107(f334(f334(f242(x94171),x94172),x94173))+~P107(f334(f334(f242(x94171),f334(f334(f87(x94171),f493(x94173,x94172,x94171)),x94172)),x94173)) % 188.18/188.26 [9553]E(f334(f196(f928(f928(x95531))),f334(f143(f928(x95531),f334(f334(f8(a927,a922,f928(x95531)),f334(f243(a927),x95532)),f196(f928(x95531)))),f186(x95531,x95533))),f334(f196(f928(x95531)),f334(f334(f171(f928(x95531)),x95533),x95532)))+~P15(a927,f334(f175(a927),f334(f334(f161(f928(x95531),a927),f196(f928(x95531))),x95533)))+~P107(f334(f334(f243(a927),x95532),f334(f196(f928(f928(x95531))),x95533))) % 188.18/188.26 [9662]~P39(x96621,x96622)+P29(x96621,f334(f334(f260(f935(f934(x96621,x96621),a922),f935(f934(x96621,x96621),a922)),x96622),x96623))+~P107(f334(f334(f242(f935(f934(x96621,x96621),a922)),f334(f334(f295(x96621,x96621,x96621),x96622),x96623)),x96622)) % 188.18/188.26 [9667]E(f334(f334(f161(f928(x96671),x96671),f334(f334(f7(f928(x96671),a927,x96671),f171(x96671)),x96672)),f334(f143(f928(x96671),f334(f334(f8(a927,a922,f928(x96671)),f334(f243(a927),x96672)),f196(f928(x96671)))),f186(x96671,x96673))),f334(f334(f171(f928(x96671)),x96673),x96672))+~P15(a927,f334(f175(a927),f334(f334(f161(f928(x96671),a927),f196(f928(x96671))),x96673)))+~P107(f334(f334(f243(a927),x96672),f334(f196(f928(f928(x96671))),x96673))) % 188.18/188.26 [9811]P55(x98111,x98112,x98113)+~P107(f334(f334(f336(f934(x98111,x98111)),f334(f334(f260(x98111,x98111),f563(x98113,x98112,x98111)),f563(x98113,x98112,x98111))),x98113))+~P107(f334(f334(f242(f935(f934(x98111,x98111),a922)),x98113),f334(f334(f262(x98111,x98111),x98112),f334(f16(f935(x98111,a922),x98111),x98112)))) % 188.18/188.26 [9812]P55(x98121,x98122,x98123)+~P107(f334(f334(f336(f934(x98121,x98121)),f334(f334(f260(x98121,x98121),f567(x98122,x98123,x98121)),f567(x98122,x98123,x98121))),x98123))+~P107(f334(f334(f242(f935(f934(x98121,x98121),a922)),x98123),f334(f334(f262(x98121,x98121),x98122),f334(f16(f935(x98121,a922),x98121),x98122)))) % 188.18/188.26 [10005]~P142(x100051)+~P126(x100051)+E(f334(f334(f296(x100051),f334(f110(x100051),f334(f334(f78(f934(a1,a1),a1,x100052,f259(a1,a1)),f221(x100052)),x100053))),f334(f110(x100051),f334(f334(f78(f934(a1,a1),a1,x100052,f264(a1,a1)),f221(x100052)),x100053))),f231(x100052,x100051,x100053)) % 188.18/188.26 [10180]~E(x101803,f2(a927))+~E(f334(f196(f928(x101801)),f334(f334(f171(f928(x101801)),x101802),f725(x101803,x101801,x101802))),x101803)+E(f334(f334(f161(a927,f928(x101801)),f334(f334(f7(a927,f928(a927),f928(x101801)),f334(f334(f8(f935(a927,x101801),f935(f928(a927),f928(x101801)),a927),f161(a927,x101801)),f334(f7(a927,a927,x101801),f334(f334(f8(f928(x101801),f935(a927,x101801),a927),f171(x101801)),f334(f171(f928(x101801)),x101802))))),f146(a927,f334(f310(a927,f2(a927)),f334(f196(f928(f928(x101801))),x101802))))),f146(a927,f334(f310(a927,f2(a927)),x101803))),f186(x101801,x101802)) % 188.18/188.26 [10181]E(x101811,f120(f928(x101812)))+~E(f334(f196(f928(x101812)),f334(f334(f171(f928(x101812)),x101811),f725(x101813,x101812,x101811))),x101813)+E(f334(f334(f161(a927,f928(x101812)),f334(f334(f7(a927,f928(a927),f928(x101812)),f334(f334(f8(f935(a927,x101812),f935(f928(a927),f928(x101812)),a927),f161(a927,x101812)),f334(f7(a927,a927,x101812),f334(f334(f8(f928(x101812),f935(a927,x101812),a927),f171(x101812)),f334(f171(f928(x101812)),x101811))))),f146(a927,f334(f310(a927,f2(a927)),f334(f196(f928(f928(x101812))),x101811))))),f146(a927,f334(f310(a927,f2(a927)),x101813))),f186(x101812,x101811)) % 188.18/188.26 [10182]~E(x101823,f2(a927))+E(f334(f334(f161(a927,f928(x101821)),f334(f334(f7(a927,f928(a927),f928(x101821)),f334(f334(f8(f935(a927,x101821),f935(f928(a927),f928(x101821)),a927),f161(a927,x101821)),f334(f7(a927,a927,x101821),f334(f334(f8(f928(x101821),f935(a927,x101821),a927),f171(x101821)),f334(f171(f928(x101821)),x101822))))),f146(a927,f334(f310(a927,f2(a927)),f334(f196(f928(f928(x101821))),x101822))))),f146(a927,f334(f310(a927,f2(a927)),x101823))),f186(x101821,x101822))+P107(f334(f334(f243(a927),f725(x101823,x101821,x101822)),f334(f196(f928(f928(x101821))),x101822))) % 188.18/188.26 [10183]E(x101831,f120(f928(x101832)))+E(f334(f334(f161(a927,f928(x101832)),f334(f334(f7(a927,f928(a927),f928(x101832)),f334(f334(f8(f935(a927,x101832),f935(f928(a927),f928(x101832)),a927),f161(a927,x101832)),f334(f7(a927,a927,x101832),f334(f334(f8(f928(x101832),f935(a927,x101832),a927),f171(x101832)),f334(f171(f928(x101832)),x101831))))),f146(a927,f334(f310(a927,f2(a927)),f334(f196(f928(f928(x101832))),x101831))))),f146(a927,f334(f310(a927,f2(a927)),x101833))),f186(x101832,x101831))+P107(f334(f334(f243(a927),f725(x101833,x101832,x101831)),f334(f196(f928(f928(x101832))),x101831))) % 188.18/188.26 [7932]E(f334(f334(f86(a927),f334(f111(a927),x79321)),f334(f334(f86(a927),f334(f111(a927),x79322)),x79323)),f334(f334(f86(a927),f334(f111(a927),f334(f334(f86(a1),x79321),x79322))),x79323))+P107(f334(a200,f334(f111(a1),x79321)))+P107(f334(a200,f334(f111(a1),x79322))) % 188.18/188.26 [8678]~P107(f334(f66(x86781),x86782))+~P107(f334(f334(f336(x86781),x86783),x86782))+E(f334(a119,f334(f40(x86781),f334(f334(f23(f935(x86781,a922)),x86782),f334(f334(f316(x86781),x86783),f195(f935(x86781,a922)))))),f334(f40(x86781),x86782)) % 188.18/188.26 [8693]~P107(f334(f66(x86931),x86932))+~P107(f334(f334(f336(x86931),x86933),x86932))+E(f334(f334(f86(a927),f84(a927)),f334(f40(x86931),f334(f334(f23(f935(x86931,a922)),x86932),f334(f334(f316(x86931),x86933),f195(f935(x86931,a922)))))),f334(f40(x86931),x86932)) % 188.18/188.26 [8782]~P109(x87821)+~P107(f334(f66(x87821),x87823))+E(f334(f334(f155(x87821,x87821,f5(x87821)),x87822),f146(x87821,f334(f334(f23(f935(x87821,a922)),x87823),f334(f334(f316(x87821),x87822),f195(f935(x87821,a922)))))),f146(x87821,f334(f334(f316(x87821),x87822),x87823))) % 188.18/188.26 [8941]~P107(f334(f66(x89411),x89413))+~P107(f334(f66(x89411),x89412))+E(f334(f334(f86(a927),f334(f40(x89411),f334(f334(f108(f935(x89411,a922)),x89412),x89413))),f334(f40(x89411),f334(f334(f109(f935(x89411,a922)),x89412),x89413))),f334(f334(f86(a927),f334(f40(x89411),x89412)),f334(f40(x89411),x89413))) % 188.18/188.26 [10140]~P27(x101401,f935(f935(x101401,a922),a922),f334(f334(f7(x101401,f935(f934(x101401,x101401),a922),f935(f935(x101401,a922),a922)),f334(f334(f8(f935(x101401,a922),f935(f935(f934(x101401,x101401),a922),f935(f935(x101401,a922),a922)),x101401),f65(x101401)),f334(f334(f7(x101401,f935(x101401,a922),f935(x101401,a922)),f316(x101401)),f195(f935(x101401,a922))))),x101403),x101402)+~P107(f334(f66(x101401),x101402))+E(f334(f40(f935(x101401,a922)),f334(f334(f65(x101401),x101402),x101403)),f334(f40(x101401),x101402)) % 188.18/188.26 [8334]~P95(x83341)+P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x83343)))+E(f334(f334(f252(x83341),x83342),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x83343)),x83343))),f84(x83341)) % 188.18/188.26 [9655]~P95(x96551)+~P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),x96553)))+E(f334(f334(f252(x96551),x96552),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x96553)),x96553))),f334(f334(f94(x96551,x96551),f334(f334(f252(x96551),x96552),f334(f111(a927),x96553))),f334(f334(f18(x96551,x96551,x96551),f334(f334(f8(x96551,f935(x96551,x96551),x96551),f87(x96551)),f334(f87(x96551),x96552))),f5(x96551)))) % 188.18/188.26 [10069]~P107(f334(f144(x100691),x100693))+~P107(f334(f334(f336(x100691),x100692),f334(f179(x100691),x100693)))+E(f334(f334(f145(x100691),f334(f196(f928(x100691)),f184(x100691,f334(f334(f8(a922,a922,x100691),a329),f334(f334(f7(x100691,x100691,a922),a331),x100692)),f334(f175(x100691),x100693)))),f334(f175(x100691),x100693)),f334(f334(f158(x100691),x100692),f334(f175(x100691),f184(x100691,f334(f334(f8(a922,a922,x100691),a329),f334(f334(f7(x100691,x100691,a922),a331),x100692)),x100693)))) % 188.18/188.26 [10124]P107(f334(f334(f242(f935(f934(x101241,x101241),a922)),f314(x101241,x101242)),x101243))+~P107(f334(f334(f242(f935(f934(x101241,x101241),a922)),f314(x101241,f195(f935(f934(x101241,x101241),a922)))),x101243))+~P107(f334(f334(f242(f935(f934(x101241,x101241),a922)),f334(f334(f295(x101241,x101241,x101241),f334(f334(f109(f935(f934(x101241,x101241),a922)),f314(x101241,x101242)),x101243)),x101242)),x101243)) % 188.18/188.26 [9979]~P107(f334(f66(x99791),f334(f270(x99791),x99793)))+~P107(f334(f66(x99791),f334(f270(x99791),x99792)))+P107(f334(f66(x99791),f334(f270(x99791),f334(f334(f18(x99791,a922,a922),f334(f334(f8(a922,f935(a922,a922),x99791),a333),x99792)),x99793)))) % 188.18/188.26 [10240]P107(f334(f334(f242(f935(f934(x102401,x102401),a922)),f334(f334(f295(x102401,x102401,x102401),x102402),f314(x102401,x102402))),x102403))+~P107(f334(f334(f242(f935(f934(x102401,x102401),a922)),x102402),x102403))+~P107(f334(f334(f242(f935(f934(x102401,x102401),a922)),f334(f334(f295(x102401,x102401,x102401),f334(f334(f109(f935(f934(x102401,x102401),a922)),f334(f334(f295(x102401,x102401,x102401),x102402),f314(x102401,x102402))),x102403)),x102402)),x102403)) % 188.18/188.26 [10200]~P107(f334(f144(x102001),x102003))+~P107(f334(f334(f336(x102001),x102002),f334(f179(x102001),x102003)))+E(f334(f175(x102001),f334(f178(x102001),f334(f334(f145(x102001),f334(f196(f928(x102001)),f184(x102001,f334(f334(f8(a922,a922,x102001),a329),f334(f334(f7(x102001,x102001,a922),a331),x102002)),x102003))),x102003))),f184(x102001,f334(f334(f8(a922,a922,x102001),a329),f334(f334(f7(x102001,x102001,a922),a331),x102002)),f334(f175(x102001),x102003))) % 188.18/188.26 [10393]~P124(x103932)+E(x103931,f2(x103932))+~E(f334(f334(f86(x103932),f334(f334(f252(x103932),x103933),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x103932),x103931),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f2(x103932)) % 188.18/188.26 [10394]~P124(x103942)+E(x103941,f2(x103942))+~E(f334(f334(f86(x103942),f334(f334(f252(x103942),x103941),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x103942),x103943),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f2(x103942)) % 188.18/188.26 [10430]~P124(x104302)+E(x104301,f2(x104302))+P107(f334(f334(f243(x104302),f2(x104302)),f334(f334(f86(x104302),f334(f334(f252(x104302),x104303),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104302),x104301),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))))) % 188.18/188.26 [10431]~P124(x104312)+E(x104311,f2(x104312))+P107(f334(f334(f243(x104312),f2(x104312)),f334(f334(f86(x104312),f334(f334(f252(x104312),x104311),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104312),x104313),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))))) % 188.18/188.26 [10454]~P124(x104541)+P107(f334(f334(f242(x104541),f2(x104541)),x104542))+~P107(f334(f334(f242(x104541),f2(x104541)),f334(f334(f252(x104541),x104542),f334(a119,f334(f334(f87(a927),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),x104543))))) % 188.18/188.26 [5729]~P26(x57291,x57294,x57293)+P26(x57291,x57292,x57293)+~P26(x57291,x57292,x57294) % 188.18/188.26 [5200]~E(x52002,f96(x52003,x52001))+P107(f334(x52001,x52002))+~P107(f334(x52001,x52004)) % 188.18/188.26 [5442]E(f73(x54423,x54422,x54424),x54422)+E(x54421,f752(x54422,x54423,x54424))+~P107(f334(x54424,x54421)) % 188.18/188.26 [6757]E(f73(x67571,x67572,x67573),f91(x67571,x67573))+~E(f792(x67572,x67571,x67573,x67574),x67574)+~P107(f334(x67573,x67574)) % 188.18/188.26 [6959]~P39(x69592,x69594)+~P39(x69591,x69593)+P39(f934(x69591,x69592),f326(x69591,x69592,x69593,x69594)) % 188.18/188.26 [6960]~P40(x69602,x69604)+~P40(x69601,x69603)+P40(f934(x69601,x69602),f326(x69601,x69602,x69603,x69604)) % 188.18/188.26 [5382]~P9(x53824,x53821)+~E(f334(x53821,x53822),f334(x53821,x53823))+P107(f334(f334(x53821,x53822),x53823)) % 188.18/188.26 [5546]~P9(x55464,x55461)+E(f334(x55461,x55462),f334(x55461,x55463))+~P107(f334(f334(x55461,x55462),x55463)) % 188.18/188.26 [5547]~P17(x55474,x55471)+E(f334(x55471,x55472),f334(x55471,x55473))+~P107(f334(f334(x55471,x55472),x55473)) % 188.18/188.26 [5638]~P20(x56383,x56384,x56381)+E(f334(x56381,x56382),f334(f68(x56383,x56384),x56382))+~P107(f334(f66(x56383),x56382)) % 188.18/188.26 [5639]~P11(x56393,x56394,x56391)+E(f334(x56391,x56392),f334(f68(x56393,x56394),x56392))+~P107(f334(f66(x56393),x56392)) % 188.18/188.26 [5762]~P9(x57624,x57621)+~P107(f334(f334(x57621,x57623),x57622))+P107(f334(f334(x57621,x57622),x57623)) % 188.18/188.26 [5763]~P53(x57634,x57631)+~P107(f334(f334(x57631,x57633),x57632))+P107(f334(f334(x57631,x57632),x57633)) % 188.18/188.26 [5764]~P17(x57644,x57641)+~P107(f334(f334(x57641,x57643),x57642))+P107(f334(f334(x57641,x57642),x57643)) % 188.18/188.26 [5765]~P17(x57653,x57651)+P107(f334(f334(x57651,x57652),x57652))+~P107(f334(f334(x57651,x57654),x57652)) % 188.18/188.26 [5766]~P17(x57663,x57661)+P107(f334(f334(x57661,x57662),x57662))+~P107(f334(f334(x57661,x57662),x57664)) % 188.18/188.26 [5844]E(x58441,x58442)+~E(f334(f259(x58443,x58444),x58441),f334(f259(x58443,x58444),x58442))+~E(f334(f264(x58443,x58444),x58441),f334(f264(x58443,x58444),x58442)) % 188.18/188.26 [5871]E(x58711,x58712)+~P107(f334(f53(x58713,x58714),x58712))+~P107(f334(f53(x58713,x58714),x58711)) % 188.18/188.26 [6064]~P76(x60642)+E(f240(x60641,x60642,x60643,x60644),f2(x60642))+P107(f334(f66(x60641),x60644)) % 188.18/188.26 [6114]~P9(x61143,x61142)+~P107(f334(x61141,x61144))+P107(f334(x61141,f837(x61141,x61142,x61143))) % 188.18/188.26 [6206]~P107(f334(f322(x62061,x62062),x62064))+P107(f334(f322(x62061,x62062),x62063))+~P107(f334(f334(x62062,x62063),x62064)) % 188.18/188.26 [6630]P51(x66301,x66302,x66303,x66304)+P107(f334(f334(x66302,x66304),x66303))+~P107(f334(f334(x66302,x66303),x66304)) % 188.18/188.26 [6994]~P31(x69941,x69943,x69944)+P107(f334(x69941,x69942))+~P107(f334(f334(f336(a1),x69942),f311(a1,x69943,x69944))) % 188.18/188.26 [7176]~P9(x71761,x71763)+~P107(f334(x71762,x71764))+P107(f334(f334(f336(x71761),f837(x71762,x71763,x71761)),f278(x71761,x71763))) % 188.18/188.26 [8043]E(x80431,f2(a927))+~P107(f334(x80432,x80433))+P107(f334(x80432,f785(x80432,x80433,x80431,x80434))) % 188.18/188.26 [8121]~P109(x81212)+~P107(f334(f144(x81211),x81214))+P107(f334(f144(x81211),f157(x81211,x81212,x81213,x81214))) % 188.18/188.26 [8162]E(f73(x81621,x81622,x81623),f91(x81621,x81623))+~P107(f334(x81623,x81624))+P107(f334(x81623,f792(x81622,x81621,x81623,x81624))) % 188.18/188.26 [8340]~P107(f334(f66(x83402),x83404))+~P107(f334(f66(x83401),x83403))+P107(f334(f66(f933(x83401,x83402)),f320(x83401,x83402,x83403,x83404))) % 188.18/188.26 [8341]~P107(f334(f144(x83412),x83414))+~P107(f334(f144(x83411),x83413))+P107(f334(f144(f934(x83411,x83412)),f64(x83411,x83412,x83413,x83414))) % 188.18/188.26 [8344]P107(f334(f334(f336(f928(x83441)),f334(f334(f141(x83441),x83442),x83443)),f168(x83441,x83444)))+~P107(f334(f334(f336(f928(x83441)),x83443),f168(x83441,x83444)))+~P107(f334(f334(f336(f928(x83441)),x83442),f168(x83441,x83444))) % 188.18/188.26 [8617]E(x86171,f2(a927))+P107(f334(x86172,x86173))+~P107(f334(x86172,f787(x86172,x86173,x86171,x86174))) % 188.18/188.26 [8653]~P109(x86533)+~P107(f334(f144(x86531),f157(x86531,x86533,x86534,x86532)))+P107(f334(f144(x86531),x86532)) % 188.18/188.26 [8930]~P107(f334(f334(f336(f934(x89301,x89301)),f334(f334(f260(x89301,x89301),x89302),x89304)),f314(x89301,x89303)))+P107(f334(f334(f336(x89301),x89302),f323(x89301,x89303)))+~P107(f334(f334(f336(x89301),x89304),f323(x89301,x89303))) % 188.18/188.26 [5366]~P72(x53662)+E(f334(f334(f9(x53661,x53662),x53663),x53664),f84(x53662))+P107(f334(f66(x53661),x53664)) % 188.18/188.26 [5369]~P76(x53692)+E(f334(f334(f6(x53691,x53692),x53693),x53694),f2(x53692))+P107(f334(f66(x53691),x53694)) % 188.18/188.26 [5370]~P121(x53701)+P59(x53701,x53702,x53703)+~E(x53703,f334(f334(f87(x53701),x53702),x53704)) % 188.18/188.26 [5511]~P73(x55113)+E(x55111,x55112)+~E(f334(f334(f86(x55113),x55114),x55111),f334(f334(f86(x55113),x55114),x55112)) % 188.18/188.26 [5512]~P74(x55123)+E(x55121,x55122)+~E(f334(f334(f86(x55123),x55124),x55121),f334(f334(f86(x55123),x55124),x55122)) % 188.18/188.26 [5514]~P73(x55143)+E(x55141,x55142)+~E(f334(f334(f86(x55143),x55141),x55144),f334(f334(f86(x55143),x55142),x55144)) % 188.18/188.26 [5634]~P7(x56343)+E(x56341,f195(f935(x56342,a922)))+E(f334(f334(f44(x56342,x56343),x56341),f334(f16(x56343,x56342),x56344)),x56344) % 188.18/188.26 [5635]~P7(x56353)+E(x56351,f195(f935(x56352,a922)))+E(f334(f334(f45(x56352,x56353),x56351),f334(f16(x56353,x56352),x56354)),x56354) % 188.18/188.26 [5835]~P119(x58351)+~P59(x58351,x58352,x58354)+P59(x58351,x58352,f334(f334(f87(x58351),x58353),x58354)) % 188.18/188.26 [5836]~P119(x58361)+~P59(x58361,x58362,x58363)+P59(x58361,x58362,f334(f334(f87(x58361),x58363),x58364)) % 188.18/188.26 [5857]~P111(x58573)+E(x58571,x58572)+~E(f311(x58573,x58574,x58571),f334(f334(f316(x58573),x58572),f195(f935(x58573,a922)))) % 188.18/188.26 [5858]~P111(x58583)+E(x58581,x58582)+~E(f311(x58583,x58581,x58582),f334(f334(f316(x58583),x58584),f195(f935(x58583,a922)))) % 188.18/188.26 [5918]~P37(x59183,x59181,x59184)+P37(x59183,x59181,f334(f334(f158(x59183),x59182),x59184))+P107(f334(x59181,x59182)) % 188.18/188.26 [5929]~P114(x59291)+~E(x59293,f2(x59291))+P59(x59291,f334(f334(f87(x59291),x59292),x59293),f334(f334(f87(x59291),x59294),x59293)) % 188.18/188.26 [5930]~P114(x59301)+~E(x59302,f2(x59301))+P59(x59301,f334(f334(f87(x59301),x59302),x59303),f334(f334(f87(x59301),x59302),x59304)) % 188.18/188.26 [6022]~P33(x60221,x60222,x60224)+~P107(f334(x60222,x60223))+P33(x60221,x60222,f334(f334(f158(x60221),x60223),x60224)) % 188.18/188.26 [6091]~P119(x60911)+P59(x60911,x60912,x60913)+~P59(x60911,f334(f334(f87(x60911),x60914),x60912),x60913) % 188.18/188.26 [6092]~P119(x60921)+P59(x60921,x60922,x60923)+~P59(x60921,f334(f334(f87(x60921),x60922),x60924),x60923) % 188.18/188.26 [6163]P107(f334(x61631,x61632))+~P107(f334(f256(x61633,x61631),x61634))+~P107(f334(f334(f336(x61633),x61632),x61634)) % 188.18/188.26 [6172]~P33(x61721,x61722,x61724)+~P33(x61721,x61722,x61723)+P33(x61721,x61722,f334(f334(f141(x61721),x61723),x61724)) % 188.18/188.26 [6185]P35(x61851,x61852,x61853)+~P35(x61851,x61852,f334(f334(f158(x61851),x61854),x61853))+P107(f334(x61852,x61854)) % 188.18/188.26 [6186]P37(x61861,x61862,x61863)+~P37(x61861,x61862,f334(f334(f158(x61861),x61864),x61863))+P107(f334(x61862,x61864)) % 188.18/188.26 [6254]~P114(x62541)+~P59(x62541,x62543,x62544)+P59(x62541,f334(f334(f87(x62541),x62542),x62543),f334(f334(f87(x62541),x62542),x62544)) % 188.18/188.26 [6255]~P114(x62551)+~P59(x62551,x62552,x62554)+P59(x62551,f334(f334(f87(x62551),x62552),x62553),f334(f334(f87(x62551),x62554),x62553)) % 188.18/188.26 [6261]P35(x62611,x62612,x62613)+P35(x62611,x62612,x62614)+~P35(x62611,x62612,f334(f334(f141(x62611),x62614),x62613)) % 188.18/188.26 [6280]~P76(x62801)+E(f334(f334(f6(a927,x62801),x62802),f334(f310(a927,x62803),f334(a119,x62804))),f2(x62801))+~P107(f334(f334(f243(a927),x62804),x62803)) % 188.18/188.26 [6285]~P6(x62851)+~E(f50(x62851,x62852,x62853),f50(x62851,x62854,x62853))+E(f50(x62851,f334(f85(x62851),x62852),x62853),f50(x62851,f334(f85(x62851),x62854),x62853)) % 188.18/188.26 [6351]P107(f334(x63511,x63512))+~E(f334(f143(x63513,x63511),x63514),x63514)+~P107(f334(f334(f336(x63513),x63512),f334(f179(x63513),x63514))) % 188.18/188.26 [6370]~E(f334(f334(f86(a927),x63703),x63702),f334(f334(f86(a927),x63701),x63704))+~P107(f334(f334(f243(a927),x63703),x63704))+P107(f334(f334(f243(a927),x63701),x63702)) % 188.18/188.26 [6376]P35(x63761,x63762,x63763)+~P107(f334(x63762,x63764))+~P107(f334(f334(f336(x63761),x63764),f334(f179(x63761),x63763))) % 188.18/188.26 [6417]~P33(x64173,x64171,x64174)+P107(f334(x64171,x64172))+~P107(f334(f334(f336(x64173),x64172),f334(f179(x64173),x64174))) % 188.18/188.26 [6419]~E(f334(f143(x64191,x64192),x64193),f120(x64191))+~P107(f334(x64192,x64194))+~P107(f334(f334(f336(x64191),x64194),f334(f179(x64191),x64193))) % 188.18/188.26 [6420]~E(f184(x64203,x64201,x64204),x64204)+P107(f334(x64201,x64202))+~P107(f334(f334(f336(x64203),x64202),f334(f179(x64203),x64204))) % 188.18/188.26 [6442]~E(x64424,f195(f935(x64422,a922)))+~E(x64423,f195(f935(x64421,a922)))+E(f320(x64421,x64422,x64423,x64424),f195(f935(f933(x64421,x64422),a922))) % 188.18/188.26 [6586]P107(f334(x65861,x65862))+~P107(f334(f167(x65863,x65861),x65864))+~P107(f334(f334(f336(x65863),x65862),f334(f179(x65863),x65864))) % 188.18/188.26 [6725]~P32(x67251,x67253,x67254)+P107(f334(x67251,x67252))+~P107(f334(f334(f336(a927),x67252),f334(f310(a927,x67253),x67254))) % 188.18/188.26 [6858]~P76(x68581)+E(f334(f334(f6(a927,x68581),x68582),f311(a927,x68583,f334(a119,x68584))),f2(x68581))+~P107(f334(f334(f243(a927),f334(a119,x68584)),x68583)) % 188.18/188.26 [6997]~P109(x69971)+E(f334(f334(f23(f935(x69971,a922)),f334(f310(x69971,x69972),x69973)),f334(f310(x69971,x69972),x69974)),f334(f310(x69971,x69974),x69973))+~P107(f334(f334(f242(x69971),x69972),x69974)) % 188.18/188.26 [7062]~E(x70623,x70624)+E(x70621,f2(a927))+P107(f334(f334(f336(x70622),x70623),f334(f179(x70622),f176(x70622,x70621,x70624)))) % 188.18/188.26 [7337]~P107(f334(f334(f336(f928(x73371)),x73374),f168(x73371,x73373)))+P107(f334(f334(f336(x73371),x73372),x73373))+~P107(f334(f334(f336(x73371),x73372),f334(f179(x73371),x73374))) % 188.18/188.26 [7344]~P39(x73441,x73442)+P107(f334(f334(f336(x73441),f627(x73442,x73441,x73443)),x73443))+~P107(f334(f334(f336(x73441),x73444),x73443)) % 188.18/188.26 [7399]~P72(x73991)+E(f334(f334(f334(f70(x73991,x73992,f87(x73991)),x73993),f84(x73991)),x73994),f334(f334(f9(x73992,x73991),x73993),x73994))+~P107(f334(f66(x73992),x73994)) % 188.18/188.26 [7401]~P76(x74011)+E(f334(f334(f334(f70(x74011,x74012,f86(x74011)),x74013),f2(x74011)),x74014),f334(f334(f6(x74012,x74011),x74013),x74014))+~P107(f334(f66(x74012),x74014)) % 188.18/188.26 [7429]P27(x74291,x74292,x74293,x74294)+~E(f334(f40(x74292),f334(f317(x74291,x74292,x74293),x74294)),f334(f40(x74291),x74294))+~P107(f334(f66(x74291),x74294)) % 188.18/188.26 [7609]~P76(x76091)+E(f334(f334(f86(x76091),f334(x76092,x76093)),f334(f334(f6(a927,x76091),x76092),f312(a927,x76093,x76094))),f334(f334(f6(a927,x76091),x76092),f311(a927,x76093,x76094)))+~P107(f334(f334(f242(a927),x76093),x76094)) % 188.18/188.26 [7619]~P72(x76191)+~P27(x76192,x76191,x76193,x76194)+E(f334(f334(f9(x76191,x76191),f32(x76191)),f334(f317(x76192,x76191,x76193),x76194)),f334(f334(f9(x76192,x76191),x76193),x76194)) % 188.18/188.26 [7620]~P76(x76201)+~P27(x76202,x76201,x76203,x76204)+E(f334(f334(f6(x76201,x76201),f32(x76201)),f334(f317(x76202,x76201,x76203),x76204)),f334(f334(f6(x76202,x76201),x76203),x76204)) % 188.18/188.26 [7669]E(f334(f40(f933(x76691,x76692)),f320(x76691,x76692,x76693,x76694)),f334(f334(f86(a927),f334(f40(x76691),x76693)),f334(f40(x76692),x76694)))+~P107(f334(f66(x76692),x76694))+~P107(f334(f66(x76691),x76693)) % 188.18/188.26 [7749]E(x77491,x77492)+P107(f334(f334(f336(x77493),x77491),f334(f179(x77493),f177(x77493,x77492,x77494))))+~P107(f334(f334(f336(x77493),x77491),f334(f179(x77493),x77494))) % 188.18/188.26 [7972]~P76(x79721)+E(f334(f334(f86(x79721),f334(f334(f6(a927,x79721),x79722),f334(f310(a927,x79723),x79724))),f334(x79722,x79724)),f334(f334(f6(a927,x79721),x79722),f334(f310(a927,x79723),f334(a119,x79724))))+P107(f334(f334(f243(a927),x79724),x79723)) % 188.18/188.26 [8024]~P27(x80241,x80242,x80243,f250(f935(x80241,a922)))+~P107(f334(f66(x80242),x80244))+P107(f334(f66(x80241),f334(f318(x80241,x80242,x80243),x80244))) % 188.18/188.26 [8136]P107(f334(f334(f336(f928(x81361)),f334(f334(f158(x81361),x81362),x81363)),f168(x81361,x81364)))+~P107(f334(f334(f336(f928(x81361)),x81363),f168(x81361,x81364)))+~P107(f334(f334(f336(x81361),x81362),x81364)) % 188.18/188.26 [8217]~E(f334(f317(x82173,x82171,x82174),f250(f935(x82173,a922))),f250(f935(x82171,a922)))+P107(f334(f66(x82171),x82172))+~P107(f334(f66(x82173),f334(f318(x82173,x82171,x82174),x82172))) % 188.18/188.26 [8312]~P27(x83121,x83123,x83124,x83122)+P107(f334(f66(x83121),x83122))+~P107(f334(f66(x83123),f334(f317(x83121,x83123,x83124),x83122))) % 188.18/188.26 [8333]~E(x83332,x83333)+P107(f334(f334(f336(f934(x83331,x83331)),f334(f334(f260(x83331,x83331),x83332),x83333)),f271(x83331,x83334)))+~P107(f334(f334(f336(x83331),x83332),x83334)) % 188.18/188.26 [8367]~P76(x83671)+E(f334(f334(f86(x83671),f334(f334(f6(a927,x83671),x83672),f311(a927,x83673,x83674))),f334(x83672,f334(a119,x83674))),f334(f334(f6(a927,x83671),x83672),f311(a927,x83673,f334(a119,x83674))))+P107(f334(f334(f243(a927),f334(a119,x83674)),x83673)) % 188.18/188.26 [8426]P107(f334(x84261,x84262))+~P107(f334(x84261,f334(f334(f171(x84263),x84264),f676(x84261,x84264,x84263))))+~P107(f334(f334(f336(x84263),x84262),f334(f179(x84263),x84264))) % 188.18/188.26 [8563]~P107(f334(f334(f336(x85631),x85632),f323(x85631,x85634)))+P107(f334(f334(f336(f928(x85631)),f334(f334(f158(x85631),x85632),x85633)),f323(f928(x85631),f164(x85631,x85634))))+~P107(f334(f334(f336(f928(x85631)),x85633),f323(f928(x85631),f164(x85631,x85634)))) % 188.18/188.26 [8578]~P27(x85782,x85783,x85784,f543(x85784,x85783,x85782,x85781))+P27(x85782,x85783,x85784,f43(f935(x85782,a922),x85781))+E(x85781,f195(f935(f935(x85782,a922),a922))) % 188.18/188.26 [8846]E(x88461,x88462)+~P107(f334(f334(f336(f934(x88463,x88463)),f334(f334(f260(x88463,x88463),x88461),x88462)),f314(x88463,x88464)))+P107(f334(f334(f336(x88463),x88461),f334(f272(x88463,x88463),x88464))) % 188.18/188.26 [9127]E(x91271,f2(a927))+P107(f334(x91272,x91273))+P107(f334(f334(f336(x91274),f787(x91272,x91273,x91271,x91274)),f334(f179(x91274),f176(x91274,x91271,x91273)))) % 188.18/188.26 [9139]E(x91391,f2(a927))+~P107(f334(x91393,x91394))+P107(f334(f334(f336(x91392),f785(x91393,x91394,x91391,x91392)),f334(f179(x91392),f176(x91392,x91391,x91394)))) % 188.18/188.26 [9141]~P28(x91411,x91412,x91413,f250(f935(x91411,a922)),f250(f935(x91412,a922)))+~P107(f334(f66(x91412),x91414))+P107(f334(f66(x91411),f334(f318(x91411,x91412,x91413),x91414))) % 188.18/188.26 [9143]P27(x91432,x91433,x91434,f43(f935(x91432,a922),x91431))+E(x91431,f195(f935(f935(x91432,a922),a922)))+P107(f334(f334(f336(f935(x91432,a922)),f543(x91434,x91433,x91432,x91431)),x91431)) % 188.18/188.26 [9257]~P28(x92573,x92571,x92574,f250(f935(x92573,a922)),f250(f935(x92571,a922)))+P107(f334(f66(x92571),x92572))+~P107(f334(f66(x92573),f334(f318(x92573,x92571,x92574),x92572))) % 188.18/188.26 [9270]P107(f334(f66(x92701),x92702))+~P107(f334(f66(x92704),f334(f317(x92701,x92704,x92703),x92702)))+P107(f334(f334(f336(x92701),f741(x92703,x92704,x92702,x92701)),x92702)) % 188.18/188.26 [9363]~P7(x93632)+E(f334(f334(f69(x93631,x93632,f334(f334(f8(x93632,f935(x93632,x93632),x93631),f108(x93632)),x93633)),f195(x93632)),x93634),f334(f334(f44(x93631,x93632),x93634),x93633))+~P107(f334(f66(x93631),x93634)) % 188.18/188.26 [9364]~P7(x93642)+E(f334(f334(f69(x93641,x93642,f334(f334(f8(x93642,f935(x93642,x93642),x93641),f109(x93642)),x93643)),f250(x93642)),x93644),f334(f334(f45(x93641,x93642),x93644),x93643))+~P107(f334(f66(x93641),x93644)) % 188.18/188.26 [9445]P107(f334(x94451,x94452))+~P107(f334(x94451,f334(f334(f171(x94453),x94454),f711(x94452,x94451,x94454,x94453))))+~P107(f334(f334(f336(x94453),x94452),f334(f179(x94453),x94454))) % 188.18/188.26 [9466]E(x94661,x94662)+~P107(f334(f334(f336(f934(x94663,x94663)),f334(f334(f260(x94663,x94663),x94661),x94662)),f314(x94663,x94664)))+P107(f334(f334(f336(f934(x94663,x94663)),f334(f334(f260(x94663,x94663),x94661),x94662)),f334(f334(f295(x94663,x94663,x94663),x94664),f314(x94663,x94664)))) % 188.18/188.26 [9523]~E(f334(f196(f928(x95231)),x95232),f334(f196(f928(x95231)),x95233))+~P107(f334(f334(f336(f934(f928(x95231),f928(x95231))),f334(f334(f260(f928(x95231),f928(x95231)),x95232),x95233)),f154(x95231,x95234)))+P107(f334(f334(f336(f934(f928(x95231),f928(x95231))),f334(f334(f260(f928(x95231),f928(x95231)),x95232),x95233)),f152(x95231,x95234))) % 188.18/188.26 [9761]P33(x97611,f334(f334(f18(x97611,a922,a922),f334(f334(f8(a922,f935(a922,a922),x97611),a333),f334(f334(f8(a922,a922,x97611),a329),x97612))),f334(a331,x97613)),x97614)+~P107(f334(x97612,x97613))+~P37(x97611,x97612,f334(f334(f158(x97611),x97613),x97614)) % 188.18/188.26 [9939]~P33(x99391,f334(f334(f18(x99391,a922,a922),f334(f334(f8(a922,f935(a922,a922),x99391),a333),f334(f334(f8(a922,a922,x99391),a329),x99392))),f334(a331,x99393)),x99394)+~P107(f334(x99392,x99393))+P37(x99391,x99392,f334(f334(f158(x99391),x99393),x99394)) % 188.18/188.26 [9943]~P37(x99431,x99432,x99434)+~P33(x99431,f334(f334(f18(x99431,a922,a922),f334(f334(f8(a922,f935(a922,a922),x99431),a333),f334(f334(f8(a922,a922,x99431),a329),x99432))),f334(a331,x99433)),x99434)+P37(x99431,x99432,f334(f334(f158(x99431),x99433),x99434)) % 188.18/188.26 [9980]~P3(x99801)+E(f334(f334(f6(a927,x99801),f334(f334(f18(a927,x99801,x99801),f334(f334(f8(x99801,f935(x99801,x99801),a927),f23(x99801)),x99802)),f334(f334(f8(a927,x99801,a927),x99802),f334(f334(f7(a927,a927,a927),f86(a927)),f84(a927))))),f311(a927,x99803,x99804)),f2(x99801))+P107(f334(f334(f242(a927),x99803),x99804)) % 188.18/188.26 [10195]~P39(x101952,x101954)+~P27(x101952,x101951,x101953,f250(f935(x101952,a922)))+P39(x101951,f334(f317(f934(x101952,x101952),f934(x101951,x101951),f266(x101952,x101951,x101952,x101951,x101953,x101953)),x101954)) % 188.18/188.26 [10408]~E(f334(f196(f928(x104081)),x104083),f334(f196(f928(x104081)),x104082))+P107(f334(f334(f336(f934(f928(x104081),f928(x104081))),f334(f334(f260(f928(x104081),f928(x104081)),x104082),x104083)),f165(x104081,x104084)))+~P107(f334(f334(f265(x104081,x104081,a922),f334(f334(f7(x104081,f935(f934(x104081,x104081),a922),f935(x104081,a922)),f334(f334(f8(f935(x104081,f935(f935(f934(x104081,x104081),a922),a922)),f935(f935(f934(x104081,x104081),a922),f935(x104081,a922)),x104081),f7(x104081,f935(f934(x104081,x104081),a922),a922)),f334(f334(f8(f935(x104081,f934(x104081,x104081)),f935(x104081,f935(f935(f934(x104081,x104081),a922),a922)),x104081),f334(f8(f934(x104081,x104081),f935(f935(f934(x104081,x104081),a922),a922),x104081),f336(f934(x104081,x104081)))),f260(x104081,x104081)))),x104084)),f678(x104084,x104083,x104082,x104081))) % 188.18/188.26 [6332]~P5(x63321)+~E(x63322,f2(x63321))+E(f334(f334(f41(x63321),f334(f334(f87(x63321),x63322),x63323)),f334(f334(f87(x63321),x63322),x63324)),f2(x63321)) % 188.18/188.26 [6373]E(x63731,f120(x63732))+E(x63733,f334(f334(f23(a927),f334(f196(f928(x63732)),x63731)),f84(a927)))+E(f151(x63732,f334(f334(f166(x63732,x63731),x63733),x63734)),f151(x63732,x63731)) % 188.18/188.26 [6408]E(x64081,x64082)+P107(f334(x64083,x64082))+~P107(f334(f334(f334(f316(x64084),x64081),x64083),x64082)) % 188.18/188.26 [6424]~P76(x64241)+~P107(f334(f144(x64242),x64244))+E(f334(f172(x64241),f334(f334(f161(x64242,x64241),x64243),x64244)),f334(f334(f6(x64242,x64241),x64243),f334(f179(x64242),x64244))) % 188.18/188.26 [6435]~P72(x64352)+~P107(f334(f66(x64351),x64354))+E(f334(f334(f9(x64351,x64352),f334(f16(x64352,x64351),x64353)),x64354),f334(f334(f252(x64352),x64353),f334(f40(x64351),x64354))) % 188.18/188.26 [6488]~P5(x64882)+E(x64881,f2(x64882))+E(f334(f334(f41(x64882),f334(f334(f87(x64882),x64883),x64881)),f334(f334(f87(x64882),x64884),x64881)),f334(f334(f41(x64882),x64883),x64884)) % 188.18/188.26 [6490]~P65(x64902)+E(x64901,f2(x64902))+E(f334(f334(f296(x64902),f334(f334(f87(x64902),x64903),x64901)),f334(f334(f87(x64902),x64904),x64901)),f334(f334(f296(x64902),x64903),x64904)) % 188.18/188.26 [6491]~P65(x64912)+E(x64911,f2(x64912))+E(f334(f334(f296(x64912),f334(f334(f87(x64912),x64911),x64913)),f334(f334(f87(x64912),x64911),x64914)),f334(f334(f296(x64912),x64913),x64914)) % 188.18/188.26 [6492]~P5(x64922)+E(x64921,f2(x64922))+E(f334(f334(f41(x64922),f334(f334(f87(x64922),x64921),x64923)),f334(f334(f87(x64922),x64921),x64924)),f334(f334(f41(x64922),x64923),x64924)) % 188.18/188.26 [6556]P107(f334(x65561,x65562))+~E(x65563,f334(f334(f86(a927),x65564),x65562))+~P107(f334(x65561,f334(f334(f23(a927),x65563),x65564))) % 188.18/188.26 [6641]~P107(f334(x66412,x66413))+~P107(f334(f167(x66411,x66412),x66414))+P107(f334(f167(x66411,x66412),f334(f334(f158(x66411),x66413),x66414))) % 188.18/188.26 [6684]E(x66841,f120(x66842))+~E(x66843,f334(f334(f23(a927),f334(f196(f928(x66842)),x66841)),f84(a927)))+E(f151(x66842,f334(f334(f166(x66842,x66841),x66843),x66844)),x66844) % 188.18/188.26 [6708]~P109(x67081)+~P107(f334(f334(f242(x67081),x67082),x67084))+P107(f334(f334(f242(x67081),x67082),f334(f334(f241(x67081),x67083),x67084))) % 188.18/188.26 [6710]~P109(x67101)+~P107(f334(f334(f242(x67101),x67102),x67103))+P107(f334(f334(f242(x67101),x67102),f334(f334(f241(x67101),x67103),x67104))) % 188.18/188.26 [6711]~P98(x67111)+~P107(f334(f334(f242(x67111),x67112),x67114))+P107(f334(f334(f242(x67111),x67112),f334(f334(f108(x67111),x67113),x67114))) % 188.18/188.26 [6712]~P98(x67121)+~P107(f334(f334(f242(x67121),x67122),x67123))+P107(f334(f334(f242(x67121),x67122),f334(f334(f108(x67121),x67123),x67124))) % 188.18/188.26 [6714]~P109(x67141)+~P107(f334(f334(f243(x67141),x67142),x67144))+P107(f334(f334(f243(x67141),x67142),f334(f334(f241(x67141),x67143),x67144))) % 188.18/188.26 [6716]~P109(x67161)+~P107(f334(f334(f243(x67161),x67162),x67163))+P107(f334(f334(f243(x67161),x67162),f334(f334(f241(x67161),x67163),x67164))) % 188.18/188.26 [6717]~P98(x67171)+~P107(f334(f334(f243(x67171),x67172),x67174))+P107(f334(f334(f243(x67171),x67172),f334(f334(f108(x67171),x67173),x67174))) % 188.18/188.26 [6718]~P98(x67181)+~P107(f334(f334(f243(x67181),x67182),x67183))+P107(f334(f334(f243(x67181),x67182),f334(f334(f108(x67181),x67183),x67184))) % 188.18/188.26 [6805]~E(f334(f334(f171(x68051),x68052),x68053),x68054)+E(f334(f334(f166(x68051,x68052),x68053),x68054),x68052)+~P107(f334(f334(f243(a927),x68053),f334(f196(f928(x68051)),x68052))) % 188.18/188.26 [6844]P107(f334(x68441,x68442))+~P107(f334(x68443,x68442))+~P107(f334(f334(f242(f935(x68444,a922)),x68443),x68441)) % 188.18/188.26 [6875]~E(f334(f334(f166(x68751,x68752),x68753),x68754),x68752)+E(f334(f334(f171(x68751),x68752),x68753),x68754)+~P107(f334(f334(f243(a927),x68753),f334(f196(f928(x68751)),x68752))) % 188.18/188.26 [6889]~P107(f334(f167(x68891,x68892),x68894))+~P107(f334(f167(x68891,x68892),x68893))+P107(f334(f167(x68891,x68892),f334(f334(f141(x68891),x68893),x68894))) % 188.18/188.26 [6993]E(x69931,f195(f935(x69932,a922)))+E(x69933,f195(f935(x69934,a922)))+~E(f334(f334(f262(x69934,x69932),x69933),f334(f16(f935(x69932,a922),x69934),x69931)),f195(f935(f934(x69934,x69932),a922))) % 188.18/188.26 [7008]E(x70081,x70082)+P107(f334(f334(f336(x70083),x70081),x70084))+~P107(f334(f334(f336(x70083),x70081),f334(f334(f316(x70083),x70082),x70084))) % 188.18/188.26 [7025]~P109(x70251)+P107(f334(f334(f242(x70251),x70252),x70253))+~P107(f334(f334(f242(x70251),x70252),f334(f334(f246(x70251),x70254),x70253))) % 188.18/188.26 [7027]~P109(x70271)+P107(f334(f334(f242(x70271),x70272),x70273))+~P107(f334(f334(f242(x70271),x70272),f334(f334(f246(x70271),x70273),x70274))) % 188.18/188.26 [7029]~P104(x70291)+P107(f334(f334(f242(x70291),x70292),x70293))+~P107(f334(f334(f242(x70291),x70292),f334(f334(f109(x70291),x70294),x70293))) % 188.18/188.26 [7031]~P104(x70311)+P107(f334(f334(f242(x70311),x70312),x70313))+~P107(f334(f334(f242(x70311),x70312),f334(f334(f109(x70311),x70313),x70314))) % 188.18/188.26 [7032]~P109(x70321)+P107(f334(f334(f243(x70321),x70322),x70323))+~P107(f334(f334(f243(x70321),x70322),f334(f334(f246(x70321),x70324),x70323))) % 188.18/188.26 [7033]~P109(x70331)+P107(f334(f334(f243(x70331),x70332),x70333))+~P107(f334(f334(f243(x70331),x70332),f334(f334(f246(x70331),x70333),x70334))) % 188.18/188.26 [7054]~E(f334(f334(f171(x70541),x70543),x70544),x70542)+P107(f334(f334(f336(x70541),x70542),f334(f179(x70541),x70543)))+~P107(f334(f334(f243(a927),x70544),f334(f196(f928(x70541)),x70543))) % 188.18/188.26 [7063]~P109(x70631)+~P15(x70631,f334(f334(f158(x70631),x70632),f334(f334(f158(x70631),x70633),x70634)))+P107(f334(f334(f242(x70631),x70632),x70633)) % 188.18/188.26 [7204]~P33(x72042,x72041,x72043)+P107(f334(x72041,f334(f334(f171(x72042),x72043),x72044)))+~P107(f334(f334(f243(a927),x72044),f334(f196(f928(x72042)),x72043))) % 188.18/188.26 [7222]E(x72221,f2(a1))+E(f334(f334(f41(a1),x72222),x72221),x72223)+~P107(f334(f54(x72222,x72221),f334(f334(f260(a1,a1),x72223),x72224))) % 188.18/188.26 [7243]E(f50(a1,x72432,x72431),x72433)+E(x72431,f2(a1))+~P107(f334(f54(x72432,x72431),f334(f334(f260(a1,a1),x72434),x72433))) % 188.18/188.26 [7361]P107(f334(f334(f336(x73611),x73612),x73613))+~P107(f334(f334(f336(x73611),x73612),x73614))+~P107(f334(f334(f243(f935(x73611,a922)),x73614),x73613)) % 188.18/188.26 [7362]P107(f334(f334(f336(x73621),x73622),x73623))+~P107(f334(f334(f336(x73621),x73622),x73624))+~P107(f334(f334(f242(f935(x73621,a922)),x73624),x73623)) % 188.18/188.26 [7473]P35(x74731,x74732,x74733)+~P107(f334(x74732,f334(f334(f171(x74731),x74733),x74734)))+~P107(f334(f334(f243(a927),x74734),f334(f196(f928(x74731)),x74733))) % 188.18/188.26 [7578]~P110(x75782)+~P107(f334(f334(f243(f935(x75781,x75782)),x75783),x75784))+P107(f334(f334(f242(f935(x75781,x75782)),x75783),x75784)) % 188.18/188.26 [7658]~P26(x76581,x76582,x76584)+P26(x76581,x76582,f334(f334(f316(f926(x76581)),x76583),x76584))+~P26(x76581,x76582,f334(f334(f316(f926(x76581)),x76583),f195(f935(f926(x76581),a922)))) % 188.18/188.26 [7700]~P107(f334(f334(f336(x77001),x77002),x77004))+P107(f334(f334(f336(x77001),x77002),f42(f935(x77001,a922),x77003)))+~P107(f334(f334(f336(f935(x77001,a922)),x77004),x77003)) % 188.18/188.26 [7728]~P84(x77281)+~P107(f334(f334(f242(x77281),x77283),x77284))+P107(f334(f334(f242(x77281),f334(f334(f86(x77281),x77282),x77283)),f334(f334(f86(x77281),x77282),x77284))) % 188.18/188.26 [7729]~P85(x77291)+~P107(f334(f334(f242(x77291),x77293),x77294))+P107(f334(f334(f242(x77291),f334(f334(f86(x77291),x77292),x77293)),f334(f334(f86(x77291),x77292),x77294))) % 188.18/188.26 [7730]~P84(x77301)+~P107(f334(f334(f242(x77301),x77302),x77304))+P107(f334(f334(f242(x77301),f334(f334(f86(x77301),x77302),x77303)),f334(f334(f86(x77301),x77304),x77303))) % 188.18/188.26 [7731]~P85(x77311)+~P107(f334(f334(f242(x77311),x77312),x77314))+P107(f334(f334(f242(x77311),f334(f334(f86(x77311),x77312),x77313)),f334(f334(f86(x77311),x77314),x77313))) % 188.18/188.26 [7732]~P84(x77321)+~P107(f334(f334(f243(x77321),x77323),x77324))+P107(f334(f334(f243(x77321),f334(f334(f86(x77321),x77322),x77323)),f334(f334(f86(x77321),x77322),x77324))) % 188.18/188.26 [7733]~P87(x77331)+~P107(f334(f334(f243(x77331),x77333),x77334))+P107(f334(f334(f243(x77331),f334(f334(f86(x77331),x77332),x77333)),f334(f334(f86(x77331),x77332),x77334))) % 188.18/188.26 [7734]~P84(x77341)+~P107(f334(f334(f243(x77341),x77342),x77344))+P107(f334(f334(f243(x77341),f334(f334(f86(x77341),x77342),x77343)),f334(f334(f86(x77341),x77344),x77343))) % 188.18/188.26 [7735]~P87(x77351)+~P107(f334(f334(f243(x77351),x77352),x77354))+P107(f334(f334(f243(x77351),f334(f334(f86(x77351),x77352),x77353)),f334(f334(f86(x77351),x77354),x77353))) % 188.18/188.26 [7742]~P113(x77421)+~P94(x77421)+E(f334(f334(f23(x77421),f334(f334(f87(x77421),x77422),f334(f111(x77421),x77423))),f334(f334(f87(x77421),x77424),f334(f111(x77421),x77423))),f334(f334(f87(x77421),f334(f334(f23(x77421),x77422),x77424)),f334(f111(x77421),x77423))) % 188.18/188.26 [7743]~P144(x77431)+~P94(x77431)+E(f334(f334(f86(x77431),f334(f334(f87(x77431),x77432),f334(f111(x77431),x77433))),f334(f334(f87(x77431),x77434),f334(f111(x77431),x77433))),f334(f334(f87(x77431),f334(f334(f86(x77431),x77432),x77434)),f334(f111(x77431),x77433))) % 188.18/188.26 [7780]~P76(x77801)+E(f334(f334(f86(x77801),f334(x77802,x77803)),f334(f334(f6(a927,x77801),x77802),f311(a927,f334(a119,x77803),x77804))),f334(f334(f6(a927,x77801),x77802),f311(a927,x77803,x77804)))+~P107(f334(f334(f242(a927),x77803),x77804)) % 188.18/188.26 [7791]~P27(x77912,x77911,x77913,f334(f179(x77912),x77914))+~P107(f334(f144(x77912),x77914))+P107(f334(f144(x77911),f334(f334(f161(x77912,x77911),x77913),x77914))) % 188.18/188.26 [7836]~P107(f334(f334(f242(a927),x78362),x78364))+~P107(f334(f334(f242(a927),x78361),x78363))+P107(f334(f334(f242(a927),f334(f334(f87(a927),x78361),x78362)),f334(f334(f87(a927),x78363),x78364))) % 188.18/188.26 [7837]~P107(f334(f334(f242(a927),x78372),x78374))+~P107(f334(f334(f242(a927),x78371),x78373))+P107(f334(f334(f242(a927),f334(f334(f86(a927),x78371),x78372)),f334(f334(f86(a927),x78373),x78374))) % 188.18/188.26 [7840]~P107(f334(f334(f243(a927),x78402),x78404))+~P107(f334(f334(f243(a927),x78401),x78403))+P107(f334(f334(f243(a927),f334(f334(f86(a927),x78401),x78402)),f334(f334(f86(a927),x78403),x78404))) % 188.18/188.26 [7841]~P107(f334(f334(f242(a1),x78412),x78414))+~P107(f334(f334(f243(a1),x78411),x78413))+P107(f334(f334(f243(a1),f334(f334(f86(a1),x78411),x78412)),f334(f334(f86(a1),x78413),x78414))) % 188.18/188.26 [7888]P107(f334(f334(f336(x78881),x78882),x78883))+~P107(f334(f334(f336(x78881),x78882),f43(f935(x78881,a922),x78884)))+~P107(f334(f334(f336(f935(x78881,a922)),x78883),x78884)) % 188.18/188.26 [7904]~P107(f334(x79041,f672(x79041,x79043,x79042)))+P107(f334(x79041,f334(f334(f171(x79042),x79043),x79044)))+~P107(f334(f334(f243(a927),x79044),f334(f196(f928(x79042)),x79043))) % 188.18/188.26 [7909]P107(f334(x79091,x79092))+~P107(f334(f334(f336(x79094),x79092),f334(f179(x79094),x79093)))+P107(f334(f334(f243(a927),f676(x79091,x79093,x79094)),f334(f196(f928(x79094)),x79093))) % 188.18/188.26 [7957]~P110(x79571)+~P107(f334(f334(f243(f935(x79572,x79571)),x79574),x79573))+~P107(f334(f334(f242(f935(x79572,x79571)),x79573),x79574)) % 188.18/188.26 [8003]~P107(f334(x80034,x80032))+~P107(f334(f334(f336(x80031),x80032),x80033))+P107(f334(f334(f336(x80031),x80032),f334(f334(f109(f935(x80031,a922)),x80033),f334(f270(x80031),x80034)))) % 188.18/188.26 [8143]~P107(f334(f334(f336(x81431),x81433),x81434))+~P107(f334(f334(f243(f935(x81431,a922)),x81432),x81434))+P107(f334(f334(f243(f935(x81431,a922)),x81432),f334(f334(f316(x81431),x81433),x81434))) % 188.18/188.26 [8145]E(f334(f334(f109(f935(x81451,a922)),x81452),x81453),f195(f935(x81451,a922)))+~E(f334(f334(f109(f935(x81451,a922)),f42(f935(x81451,a922),x81454)),x81453),f195(f935(x81451,a922)))+~P107(f334(f334(f336(f935(x81451,a922)),x81452),x81454)) % 188.18/188.26 [8213]P107(f334(f334(f336(x82131),x82132),x82133))+~P107(f334(f334(f242(f935(x82131,a922)),x82133),f334(f334(f316(x82131),x82132),x82134)))+P107(f334(f334(f242(f935(x82131,a922)),x82133),x82134)) % 188.18/188.26 [8230]P107(f334(f334(f336(x82302),f672(x82301,x82303,x82302)),f334(f179(x82302),x82303)))+P107(f334(x82301,f334(f334(f171(x82302),x82303),x82304)))+~P107(f334(f334(f243(a927),x82304),f334(f196(f928(x82302)),x82303))) % 188.18/188.26 [8238]~P107(f334(f334(f242(f935(x82381,a922)),x82382),x82384))+P107(f334(f334(f242(f935(x82381,a922)),x82382),x82383))+~P107(f334(f334(f242(f935(x82381,a922)),x82384),x82383)) % 188.18/188.26 [8239]~P107(f334(f334(f243(f935(x82391,a922)),x82392),x82394))+~P107(f334(f334(f242(f935(x82391,a922)),x82394),x82393))+P107(f334(f334(f243(f935(x82391,a922)),x82392),x82393)) % 188.18/188.26 [8240]~P107(f334(f334(f242(f935(x82401,a922)),x82402),x82404))+~P107(f334(f334(f243(f935(x82401,a922)),x82404),x82403))+P107(f334(f334(f243(f935(x82401,a922)),x82402),x82403)) % 188.18/188.26 [8241]~P107(f334(f334(f243(f935(x82411,a922)),x82412),x82414))+P107(f334(f334(f243(f935(x82411,a922)),x82412),x82413))+~P107(f334(f334(f243(f935(x82411,a922)),x82414),x82413)) % 188.18/188.26 [8289]~P107(f334(f334(f336(x82891),x82894),x82893))+~P107(f334(f334(f243(f935(x82891,a922)),x82892),f334(f334(f316(x82891),x82894),x82893)))+P107(f334(f334(f243(f935(x82891,a922)),x82892),x82893)) % 188.18/188.26 [8298]~P84(x82981)+P107(f334(f334(f242(x82981),x82982),x82983))+~P107(f334(f334(f242(x82981),f334(f334(f86(x82981),x82984),x82982)),f334(f334(f86(x82981),x82984),x82983))) % 188.18/188.26 [8300]~P84(x83001)+P107(f334(f334(f242(x83001),x83002),x83003))+~P107(f334(f334(f242(x83001),f334(f334(f86(x83001),x83002),x83004)),f334(f334(f86(x83001),x83003),x83004))) % 188.18/188.26 [8302]~P84(x83021)+P107(f334(f334(f243(x83021),x83022),x83023))+~P107(f334(f334(f243(x83021),f334(f334(f86(x83021),x83024),x83022)),f334(f334(f86(x83021),x83024),x83023))) % 188.18/188.26 [8304]~P84(x83041)+P107(f334(f334(f243(x83041),x83042),x83043))+~P107(f334(f334(f243(x83041),f334(f334(f86(x83041),x83042),x83044)),f334(f334(f86(x83041),x83043),x83044))) % 188.18/188.26 [8351]P107(f334(x83511,x83512))+~E(f334(f334(f145(x83513),f334(f196(f928(x83513)),f184(x83513,x83511,x83514))),x83514),f120(x83513))+~P107(f334(f334(f336(x83513),x83512),f334(f179(x83513),x83514))) % 188.18/188.26 [8468]P107(f334(x84681,x84682))+~P107(f334(f334(f336(x84683),x84682),f334(f179(x84683),x84684)))+P107(f334(f334(f243(a927),f334(f196(f928(x84683)),f334(f143(x84683,x84681),x84684))),f334(f196(f928(x84683)),x84684))) % 188.18/188.26 [8946]~P107(f334(x89461,f766(x89461,x89463,x89462,x89464)))+P107(f334(x89461,f334(f334(f171(x89462),x89463),x89464)))+~P107(f334(f334(f243(a927),x89464),f334(f196(f928(x89462)),x89463))) % 188.18/188.26 [8964]~P27(x89644,x89643,x89641,f250(f935(x89644,a922)))+E(f334(x89641,f461(x89642,x89641,x89643,x89644)),x89642)+~P107(f334(f334(f336(x89643),x89642),f334(f317(x89644,x89643,x89641),f250(f935(x89644,a922))))) % 188.18/188.26 [9039]E(f184(x90391,x90392,x90393),f334(f334(f182(x90391),x90394),x90393))+P107(f334(f334(f243(a927),f736(x90392,x90393,x90391,x90394)),x90394))+P107(f334(f334(f243(a927),x90394),f334(f196(f928(x90391)),x90393))) % 188.18/188.26 [9042]E(f184(x90421,x90422,x90423),f334(f334(f182(x90421),x90424),x90423))+P107(f334(f334(f243(a927),f736(x90422,x90423,x90421,x90424)),x90424))+P107(f334(x90422,f334(f334(f171(x90421),x90423),x90424))) % 188.18/188.26 [9081]P107(f334(x90811,x90812))+~P107(f334(f334(f336(x90814),x90812),f334(f179(x90814),x90813)))+P107(f334(f334(f243(a927),f711(x90812,x90811,x90813,x90814)),f334(f196(f928(x90814)),x90813))) % 188.18/188.26 [9083]E(f184(x90831,x90832,x90833),f334(f334(f182(x90831),x90834),x90833))+P107(f334(f334(f243(a927),x90834),f334(f196(f928(x90831)),x90833)))+P107(f334(f334(f243(a927),f736(x90832,x90833,x90831,x90834)),f334(f196(f928(x90831)),x90833))) % 188.18/188.26 [9089]E(f184(x90891,x90892,x90893),f334(f334(f182(x90891),x90894),x90893))+P107(f334(x90892,f334(f334(f171(x90891),x90893),x90894)))+P107(f334(f334(f243(a927),f736(x90892,x90893,x90891,x90894)),f334(f196(f928(x90891)),x90893))) % 188.18/188.26 [9117]~P127(x91174)+P107(f334(f334(f336(x91171),f656(x91172,x91173,x91171,x91174)),x91173))+P107(f334(f334(f243(x91174),f2(x91174)),f334(f334(f9(x91171,x91174),x91172),x91173))) % 188.18/188.26 [9118]~P127(x91184)+P107(f334(f334(f336(x91181),f660(x91182,x91183,x91181,x91184)),x91183))+P107(f334(f334(f242(x91184),f2(x91184)),f334(f334(f9(x91181,x91184),x91182),x91183))) % 188.18/188.26 [9145]~P107(f334(f66(x91451),x91454))+P107(f334(f334(f336(x91451),f554(x91452,x91453,x91454,x91451)),x91454))+P107(f334(f66(f934(x91451,x91453)),f334(f334(f262(x91451,x91453),x91454),x91452))) % 188.18/188.26 [9177]P107(f334(f334(f336(x91772),f766(x91771,x91773,x91772,x91774)),f334(f179(x91772),x91773)))+P107(f334(x91771,f334(f334(f171(x91772),x91773),x91774)))+~P107(f334(f334(f243(a927),x91774),f334(f196(f928(x91772)),x91773))) % 188.18/188.26 [9295]P107(f334(f334(f242(a927),x92954),f334(f196(f928(x92952)),f184(x92952,x92953,x92951))))+P107(f334(f334(f243(a927),f737(x92951,x92952,x92953,x92954)),x92954))+~P107(f334(f334(f242(a927),x92954),f334(f196(f928(x92952)),x92951))) % 188.18/188.26 [9449]E(f184(x94491,x94492,x94493),f334(f334(f182(x94491),x94494),x94493))+~P107(f334(x94492,f334(f334(f171(x94491),x94493),f736(x94492,x94493,x94491,x94494))))+P107(f334(f334(f243(a927),x94494),f334(f196(f928(x94491)),x94493))) % 188.18/188.26 [9456]E(f184(x94561,x94562,x94563),f334(f334(f182(x94561),x94564),x94563))+~P107(f334(x94562,f334(f334(f171(x94561),x94563),f736(x94562,x94563,x94561,x94564))))+P107(f334(x94562,f334(f334(f171(x94561),x94563),x94564))) % 188.18/188.26 [9460]~P107(f334(f66(x94601),x94603))+~P107(f334(f66(x94602),f334(x94604,f554(x94604,x94602,x94603,x94601))))+P107(f334(f66(f934(x94601,x94602)),f334(f334(f262(x94601,x94602),x94603),x94604))) % 188.18/188.26 [9468]~P127(x94681)+~P107(f334(f334(f242(x94681),f2(x94681)),f334(x94683,f660(x94683,x94684,x94682,x94681))))+P107(f334(f334(f242(x94681),f2(x94681)),f334(f334(f9(x94682,x94681),x94683),x94684))) % 188.18/188.26 [9469]~P127(x94691)+~P107(f334(f334(f243(x94691),f2(x94691)),f334(x94693,f656(x94693,x94694,x94692,x94691))))+P107(f334(f334(f243(x94691),f2(x94691)),f334(f334(f9(x94692,x94691),x94693),x94694))) % 188.18/188.26 [9477]~E(f334(f196(f928(x94774)),x94772),f334(f196(f928(x94774)),x94773))+P107(f334(f334(f336(f934(f928(x94774),f928(x94774))),f334(f334(f260(f928(x94774),f928(x94774)),x94773),x94772)),f165(x94774,x94771)))+P107(f334(f334(f243(a927),f661(x94771,x94772,x94773,x94774)),f334(f196(f928(x94774)),x94773))) % 188.18/188.26 [9532]~P107(f334(x95323,f334(f334(f171(x95322),x95324),f737(x95324,x95322,x95323,x95321))))+P107(f334(f334(f242(a927),x95321),f334(f196(f928(x95322)),f184(x95322,x95323,x95324))))+~P107(f334(f334(f242(a927),x95321),f334(f196(f928(x95322)),x95324))) % 188.18/188.26 [9615]E(f334(f334(f182(x96151),f674(x96152,x96153,x96154,x96151)),x96153),f334(f334(f182(x96151),f674(x96152,x96153,x96154,x96151)),x96154))+~P107(f334(f334(f336(f934(f928(x96151),f928(x96151))),f334(f334(f260(f928(x96151),f928(x96151)),x96154),x96153)),f154(x96151,x96152)))+P107(f334(f334(f243(a927),f334(f196(f928(x96151)),x96154)),f334(f196(f928(x96151)),x96153))) % 188.18/188.26 [9664]~P107(f334(f334(f243(a927),f2(a927)),x96643))+~P107(f334(f334(f243(a927),x96644),x96641))+P107(f334(f334(f243(a927),f334(f334(f86(a927),f334(f334(f87(a927),x96641),f50(a927,x96642,x96643))),x96644)),f334(f334(f87(a927),x96641),x96643))) % 188.18/188.26 [9880]~P110(x98802)+~P107(f334(f334(f242(x98802),f334(x98803,f435(x98804,x98803,x98801,x98802))),f334(x98804,f435(x98804,x98803,x98801,x98802))))+P107(f334(f334(f242(f935(x98801,x98802)),x98803),x98804)) % 188.18/188.26 [9985]~P3(x99851)+E(f334(f334(f6(a927,x99851),f334(f334(f18(a927,x99851,x99851),f334(f334(f8(x99851,f935(x99851,x99851),a927),f23(x99851)),x99852)),f334(f334(f8(a927,x99851,a927),x99852),f334(f334(f7(a927,a927,a927),f86(a927)),f84(a927))))),f311(a927,x99853,x99854)),f334(f334(f23(x99851),f334(x99852,x99853)),f334(x99852,f334(f334(f86(a927),x99854),f84(a927)))))+~P107(f334(f334(f242(a927),x99853),x99854)) % 188.18/188.26 [10068]~P39(x100683,f334(f334(f295(x100683,x100683,x100683),x100682),f314(x100683,x100682)))+~P107(f334(f334(f336(f934(x100683,x100683)),f334(f334(f260(x100683,x100683),f334(x100681,f334(a119,f849(x100682,x100681,x100683)))),f334(x100681,f849(x100682,x100681,x100683)))),f314(x100683,x100682)))+E(f334(x100681,f334(f334(f86(a927),f848(x100682,x100681,x100683)),x100684)),f334(x100681,f848(x100682,x100681,x100683))) % 188.18/188.26 [6754]~P5(x67541)+~P59(x67541,x67544,x67543)+E(f334(f334(f41(x67541),f334(f334(f87(x67541),x67542),x67543)),x67544),f334(f334(f87(x67541),x67542),f334(f334(f41(x67541),x67543),x67544))) % 188.18/188.26 [7043]~P5(x70431)+~P59(x70431,x70434,x70432)+E(f334(f334(f41(x70431),f334(f334(f87(x70431),x70432),x70433)),x70434),f334(f334(f87(x70431),f334(f334(f41(x70431),x70432),x70434)),x70433)) % 188.18/188.26 [7057]E(f334(f334(f141(x70571),x70572),x70573),x70574)+~E(x70573,f334(f334(f145(x70571),f334(f196(f928(x70571)),x70572)),x70574))+~E(f334(f334(f182(x70571),f334(f196(f928(x70571)),x70572)),x70574),x70572) % 188.18/188.26 [7110]~P66(x71102)+E(x71101,f2(x71102))+E(f334(f334(f296(x71102),f334(f334(f252(x71102),x71103),x71104)),f334(f334(f252(x71102),x71101),x71104)),f334(f334(f252(x71102),f334(f334(f296(x71102),x71103),x71101)),x71104)) % 188.18/188.26 [7260]~P109(x72601)+~P107(f334(f334(f242(x72601),x72603),x72604))+P107(f334(f334(f242(x72601),f334(f334(f246(x72601),x72602),x72603)),x72604)) % 188.18/188.26 [7262]~P109(x72621)+~P107(f334(f334(f242(x72621),x72622),x72624))+P107(f334(f334(f242(x72621),f334(f334(f246(x72621),x72622),x72623)),x72624)) % 188.18/188.26 [7263]~P104(x72631)+~P107(f334(f334(f242(x72631),x72633),x72634))+P107(f334(f334(f242(x72631),f334(f334(f109(x72631),x72632),x72633)),x72634)) % 188.18/188.26 [7264]~P104(x72641)+~P107(f334(f334(f242(x72641),x72642),x72644))+P107(f334(f334(f242(x72641),f334(f334(f109(x72641),x72642),x72643)),x72644)) % 188.18/188.26 [7266]~P109(x72661)+~P107(f334(f334(f243(x72661),x72663),x72664))+P107(f334(f334(f243(x72661),f334(f334(f246(x72661),x72662),x72663)),x72664)) % 188.18/188.26 [7268]~P109(x72681)+~P107(f334(f334(f243(x72681),x72682),x72684))+P107(f334(f334(f243(x72681),f334(f334(f246(x72681),x72682),x72683)),x72684)) % 188.18/188.26 [7269]~P104(x72691)+~P107(f334(f334(f243(x72691),x72693),x72694))+P107(f334(f334(f243(x72691),f334(f334(f109(x72691),x72692),x72693)),x72694)) % 188.18/188.26 [7270]~P104(x72701)+~P107(f334(f334(f243(x72701),x72702),x72704))+P107(f334(f334(f243(x72701),f334(f334(f109(x72701),x72702),x72703)),x72704)) % 188.18/188.26 [7293]~P107(f334(x72933,x72934))+~P107(f334(x72932,x72934))+P107(f334(f334(f334(f109(f935(x72931,a922)),x72932),x72933),x72934)) % 188.18/188.26 [7416]P26(x74161,x74162,x74163)+~P26(x74161,x74162,x74164)+~P107(f334(f334(f242(f935(f926(x74161),a922)),x74163),x74164)) % 188.18/188.26 [7770]~P76(x77701)+E(f334(f334(f86(x77701),f334(x77702,x77703)),f334(f334(f6(a927,x77701),x77702),f334(f310(a927,f334(a119,x77703)),x77704))),f334(f334(f6(a927,x77701),x77702),f334(f310(a927,x77703),x77704)))+~P107(f334(f334(f243(a927),x77703),x77704)) % 188.18/188.26 [7788]E(x77881,x77882)+P107(f334(f334(f179(x77883),x77884),x77882))+~P107(f334(f334(f179(x77883),f334(f334(f158(x77883),x77881),x77884)),x77882)) % 188.18/188.26 [7799]~P109(x77991)+P107(f334(f334(f242(x77991),x77992),x77993))+~P107(f334(f334(f242(x77991),f334(f334(f241(x77991),x77994),x77992)),x77993)) % 188.18/188.26 [7801]~P109(x78011)+P107(f334(f334(f242(x78011),x78012),x78013))+~P107(f334(f334(f242(x78011),f334(f334(f241(x78011),x78012),x78014)),x78013)) % 188.18/188.26 [7803]~P98(x78031)+P107(f334(f334(f242(x78031),x78032),x78033))+~P107(f334(f334(f242(x78031),f334(f334(f108(x78031),x78034),x78032)),x78033)) % 188.18/188.26 [7805]~P98(x78051)+P107(f334(f334(f242(x78051),x78052),x78053))+~P107(f334(f334(f242(x78051),f334(f334(f108(x78051),x78052),x78054)),x78053)) % 188.18/188.26 [7806]~P109(x78061)+P107(f334(f334(f243(x78061),x78062),x78063))+~P107(f334(f334(f243(x78061),f334(f334(f241(x78061),x78064),x78062)),x78063)) % 188.18/188.26 [7807]~P109(x78071)+P107(f334(f334(f243(x78071),x78072),x78073))+~P107(f334(f334(f243(x78071),f334(f334(f241(x78071),x78072),x78074)),x78073)) % 188.18/188.26 [7880]~P107(f334(f334(f336(x78801),x78802),x78804))+P107(f334(f334(f336(x78801),x78802),x78803))+P107(f334(f334(f336(x78801),x78802),f334(f334(f23(f935(x78801,a922)),x78804),x78803))) % 188.18/188.26 [7964]P107(f334(x79641,x79642))+P107(f334(x79643,x79642))+~P107(f334(f334(f334(f108(f935(x79644,a922)),x79643),x79641),x79642)) % 188.18/188.26 [7975]~P107(f334(f334(f336(x79751),x79752),x79754))+~P107(f334(f334(f336(x79751),x79752),x79753))+P107(f334(f334(f336(x79751),x79752),f334(f334(f109(f935(x79751,a922)),x79753),x79754))) % 188.18/188.26 [8025]~P109(x80251)+~P107(f334(f66(x80251),x80254))+E(f334(f334(f69(x80251,x80251,f246(x80251)),x80252),f334(f334(f316(x80251),x80253),x80254)),f334(f334(f246(x80251),x80253),f334(f334(f69(x80251,x80251,f246(x80251)),x80252),x80254))) % 188.18/188.26 [8026]~P109(x80261)+~P107(f334(f66(x80261),x80264))+E(f334(f334(f69(x80261,x80261,f241(x80261)),x80262),f334(f334(f316(x80261),x80263),x80264)),f334(f334(f241(x80261),x80263),f334(f334(f69(x80261,x80261,f241(x80261)),x80262),x80264))) % 188.18/188.26 [8027]~P98(x80271)+~P107(f334(f66(x80271),x80274))+E(f334(f334(f69(x80271,x80271,f108(x80271)),x80272),f334(f334(f316(x80271),x80273),x80274)),f334(f334(f108(x80271),x80273),f334(f334(f69(x80271,x80271,f108(x80271)),x80272),x80274))) % 188.18/188.26 [8028]~P104(x80281)+~P107(f334(f66(x80281),x80284))+E(f334(f334(f69(x80281,x80281,f109(x80281)),x80282),f334(f334(f316(x80281),x80283),x80284)),f334(f334(f109(x80281),x80283),f334(f334(f69(x80281,x80281,f109(x80281)),x80282),x80284))) % 188.18/188.26 [8029]~P113(x80291)+~P94(x80291)+E(f334(f334(f23(x80291),f334(f334(f87(x80291),f334(f111(x80291),x80292)),x80293)),f334(f334(f87(x80291),f334(f111(x80291),x80292)),x80294)),f334(f334(f87(x80291),f334(f111(x80291),x80292)),f334(f334(f23(x80291),x80293),x80294))) % 188.18/188.26 [8030]~P144(x80301)+~P94(x80301)+E(f334(f334(f86(x80301),f334(f334(f87(x80301),f334(f111(x80301),x80302)),x80303)),f334(f334(f87(x80301),f334(f111(x80301),x80302)),x80304)),f334(f334(f87(x80301),f334(f111(x80301),x80302)),f334(f334(f86(x80301),x80303),x80304))) % 188.18/188.26 [8141]E(x81411,x81412)+P107(f334(f334(f336(x81413),x81411),f334(f179(x81413),x81414)))+~P107(f334(f334(f336(x81413),x81411),f334(f179(x81413),f334(f334(f158(x81413),x81412),x81414)))) % 188.18/188.26 [8309]P57(x83091,x83092,x83093)+~P57(x83091,x83092,x83094)+~P107(f334(f334(f242(f935(f934(x83091,x83092),a922)),x83093),x83094)) % 188.18/188.26 [8353]P107(f334(f334(f336(x83531),x83532),x83533))+P107(f334(f334(f336(x83531),x83532),x83534))+~P107(f334(f334(f336(x83531),x83532),f334(f334(f108(f935(x83531,a922)),x83534),x83533))) % 188.18/188.26 [8363]~P55(x83631,x83634,x83633)+~P107(f334(f334(f336(x83631),x83632),x83634))+P107(f334(f334(f336(f934(x83631,x83631)),f334(f334(f260(x83631,x83631),x83632),x83632)),x83633)) % 188.18/188.26 [8375]~P107(f334(f66(x83752),x83754))+~P107(f334(f66(x83751),x83753))+P107(f334(f66(f934(x83751,x83752)),f334(f334(f262(x83751,x83752),x83753),f334(f16(f935(x83752,a922),x83751),x83754)))) % 188.18/188.26 [8376]~P107(f334(f334(f336(x83761),x83762),x83764))+~P107(f334(f334(f242(f935(x83761,a922)),x83763),x83764))+P107(f334(f334(f242(f935(x83761,a922)),f334(f334(f316(x83761),x83762),x83763)),x83764)) % 188.18/188.26 [8383]~P72(x83832)+~P147(x83832)+E(f334(f334(f9(x83831,x83832),f334(f334(f8(a927,x83832,x83831),f107(x83832)),x83833)),x83834),f334(f107(x83832),f334(f334(f9(x83831,a927),x83833),x83834))) % 188.18/188.26 [8384]~P72(x83842)+~P142(x83842)+E(f334(f334(f9(x83841,x83842),f334(f334(f8(a1,x83842,x83841),f110(x83842)),x83843)),x83844),f334(f110(x83842),f334(f334(f9(x83841,a1),x83843),x83844))) % 188.18/188.26 [8409]E(f334(f334(f23(f935(x84091,a922)),x84092),f334(f334(f23(f935(x84091,a922)),x84093),x84094)),x84094)+~P107(f334(f334(f242(f935(x84091,a922)),x84092),x84093))+~P107(f334(f334(f242(f935(x84091,a922)),x84094),x84092)) % 188.18/188.26 [8504]~P107(f334(f66(x85041),x85044))+E(f334(f334(f23(a927),f334(f334(f6(x85041,a927),x85042),x85043)),f334(f334(f6(x85041,a927),x85042),x85044)),f334(f334(f6(x85041,a927),x85042),f334(f334(f23(f935(x85041,a922)),x85043),x85044)))+~P107(f334(f334(f242(f935(x85041,a922)),x85044),x85043)) % 188.18/188.26 [8649]~P10(x86491,x86494,x86493)+~P107(f334(f334(f336(x86491),x86492),x86494))+P107(f334(f334(f336(x86491),x86492),f334(f292(x86491,x86491,x86493),f334(f334(f316(x86491),x86492),f195(f935(x86491,a922)))))) % 188.18/188.26 [8710]~P107(f334(f334(f242(f935(x87101,a922)),x87102),x87103))+~P107(f334(f334(f242(f935(x87101,a922)),x87102),x87104))+P107(f334(f334(f242(f935(x87101,a922)),x87102),f334(f334(f109(f935(x87101,a922)),x87103),x87104))) % 188.18/188.26 [8813]E(x88131,f195(f935(x88132,a922)))+P107(f334(f66(x88133),x88134))+~P107(f334(f66(f934(x88133,x88132)),f334(f334(f262(x88133,x88132),x88134),f334(f16(f935(x88132,a922),x88133),x88131)))) % 188.18/188.26 [8814]E(x88141,f195(f935(x88142,a922)))+P107(f334(f66(x88143),x88144))+~P107(f334(f66(f934(x88142,x88143)),f334(f334(f262(x88142,x88143),x88141),f334(f16(f935(x88143,a922),x88142),x88144)))) % 188.18/188.26 [8883]P107(f334(f334(f336(x88831),x88832),f323(x88831,x88833)))+~P107(f334(f334(f336(x88831),x88834),f323(x88831,x88833)))+~P107(f334(f334(f336(f934(x88831,x88831)),f334(f334(f260(x88831,x88831),x88832),x88834)),x88833)) % 188.18/188.26 [8938]~P39(x89381,x89384)+P107(f334(f334(f336(f934(x89381,x89381)),f334(f334(f260(x89381,x89381),x89383),x89382)),f314(x89381,x89384)))+P39(x89381,f334(f334(f316(f934(x89381,x89381)),f334(f334(f260(x89381,x89381),x89382),x89383)),x89384)) % 188.18/188.26 [8939]~P61(x89391,x89394)+P107(f334(f334(f336(f934(x89391,x89391)),f334(f334(f260(x89391,x89391),x89393),x89392)),f314(x89391,x89394)))+P61(x89391,f334(f334(f316(f934(x89391,x89391)),f334(f334(f260(x89391,x89391),x89392),x89393)),x89394)) % 188.18/188.26 [9020]~E(x90202,x90203)+~P107(f334(f334(f336(x90201),x90202),f334(f179(x90201),x90204)))+P107(f334(f334(f336(f934(x90201,x90201)),f334(f334(f260(x90201,x90201),x90202),x90203)),f334(f179(f934(x90201,x90201)),f334(f334(f188(x90201,x90201),x90204),x90204)))) % 188.18/188.26 [9116]~E(x91163,x91164)+P107(f334(f334(f265(x91161,x91161,a922),a331),x91162))+~P107(f334(f334(f336(f934(x91161,x91161)),x91162),f334(f179(f934(x91161,x91161)),f334(f334(f188(x91161,x91161),x91163),x91164)))) % 188.18/188.26 [9162]P107(f334(f334(f336(f934(f928(x91621),f928(x91621))),f334(f334(f260(f928(x91621),f928(x91621)),x91622),x91623)),f154(x91621,x91624)))+~E(f334(f334(f182(x91621),f334(f196(f928(x91621)),x91622)),x91623),x91622)+~P107(f334(f334(f243(a927),f334(f196(f928(x91621)),x91622)),f334(f196(f928(x91621)),x91623))) % 188.18/188.26 [9165]~P54(x91651,x91654)+~P107(f334(f334(f336(f934(x91651,x91651)),f334(f334(f260(x91651,x91651),x91653),x91652)),x91654))+P107(f334(f334(f336(f934(x91651,x91651)),f334(f334(f260(x91651,x91651),x91652),x91653)),x91654)) % 188.18/188.26 [9255]~P107(f334(f66(x92551),x92554))+P107(f334(f334(f336(x92551),f393(x92552,x92553,x92554,x92551)),x92554))+P107(f334(f66(x92553),f334(f334(f44(x92551,f935(x92553,a922)),x92554),x92552))) % 188.18/188.26 [9256]~P107(f334(f66(x92561),x92564))+P107(f334(f334(f336(x92561),f586(x92562,x92563,x92564,x92561)),x92564))+P107(f334(f66(x92563),f334(f334(f44(x92561,f935(x92563,a922)),x92564),x92562))) % 188.18/188.26 [9334]P107(f334(f334(f336(f934(x93341,x93341)),x93342),f334(f334(f295(x93341,x93341,x93341),x93343),f314(x93341,x93343))))+~P107(f334(f334(f243(a927),f2(a927)),x93344))+~P107(f334(f334(f336(f934(x93341,x93341)),x93342),f334(f334(f190(f934(x93341,x93341),a922),x93344),x93343))) % 188.18/188.26 [9343]~P39(x93431,x93432)+~P107(f334(f334(f336(f934(x93431,x93431)),f334(f334(f260(x93431,x93431),x93434),x93433)),x93432))+~P107(f334(f334(f336(f934(x93431,x93431)),f334(f334(f260(x93431,x93431),x93433),x93434)),x93432)) % 188.18/188.26 [9467]~P107(f334(f66(x94671),x94674))+E(f334(f334(f6(x94671,a927),f334(f334(f8(f935(x94672,a922),a927,x94671),f40(x94672)),x94673)),x94674),f334(f40(f934(x94671,x94672)),f334(f334(f262(x94671,x94672),x94674),x94673)))+P107(f334(f334(f336(x94671),f555(x94673,x94672,x94674,x94671)),x94674)) % 188.18/188.26 [9471]~P107(f334(f144(x94711),x94712))+P107(f334(f144(x94711),f334(f334(f166(x94711,x94712),x94713),x94714)))+P107(f334(f334(f336(x94711),x94714),f334(f334(f23(f935(x94711,a922)),f334(f179(x94711),x94712)),f334(f334(f316(x94711),f334(f334(f171(x94711),x94712),x94713)),f195(f935(x94711,a922)))))) % 188.18/188.26 [9488]~P107(f334(f66(x94882),x94883))+~P107(f334(f66(x94881),f334(x94884,f393(x94884,x94881,x94883,x94882))))+P107(f334(f66(x94881),f334(f334(f44(x94882,f935(x94881,a922)),x94883),x94884))) % 188.18/188.26 [9489]~P107(f334(f66(x94892),x94893))+~P107(f334(f66(x94891),f334(x94894,f586(x94894,x94891,x94893,x94892))))+P107(f334(f66(x94891),f334(f334(f44(x94892,f935(x94891,a922)),x94893),x94894))) % 188.18/188.26 [9570]~P107(f334(f334(f336(f934(x95701,x95701)),x95702),f334(f334(f295(x95701,x95701,x95701),x95704),f314(x95701,x95704))))+P107(f334(f334(f336(f934(x95701,x95701)),x95702),f334(f334(f295(x95701,x95701,x95701),x95703),f314(x95701,x95703))))+~P107(f334(f334(f242(f935(f934(x95701,x95701),a922)),x95704),x95703)) % 188.18/188.26 [9578]E(f334(f334(f182(x95781),f674(x95784,x95783,x95782,x95781)),x95783),f334(f334(f182(x95781),f674(x95784,x95783,x95782,x95781)),x95782))+~P107(f334(f334(f336(f934(f928(x95781),f928(x95781))),f334(f334(f260(f928(x95781),f928(x95781)),x95782),x95783)),f154(x95781,x95784)))+E(f334(f334(f182(x95781),f334(f196(f928(x95781)),x95782)),x95783),x95782) % 188.18/188.26 [9597]~P107(f334(f66(x95971),x95974))+E(f334(f334(f6(x95971,a927),f334(f334(f8(f935(x95972,a922),a927,x95971),f40(x95972)),x95973)),x95974),f334(f40(f934(x95971,x95972)),f334(f334(f262(x95971,x95972),x95974),x95973)))+~P107(f334(f66(x95972),f334(x95973,f555(x95973,x95972,x95974,x95971)))) % 188.18/188.26 [9602]~E(f334(f196(f928(x96021)),x96023),f334(f196(f928(x96021)),x96022))+P107(f334(f334(f336(f934(f928(x96021),f928(x96021))),f334(f334(f260(f928(x96021),f928(x96021)),x96022),x96023)),f165(x96021,x96024)))+P107(f334(f334(f336(f934(x96021,x96021)),f678(x96024,x96023,x96022,x96021)),f334(f179(f934(x96021,x96021)),f334(f334(f188(x96021,x96021),x96022),x96023)))) % 188.18/188.26 [9673]~P107(f334(f334(f336(f934(f928(x96731),f928(x96731))),f334(f334(f260(f928(x96731),f928(x96731)),x96732),x96733)),f154(x96731,x96734)))+E(f334(f334(f182(x96731),f334(f196(f928(x96731)),x96732)),x96733),x96732)+P107(f334(f334(f243(a927),f674(x96734,x96733,x96732,x96731)),f334(f334(f246(a927),f334(f196(f928(x96731)),x96732)),f334(f196(f928(x96731)),x96733)))) % 188.18/188.26 [9697]~P107(f334(f334(f336(f934(f928(x96971),f928(x96971))),f334(f334(f260(f928(x96971),f928(x96971)),x96972),x96973)),f154(x96971,x96974)))+P107(f334(f334(f243(a927),f334(f196(f928(x96971)),x96972)),f334(f196(f928(x96971)),x96973)))+P107(f334(f334(f243(a927),f674(x96974,x96973,x96972,x96971)),f334(f334(f246(a927),f334(f196(f928(x96971)),x96972)),f334(f196(f928(x96971)),x96973)))) % 188.18/188.26 [10129]~P107(f334(f334(f336(f934(f928(x101291),f928(x101291))),f334(f334(f260(f928(x101291),f928(x101291)),x101292),x101293)),f154(x101291,x101294)))+E(f334(f334(f182(x101291),f334(f196(f928(x101291)),x101292)),x101293),x101292)+P107(f334(f334(f336(f934(x101291,x101291)),f334(f334(f260(x101291,x101291),f334(f334(f171(x101291),x101292),f674(x101294,x101293,x101292,x101291))),f334(f334(f171(x101291),x101293),f674(x101294,x101293,x101292,x101291)))),x101294)) % 188.18/188.26 [10130]~P107(f334(f334(f336(f934(f928(x101301),f928(x101301))),f334(f334(f260(f928(x101301),f928(x101301)),x101302),x101303)),f154(x101301,x101304)))+P107(f334(f334(f243(a927),f334(f196(f928(x101301)),x101302)),f334(f196(f928(x101301)),x101303)))+P107(f334(f334(f336(f934(x101301,x101301)),f334(f334(f260(x101301,x101301),f334(f334(f171(x101301),x101302),f674(x101304,x101303,x101302,x101301))),f334(f334(f171(x101301),x101303),f674(x101304,x101303,x101302,x101301)))),x101304)) % 188.18/188.26 [10175]~E(f334(f196(f928(x101751)),x101752),f334(f196(f928(x101751)),x101753))+P107(f334(f334(f336(f934(f928(x101751),f928(x101751))),f334(f334(f260(f928(x101751),f928(x101751)),x101752),x101753)),f165(x101751,x101754)))+~P107(f334(f334(f336(f934(x101751,x101751)),f334(f334(f260(x101751,x101751),f334(f334(f171(x101751),x101752),f661(x101754,x101753,x101752,x101751))),f334(f334(f171(x101751),x101753),f661(x101754,x101753,x101752,x101751)))),x101754)) % 188.18/188.26 [10319]~P76(x103191)+~P107(f334(f66(x103192),x103194))+E(f334(f172(x103191),f334(f334(f161(x103192,x103191),x103193),f96(f928(x103192),f334(f334(f18(f928(x103192),a922,a922),f334(f334(f8(a922,f935(a922,a922),f928(x103192)),a332),f334(f334(f7(f928(x103192),f935(x103192,a922),a922),f334(f334(f8(f935(x103192,a922),f935(f935(x103192,a922),a922),f928(x103192)),a331),f179(x103192))),x103194))),f144(x103192))))),f240(x103192,x103191,x103193,x103194)) % 188.18/188.26 [7621]~P65(x76212)+E(x76211,f2(x76212))+E(f334(f334(f296(x76212),f334(f334(f86(x76212),x76213),f334(f334(f87(x76212),x76214),x76211))),x76211),f334(f334(f86(x76212),x76214),f334(f334(f296(x76212),x76213),x76211))) % 188.18/188.26 [7622]~P5(x76222)+E(x76221,f2(x76222))+E(f334(f334(f41(x76222),f334(f334(f86(x76222),x76223),f334(f334(f87(x76222),x76224),x76221))),x76221),f334(f334(f86(x76222),x76224),f334(f334(f41(x76222),x76223),x76221))) % 188.18/188.26 [7623]~P5(x76232)+E(x76231,f2(x76232))+E(f334(f334(f41(x76232),f334(f334(f86(x76232),x76233),f334(f334(f87(x76232),x76231),x76234))),x76231),f334(f334(f86(x76232),x76234),f334(f334(f41(x76232),x76233),x76231))) % 188.18/188.26 [7844]~P66(x78442)+E(x78441,f2(x78442))+E(f334(f334(f296(x78442),f334(f334(f23(x78442),x78443),f334(f334(f87(x78442),x78441),x78444))),x78441),f334(f334(f23(x78442),f334(f334(f296(x78442),x78443),x78441)),x78444)) % 188.18/188.26 [7845]~P65(x78452)+E(x78451,f2(x78452))+E(f334(f334(f296(x78452),f334(f334(f86(x78452),x78453),f334(f334(f87(x78452),x78454),x78451))),x78451),f334(f334(f86(x78452),f334(f334(f296(x78452),x78453),x78451)),x78454)) % 188.18/188.26 [7846]~P66(x78462)+E(x78461,f2(x78462))+E(f334(f334(f296(x78462),f334(f334(f86(x78462),x78463),f334(f334(f87(x78462),x78461),x78464))),x78461),f334(f334(f86(x78462),f334(f334(f296(x78462),x78463),x78461)),x78464)) % 188.18/188.26 [8535]~P107(f334(f167(x85351,x85353),x85354))+~P107(f334(f167(x85351,x85352),x85354))+P107(f334(f167(x85351,f334(f334(f109(f935(x85351,a922)),x85352),x85353)),x85354)) % 188.18/188.26 [8896]~E(f334(f334(f295(x88961,x88961,x88961),x88962),x88964),f195(f935(f934(x88961,x88961),a922)))+~E(f334(f334(f295(x88961,x88961,x88961),x88962),x88963),f195(f935(f934(x88961,x88961),a922)))+E(f334(f334(f295(x88961,x88961,x88961),x88962),f334(f334(f108(f935(f934(x88961,x88961),a922)),x88963),x88964)),f195(f935(f934(x88961,x88961),a922))) % 188.18/188.26 [9021]~P107(f334(f334(f242(f935(x90211,a922)),x90213),x90214))+~P107(f334(f334(f242(f935(x90211,a922)),x90212),x90214))+P107(f334(f334(f242(f935(x90211,a922)),f334(f334(f108(f935(x90211,a922)),x90212),x90213)),x90214)) % 188.18/188.26 [9399]~P107(f334(f66(x93991),x93994))+~P107(f334(f66(x93991),x93993))+E(f334(f334(f23(a927),f334(f334(f86(a927),f334(f334(f6(x93991,a927),x93992),x93993)),f334(f334(f6(x93991,a927),x93992),x93994))),f334(f334(f6(x93991,a927),x93992),f334(f334(f109(f935(x93991,a922)),x93993),x93994))),f334(f334(f6(x93991,a927),x93992),f334(f334(f108(f935(x93991,a922)),x93993),x93994))) % 188.18/188.26 [9485]~P107(f334(f334(f336(x94851),x94853),x94852))+~P107(f334(f334(f242(f935(x94851,a922)),x94852),f334(f334(f316(x94851),x94853),x94854)))+P107(f334(f334(f242(f935(x94851,a922)),f334(f334(f23(f935(x94851,a922)),x94852),f334(f334(f316(x94851),x94853),f195(f935(x94851,a922))))),x94854)) % 188.18/188.26 [9649]~P107(f334(f334(f336(x96491),x96493),x96492))+P107(f334(f334(f242(f935(x96491,a922)),x96492),f334(f334(f316(x96491),x96493),x96494)))+~P107(f334(f334(f242(f935(x96491,a922)),f334(f334(f23(f935(x96491,a922)),x96492),f334(f334(f316(x96491),x96493),f195(f935(x96491,a922))))),x96494)) % 188.18/188.26 [9750]~P107(f334(f334(f242(a927),x97501),x97503))+~P107(f334(f334(f243(a927),x97502),x97504))+P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),f334(f334(f260(a927,a927),x97501),x97502)),f334(f334(f260(a927,a927),x97503),x97504))),a38)) % 188.18/188.26 [9751]~P107(f334(f334(f242(a927),x97512),x97514))+~P107(f334(f334(f242(a927),x97511),x97513))+P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),f334(f334(f260(a927,a927),x97511),x97512)),f334(f334(f260(a927,a927),x97513),x97514))),a76)) % 188.18/188.26 [10066]~P107(f334(f334(f336(f928(x100661)),x100664),f168(x100661,x100663)))+~P107(f334(f334(f336(f928(x100661)),x100664),f168(x100661,x100662)))+P107(f334(f167(x100661,f334(f334(f109(f935(x100661,a922)),f334(f334(f7(x100661,f935(x100661,a922),a922),f336(x100661)),x100662)),f334(f334(f7(x100661,f935(x100661,a922),a922),f336(x100661)),x100663))),x100664)) % 188.18/188.26 [10150]~P27(x101501,f935(f935(x101501,a922),a922),f334(f334(f7(x101501,f935(f934(x101501,x101501),a922),f935(f935(x101501,a922),a922)),f334(f334(f8(f935(x101501,a922),f935(f935(f934(x101501,x101501),a922),f935(f935(x101501,a922),a922)),x101501),f65(x101501)),f334(f334(f7(x101501,f935(x101501,a922),f935(x101501,a922)),f316(x101501)),f195(f935(x101501,a922))))),x101503),x101502)+~P107(f334(f334(f336(x101501),x101504),x101502))+E(f334(f334(f23(f935(f935(x101501,a922),a922)),f334(f334(f65(x101501),x101502),x101503)),f334(f334(f65(x101501),f334(f334(f316(x101501),x101504),f195(f935(x101501,a922)))),x101503)),f334(f334(f65(x101501),f334(f334(f23(f935(x101501,a922)),x101502),f334(f334(f316(x101501),x101504),f195(f935(x101501,a922))))),x101503)) % 188.18/188.26 [10266]~P55(x102661,x102662,x102664)+~P107(f334(f334(f336(f934(x102661,x102661)),x102663),x102664))+P107(f334(f334(f265(x102661,x102661,a922),f334(f334(f7(x102661,f935(x102661,a922),f935(x102661,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x102661,a922),f935(x102661,a922)),x102661),f8(a922,a922,x102661)),f334(f334(f8(a922,f935(a922,a922),x102661),a332),f334(f334(f7(x102661,f935(x102661,a922),a922),f336(x102661)),x102662)))),f334(f334(f7(x102661,f935(x102661,a922),a922),f336(x102661)),x102662))),x102663)) % 188.18/188.26 [10280]P107(f334(f66(x102801),x102802))+~P107(f334(f66(x102803),f334(f317(x102801,x102803,x102804),x102802)))+~P107(f334(f66(x102801),f334(f270(x102801),f334(f334(f18(x102801,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102801),a332),f334(f334(f7(x102801,f935(x102801,a922),a922),f336(x102801)),x102802))),f334(f334(f7(x102801,x102803,a922),f334(f334(f8(x102803,f935(x102803,a922),x102801),a331),x102804)),f334(x102804,f741(x102804,x102803,x102802,x102801))))))) % 188.18/188.26 [8293]~P66(x82932)+E(x82931,f2(x82932))+E(f334(f334(f296(x82932),f334(f334(f23(x82932),f334(f334(f87(x82932),x82931),x82933)),x82934)),x82931),f334(f334(f23(x82932),x82933),f334(f334(f296(x82932),x82934),x82931))) % 188.18/188.26 [8294]~P66(x82942)+E(x82941,f2(x82942))+E(f334(f334(f296(x82942),f334(f334(f86(x82942),f334(f334(f87(x82942),x82941),x82943)),x82944)),x82941),f334(f334(f86(x82942),x82943),f334(f334(f296(x82942),x82944),x82941))) % 188.18/188.26 [9191]~E(f334(f334(f295(x91911,x91911,x91911),x91913),x91914),f195(f935(f934(x91911,x91911),a922)))+~E(f334(f334(f295(x91911,x91911,x91911),x91912),x91914),f195(f935(f934(x91911,x91911),a922)))+E(f334(f334(f295(x91911,x91911,x91911),f334(f334(f108(f935(f934(x91911,x91911),a922)),x91912),x91913)),x91914),f195(f935(f934(x91911,x91911),a922))) % 188.18/188.26 [9971]~P107(f334(f167(x99711,x99713),x99714))+~P107(f334(f167(x99711,x99712),x99714))+P107(f334(f167(x99711,f334(f334(f18(x99711,a922,a922),f334(f334(f8(a922,f935(a922,a922),x99711),a332),x99712)),x99713)),x99714)) % 188.18/188.26 [10205]P107(f334(x102051,f351(x102052,x102053,x102051,x102054)))+~P107(f334(f66(x102054),f334(f270(x102054),x102051)))+P107(f334(f66(x102053),f334(f270(x102053),f334(f334(f8(f935(x102054,a922),a922,x102053),f92(x102054)),f334(f334(f8(f935(x102054,a922),f935(x102054,a922),x102053),f334(f18(x102054,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102054),a332),x102051))),x102052))))) % 188.18/188.26 [10224]~P107(f334(f66(x102242),f334(f270(x102242),x102243)))+~P107(f334(f66(x102241),f334(f270(x102241),f334(f334(f7(x102241,x102242,a922),x102244),f351(x102244,x102241,x102243,x102242)))))+P107(f334(f66(x102241),f334(f270(x102241),f334(f334(f8(f935(x102242,a922),a922,x102241),f92(x102242)),f334(f334(f8(f935(x102242,a922),f935(x102242,a922),x102241),f334(f18(x102242,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102242),a332),x102243))),x102244))))) % 188.18/188.26 [10290]~P107(f334(f66(x102901),x102904))+P107(f334(f334(f336(x102901),f811(x102902,x102903,x102904,x102901)),x102904))+P107(f334(f66(x102903),f334(f270(x102903),f334(f334(f8(f935(x102901,a922),a922,x102903),f92(x102901)),f334(f334(f8(f935(x102901,a922),f935(x102901,a922),x102903),f334(f18(x102901,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102901),a332),f334(f334(f7(x102901,f935(x102901,a922),a922),f336(x102901)),x102904)))),x102902))))) % 188.18/188.26 [10296]~P107(f334(f66(x102962),x102963))+~P107(f334(f66(x102961),f334(f270(x102961),f334(f334(f7(x102961,x102962,a922),x102964),f811(x102964,x102961,x102963,x102962)))))+P107(f334(f66(x102961),f334(f270(x102961),f334(f334(f8(f935(x102962,a922),a922,x102961),f92(x102962)),f334(f334(f8(f935(x102962,a922),f935(x102962,a922),x102961),f334(f18(x102962,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102962),a332),f334(f334(f7(x102962,f935(x102962,a922),a922),f336(x102962)),x102963)))),x102964))))) % 188.18/188.26 [5276]~E(x52762,x52764)+E(f176(x52761,x52762,x52763),f176(x52761,x52764,x52765))+~E(x52762,f2(a927)) % 188.18/188.26 [5528]E(x55281,x55282)+~E(f176(x55284,x55283,x55281),f176(x55284,x55285,x55282))+E(x55283,f2(a927)) % 188.18/188.26 [6784]E(x67841,x67842)+~E(f334(x67843,x67841),f334(x67843,x67842))+~P27(x67844,x67845,x67843,f250(f935(x67844,a922))) % 188.18/188.26 [7653]E(x76531,x76532)+~P27(x76533,x76534,x76535,f250(f935(x76533,a922)))+~E(f334(f317(x76533,x76534,x76535),x76531),f334(f317(x76533,x76534,x76535),x76532)) % 188.18/188.26 [7897]P27(x78972,x78973,f494(x78974,x78973,x78972,x78971),x78971)+~E(f334(f317(x78973,x78972,x78975),x78974),x78971)+E(x78971,f195(f935(x78972,a922))) % 188.18/188.26 [8420]~P107(f334(f334(x84203,x84202),x84205))+~P107(f334(f334(x84203,x84204),x84202))+P107(f334(f334(f336(x84201),x84202),f305(x84201,x84203,x84204,x84205))) % 188.18/188.26 [8421]~P107(f334(f334(x84213,x84212),x84215))+~P107(f334(f334(x84213,x84214),x84212))+P107(f334(f334(f336(x84211),x84212),f302(x84211,x84213,x84214,x84215))) % 188.18/188.26 [8717]~P27(x87171,x87172,x87173,x87174)+P28(x87171,x87172,x87173,x87174,x87175)+~E(f334(f317(x87171,x87172,x87173),x87174),x87175) % 188.18/188.26 [8853]~P28(x88531,x88533,x88534,x88532,x88535)+~P107(f334(f66(x88533),x88535))+P107(f334(f66(x88531),x88532)) % 188.18/188.26 [8854]~P28(x88543,x88541,x88544,x88545,x88542)+~P107(f334(f66(x88543),x88545))+P107(f334(f66(x88541),x88542)) % 188.18/188.26 [8978]~P27(x89781,x89783,x89785,f250(f935(x89781,a922)))+~P27(x89783,x89782,x89784,f250(f935(x89783,a922)))+P27(x89781,x89782,f334(f78(x89783,x89782,x89781,x89784),x89785),f250(f935(x89781,a922))) % 188.18/188.26 [9547]P107(f334(f334(f336(f934(x95471,x95471)),f334(f334(f260(x95471,x95471),x95472),x95473)),f314(x95471,x95474)))+~P107(f334(f334(f336(f934(x95471,x95471)),f334(f334(f260(x95471,x95471),x95472),x95475)),f314(x95471,x95474)))+~P107(f334(f334(f336(f934(x95471,x95471)),f334(f334(f260(x95471,x95471),x95475),x95473)),f314(x95471,x95474))) % 188.18/188.26 [9585]~P109(x95852)+~P107(f334(f144(x95851),x95855))+P107(f334(f144(x95851),f156(x95851,x95852,x95853,x95854,x95855))) % 188.18/188.26 [5602]~E(x56022,f120(x56021))+E(f334(f334(f141(x56021),x56022),x56023),f334(f334(f158(x56021),x56024),x56025))+~E(x56023,f334(f334(f158(x56021),x56024),x56025)) % 188.18/188.26 [5603]~E(x56032,f120(x56031))+E(f334(f334(f141(x56031),x56032),x56033),f334(f334(f158(x56031),x56034),x56035))+~E(f334(f334(f158(x56031),x56034),x56035),x56033) % 188.18/188.26 [6742]~E(f334(f196(f928(x67421)),x67425),f334(f196(f928(x67422)),x67424))+E(f334(f334(f161(f934(x67421,x67422),x67422),f264(x67421,x67422)),x67423),x67424)+~E(f334(f334(f188(x67421,x67422),x67425),x67424),x67423) % 188.18/188.26 [6743]~E(f334(f196(f928(x67431)),x67434),f334(f196(f928(x67432)),x67435))+E(f334(f334(f161(f934(x67431,x67432),x67431),f259(x67431,x67432)),x67433),x67434)+~E(f334(f334(f188(x67431,x67432),x67434),x67435),x67433) % 188.18/188.26 [7205]~P109(x72051)+~P15(x72051,f334(f334(f161(x72052,x72051),x72053),x72055))+P15(x72051,f334(f334(f161(x72052,x72051),x72053),f334(f143(x72052,x72054),x72055))) % 188.18/188.26 [7247]~P107(f334(x72473,x72475))+~P107(f334(f334(x72472,x72474),x72475))+P107(f334(f334(f99(x72471,x72472,x72473),x72474),x72475)) % 188.18/188.26 [7345]~P109(x73451)+P15(x73451,f334(f334(f161(x73452,x73451),x73453),f177(x73452,x73454,x73455)))+~P15(x73451,f334(f334(f161(x73452,x73451),x73453),x73455)) % 188.18/188.26 [7368]~P57(x73683,x73682,x73685)+~P57(x73681,x73683,x73684)+P57(x73681,x73682,f334(f334(f295(x73681,x73683,x73682),x73684),x73685)) % 188.18/188.26 [7462]E(x74621,x74622)+~P27(x74623,x74624,x74625,f250(f935(x74623,a922)))+~E(f334(f334(f161(x74623,x74624),x74625),x74621),f334(f334(f161(x74623,x74624),x74625),x74622)) % 188.18/188.26 [7607]~P107(f334(f334(f242(a927),x76071),f334(x76073,x76075)))+P107(f334(f334(f242(a927),x76071),f162(x76072,x76073,x76074)))+~P107(f334(f334(f336(x76072),x76075),f334(f179(x76072),x76074))) % 188.18/188.26 [7608]~P107(f334(f334(f243(a927),x76081),f334(x76083,x76085)))+P107(f334(f334(f243(a927),x76081),f162(x76082,x76083,x76084)))+~P107(f334(f334(f336(x76082),x76085),f334(f179(x76082),x76084))) % 188.18/188.26 [7995]P107(f334(x79951,x79952))+~P107(f334(x79951,x79953))+~P107(f334(f334(f336(x79954),x79952),f334(f179(x79954),f176(x79954,x79955,x79953)))) % 188.18/188.26 [7996]P107(f334(x79961,x79962))+~P107(f334(x79961,x79963))+~P107(f334(f334(f336(x79964),x79963),f334(f179(x79964),f176(x79964,x79965,x79962)))) % 188.18/188.26 [8000]~P111(x80001)+P107(f334(f334(f242(f935(x80001,a922)),f311(x80001,x80002,x80003)),f311(x80001,x80004,x80005)))+P107(f334(f334(f242(x80001),x80002),x80003)) % 188.18/188.26 [8023]~P7(x80231)+P107(f334(f334(f242(x80231),f334(f334(f45(x80232,x80231),x80233),x80234)),f334(x80234,x80235)))+~P107(f334(f334(f336(x80232),x80235),x80233)) % 188.18/188.26 [8092]~P27(x80921,x80922,x80924,x80923)+E(f334(f83(x80921,x80922,x80923,x80924),f334(x80924,x80925)),x80925)+~P107(f334(f334(f336(x80921),x80925),x80923)) % 188.18/188.26 [8093]~P27(x80931,x80932,x80934,x80933)+E(f334(f97(x80931,x80932,x80933,x80934),f334(x80934,x80935)),x80935)+~P107(f334(f334(f336(x80931),x80935),x80933)) % 188.18/188.26 [8284]~P107(f334(x82841,x82845))+P107(f334(x82841,f377(x82841,x82842,x82843,x82844)))+~P107(f334(f334(f336(x82844),x82845),x82843)) % 188.18/188.26 [8285]~P107(f334(x82851,x82855))+P107(f334(x82851,f377(x82851,x82852,x82853,x82854)))+~P107(f334(f334(f336(x82854),x82855),x82852)) % 188.18/188.26 [8373]P107(f334(f66(x83731),x83732))+~P107(f334(f66(x83733),x83734))+~P107(f334(f334(f242(f935(x83731,a922)),x83732),f334(f317(x83733,x83731,x83735),x83734))) % 188.18/188.26 [8539]E(x85391,x85392)+~P27(x85393,x85394,x85395,f334(f334(f108(f935(x85393,a922)),f334(f179(x85393),x85391)),f334(f179(x85393),x85392)))+~E(f334(f334(f161(x85393,x85394),x85395),x85391),f334(f334(f161(x85393,x85394),x85395),x85392)) % 188.18/188.26 [8589]~P111(x85891)+~P107(f334(f334(f243(f935(x85891,a922)),f311(x85891,x85894,x85895)),f311(x85891,x85892,x85893)))+P107(f334(f334(f242(x85891),x85892),x85893)) % 188.18/188.26 [8648]~P27(x86481,x86484,x86485,f250(f935(x86481,a922)))+~P107(f334(f334(f336(x86484),f334(x86485,x86482)),f334(f317(x86481,x86484,x86485),x86483)))+P107(f334(f334(f336(x86481),x86482),x86483)) % 188.18/188.26 [8723]P107(f334(x87231,x87232))+~P107(f334(x87231,f381(x87231,x87233,x87234,x87235)))+~P107(f334(f334(f336(x87235),x87232),x87234)) % 188.18/188.26 [8724]P107(f334(x87241,x87242))+~P107(f334(x87241,f381(x87241,x87243,x87244,x87245)))+~P107(f334(f334(f336(x87245),x87242),x87243)) % 188.18/188.26 [9018]~P27(x90182,x90183,x90181,x90184)+E(f334(x90181,f334(f83(x90182,x90183,x90184,x90181),x90185)),x90185)+~P107(f334(f334(f336(x90183),x90185),f334(f317(x90182,x90183,x90181),x90184))) % 188.18/188.26 [9132]E(x91321,f120(x91322))+E(f334(f334(f158(x91322),x91323),f693(x91324,x91323,x91325,x91321,x91322)),x91321)+~E(f334(f334(f141(x91322),x91321),x91325),f334(f334(f158(x91322),x91323),x91324)) % 188.18/188.26 [9133]E(x91331,f120(x91332))+E(f334(f334(f158(x91332),x91333),f694(x91334,x91331,x91335,x91333,x91332)),x91331)+~E(f334(f334(f141(x91332),x91331),x91334),f334(f334(f158(x91332),x91333),x91335)) % 188.18/188.26 [9150]E(f334(f334(f158(x91502),x91503),f693(x91504,x91503,x91501,x91505,x91502)),x91505)+~E(f334(f334(f141(x91502),x91505),x91501),f334(f334(f158(x91502),x91503),x91504))+E(x91501,f334(f334(f158(x91502),x91503),x91504)) % 188.18/188.26 [9151]E(f334(f334(f158(x91511),x91512),f694(x91514,x91515,x91513,x91512,x91511)),x91515)+~E(f334(f334(f141(x91511),x91515),x91514),f334(f334(f158(x91511),x91512),x91513))+E(f334(f334(f158(x91511),x91512),x91513),x91514) % 188.18/188.26 [9226]~E(f334(f317(x92263,x92262,x92264),f250(f935(x92263,a922))),f250(f935(x92262,a922)))+~E(f334(f317(x92261,x92263,x92265),f250(f935(x92261,a922))),f250(f935(x92263,a922)))+E(f334(f317(x92261,x92262,f334(f78(x92263,x92262,x92261,x92264),x92265)),f250(f935(x92261,a922))),f250(f935(x92262,a922))) % 188.18/188.26 [9594]E(x95941,f120(x95942))+~E(f334(f334(f141(x95942),x95941),x95943),f334(f334(f158(x95942),x95945),x95944))+E(f334(f334(f141(x95942),f694(x95943,x95941,x95944,x95945,x95942)),x95943),x95944) % 188.18/188.26 [9595]E(x95951,f120(x95952))+~E(f334(f334(f141(x95952),x95951),x95955),f334(f334(f158(x95952),x95954),x95953))+E(f334(f334(f141(x95952),f693(x95953,x95954,x95955,x95951,x95952)),x95955),x95953) % 188.18/188.26 [9603]E(f334(f334(f141(x96032),f693(x96034,x96033,x96031,x96035,x96032)),x96031),x96034)+~E(f334(f334(f141(x96032),x96035),x96031),f334(f334(f158(x96032),x96033),x96034))+E(x96031,f334(f334(f158(x96032),x96033),x96034)) % 188.18/188.26 [9604]~E(f334(f334(f141(x96041),x96045),x96044),f334(f334(f158(x96041),x96042),x96043))+E(f334(f334(f141(x96041),f694(x96044,x96045,x96043,x96042,x96041)),x96044),x96043)+E(f334(f334(f158(x96041),x96042),x96043),x96044) % 188.18/188.26 [9605]E(f334(f334(f141(x96051),x96055),f697(x96053,x96052,x96054,x96055,x96051)),x96052)+E(f334(f334(f141(x96051),x96052),f696(x96053,x96052,x96054,x96055,x96051)),x96055)+~E(f334(f334(f141(x96051),x96055),x96054),f334(f334(f141(x96051),x96052),x96053)) % 188.18/188.26 [9634]~P109(x96341)+P15(x96341,f334(f334(f161(x96342,x96341),x96343),f156(x96342,x96341,x96343,x96344,x96345)))+~P15(x96341,f334(f334(f161(x96342,x96341),x96343),x96345)) % 188.18/188.26 [9646]~P62(x96465,x96461,x96464,x96463)+P107(f334(f334(x96461,x96462),f524(x96463,x96464,x96461,x96465,x96462)))+~P107(f334(f334(f336(x96465),x96462),x96464)) % 188.18/188.26 [9647]~P62(x96475,x96471,x96474,x96473)+P107(f334(f334(x96471,x96472),f815(x96473,x96474,x96471,x96475,x96472)))+~P107(f334(f334(f336(x96475),x96472),x96474)) % 188.18/188.26 [9762]~P107(f334(f334(f336(f934(x97621,x97621)),f334(f334(f260(x97621,x97621),x97625),x97623)),f314(x97621,x97624)))+P107(f334(f334(f336(f934(x97621,x97621)),f334(f334(f260(x97621,x97621),x97622),x97623)),f334(f334(f295(x97621,x97621,x97621),x97624),f314(x97621,x97624))))+~P107(f334(f334(f336(f934(x97621,x97621)),f334(f334(f260(x97621,x97621),x97622),x97625)),f334(f334(f295(x97621,x97621,x97621),x97624),f314(x97621,x97624)))) % 188.18/188.26 [9763]~P107(f334(f334(f336(f934(x97631,x97631)),f334(f334(f260(x97631,x97631),x97632),x97635)),f314(x97631,x97634)))+P107(f334(f334(f336(f934(x97631,x97631)),f334(f334(f260(x97631,x97631),x97632),x97633)),f334(f334(f295(x97631,x97631,x97631),x97634),f314(x97631,x97634))))+~P107(f334(f334(f336(f934(x97631,x97631)),f334(f334(f260(x97631,x97631),x97635),x97633)),f334(f334(f295(x97631,x97631,x97631),x97634),f314(x97631,x97634)))) % 188.18/188.26 [9765]P107(f334(f334(f336(f934(f928(x97651),f928(x97651))),f334(f334(f260(f928(x97651),f928(x97651)),x97652),x97653)),f165(x97651,f314(x97651,x97654))))+~P107(f334(f334(f336(f934(f928(x97651),f928(x97651))),f334(f334(f260(f928(x97651),f928(x97651)),x97652),x97655)),f165(x97651,f314(x97651,x97654))))+~P107(f334(f334(f336(f934(f928(x97651),f928(x97651))),f334(f334(f260(f928(x97651),f928(x97651)),x97655),x97653)),f165(x97651,f314(x97651,x97654)))) % 188.18/188.26 [9769]E(f334(f334(f141(x97691),x97692),f696(x97693,x97692,x97694,x97695,x97691)),x97695)+E(f334(f334(f141(x97691),f697(x97693,x97692,x97694,x97695,x97691)),x97693),x97694)+~E(f334(f334(f141(x97691),x97692),x97693),f334(f334(f141(x97691),x97695),x97694)) % 188.18/188.26 [9770]E(f334(f334(f141(x97701),x97702),f697(x97703,x97704,x97705,x97702,x97701)),x97704)+E(f334(f334(f141(x97701),f696(x97703,x97704,x97705,x97702,x97701)),x97705),x97703)+~E(f334(f334(f141(x97701),x97702),x97705),f334(f334(f141(x97701),x97704),x97703)) % 188.18/188.26 [9829]P107(f334(f334(f336(f934(x98291,x98291)),f334(f334(f260(x98291,x98291),x98292),x98293)),f334(f334(f295(x98291,x98291,x98291),x98294),f314(x98291,x98294))))+~P107(f334(f334(f336(f934(x98291,x98291)),f334(f334(f260(x98291,x98291),x98292),x98295)),f334(f334(f295(x98291,x98291,x98291),x98294),f314(x98291,x98294))))+~P107(f334(f334(f336(f934(x98291,x98291)),f334(f334(f260(x98291,x98291),x98295),x98293)),f334(f334(f295(x98291,x98291,x98291),x98294),f314(x98291,x98294)))) % 188.18/188.26 [9860]P36(x98601,x98602,x98603,x98604,x98605)+~E(f334(f196(f928(x98601)),x98604),f334(f196(f928(x98602)),x98605))+~P107(f334(f334(f265(x98601,x98602,a922),x98603),f712(x98605,x98604,x98603,x98602,x98601))) % 188.18/188.26 [9861]P36(x98611,x98612,x98613,x98614,x98615)+~E(f334(f196(f928(x98611)),x98614),f334(f196(f928(x98612)),x98615))+~P107(f334(f334(f265(x98611,x98612,a922),x98613),f713(x98613,x98615,x98614,x98612,x98611))) % 188.18/188.26 [9867]E(f334(f334(f141(x98671),f696(x98672,x98673,x98674,x98675,x98671)),x98674),x98672)+~E(f334(f334(f141(x98671),x98673),x98672),f334(f334(f141(x98671),x98675),x98674))+E(f334(f334(f141(x98671),f697(x98672,x98673,x98674,x98675,x98671)),x98672),x98674) % 188.18/188.26 [9886]~P109(x98862)+E(f334(f334(f155(x98861,x98862,x98863),x98864),x98865),f334(f334(f158(x98861),x98864),x98865))+P107(f334(f334(f336(x98861),f757(x98864,x98863,x98865,x98861,x98862)),f334(f179(x98861),x98865))) % 188.18/188.26 [9890]~P62(x98901,x98904,x98903,x98902)+~P107(f334(f334(f336(x98901),x98905),x98903))+P107(f334(f334(f336(x98901),f524(x98902,x98903,x98904,x98901,x98905)),x98902)) % 188.18/188.26 [9891]~P62(x98911,x98914,x98913,x98912)+~P107(f334(f334(f336(x98911),x98915),x98913))+P107(f334(f334(f336(x98911),f815(x98912,x98913,x98914,x98911,x98915)),x98912)) % 188.18/188.26 [10018]~P107(f334(f334(f336(f934(f935(x100181,a922),f935(x100181,a922))),f334(f334(f260(f935(x100181,a922),f935(x100181,a922)),x100184),x100183)),f325(x100181,x100182)))+~P107(f334(f334(f336(x100181),x100185),x100184))+P107(f334(f334(f336(x100181),f607(x100182,x100183,x100184,x100181,x100185)),x100183)) % 188.18/188.26 [10027]~P109(x100272)+E(f334(f334(f155(x100271,x100272,x100273),x100274),x100275),f334(f334(f158(x100271),x100274),x100275))+~P107(f334(f334(f242(x100272),f334(x100273,x100274)),f334(x100273,f757(x100274,x100273,x100275,x100271,x100272)))) % 188.18/188.26 [10075]~P27(x100753,x100754,x100755,f250(f935(x100753,a922)))+P107(f334(x100751,x100752))+~P107(f334(x100751,f334(f97(x100753,x100754,f250(f935(x100753,a922)),x100755),f595(x100752,x100751,x100755,x100754,x100753)))) % 188.18/188.26 [10190]P36(x101901,x101902,x101903,x101904,x101905)+~E(f334(f196(f928(x101901)),x101904),f334(f196(f928(x101902)),x101905))+~P107(f334(f334(x101903,f334(f334(f171(x101901),x101904),f714(x101905,x101904,x101903,x101902,x101901))),f334(f334(f171(x101902),x101905),f714(x101905,x101904,x101903,x101902,x101901)))) % 188.18/188.26 [10191]P36(x101911,x101912,x101913,x101914,x101915)+~E(f334(f196(f928(x101911)),x101914),f334(f196(f928(x101912)),x101915))+~P107(f334(f334(x101913,f334(f334(f171(x101911),x101914),f750(x101913,x101915,x101912,x101914,x101911))),f334(f334(f171(x101912),x101915),f750(x101913,x101915,x101912,x101914,x101911)))) % 188.18/188.26 [6814]~P19(x68142,x68145,x68141)+~P107(f334(f66(x68142),x68144))+E(f334(x68141,f334(f334(f316(x68142),x68143),x68144)),f334(f334(f69(x68142,x68142,x68145),x68143),x68144)) % 188.18/188.26 [6815]~E(x68153,x68154)+~E(x68152,x68155)+E(f334(f334(f316(x68151),x68152),f334(f334(f316(x68151),x68153),f195(f935(x68151,a922)))),f334(f334(f316(x68151),x68154),f334(f334(f316(x68151),x68155),f195(f935(x68151,a922))))) % 188.18/188.26 [6825]P107(f334(x68252,x68255))+E(f184(x68251,x68252,f334(f334(f141(x68251),x68253),x68254)),f184(x68251,x68252,x68253))+~P107(f334(f334(f336(x68251),x68255),f334(f179(x68251),x68253))) % 188.18/188.26 [6861]E(f334(x68611,x68612),f195(f935(x68613,a922)))+~E(f334(f334(f44(x68614,f935(x68613,a922)),x68615),x68611),f195(f935(x68613,a922)))+~P107(f334(f334(f336(x68614),x68612),x68615)) % 188.18/188.26 [6862]E(f334(x68621,x68622),f250(f935(x68623,a922)))+~E(f334(f334(f45(x68624,f935(x68623,a922)),x68625),x68621),f250(f935(x68623,a922)))+~P107(f334(f334(f336(x68624),x68622),x68625)) % 188.18/188.26 [7355]~E(x73552,x73554)+~P143(x73551)+E(f334(f334(f86(x73551),f334(f334(f87(x73551),x73552),x73553)),f334(f334(f87(x73551),x73554),x73555)),f334(f334(f86(x73551),f334(f334(f87(x73551),x73552),x73555)),f334(f334(f87(x73551),x73554),x73553))) % 188.18/188.26 [7415]~P7(x74151)+~P107(f334(f334(f336(x74154),x74153),x74155))+P107(f334(f334(f242(x74151),f334(x74152,x74153)),f334(f334(f44(x74154,x74151),x74155),x74152))) % 188.18/188.26 [7467]~P110(x74671)+P107(f334(f334(f242(x74671),f334(x74672,x74673)),f334(x74674,x74673)))+~P107(f334(f334(f242(f935(x74675,x74671)),x74672),x74674)) % 188.18/188.26 [7579]E(x75791,x75792)+E(x75793,x75791)+~E(f334(f334(f316(x75794),x75791),f334(f334(f316(x75794),x75795),f195(f935(x75794,a922)))),f334(f334(f316(x75794),x75792),f334(f334(f316(x75794),x75793),f195(f935(x75794,a922))))) % 188.18/188.26 [7580]E(x75801,x75802)+E(x75803,x75801)+~E(f334(f334(f316(x75804),x75803),f334(f334(f316(x75804),x75802),f195(f935(x75804,a922)))),f334(f334(f316(x75804),x75805),f334(f334(f316(x75804),x75801),f195(f935(x75804,a922))))) % 188.18/188.26 [7581]E(x75811,x75812)+E(x75811,x75813)+~E(f334(f334(f316(x75814),x75813),f334(f334(f316(x75814),x75812),f195(f935(x75814,a922)))),f334(f334(f316(x75814),x75815),f334(f334(f316(x75814),x75811),f195(f935(x75814,a922))))) % 188.18/188.26 [7582]E(x75821,x75822)+E(x75821,x75823)+~E(f334(f334(f316(x75824),x75821),f334(f334(f316(x75824),x75825),f195(f935(x75824,a922)))),f334(f334(f316(x75824),x75822),f334(f334(f316(x75824),x75823),f195(f935(x75824,a922))))) % 188.18/188.26 [8098]P27(x80981,x80982,x80983,x80984)+~P27(x80981,x80982,x80983,x80985)+~P107(f334(f334(f242(f935(x80981,a922)),x80984),x80985)) % 188.18/188.26 [8127]~E(f334(x81273,x81275),x81274)+~P27(x81271,x81272,x81273,f250(f935(x81271,a922)))+E(f334(f97(x81271,x81272,f250(f935(x81271,a922)),x81273),x81274),x81275) % 188.18/188.26 [8269]E(x82691,x82692)+~E(f334(f317(x82693,x82694,x82695),x82691),f334(f317(x82693,x82694,x82695),x82692))+~P27(x82693,x82694,x82695,f334(f334(f108(f935(x82693,a922)),x82691),x82692)) % 188.18/188.26 [8343]P107(f334(x83432,x83434))+E(f334(f334(f145(x83431),f334(f196(f928(x83431)),f184(x83431,x83432,x83433))),x83433),f334(f334(f158(x83431),x83434),x83435))+~E(f334(f334(f141(x83431),f184(x83431,x83432,x83433)),f334(f334(f158(x83431),x83434),x83435)),x83433) % 188.18/188.26 [8371]~P27(x83711,x83712,x83713,x83715)+~P27(x83711,x83712,x83713,x83714)+P27(x83711,x83712,x83713,f334(f334(f109(f935(x83711,a922)),x83714),x83715)) % 188.18/188.26 [8478]~P76(x84781)+E(f334(f334(f86(x84781),f334(x84782,x84783)),f334(f172(x84781),f334(f334(f161(x84784,x84781),x84782),f177(x84784,x84783,x84785)))),f334(f172(x84781),f334(f334(f161(x84784,x84781),x84782),x84785)))+~P107(f334(f334(f336(x84784),x84783),f334(f179(x84784),x84785))) % 188.18/188.26 [8562]~P109(x85621)+~P15(x85621,f334(f334(f161(x85622,x85621),x85623),x85625))+P15(x85621,f334(f334(f161(x85622,x85621),x85623),f334(f334(f155(x85622,x85621,x85623),x85624),x85625))) % 188.18/188.26 [8644]~P7(x86441)+P107(f334(f334(f242(x86441),f334(f334(f44(x86442,x86441),x86443),x86444)),f334(f334(f44(x86442,x86441),x86445),x86444)))+~P107(f334(f334(f242(f935(x86442,a922)),x86443),x86445)) % 188.18/188.26 [8645]~P7(x86451)+P107(f334(f334(f242(x86451),f334(f334(f45(x86452,x86451),x86453),x86454)),f334(f334(f45(x86452,x86451),x86455),x86454)))+~P107(f334(f334(f242(f935(x86452,a922)),x86455),x86453)) % 188.18/188.26 [8679]~P109(x86793)+P107(f334(f144(x86791),x86792))+~P107(f334(f144(x86791),f334(f334(f155(x86791,x86793,x86794),x86795),x86792))) % 188.18/188.26 [8824]~P109(x88241)+~P107(f334(f334(f336(x88242),x88243),f334(f179(x88242),x88244)))+~P107(f334(f144(x88242),f334(f334(f155(x88242,x88241,x88245),x88243),x88244))) % 188.18/188.26 [8908]~P109(x89081)+P15(x89081,f334(f334(f161(x89082,x89081),x89083),x89084))+~P15(x89081,f334(f334(f161(x89082,x89081),x89083),f334(f334(f155(x89082,x89081,x89083),x89085),x89084))) % 188.18/188.26 [8955]~P27(x89552,x89551,x89554,x89553)+E(f334(f317(x89551,x89552,f97(x89552,x89551,x89553,x89554)),f334(f317(x89552,x89551,x89554),x89555)),x89555)+~P107(f334(f334(f242(f935(x89552,a922)),x89555),x89553)) % 188.18/188.26 [9006]~P109(x90062)+E(f334(f334(f155(x90061,x90062,x90063),x90064),x90065),f156(x90061,x90062,x90063,x90064,x90065))+P107(f334(f334(f336(x90062),f334(x90063,x90064)),f334(f317(x90061,x90062,x90063),f334(f179(x90061),x90065)))) % 188.18/188.26 [9092]~P109(x90922)+E(f156(x90921,x90922,x90923,x90924,x90925),x90925)+~P107(f334(f334(f336(x90922),f334(x90923,x90924)),f334(f317(x90921,x90922,x90923),f334(f179(x90921),x90925)))) % 188.18/188.26 [9109]~P27(x91092,x91091,x91093,x91095)+P107(f334(f334(f243(f935(x91091,a922)),f334(f317(x91092,x91091,x91093),x91094)),f334(f317(x91092,x91091,x91093),x91095)))+~P107(f334(f334(f243(f935(x91092,a922)),x91094),x91095)) % 188.18/188.26 [9263]~P27(x92631,x92632,x92633,f250(f935(x92631,a922)))+~P107(f334(f334(f242(f935(x92632,a922)),x92634),f334(f317(x92631,x92632,x92633),x92635)))+P107(f334(f334(f242(f935(x92631,a922)),f334(f318(x92631,x92632,x92633),x92634)),x92635)) % 188.18/188.26 [9285]~E(f334(f317(x92853,x92851,x92854),f250(f935(x92853,a922))),f250(f935(x92851,a922)))+P107(f334(f334(f242(f935(x92851,a922)),x92852),f334(f317(x92853,x92851,x92854),x92855)))+~P107(f334(f334(f242(f935(x92853,a922)),f334(f318(x92853,x92851,x92854),x92852)),x92855)) % 188.18/188.26 [9392]~P27(x93921,x93924,x93925,f250(f935(x93921,a922)))+~P107(f334(f334(f242(f935(x93924,a922)),f334(f317(x93921,x93924,x93925),x93922)),f334(f317(x93921,x93924,x93925),x93923)))+P107(f334(f334(f242(f935(x93921,a922)),x93922),x93923)) % 188.18/188.26 [9515]~P82(x95151)+~E(f334(x95153,f733(x95153,x95154,x95155,x95152,x95151)),f2(x95151))+E(f334(f172(x95151),f334(f334(f161(x95152,x95151),x95153),f334(f143(x95152,x95154),x95155))),f334(f172(x95151),f334(f334(f161(x95152,x95151),x95153),x95155))) % 188.18/188.26 [9542]~P28(x95421,x95422,x95423,f250(f935(x95421,a922)),f250(f935(x95422,a922)))+~P107(f334(f334(f242(f935(x95422,a922)),x95424),f334(f317(x95421,x95422,x95423),x95425)))+P107(f334(f334(f242(f935(x95421,a922)),f334(f318(x95421,x95422,x95423),x95424)),x95425)) % 188.18/188.26 [9571]~P28(x95713,x95711,x95714,f250(f935(x95713,a922)),f250(f935(x95711,a922)))+P107(f334(f334(f242(f935(x95711,a922)),x95712),f334(f317(x95713,x95711,x95714),x95715)))+~P107(f334(f334(f242(f935(x95713,a922)),f334(f318(x95713,x95711,x95714),x95712)),x95715)) % 188.18/188.26 [9690]~P18(x96901,x96902,x96903)+~P107(f334(f66(x96901),x96905))+P107(f334(f71(x96901,x96902,x96903,x96904,x96905),f334(f334(f69(x96901,x96902,x96903),x96904),x96905))) % 188.18/188.26 [9782]~P28(x97822,x97821,x97824,f250(f935(x97822,a922)),f250(f935(x97821,a922)))+~P28(x97821,x97823,x97825,f250(f935(x97821,a922)),f250(f935(x97823,a922)))+E(f334(f78(x97821,x97822,x97823,f97(x97822,x97821,f250(f935(x97822,a922)),x97824)),f97(x97821,x97823,f250(f935(x97821,a922)),x97825)),f97(x97822,x97823,f250(f935(x97822,a922)),f334(f78(x97821,x97823,x97822,x97825),x97824))) % 188.18/188.26 [9783]P107(f334(x97831,f653(x97832,x97831,x97833,x97834,x97835)))+~P107(f334(f334(f242(f935(x97835,a922)),x97834),x97833))+P107(f334(f334(f242(f935(x97835,a922)),f334(f334(f109(f935(x97835,a922)),x97834),f334(f270(x97835),x97831))),f334(f334(f109(f935(x97835,a922)),x97833),f334(f270(x97835),x97832)))) % 188.18/188.26 [9797]~P82(x97971)+~P107(f334(x97974,f733(x97973,x97974,x97975,x97972,x97971)))+E(f334(f172(x97971),f334(f334(f161(x97972,x97971),x97973),f334(f143(x97972,x97974),x97975))),f334(f172(x97971),f334(f334(f161(x97972,x97971),x97973),x97975))) % 188.18/188.26 [9888]~P7(x98885)+P107(f334(f334(f336(x98881),f502(x98882,x98883,x98881,x98884,x98885)),x98883))+P107(f334(f334(f242(x98885),x98884),f334(f334(f45(x98881,x98885),x98883),x98882))) % 188.18/188.26 [9892]~P82(x98921)+E(f334(f172(x98921),f334(f334(f161(x98922,x98921),x98923),f334(f143(x98922,x98924),x98925))),f334(f172(x98921),f334(f334(f161(x98922,x98921),x98923),x98925)))+P107(f334(f334(f336(x98922),f733(x98923,x98924,x98925,x98922,x98921)),f334(f179(x98922),x98925))) % 188.18/188.26 [9899]~P107(f334(x98995,f653(x98995,x98993,x98994,x98992,x98991)))+~P107(f334(f334(f242(f935(x98991,a922)),x98992),x98994))+P107(f334(f334(f242(f935(x98991,a922)),f334(f334(f109(f935(x98991,a922)),x98992),f334(f270(x98991),x98993))),f334(f334(f109(f935(x98991,a922)),x98994),f334(f270(x98991),x98995)))) % 188.18/188.26 [9915]~P27(x99155,x99153,x99154,f250(f935(x99155,a922)))+P107(f334(x99151,x99152))+P107(f334(f334(f336(x99153),f595(x99152,x99151,x99154,x99153,x99155)),f334(f317(x99155,x99153,x99154),f250(f935(x99155,a922))))) % 188.18/188.26 [9940]P36(x99401,x99402,x99403,x99404,x99405)+~E(f334(f196(f928(x99402)),x99405),f334(f196(f928(x99401)),x99404))+P107(f334(f334(f243(a927),f714(x99405,x99404,x99403,x99402,x99401)),f334(f196(f928(x99401)),x99404))) % 188.18/188.26 [9941]P36(x99411,x99412,x99413,x99414,x99415)+~E(f334(f196(f928(x99412)),x99415),f334(f196(f928(x99411)),x99414))+P107(f334(f334(f243(a927),f750(x99413,x99415,x99412,x99414,x99411)),f334(f196(f928(x99411)),x99414))) % 188.18/188.26 [9972]P107(f334(f334(f336(x99721),f653(x99722,x99723,x99724,x99725,x99721)),x99725))+~P107(f334(f334(f242(f935(x99721,a922)),x99725),x99724))+P107(f334(f334(f242(f935(x99721,a922)),f334(f334(f109(f935(x99721,a922)),x99725),f334(f270(x99721),x99723))),f334(f334(f109(f935(x99721,a922)),x99724),f334(f270(x99721),x99722)))) % 188.18/188.26 [10028]~P7(x100281)+~P107(f334(f334(f242(x100281),x100282),f334(x100285,f502(x100285,x100284,x100283,x100282,x100281))))+P107(f334(f334(f242(x100281),x100282),f334(f334(f45(x100283,x100281),x100284),x100285))) % 188.18/188.26 [10064]~P72(x100641)+~P107(f334(f66(x100642),x100645))+E(f334(f334(f334(f70(x100641,x100642,f87(x100641)),f334(f334(f18(x100642,x100641,x100641),f334(f334(f8(x100641,f935(x100641,x100641),x100642),f87(x100641)),x100643)),x100644)),f84(x100641)),x100645),f334(f334(f87(x100641),f334(f334(f334(f70(x100641,x100642,f87(x100641)),x100643),f84(x100641)),x100645)),f334(f334(f334(f70(x100641,x100642,f87(x100641)),x100644),f84(x100641)),x100645))) % 188.18/188.26 [10115]~P107(f334(f334(f336(f934(f935(x101151,a922),f935(x101151,a922))),f334(f334(f260(f935(x101151,a922),f935(x101151,a922)),x101155),x101154)),f325(x101151,x101153)))+~P107(f334(f334(f336(x101151),x101152),x101155))+P107(f334(f334(f336(f934(x101151,x101151)),f334(f334(f260(x101151,x101151),x101152),f607(x101153,x101154,x101155,x101151,x101152))),x101153)) % 188.18/188.26 [10219]~P107(f334(f334(f336(f934(f928(x102191),f928(x102191))),f334(f334(f260(f928(x102191),f928(x102191)),f334(f334(f141(x102191),x102195),x102192)),f334(f334(f141(x102191),x102195),x102193))),f154(x102191,x102194)))+P107(f334(f334(f336(f934(f928(x102191),f928(x102191))),f334(f334(f260(f928(x102191),f928(x102191)),x102192),x102193)),f154(x102191,x102194)))+P107(f334(f334(f336(f934(x102191,x102191)),f334(f334(f260(x102191,x102191),f702(x102194,x102193,x102192,x102195,x102191)),f702(x102194,x102193,x102192,x102195,x102191))),x102194)) % 188.18/188.26 [7470]~E(x74703,x74705)+E(f334(f334(f171(x74701),f334(f334(f166(x74701,x74702),x74703),x74704)),x74705),x74704)+~P107(f334(f334(f243(a927),x74703),f334(f196(f928(x74701)),x74702))) % 188.18/188.26 [7576]~E(f334(f334(f141(x75761),x75762),x75764),f334(f334(f141(x75761),x75763),x75765))+E(f334(f334(f182(x75761),f334(f196(f928(x75761)),x75762)),x75763),x75762)+P107(f334(f334(f242(a927),f334(f196(f928(x75761)),x75763)),f334(f196(f928(x75761)),x75762))) % 188.18/188.26 [8063]~E(f334(f334(f141(x80631),x80632),x80634),f334(f334(f141(x80631),x80633),x80635))+E(f334(f334(f182(x80631),f334(f196(f928(x80631)),x80632)),x80633),x80632)+~P107(f334(f334(f242(a927),f334(f196(f928(x80631)),x80632)),f334(f196(f928(x80631)),x80633))) % 188.18/188.26 [8087]~P107(f334(f66(x80871),f334(x80874,x80875)))+~P107(f334(f334(f336(x80872),x80875),x80873))+P107(f334(f66(x80871),f334(f334(f45(x80872,f935(x80871,a922)),x80873),x80874))) % 188.18/188.26 [8252]~P55(x82521,x82523,x82525)+~P55(x82521,x82522,x82524)+P55(x82521,f334(f334(f108(f935(x82521,a922)),x82522),x82523),f334(f334(f108(f935(f934(x82521,x82521),a922)),x82524),x82525)) % 188.18/188.26 [8253]~P55(x82531,x82533,x82535)+~P55(x82531,x82532,x82534)+P55(x82531,f334(f334(f109(f935(x82531,a922)),x82532),x82533),f334(f334(f109(f935(f934(x82531,x82531),a922)),x82534),x82535)) % 188.18/188.26 [8601]E(f334(f334(f260(x86011,x86012),f334(f334(f171(x86011),x86013),x86014)),f334(f334(f171(x86012),x86015),x86014)),f334(f334(f171(f934(x86011,x86012)),f334(f334(f188(x86011,x86012),x86013),x86015)),x86014))+~P107(f334(f334(f243(a927),x86014),f334(f196(f928(x86011)),x86013)))+~P107(f334(f334(f243(a927),x86014),f334(f196(f928(x86012)),x86015))) % 188.18/188.26 [8755]~P55(x87551,x87553,x87554)+P107(f334(f334(f336(x87551),x87552),x87553))+~P107(f334(f334(f336(f934(x87551,x87551)),f334(f334(f260(x87551,x87551),x87555),x87552)),x87554)) % 188.18/188.26 [8756]~P55(x87561,x87563,x87564)+P107(f334(f334(f336(x87561),x87562),x87563))+~P107(f334(f334(f336(f934(x87561,x87561)),f334(f334(f260(x87561,x87561),x87562),x87565)),x87564)) % 188.18/188.26 [8757]~P10(x87571,x87573,x87574)+P107(f334(f334(f336(x87571),x87572),x87573))+~P107(f334(f334(f336(f934(x87571,x87571)),f334(f334(f260(x87571,x87571),x87575),x87572)),x87574)) % 188.18/188.26 [8758]~P10(x87581,x87583,x87584)+P107(f334(f334(f336(x87581),x87582),x87583))+~P107(f334(f334(f336(f934(x87581,x87581)),f334(f334(f260(x87581,x87581),x87582),x87585)),x87584)) % 188.18/188.26 [9032]~P10(x90321,x90325,x90322)+E(f334(f292(x90321,x90321,x90322),f334(f334(f316(x90321),x90323),f195(f935(x90321,a922)))),f334(f292(x90321,x90321,x90322),f334(f334(f316(x90321),x90324),f195(f935(x90321,a922)))))+~P107(f334(f334(f336(f934(x90321,x90321)),f334(f334(f260(x90321,x90321),x90323),x90324)),x90322)) % 188.18/188.26 [9223]P107(f334(x92231,x92232))+~P107(f334(f334(f336(x92233),x92232),x92235))+P107(f334(f334(f336(x92233),f381(x92231,x92234,x92235,x92233)),f334(f334(f108(f935(x92233,a922)),x92235),x92234))) % 188.18/188.26 [9224]P107(f334(x92241,x92242))+~P107(f334(f334(f336(x92243),x92242),x92244))+P107(f334(f334(f336(x92243),f381(x92241,x92244,x92245,x92243)),f334(f334(f108(f935(x92243,a922)),x92245),x92244))) % 188.18/188.26 [9232]~P107(f334(x92322,x92325))+~P107(f334(f334(f336(x92321),x92325),x92324))+P107(f334(f334(f336(x92321),f377(x92322,x92323,x92324,x92321)),f334(f334(f108(f935(x92321,a922)),x92324),x92323))) % 188.18/188.26 [9233]~P107(f334(x92332,x92335))+~P107(f334(f334(f336(x92331),x92335),x92333))+P107(f334(f334(f336(x92331),f377(x92332,x92333,x92334,x92331)),f334(f334(f108(f935(x92331,a922)),x92334),x92333))) % 188.18/188.26 [9248]~P107(f334(f334(f242(f935(x92481,a922)),x92485),x92483))+~P107(f334(f334(f242(f935(x92481,a922)),x92482),x92484))+P107(f334(f334(f242(f935(x92481,a922)),f334(f334(f23(f935(x92481,a922)),x92482),x92483)),f334(f334(f23(f935(x92481,a922)),x92484),x92485))) % 188.18/188.26 [9249]~P107(f334(f334(f242(f935(x92491,a922)),x92493),x92495))+~P107(f334(f334(f242(f935(x92491,a922)),x92492),x92494))+P107(f334(f334(f242(f935(x92491,a922)),f334(f334(f108(f935(x92491,a922)),x92492),x92493)),f334(f334(f108(f935(x92491,a922)),x92494),x92495))) % 188.18/188.26 [9250]~P107(f334(f334(f242(f935(x92501,a922)),x92503),x92505))+~P107(f334(f334(f242(f935(x92501,a922)),x92502),x92504))+P107(f334(f334(f242(f935(x92501,a922)),f334(f334(f109(f935(x92501,a922)),x92502),x92503)),f334(f334(f109(f935(x92501,a922)),x92504),x92505))) % 188.18/188.26 [9338]P107(f334(f334(f336(f934(x93381,x93381)),f334(f334(f260(x93381,x93381),x93382),x93383)),f328(x93381,x93384,x93385)))+~P107(f334(f334(f242(a927),f334(x93384,x93382)),f334(x93384,x93383)))+~P107(f334(f334(f336(f934(x93381,x93381)),f334(f334(f260(x93381,x93381),x93382),x93383)),x93385)) % 188.18/188.26 [9529]P107(f334(f334(f336(f934(x95291,x95291)),f334(f334(f260(x95291,x95291),x95292),x95293)),f314(x95291,x95294)))+~P107(f334(f334(f336(f934(x95291,x95291)),f334(f334(f260(x95291,x95291),x95292),x95295)),f314(x95291,x95294)))+~P107(f334(f334(f336(f934(x95291,x95291)),f334(f334(f260(x95291,x95291),x95295),x95293)),x95294)) % 188.18/188.26 [9530]P107(f334(f334(f336(f934(x95301,x95301)),f334(f334(f260(x95301,x95301),x95302),x95303)),f314(x95301,x95304)))+~P107(f334(f334(f336(f934(x95301,x95301)),f334(f334(f260(x95301,x95301),x95305),x95303)),f314(x95301,x95304)))+~P107(f334(f334(f336(f934(x95301,x95301)),f334(f334(f260(x95301,x95301),x95302),x95305)),x95304)) % 188.18/188.26 [9625]E(x96251,x96252)+E(f334(a119,f633(x96253,x96254,x96251,x96252,x96255)),x96254)+~P107(f334(f334(f336(f934(x96255,x96255)),f334(f334(f260(x96255,x96255),x96252),x96251)),f334(f334(f190(f934(x96255,x96255),a922),x96254),x96253))) % 188.18/188.26 [9626]E(x96261,x96262)+E(f334(a119,f635(x96263,x96264,x96261,x96262,x96265)),x96264)+~P107(f334(f334(f336(f934(x96265,x96265)),f334(f334(f260(x96265,x96265),x96262),x96261)),f334(f334(f190(f934(x96265,x96265),a922),x96264),x96263))) % 188.18/188.26 [9627]E(x96271,f2(a927))+E(f334(a119,f633(x96272,x96271,x96273,x96274,x96275)),x96271)+~P107(f334(f334(f336(f934(x96275,x96275)),f334(f334(f260(x96275,x96275),x96274),x96273)),f334(f334(f190(f934(x96275,x96275),a922),x96271),x96272))) % 188.18/188.26 [9628]E(x96281,f2(a927))+E(f334(a119,f635(x96282,x96281,x96283,x96284,x96285)),x96281)+~P107(f334(f334(f336(f934(x96285,x96285)),f334(f334(f260(x96285,x96285),x96284),x96283)),f334(f334(f190(f934(x96285,x96285),a922),x96281),x96282))) % 188.18/188.26 [9645]P107(f334(f334(f336(f934(x96451,x96451)),f334(f334(f260(x96451,x96451),x96452),x96453)),f334(f334(f295(x96451,x96451,x96451),x96454),f314(x96451,x96454))))+~P107(f334(f334(f336(f934(x96451,x96451)),f334(f334(f260(x96451,x96451),x96452),x96455)),x96454))+~P107(f334(f334(f336(f934(x96451,x96451)),f334(f334(f260(x96451,x96451),x96455),x96453)),x96454)) % 188.18/188.26 [9650]~P107(f334(f334(f336(f934(x96501,x96501)),f334(f334(f260(x96501,x96501),x96502),x96505)),f314(x96501,x96504)))+P107(f334(f334(f336(f934(x96501,x96501)),f334(f334(f260(x96501,x96501),x96502),x96503)),f334(f334(f295(x96501,x96501,x96501),x96504),f314(x96501,x96504))))+~P107(f334(f334(f336(f934(x96501,x96501)),f334(f334(f260(x96501,x96501),x96505),x96503)),x96504)) % 188.18/188.26 [9684]~P10(x96841,x96845,x96842)+~P107(f334(f334(f336(f934(x96841,x96841)),f334(f334(f260(x96841,x96841),x96843),x96844)),x96842))+P107(f334(f334(f242(f935(x96841,a922)),f334(f292(x96841,x96841,x96842),f334(f334(f316(x96841),x96843),f195(f935(x96841,a922))))),f334(f292(x96841,x96841,x96842),f334(f334(f316(x96841),x96844),f195(f935(x96841,a922)))))) % 188.18/188.26 [9755]P107(f334(f334(f336(f934(x97551,x97551)),f334(f334(f260(x97551,x97551),x97552),x97553)),f334(f334(f295(x97551,x97551,x97551),x97554),f314(x97551,x97554))))+~P107(f334(f334(f336(f934(x97551,x97551)),f334(f334(f260(x97551,x97551),x97552),x97555)),f334(f334(f295(x97551,x97551,x97551),x97554),f314(x97551,x97554))))+~P107(f334(f334(f336(f934(x97551,x97551)),f334(f334(f260(x97551,x97551),x97555),x97553)),x97554)) % 188.18/188.26 [9756]P107(f334(f334(f336(f934(x97561,x97561)),f334(f334(f260(x97561,x97561),x97562),x97563)),f334(f334(f295(x97561,x97561,x97561),x97564),f314(x97561,x97564))))+~P107(f334(f334(f336(f934(x97561,x97561)),f334(f334(f260(x97561,x97561),x97565),x97563)),f334(f334(f295(x97561,x97561,x97561),x97564),f314(x97561,x97564))))+~P107(f334(f334(f336(f934(x97561,x97561)),f334(f334(f260(x97561,x97561),x97562),x97565)),x97564)) % 188.18/188.26 [9804]~P107(f334(f71(x98041,x98041,x98044,x98042,x98043),x98045))+P107(f334(f334(f336(x98041),x98042),x98043))+P107(f334(f67(x98041,x98044,f334(f334(f316(x98041),x98042),x98043)),x98045)) % 188.18/188.26 [9849]~E(f334(f317(x98493,x98492,x98495),x98494),x98491)+E(x98491,f195(f935(x98492,a922)))+P107(f334(f334(f242(f935(x98493,a922)),f334(f317(x98492,x98493,f494(x98494,x98493,x98492,x98491)),x98491)),x98494)) % 188.18/188.26 [9902]~P7(x99025)+P107(f334(f334(f336(x99021),f407(x99022,x99023,x99024,x99021,x99025)),x99024))+P107(f334(f334(f242(x99025),f334(f334(f44(x99021,x99025),x99024),x99023)),x99022)) % 188.18/188.26 [9959]P36(x99591,x99592,x99593,x99594,x99595)+~E(f334(f196(f928(x99591)),x99594),f334(f196(f928(x99592)),x99595))+P107(f334(f334(f336(f934(x99591,x99592)),f712(x99595,x99594,x99593,x99592,x99591)),f334(f179(f934(x99591,x99592)),f334(f334(f188(x99591,x99592),x99594),x99595)))) % 188.18/188.26 [9960]P36(x99601,x99602,x99603,x99604,x99605)+~E(f334(f196(f928(x99601)),x99604),f334(f196(f928(x99602)),x99605))+P107(f334(f334(f336(f934(x99601,x99602)),f713(x99603,x99605,x99604,x99602,x99601)),f334(f179(f934(x99601,x99602)),f334(f334(f188(x99601,x99602),x99604),x99605)))) % 188.18/188.26 [10093]E(x100931,x100932)+P107(f334(f334(f336(f934(x100933,x100933)),f334(f334(f260(x100933,x100933),x100931),f634(x100934,x100935,x100932,x100931,x100933))),x100934))+~P107(f334(f334(f336(f934(x100933,x100933)),f334(f334(f260(x100933,x100933),x100931),x100932)),f334(f334(f190(f934(x100933,x100933),a922),x100935),x100934))) % 188.18/188.26 [10094]E(x100941,f2(a927))+P107(f334(f334(f336(f934(x100942,x100942)),f334(f334(f260(x100942,x100942),x100943),f634(x100944,x100941,x100945,x100943,x100942))),x100944))+~P107(f334(f334(f336(f934(x100942,x100942)),f334(f334(f260(x100942,x100942),x100943),x100945)),f334(f334(f190(f934(x100942,x100942),a922),x100941),x100944))) % 188.18/188.26 [10131]~P7(x101311)+~P107(f334(f334(f242(x101311),f334(x101314,f407(x101315,x101314,x101313,x101312,x101311))),x101315))+P107(f334(f334(f242(x101311),f334(f334(f44(x101312,x101311),x101313),x101314)),x101315)) % 188.18/188.26 [10157]E(x101571,x101572)+P107(f334(f334(f336(f934(x101573,x101573)),f334(f334(f260(x101573,x101573),f636(x101574,x101575,x101571,x101572,x101573)),x101571)),x101574))+~P107(f334(f334(f336(f934(x101573,x101573)),f334(f334(f260(x101573,x101573),x101572),x101571)),f334(f334(f190(f934(x101573,x101573),a922),x101575),x101574))) % 188.18/188.26 [10158]E(x101581,f2(a927))+P107(f334(f334(f336(f934(x101582,x101582)),f334(f334(f260(x101582,x101582),f636(x101583,x101581,x101584,x101585,x101582)),x101584)),x101583))+~P107(f334(f334(f336(f934(x101582,x101582)),f334(f334(f260(x101582,x101582),x101585),x101584)),f334(f334(f190(f934(x101582,x101582),a922),x101581),x101583))) % 188.18/188.26 [10168]E(x101681,x101682)+P107(f334(f334(f336(f934(x101683,x101683)),f334(f334(f260(x101683,x101683),x101681),f636(x101684,x101685,x101682,x101681,x101683))),f334(f334(f190(f934(x101683,x101683),a922),f635(x101684,x101685,x101682,x101681,x101683)),x101684)))+~P107(f334(f334(f336(f934(x101683,x101683)),f334(f334(f260(x101683,x101683),x101681),x101682)),f334(f334(f190(f934(x101683,x101683),a922),x101685),x101684))) % 188.18/188.26 [10169]E(x101691,f2(a927))+P107(f334(f334(f336(f934(x101692,x101692)),f334(f334(f260(x101692,x101692),x101693),f636(x101694,x101691,x101695,x101693,x101692))),f334(f334(f190(f934(x101692,x101692),a922),f635(x101694,x101691,x101695,x101693,x101692)),x101694)))+~P107(f334(f334(f336(f934(x101692,x101692)),f334(f334(f260(x101692,x101692),x101693),x101695)),f334(f334(f190(f934(x101692,x101692),a922),x101691),x101694))) % 188.18/188.26 [10211]E(x102111,x102112)+P107(f334(f334(f336(f934(x102113,x102113)),f334(f334(f260(x102113,x102113),f634(x102114,x102115,x102111,x102112,x102113)),x102111)),f334(f334(f190(f934(x102113,x102113),a922),f633(x102114,x102115,x102111,x102112,x102113)),x102114)))+~P107(f334(f334(f336(f934(x102113,x102113)),f334(f334(f260(x102113,x102113),x102112),x102111)),f334(f334(f190(f934(x102113,x102113),a922),x102115),x102114))) % 188.18/188.26 [10212]E(x102121,f2(a927))+P107(f334(f334(f336(f934(x102122,x102122)),f334(f334(f260(x102122,x102122),f634(x102123,x102121,x102124,x102125,x102122)),x102124)),f334(f334(f190(f934(x102122,x102122),a922),f633(x102123,x102121,x102124,x102125,x102122)),x102123)))+~P107(f334(f334(f336(f934(x102122,x102122)),f334(f334(f260(x102122,x102122),x102125),x102124)),f334(f334(f190(f934(x102122,x102122),a922),x102121),x102123))) % 188.18/188.26 [10249]~P76(x102492)+~P107(f334(f66(x102491),x102495))+E(f334(f334(f6(x102491,x102492),f334(f334(f7(x102491,x102492,x102492),f334(f334(f18(x102491,x102492,f935(x102492,x102492)),f334(f334(f8(a922,f935(x102492,f935(x102492,x102492)),x102491),f103(x102492)),f334(f334(f7(x102491,f935(x102491,a922),a922),f336(x102491)),x102493))),x102494)),f2(x102492))),x102495),f334(f334(f6(x102491,x102492),x102494),f334(f334(f109(f935(x102491,a922)),x102495),x102493))) % 188.18/188.26 [8821]~P72(x88211)+~P107(f334(f66(x88214),x88215))+E(f334(f334(f87(x88211),f334(x88212,x88213)),f334(f334(f9(x88214,x88211),x88212),f334(f334(f23(f935(x88214,a922)),x88215),f334(f334(f316(x88214),x88213),f195(f935(x88214,a922)))))),f334(f334(f9(x88214,x88211),x88212),f334(f334(f316(x88214),x88213),x88215))) % 188.18/188.26 [8822]~P76(x88221)+~P107(f334(f66(x88224),x88225))+E(f334(f334(f86(x88221),f334(x88222,x88223)),f334(f334(f6(x88224,x88221),x88222),f334(f334(f23(f935(x88224,a922)),x88225),f334(f334(f316(x88224),x88223),f195(f935(x88224,a922)))))),f334(f334(f6(x88224,x88221),x88222),f334(f334(f316(x88224),x88223),x88225))) % 188.18/188.26 [9157]~P109(x91572)+~P15(x91572,f334(f175(x91572),f334(f334(f161(x91571,x91572),x91574),x91575)))+E(f334(f143(x91571,f334(f334(f8(x91572,a922,x91571),f334(f243(x91572),x91573)),x91574)),x91575),f184(x91571,f334(f334(f8(x91572,a922,x91571),f334(f243(x91572),x91573)),x91574),x91575)) % 188.18/188.26 [9181]~P76(x91811)+E(f334(f334(f86(x91811),f334(f334(f6(a927,x91811),x91812),f311(a927,x91813,x91814))),f334(f334(f6(a927,x91811),x91812),f311(a927,f334(f334(f86(a927),x91814),f84(a927)),f334(f334(f86(a927),x91814),x91815)))),f334(f334(f6(a927,x91811),x91812),f311(a927,x91813,f334(f334(f86(a927),x91814),x91815))))+~P107(f334(f334(f242(a927),x91813),f334(f334(f86(a927),x91814),f84(a927)))) % 188.18/188.26 [9182]~P107(f334(f334(f336(x91821),x91824),x91825))+~P107(f334(f334(f242(f935(x91821,a922)),f334(f179(x91821),x91822)),x91825))+P107(f334(f334(f242(f935(x91821,a922)),f334(f179(x91821),f334(f334(f166(x91821,x91822),x91823),x91824))),x91825)) % 188.18/188.26 [9400]~P7(x94002)+~P107(f334(f66(x94001),x94005))+E(f334(f334(f69(x94001,x94002,f334(f334(f8(x94002,f935(x94002,x94002),x94001),f108(x94002)),x94003)),x94004),x94005),f334(f334(f108(x94002),x94004),f334(f334(f44(x94001,x94002),x94005),x94003))) % 188.18/188.26 [9401]~P7(x94012)+~P107(f334(f66(x94011),x94015))+E(f334(f334(f69(x94011,x94012,f334(f334(f8(x94012,f935(x94012,x94012),x94011),f109(x94012)),x94013)),x94014),x94015),f334(f334(f109(x94012),x94014),f334(f334(f45(x94011,x94012),x94015),x94013))) % 188.18/188.26 [9447]E(f334(x94471,x94472),f334(x94471,x94473))+P107(f334(f334(f243(a927),f334(x94471,x94472)),f334(x94471,x94473)))+~P107(f334(f334(f336(f934(x94474,x94474)),f334(f334(f260(x94474,x94474),x94472),x94473)),f160(x94474,f334(f334(f158(f935(x94474,a927)),x94471),x94475)))) % 188.18/188.26 [9480]~E(f334(x94804,x94802),f334(x94804,x94803))+~P107(f334(f334(f336(f934(x94801,x94801)),f334(f334(f260(x94801,x94801),x94802),x94803)),f160(x94801,x94805)))+P107(f334(f334(f336(f934(x94801,x94801)),f334(f334(f260(x94801,x94801),x94802),x94803)),f160(x94801,f334(f334(f158(f935(x94801,a927)),x94804),x94805)))) % 188.18/188.26 [9500]~P27(x95001,x95002,x95003,x95005)+P27(x95001,x95002,x95003,f334(f334(f316(x95001),x95004),x95005))+P107(f334(f334(f336(x95002),f334(x95003,x95004)),f334(f317(x95001,x95002,x95003),f334(f334(f23(f935(x95001,a922)),x95005),f334(f334(f316(x95001),x95004),f195(f935(x95001,a922))))))) % 188.18/188.26 [9505]P107(f334(x95052,x95055))+~P107(f334(f334(f336(x95051),x95055),f334(f179(x95051),x95053)))+E(f334(f334(f145(x95051),f334(f196(f928(x95051)),f184(x95051,x95052,f334(f334(f141(x95051),x95053),x95054)))),f334(f334(f141(x95051),x95053),x95054)),f334(f334(f141(x95051),f334(f334(f145(x95051),f334(f196(f928(x95051)),f184(x95051,x95052,x95053))),x95053)),x95054)) % 188.18/188.26 [9511]~P107(f334(f334(f336(f934(x95111,x95111)),f334(f334(f260(x95111,x95111),x95112),x95113)),f160(x95111,x95115)))+~P107(f334(f334(f242(a927),f334(x95114,x95112)),f334(x95114,x95113)))+P107(f334(f334(f336(f934(x95111,x95111)),f334(f334(f260(x95111,x95111),x95112),x95113)),f160(x95111,f334(f334(f158(f935(x95111,a927)),x95114),x95115)))) % 188.18/188.26 [9576]P107(f334(f334(f336(f934(x95764,x95764)),f334(f334(f260(x95764,x95764),x95762),x95763)),f160(x95764,x95765)))+P107(f334(f334(f243(a927),f334(x95761,x95762)),f334(x95761,x95763)))+~P107(f334(f334(f336(f934(x95764,x95764)),f334(f334(f260(x95764,x95764),x95762),x95763)),f160(x95764,f334(f334(f158(f935(x95764,a927)),x95761),x95765)))) % 188.18/188.26 [9717]~P107(f334(f334(f336(f934(f928(x97171),f928(x97171))),f334(f334(f260(f928(x97171),f928(x97171)),x97172),x97174)),f165(x97171,x97175)))+~P107(f334(f334(f243(a927),x97173),f334(f196(f928(x97171)),x97172)))+P107(f334(f334(f336(f934(x97171,x97171)),f334(f334(f260(x97171,x97171),f334(f334(f171(x97171),x97172),x97173)),f334(f334(f171(x97171),x97174),x97173))),x97175)) % 188.18/188.26 [9986]E(x99861,f2(a1))+~P107(f334(f54(x99863,x99861),f334(f334(f260(a1,a1),x99864),x99865)))+P107(f334(f54(f334(f334(f87(a1),x99862),x99863),x99861),f334(f334(f260(a1,a1),f334(f334(f86(a1),f334(f334(f87(a1),x99862),x99864)),f334(f334(f41(a1),f334(f334(f87(a1),x99862),x99865)),x99861))),f50(a1,f334(f334(f87(a1),x99862),x99865),x99861)))) % 188.18/188.26 [9993]~P107(f334(f334(f243(a927),f2(a927)),x99933))+~P107(f334(f53(x99932,x99933),f334(f334(f260(a927,a927),x99934),x99935)))+P107(f334(f53(f334(f334(f87(a927),x99931),x99932),x99933),f334(f334(f260(a927,a927),f334(f334(f86(a927),f334(f334(f87(a927),x99931),x99934)),f334(f334(f41(a927),f334(f334(f87(a927),x99931),x99935)),x99933))),f50(a927,f334(f334(f87(a927),x99931),x99935),x99933)))) % 188.18/188.26 [10267]~P76(x102672)+~P107(f334(f66(x102671),x102674))+E(f334(f334(f6(x102671,x102672),x102673),f334(f270(x102671),f334(f334(f18(x102671,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102671),a332),f334(f334(f7(x102671,f935(x102671,a922),a922),f336(x102671)),x102674))),f334(f334(f7(x102671,f935(x102671,a922),a922),f336(x102671)),x102675)))),f334(f334(f6(x102671,x102672),f334(f334(f7(x102671,x102672,x102672),f334(f334(f18(x102671,x102672,f935(x102672,x102672)),f334(f334(f8(a922,f935(x102672,f935(x102672,x102672)),x102671),f103(x102672)),f334(f334(f7(x102671,f935(x102671,a922),a922),f336(x102671)),x102675))),x102673)),f2(x102672))),x102674)) % 188.18/188.26 [8456]~E(f334(f334(f141(x84561),x84562),x84565),f334(f334(f141(x84561),x84563),x84564))+E(f334(f334(f141(x84561),f334(f334(f145(x84561),f334(f196(f928(x84561)),x84562)),x84563)),x84564),x84565)+P107(f334(f334(f242(a927),f334(f196(f928(x84561)),x84563)),f334(f196(f928(x84561)),x84562))) % 188.18/188.26 [8647]~E(f334(f334(f141(x86472),x86473),x86471),f334(f334(f141(x86472),x86474),x86475))+E(x86471,f334(f334(f141(x86472),f334(f334(f145(x86472),f334(f196(f928(x86472)),x86473)),x86474)),x86475))+~P107(f334(f334(f242(a927),f334(f196(f928(x86472)),x86473)),f334(f196(f928(x86472)),x86474))) % 188.18/188.26 [8738]~E(f334(f334(f86(a927),f334(f334(f87(a927),x87383),x87384)),x87381),f334(f334(f86(a927),f334(f334(f87(a927),x87382),x87384)),x87385))+~P107(f334(f334(f242(a927),x87383),x87382))+E(x87381,f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x87382),x87383)),x87384)),x87385)) % 188.18/188.26 [8739]~E(f334(f334(f86(a927),f334(f334(f87(a927),x87391),x87393)),x87394),f334(f334(f86(a927),f334(f334(f87(a927),x87392),x87393)),x87395))+~P107(f334(f334(f242(a927),x87392),x87391))+E(f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x87391),x87392)),x87393)),x87394),x87395) % 188.18/188.26 [8899]E(f334(f334(f86(a927),f334(f334(f87(a927),x88991),x88992)),x88993),f334(f334(f86(a927),f334(f334(f87(a927),x88994),x88992)),x88995))+~P107(f334(f334(f242(a927),x88994),x88991))+~E(x88995,f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x88991),x88994)),x88992)),x88993)) % 188.18/188.26 [8900]E(f334(f334(f86(a927),f334(f334(f87(a927),x89001),x89002)),x89003),f334(f334(f86(a927),f334(f334(f87(a927),x89004),x89002)),x89005))+~P107(f334(f334(f242(a927),x89004),x89001))+~E(f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x89001),x89004)),x89002)),x89003),x89005) % 188.18/188.26 [9780]~P65(x97802)+~P107(f334(f66(x97801),x97805))+E(f334(f334(f9(x97801,x97802),f334(f334(f18(x97801,x97802,x97802),f334(f334(f8(x97802,f935(x97802,x97802),x97801),f296(x97802)),x97803)),x97804)),x97805),f334(f334(f296(x97802),f334(f334(f9(x97801,x97802),x97803),x97805)),f334(f334(f9(x97801,x97802),x97804),x97805))) % 188.18/188.26 [9922]~E(f638(x99225,x99224,x99223,x99222,x99221),f639(x99225,x99224,x99223,x99222,x99221))+P107(f334(f334(f336(f934(x99221,x99221)),f334(f334(f260(x99221,x99221),x99222),x99223)),f314(x99221,x99224)))+~P107(f334(f334(f336(f934(x99221,x99221)),f334(f334(f260(x99221,x99221),x99222),x99223)),f314(x99221,f334(f334(f108(f935(f934(x99221,x99221),a922)),x99224),x99225)))) % 188.18/188.26 [9923]~E(f640(x99235,x99234,x99233,x99232,x99231),f641(x99235,x99234,x99233,x99232,x99231))+P107(f334(f334(f336(f934(x99231,x99231)),f334(f334(f260(x99231,x99231),x99232),x99233)),f314(x99231,x99234)))+~P107(f334(f334(f336(f934(x99231,x99231)),f334(f334(f260(x99231,x99231),x99232),x99233)),f314(x99231,f334(f334(f108(f935(f934(x99231,x99231),a922)),x99234),x99235)))) % 188.18/188.26 [10123]P107(f334(f334(f336(f934(x101231,x101231)),f334(f334(f260(x101231,x101231),x101232),f639(x101235,x101234,x101233,x101232,x101231))),f314(x101231,x101234)))+P107(f334(f334(f336(f934(x101231,x101231)),f334(f334(f260(x101231,x101231),x101232),x101233)),f314(x101231,x101234)))+~P107(f334(f334(f336(f934(x101231,x101231)),f334(f334(f260(x101231,x101231),x101232),x101233)),f314(x101231,f334(f334(f108(f935(f934(x101231,x101231),a922)),x101234),x101235)))) % 188.18/188.26 [10187]P107(f334(f334(f336(f934(x101871,x101871)),f334(f334(f260(x101871,x101871),f641(x101875,x101874,x101873,x101872,x101871)),x101873)),f314(x101871,x101874)))+P107(f334(f334(f336(f934(x101871,x101871)),f334(f334(f260(x101871,x101871),x101872),x101873)),f314(x101871,x101874)))+~P107(f334(f334(f336(f934(x101871,x101871)),f334(f334(f260(x101871,x101871),x101872),x101873)),f314(x101871,f334(f334(f108(f935(f934(x101871,x101871),a922)),x101874),x101875)))) % 188.18/188.26 [10217]P107(f334(f334(f336(f934(x102171,x102171)),f334(f334(f260(x102171,x102171),x102172),x102173)),f314(x102171,x102174)))+P107(f334(f334(f336(f934(x102171,x102171)),f334(f334(f260(x102171,x102171),f639(x102175,x102174,x102173,x102172,x102171)),f638(x102175,x102174,x102173,x102172,x102171))),x102175))+~P107(f334(f334(f336(f934(x102171,x102171)),f334(f334(f260(x102171,x102171),x102172),x102173)),f314(x102171,f334(f334(f108(f935(f934(x102171,x102171),a922)),x102174),x102175)))) % 188.18/188.26 [10218]P107(f334(f334(f336(f934(x102181,x102181)),f334(f334(f260(x102181,x102181),x102182),x102183)),f314(x102181,x102184)))+P107(f334(f334(f336(f934(x102181,x102181)),f334(f334(f260(x102181,x102181),f640(x102185,x102184,x102183,x102182,x102181)),f641(x102185,x102184,x102183,x102182,x102181))),x102185))+~P107(f334(f334(f336(f934(x102181,x102181)),f334(f334(f260(x102181,x102181),x102182),x102183)),f314(x102181,f334(f334(f108(f935(f934(x102181,x102181),a922)),x102184),x102185)))) % 188.18/188.26 [10392]~P107(f334(f334(f336(f934(f928(x103921),f928(x103921))),f334(f334(f260(f928(x103921),f928(x103921)),x103924),x103925)),f165(x103921,x103922)))+~P107(f334(f334(f336(f934(x103921,x103921)),x103923),f334(f179(f934(x103921,x103921)),f334(f334(f188(x103921,x103921),x103924),x103925))))+P107(f334(f334(f265(x103921,x103921,a922),f334(f334(f7(x103921,f935(f934(x103921,x103921),a922),f935(x103921,a922)),f334(f334(f8(f935(x103921,f935(f935(f934(x103921,x103921),a922),a922)),f935(f935(f934(x103921,x103921),a922),f935(x103921,a922)),x103921),f7(x103921,f935(f934(x103921,x103921),a922),a922)),f334(f334(f8(f935(x103921,f934(x103921,x103921)),f935(x103921,f935(f935(f934(x103921,x103921),a922),a922)),x103921),f334(f8(f934(x103921,x103921),f935(f935(f934(x103921,x103921),a922),a922),x103921),f336(f934(x103921,x103921)))),f260(x103921,x103921)))),x103922)),x103923)) % 188.18/188.26 [9808]~P107(f334(f334(f242(a927),x98083),x98082))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),f334(f334(f87(a927),x98083),x98084)),x98081)),f334(f334(f86(a927),f334(f334(f87(a927),x98082),x98084)),x98085)))+P107(f334(f334(f242(a927),x98081),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x98082),x98083)),x98084)),x98085))) % 188.18/188.26 [9809]~P107(f334(f334(f242(a927),x98093),x98092))+~P107(f334(f334(f243(a927),f334(f334(f86(a927),f334(f334(f87(a927),x98093),x98094)),x98091)),f334(f334(f86(a927),f334(f334(f87(a927),x98092),x98094)),x98095)))+P107(f334(f334(f243(a927),x98091),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x98092),x98093)),x98094)),x98095))) % 188.18/188.26 [9833]~P107(f334(f334(f242(a927),x98331),x98334))+P107(f334(f334(f242(a927),f334(f334(f86(a927),f334(f334(f87(a927),x98331),x98332)),x98333)),f334(f334(f86(a927),f334(f334(f87(a927),x98334),x98332)),x98335)))+~P107(f334(f334(f242(a927),x98333),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x98334),x98331)),x98332)),x98335))) % 188.18/188.26 [9834]~P107(f334(f334(f242(a927),x98341),x98344))+P107(f334(f334(f243(a927),f334(f334(f86(a927),f334(f334(f87(a927),x98341),x98342)),x98343)),f334(f334(f86(a927),f334(f334(f87(a927),x98344),x98342)),x98345)))+~P107(f334(f334(f243(a927),x98343),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x98344),x98341)),x98342)),x98345))) % 188.18/188.26 [9957]~P107(f334(f334(f242(a927),x99572),x99571))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),f334(f334(f87(a927),x99571),x99573)),x99574)),f334(f334(f86(a927),f334(f334(f87(a927),x99572),x99573)),x99575)))+P107(f334(f334(f242(a927),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x99571),x99572)),x99573)),x99574)),x99575)) % 188.18/188.26 [9958]~P107(f334(f334(f242(a927),x99582),x99581))+~P107(f334(f334(f243(a927),f334(f334(f86(a927),f334(f334(f87(a927),x99581),x99583)),x99584)),f334(f334(f86(a927),f334(f334(f87(a927),x99582),x99583)),x99585)))+P107(f334(f334(f243(a927),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x99581),x99582)),x99583)),x99584)),x99585)) % 188.18/188.26 [10015]~P107(f334(f334(f242(a927),x100154),x100151))+P107(f334(f334(f242(a927),f334(f334(f86(a927),f334(f334(f87(a927),x100151),x100152)),x100153)),f334(f334(f86(a927),f334(f334(f87(a927),x100154),x100152)),x100155)))+~P107(f334(f334(f242(a927),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x100151),x100154)),x100152)),x100153)),x100155)) % 188.18/188.26 [10016]~P107(f334(f334(f242(a927),x100164),x100161))+P107(f334(f334(f243(a927),f334(f334(f86(a927),f334(f334(f87(a927),x100161),x100162)),x100163)),f334(f334(f86(a927),f334(f334(f87(a927),x100164),x100162)),x100165)))+~P107(f334(f334(f243(a927),f334(f334(f86(a927),f334(f334(f87(a927),f334(f334(f23(a927),x100161),x100164)),x100162)),x100163)),x100165)) % 188.18/188.26 [10206]~P13(x102061,x102062,x102065,x102063)+~P107(f334(f334(f336(f934(x102061,x102061)),x102064),x102065))+P107(f334(f334(f265(x102061,x102061,a922),f334(f334(f7(x102061,f935(x102061,x102062),f935(x102061,a922)),f334(f334(f8(f935(x102062,a922),f935(f935(x102061,x102062),f935(x102061,a922)),x102061),f8(x102062,a922,x102061)),f334(f334(f8(x102062,f935(x102062,a922),x102061),a331),x102063))),x102063)),x102064)) % 188.18/188.26 [8613]~P21(x86136,x86131,x86132,x86134)+E(f334(f78(x86131,x86131,x86131,f334(x86132,x86133)),f334(x86134,x86135)),f334(f78(x86131,x86131,x86131,f334(x86134,x86135)),f334(x86132,x86133)))+~P107(f334(f66(x86136),x86135)) % 188.18/188.26 [9044]~P27(x90441,x90443,x90445,x90446)+~P27(x90443,x90442,x90444,f334(f317(x90441,x90443,x90445),x90446))+P27(x90441,x90442,f334(f78(x90443,x90442,x90441,x90444),x90445),x90446) % 188.18/188.26 [9612]~P107(f334(f334(x96123,x96122),x96126))+~P107(f334(f334(x96124,x96125),x96122))+P107(f334(f334(f336(x96121),x96122),f306(x96121,x96123,x96124,x96125,x96126))) % 188.18/188.26 [9613]~P107(f334(f334(x96134,x96132),x96136))+~P107(f334(f334(x96133,x96135),x96132))+P107(f334(f334(f336(x96131),x96132),f303(x96131,x96133,x96134,x96135,x96136))) % 188.18/188.26 [9718]E(x97181,x97182)+E(x97183,x97184)+~P107(f334(f334(f336(f934(f928(x97185),f928(x97185))),f334(f334(f260(f928(x97185),f928(x97185)),f334(f334(f158(x97185),x97183),x97181)),f334(f334(f158(x97185),x97184),x97182))),f164(x97185,x97186))) % 188.18/188.26 [9732]~E(x97322,x97324)+P107(f334(f334(f336(f934(f928(x97321),f928(x97321))),f334(f334(f260(f928(x97321),f928(x97321)),f334(f334(f158(x97321),x97322),x97323)),f334(f334(f158(x97321),x97324),x97325))),f152(x97321,x97326)))+~P107(f334(f334(f336(f934(f928(x97321),f928(x97321))),f334(f334(f260(f928(x97321),f928(x97321)),x97323),x97325)),f152(x97321,x97326))) % 188.18/188.26 [9733]~E(x97332,x97334)+P107(f334(f334(f336(f934(f928(x97331),f928(x97331))),f334(f334(f260(f928(x97331),f928(x97331)),f334(f334(f158(x97331),x97332),x97333)),f334(f334(f158(x97331),x97334),x97335))),f154(x97331,x97336)))+~P107(f334(f334(f336(f934(f928(x97331),f928(x97331))),f334(f334(f260(f928(x97331),f928(x97331)),x97333),x97335)),f154(x97331,x97336))) % 188.18/188.26 [9734]~E(x97342,x97344)+P107(f334(f334(f336(f934(f928(x97341),f928(x97341))),f334(f334(f260(f928(x97341),f928(x97341)),f334(f334(f158(x97341),x97342),x97343)),f334(f334(f158(x97341),x97344),x97345))),f164(x97341,x97346)))+~P107(f334(f334(f336(f934(f928(x97341),f928(x97341))),f334(f334(f260(f928(x97341),f928(x97341)),x97343),x97345)),f164(x97341,x97346))) % 188.18/188.26 [9735]~E(x97352,x97354)+P107(f334(f334(f336(f934(f928(x97351),f928(x97351))),f334(f334(f260(f928(x97351),f928(x97351)),f334(f334(f141(x97351),x97352),x97353)),f334(f334(f141(x97351),x97354),x97355))),f164(x97351,x97356)))+~P107(f334(f334(f336(f934(f928(x97351),f928(x97351))),f334(f334(f260(f928(x97351),f928(x97351)),x97353),x97355)),f164(x97351,x97356))) % 188.18/188.26 [9736]~E(x97363,x97365)+P107(f334(f334(f336(f934(f928(x97361),f928(x97361))),f334(f334(f260(f928(x97361),f928(x97361)),f334(f334(f141(x97361),x97362),x97363)),f334(f334(f141(x97361),x97364),x97365))),f164(x97361,x97366)))+~P107(f334(f334(f336(f934(f928(x97361),f928(x97361))),f334(f334(f260(f928(x97361),f928(x97361)),x97362),x97364)),f164(x97361,x97366))) % 188.18/188.26 [9798]E(x97981,x97982)+P107(f334(f334(f336(f934(f928(x97983),f928(x97983))),f334(f334(f260(f928(x97983),f928(x97983)),x97981),x97982)),f164(x97983,x97984)))+~P107(f334(f334(f336(f934(f928(x97983),f928(x97983))),f334(f334(f260(f928(x97983),f928(x97983)),f334(f334(f158(x97983),x97985),x97981)),f334(f334(f158(x97983),x97986),x97982))),f164(x97983,x97984))) % 188.18/188.26 [9961]~E(x99613,x99615)+P107(f334(f334(f336(f934(f928(x99611),f928(x99611))),f334(f334(f260(f928(x99611),f928(x99611)),f334(f334(f141(x99611),x99612),f334(f334(f158(x99611),x99613),f120(x99611)))),f334(f334(f141(x99611),x99614),f334(f334(f158(x99611),x99615),f120(x99611))))),f164(x99611,x99616)))+~P107(f334(f334(f336(f934(f928(x99611),f928(x99611))),f334(f334(f260(f928(x99611),f928(x99611)),x99612),x99614)),f164(x99611,x99616))) % 188.18/188.26 [10019]E(x100191,x100192)+E(x100193,x100194)+~P107(f334(f334(f336(f934(f928(x100195),f928(x100195))),f334(f334(f260(f928(x100195),f928(x100195)),f334(f334(f141(x100195),x100193),f334(f334(f158(x100195),x100191),f120(x100195)))),f334(f334(f141(x100195),x100194),f334(f334(f158(x100195),x100192),f120(x100195))))),f164(x100195,x100196))) % 188.18/188.26 [10042]E(x100421,x100422)+~P107(f334(f334(f336(f934(f928(x100423),f928(x100423))),f334(f334(f260(f928(x100423),f928(x100423)),f334(f334(f141(x100423),x100421),f334(f334(f158(x100423),x100425),f120(x100423)))),f334(f334(f141(x100423),x100422),f334(f334(f158(x100423),x100426),f120(x100423))))),f164(x100423,x100424)))+P107(f334(f334(f336(f934(f928(x100423),f928(x100423))),f334(f334(f260(f928(x100423),f928(x100423)),x100421),x100422)),f164(x100423,x100424))) % 188.18/188.26 [10085]~P107(f334(f334(f336(f934(f935(x100851,a922),f935(x100851,a922))),f334(f334(f260(f935(x100851,a922),f935(x100851,a922)),x100852),x100854)),f325(x100851,x100856)))+~P107(f334(f334(f336(f934(f935(x100851,a922),f935(x100851,a922))),f334(f334(f260(f935(x100851,a922),f935(x100851,a922)),x100853),x100855)),f325(x100851,x100856)))+P107(f334(f334(f336(f934(f935(x100851,a922),f935(x100851,a922))),f334(f334(f260(f935(x100851,a922),f935(x100851,a922)),f334(f334(f108(f935(x100851,a922)),x100852),x100853)),f334(f334(f108(f935(x100851,a922)),x100854),x100855))),f325(x100851,x100856))) % 188.18/188.26 [5910]~E(f334(f334(f141(x59101),x59106),x59103),x59105)+E(f334(f334(f141(x59101),x59102),x59103),f334(f334(f158(x59101),x59104),x59105))+~E(x59102,f334(f334(f158(x59101),x59104),x59106)) % 188.18/188.26 [5911]~E(f334(f334(f141(x59111),x59116),x59113),x59115)+E(f334(f334(f141(x59111),x59112),x59113),f334(f334(f141(x59111),x59114),x59115))+~E(x59112,f334(f334(f141(x59111),x59114),x59116)) % 188.18/188.26 [5913]E(f334(f334(f141(x59131),x59132),x59133),f334(f334(f158(x59131),x59134),x59135))+~E(f334(f334(f158(x59131),x59134),x59136),x59132)+~E(x59135,f334(f334(f141(x59131),x59136),x59133)) % 188.18/188.26 [5915]~E(f334(f334(f141(x59151),x59152),x59156),x59154)+E(f334(f334(f141(x59151),x59152),x59153),f334(f334(f141(x59151),x59154),x59155))+~E(x59153,f334(f334(f141(x59151),x59156),x59155)) % 188.18/188.26 [7040]E(f334(x70401,x70402),f334(x70403,x70402))+~E(f334(f334(f161(x70404,x70405),x70401),x70406),f334(f334(f161(x70404,x70405),x70403),x70406))+~P107(f334(f334(f336(x70404),x70402),f334(f179(x70404),x70406))) % 188.18/188.26 [7417]~P21(x74174,x74175,x74176,x74171)+E(f334(f334(x74171,x74172),x74173),f334(f334(f69(x74174,x74175,x74176),x74173),x74172))+~P107(f334(f66(x74174),x74172)) % 188.18/188.26 [7488]~E(x74882,f334(x74884,x74886))+~P107(f334(f334(f336(x74883),x74886),x74885))+P107(f334(f334(f336(x74881),x74882),f334(f317(x74883,x74881,x74884),x74885))) % 188.18/188.26 [7489]~E(f334(x74894,x74892),x74896)+~P107(f334(f334(f336(x74893),x74896),x74895))+P107(f334(f334(f336(x74891),x74892),f334(f318(x74891,x74893,x74894),x74895))) % 188.18/188.26 [7917]~P34(x79171,x79172,x79174,x79176)+P34(x79171,x79172,f334(f334(f158(x79171),x79173),x79174),f334(f334(f158(x79171),x79175),x79176))+~P107(f334(f334(x79172,x79173),x79175)) % 188.18/188.26 [8909]~P60(x89094,x89095,x89091,x89092,x89096)+E(f334(x89091,f334(x89092,x89093)),x89093)+~P107(f334(f334(f336(x89095),x89093),x89096)) % 188.18/188.26 [9409]~P28(x94092,x94091,x94095,x94094,x94093)+E(f334(f97(x94091,x94092,x94093,f97(x94092,x94091,x94094,x94095)),x94096),f334(x94095,x94096))+~P107(f334(f334(f336(x94092),x94096),x94094)) % 188.18/188.26 [9420]~P27(x94201,x94202,x94203,x94206)+P27(x94201,x94202,f80(x94201,x94202,x94203,x94204,x94205),x94206)+P107(f334(f334(f336(x94202),x94205),f334(f317(x94201,x94202,x94203),x94206))) % 188.18/188.26 [9721]E(x97211,x97212)+E(f334(f196(f928(x97213)),x97214),f334(f196(f928(x97213)),x97215))+~P107(f334(f334(f336(f934(f928(x97213),f928(x97213))),f334(f334(f260(f928(x97213),f928(x97213)),f334(f334(f158(x97213),x97211),x97214)),f334(f334(f158(x97213),x97212),x97215))),f152(x97213,x97216))) % 188.18/188.26 [9793]~P18(x97931,x97932,x97933)+E(f334(f334(f69(x97931,x97932,x97933),x97934),x97935),x97936)+~P107(f334(f71(x97931,x97932,x97933,x97934,x97935),x97936)) % 188.18/188.26 [9799]E(f334(f196(f928(x97991)),x97992),f334(f196(f928(x97991)),x97993))+P107(f334(f334(f336(f934(f928(x97991),f928(x97991))),f334(f334(f260(f928(x97991),f928(x97991)),x97992),x97993)),f152(x97991,x97994)))+~P107(f334(f334(f336(f934(f928(x97991),f928(x97991))),f334(f334(f260(f928(x97991),f928(x97991)),f334(f334(f158(x97991),x97995),x97992)),f334(f334(f158(x97991),x97996),x97993))),f152(x97991,x97994))) % 188.18/188.26 [9827]~P107(f334(f334(f336(f934(x98271,x98271)),f334(f334(f260(x98271,x98271),x98272),x98274)),f314(x98271,x98276)))+P107(f334(f334(f336(f934(f928(x98271),f928(x98271))),f334(f334(f260(f928(x98271),f928(x98271)),f334(f334(f158(x98271),x98272),x98273)),f334(f334(f158(x98271),x98274),x98275))),f314(f928(x98271),f164(x98271,x98276))))+~P107(f334(f334(f336(f934(f928(x98271),f928(x98271))),f334(f334(f260(f928(x98271),f928(x98271)),x98273),x98275)),f314(f928(x98271),f164(x98271,x98276)))) % 188.18/188.26 [10024]~P107(f334(x100242,x100246))+~E(f334(f143(x100241,x100242),x100243),f334(f334(f158(x100241),x100244),x100245))+~P107(f334(f334(f336(x100241),x100246),f334(f179(x100241),f756(x100245,x100244,x100243,x100242,x100241)))) % 188.18/188.26 [10025]~P107(f334(x100254,x100256))+~E(f334(f334(f158(x100251),x100252),x100253),f334(f143(x100251,x100254),x100255))+~P107(f334(f334(f336(x100251),x100256),f334(f179(x100251),f759(x100255,x100254,x100253,x100252,x100251)))) % 188.18/188.26 [10310]~P76(x103102)+E(f334(f334(f6(x103101,x103102),f334(f334(f8(f935(x103103,a922),x103102,x103101),f334(f6(x103103,x103102),x103104)),f334(f334(f8(f935(x103103,a922),f935(x103103,a922),x103101),f270(x103103)),f334(f334(f8(f935(x103103,a922),f935(x103103,a922),x103101),f334(f18(x103103,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103103),a332),f334(f334(f7(x103103,f935(x103103,a922),a922),f336(x103103)),x103105)))),f334(f7(x103103,x103101,a922),f334(f334(f8(x103101,f935(x103101,a922),x103103),a331),x103106)))))),f334(f317(x103103,x103101,x103106),x103105)),f334(f334(f6(x103103,x103102),x103104),x103105))+~P107(f334(f66(x103103),x103105)) % 188.18/188.26 [7094]~P109(x70943)+P107(f334(x70942,x70945))+E(f334(f143(x70941,x70942),f334(f334(f155(x70941,x70943,x70944),x70945),x70946)),f334(f143(x70941,x70942),x70946)) % 188.18/188.26 [7096]P107(f334(x70961,x70962))+~E(f173(x70963,x70961,x70964),f334(f334(f260(f928(x70963),f928(x70963)),x70965),x70966))+~P107(f334(f334(f336(x70963),x70962),f334(f179(x70963),x70965))) % 188.18/188.26 [7140]~P107(f334(x71402,x71406))+~E(f173(x71401,x71402,x71403),f334(f334(f260(f928(x71401),f928(x71401)),x71404),x71405))+~P107(f334(f334(f336(x71401),x71406),f334(f179(x71401),x71405))) % 188.18/188.26 [7787]~P16(x77871,x77872,x77873)+~P107(f334(f66(x77871),x77876))+E(f334(f334(f69(x77871,x77872,x77873),x77874),f334(f334(f316(x77871),x77875),x77876)),f334(f334(f69(x77871,x77872,x77873),f334(f334(x77873,x77875),x77874)),x77876)) % 188.18/188.26 [7835]~P109(x78352)+~P107(f334(f334(f242(x78352),f334(x78353,x78354)),f334(x78353,x78355)))+E(f334(f334(f155(x78351,x78352,x78353),x78354),f334(f334(f158(x78351),x78355),x78356)),f334(f334(f158(x78351),x78354),f334(f334(f158(x78351),x78355),x78356))) % 188.18/188.26 [7947]E(x79471,x79472)+~E(f334(f334(f262(x79473,x79474),x79471),f334(f16(f935(x79474,a922),x79473),x79475)),f334(f334(f262(x79473,x79474),x79472),f334(f16(f935(x79474,a922),x79473),x79475)))+~P107(f334(f334(f336(x79474),x79476),x79475)) % 188.18/188.26 [8015]~P16(x80151,x80152,x80153)+~P107(f334(f66(x80151),x80156))+E(f334(f334(f69(x80151,x80152,x80153),x80154),f334(f334(f316(x80151),x80155),x80156)),f334(f334(x80153,x80155),f334(f334(f69(x80151,x80152,x80153),x80154),x80156))) % 188.18/188.26 [8128]~P18(x81281,x81282,x81283)+~P107(f334(f66(x81281),x81286))+E(f334(f334(f69(x81281,x81282,x81283),f334(f334(x81283,x81284),x81285)),x81286),f334(f334(x81283,x81284),f334(f334(f69(x81281,x81282,x81283),x81285),x81286))) % 188.18/188.26 [8192]~P22(x81922,x81925,x81926,x81921)+~P107(f334(f66(x81922),x81924))+E(f334(x81921,f334(f334(f316(x81922),x81923),x81924)),f334(f78(x81925,x81925,x81925,f334(x81921,x81924)),f334(x81926,x81923))) % 188.18/188.26 [8223]~P109(x82232)+P107(f334(f334(f242(x82232),f334(x82233,x82234)),f334(x82233,x82235)))+E(f334(f334(f155(x82231,x82232,x82233),x82234),f334(f334(f158(x82231),x82235),x82236)),f334(f334(f158(x82231),x82235),f334(f334(f155(x82231,x82232,x82233),x82234),x82236))) % 188.18/188.26 [8364]~E(f334(f196(f928(x83641)),x83645),f334(f196(f928(x83642)),x83646))+~E(f334(f196(f928(x83641)),x83643),f334(f196(f928(x83642)),x83644))+E(f334(f334(f141(f934(x83641,x83642)),f334(f334(f188(x83641,x83642),x83643),x83644)),f334(f334(f188(x83641,x83642),x83645),x83646)),f334(f334(f188(x83641,x83642),f334(f334(f141(x83641),x83643),x83645)),f334(f334(f141(x83642),x83644),x83646))) % 188.18/188.26 [8474]~E(x84742,f334(f317(x84743,x84741,x84744),x84746))+P107(f334(f334(f242(f935(x84741,a922)),x84742),f334(f317(x84743,x84741,x84744),x84745)))+~P107(f334(f334(f242(f935(x84743,a922)),x84746),x84745)) % 188.18/188.26 [8573]~P109(x85735)+E(f334(x85731,x85732),f334(x85731,x85733))+E(f334(f334(f155(x85734,x85735,x85731),x85732),f334(f334(f155(x85734,x85735,x85731),x85733),x85736)),f334(f334(f155(x85734,x85735,x85731),x85733),f334(f334(f155(x85734,x85735,x85731),x85732),x85736))) % 188.18/188.26 [8747]~P107(f334(f334(f336(x87472),x87474),f334(x87476,x87473)))+~P107(f334(f334(f336(x87471),x87473),x87475))+P107(f334(f334(f336(f934(x87471,x87472)),f334(f334(f260(x87471,x87472),x87473),x87474)),f334(f334(f262(x87471,x87472),x87475),x87476))) % 188.18/188.26 [9221]~P72(x92212)+~P27(x92214,x92211,x92215,x92216)+E(f334(f334(f9(x92211,x92212),x92213),f334(f317(x92214,x92211,x92215),x92216)),f334(f334(f9(x92214,x92212),f334(f78(x92211,x92212,x92214,x92213),x92215)),x92216)) % 188.18/188.26 [9222]~P76(x92222)+~P27(x92224,x92221,x92225,x92226)+E(f334(f334(f6(x92221,x92222),x92223),f334(f317(x92224,x92221,x92225),x92226)),f334(f334(f6(x92224,x92222),f334(f78(x92221,x92222,x92224,x92223),x92225)),x92226)) % 188.18/188.26 [9265]~P36(x92652,x92655,x92651,x92653,x92656)+P107(f334(f334(x92651,f334(f334(f171(x92652),x92653),x92654)),f334(f334(f171(x92655),x92656),x92654)))+~P107(f334(f334(f243(a927),x92654),f334(f196(f928(x92655)),x92656))) % 188.18/188.26 [9266]~P36(x92662,x92665,x92661,x92663,x92666)+P107(f334(f334(x92661,f334(f334(f171(x92662),x92663),x92664)),f334(f334(f171(x92665),x92666),x92664)))+~P107(f334(f334(f243(a927),x92664),f334(f196(f928(x92662)),x92663))) % 188.18/188.26 [9275]~E(f334(f317(x92751,x92752,x92753),x92754),x92756)+E(f334(f317(x92751,x92752,x92753),f334(f317(x92752,x92751,f97(x92751,x92752,x92754,x92753)),x92755)),x92755)+~P107(f334(f334(f242(f935(x92752,a922)),x92755),x92756)) % 188.18/188.26 [9475]~P21(x94753,x94751,x94756,x94752)+~P107(f334(f66(x94753),x94754))+E(f334(f78(x94751,x94751,x94751,f334(x94752,f334(f334(f23(f935(x94753,a922)),x94754),f334(f334(f316(x94753),x94755),f195(f935(x94753,a922)))))),f334(x94756,x94755)),f334(x94752,f334(f334(f316(x94753),x94755),x94754))) % 188.18/188.26 [10106]~E(f334(f317(x101062,x101064,x101066),f250(f935(x101062,a922))),f250(f935(x101064,a922)))+~E(f334(f317(x101061,x101063,x101065),f250(f935(x101061,a922))),f250(f935(x101063,a922)))+E(f334(f317(f934(x101061,x101062),f934(x101063,x101064),f266(x101061,x101063,x101062,x101064,x101065,x101066)),f250(f935(f934(x101061,x101062),a922))),f250(f935(f934(x101063,x101064),a922))) % 188.18/188.26 [10148]~P27(x101483,x101484,x101485,f334(x101486,f575(x101486,x101485,x101484,x101483,x101482,x101481)))+P27(x101483,x101484,x101485,f334(f334(f45(x101482,f935(x101483,a922)),x101481),x101486))+E(x101481,f195(f935(x101482,a922))) % 188.18/188.26 [10194]P27(x101946,x101945,x101944,f334(f334(f45(x101942,f935(x101946,a922)),x101941),x101943))+E(x101941,f195(f935(x101942,a922)))+P107(f334(f334(f336(x101942),f575(x101943,x101944,x101945,x101946,x101942,x101941)),x101941)) % 188.18/188.26 [10197]P107(f334(f334(f336(x101971),f602(x101972,x101973,x101974,x101975,x101976,x101971)),x101976))+P107(f334(f334(f242(f935(f934(x101971,x101974),a922)),f334(f334(f262(x101971,x101974),x101976),x101973)),f334(f334(f262(x101971,x101974),x101975),x101972)))+~P107(f334(f334(f242(f935(x101971,a922)),x101976),x101975)) % 188.18/188.26 [10236]P26(x102366,x102365,f334(f334(f316(f926(x102366)),f98(x102366,x102364,x102363,x102362)),f195(f935(f926(x102366),a922))))+~P26(x102366,x102365,f334(f334(f316(f926(x102366)),f98(x102366,x102364,x102363,x102361)),f195(f935(f926(x102366),a922))))+P107(f334(f334(x102361,f788(x102362,x102361,x102363,x102364,x102365,x102366)),f880(x102362,x102361,x102363,x102364,x102365,x102366))) % 188.18/188.26 [10237]P26(x102376,x102375,f334(f334(f316(f926(x102376)),f98(x102376,x102371,x102373,x102372)),f195(f935(f926(x102376),a922))))+~P26(x102376,x102375,f334(f334(f316(f926(x102376)),f98(x102376,x102374,x102373,x102372)),f195(f935(f926(x102376),a922))))+P107(f334(f334(x102371,f891(x102371,x102372,x102373,x102374,x102375,x102376)),f900(x102371,x102372,x102373,x102374,x102375,x102376))) % 188.18/188.26 [10276]~P26(x102761,x102762,f334(f334(f316(f926(x102761)),f98(x102761,x102763,x102764,x102766)),f195(f935(f926(x102761),a922))))+P26(x102761,x102762,f334(f334(f316(f926(x102761)),f98(x102761,x102763,x102764,x102765)),f195(f935(f926(x102761),a922))))+~P107(f334(f334(x102765,f788(x102765,x102766,x102764,x102763,x102762,x102761)),f880(x102765,x102766,x102764,x102763,x102762,x102761))) % 188.18/188.26 [10277]~P26(x102771,x102772,f334(f334(f316(f926(x102771)),f98(x102771,x102776,x102774,x102775)),f195(f935(f926(x102771),a922))))+P26(x102771,x102772,f334(f334(f316(f926(x102771)),f98(x102771,x102773,x102774,x102775)),f195(f935(f926(x102771),a922))))+~P107(f334(f334(x102776,f891(x102773,x102775,x102774,x102776,x102772,x102771)),f900(x102773,x102775,x102774,x102776,x102772,x102771))) % 188.18/188.26 [10322]~P107(f334(f334(f242(f935(x103222,a922)),f334(x103224,f602(x103226,x103224,x103222,x103225,x103223,x103221))),f334(x103226,f602(x103226,x103224,x103222,x103225,x103223,x103221))))+~P107(f334(f334(f242(f935(x103221,a922)),x103223),x103225))+P107(f334(f334(f242(f935(f934(x103221,x103222),a922)),f334(f334(f262(x103221,x103222),x103223),x103224)),f334(f334(f262(x103221,x103222),x103225),x103226))) % 188.18/188.26 [7969]~P107(f334(x79691,x79695))+~P107(f334(x79696,x79694))+P107(f334(x79691,f334(f264(x79692,x79693),f334(f334(f260(x79692,x79693),x79694),x79695)))) % 188.18/188.26 [7970]~P107(f334(x79701,x79704))+~P107(f334(x79706,x79705))+P107(f334(x79701,f334(f259(x79702,x79703),f334(f334(f260(x79702,x79703),x79704),x79705)))) % 188.18/188.26 [8020]~P107(f334(f334(x80204,x80206),x80205))+~P107(f334(f334(f336(x80201),x80206),x80203))+P107(f334(f334(f334(f44(x80201,f935(x80202,a922)),x80203),x80204),x80205)) % 188.18/188.26 [8316]~P107(f334(f334(f336(x83161),x83162),f334(x83165,x83166)))+~P107(f334(f334(f336(x83163),x83166),x83164))+P107(f334(f334(f336(x83161),x83162),f334(f334(f44(x83163,f935(x83161,a922)),x83164),x83165))) % 188.18/188.26 [8358]P107(f334(f334(x83581,x83582),x83583))+~P107(f334(f334(x83584,x83582),x83583))+~P107(f334(f334(f242(f935(x83585,f935(x83586,a922))),x83584),x83581)) % 188.18/188.26 [8498]P107(f334(f334(x84981,x84982),x84983))+~P107(f334(f334(f336(x84984),x84982),x84985))+~P107(f334(f334(f334(f45(x84984,f935(x84986,a922)),x84985),x84981),x84983)) % 188.18/188.26 [8626]P107(f334(f334(f336(x86261),x86262),f334(x86263,x86264)))+~P107(f334(f334(f336(x86265),x86264),x86266))+~P107(f334(f334(f336(x86261),x86262),f334(f334(f45(x86265,f935(x86261,a922)),x86266),x86263))) % 188.18/188.26 [8889]~P13(x88894,x88895,x88896,x88891)+E(f334(x88891,x88892),f334(x88891,x88893))+~P107(f334(f334(f336(f934(x88894,x88894)),f334(f334(f260(x88894,x88894),x88892),x88893)),x88896)) % 188.18/188.26 [8923]P107(f334(f334(f242(f935(x89231,a922)),x89232),f334(x89233,x89234)))+~P107(f334(f334(f336(x89235),x89234),x89236))+~P107(f334(f334(f242(f935(x89231,a922)),x89232),f334(f334(f45(x89235,f935(x89231,a922)),x89236),x89233))) % 188.18/188.26 [8957]~P57(x89573,x89574,f334(f293(x89574,x89573),x89575))+E(x89571,f195(f935(x89572,a922)))+E(f334(f334(f45(x89572,f935(x89573,a922)),x89571),f334(f334(f8(f935(x89574,a922),f935(x89573,a922),x89572),f292(x89574,x89573,x89575)),x89576)),f334(f292(x89574,x89573,x89575),f334(f334(f45(x89572,f935(x89574,a922)),x89571),x89576))) % 188.18/188.26 [9035]P107(f334(f334(f336(x90351),x90352),f334(f292(x90353,x90351,x90354),x90355)))+~P107(f334(f334(f336(x90353),x90356),x90355))+~P107(f334(f334(f336(f934(x90353,x90351)),f334(f334(f260(x90353,x90351),x90356),x90352)),x90354)) % 188.18/188.26 [9340]P107(f334(f334(f242(f935(x93401,a922)),f334(f292(x93402,x93401,x93403),x93404)),f334(f292(x93402,x93401,x93405),x93406)))+~P107(f334(f334(f242(f935(x93402,a922)),x93404),x93406))+~P107(f334(f334(f242(f935(f934(x93402,x93401),a922)),x93403),x93405)) % 188.18/188.26 [9531]~P107(f334(f334(f336(x95312),x95316),x95314))+~P107(f334(f334(f242(f935(x95311,a922)),x95313),x95315))+P107(f334(f334(f242(f935(f934(x95311,x95312),a922)),f334(f334(f262(x95311,x95312),x95313),f334(f16(f935(x95312,a922),x95311),x95314))),f334(f334(f262(x95311,x95312),x95315),f334(f16(f935(x95312,a922),x95311),x95314)))) % 188.18/188.26 [9539]~P36(x95391,x95392,x95393,x95395,x95396)+P107(f334(f334(f265(x95391,x95392,a922),x95393),x95394))+~P107(f334(f334(f336(f934(x95391,x95392)),x95394),f334(f179(f934(x95391,x95392)),f334(f334(f188(x95391,x95392),x95395),x95396)))) % 188.18/188.26 [9671]~E(x96713,x96715)+P107(f334(f334(f336(f934(f928(x96711),f928(x96711))),f334(f334(f260(f928(x96711),f928(x96711)),f334(f334(f158(x96711),x96712),x96713)),f334(f334(f158(x96711),x96714),x96715))),f164(x96711,x96716)))+~P107(f334(f334(f336(f934(x96711,x96711)),f334(f334(f260(x96711,x96711),x96712),x96714)),x96716)) % 188.18/188.26 [9677]~E(f334(f196(f928(x96771)),x96773),f334(f196(f928(x96771)),x96775))+P107(f334(f334(f336(f934(f928(x96771),f928(x96771))),f334(f334(f260(f928(x96771),f928(x96771)),f334(f334(f158(x96771),x96772),x96773)),f334(f334(f158(x96771),x96774),x96775))),f152(x96771,x96776)))+~P107(f334(f334(f336(f934(x96771,x96771)),f334(f334(f260(x96771,x96771),x96772),x96774)),x96776)) % 188.18/188.26 [9713]P107(f334(f334(f336(f934(x97131,x97131)),f334(f334(f260(x97131,x97131),x97132),x97133)),f334(f334(f190(f934(x97131,x97131),a922),f334(a119,x97134)),x97135)))+~P107(f334(f334(f336(f934(x97131,x97131)),f334(f334(f260(x97131,x97131),x97136),x97133)),x97135))+~P107(f334(f334(f336(f934(x97131,x97131)),f334(f334(f260(x97131,x97131),x97132),x97136)),f334(f334(f190(f934(x97131,x97131),a922),x97134),x97135))) % 188.18/188.26 [9714]P107(f334(f334(f336(f934(x97141,x97141)),f334(f334(f260(x97141,x97141),x97142),x97143)),f334(f334(f190(f934(x97141,x97141),a922),f334(a119,x97144)),x97145)))+~P107(f334(f334(f336(f934(x97141,x97141)),f334(f334(f260(x97141,x97141),x97142),x97146)),x97145))+~P107(f334(f334(f336(f934(x97141,x97141)),f334(f334(f260(x97141,x97141),x97146),x97143)),f334(f334(f190(f934(x97141,x97141),a922),x97144),x97145))) % 188.18/188.26 [9716]~P107(f334(f334(f336(x97164),x97165),x97166))+P107(f334(f334(f242(f935(x97161,a922)),x97162),x97163))+~P107(f334(f334(f242(f935(f934(x97161,x97164),a922)),f334(f334(f262(x97161,x97164),x97162),f334(f16(f935(x97164,a922),x97161),x97166))),f334(f334(f262(x97161,x97164),x97163),f334(f16(f935(x97164,a922),x97161),x97166)))) % 188.18/188.26 [9771]E(x97711,x97712)+~P107(f334(f334(f336(f934(f928(x97713),f928(x97713))),f334(f334(f260(f928(x97713),f928(x97713)),f334(f334(f158(x97713),x97711),x97715)),f334(f334(f158(x97713),x97712),x97716))),f152(x97713,x97714)))+P107(f334(f334(f336(f934(x97713,x97713)),f334(f334(f260(x97713,x97713),x97711),x97712)),x97714)) % 188.18/188.26 [9772]E(x97721,x97722)+~P107(f334(f334(f336(f934(f928(x97723),f928(x97723))),f334(f334(f260(f928(x97723),f928(x97723)),f334(f334(f158(x97723),x97721),x97725)),f334(f334(f158(x97723),x97722),x97726))),f154(x97723,x97724)))+P107(f334(f334(f336(f934(x97723,x97723)),f334(f334(f260(x97723,x97723),x97721),x97722)),x97724)) % 188.18/188.26 [9773]E(x97731,x97732)+~P107(f334(f334(f336(f934(f928(x97733),f928(x97733))),f334(f334(f260(f928(x97733),f928(x97733)),f334(f334(f158(x97733),x97731),x97735)),f334(f334(f158(x97733),x97732),x97736))),f164(x97733,x97734)))+P107(f334(f334(f336(f934(x97733,x97733)),f334(f334(f260(x97733,x97733),x97731),x97732)),x97734)) % 188.18/188.26 [9807]P107(f334(f334(f336(f934(f928(x98071),f928(x98071))),f334(f334(f260(f928(x98071),f928(x98071)),f334(f334(f158(x98071),x98072),x98073)),f334(f334(f158(x98071),x98074),x98075))),f165(x98071,x98076)))+~P107(f334(f334(f336(f934(f928(x98071),f928(x98071))),f334(f334(f260(f928(x98071),f928(x98071)),x98073),x98075)),f165(x98071,x98076)))+~P107(f334(f334(f336(f934(x98071,x98071)),f334(f334(f260(x98071,x98071),x98072),x98074)),x98076)) % 188.18/188.26 [9831]P107(f334(x98311,x98312))+~P107(f334(x98311,f401(x98311,x98313,x98314,x98315,x98316)))+~P107(f334(f334(f336(x98316),x98312),f334(f334(f44(x98315,f935(x98316,a922)),x98314),x98313))) % 188.18/188.26 [9836]~P107(f334(f334(f336(f934(f928(x98361),f928(x98361))),f334(f334(f260(f928(x98361),f928(x98361)),f334(f334(f158(x98361),x98362),x98365)),f334(f334(f158(x98361),x98363),x98366))),f152(x98361,x98364)))+P107(f334(f334(f336(f934(f928(x98361),f928(x98361))),f334(f334(f260(f928(x98361),f928(x98361)),x98365),x98366)),f152(x98361,x98364)))+P107(f334(f334(f336(f934(x98361,x98361)),f334(f334(f260(x98361,x98361),x98362),x98363)),x98364)) % 188.18/188.26 [9837]~P107(f334(f334(f336(f934(f928(x98371),f928(x98371))),f334(f334(f260(f928(x98371),f928(x98371)),f334(f334(f158(x98371),x98372),x98375)),f334(f334(f158(x98371),x98373),x98376))),f154(x98371,x98374)))+P107(f334(f334(f336(f934(f928(x98371),f928(x98371))),f334(f334(f260(f928(x98371),f928(x98371)),x98375),x98376)),f154(x98371,x98374)))+P107(f334(f334(f336(f934(x98371,x98371)),f334(f334(f260(x98371,x98371),x98372),x98373)),x98374)) % 188.18/188.26 [9838]~P107(f334(f334(f336(f934(f928(x98381),f928(x98381))),f334(f334(f260(f928(x98381),f928(x98381)),f334(f334(f158(x98381),x98382),x98385)),f334(f334(f158(x98381),x98383),x98386))),f164(x98381,x98384)))+P107(f334(f334(f336(f934(f928(x98381),f928(x98381))),f334(f334(f260(f928(x98381),f928(x98381)),x98385),x98386)),f164(x98381,x98384)))+P107(f334(f334(f336(f934(x98381,x98381)),f334(f334(f260(x98381,x98381),x98382),x98383)),x98384)) % 188.18/188.26 [9934]P107(f334(x99341,x99342))+P107(f334(f334(f336(x99343),f402(x99341,x99344,x99345,x99343,x99346)),x99345))+~P107(f334(f334(f336(x99346),x99342),f334(f334(f44(x99343,f935(x99346,a922)),x99345),x99344))) % 188.18/188.26 [9945]~E(x99452,x99454)+P107(f334(f334(f336(f934(f928(x99451),f928(x99451))),f334(f334(f260(f928(x99451),f928(x99451)),f334(f334(f141(x99451),x99452),f334(f334(f158(x99451),x99453),f120(x99451)))),f334(f334(f141(x99451),x99454),f334(f334(f158(x99451),x99455),f120(x99451))))),f164(x99451,x99456)))+~P107(f334(f334(f336(f934(x99451,x99451)),f334(f334(f260(x99451,x99451),x99453),x99455)),x99456)) % 188.18/188.26 [10032]E(x100321,x100322)+~P107(f334(f334(f336(f934(f928(x100323),f928(x100323))),f334(f334(f260(f928(x100323),f928(x100323)),f334(f334(f141(x100323),x100325),f334(f334(f158(x100323),x100321),f120(x100323)))),f334(f334(f141(x100323),x100326),f334(f334(f158(x100323),x100322),f120(x100323))))),f164(x100323,x100324)))+P107(f334(f334(f336(f934(x100323,x100323)),f334(f334(f260(x100323,x100323),x100321),x100322)),x100324)) % 188.18/188.26 [10062]~P107(f334(f334(f336(f934(f928(x100621),f928(x100621))),f334(f334(f260(f928(x100621),f928(x100621)),f334(f334(f141(x100621),x100625),f334(f334(f158(x100621),x100622),f120(x100621)))),f334(f334(f141(x100621),x100626),f334(f334(f158(x100621),x100623),f120(x100621))))),f164(x100621,x100624)))+P107(f334(f334(f336(f934(f928(x100621),f928(x100621))),f334(f334(f260(f928(x100621),f928(x100621)),x100625),x100626)),f164(x100621,x100624)))+P107(f334(f334(f336(f934(x100621,x100621)),f334(f334(f260(x100621,x100621),x100622),x100623)),x100624)) % 188.18/188.26 [10086]P107(f334(x100861,x100862))+P107(f334(f334(f336(x100863),f401(x100861,x100864,x100865,x100866,x100863)),f334(x100864,f402(x100861,x100864,x100865,x100866,x100863))))+~P107(f334(f334(f336(x100863),x100862),f334(f334(f44(x100866,f935(x100863,a922)),x100865),x100864))) % 188.18/188.26 [10201]P107(f334(f334(f336(x102011),f850(x102012,x102013,x102014,x102015,x102016,x102011)),x102015))+~P107(f334(f334(f242(f935(x102011,a922)),x102016),x102015))+P107(f334(f334(f242(f935(x102014,a922)),f334(f334(f45(x102011,f935(x102014,a922)),x102015),x102013)),f334(f334(f45(x102011,f935(x102014,a922)),x102015),x102012))) % 188.18/188.26 [10323]~P107(f334(f334(f242(f935(x103231,a922)),f334(x103234,f850(x103235,x103234,x103231,x103233,x103236,x103232))),f334(x103235,f850(x103235,x103234,x103231,x103233,x103236,x103232))))+~P107(f334(f334(f242(f935(x103232,a922)),x103236),x103233))+P107(f334(f334(f242(f935(x103231,a922)),f334(f334(f45(x103232,f935(x103231,a922)),x103233),x103234)),f334(f334(f45(x103232,f935(x103231,a922)),x103233),x103235))) % 188.18/188.26 [9058]~P18(x90583,x90584,x90581)+~P107(f334(f66(x90583),x90586))+E(f334(f334(x90581,x90582),f334(f334(f69(x90583,x90584,x90581),x90585),f334(f334(f23(f935(x90583,a922)),x90586),f334(f334(f316(x90583),x90582),f195(f935(x90583,a922)))))),f334(f334(f69(x90583,x90584,x90581),x90585),f334(f334(f316(x90583),x90582),x90586))) % 188.18/188.26 [9349]~P107(f334(f334(f336(x93495),x93493),x93496))+P107(f334(f334(f242(f935(x93491,a922)),f334(x93492,x93493)),x93494))+~P107(f334(f334(f242(f935(x93491,a922)),f334(f334(f44(x93495,f935(x93491,a922)),x93496),x93492)),x93494)) % 188.18/188.26 [10004]~P10(x100041,x100045,x100044)+P107(f334(f334(f336(f934(x100041,x100041)),f334(f334(f260(x100041,x100041),x100042),x100043)),x100044))+~P107(f334(f334(f336(x100041),x100046),f334(f334(f109(f935(x100041,a922)),f334(f292(x100041,x100041,x100044),f334(f334(f316(x100041),x100042),f195(f935(x100041,a922))))),f334(f292(x100041,x100041,x100044),f334(f334(f316(x100041),x100043),f195(f935(x100041,a922))))))) % 188.18/188.26 [8783]~P113(x87832)+~E(f334(f334(f86(x87832),f334(f334(f87(x87832),x87834),x87835)),x87831),f334(f334(f86(x87832),f334(f334(f87(x87832),x87833),x87835)),x87836))+E(x87831,f334(f334(f86(x87832),f334(f334(f87(x87832),f334(f334(f23(x87832),x87833),x87834)),x87835)),x87836)) % 188.18/188.26 [8784]~P113(x87841)+~E(f334(f334(f86(x87841),f334(f334(f87(x87841),x87842),x87844)),x87845),f334(f334(f86(x87841),f334(f334(f87(x87841),x87843),x87844)),x87846))+E(f334(f334(f86(x87841),f334(f334(f87(x87841),f334(f334(f23(x87841),x87842),x87843)),x87844)),x87845),x87846) % 188.18/188.26 [8960]~P113(x89601)+E(f334(f334(f86(x89601),f334(f334(f87(x89601),x89602),x89603)),x89604),f334(f334(f86(x89601),f334(f334(f87(x89601),x89605),x89603)),x89606))+~E(x89606,f334(f334(f86(x89601),f334(f334(f87(x89601),f334(f334(f23(x89601),x89602),x89605)),x89603)),x89604)) % 188.18/188.26 [8961]~P113(x89611)+E(f334(f334(f86(x89611),f334(f334(f87(x89611),x89612),x89613)),x89614),f334(f334(f86(x89611),f334(f334(f87(x89611),x89615),x89613)),x89616))+~E(f334(f334(f86(x89611),f334(f334(f87(x89611),f334(f334(f23(x89611),x89612),x89615)),x89613)),x89614),x89616) % 188.18/188.26 [9287]~P107(f334(f334(x92874,x92875),x92876))+~P107(f334(f334(x92873,x92875),x92876))+P107(f334(f334(f334(f334(f109(f935(x92871,f935(x92872,a922))),x92873),x92874),x92875),x92876)) % 188.18/188.26 [9548]P107(f334(f334(x95481,x95482),x95483))+P107(f334(f334(x95484,x95482),x95483))+~P107(f334(f334(f334(f334(f108(f935(x95485,f935(x95486,a922))),x95484),x95481),x95482),x95483)) % 188.18/188.26 [9851]~P130(x98511)+~P107(f334(f334(f242(x98511),f334(f334(f86(x98511),f334(f334(f87(x98511),x98514),x98515)),x98512)),f334(f334(f86(x98511),f334(f334(f87(x98511),x98513),x98515)),x98516)))+P107(f334(f334(f242(x98511),x98512),f334(f334(f86(x98511),f334(f334(f87(x98511),f334(f334(f23(x98511),x98513),x98514)),x98515)),x98516))) % 188.18/188.26 [9852]~P130(x98521)+~P107(f334(f334(f243(x98521),f334(f334(f86(x98521),f334(f334(f87(x98521),x98524),x98525)),x98522)),f334(f334(f86(x98521),f334(f334(f87(x98521),x98523),x98525)),x98526)))+P107(f334(f334(f243(x98521),x98522),f334(f334(f86(x98521),f334(f334(f87(x98521),f334(f334(f23(x98521),x98523),x98524)),x98525)),x98526))) % 188.18/188.26 [9884]~P130(x98841)+P107(f334(f334(f242(x98841),f334(f334(f86(x98841),f334(f334(f87(x98841),x98842),x98843)),x98844)),f334(f334(f86(x98841),f334(f334(f87(x98841),x98845),x98843)),x98846)))+~P107(f334(f334(f242(x98841),x98844),f334(f334(f86(x98841),f334(f334(f87(x98841),f334(f334(f23(x98841),x98845),x98842)),x98843)),x98846))) % 188.18/188.26 [9885]~P130(x98851)+P107(f334(f334(f243(x98851),f334(f334(f86(x98851),f334(f334(f87(x98851),x98852),x98853)),x98854)),f334(f334(f86(x98851),f334(f334(f87(x98851),x98855),x98853)),x98856)))+~P107(f334(f334(f243(x98851),x98854),f334(f334(f86(x98851),f334(f334(f87(x98851),f334(f334(f23(x98851),x98855),x98852)),x98853)),x98856))) % 188.18/188.26 [9996]~P130(x99961)+~P107(f334(f334(f242(x99961),f334(f334(f86(x99961),f334(f334(f87(x99961),x99962),x99964)),x99965)),f334(f334(f86(x99961),f334(f334(f87(x99961),x99963),x99964)),x99966)))+P107(f334(f334(f242(x99961),f334(f334(f86(x99961),f334(f334(f87(x99961),f334(f334(f23(x99961),x99962),x99963)),x99964)),x99965)),x99966)) % 188.18/188.26 [9997]~P130(x99971)+~P107(f334(f334(f243(x99971),f334(f334(f86(x99971),f334(f334(f87(x99971),x99972),x99974)),x99975)),f334(f334(f86(x99971),f334(f334(f87(x99971),x99973),x99974)),x99976)))+P107(f334(f334(f243(x99971),f334(f334(f86(x99971),f334(f334(f87(x99971),f334(f334(f23(x99971),x99972),x99973)),x99974)),x99975)),x99976)) % 188.18/188.26 [10045]~P130(x100451)+P107(f334(f334(f242(x100451),f334(f334(f86(x100451),f334(f334(f87(x100451),x100452),x100453)),x100454)),f334(f334(f86(x100451),f334(f334(f87(x100451),x100455),x100453)),x100456)))+~P107(f334(f334(f242(x100451),f334(f334(f86(x100451),f334(f334(f87(x100451),f334(f334(f23(x100451),x100452),x100455)),x100453)),x100454)),x100456)) % 188.18/188.26 [10046]~P130(x100461)+P107(f334(f334(f243(x100461),f334(f334(f86(x100461),f334(f334(f87(x100461),x100462),x100463)),x100464)),f334(f334(f86(x100461),f334(f334(f87(x100461),x100465),x100463)),x100466)))+~P107(f334(f334(f243(x100461),f334(f334(f86(x100461),f334(f334(f87(x100461),f334(f334(f23(x100461),x100462),x100465)),x100463)),x100464)),x100466)) % 188.18/188.26 [10188]~P76(x101882)+~P107(f334(f66(x101881),x101886))+E(f334(f334(f6(x101881,x101882),f334(f334(f18(x101881,x101882,x101882),f334(f334(f18(x101881,x101882,f935(x101882,x101882)),f334(f334(f8(a922,f935(x101882,f935(x101882,x101882)),x101881),f103(x101882)),x101883)),x101884)),x101885)),x101886),f334(f334(f86(x101882),f334(f334(f6(x101881,x101882),x101884),f334(f334(f109(f935(x101881,a922)),x101886),f334(f270(x101881),x101883)))),f334(f334(f6(x101881,x101882),x101885),f334(f334(f109(f935(x101881,a922)),x101886),f334(f85(f935(x101881,a922)),f334(f270(x101881),x101883)))))) % 188.18/188.26 [10245]P107(f334(f334(f336(x102452),x102454),x102456))+P107(f334(f334(f336(x102452),x102455),x102456))+E(f334(f318(x102451,x102452,f334(f334(f7(x102451,x102452,x102452),f334(f334(f7(x102451,x102452,f935(x102452,x102452)),f334(f334(f8(a922,f935(x102452,f935(x102452,x102452)),x102451),f103(x102452)),f334(f334(f7(x102451,f935(x102451,a922),a922),f336(x102451)),x102453))),x102454)),x102455)),x102456),f195(f935(x102451,a922))) % 188.18/188.26 [10246]P107(f334(f334(f336(x102462),x102465),x102466))+~P107(f334(f334(f336(x102462),x102464),x102466))+E(f334(f318(x102461,x102462,f334(f334(f7(x102461,x102462,x102462),f334(f334(f7(x102461,x102462,f935(x102462,x102462)),f334(f334(f8(a922,f935(x102462,f935(x102462,x102462)),x102461),f103(x102462)),f334(f334(f7(x102461,f935(x102461,a922),a922),f336(x102461)),x102463))),x102464)),x102465)),x102466),x102463) % 188.18/188.26 [10247]P107(f334(f334(f336(x102472),x102474),x102476))+~P107(f334(f334(f336(x102472),x102475),x102476))+E(f334(f318(x102471,x102472,f334(f334(f7(x102471,x102472,x102472),f334(f334(f7(x102471,x102472,f935(x102472,x102472)),f334(f334(f8(a922,f935(x102472,f935(x102472,x102472)),x102471),f103(x102472)),f334(f334(f7(x102471,f935(x102471,a922),a922),f336(x102471)),x102473))),x102474)),x102475)),x102476),f334(f85(f935(x102471,a922)),x102473)) % 188.18/188.26 [10248]~P107(f334(f334(f336(x102482),x102484),x102486))+~P107(f334(f334(f336(x102482),x102485),x102486))+E(f334(f318(x102481,x102482,f334(f334(f7(x102481,x102482,x102482),f334(f334(f7(x102481,x102482,f935(x102482,x102482)),f334(f334(f8(a922,f935(x102482,f935(x102482,x102482)),x102481),f103(x102482)),f334(f334(f7(x102481,f935(x102481,a922),a922),f336(x102481)),x102483))),x102484)),x102485)),x102486),f250(f935(x102481,a922))) % 188.18/188.26 [8815]E(x88151,x88152)+~P60(x88154,x88155,x88153,x88156,x88157)+~E(f334(x88153,x88151),f334(x88153,x88152)) % 188.18/188.26 [8845]~P12(x88456,x88455,x88457,x88454,x88451)+E(f334(f334(x88451,x88452),x88453),x88454)+P107(f334(f66(x88455),x88453)) % 188.18/188.26 [9700]P44(x97001,x97002,x97003,x97004,x97005,f334(f334(x97003,x97006),x97007))+~E(f334(f334(x97003,x97006),x97007),x97004)+~E(x97005,f195(f935(x97001,a922))) % 188.18/188.26 [9903]~P107(f334(x99036,x99033))+~P107(f334(f334(f336(f934(x99032,x99032)),f334(f334(f260(x99032,x99032),x99034),x99035)),f334(x99037,x99033)))+P107(f334(f334(f336(f934(f934(x99031,x99032),f934(x99031,x99032))),f334(f334(f260(f934(x99031,x99032),f934(x99031,x99032)),f334(f334(f260(x99031,x99032),x99033),x99034)),f334(f334(f260(x99031,x99032),x99033),x99035))),f288(x99031,x99032,x99036,x99037))) % 188.18/188.26 [10313]~P44(x103132,x103137,x103133,x103136,x103131,f334(f334(x103133,x103135),x103134))+E(f334(f334(x103133,f520(x103134,x103135,x103131,x103136,x103133,x103137,x103132)),f527(x103134,x103135,x103131,x103136,x103133,x103137,x103132)),f334(f334(x103133,x103135),x103134))+E(x103131,f195(f935(x103132,a922))) % 188.18/188.26 [10314]~P44(x103147,x103146,x103141,x103144,x103145,f334(f334(x103141,x103142),x103143))+E(f334(f334(x103141,f520(x103143,x103142,x103145,x103144,x103141,x103146,x103147)),f527(x103143,x103142,x103145,x103144,x103141,x103146,x103147)),f334(f334(x103141,x103142),x103143))+E(f334(f334(x103141,x103142),x103143),x103144) % 188.18/188.26 [9386]~P36(x93861,x93862,x93863,x93865,x93867)+P36(x93861,x93862,x93863,f334(f334(f158(x93861),x93864),x93865),f334(f334(f158(x93862),x93866),x93867))+~P107(f334(f334(x93863,x93864),x93866)) % 188.18/188.26 [9402]P36(x94021,x94022,x94023,x94024,x94025)+~P36(x94021,x94022,x94023,f334(f334(f141(x94021),x94026),x94024),f334(f334(f141(x94022),x94027),x94025))+~E(f334(f196(f928(x94021)),x94026),f334(f196(f928(x94022)),x94027)) % 188.18/188.26 [9403]P36(x94031,x94032,x94033,x94034,x94035)+~P36(x94031,x94032,x94033,f334(f334(f141(x94031),x94034),x94036),f334(f334(f141(x94032),x94035),x94037))+~E(f334(f196(f928(x94031)),x94034),f334(f196(f928(x94032)),x94035)) % 188.18/188.26 [9616]~P36(x96161,x96162,x96163,x96165,x96167)+~P36(x96161,x96162,x96163,x96164,x96166)+P36(x96161,x96162,x96163,f334(f334(f141(x96161),x96164),x96165),f334(f334(f141(x96162),x96166),x96167)) % 188.18/188.26 [9983]~P107(f334(f71(x99831,x99834,x99835,x99836,x99833),x99837))+P107(f334(f71(x99831,x99834,x99835,x99836,f334(f334(f316(x99831),x99832),x99833)),f334(f334(x99835,x99832),x99837)))+P107(f334(f334(f336(x99831),x99832),x99833)) % 188.18/188.26 [10340]~P44(x103402,x103407,x103406,x103405,x103401,f334(f334(x103406,x103404),x103403))+E(x103401,f195(f935(x103402,a922)))+P107(f334(f334(f336(x103402),f520(x103403,x103404,x103401,x103405,x103406,x103407,x103402)),x103401)) % 188.18/188.26 [10341]~P44(x103415,x103417,x103411,x103414,x103416,f334(f334(x103411,x103412),x103413))+E(f334(f334(x103411,x103412),x103413),x103414)+P107(f334(f334(f336(x103415),f520(x103413,x103412,x103416,x103414,x103411,x103417,x103415)),x103416)) % 188.18/188.26 [10475]E(f334(f334(f260(x104751,x104752),x104753),x104754),f334(f334(f260(x104751,x104752),x104755),x104756))+P107(f334(f334(f336(f934(f934(x104751,x104752),f934(x104751,x104752))),f334(f334(f260(f934(x104751,x104752),f934(x104751,x104752)),f334(f334(f260(x104751,x104752),f852(x104757,x104754,x104753,x104756,x104755,x104752,x104751)),f853(x104757,x104754,x104753,x104756,x104755,x104752,x104751))),f334(f334(f260(x104751,x104752),x104753),x104754))),f314(f934(x104751,x104752),x104757)))+~P107(f334(f334(f336(f934(f934(x104751,x104752),f934(x104751,x104752))),f334(f334(f260(f934(x104751,x104752),f934(x104751,x104752)),f334(f334(f260(x104751,x104752),x104755),x104756)),f334(f334(f260(x104751,x104752),x104753),x104754))),f314(f934(x104751,x104752),x104757))) % 188.18/188.26 [9084]~P23(x90844,x90845,x90846,x90847,x90841)+~P107(f334(f66(x90845),x90843))+E(f334(f334(x90841,x90842),x90843),f334(f334(f334(f70(x90844,x90845,x90846),x90842),x90847),x90843)) % 188.18/188.26 [9085]~P12(x90854,x90855,x90856,x90857,x90851)+~P107(f334(f66(x90855),x90853))+E(f334(f334(x90851,x90852),x90853),f334(f334(f334(f70(x90854,x90855,x90856),x90852),x90857),x90853)) % 188.18/188.26 [9866]~P26(x98661,x98662,f334(f334(f316(f926(x98661)),f98(x98661,x98663,x98664,x98667)),f195(f935(f926(x98661),a922))))+P26(x98661,x98662,f334(f334(f316(f926(x98661)),f98(x98661,x98663,f31(x98664,x98665),x98666)),f195(f935(f926(x98661),a922))))+~P26(x98661,x98662,f334(f334(f316(f926(x98661)),f98(x98661,x98667,x98665,x98666)),f195(f935(f926(x98661),a922)))) % 188.18/188.26 [9879]~P25(x98793,x98794,x98795,x98797,x98796,x98791)+~P107(f334(f66(x98794),x98792))+E(f334(x98791,x98792),f334(f334(f334(f70(x98793,x98794,x98795),x98796),x98797),x98792)) % 188.18/188.26 [10040]P44(x100401,x100402,x100403,x100404,x100405,f334(f334(x100403,x100406),x100407))+~P44(x100401,x100402,x100403,x100404,f334(f334(f23(f935(x100401,a922)),x100405),f334(f334(f316(x100401),x100406),f195(f935(x100401,a922)))),x100407)+~P107(f334(f334(f336(x100401),x100406),x100405)) % 188.18/188.26 [10145]~P26(x101451,x101452,f334(f334(f316(f926(x101451)),f98(x101451,f99(x101451,x101453,x101454),x101455,x101457)),f195(f935(f926(x101451),a922))))+P26(x101451,x101452,f334(f334(f316(f926(x101451)),f98(x101451,x101453,f28(x101454,x101455,x101456),x101457)),f195(f935(f926(x101451),a922))))+~P26(x101451,x101452,f334(f334(f316(f926(x101451)),f98(x101451,f99(x101451,x101453,f334(f78(a922,a922,a923,a329),x101454)),x101456,x101457)),f195(f935(f926(x101451),a922)))) % 188.18/188.26 [10387]P107(f334(f334(x103877,f805(x103874,x103875,x103871,x103876,x103873,x103872,x103877)),f806(x103874,x103875,x103871,x103876,x103873,x103872,x103877)))+~P107(f334(f334(x103877,f334(f264(x103872,x103873),x103876)),f334(f259(x103872,x103873),x103876)))+P107(f334(x103871,f334(f334(f265(x103872,x103873,x103874),x103875),x103876))) % 188.18/188.26 [10388]P26(x103887,x103886,f334(f334(f316(f926(x103887)),f98(x103887,x103881,x103884,x103882)),f195(f935(f926(x103887),a922))))+~P26(x103887,x103886,f334(f334(f316(f926(x103887)),f98(x103887,x103885,x103884,x103883)),f195(f935(f926(x103887),a922))))+P107(f334(f334(x103881,f911(x103882,x103881,x103883,x103884,x103885,x103886,x103887)),f920(x103882,x103881,x103883,x103884,x103885,x103886,x103887))) % 188.18/188.26 [10400]~P44(x104002,x104003,x104004,x104005,x104001,f334(f334(x104004,x104007),x104006))+P44(x104002,x104003,x104004,x104005,f334(f334(f23(f935(x104002,a922)),x104001),f334(f334(f316(x104002),f520(x104006,x104007,x104001,x104005,x104004,x104003,x104002)),f195(f935(x104002,a922)))),f527(x104006,x104007,x104001,x104005,x104004,x104003,x104002))+E(x104001,f195(f935(x104002,a922))) % 188.18/188.26 [10401]~P44(x104015,x104016,x104011,x104014,x104017,f334(f334(x104011,x104012),x104013))+P44(x104015,x104016,x104011,x104014,f334(f334(f23(f935(x104015,a922)),x104017),f334(f334(f316(x104015),f520(x104013,x104012,x104017,x104014,x104011,x104016,x104015)),f195(f935(x104015,a922)))),f527(x104013,x104012,x104017,x104014,x104011,x104016,x104015))+E(f334(f334(x104011,x104012),x104013),x104014) % 188.18/188.26 [10402]~P26(x104021,x104022,f334(f334(f316(f926(x104021)),f98(x104021,x104027,x104024,x104026)),f195(f935(f926(x104021),a922))))+P26(x104021,x104022,f334(f334(f316(f926(x104021)),f98(x104021,x104023,x104024,x104025)),f195(f935(f926(x104021),a922))))+~P107(f334(f334(x104025,f911(x104025,x104023,x104026,x104024,x104027,x104022,x104021)),f355(x104025,x104023,x104026,x104024,x104027,x104022,x104021))) % 188.18/188.26 [10433]~P107(f334(x104331,f334(f334(x104335,f806(x104334,x104335,x104331,x104336,x104333,x104332,x104337)),f805(x104334,x104335,x104331,x104336,x104333,x104332,x104337))))+~P107(f334(f334(x104337,f334(f264(x104332,x104333),x104336)),f334(f259(x104332,x104333),x104336)))+P107(f334(x104331,f334(f334(f265(x104332,x104333,x104334),x104335),x104336))) % 188.18/188.26 [9685]P107(f334(f334(f242(f935(f934(x96851,x96852),a922)),f334(f334(f295(x96851,x96853,x96852),x96854),x96855)),f334(f334(f295(x96851,x96853,x96852),x96856),x96857)))+~P107(f334(f334(f242(f935(f934(x96853,x96852),a922)),x96855),x96857))+~P107(f334(f334(f242(f935(f934(x96851,x96853),a922)),x96854),x96856)) % 188.18/188.26 [10466]E(f334(f334(f260(x104661,x104662),x104663),x104664),f334(f334(f260(x104661,x104662),x104665),x104666))+~P107(f334(f334(f336(f934(f934(x104661,x104662),f934(x104661,x104662))),f334(f334(f260(f934(x104661,x104662),f934(x104661,x104662)),f334(f334(f260(x104661,x104662),x104663),x104664)),f334(f334(f260(x104661,x104662),x104665),x104666))),f314(f934(x104661,x104662),x104667)))+P107(f334(f334(f336(f934(f934(x104661,x104662),f934(x104661,x104662))),f334(f334(f260(f934(x104661,x104662),f934(x104661,x104662)),f334(f334(f260(x104661,x104662),x104663),x104664)),f334(f334(f260(x104661,x104662),f852(x104667,x104666,x104665,x104664,x104663,x104662,x104661)),f853(x104667,x104666,x104665,x104664,x104663,x104662,x104661)))),x104667)) % 188.18/188.26 [10051]~P107(f334(f334(f336(x100511),x100516),x100515))+P107(f334(f71(x100511,x100512,x100513,x100514,x100515),f334(f334(x100513,x100516),x100517)))+~P107(f334(f71(x100511,x100512,x100513,x100514,f334(f334(f23(f935(x100511,a922)),x100515),f334(f334(f316(x100511),x100516),f195(f935(x100511,a922))))),x100517)) % 188.18/188.26 [10482]~P148(x104821)+~P27(f934(x104822,x104823),x104821,f334(f265(x104822,x104823,x104821),f334(f334(f7(x104822,f935(x104823,x104821),f935(x104823,x104821)),f334(f334(f8(f935(x104821,x104821),f935(f935(x104823,x104821),f935(x104823,x104821)),x104822),f8(x104821,x104821,x104823)),f334(f334(f8(x104821,f935(x104821,x104821),x104822),f87(x104821)),x104824))),x104825)),f334(f334(f262(x104822,x104823),x104826),f334(f16(f935(x104823,a922),x104822),x104827)))+E(f334(f334(f6(x104821,x104821),f32(x104821)),f334(f270(x104821),f334(f334(f8(f935(x104822,a922),a922,x104821),f92(x104822)),f334(f334(f8(f935(x104822,f935(x104823,a922)),f935(x104822,a922),x104821),f334(f8(f935(x104823,a922),a922,x104822),f92(x104823))),f334(f334(f7(x104821,f935(x104822,f935(x104823,a922)),f935(x104822,f935(x104823,a922))),f334(f334(f8(f935(x104822,f935(f935(x104823,a922),f935(x104823,a922))),f935(f935(x104822,f935(x104823,a922)),f935(x104822,f935(x104823,a922))),x104821),f18(x104822,f935(x104823,a922),f935(x104823,a922))),f334(f334(f8(f935(x104822,f935(x104823,f935(a922,a922))),f935(x104822,f935(f935(x104823,a922),f935(x104823,a922))),x104821),f334(f8(f935(x104823,f935(a922,a922)),f935(f935(x104823,a922),f935(x104823,a922)),x104822),f18(x104823,a922,a922))),f334(f334(f8(f935(x104822,f935(x104823,a922)),f935(x104822,f935(x104823,f935(a922,a922))),x104821),f334(f8(f935(x104823,a922),f935(x104823,f935(a922,a922)),x104822),f334(f8(a922,f935(a922,a922),x104823),a332))),f334(f334(f7(x104821,f935(x104822,f935(x104823,x104821)),f935(x104822,f935(x104823,a922))),f334(f334(f8(f935(f935(x104823,x104821),f935(x104823,a922)),f935(f935(x104822,f935(x104823,x104821)),f935(x104822,f935(x104823,a922))),x104821),f8(f935(x104823,x104821),f935(x104823,a922),x104822)),f334(f334(f8(f935(x104821,a922),f935(f935(x104823,x104821),f935(x104823,a922)),x104821),f8(x104821,a922,x104823)),a331))),f334(f334(f7(x104822,f935(x104823,x104821),f935(x104823,x104821)),f334(f334(f8(f935(x104821,x104821),f935(f935(x104823,x104821),f935(x104823,x104821)),x104822),f8(x104821,x104821,x104823)),f334(f334(f8(x104821,f935(x104821,x104821),x104822),f87(x104821)),x104824))),x104825)))))),f334(f334(f7(x104822,f935(x104823,a922),f935(x104823,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x104823,a922),f935(x104823,a922)),x104822),f8(a922,a922,x104823)),f334(f334(f8(a922,f935(a922,a922),x104822),a332),f334(f334(f7(x104822,f935(x104822,a922),a922),f336(x104822)),x104826)))),f334(f334(f7(x104823,f935(x104823,a922),a922),f336(x104823)),x104827))))))),f334(f334(f87(x104821),f334(f334(f6(x104822,x104821),x104824),x104826)),f334(f334(f6(x104823,x104821),x104825),x104827))) % 188.18/188.26 [9689]~P28(x96891,x96893,x96895,x96896,x96898)+~P28(x96893,x96892,x96894,x96898,x96897)+P28(x96891,x96892,f334(f78(x96893,x96892,x96891,x96894),x96895),x96896,x96897) % 188.18/188.26 [9722]P28(x97221,x97222,x97223,x97224,x97225)+~P28(x97226,x97221,x97227,x97228,x97224)+~P28(x97226,x97222,f334(f78(x97221,x97222,x97226,x97223),x97227),x97228,x97225) % 188.18/188.26 [9877]~P107(f334(f334(x98774,x98776),x98778))+~P107(f334(f334(x98775,x98778),x98777))+P107(f334(f334(f261(x98771,x98772,x98773,x98774,x98775),x98776),x98777)) % 188.18/188.26 [9452]~P21(x94528,x94521,x94523,x94525)+~P107(f334(f66(x94528),x94526))+E(f334(f78(x94521,x94521,x94522,f334(x94523,x94524)),f334(f78(x94521,x94521,x94522,f334(x94525,x94526)),x94527)),f334(f78(x94521,x94521,x94522,f334(x94525,x94526)),f334(f78(x94521,x94521,x94522,f334(x94523,x94524)),x94527))) % 188.18/188.26 [9862]~P24(x98627,x98622,x98625,x98628,x98626,x98621)+~P107(f334(f66(x98622),x98624))+E(f334(x98621,f334(f334(f316(x98622),x98623),x98624)),f334(f334(x98625,f334(x98626,x98623)),f334(x98621,x98624))) % 188.18/188.26 [9994]~P27(x99942,x99944,x99946,x99948)+~P27(x99941,x99943,x99945,x99947)+P27(f934(x99941,x99942),f934(x99943,x99944),f266(x99941,x99943,x99942,x99944,x99945,x99946),f334(f334(f262(x99941,x99942),x99947),f334(f16(f935(x99942,a922),x99941),x99948))) % 188.18/188.26 [9635]P107(f334(f334(f336(f934(x96351,x96352)),f334(f334(f260(x96351,x96352),x96353),x96354)),f334(f334(f295(x96351,x96355,x96352),x96356),x96357)))+~P107(f334(f334(f336(f934(x96351,x96355)),f334(f334(f260(x96351,x96355),x96353),x96358)),x96356))+~P107(f334(f334(f336(f934(x96355,x96352)),f334(f334(f260(x96355,x96352),x96358),x96354)),x96357)) % 188.18/188.26 [9839]~P107(f334(f334(f242(f935(f934(x98393,x98392),a922)),x98395),f334(f334(f262(x98393,x98392),x98398),f334(f16(f935(x98392,a922),x98393),x98397))))+~P107(f334(f334(f242(f935(f934(x98391,x98393),a922)),x98394),f334(f334(f262(x98391,x98393),x98396),f334(f16(f935(x98393,a922),x98391),x98398))))+P107(f334(f334(f242(f935(f934(x98391,x98392),a922)),f334(f334(f295(x98391,x98393,x98392),x98394),x98395)),f334(f334(f262(x98391,x98392),x98396),f334(f16(f935(x98392,a922),x98391),x98397)))) % 188.18/188.26 [9898]~E(x98983,x98985)+P107(f334(f334(f336(f934(f934(x98981,x98982),f934(x98981,x98982))),f334(f334(f260(f934(x98981,x98982),f934(x98981,x98982)),f334(f334(f260(x98981,x98982),x98983),x98984)),f334(f334(f260(x98981,x98982),x98985),x98986))),f326(x98981,x98982,x98987,x98988)))+~P107(f334(f334(f336(f934(x98982,x98982)),f334(f334(f260(x98982,x98982),x98984),x98986)),x98988)) % 188.18/188.26 [10017]E(x100171,x100172)+~P107(f334(f334(f336(f934(f934(x100173,x100175),f934(x100173,x100175))),f334(f334(f260(f934(x100173,x100175),f934(x100173,x100175)),f334(f334(f260(x100173,x100175),x100171),x100176)),f334(f334(f260(x100173,x100175),x100172),x100177))),f326(x100173,x100175,x100174,x100178)))+P107(f334(f334(f336(f934(x100173,x100173)),f334(f334(f260(x100173,x100173),x100171),x100172)),x100174)) % 188.18/188.26 [10031]~P107(f334(f334(f336(f934(f934(x100311,x100315),f934(x100311,x100315))),f334(f334(f260(f934(x100311,x100315),f934(x100311,x100315)),f334(f334(f260(x100311,x100315),x100312),x100316)),f334(f334(f260(x100311,x100315),x100313),x100317))),f326(x100311,x100315,x100314,x100318)))+P107(f334(f334(f336(f934(x100311,x100311)),f334(f334(f260(x100311,x100311),x100312),x100313)),x100314))+P107(f334(f334(f336(f934(x100315,x100315)),f334(f334(f260(x100315,x100315),x100316),x100317)),x100318)) % 188.18/188.26 [9935]~P25(x99357,x99355,x99351,x99358,x99352,x99354)+~P107(f334(f66(x99355),x99356))+E(f334(f334(x99351,f334(x99352,x99353)),f334(x99354,f334(f334(f23(f935(x99355,a922)),x99356),f334(f334(f316(x99355),x99353),f195(f935(x99355,a922)))))),f334(x99354,f334(f334(f316(x99355),x99353),x99356))) % 188.18/188.26 [9408]~P107(f334(f334(f334(x94085,x94088),x94086),x94087))+~P107(f334(f334(f336(x94081),x94088),x94084))+P107(f334(f334(f334(f334(f44(x94081,f935(x94082,f935(x94083,a922))),x94084),x94085),x94086),x94087)) % 188.18/188.26 [9624]P107(f334(f334(f334(x96241,x96242),x96243),x96244))+~P107(f334(f334(f336(x96245),x96242),x96246))+~P107(f334(f334(f334(f334(f45(x96245,f935(x96247,f935(x96248,a922))),x96246),x96241),x96243),x96244)) % 188.18/188.26 [9832]~P23(x98323,x98322,x98324,x98328,x98321)+~P107(f334(f66(x98322),x98327))+E(f334(f334(x98321,f334(f334(f18(x98322,x98323,x98323),f334(f334(f8(x98323,f935(x98323,x98323),x98322),x98324),x98325)),x98326)),x98327),f334(f334(x98324,f334(f334(x98321,x98325),x98327)),f334(f334(x98321,x98326),x98327))) % 188.18/188.26 [10112]~E(f334(f317(x101122,x101124,x101126),x101128),x1011210)+~E(f334(f317(x101121,x101123,x101125),x101127),x101129)+E(f334(f317(f934(x101121,x101122),f934(x101123,x101124),f266(x101121,x101123,x101122,x101124,x101125,x101126)),f334(f334(f262(x101121,x101122),x101127),f334(f16(f935(x101122,a922),x101121),x101128))),f334(f334(f262(x101123,x101124),x101129),f334(f16(f935(x101124,a922),x101123),x1011210))) % 188.18/188.26 [5122]~P45(x51221,x51222)+~P52(x51221,x51222)+~P53(x51221,x51222)+P9(x51221,x51222) % 188.18/188.26 [5078]~P109(x50782)+~P15(x50782,x50781)+P15(x50782,f121(x50782,x50781))+E(x50781,f120(x50782)) % 188.18/188.26 [5079]~P109(x50792)+~P15(x50792,x50791)+P15(x50792,f721(x50791,x50792))+E(x50791,f120(x50792)) % 188.18/188.26 [5319]~P7(x53192)+E(f10(x53192,x53191),f43(x53192,x53191))+E(x53191,f195(f935(x53192,a922)))+~P107(f334(f66(x53192),x53191)) % 188.18/188.26 [5320]~P7(x53202)+E(f13(x53202,x53201),f42(x53202,x53201))+E(x53201,f195(f935(x53202,a922)))+~P107(f334(f66(x53202),x53201)) % 188.18/188.26 [5477]~P109(x54772)+~P15(x54772,x54771)+E(x54771,f120(x54772))+E(f334(f334(f158(x54772),f740(x54771,x54772)),f721(x54771,x54772)),x54771) % 188.18/188.26 [6291]~P99(x62912)+E(x62911,f195(f935(x62912,a922)))+P107(f334(f334(f242(x62912),f10(x62912,x62911)),f13(x62912,x62911)))+~P107(f334(f66(x62912),x62911)) % 188.18/188.26 [6300]~P42(x63002)+~P42(x63001)+E(x63001,x63002)+~E(f334(f317(a1,a927,a112),x63001),f334(f317(a1,a927,a112),x63002)) % 188.18/188.26 [9267]~P124(x92671)+~P107(f334(f334(f336(x92671),x92672),f117(x92671)))+P107(f334(f334(f243(x92671),f334(f334(f86(x92671),f334(f334(f86(x92671),f84(x92671)),x92672)),x92672)),f2(x92671)))+~P107(f334(f334(f243(x92671),x92672),f2(x92671))) % 188.18/188.26 [9508]~P124(x95081)+~P107(f334(f334(f336(x95081),x95082),f117(x95081)))+~P107(f334(f334(f243(x95081),f334(f334(f86(x95081),f334(f334(f86(x95081),f84(x95081)),x95082)),x95082)),f2(x95081)))+P107(f334(f334(f243(x95081),x95082),f2(x95081))) % 188.18/188.26 [5137]~P116(x51372)+~P148(x51372)+E(x51371,f2(a927))+E(f334(f334(f252(x51372),f2(x51372)),x51371),f2(x51372)) % 188.18/188.26 [5140]~P116(x51401)+~P148(x51401)+~E(x51402,f2(a927))+E(f334(f334(f252(x51401),f2(x51401)),x51402),f84(x51401)) % 188.18/188.26 [5305]~P141(x53052)+E(x53051,f84(x53052))+E(x53051,f334(f85(x53052),f84(x53052)))+~E(f334(f334(f87(x53052),x53051),x53051),f84(x53052)) % 188.18/188.26 [5557]~P89(x55572)+E(x55571,f2(x55572))+E(f88(x55572,x55571),f334(f85(x55572),f84(x55572)))+P107(f334(f334(f243(x55572),f2(x55572)),x55571)) % 188.18/188.26 [5795]~P89(x57952)+E(f88(x57952,x57951),f84(x57952))+E(x57951,f2(x57952))+~P107(f334(f334(f243(x57952),f2(x57952)),x57951)) % 188.18/188.26 [5804]E(x58041,x58042)+~E(f334(f111(a927),x58041),f334(f111(a927),x58042))+P107(f334(a200,f334(f111(a1),x58042)))+P107(f334(a200,f334(f111(a1),x58041))) % 188.18/188.26 [5860]~P93(x58601)+~E(x58602,f2(x58601))+E(f334(f334(f86(x58601),x58602),x58602),f2(x58601))+~P107(f334(f334(f336(x58601),x58602),f117(x58601))) % 188.18/188.26 [5899]E(x58991,f2(a1))+~E(f334(f334(f41(a1),x58992),x58991),f2(a1))+P107(f334(f334(f243(a1),x58991),x58992))+P107(f334(f334(f243(a1),x58992),x58991)) % 188.18/188.26 [5931]E(x59311,f2(a1))+~E(f334(f334(f41(a1),x59312),x59311),f2(a1))+P107(f334(f334(f242(a1),x59312),f2(a1)))+P107(f334(f334(f243(a1),x59312),x59311)) % 188.18/188.26 [5965]E(x59651,f2(a1))+~E(f334(f334(f41(a1),x59652),x59651),f2(a1))+P107(f334(f334(f242(a1),f2(a1)),x59652))+P107(f334(f334(f243(a1),x59651),x59652)) % 188.18/188.26 [6000]~P93(x60002)+E(x60001,f2(x60002))+~E(f334(f334(f86(x60002),x60001),x60001),f2(x60002))+~P107(f334(f334(f336(x60002),x60001),f117(x60002))) % 188.18/188.26 [6062]E(f334(f111(a927),x60621),f334(f111(a927),x60622))+~E(f334(f111(a1),x60622),f2(a1))+P107(f334(a200,f334(f111(a1),x60622)))+~P107(f334(a200,f334(f111(a1),x60621))) % 188.18/188.26 [6093]~E(f334(f111(a927),x60932),f334(f111(a927),x60931))+E(f334(f111(a1),x60931),f2(a1))+P107(f334(a200,f334(f111(a1),x60931)))+~P107(f334(a200,f334(f111(a1),x60932))) % 188.18/188.26 [6103]~P109(x61032)+E(x61031,f195(f935(x61032,a922)))+~P107(f334(f66(x61032),x61031))+P107(f334(f334(f336(x61032),f14(x61032,x61031)),x61031)) % 188.18/188.26 [6104]~P109(x61042)+E(x61041,f195(f935(x61042,a922)))+~P107(f334(f66(x61042),x61041))+P107(f334(f334(f336(x61042),f15(x61042,x61041)),x61041)) % 188.18/188.26 [6268]~P124(x62681)+~P95(x62681)+P107(f334(f334(f242(x62681),f2(x62681)),f334(f111(x62681),x62682)))+~P107(f334(f334(f242(a1),a89),x62682)) % 188.18/188.26 [6269]~P124(x62691)+~P95(x62691)+P107(f334(f334(f243(x62691),f2(x62691)),f334(f111(x62691),x62692)))+~P107(f334(f334(f243(a1),a89),x62692)) % 188.18/188.26 [6290]~P124(x62901)+~P95(x62901)+E(f334(f81(x62901),f334(f111(x62901),x62902)),f334(f111(x62901),x62902))+P107(f334(f334(f243(x62901),f334(f111(x62901),x62902)),f2(x62901))) % 188.18/188.26 [6324]E(x63241,x63242)+~E(f334(a112,x63241),f334(a112,x63242))+~P107(f334(f334(f242(a1),f2(a1)),x63242))+~P107(f334(f334(f242(a1),f2(a1)),x63241)) % 188.18/188.26 [6515]~P95(x65152)+~P124(x65152)+~P107(f334(f334(f242(x65152),f2(x65152)),f334(f111(x65152),x65151)))+P107(f334(f334(f242(a1),a89),x65151)) % 188.18/188.26 [6516]~P95(x65162)+~P124(x65162)+~P107(f334(f334(f243(x65162),f2(x65162)),f334(f111(x65162),x65161)))+P107(f334(f334(f243(a1),a89),x65161)) % 188.18/188.26 [6521]~P124(x65211)+~P95(x65211)+P107(f334(f334(f242(x65211),f334(f111(x65211),x65212)),f2(x65211)))+~P107(f334(f334(f242(a1),x65212),a89)) % 188.18/188.26 [6522]~P124(x65221)+~P95(x65221)+P107(f334(f334(f243(x65221),f334(f111(x65221),x65222)),f2(x65221)))+~P107(f334(f334(f243(a1),x65222),a89)) % 188.18/188.26 [6835]~P95(x68352)+~P124(x68352)+~P107(f334(f334(f242(x68352),f334(f111(x68352),x68351)),f2(x68352)))+P107(f334(f334(f242(a1),x68351),a89)) % 188.18/188.26 [6836]~P95(x68362)+~P124(x68362)+~P107(f334(f334(f243(x68362),f334(f111(x68362),x68361)),f2(x68362)))+P107(f334(f334(f243(a1),x68361),a89)) % 188.18/188.26 [6926]~P124(x69261)+~P95(x69261)+E(f334(f81(x69261),f334(f111(x69261),x69262)),f334(f85(x69261),f334(f111(x69261),x69262)))+~P107(f334(f334(f243(x69261),f334(f111(x69261),x69262)),f2(x69261))) % 188.18/188.26 [6944]E(f334(f111(a927),x69441),f334(f111(a927),x69442))+~E(f334(f111(a1),x69442),f2(a1))+~P107(f334(f334(f242(a1),f334(f111(a1),x69441)),f2(a1)))+~P107(f334(a200,f334(f111(a1),x69441))) % 188.18/188.26 [7793]~P109(x77932)+E(x77931,f195(f935(x77932,a922)))+~P107(f334(f66(x77932),x77931))+P107(f334(f334(f242(x77932),f11(x77932,f246(x77932),x77931)),f12(x77932,f241(x77932),x77931))) % 188.18/188.26 [8104]~P42(x81042)+~P8(x81041)+P107(f334(f334(f336(a1),x81041),x81042))+~P107(f334(f334(f336(a927),f334(a112,x81041)),f334(f317(a1,a927,a112),x81042))) % 188.18/188.26 [6099]~P142(x60992)+E(x60991,f2(a1))+E(f334(f85(x60992),f334(f110(x60992),f334(f85(a1),x60991))),f334(f110(x60992),x60991))+~P107(f334(f334(f243(a1),x60991),f2(a1))) % 188.18/188.26 [6504]~P77(x65042)+E(x65041,f195(f935(x65042,a922)))+E(f15(x65042,f334(f317(x65042,x65042,f85(x65042)),x65041)),f334(f85(x65042),f14(x65042,x65041)))+~P107(f334(f66(x65042),x65041)) % 188.18/188.26 [6505]~P77(x65052)+E(x65051,f195(f935(x65052,a922)))+E(f14(x65052,f334(f317(x65052,x65052,f85(x65052)),x65051)),f334(f85(x65052),f15(x65052,x65051)))+~P107(f334(f66(x65052),x65051)) % 188.18/188.26 [6626]E(x66261,f2(a1))+E(f334(a56,f55(f334(f85(a1),x66261),f334(f85(a1),x66262))),f51(x66261,x66262))+P107(f334(f334(f242(a1),f2(a1)),x66262))+~P107(f334(f334(f242(a1),f2(a1)),x66261)) % 188.18/188.26 [8868]~P42(x88682)+~P42(x88681)+P107(f334(f334(f243(f935(a927,a922)),f334(f317(a1,a927,a112),x88681)),f334(f317(a1,a927,a112),x88682)))+~P107(f334(f334(f243(f935(a1,a922)),x88681),x88682)) % 188.18/188.26 [9104]~E(f743(x91042,x91041),f744(x91042,x91041))+~P107(f334(f144(x91041),f745(x91042,x91041)))+~P107(f334(f144(f928(x91041)),x91042))+P107(f334(f144(x91041),f334(f149(f928(x91041),f928(x91041),f141(x91041),f120(x91041)),x91042))) % 188.18/188.26 [9192]~P42(x91922)+~P42(x91921)+~P107(f334(f334(f242(f935(a927,a922)),f334(f317(a1,a927,a112),x91921)),f334(f317(a1,a927,a112),x91922)))+P107(f334(f334(f242(f935(a1,a922)),x91921),x91922)) % 188.18/188.26 [9193]~P42(x91932)+~P42(x91931)+~P107(f334(f334(f243(f935(a927,a922)),f334(f317(a1,a927,a112),x91931)),f334(f317(a1,a927,a112),x91932)))+P107(f334(f334(f243(f935(a1,a922)),x91931),x91932)) % 188.18/188.26 [9199]~E(f743(x91992,x91991),f744(x91992,x91991))+~P107(f334(f144(f928(x91991)),x91992))+P107(f334(f144(x91991),f334(f149(f928(x91991),f928(x91991),f141(x91991),f120(x91991)),x91992)))+P107(f334(f334(f336(f928(x91991)),f745(x91992,x91991)),f334(f179(f928(x91991)),x91992))) % 188.18/188.26 [9239]~P107(f334(f144(x92391),f745(x92392,x92391)))+~P107(f334(f144(f928(x92391)),x92392))+P107(f334(f144(x92391),f334(f149(f928(x92391),f928(x92391),f141(x92391),f120(x92391)),x92392)))+P107(f334(f334(f336(f928(x92391)),f744(x92392,x92391)),f334(f179(f928(x92391)),x92392))) % 188.18/188.26 [9240]~P107(f334(f144(x92401),f745(x92402,x92401)))+~P107(f334(f144(f928(x92401)),x92402))+P107(f334(f144(x92401),f334(f149(f928(x92401),f928(x92401),f141(x92401),f120(x92401)),x92402)))+P107(f334(f334(f336(f928(x92401)),f743(x92402,x92401)),f334(f179(f928(x92401)),x92402))) % 188.18/188.26 [9306]~P107(f334(f144(f928(x93061)),x93062))+P107(f334(f144(x93061),f334(f149(f928(x93061),f928(x93061),f141(x93061),f120(x93061)),x93062)))+P107(f334(f334(f336(f928(x93061)),f744(x93062,x93061)),f334(f179(f928(x93061)),x93062)))+P107(f334(f334(f336(f928(x93061)),f745(x93062,x93061)),f334(f179(f928(x93061)),x93062))) % 188.18/188.26 [9307]~P107(f334(f144(f928(x93071)),x93072))+P107(f334(f144(x93071),f334(f149(f928(x93071),f928(x93071),f141(x93071),f120(x93071)),x93072)))+P107(f334(f334(f336(f928(x93071)),f743(x93072,x93071)),f334(f179(f928(x93071)),x93072)))+P107(f334(f334(f336(f928(x93071)),f745(x93072,x93071)),f334(f179(f928(x93071)),x93072))) % 188.18/188.26 [9321]~E(f334(f334(f109(f935(x93211,a922)),f334(f179(x93211),f744(x93212,x93211))),f334(f179(x93211),f743(x93212,x93211))),f195(f935(x93211,a922)))+~P107(f334(f144(x93211),f745(x93212,x93211)))+~P107(f334(f144(f928(x93211)),x93212))+P107(f334(f144(x93211),f334(f149(f928(x93211),f928(x93211),f141(x93211),f120(x93211)),x93212))) % 188.18/188.26 [9390]~E(f334(f334(f109(f935(x93901,a922)),f334(f179(x93901),f744(x93902,x93901))),f334(f179(x93901),f743(x93902,x93901))),f195(f935(x93901,a922)))+~P107(f334(f144(f928(x93901)),x93902))+P107(f334(f144(x93901),f334(f149(f928(x93901),f928(x93901),f141(x93901),f120(x93901)),x93902)))+P107(f334(f334(f336(f928(x93901)),f745(x93902,x93901)),f334(f179(f928(x93901)),x93902))) % 188.18/188.26 [9660]E(x96601,f2(a1))+E(x96602,f2(a1))+E(f334(f334(f94(a1,f934(a1,a1)),f334(f334(a226,x96602),x96601)),f334(f334(f18(a1,a1,f934(a1,a1)),f334(f334(f8(a1,f935(a1,f934(a1,a1)),a1),f260(a1,a1)),f334(f41(a1),x96602))),f334(f41(a1),x96601))),f224(x96602,x96601))+P107(f334(f334(f243(a1),x96601),f2(a1))) % 188.18/188.26 [8547]~P95(x85472)+~P124(x85472)+~P107(f334(f334(f242(x85472),f334(f111(x85472),x85471)),f84(x85472)))+P107(f334(f334(f242(a1),x85471),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))) % 188.18/188.26 [8548]~P95(x85482)+~P124(x85482)+~P107(f334(f334(f243(x85482),f334(f111(x85482),x85481)),f84(x85482)))+P107(f334(f334(f243(a1),x85481),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))) % 188.18/188.26 [8826]~P124(x88261)+~P95(x88261)+P107(f334(f334(f242(x88261),f334(f111(x88261),x88262)),f84(x88261)))+~P107(f334(f334(f242(a1),x88262),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))) % 188.18/188.26 [8827]~P124(x88271)+~P95(x88271)+P107(f334(f334(f243(x88271),f334(f111(x88271),x88272)),f84(x88271)))+~P107(f334(f334(f243(a1),x88272),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))) % 188.18/188.26 [9029]~P95(x90292)+~P124(x90292)+~P107(f334(f334(f242(x90292),f84(x90292)),f334(f111(x90292),x90291)))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),x90291)) % 188.18/188.26 [9030]~P95(x90302)+~P124(x90302)+~P107(f334(f334(f243(x90302),f84(x90302)),f334(f111(x90302),x90301)))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),x90301)) % 188.18/188.26 [9379]~P124(x93791)+~P95(x93791)+P107(f334(f334(f242(x93791),f84(x93791)),f334(f111(x93791),x93792)))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),x93792)) % 188.18/188.26 [9380]~P124(x93801)+~P95(x93801)+P107(f334(f334(f243(x93801),f84(x93801)),f334(f111(x93801),x93802)))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89)),x93802)) % 188.18/188.26 [9506]~P93(x95061)+~P95(x95061)+~P30(x95061,f334(f111(x95061),x95062))+P30(x95061,f334(f111(x95061),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x95062)),x95062)),a104))) % 188.18/188.26 [9725]~P93(x97251)+~P95(x97251)+P30(x97251,f334(f111(x97251),x97252))+~P30(x97251,f334(f111(x97251),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),x97252)),x97252)),a104))) % 188.18/188.26 [10221]~P141(x102212)+E(x102211,f84(x102212))+E(x102211,f334(f85(x102212),f84(x102212)))+~E(f334(f334(f252(x102212),x102211),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f84(x102212)) % 188.18/188.26 [10306]~P95(x103061)+~P67(x103061)+~P107(f334(f334(f243(x103061),f2(x103061)),x103062))+P107(f334(f334(f243(x103061),f2(x103061)),f334(f334(f296(x103061),x103062),f334(f111(x103061),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.26 [10350]~P95(x103501)+~P67(x103501)+P107(f334(f334(f243(x103501),f2(x103501)),x103502))+~P107(f334(f334(f243(x103501),f2(x103501)),f334(f334(f296(x103501),x103502),f334(f111(x103501),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.26 [10440]~P142(x104402)+E(x104401,f2(a1))+P107(f334(f334(f243(a1),x104401),f2(a1)))+E(f334(f334(f265(a1,a1,x104402),f334(f334(f7(a1,f935(a1,f935(x104402,x104402)),f935(a1,x104402)),f334(f334(f8(f935(f935(x104402,x104402),x104402),f935(f935(a1,f935(x104402,x104402)),f935(a1,x104402)),a1),f8(f935(x104402,x104402),x104402,a1)),f334(f334(f8(x104402,f935(f935(x104402,x104402),x104402),a1),f94(x104402,x104402)),f110(x104402)))),f334(f334(f7(a1,f935(x104402,x104402),f935(x104402,x104402)),f334(f334(f8(f935(x104402,f935(x104402,x104402)),f935(f935(x104402,x104402),f935(x104402,x104402)),a1),f18(x104402,x104402,x104402)),f334(f334(f7(a1,f935(x104402,x104402),f935(x104402,f935(x104402,x104402))),f334(f334(f8(f935(x104402,f935(x104402,x104402)),f935(f935(x104402,x104402),f935(x104402,f935(x104402,x104402))),a1),f8(x104402,f935(x104402,x104402),x104402)),f334(f334(f8(a922,f935(x104402,f935(x104402,x104402)),a1),f103(x104402)),f334(f334(f7(a1,a1,a922),a331),f2(a1))))),f334(f334(f18(x104402,x104402,x104402),f86(x104402)),f5(x104402))))),f334(f334(f7(x104402,x104402,x104402),f334(f334(f8(x104402,f935(x104402,x104402),x104402),f86(x104402)),f334(f334(f18(x104402,x104402,x104402),f86(x104402)),f5(x104402)))),f84(x104402))))),f51(x104401,f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f110(x104402),x104401)) % 188.18/188.26 [5566]~P40(x55661,x55663)+~P54(x55661,x55663)+~P55(x55661,x55662,x55663)+P10(x55661,x55662,x55663) % 188.18/188.26 [5106]~P93(x51063)+~P95(x51063)+E(x51061,x51062)+~E(f334(f111(x51063),x51061),f334(f111(x51063),x51062)) % 188.18/188.26 [5576]~P52(x55761,x55762)+~P53(x55761,x55762)+P17(x55761,x55762)+~P107(f334(f334(x55762,x55763),x55763)) % 188.18/188.26 [6077]P17(x60772,x60771)+E(f334(x60771,f822(x60771)),f334(x60771,f823(x60771)))+P107(f334(f334(x60771,f822(x60771)),f823(x60771)))+~P107(f334(f334(x60771,x60773),x60773)) % 188.18/188.26 [6278]~P107(f334(x62781,x62782))+~P107(f334(x62781,x62783))+~P107(f334(f334(f242(a927),x62783),f889(x62782,x62781)))+P107(f334(x62781,f2(a927))) % 188.18/188.26 [6343]P17(x63431,x63432)+P107(f334(f334(x63432,f822(x63432)),f822(x63432)))+P107(f334(f334(x63432,f822(x63432)),f823(x63432)))+~P107(f334(f334(x63432,x63433),x63433)) % 188.18/188.26 [6344]P17(x63441,x63442)+P107(f334(f334(x63442,f822(x63442)),f823(x63442)))+P107(f334(f334(x63442,f823(x63442)),f823(x63442)))+~P107(f334(f334(x63442,x63443),x63443)) % 188.18/188.26 [6694]P150(x66942,x66943,x66941)+E(x66941,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f867(x66941,x66943,x66942)))+P107(f334(f334(f243(a1),x66941),f2(a1))) % 188.18/188.26 [6695]P149(x66952,x66953,x66951)+E(x66951,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f876(x66951,x66953,x66952)))+P107(f334(f334(f243(a1),x66951),f2(a1))) % 188.18/188.26 [6816]P149(x68161,x68162,x68163)+~P107(f334(x68161,x68162))+P107(f334(f334(f242(a1),f2(a1)),f876(x68163,x68162,x68161)))+P107(f334(f334(f243(a1),x68163),f2(a1))) % 188.18/188.26 [6841]P150(x68411,x68412,x68413)+P107(f334(f334(f242(a1),f2(a1)),f867(x68413,x68412,x68411)))+~P107(f334(x68411,f2(a1)))+P107(f334(f334(f243(a1),x68413),f2(a1))) % 188.18/188.26 [6869]P150(x68692,x68693,x68691)+E(x68691,f2(a1))+~P107(f334(x68692,f868(x68691,x68693,x68692)))+P107(f334(f334(f243(a1),x68691),f2(a1))) % 188.18/188.26 [6870]P149(x68702,x68703,x68701)+E(x68701,f2(a1))+~P107(f334(x68702,f876(x68701,x68703,x68702)))+P107(f334(f334(f243(a1),x68701),f2(a1))) % 188.18/188.26 [6968]~P109(x69681)+~P7(x69681)+~P107(f334(f334(f243(x69681),x69682),f42(x69681,x69683)))+P107(f334(f334(f243(x69681),x69682),f513(x69683,x69682,x69681))) % 188.18/188.26 [6977]P149(x69771,x69772,x69773)+~P107(f334(x69771,x69772))+~P107(f334(x69771,f876(x69773,x69772,x69771)))+P107(f334(f334(f243(a1),x69773),f2(a1))) % 188.18/188.26 [7004]P150(x70041,x70042,x70043)+~P107(f334(x70041,f868(x70043,x70042,x70041)))+~P107(f334(x70041,f2(a1)))+P107(f334(f334(f243(a1),x70043),f2(a1))) % 188.18/188.26 [7248]P150(x72482,x72483,x72481)+E(x72481,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f867(x72481,x72483,x72482)))+P107(f334(f334(f243(a1),x72481),f866(x72481,x72483,x72482))) % 188.18/188.26 [7249]P149(x72492,x72493,x72491)+E(x72491,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f876(x72491,x72493,x72492)))+P107(f334(f334(f243(a1),x72491),f875(x72491,x72493,x72492))) % 188.18/188.26 [7367]P149(x73671,x73672,x73673)+~P107(f334(x73671,x73672))+P107(f334(f334(f242(a1),f2(a1)),f876(x73673,x73672,x73671)))+P107(f334(f334(f243(a1),x73673),f875(x73673,x73672,x73671))) % 188.18/188.26 [7386]P150(x73861,x73862,x73863)+P107(f334(f334(f242(a1),f2(a1)),f867(x73863,x73862,x73861)))+P107(f334(f334(f243(a1),x73863),f866(x73863,x73862,x73861)))+~P107(f334(x73861,f2(a1))) % 188.18/188.26 [7418]P150(x74182,x74183,x74181)+E(x74181,f2(a1))+~P107(f334(x74182,f868(x74181,x74183,x74182)))+P107(f334(f334(f243(a1),x74181),f866(x74181,x74183,x74182))) % 188.18/188.26 [7419]P149(x74192,x74193,x74191)+E(x74191,f2(a1))+~P107(f334(x74192,f876(x74191,x74193,x74192)))+P107(f334(f334(f243(a1),x74191),f875(x74191,x74193,x74192))) % 188.18/188.26 [7463]P150(x74632,x74633,x74631)+E(x74631,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f867(x74631,x74633,x74632)))+~P107(f334(x74632,f873(x74631,x74633,x74632))) % 188.18/188.26 [7464]P149(x74642,x74643,x74641)+E(x74641,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f876(x74641,x74643,x74642)))+~P107(f334(x74642,f875(x74641,x74643,x74642))) % 188.18/188.26 [7557]P149(x75571,x75572,x75573)+~P107(f334(x75571,x75572))+~P107(f334(x75571,f876(x75573,x75572,x75571)))+P107(f334(f334(f243(a1),x75573),f875(x75573,x75572,x75571))) % 188.18/188.26 [7566]P150(x75661,x75662,x75663)+~P107(f334(x75661,f868(x75663,x75662,x75661)))+P107(f334(f334(f243(a1),x75663),f866(x75663,x75662,x75661)))+~P107(f334(x75661,f2(a1))) % 188.18/188.26 [7569]P149(x75691,x75692,x75693)+~P107(f334(x75691,x75692))+P107(f334(f334(f242(a1),f2(a1)),f876(x75693,x75692,x75691)))+~P107(f334(x75691,f875(x75693,x75692,x75691))) % 188.18/188.26 [7585]P150(x75851,x75852,x75853)+P107(f334(f334(f242(a1),f2(a1)),f867(x75853,x75852,x75851)))+~P107(f334(x75851,f873(x75853,x75852,x75851)))+~P107(f334(x75851,f2(a1))) % 188.18/188.26 [7605]P150(x76052,x76053,x76051)+E(x76051,f2(a1))+~P107(f334(x76052,f868(x76051,x76053,x76052)))+~P107(f334(x76052,f873(x76051,x76053,x76052))) % 188.18/188.26 [7606]P149(x76062,x76063,x76061)+E(x76061,f2(a1))+~P107(f334(x76062,f876(x76061,x76063,x76062)))+~P107(f334(x76062,f875(x76061,x76063,x76062))) % 188.18/188.26 [7692]P149(x76921,x76922,x76923)+~P107(f334(x76921,x76922))+~P107(f334(x76921,f876(x76923,x76922,x76921)))+~P107(f334(x76921,f875(x76923,x76922,x76921))) % 188.18/188.26 [7709]P150(x77091,x77092,x77093)+~P107(f334(x77091,f868(x77093,x77092,x77091)))+~P107(f334(x77091,f873(x77093,x77092,x77091)))+~P107(f334(x77091,f2(a1))) % 188.18/188.26 [7753]P150(x77532,x77533,x77531)+E(x77531,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f867(x77531,x77533,x77532)))+P107(f334(f334(f242(a1),f866(x77531,x77533,x77532)),f2(a1))) % 188.18/188.26 [7754]P149(x77542,x77543,x77541)+E(x77541,f2(a1))+P107(f334(f334(f242(a1),f2(a1)),f876(x77541,x77543,x77542)))+P107(f334(f334(f242(a1),f875(x77541,x77543,x77542)),f2(a1))) % 188.18/188.26 [7755]~P142(x77551)+~P107(f334(f334(f336(x77551),x77553),f117(x77551)))+~P107(f334(f334(f336(x77551),x77552),f117(x77551)))+P107(f334(f334(f336(x77551),f334(f334(f23(x77551),x77552),x77553)),f117(x77551))) % 188.18/188.26 [7756]~P142(x77561)+~P107(f334(f334(f336(x77561),x77563),f117(x77561)))+~P107(f334(f334(f336(x77561),x77562),f117(x77561)))+P107(f334(f334(f336(x77561),f334(f334(f87(x77561),x77562),x77563)),f117(x77561))) % 188.18/188.26 [7757]~P147(x77571)+~P107(f334(f334(f336(x77571),x77573),f193(x77571)))+~P107(f334(f334(f336(x77571),x77572),f193(x77571)))+P107(f334(f334(f336(x77571),f334(f334(f87(x77571),x77572),x77573)),f193(x77571))) % 188.18/188.26 [7758]~P142(x77581)+~P107(f334(f334(f336(x77581),x77583),f117(x77581)))+~P107(f334(f334(f336(x77581),x77582),f117(x77581)))+P107(f334(f334(f336(x77581),f334(f334(f86(x77581),x77582),x77583)),f117(x77581))) % 188.18/188.26 [7759]~P147(x77591)+~P107(f334(f334(f336(x77591),x77593),f193(x77591)))+~P107(f334(f334(f336(x77591),x77592),f193(x77591)))+P107(f334(f334(f336(x77591),f334(f334(f86(x77591),x77592),x77593)),f193(x77591))) % 188.18/188.26 [7760]~P88(x77601)+~P107(f334(f334(f242(x77601),x77603),f2(x77601)))+~P107(f334(f334(f242(x77601),x77602),f2(x77601)))+P107(f334(f334(f242(x77601),f334(f334(f86(x77601),x77602),x77603)),f2(x77601))) % 188.18/188.26 [7761]~P88(x77611)+~P107(f334(f334(f242(x77611),x77613),f2(x77611)))+~P107(f334(f334(f243(x77611),x77612),f2(x77611)))+P107(f334(f334(f243(x77611),f334(f334(f86(x77611),x77612),x77613)),f2(x77611))) % 188.18/188.26 [7762]~P88(x77621)+~P107(f334(f334(f242(x77621),x77622),f2(x77621)))+~P107(f334(f334(f243(x77621),x77623),f2(x77621)))+P107(f334(f334(f243(x77621),f334(f334(f86(x77621),x77622),x77623)),f2(x77621))) % 188.18/188.26 [7763]~P88(x77631)+~P107(f334(f334(f243(x77631),x77633),f2(x77631)))+~P107(f334(f334(f243(x77631),x77632),f2(x77631)))+P107(f334(f334(f243(x77631),f334(f334(f86(x77631),x77632),x77633)),f2(x77631))) % 188.18/188.26 [7789]P150(x77893,x77892,x77891)+E(x77891,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x77891),f868(x77891,x77892,x77893))),f867(x77891,x77892,x77893)),x77892)+P107(f334(f334(f243(a1),x77891),f2(a1))) % 188.18/188.26 [7790]P149(x77903,x77902,x77901)+E(x77901,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x77901),f877(x77901,x77902,x77903))),f876(x77901,x77902,x77903)),x77902)+P107(f334(f334(f243(a1),x77901),f2(a1))) % 188.18/188.26 [7869]P149(x78691,x78692,x78693)+~P107(f334(x78691,x78692))+P107(f334(f334(f242(a1),f2(a1)),f876(x78693,x78692,x78691)))+P107(f334(f334(f242(a1),f875(x78693,x78692,x78691)),f2(a1))) % 188.18/188.26 [7898]P150(x78981,x78982,x78983)+P107(f334(f334(f242(a1),f2(a1)),f867(x78983,x78982,x78981)))+~P107(f334(x78981,f2(a1)))+P107(f334(f334(f242(a1),f866(x78983,x78982,x78981)),f2(a1))) % 188.18/188.26 [7907]P149(x79073,x79072,x79071)+~P107(f334(x79073,x79072))+E(f334(f334(f86(a1),f334(f334(f87(a1),x79071),f877(x79071,x79072,x79073))),f876(x79071,x79072,x79073)),x79072)+P107(f334(f334(f243(a1),x79071),f2(a1))) % 188.18/188.26 [7913]P150(x79132,x79133,x79131)+E(x79131,f2(a1))+~P107(f334(x79132,f868(x79131,x79133,x79132)))+P107(f334(f334(f242(a1),f866(x79131,x79133,x79132)),f2(a1))) % 188.18/188.26 [7914]P149(x79142,x79143,x79141)+E(x79141,f2(a1))+~P107(f334(x79142,f876(x79141,x79143,x79142)))+P107(f334(f334(f242(a1),f875(x79141,x79143,x79142)),f2(a1))) % 188.18/188.26 [7918]P150(x79183,x79182,x79181)+E(f334(f334(f86(a1),f334(f334(f87(a1),x79181),f868(x79181,x79182,x79183))),f867(x79181,x79182,x79183)),x79182)+~P107(f334(x79183,f2(a1)))+P107(f334(f334(f243(a1),x79181),f2(a1))) % 188.18/188.26 [7976]P149(x79761,x79762,x79763)+~P107(f334(x79761,x79762))+~P107(f334(x79761,f876(x79763,x79762,x79761)))+P107(f334(f334(f242(a1),f875(x79763,x79762,x79761)),f2(a1))) % 188.18/188.26 [7981]P150(x79811,x79812,x79813)+~P107(f334(x79811,f868(x79813,x79812,x79811)))+~P107(f334(x79811,f2(a1)))+P107(f334(f334(f242(a1),f866(x79813,x79812,x79811)),f2(a1))) % 188.18/188.26 [8050]~P129(x80501)+~P107(f334(f334(f242(x80501),f334(f334(f87(x80501),x80503),x80502)),f2(x80501)))+P107(f334(f334(f242(x80501),x80502),f2(x80501)))+P107(f334(f334(f242(x80501),x80503),f2(x80501))) % 188.18/188.26 [8051]~P67(x80511)+~P107(f334(f334(f242(x80511),f334(f334(f296(x80511),x80513),x80512)),f2(x80511)))+P107(f334(f334(f242(x80511),x80512),f2(x80511)))+P107(f334(f334(f242(x80511),x80513),f2(x80511))) % 188.18/188.26 [8052]~P67(x80521)+~P107(f334(f334(f243(x80521),f334(f334(f296(x80521),x80523),x80522)),f2(x80521)))+P107(f334(f334(f243(x80521),x80522),f2(x80521)))+P107(f334(f334(f243(x80521),x80523),f2(x80521))) % 188.18/188.26 [8156]P150(x81563,x81562,x81561)+E(x81561,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x81561),f868(x81561,x81562,x81563))),f867(x81561,x81562,x81563)),x81562)+P107(f334(f334(f243(a1),x81561),f866(x81561,x81562,x81563))) % 188.18/188.26 [8157]P149(x81573,x81572,x81571)+E(x81571,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x81571),f877(x81571,x81572,x81573))),f876(x81571,x81572,x81573)),x81572)+P107(f334(f334(f243(a1),x81571),f875(x81571,x81572,x81573))) % 188.18/188.26 [8170]P150(x81703,x81702,x81701)+E(x81701,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x81701),f873(x81701,x81702,x81703))),f866(x81701,x81702,x81703)),x81702)+P107(f334(f334(f242(a1),f2(a1)),f867(x81701,x81702,x81703))) % 188.18/188.26 [8171]P149(x81713,x81712,x81711)+E(x81711,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x81711),f878(x81711,x81712,x81713))),f875(x81711,x81712,x81713)),x81712)+P107(f334(f334(f242(a1),f2(a1)),f876(x81711,x81712,x81713))) % 188.18/188.26 [8211]P149(x82113,x82112,x82111)+~P107(f334(x82113,x82112))+E(f334(f334(f86(a1),f334(f334(f87(a1),x82111),f877(x82111,x82112,x82113))),f876(x82111,x82112,x82113)),x82112)+P107(f334(f334(f243(a1),x82111),f875(x82111,x82112,x82113))) % 188.18/188.26 [8220]P150(x82203,x82202,x82201)+E(f334(f334(f86(a1),f334(f334(f87(a1),x82201),f868(x82201,x82202,x82203))),f867(x82201,x82202,x82203)),x82202)+P107(f334(f334(f243(a1),x82201),f866(x82201,x82202,x82203)))+~P107(f334(x82203,f2(a1))) % 188.18/188.26 [8226]P149(x82263,x82262,x82261)+~P107(f334(x82263,x82262))+E(f334(f334(f86(a1),f334(f334(f87(a1),x82261),f878(x82261,x82262,x82263))),f875(x82261,x82262,x82263)),x82262)+P107(f334(f334(f242(a1),f2(a1)),f876(x82261,x82262,x82263))) % 188.18/188.26 [8232]P150(x82323,x82322,x82321)+E(f334(f334(f86(a1),f334(f334(f87(a1),x82321),f873(x82321,x82322,x82323))),f866(x82321,x82322,x82323)),x82322)+P107(f334(f334(f242(a1),f2(a1)),f867(x82321,x82322,x82323)))+~P107(f334(x82323,f2(a1))) % 188.18/188.26 [8243]P150(x82433,x82432,x82431)+E(x82431,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x82431),f868(x82431,x82432,x82433))),f867(x82431,x82432,x82433)),x82432)+~P107(f334(x82433,f873(x82431,x82432,x82433))) % 188.18/188.26 [8244]P149(x82443,x82442,x82441)+E(x82441,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x82441),f877(x82441,x82442,x82443))),f876(x82441,x82442,x82443)),x82442)+~P107(f334(x82443,f875(x82441,x82442,x82443))) % 188.18/188.26 [8245]P150(x82453,x82452,x82451)+E(x82451,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x82451),f873(x82451,x82452,x82453))),f866(x82451,x82452,x82453)),x82452)+~P107(f334(x82453,f868(x82451,x82452,x82453))) % 188.18/188.26 [8246]P149(x82463,x82462,x82461)+E(x82461,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x82461),f878(x82461,x82462,x82463))),f875(x82461,x82462,x82463)),x82462)+~P107(f334(x82463,f876(x82461,x82462,x82463))) % 188.18/188.26 [8307]P149(x83073,x83072,x83071)+~P107(f334(x83073,x83072))+E(f334(f334(f86(a1),f334(f334(f87(a1),x83071),f877(x83071,x83072,x83073))),f876(x83071,x83072,x83073)),x83072)+~P107(f334(x83073,f875(x83071,x83072,x83073))) % 188.18/188.26 [8308]P149(x83083,x83082,x83081)+~P107(f334(x83083,x83082))+E(f334(f334(f86(a1),f334(f334(f87(a1),x83081),f878(x83081,x83082,x83083))),f875(x83081,x83082,x83083)),x83082)+~P107(f334(x83083,f876(x83081,x83082,x83083))) % 188.18/188.26 [8319]P150(x83193,x83192,x83191)+E(f334(f334(f86(a1),f334(f334(f87(a1),x83191),f868(x83191,x83192,x83193))),f867(x83191,x83192,x83193)),x83192)+~P107(f334(x83193,f873(x83191,x83192,x83193)))+~P107(f334(x83193,f2(a1))) % 188.18/188.26 [8320]P150(x83203,x83202,x83201)+E(f334(f334(f86(a1),f334(f334(f87(a1),x83201),f873(x83201,x83202,x83203))),f866(x83201,x83202,x83203)),x83202)+~P107(f334(x83203,f868(x83201,x83202,x83203)))+~P107(f334(x83203,f2(a1))) % 188.18/188.26 [8417]P150(x84173,x84172,x84171)+E(x84171,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x84171),f868(x84171,x84172,x84173))),f867(x84171,x84172,x84173)),x84172)+P107(f334(f334(f242(a1),f866(x84171,x84172,x84173)),f2(a1))) % 188.18/188.26 [8418]P149(x84183,x84182,x84181)+E(x84181,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x84181),f877(x84181,x84182,x84183))),f876(x84181,x84182,x84183)),x84182)+P107(f334(f334(f242(a1),f875(x84181,x84182,x84183)),f2(a1))) % 188.18/188.26 [8455]P149(x84553,x84552,x84551)+~P107(f334(x84553,x84552))+E(f334(f334(f86(a1),f334(f334(f87(a1),x84551),f877(x84551,x84552,x84553))),f876(x84551,x84552,x84553)),x84552)+P107(f334(f334(f242(a1),f875(x84551,x84552,x84553)),f2(a1))) % 188.18/188.26 [8460]P150(x84603,x84602,x84601)+E(f334(f334(f86(a1),f334(f334(f87(a1),x84601),f868(x84601,x84602,x84603))),f867(x84601,x84602,x84603)),x84602)+~P107(f334(x84603,f2(a1)))+P107(f334(f334(f242(a1),f866(x84601,x84602,x84603)),f2(a1))) % 188.18/188.26 [8591]P150(x85913,x85912,x85911)+E(x85911,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x85911),f873(x85911,x85912,x85913))),f866(x85911,x85912,x85913)),x85912)+E(f334(f334(f86(a1),f334(f334(f87(a1),x85911),f868(x85911,x85912,x85913))),f867(x85911,x85912,x85913)),x85912) % 188.18/188.26 [8592]P149(x85923,x85922,x85921)+E(x85921,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x85921),f878(x85921,x85922,x85923))),f875(x85921,x85922,x85923)),x85922)+E(f334(f334(f86(a1),f334(f334(f87(a1),x85921),f877(x85921,x85922,x85923))),f876(x85921,x85922,x85923)),x85922) % 188.18/188.26 [8612]P149(x86123,x86122,x86121)+~P107(f334(x86123,x86122))+E(f334(f334(f86(a1),f334(f334(f87(a1),x86121),f878(x86121,x86122,x86123))),f875(x86121,x86122,x86123)),x86122)+E(f334(f334(f86(a1),f334(f334(f87(a1),x86121),f877(x86121,x86122,x86123))),f876(x86121,x86122,x86123)),x86122) % 188.18/188.26 [8619]P150(x86193,x86192,x86191)+E(f334(f334(f86(a1),f334(f334(f87(a1),x86191),f873(x86191,x86192,x86193))),f866(x86191,x86192,x86193)),x86192)+E(f334(f334(f86(a1),f334(f334(f87(a1),x86191),f868(x86191,x86192,x86193))),f867(x86191,x86192,x86193)),x86192)+~P107(f334(x86193,f2(a1))) % 188.18/188.26 [9280]~P129(x92801)+~E(x92803,f2(x92801))+~E(x92802,f2(x92801))+P107(f334(f334(f242(x92801),f334(f334(f86(x92801),f334(f334(f87(x92801),x92802),x92802)),f334(f334(f87(x92801),x92803),x92803))),f2(x92801))) % 188.18/188.26 [10453]~P124(x104531)+~E(x104533,f2(x104531))+~E(x104532,f2(x104531))+P107(f334(f334(f242(x104531),f334(f334(f86(x104531),f334(f334(f252(x104531),x104532),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104531),x104533),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))),f2(x104531))) % 188.18/188.26 [5056]~E(x50563,x50561)+~P122(x50562)+E(x50561,f2(x50562))+E(f334(f334(f296(x50562),x50563),x50561),f84(x50562)) % 188.18/188.26 [5107]~P101(x51071)+~E(x51073,f195(x51071))+~E(x51072,f195(x51071))+E(f334(f334(f108(x51071),x51072),x51073),f195(x51071)) % 188.18/188.26 [5108]~P100(x51081)+~E(x51083,f250(x51081))+~E(x51082,f250(x51081))+E(f334(f334(f109(x51081),x51082),x51083),f250(x51081)) % 188.18/188.26 [5201]~P122(x52013)+E(x52011,x52012)+E(x52012,f2(x52013))+~E(f334(f334(f296(x52013),x52011),x52012),f84(x52013)) % 188.18/188.26 [5218]~P145(x52182)+E(x52181,f2(x52182))+E(x52183,f2(x52182))+~E(f334(f334(f87(x52182),x52183),x52181),f2(x52182)) % 188.18/188.26 [5220]~P136(x52202)+E(x52201,f2(x52202))+E(x52203,f2(x52202))+~E(f334(f334(f87(x52202),x52203),x52201),f2(x52202)) % 188.18/188.26 [5595]~P114(x55953)+E(x55951,x55952)+E(x55951,f334(f85(x55953),x55952))+~E(f334(f334(f87(x55953),x55951),x55951),f334(f334(f87(x55953),x55952),x55952)) % 188.18/188.26 [5633]~P91(x56331)+E(f334(f85(x56331),x56332),x56333)+~E(f334(f334(f108(x56331),x56332),x56333),f250(x56331))+~E(f334(f334(f109(x56331),x56332),x56333),f195(x56331)) % 188.18/188.26 [5712]~P124(x57123)+E(x57121,x57122)+P107(f334(f334(f243(x57123),x57122),x57121))+P107(f334(f334(f243(x57123),x57121),x57122)) % 188.18/188.26 [5713]~P109(x57133)+E(x57131,x57132)+P107(f334(f334(f243(x57133),x57132),x57131))+P107(f334(f334(f243(x57133),x57131),x57132)) % 188.18/188.26 [5714]~E(x57142,x57143)+~P109(x57141)+P107(f334(f334(f243(x57141),x57142),x57143))+P107(f334(f334(f242(x57141),x57142),x57143)) % 188.18/188.26 [5981]~P111(x59813)+E(x59811,x59812)+~P107(f334(f334(f242(x59813),x59812),x59811))+P107(f334(f334(f243(x59813),x59812),x59811)) % 188.18/188.26 [5983]~P109(x59833)+E(x59831,x59832)+~P107(f334(f334(f242(x59833),x59831),x59832))+P107(f334(f334(f243(x59833),x59831),x59832)) % 188.18/188.26 [5989]~P111(x59893)+E(x59891,x59892)+~P107(f334(f334(f242(x59893),x59891),x59892))+P107(f334(f334(f243(x59893),x59891),x59892)) % 188.18/188.26 [6096]P149(x60961,x60962,x60963)+~P107(f334(x60961,x60962))+P107(f334(f334(f243(a1),x60963),f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x60963)) % 188.18/188.26 [6147]P150(x61471,x61472,x61473)+~P107(f334(x61471,f2(a1)))+P107(f334(f334(f243(a1),x61473),f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x61473)) % 188.18/188.26 [6152]~P99(x61521)+E(f334(f334(f108(x61521),x61522),f10(x61521,x61523)),x61522)+~P107(f334(f66(x61521),x61523))+~P107(f334(f334(f336(x61521),x61522),x61523)) % 188.18/188.26 [6153]~P99(x61531)+E(f334(f334(f109(x61531),x61532),f13(x61531,x61533)),x61532)+~P107(f334(f66(x61531),x61533))+~P107(f334(f334(f336(x61531),x61532),x61533)) % 188.18/188.26 [6189]~P109(x61891)+E(f334(f334(f246(x61891),x61892),f14(x61891,x61893)),f14(x61891,x61893))+~P107(f334(f66(x61891),x61893))+~P107(f334(f334(f336(x61891),x61892),x61893)) % 188.18/188.26 [6190]~P109(x61901)+E(f334(f334(f241(x61901),x61902),f15(x61901,x61903)),f15(x61901,x61903))+~P107(f334(f66(x61901),x61903))+~P107(f334(f334(f336(x61901),x61902),x61903)) % 188.18/188.26 [6191]~P99(x61911)+E(f334(f334(f108(x61911),x61912),f13(x61911,x61913)),f13(x61911,x61913))+~P107(f334(f66(x61911),x61913))+~P107(f334(f334(f336(x61911),x61912),x61913)) % 188.18/188.26 [6192]~P99(x61921)+E(f334(f334(f109(x61921),x61922),f10(x61921,x61923)),f10(x61921,x61923))+~P107(f334(f66(x61921),x61923))+~P107(f334(f334(f336(x61921),x61922),x61923)) % 188.18/188.26 [6230]E(x62301,x62302)+~P111(x62303)+~P107(f334(f334(f242(x62303),x62302),x62301))+~P107(f334(f334(f242(x62303),x62301),x62302)) % 188.18/188.26 [6371]~P108(x63711)+P107(f334(f334(f243(x63711),x63713),x63712))+~P107(f334(f334(f242(x63711),x63713),x63712))+P107(f334(f334(f242(x63711),x63712),x63713)) % 188.18/188.26 [6399]~P109(x63991)+~P107(f334(f66(x63991),x63993))+P107(f334(f334(f242(x63991),x63992),f15(x63991,x63993)))+~P107(f334(f334(f336(x63991),x63992),x63993)) % 188.18/188.26 [6440]~P109(x64401)+E(f334(f334(f246(x64401),x64402),f12(x64401,f241(x64401),x64403)),x64402)+~P107(f334(f66(x64401),x64403))+~P107(f334(f334(f336(x64401),x64402),x64403)) % 188.18/188.26 [6441]~P109(x64411)+E(f334(f334(f241(x64411),x64412),f11(x64411,f246(x64411),x64413)),x64412)+~P107(f334(f66(x64411),x64413))+~P107(f334(f334(f336(x64411),x64412),x64413)) % 188.18/188.26 [6579]E(x65791,x65792)+~E(f334(f334(f23(a927),x65791),x65793),f334(f334(f23(a927),x65792),x65793))+~P107(f334(f334(f242(a927),x65793),x65791))+~P107(f334(f334(f242(a927),x65793),x65792)) % 188.18/188.26 [6605]~P109(x66051)+~P107(f334(f66(x66051),x66052))+~P107(f334(f334(f336(x66051),x66053),x66052))+P107(f334(f334(f242(x66051),f14(x66051,x66052)),x66053)) % 188.18/188.26 [6671]P150(x66712,x66713,x66711)+E(x66711,f2(a1))+P107(f334(f334(f243(a1),x66711),f866(x66711,x66713,x66712)))+P107(f334(f334(f243(a1),f2(a1)),x66711)) % 188.18/188.26 [6672]P149(x66722,x66723,x66721)+E(x66721,f2(a1))+P107(f334(f334(f243(a1),x66721),f875(x66721,x66723,x66722)))+P107(f334(f334(f243(a1),f2(a1)),x66721)) % 188.18/188.26 [6673]~P109(x66731)+E(f334(f334(f246(x66731),x66732),f11(x66731,f246(x66731),x66733)),f11(x66731,f246(x66731),x66733))+~P107(f334(f66(x66731),x66733))+~P107(f334(f334(f336(x66731),x66732),x66733)) % 188.18/188.26 [6674]~P109(x66741)+E(f334(f334(f241(x66741),x66742),f12(x66741,f241(x66741),x66743)),f12(x66741,f241(x66741),x66743))+~P107(f334(f66(x66741),x66743))+~P107(f334(f334(f336(x66741),x66742),x66743)) % 188.18/188.26 [6681]~P107(f334(x66811,x66812))+P107(f334(x66811,f599(x66812,x66811,x66813)))+P107(f334(x66811,f2(a927)))+~P107(f334(f334(f243(a927),x66812),x66813)) % 188.18/188.26 [6737]~P107(f334(x67371,x67372))+~P107(f334(f66(x67373),x67372))+P107(f334(x67371,f681(x67371,x67372,x67373)))+P107(f334(x67371,f195(f935(x67373,a922)))) % 188.18/188.26 [6750]~P124(x67501)+~P95(x67501)+P107(f334(f334(f242(x67501),f334(f111(x67501),x67502)),f334(f111(x67501),x67503)))+~P107(f334(f334(f242(a1),x67502),x67503)) % 188.18/188.26 [6751]~P124(x67511)+~P95(x67511)+P107(f334(f334(f243(x67511),f334(f111(x67511),x67512)),f334(f111(x67511),x67513)))+~P107(f334(f334(f243(a1),x67512),x67513)) % 188.18/188.26 [6755]~P107(f334(x67551,x67553))+~P107(f334(f66(x67552),x67553))+P107(f334(f66(x67552),f681(x67551,x67553,x67552)))+P107(f334(x67551,f195(f935(x67552,a922)))) % 188.18/188.26 [6786]P149(x67861,x67862,x67863)+~P107(f334(x67861,x67862))+P107(f334(f334(f243(a1),x67863),f875(x67863,x67862,x67861)))+P107(f334(f334(f243(a1),f2(a1)),x67863)) % 188.18/188.26 [6822]P150(x68221,x68222,x68223)+P107(f334(f334(f243(a1),x68223),f866(x68223,x68222,x68221)))+~P107(f334(x68221,f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x68223)) % 188.18/188.26 [6852]~P110(x68521)+~P94(x68521)+E(f334(f334(f246(x68521),f334(f111(x68521),x68522)),f334(f111(x68521),x68523)),f334(f111(x68521),x68523))+P107(f334(f334(f242(x68521),f334(f111(x68521),x68522)),f334(f111(x68521),x68523))) % 188.18/188.26 [6853]~P110(x68531)+~P94(x68531)+E(f334(f334(f241(x68531),f334(f111(x68531),x68532)),f334(f111(x68531),x68533)),f334(f111(x68531),x68532))+P107(f334(f334(f242(x68531),f334(f111(x68531),x68532)),f334(f111(x68531),x68533))) % 188.18/188.26 [6909]P150(x69092,x69093,x69091)+E(x69091,f2(a1))+~P107(f334(x69092,f873(x69091,x69093,x69092)))+P107(f334(f334(f243(a1),f2(a1)),x69091)) % 188.18/188.26 [6910]P149(x69102,x69103,x69101)+E(x69101,f2(a1))+~P107(f334(x69102,f875(x69101,x69103,x69102)))+P107(f334(f334(f243(a1),f2(a1)),x69101)) % 188.18/188.26 [6914]P107(f334(x69141,x69142))+~P107(f334(f66(x69143),x69142))+P107(f334(x69141,f772(x69141,x69142,x69143)))+~P107(f334(x69141,f195(f935(x69143,a922)))) % 188.18/188.26 [6935]P107(f334(x69351,x69352))+P107(f334(f66(x69353),f772(x69351,x69352,x69353)))+~P107(f334(f66(x69353),x69352))+~P107(f334(x69351,f195(f935(x69353,a922)))) % 188.18/188.26 [6998]P149(x69981,x69982,x69983)+~P107(f334(x69981,x69982))+~P107(f334(x69981,f875(x69983,x69982,x69981)))+P107(f334(f334(f243(a1),f2(a1)),x69983)) % 188.18/188.26 [7023]P150(x70231,x70232,x70233)+~P107(f334(x70231,f873(x70233,x70232,x70231)))+~P107(f334(x70231,f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x70233)) % 188.18/188.26 [7127]~P95(x71273)+~P124(x71273)+~P107(f334(f334(f242(x71273),f334(f111(x71273),x71271)),f334(f111(x71273),x71272)))+P107(f334(f334(f242(a1),x71271),x71272)) % 188.18/188.26 [7128]~P95(x71283)+~P124(x71283)+~P107(f334(f334(f243(x71283),f334(f111(x71283),x71281)),f334(f111(x71283),x71282)))+P107(f334(f334(f243(a1),x71281),x71282)) % 188.18/188.26 [7155]~P109(x71551)+~P15(x71551,x71553)+P15(x71551,f334(f334(f158(x71551),x71552),x71553))+~P107(f334(f334(f242(x71551),x71552),f724(x71553,x71552,x71551))) % 188.18/188.26 [7156]~P109(x71561)+~P15(x71561,x71563)+P15(x71561,f334(f334(f158(x71561),x71562),x71563))+~P107(f334(f334(f242(x71561),x71562),f726(x71563,x71562,x71561))) % 188.18/188.26 [7157]~P109(x71571)+~P15(x71571,x71573)+P15(x71571,f334(f334(f158(x71571),x71572),x71573))+~P107(f334(f334(f242(x71571),x71572),f765(x71572,x71573,x71571))) % 188.18/188.26 [7241]P150(x72412,x72413,x72411)+E(x72411,f2(a1))+P107(f334(f334(f243(a1),x72411),f2(a1)))+P107(f334(f334(f243(a1),f867(x72411,x72413,x72412)),x72411)) % 188.18/188.26 [7242]P149(x72422,x72423,x72421)+E(x72421,f2(a1))+P107(f334(f334(f243(a1),x72421),f2(a1)))+P107(f334(f334(f243(a1),f876(x72421,x72423,x72422)),x72421)) % 188.18/188.26 [7278]P150(x72782,x72783,x72781)+E(x72781,f2(a1))+P107(f334(f334(f242(a1),f866(x72781,x72783,x72782)),f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x72781)) % 188.18/188.26 [7279]P149(x72792,x72793,x72791)+E(x72791,f2(a1))+P107(f334(f334(f242(a1),f875(x72791,x72793,x72792)),f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x72791)) % 188.18/188.26 [7304]~P109(x73041)+~P15(x73041,x73043)+E(f334(f334(f155(x73041,x73041,f5(x73041)),x73042),f177(x73041,x73042,x73043)),x73043)+~P107(f334(f334(f336(x73041),x73042),f334(f179(x73041),x73043))) % 188.18/188.26 [7350]P149(x73501,x73502,x73503)+~P107(f334(x73501,x73502))+P107(f334(f334(f243(a1),x73503),f2(a1)))+P107(f334(f334(f243(a1),f876(x73503,x73502,x73501)),x73503)) % 188.18/188.26 [7356]~P110(x73561)+~P94(x73561)+E(f334(f334(f246(x73561),f334(f111(x73561),x73562)),f334(f111(x73561),x73563)),f334(f111(x73561),x73562))+~P107(f334(f334(f242(x73561),f334(f111(x73561),x73562)),f334(f111(x73561),x73563))) % 188.18/188.26 [7357]~P110(x73571)+~P94(x73571)+E(f334(f334(f241(x73571),f334(f111(x73571),x73572)),f334(f111(x73571),x73573)),f334(f111(x73571),x73573))+~P107(f334(f334(f242(x73571),f334(f111(x73571),x73572)),f334(f111(x73571),x73573))) % 188.18/188.26 [7371]P150(x73711,x73712,x73713)+~P107(f334(x73711,f2(a1)))+P107(f334(f334(f243(a1),x73713),f2(a1)))+P107(f334(f334(f243(a1),f867(x73713,x73712,x73711)),x73713)) % 188.18/188.26 [7379]P149(x73791,x73792,x73793)+~P107(f334(x73791,x73792))+P107(f334(f334(f242(a1),f875(x73793,x73792,x73791)),f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x73793)) % 188.18/188.26 [7403]P150(x74031,x74032,x74033)+~P107(f334(x74031,f2(a1)))+P107(f334(f334(f242(a1),f866(x74033,x74032,x74031)),f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x74033)) % 188.18/188.26 [7430]~P107(f334(x74301,x74302))+P107(f334(x74301,f2(a927)))+~P107(f334(f334(f243(a927),x74302),x74303))+P107(f334(f334(f243(a927),f599(x74302,x74301,x74303)),x74303)) % 188.18/188.26 [7447]~P109(x74471)+~P15(x74471,x74473)+P15(x74471,f334(f334(f158(x74471),x74472),x74473))+P107(f334(f334(f336(x74471),f724(x74473,x74472,x74471)),f334(f179(x74471),x74473))) % 188.18/188.26 [7448]~P109(x74481)+~P15(x74481,x74483)+P15(x74481,f334(f334(f158(x74481),x74482),x74483))+P107(f334(f334(f336(x74481),f726(x74483,x74482,x74481)),f334(f179(x74481),x74483))) % 188.18/188.26 [7449]~P109(x74491)+~P15(x74491,x74493)+P15(x74491,f334(f334(f158(x74491),x74492),x74493))+P107(f334(f334(f336(x74491),f765(x74492,x74493,x74491)),f334(f179(x74491),x74493))) % 188.18/188.26 [7561]~P109(x75611)+~P7(x75611)+~P107(f334(f334(f243(x75611),x75613),f42(x75611,x75612)))+P107(f334(f334(f336(x75611),f513(x75612,x75613,x75611)),x75612)) % 188.18/188.26 [7707]~P109(x77071)+~P7(x77071)+~P107(f334(f334(f243(x77071),f43(x77071,x77073)),x77072))+P107(f334(f334(f336(x77071),f515(x77072,x77073,x77071)),x77073)) % 188.18/188.26 [7708]~P109(x77081)+~P7(x77081)+~P107(f334(f334(f243(x77081),f43(x77081,x77083)),x77082))+P107(f334(f334(f243(x77081),f515(x77082,x77083,x77081)),x77082)) % 188.18/188.26 [7720]P150(x77202,x77203,x77201)+E(x77201,f2(a1))+P107(f334(f334(f243(a1),x77201),f866(x77201,x77203,x77202)))+P107(f334(f334(f243(a1),f867(x77201,x77203,x77202)),x77201)) % 188.18/188.26 [7721]P149(x77212,x77213,x77211)+E(x77211,f2(a1))+P107(f334(f334(f243(a1),x77211),f875(x77211,x77213,x77212)))+P107(f334(f334(f243(a1),f876(x77211,x77213,x77212)),x77211)) % 188.18/188.26 [7808]P150(x78083,x78082,x78081)+E(x78081,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x78081),f873(x78081,x78082,x78083))),f866(x78081,x78082,x78083)),x78082)+P107(f334(f334(f243(a1),f2(a1)),x78081)) % 188.18/188.26 [7809]P149(x78093,x78092,x78091)+E(x78091,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x78091),f878(x78091,x78092,x78093))),f875(x78091,x78092,x78093)),x78092)+P107(f334(f334(f243(a1),f2(a1)),x78091)) % 188.18/188.26 [7811]~P129(x78111)+~P107(f334(f334(f242(x78111),x78113),f2(x78111)))+P107(f334(f334(f242(x78111),f334(f334(f87(x78111),x78112),x78113)),f2(x78111)))+~P107(f334(f334(f242(x78111),f2(x78111)),x78112)) % 188.18/188.26 [7812]~P129(x78121)+~P107(f334(f334(f242(x78121),x78122),f2(x78121)))+P107(f334(f334(f242(x78121),f334(f334(f87(x78121),x78122),x78123)),f2(x78121)))+~P107(f334(f334(f242(x78121),f2(x78121)),x78123)) % 188.18/188.26 [7814]~P137(x78141)+~P107(f334(f334(f242(x78141),x78143),f2(x78141)))+P107(f334(f334(f242(x78141),f334(f334(f87(x78141),x78142),x78143)),f2(x78141)))+~P107(f334(f334(f242(x78141),f2(x78141)),x78142)) % 188.18/188.26 [7816]~P137(x78161)+~P107(f334(f334(f242(x78161),x78162),f2(x78161)))+P107(f334(f334(f242(x78161),f334(f334(f87(x78161),x78162),x78163)),f2(x78161)))+~P107(f334(f334(f242(x78161),f2(x78161)),x78163)) % 188.18/188.26 [7817]~P67(x78171)+~P107(f334(f334(f242(x78171),x78173),f2(x78171)))+P107(f334(f334(f242(x78171),f334(f334(f296(x78171),x78172),x78173)),f2(x78171)))+~P107(f334(f334(f242(x78171),f2(x78171)),x78172)) % 188.18/188.26 [7818]~P67(x78181)+~P107(f334(f334(f242(x78181),x78182),f2(x78181)))+P107(f334(f334(f242(x78181),f334(f334(f296(x78181),x78182),x78183)),f2(x78181)))+~P107(f334(f334(f242(x78181),f2(x78181)),x78183)) % 188.18/188.26 [7819]~P68(x78191)+~P107(f334(f334(f242(x78191),x78192),f2(x78191)))+P107(f334(f334(f242(x78191),f334(f334(f296(x78191),x78192),x78193)),f2(x78191)))+~P107(f334(f334(f243(x78191),f2(x78191)),x78193)) % 188.18/188.26 [7820]~P68(x78201)+~P107(f334(f334(f243(x78201),x78203),f2(x78201)))+P107(f334(f334(f242(x78201),f334(f334(f296(x78201),x78202),x78203)),f2(x78201)))+~P107(f334(f334(f242(x78201),f2(x78201)),x78202)) % 188.18/188.26 [7822]~P135(x78221)+~P107(f334(f334(f243(x78221),x78223),f2(x78221)))+P107(f334(f334(f243(x78221),f334(f334(f87(x78221),x78222),x78223)),f2(x78221)))+~P107(f334(f334(f243(x78221),f2(x78221)),x78222)) % 188.18/188.26 [7823]~P135(x78231)+~P107(f334(f334(f243(x78231),x78232),f2(x78231)))+P107(f334(f334(f243(x78231),f334(f334(f87(x78231),x78232),x78233)),f2(x78231)))+~P107(f334(f334(f243(x78231),f2(x78231)),x78233)) % 188.18/188.26 [7824]~P67(x78241)+~P107(f334(f334(f243(x78241),x78243),f2(x78241)))+P107(f334(f334(f243(x78241),f334(f334(f296(x78241),x78242),x78243)),f2(x78241)))+~P107(f334(f334(f243(x78241),f2(x78241)),x78242)) % 188.18/188.26 [7825]~P67(x78251)+~P107(f334(f334(f243(x78251),x78252),f2(x78251)))+P107(f334(f334(f243(x78251),f334(f334(f296(x78251),x78252),x78253)),f2(x78251)))+~P107(f334(f334(f243(x78251),f2(x78251)),x78253)) % 188.18/188.26 [7826]~P68(x78261)+~P107(f334(f334(f243(x78261),x78263),f2(x78261)))+P107(f334(f334(f243(x78261),f334(f334(f296(x78261),x78262),x78263)),f2(x78261)))+~P107(f334(f334(f243(x78261),f2(x78261)),x78262)) % 188.18/188.26 [7827]~P68(x78271)+~P107(f334(f334(f243(x78271),x78272),f2(x78271)))+P107(f334(f334(f243(x78271),f334(f334(f296(x78271),x78272),x78273)),f2(x78271)))+~P107(f334(f334(f243(x78271),f2(x78271)),x78273)) % 188.18/188.26 [7842]P149(x78421,x78422,x78423)+~P107(f334(x78421,x78422))+P107(f334(f334(f243(a1),x78423),f875(x78423,x78422,x78421)))+P107(f334(f334(f243(a1),f876(x78423,x78422,x78421)),x78423)) % 188.18/188.26 [7855]P150(x78551,x78552,x78553)+P107(f334(f334(f243(a1),x78553),f866(x78553,x78552,x78551)))+~P107(f334(x78551,f2(a1)))+P107(f334(f334(f243(a1),f867(x78553,x78552,x78551)),x78553)) % 188.18/188.26 [7905]P150(x79052,x79053,x79051)+E(x79051,f2(a1))+~P107(f334(x79052,f873(x79051,x79053,x79052)))+P107(f334(f334(f243(a1),f867(x79051,x79053,x79052)),x79051)) % 188.18/188.26 [7906]P149(x79062,x79063,x79061)+E(x79061,f2(a1))+~P107(f334(x79062,f875(x79061,x79063,x79062)))+P107(f334(f334(f243(a1),f876(x79061,x79063,x79062)),x79061)) % 188.18/188.26 [7915]P149(x79153,x79152,x79151)+~P107(f334(x79153,x79152))+E(f334(f334(f86(a1),f334(f334(f87(a1),x79151),f878(x79151,x79152,x79153))),f875(x79151,x79152,x79153)),x79152)+P107(f334(f334(f243(a1),f2(a1)),x79151)) % 188.18/188.26 [7931]P150(x79313,x79312,x79311)+E(f334(f334(f86(a1),f334(f334(f87(a1),x79311),f873(x79311,x79312,x79313))),f866(x79311,x79312,x79313)),x79312)+~P107(f334(x79313,f2(a1)))+P107(f334(f334(f243(a1),f2(a1)),x79311)) % 188.18/188.26 [7960]~P107(f334(x79601,x79603))+~P107(f334(f66(x79602),x79603))+P107(f334(f334(f336(x79602),f673(x79601,x79603,x79602)),f681(x79601,x79603,x79602)))+P107(f334(x79601,f195(f935(x79602,a922)))) % 188.18/188.26 [7971]P149(x79711,x79712,x79713)+~P107(f334(x79711,x79712))+~P107(f334(x79711,f875(x79713,x79712,x79711)))+P107(f334(f334(f243(a1),f876(x79713,x79712,x79711)),x79713)) % 188.18/188.26 [7977]P150(x79771,x79772,x79773)+~P107(f334(x79771,f873(x79773,x79772,x79771)))+~P107(f334(x79771,f2(a1)))+P107(f334(f334(f243(a1),f867(x79773,x79772,x79771)),x79773)) % 188.18/188.26 [8081]~P129(x80811)+~P107(f334(f334(f242(x80811),f334(f334(f87(x80811),x80813),x80812)),f2(x80811)))+P107(f334(f334(f242(x80811),x80812),f2(x80811)))+P107(f334(f334(f242(x80811),f2(x80811)),x80812)) % 188.18/188.26 [8082]~P129(x80821)+~P107(f334(f334(f242(x80821),f334(f334(f87(x80821),x80822),x80823)),f2(x80821)))+P107(f334(f334(f242(x80821),x80822),f2(x80821)))+P107(f334(f334(f242(x80821),f2(x80821)),x80822)) % 188.18/188.26 [8083]~P67(x80831)+~P107(f334(f334(f242(x80831),f334(f334(f296(x80831),x80833),x80832)),f2(x80831)))+P107(f334(f334(f242(x80831),x80832),f2(x80831)))+P107(f334(f334(f242(x80831),f2(x80831)),x80832)) % 188.18/188.26 [8084]~P67(x80841)+~P107(f334(f334(f242(x80841),f334(f334(f296(x80841),x80842),x80843)),f2(x80841)))+P107(f334(f334(f242(x80841),x80842),f2(x80841)))+P107(f334(f334(f242(x80841),f2(x80841)),x80842)) % 188.18/188.26 [8085]~P67(x80851)+~P107(f334(f334(f243(x80851),f334(f334(f296(x80851),x80853),x80852)),f2(x80851)))+P107(f334(f334(f243(x80851),x80852),f2(x80851)))+P107(f334(f334(f243(x80851),f2(x80851)),x80852)) % 188.18/188.26 [8086]~P67(x80861)+~P107(f334(f334(f243(x80861),f334(f334(f296(x80861),x80862),x80863)),f2(x80861)))+P107(f334(f334(f243(x80861),x80862),f2(x80861)))+P107(f334(f334(f243(x80861),f2(x80861)),x80862)) % 188.18/188.26 [8105]~P129(x81051)+~P107(f334(f334(f242(x81051),f334(f334(f87(x81051),x81052),x81053)),f2(x81051)))+P107(f334(f334(f242(x81051),f2(x81051)),x81052))+P107(f334(f334(f242(x81051),f2(x81051)),x81053)) % 188.18/188.26 [8106]~P67(x81061)+~P107(f334(f334(f242(x81061),f334(f334(f296(x81061),x81062),x81063)),f2(x81061)))+P107(f334(f334(f242(x81061),f2(x81061)),x81062))+P107(f334(f334(f242(x81061),f2(x81061)),x81063)) % 188.18/188.26 [8107]~P67(x81071)+~P107(f334(f334(f243(x81071),f334(f334(f296(x81071),x81072),x81073)),f2(x81071)))+P107(f334(f334(f243(x81071),f2(x81071)),x81072))+P107(f334(f334(f243(x81071),f2(x81071)),x81073)) % 188.18/188.26 [8129]P150(x81292,x81293,x81291)+E(x81291,f2(a1))+P107(f334(f334(f242(a1),f866(x81291,x81293,x81292)),f2(a1)))+P107(f334(f334(f243(a1),f867(x81291,x81293,x81292)),x81291)) % 188.18/188.26 [8130]P149(x81302,x81303,x81301)+E(x81301,f2(a1))+P107(f334(f334(f242(a1),f875(x81301,x81303,x81302)),f2(a1)))+P107(f334(f334(f243(a1),f876(x81301,x81303,x81302)),x81301)) % 188.18/188.26 [8137]~P127(x81371)+~P107(f334(f334(f243(x81371),x81372),f84(x81371)))+P107(f334(f334(f243(x81371),f334(f334(f252(x81371),x81372),f334(a119,x81373))),f84(x81371)))+~P107(f334(f334(f243(x81371),f2(x81371)),x81372)) % 188.18/188.26 [8186]~P109(x81861)+~E(x81863,f120(x81861))+~P15(x81861,f334(f175(x81861),x81863))+E(f334(f149(x81861,x81861,f334(f7(x81861,x81861,x81861),f241(x81861)),x81862),f334(f175(x81861),x81863)),x81862) % 188.18/188.26 [8189]P149(x81891,x81892,x81893)+~P107(f334(x81891,x81892))+P107(f334(f334(f242(a1),f875(x81893,x81892,x81891)),f2(a1)))+P107(f334(f334(f243(a1),f876(x81893,x81892,x81891)),x81893)) % 188.18/188.26 [8195]P150(x81951,x81952,x81953)+~P107(f334(x81951,f2(a1)))+P107(f334(f334(f242(a1),f866(x81953,x81952,x81951)),f2(a1)))+P107(f334(f334(f243(a1),f867(x81953,x81952,x81951)),x81953)) % 188.18/188.26 [8412]P150(x84123,x84122,x84121)+E(x84121,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x84121),f873(x84121,x84122,x84123))),f866(x84121,x84122,x84123)),x84122)+P107(f334(f334(f243(a1),f867(x84121,x84122,x84123)),x84121)) % 188.18/188.26 [8413]P149(x84133,x84132,x84131)+E(x84131,f2(a1))+E(f334(f334(f86(a1),f334(f334(f87(a1),x84131),f878(x84131,x84132,x84133))),f875(x84131,x84132,x84133)),x84132)+P107(f334(f334(f243(a1),f876(x84131,x84132,x84133)),x84131)) % 188.18/188.26 [8446]P149(x84463,x84462,x84461)+~P107(f334(x84463,x84462))+E(f334(f334(f86(a1),f334(f334(f87(a1),x84461),f878(x84461,x84462,x84463))),f875(x84461,x84462,x84463)),x84462)+P107(f334(f334(f243(a1),f876(x84461,x84462,x84463)),x84461)) % 188.18/188.26 [8447]~P72(x84471)+~P76(x84471)+~P42(x84473)+E(f334(f334(f9(a927,x84471),f334(f334(f8(a1,x84471,a927),x84472),f107(a1))),f334(f317(a1,a927,a112),x84473)),f334(f334(f9(a1,x84471),x84472),x84473)) % 188.18/188.26 [8448]~P72(x84481)+~P76(x84481)+~P42(x84483)+E(f334(f334(f6(a927,x84481),f334(f334(f8(a1,x84481,a927),x84482),f107(a1))),f334(f317(a1,a927,a112),x84483)),f334(f334(f6(a1,x84481),x84482),x84483)) % 188.18/188.26 [8457]P150(x84573,x84572,x84571)+E(f334(f334(f86(a1),f334(f334(f87(a1),x84571),f873(x84571,x84572,x84573))),f866(x84571,x84572,x84573)),x84572)+~P107(f334(x84573,f2(a1)))+P107(f334(f334(f243(a1),f867(x84571,x84572,x84573)),x84571)) % 188.18/188.26 [8480]~E(x84802,f2(a927))+~E(f334(f259(a927,a927),x84803),f2(a927))+~E(x84801,f334(f334(f86(a927),f334(f334(f87(a927),f334(f259(a927,a927),x84803)),x84802)),f334(f264(a927,a927),x84803)))+P107(f334(f53(x84801,x84802),x84803)) % 188.18/188.26 [8536]P107(f334(x85361,x85362))+~P107(f334(f334(f336(x85363),f779(x85361,x85362,x85363)),f772(x85361,x85362,x85363)))+~P107(f334(f66(x85363),x85362))+~P107(f334(x85361,f195(f935(x85363,a922)))) % 188.18/188.26 [9158]P107(f334(x91581,x91582))+~P107(f334(f66(x91583),x91582))+~P107(f334(x91581,f334(f334(f316(x91583),f779(x91581,x91582,x91583)),f772(x91581,x91582,x91583))))+~P107(f334(x91581,f195(f935(x91583,a922)))) % 188.18/188.26 [9385]P107(f334(f334(f242(a1),x93851),f2(a1)))+~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f87(a1),x93853),x93851)),x93852)),f2(a1)))+~P107(f334(f334(f242(a1),f2(a1)),x93852))+~P107(f334(f334(f243(a1),f2(a1)),x93853)) % 188.18/188.26 [6051]~P109(x60512)+E(x60511,f195(f935(x60512,a922)))+~P107(f334(f66(x60512),x60511))+E(f14(x60512,f334(f334(f316(x60512),x60513),x60511)),f334(f334(f246(x60512),x60513),f14(x60512,x60511))) % 188.18/188.26 [6052]~P109(x60522)+E(x60521,f195(f935(x60522,a922)))+~P107(f334(f66(x60522),x60521))+E(f15(x60522,f334(f334(f316(x60522),x60523),x60521)),f334(f334(f241(x60522),x60523),f15(x60522,x60521))) % 188.18/188.26 [6053]~P99(x60532)+E(x60531,f195(f935(x60532,a922)))+~P107(f334(f66(x60532),x60531))+E(f10(x60532,f334(f334(f316(x60532),x60533),x60531)),f334(f334(f109(x60532),x60533),f10(x60532,x60531))) % 188.18/188.26 [6054]~P99(x60542)+E(x60541,f195(f935(x60542,a922)))+~P107(f334(f66(x60542),x60541))+E(f13(x60542,f334(f334(f316(x60542),x60543),x60541)),f334(f334(f108(x60542),x60543),f13(x60542,x60541))) % 188.18/188.26 [6368]~P129(x63681)+~E(x63683,f2(x63681))+~E(x63682,f2(x63681))+E(f334(f334(f86(x63681),f334(f334(f87(x63681),x63682),x63682)),f334(f334(f87(x63681),x63683),x63683)),f2(x63681)) % 188.18/188.26 [6433]~P96(x64332)+E(x64331,f195(f935(x64332,a922)))+~P107(f334(f66(x64332),x64331))+E(f334(f68(x64332,f87(x64332)),f334(f334(f316(x64332),x64333),x64331)),f334(f334(f87(x64332),x64333),f334(f68(x64332,f87(x64332)),x64331))) % 188.18/188.26 [6557]~P109(x65572)+E(x65571,f195(f935(x65572,a922)))+~P107(f334(f66(x65572),x65571))+E(f11(x65572,f246(x65572),f334(f334(f316(x65572),x65573),x65571)),f334(f334(f246(x65572),x65573),f11(x65572,f246(x65572),x65571))) % 188.18/188.26 [6558]~P109(x65582)+E(x65581,f195(f935(x65582,a922)))+~P107(f334(f66(x65582),x65581))+E(f12(x65582,f241(x65582),f334(f334(f316(x65582),x65583),x65581)),f334(f334(f241(x65582),x65583),f12(x65582,f241(x65582),x65581))) % 188.18/188.26 [7056]~P70(x70561)+~P107(f334(f66(x70561),x70563))+E(f334(f68(x70561,f87(x70561)),f334(f334(f316(x70561),x70562),x70563)),f334(f334(f69(x70561,x70561,f87(x70561)),x70562),x70563))+P107(f334(f334(f336(x70561),x70562),x70563)) % 188.18/188.26 [7134]~E(f334(f334(f86(a1),x71342),f334(f334(f87(a1),x71343),x71341)),x71343)+~P107(f334(f334(f243(a1),f2(a1)),x71343))+P107(f334(f334(f242(a1),f84(a1)),x71341))+~P107(f334(f334(f243(a1),x71342),x71343)) % 188.18/188.26 [7162]~E(f334(f334(f86(a1),x71622),f334(f334(f87(a1),x71623),x71621)),x71623)+P107(f334(f334(f242(a1),x71621),f84(a1)))+~P107(f334(f334(f242(a1),f2(a1)),x71622))+~P107(f334(f334(f243(a1),f2(a1)),x71623)) % 188.18/188.26 [7178]E(x71781,f2(a927))+~P107(f334(f53(x71783,x71781),x71782))+~P107(f334(f334(f243(a927),f2(a927)),x71781))+P107(f334(f334(f243(a927),f334(f264(a927,a927),x71782)),x71781)) % 188.18/188.26 [7209]~P140(x72091)+~P107(f334(f334(f242(x72091),x72092),f2(x72091)))+~P107(f334(f334(f242(x72091),x72093),f2(x72091)))+E(f334(f334(f87(x72091),f334(f81(x72091),x72092)),f334(f81(x72091),x72093)),f334(f81(x72091),f334(f334(f87(x72091),x72092),x72093))) % 188.18/188.26 [7255]~P140(x72551)+~P107(f334(f334(f242(x72551),x72552),f2(x72551)))+E(f334(f334(f87(x72551),f334(f81(x72551),x72552)),f334(f81(x72551),x72553)),f334(f81(x72551),f334(f334(f87(x72551),x72552),x72553)))+~P107(f334(f334(f242(x72551),f2(x72551)),x72553)) % 188.18/188.26 [7256]~P140(x72561)+~P107(f334(f334(f242(x72561),x72563),f2(x72561)))+E(f334(f334(f87(x72561),f334(f81(x72561),x72562)),f334(f81(x72561),x72563)),f334(f81(x72561),f334(f334(f87(x72561),x72562),x72563)))+~P107(f334(f334(f242(x72561),f2(x72561)),x72562)) % 188.18/188.26 [7311]~P140(x73111)+E(f334(f334(f87(x73111),f334(f81(x73111),x73112)),f334(f81(x73111),x73113)),f334(f81(x73111),f334(f334(f87(x73111),x73112),x73113)))+~P107(f334(f334(f242(x73111),f2(x73111)),x73112))+~P107(f334(f334(f242(x73111),f2(x73111)),x73113)) % 188.18/188.26 [7328]~P130(x73281)+~P107(f334(f334(f242(x73281),x73283),f2(x73281)))+~P107(f334(f334(f242(x73281),x73282),f2(x73281)))+P107(f334(f334(f242(x73281),f2(x73281)),f334(f334(f87(x73281),x73282),x73283))) % 188.18/188.26 [7329]~P129(x73291)+~P107(f334(f334(f242(x73291),x73293),f2(x73291)))+~P107(f334(f334(f242(x73291),x73292),f2(x73291)))+P107(f334(f334(f242(x73291),f2(x73291)),f334(f334(f87(x73291),x73292),x73293))) % 188.18/188.26 [7330]~P67(x73301)+~P107(f334(f334(f242(x73301),x73303),f2(x73301)))+~P107(f334(f334(f242(x73301),x73302),f2(x73301)))+P107(f334(f334(f242(x73301),f2(x73301)),f334(f334(f296(x73301),x73302),x73303))) % 188.18/188.26 [7331]~P68(x73311)+~P107(f334(f334(f243(x73311),x73313),f2(x73311)))+~P107(f334(f334(f242(x73311),x73312),f2(x73311)))+P107(f334(f334(f242(x73311),f2(x73311)),f334(f334(f296(x73311),x73312),x73313))) % 188.18/188.26 [7332]~P129(x73321)+~P107(f334(f334(f243(x73321),x73323),f2(x73321)))+~P107(f334(f334(f243(x73321),x73322),f2(x73321)))+P107(f334(f334(f243(x73321),f2(x73321)),f334(f334(f87(x73321),x73322),x73323))) % 188.18/188.26 [7333]~P67(x73331)+~P107(f334(f334(f243(x73331),x73333),f2(x73331)))+~P107(f334(f334(f243(x73331),x73332),f2(x73331)))+P107(f334(f334(f243(x73331),f2(x73331)),f334(f334(f296(x73331),x73332),x73333))) % 188.18/188.26 [7334]~P68(x73341)+~P107(f334(f334(f243(x73341),x73343),f2(x73341)))+~P107(f334(f334(f243(x73341),x73342),f2(x73341)))+P107(f334(f334(f243(x73341),f2(x73341)),f334(f334(f296(x73341),x73342),x73343))) % 188.18/188.26 [7335]~P127(x73351)+~P107(f334(f334(f243(a927),f2(a927)),x73353))+~P107(f334(f334(f243(x73351),f84(x73351)),x73352))+P107(f334(f334(f243(x73351),f84(x73351)),f334(f334(f252(x73351),x73352),x73353))) % 188.18/188.26 [7431]~P130(x74311)+~P107(f334(f334(f242(x74311),f2(x74311)),x74313))+~P107(f334(f334(f242(x74311),f2(x74311)),x74312))+P107(f334(f334(f242(x74311),f2(x74311)),f334(f334(f87(x74311),x74312),x74313))) % 188.18/188.26 [7432]~P129(x74321)+~P107(f334(f334(f242(x74321),f2(x74321)),x74323))+~P107(f334(f334(f242(x74321),f2(x74321)),x74322))+P107(f334(f334(f242(x74321),f2(x74321)),f334(f334(f87(x74321),x74322),x74323))) % 188.18/188.26 [7433]~P137(x74331)+~P107(f334(f334(f242(x74331),f2(x74331)),x74333))+~P107(f334(f334(f242(x74331),f2(x74331)),x74332))+P107(f334(f334(f242(x74331),f2(x74331)),f334(f334(f87(x74331),x74332),x74333))) % 188.18/188.26 [7435]~P67(x74351)+~P107(f334(f334(f242(x74351),f2(x74351)),x74353))+~P107(f334(f334(f242(x74351),f2(x74351)),x74352))+P107(f334(f334(f242(x74351),f2(x74351)),f334(f334(f296(x74351),x74352),x74353))) % 188.18/188.26 [7436]~P68(x74361)+~P107(f334(f334(f243(x74361),f2(x74361)),x74363))+~P107(f334(f334(f242(x74361),f2(x74361)),x74362))+P107(f334(f334(f242(x74361),f2(x74361)),f334(f334(f296(x74361),x74362),x74363))) % 188.18/188.26 [7437]~P127(x74371)+~P107(f334(f334(f243(x74371),f84(x74371)),x74373))+~P107(f334(f334(f243(x74371),f84(x74371)),x74372))+P107(f334(f334(f243(x74371),f84(x74371)),f334(f334(f87(x74371),x74372),x74373))) % 188.18/188.26 [7438]~P135(x74381)+~P107(f334(f334(f243(x74381),f2(x74381)),x74383))+~P107(f334(f334(f243(x74381),f2(x74381)),x74382))+P107(f334(f334(f243(x74381),f2(x74381)),f334(f334(f87(x74381),x74382),x74383))) % 188.18/188.26 [7441]~P88(x74411)+~P107(f334(f334(f243(x74411),f2(x74411)),x74413))+~P107(f334(f334(f243(x74411),f2(x74411)),x74412))+P107(f334(f334(f243(x74411),f2(x74411)),f334(f334(f86(x74411),x74412),x74413))) % 188.18/188.26 [7442]~P67(x74421)+~P107(f334(f334(f243(x74421),f2(x74421)),x74423))+~P107(f334(f334(f243(x74421),f2(x74421)),x74422))+P107(f334(f334(f243(x74421),f2(x74421)),f334(f334(f296(x74421),x74422),x74423))) % 188.18/188.26 [7443]~P68(x74431)+~P107(f334(f334(f243(x74431),f2(x74431)),x74433))+~P107(f334(f334(f243(x74431),f2(x74431)),x74432))+P107(f334(f334(f243(x74431),f2(x74431)),f334(f334(f296(x74431),x74432),x74433))) % 188.18/188.26 [7520]~P109(x75201)+~P107(f334(f66(x75201),x75203))+E(f14(x75201,f334(f334(f316(x75201),x75202),x75203)),x75202)+~E(f334(f334(f23(f935(x75201,a922)),x75203),f334(f334(f316(x75201),x75202),f195(f935(x75201,a922)))),f195(f935(x75201,a922))) % 188.18/188.26 [7521]~P109(x75211)+~P107(f334(f66(x75211),x75213))+E(f15(x75211,f334(f334(f316(x75211),x75212),x75213)),x75212)+~E(f334(f334(f23(f935(x75211,a922)),x75213),f334(f334(f316(x75211),x75212),f195(f935(x75211,a922)))),f195(f935(x75211,a922))) % 188.18/188.26 [7522]~P99(x75221)+~P107(f334(f66(x75221),x75223))+E(f10(x75221,f334(f334(f316(x75221),x75222),x75223)),x75222)+~E(f334(f334(f23(f935(x75221,a922)),x75223),f334(f334(f316(x75221),x75222),f195(f935(x75221,a922)))),f195(f935(x75221,a922))) % 188.18/188.26 [7523]~P99(x75231)+~P107(f334(f66(x75231),x75233))+E(f13(x75231,f334(f334(f316(x75231),x75232),x75233)),x75232)+~E(f334(f334(f23(f935(x75231,a922)),x75233),f334(f334(f316(x75231),x75232),f195(f935(x75231,a922)))),f195(f935(x75231,a922))) % 188.18/188.26 [7525]~P129(x75251)+P107(f334(f334(f242(x75251),x75252),f2(x75251)))+P107(f334(f334(f242(x75251),f2(x75251)),x75253))+~P107(f334(f334(f242(x75251),f2(x75251)),f334(f334(f87(x75251),x75253),x75252))) % 188.18/188.26 [7526]~P129(x75261)+P107(f334(f334(f242(x75261),x75262),f2(x75261)))+P107(f334(f334(f242(x75261),f2(x75261)),x75263))+~P107(f334(f334(f242(x75261),f2(x75261)),f334(f334(f87(x75261),x75262),x75263))) % 188.18/188.26 [7527]~P67(x75271)+P107(f334(f334(f242(x75271),x75272),f2(x75271)))+P107(f334(f334(f242(x75271),f2(x75271)),x75273))+~P107(f334(f334(f242(x75271),f2(x75271)),f334(f334(f296(x75271),x75273),x75272))) % 188.18/188.26 [7528]~P67(x75281)+P107(f334(f334(f242(x75281),x75282),f2(x75281)))+P107(f334(f334(f242(x75281),f2(x75281)),x75283))+~P107(f334(f334(f242(x75281),f2(x75281)),f334(f334(f296(x75281),x75282),x75283))) % 188.18/188.26 [7529]~P129(x75291)+P107(f334(f334(f242(x75291),x75292),f2(x75291)))+P107(f334(f334(f242(x75291),f2(x75291)),x75292))+~P107(f334(f334(f242(x75291),f2(x75291)),f334(f334(f87(x75291),x75293),x75292))) % 188.18/188.26 [7530]~P129(x75301)+P107(f334(f334(f242(x75301),x75302),f2(x75301)))+P107(f334(f334(f242(x75301),f2(x75301)),x75302))+~P107(f334(f334(f242(x75301),f2(x75301)),f334(f334(f87(x75301),x75302),x75303))) % 188.18/188.26 [7531]~P67(x75311)+P107(f334(f334(f242(x75311),x75312),f2(x75311)))+P107(f334(f334(f242(x75311),f2(x75311)),x75312))+~P107(f334(f334(f242(x75311),f2(x75311)),f334(f334(f296(x75311),x75313),x75312))) % 188.18/188.26 [7532]~P67(x75321)+P107(f334(f334(f242(x75321),x75322),f2(x75321)))+P107(f334(f334(f242(x75321),f2(x75321)),x75322))+~P107(f334(f334(f242(x75321),f2(x75321)),f334(f334(f296(x75321),x75322),x75323))) % 188.18/188.26 [7533]~P67(x75331)+P107(f334(f334(f243(x75331),x75332),f2(x75331)))+P107(f334(f334(f243(x75331),f2(x75331)),x75333))+~P107(f334(f334(f243(x75331),f2(x75331)),f334(f334(f296(x75331),x75333),x75332))) % 188.18/188.26 [7534]~P67(x75341)+P107(f334(f334(f243(x75341),x75342),f2(x75341)))+P107(f334(f334(f243(x75341),f2(x75341)),x75343))+~P107(f334(f334(f243(x75341),f2(x75341)),f334(f334(f296(x75341),x75342),x75343))) % 188.18/188.26 [7535]~P67(x75351)+P107(f334(f334(f243(x75351),x75352),f2(x75351)))+P107(f334(f334(f243(x75351),f2(x75351)),x75352))+~P107(f334(f334(f243(x75351),f2(x75351)),f334(f334(f296(x75351),x75353),x75352))) % 188.18/188.26 [7536]~P67(x75361)+P107(f334(f334(f243(x75361),x75362),f2(x75361)))+P107(f334(f334(f243(x75361),f2(x75361)),x75362))+~P107(f334(f334(f243(x75361),f2(x75361)),f334(f334(f296(x75361),x75362),x75363))) % 188.18/188.26 [7613]~E(f334(f334(f109(f935(x76131,a922)),f334(f179(x76131),x76132)),f334(f179(x76131),x76133)),f195(f935(x76131,a922)))+~P107(f334(f144(x76131),x76133))+~P107(f334(f144(x76131),x76132))+P107(f334(f144(x76131),f334(f334(f141(x76131),x76132),x76133))) % 188.18/188.26 [7614]~P109(x76141)+~P107(f334(f66(x76141),x76143))+E(f11(x76141,f246(x76141),f334(f334(f316(x76141),x76142),x76143)),x76142)+~E(f334(f334(f23(f935(x76141,a922)),x76143),f334(f334(f316(x76141),x76142),f195(f935(x76141,a922)))),f195(f935(x76141,a922))) % 188.18/188.26 [7615]~P109(x76151)+~P107(f334(f66(x76151),x76153))+E(f12(x76151,f241(x76151),f334(f334(f316(x76151),x76152),x76153)),x76152)+~E(f334(f334(f23(f935(x76151,a922)),x76153),f334(f334(f316(x76151),x76152),f195(f935(x76151,a922)))),f195(f935(x76151,a922))) % 188.18/188.26 [7629]~P86(x76291)+~P107(f334(f334(f242(x76291),x76292),x76293))+~P107(f334(f334(f242(x76291),f334(f85(x76291),x76292)),x76293))+P107(f334(f334(f242(x76291),f334(f81(x76291),x76292)),x76293)) % 188.18/188.26 [7630]~P124(x76301)+~P107(f334(f334(f243(x76301),x76302),x76303))+~P107(f334(f334(f243(x76301),f334(f85(x76301),x76302)),x76303))+P107(f334(f334(f243(x76301),f334(f81(x76301),x76302)),x76303)) % 188.18/188.26 [7697]~P135(x76971)+P107(f334(f334(f243(x76971),f2(x76971)),x76972))+~P107(f334(f334(f243(x76971),f2(x76971)),x76973))+~P107(f334(f334(f243(x76971),f2(x76971)),f334(f334(f87(x76971),x76973),x76972))) % 188.18/188.26 [7698]~P135(x76981)+P107(f334(f334(f243(x76981),f2(x76981)),x76982))+~P107(f334(f334(f243(x76981),f2(x76981)),x76983))+~P107(f334(f334(f243(x76981),f2(x76981)),f334(f334(f87(x76981),x76982),x76983))) % 188.18/188.26 [7992]E(x79921,x79922)+~P107(f334(f66(x79923),x79921))+~P107(f334(f334(f242(a927),f334(f40(x79923),x79921)),f334(f40(x79923),x79922)))+~P107(f334(f334(f242(f935(x79923,a922)),x79922),x79921)) % 188.18/188.26 [8134]~P107(f334(f334(f243(a1),x81341),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x81342))+~P107(f334(f334(f242(a1),x81342),x81343))+P107(f334(f334(f242(a1),f334(f334(f41(a1),x81341),x81342)),f334(f334(f41(a1),x81341),x81343))) % 188.18/188.26 [8144]~P107(f334(f334(f242(a1),f2(a1)),x81441))+~P107(f334(f334(f243(a1),f2(a1)),x81443))+~P107(f334(f334(f242(a1),x81443),x81442))+P107(f334(f334(f242(a1),f334(f334(f41(a1),x81441),x81442)),f334(f334(f41(a1),x81441),x81443))) % 188.18/188.26 [8274]E(f334(x82741,f551(x82742,x82741,x82743)),x82742)+~P107(f334(f334(f242(a1),x82742),f334(x82741,x82743)))+P107(f334(f334(f243(a927),f552(x82742,x82741,x82743)),x82743))+~P107(f334(f334(f242(a1),f334(x82741,f2(a927))),x82742)) % 188.18/188.26 [8275]E(f334(x82751,f565(x82752,x82751,x82753)),x82752)+~P107(f334(f334(f242(a1),x82752),f334(x82751,x82753)))+P107(f334(f334(f243(a927),f566(x82752,x82751,x82753)),x82753))+~P107(f334(f334(f242(a1),f334(x82751,f2(a927))),x82752)) % 188.18/188.26 [8374]~P107(f334(f66(x83741),x83743))+~P107(f334(f334(f243(a927),f334(f40(x83741),x83742)),f334(f40(x83741),x83743)))+~P107(f334(f334(f242(f935(x83741,a922)),x83742),x83743))+P107(f334(f334(f243(f935(x83741,a922)),x83742),x83743)) % 188.18/188.26 [8401]E(f334(f334(f86(a1),f427(x84013,x84011,x84012)),f428(x84013,x84011,x84012)),x84011)+E(f334(f334(f23(a1),x84011),x84012),x84011)+~P107(f334(f334(f243(a1),f2(a1)),x84012))+~P107(f334(f334(f336(a1),f334(f334(f23(a1),x84011),f84(a1))),x84013)) % 188.18/188.26 [8402]E(f334(f334(f23(a1),f429(x84023,x84021,x84022)),f430(x84023,x84021,x84022)),x84021)+E(f334(f334(f86(a1),x84021),x84022),x84021)+~P107(f334(f334(f243(a1),f2(a1)),x84022))+~P107(f334(f334(f336(a1),f334(f334(f86(a1),x84021),f84(a1))),x84023)) % 188.18/188.26 [8452]~P107(f334(f334(f242(a927),x84523),x84521))+P107(f334(f334(f242(a927),x84521),x84522))+~P107(f334(f334(f242(a927),x84523),x84522))+~P107(f334(f334(f242(a927),f334(f334(f23(a927),x84521),x84523)),f334(f334(f23(a927),x84522),x84523))) % 188.18/188.26 [8453]~P107(f334(f334(f242(a927),x84533),x84531))+P107(f334(f334(f243(a927),x84531),x84532))+~P107(f334(f334(f242(a927),x84533),x84532))+~P107(f334(f334(f243(a927),f334(f334(f23(a927),x84531),x84533)),f334(f334(f23(a927),x84532),x84533))) % 188.18/188.26 [8472]~P109(x84722)+E(x84721,f120(x84722))+~P15(x84722,f334(f175(x84722),x84721))+E(f334(f149(x84722,x84722,f334(f7(x84722,x84722,x84722),f241(x84722)),x84723),f334(f175(x84722),x84721)),f334(f334(f241(x84722),f334(f334(f171(x84722),x84721),f2(a927))),x84723)) % 188.18/188.26 [8541]E(f334(f334(f23(a1),x85411),x85412),x85411)+~P107(f334(f334(f243(a1),f2(a1)),x85412))+P107(f334(f334(f336(a1),f427(x85413,x85411,x85412)),x85413))+~P107(f334(f334(f336(a1),f334(f334(f23(a1),x85411),f84(a1))),x85413)) % 188.18/188.26 [8542]E(f334(f334(f86(a1),x85421),x85422),x85421)+~P107(f334(f334(f243(a1),f2(a1)),x85422))+P107(f334(f334(f336(a1),f429(x85423,x85421,x85422)),x85423))+~P107(f334(f334(f336(a1),f334(f334(f86(a1),x85421),f84(a1))),x85423)) % 188.18/188.26 [8610]~P107(f334(f334(f242(a1),x86101),f334(x86102,x86103)))+P107(f334(f334(f243(a927),f552(x86101,x86102,x86103)),x86103))+P107(f334(f334(f242(a927),f551(x86101,x86102,x86103)),x86103))+~P107(f334(f334(f242(a1),f334(x86102,f2(a927))),x86101)) % 188.18/188.26 [8611]~P107(f334(f334(f242(a1),x86111),f334(x86112,x86113)))+P107(f334(f334(f243(a927),f566(x86111,x86112,x86113)),x86113))+P107(f334(f334(f242(a927),f565(x86111,x86112,x86113)),x86113))+~P107(f334(f334(f242(a1),f334(x86112,f2(a927))),x86111)) % 188.18/188.26 [8682]E(f334(f334(f23(a1),x86821),x86822),x86821)+~P107(f334(f334(f243(a1),f2(a1)),x86822))+P107(f334(f334(f336(a1),f428(x86823,x86821,x86822)),f311(a1,f84(a1),x86822)))+~P107(f334(f334(f336(a1),f334(f334(f23(a1),x86821),f84(a1))),x86823)) % 188.18/188.26 [8683]E(f334(f334(f86(a1),x86831),x86832),x86831)+~P107(f334(f334(f243(a1),f2(a1)),x86832))+P107(f334(f334(f336(a1),f430(x86833,x86831,x86832)),f311(a1,f84(a1),x86832)))+~P107(f334(f334(f336(a1),f334(f334(f86(a1),x86831),f84(a1))),x86833)) % 188.18/188.26 [8816]~P127(x88161)+~P107(f334(f334(f243(x88161),x88162),f84(x88161)))+~P107(f334(f334(f243(x88161),f2(x88161)),x88162))+P107(f334(f334(f243(x88161),f334(f334(f87(x88161),x88162),f334(f334(f252(x88161),x88162),x88163))),f334(f334(f252(x88161),x88162),x88163))) % 188.18/188.26 [8903]~P107(f334(x89031,x89032))+P107(f334(x89031,f2(a927)))+~P107(f334(f334(f243(a927),x89032),x89033))+~P107(f334(x89031,f50(a927,f334(a119,f599(x89032,x89031,x89033)),x89033))) % 188.18/188.26 [9059]E(f522(x90591,x90592,x90593),f2(a927))+P107(f334(f334(x90591,x90593),x90592))+P107(f334(f334(x90591,f522(x90591,x90592,x90593)),f50(a927,f521(x90591,x90592,x90593),f522(x90591,x90592,x90593))))+~P107(f334(f322(f934(a927,a927),a228),f334(f334(f260(a927,a927),x90593),x90592))) % 188.18/188.26 [9097]~P27(x90971,x90971,x90972,x90973)+E(f334(f317(x90971,x90971,x90972),x90973),x90973)+~P107(f334(f66(x90971),x90973))+~P107(f334(f334(f242(f935(x90971,a922)),f334(f317(x90971,x90971,x90972),x90973)),x90973)) % 188.18/188.26 [9303]P107(f334(f334(x93031,x93032),x93033))+P107(f334(f334(f243(a1),f789(x93031,x93033,x93032)),f790(x93031,x93033,x93032)))+P107(f334(f334(x93031,f789(x93031,x93033,x93032)),f334(f334(f86(a1),f790(x93031,x93033,x93032)),f84(a1))))+~P107(f334(f322(f934(a1,a1),a140),f334(f334(f260(a1,a1),x93032),x93033))) % 188.18/188.26 [9320]P107(f334(f334(x93201,x93202),x93203))+~P107(f334(f334(f243(a1),f368(x93201,x93203,x93202)),f2(a1)))+P107(f334(f334(x93201,f334(f85(a1),f367(x93201,x93203,x93202))),f334(f85(a1),f368(x93201,x93203,x93202))))+~P107(f334(f322(f934(a1,a1),a230),f334(f334(f260(a1,a1),x93202),x93203))) % 188.18/188.26 [9514]P107(f334(f334(x95141,x95142),x95143))+P107(f334(f334(x95141,f334(f334(f86(a1),f690(x95141,x95143,x95142)),f84(a1))),f692(x95141,x95143,x95142)))+~P107(f334(f334(f242(a1),f690(x95141,x95143,x95142)),f692(x95141,x95143,x95142)))+~P107(f334(f322(f934(a1,a1),a189),f334(f334(f260(a1,a1),x95142),x95143))) % 188.18/188.26 [9966]~P64(x99662)+~P64(x99661)+~P107(f334(f61(f934(x99661,x99662)),x99663))+P107(f334(f61(x99661),f334(f334(f8(f935(x99662,a922),a922,x99661),f61(x99662)),f334(f334(f8(f935(x99662,f934(x99661,x99662)),f935(x99662,a922),x99661),f334(f8(f934(x99661,x99662),a922,x99662),x99663)),f260(x99661,x99662))))) % 188.18/188.26 [9967]~P64(x99672)+~P64(x99671)+~P107(f334(f62(f934(x99671,x99672)),x99673))+P107(f334(f62(x99671),f334(f334(f8(f935(x99672,a922),a922,x99671),f62(x99672)),f334(f334(f8(f935(x99672,f934(x99671,x99672)),f935(x99672,a922),x99671),f334(f8(f934(x99671,x99672),a922,x99672),x99673)),f260(x99671,x99672))))) % 188.18/188.26 [10073]~P64(x100732)+~P64(x100731)+P107(f334(f61(f934(x100731,x100732)),x100733))+~P107(f334(f61(x100731),f334(f334(f8(f935(x100732,a922),a922,x100731),f61(x100732)),f334(f334(f8(f935(x100732,f934(x100731,x100732)),f935(x100732,a922),x100731),f334(f8(f934(x100731,x100732),a922,x100732),x100733)),f260(x100731,x100732))))) % 188.18/188.26 [10074]~P64(x100742)+~P64(x100741)+P107(f334(f62(f934(x100741,x100742)),x100743))+~P107(f334(f62(x100741),f334(f334(f8(f935(x100742,a922),a922,x100741),f62(x100742)),f334(f334(f8(f935(x100742,f934(x100741,x100742)),f935(x100742,a922),x100741),f334(f8(f934(x100741,x100742),a922,x100742),x100743)),f260(x100741,x100742))))) % 188.18/188.26 [10209]E(f334(x102091,f551(x102092,x102091,x102093)),x102092)+~P107(f334(f334(f242(a1),x102092),f334(x102091,x102093)))+~P107(f334(f334(f242(a1),f334(f81(a1),f334(f334(f23(a1),f334(x102091,f334(f334(f86(a927),f552(x102092,x102091,x102093)),f84(a927)))),f334(x102091,f552(x102092,x102091,x102093))))),f84(a1)))+~P107(f334(f334(f242(a1),f334(x102091,f2(a927))),x102092)) % 188.18/188.26 [10210]E(f334(x102101,f565(x102102,x102101,x102103)),x102102)+~P107(f334(f334(f242(a1),x102102),f334(x102101,x102103)))+~P107(f334(f334(f242(a1),f334(f81(a1),f334(f334(f23(a1),f334(x102101,f334(f334(f86(a927),f566(x102102,x102101,x102103)),f84(a927)))),f334(x102101,f566(x102102,x102101,x102103))))),f84(a1)))+~P107(f334(f334(f242(a1),f334(x102101,f2(a927))),x102102)) % 188.18/188.26 [10213]~P107(f334(f334(f242(a1),x102131),f334(x102132,x102133)))+~P107(f334(f334(f242(a1),f334(f81(a1),f334(f334(f23(a1),f334(x102132,f334(f334(f86(a927),f552(x102131,x102132,x102133)),f84(a927)))),f334(x102132,f552(x102131,x102132,x102133))))),f84(a1)))+P107(f334(f334(f242(a927),f551(x102131,x102132,x102133)),x102133))+~P107(f334(f334(f242(a1),f334(x102132,f2(a927))),x102131)) % 188.18/188.26 [10214]~P107(f334(f334(f242(a1),x102141),f334(x102142,x102143)))+~P107(f334(f334(f242(a1),f334(f81(a1),f334(f334(f23(a1),f334(x102142,f334(f334(f86(a927),f566(x102141,x102142,x102143)),f84(a927)))),f334(x102142,f566(x102141,x102142,x102143))))),f84(a1)))+P107(f334(f334(f242(a927),f565(x102141,x102142,x102143)),x102143))+~P107(f334(f334(f242(a1),f334(x102142,f2(a927))),x102141)) % 188.18/188.26 [10270]E(x102701,x102702)+~E(f334(f149(f928(x102703),f928(x102703),f141(x102703),f120(x102703)),x102701),f334(f149(f928(x102703),f928(x102703),f141(x102703),f120(x102703)),x102702))+~E(f334(f196(f928(f928(x102703))),x102701),f334(f196(f928(f928(x102703))),x102702))+~P107(f334(f334(f265(f928(x102703),f928(x102703),a922),f334(f334(f7(f928(x102703),f935(f928(x102703),a927),f935(f928(x102703),a922)),f334(f334(f8(f935(a927,a922),f935(f935(f928(x102703),a927),f935(f928(x102703),a922)),f928(x102703)),f8(a927,a922,f928(x102703))),f334(f334(f8(a927,f935(a927,a922),f928(x102703)),a331),f196(f928(x102703))))),f196(f928(x102703)))),f717(x102702,x102701,x102703))) % 188.18/188.26 [10271]E(x102711,x102712)+~E(f334(f149(f928(x102713),f928(x102713),f141(x102713),f120(x102713)),x102711),f334(f149(f928(x102713),f928(x102713),f141(x102713),f120(x102713)),x102712))+~E(f334(f196(f928(f928(x102713))),x102711),f334(f196(f928(f928(x102713))),x102712))+~P107(f334(f334(f265(f928(x102713),f928(x102713),a922),f334(f334(f7(f928(x102713),f935(f928(x102713),a927),f935(f928(x102713),a922)),f334(f334(f8(f935(a927,a922),f935(f935(f928(x102713),a927),f935(f928(x102713),a922)),f928(x102713)),f8(a927,a922,f928(x102713))),f334(f334(f8(a927,f935(a927,a922),f928(x102713)),a331),f196(f928(x102713))))),f196(f928(x102713)))),f718(x102711,x102712,x102713))) % 188.18/188.26 [7046]~E(f84(a927),f2(a927))+~P107(f334(f66(x70461),x70463))+~P107(f334(f66(x70461),x70462))+E(f334(f334(f86(a927),f334(f40(x70461),x70462)),f334(f40(x70461),x70463)),f334(f40(x70461),f334(f334(f108(f935(x70461,a922)),x70462),x70463))) % 188.18/188.26 [7450]~P109(x74501)+~P107(f334(f66(x74501),x74502))+~P107(f334(f334(f336(x74501),x74503),x74502))+P107(f334(f334(f242(x74501),f334(f68(x74501,f246(x74501)),x74502)),x74503)) % 188.18/188.26 [7451]~P104(x74511)+~P107(f334(f66(x74511),x74512))+~P107(f334(f334(f336(x74511),x74513),x74512))+P107(f334(f334(f242(x74511),f334(f68(x74511,f109(x74511)),x74512)),x74513)) % 188.18/188.26 [7691]~P107(f334(f66(x76911),x76913))+~P107(f334(f66(x76911),x76912))+~E(f334(f334(f109(f935(x76911,a922)),x76912),x76913),f195(f935(x76911,a922)))+E(f334(f334(f86(a927),f334(f40(x76911),x76912)),f334(f40(x76911),x76913)),f334(f40(x76911),f334(f334(f108(f935(x76911,a922)),x76912),x76913))) % 188.18/188.26 [8458]~P39(x84581,x84583)+~P39(x84581,x84582)+~E(f334(f334(f109(f935(x84581,a922)),f334(f272(x84581,x84581),x84582)),f334(f291(x84581,x84581),x84583)),f195(f935(x84581,a922)))+P39(x84581,f334(f334(f108(f935(f934(x84581,x84581),a922)),x84582),x84583)) % 188.18/188.26 [8550]E(x85501,f334(f334(f41(a927),x85502),x85503))+~P107(f334(f334(f243(a927),f2(a927)),x85503))+~P107(f334(f334(f243(a927),x85502),f334(f334(f87(a927),x85503),f334(a119,x85501))))+~P107(f334(f334(f242(a927),f334(f334(f87(a927),x85503),x85501)),x85502)) % 188.18/188.26 [8680]~P107(f334(f66(x86801),x86802))+~P107(f334(f66(x86801),x86803))+E(f334(f334(f86(a927),f334(f40(x86801),x86802)),f334(f40(x86801),x86803)),f334(f40(x86801),f334(f334(f108(f935(x86801,a922)),x86802),x86803)))+P107(f334(f334(f336(x86801),f475(x86803,x86802,x86801)),f334(f334(f109(f935(x86801,a922)),x86802),x86803))) % 188.18/188.26 [9072]~P129(x90722)+~E(x90721,f2(x90722))+~E(x90723,f2(x90722))+~P107(f334(f334(f243(x90722),f2(x90722)),f334(f334(f86(x90722),f334(f334(f87(x90722),x90723),x90723)),f334(f334(f87(x90722),x90721),x90721)))) % 188.18/188.26 [9596]~P39(x95961,x95963)+~P39(x95961,x95962)+P39(x95961,f334(f334(f108(f935(f934(x95961,x95961),a922)),x95962),x95963))+~P107(f334(f334(f242(f935(f934(x95961,x95961),a922)),f334(f334(f295(x95961,x95961,x95961),x95962),x95963)),x95962)) % 188.18/188.26 [9719]~P107(f334(x97191,x97193))+~P107(f334(f66(x97192),x97193))+P107(f334(x97191,f195(f935(x97192,a922))))+~P107(f334(x97191,f334(f334(f23(f935(x97192,a922)),f681(x97191,x97193,x97192)),f334(f334(f316(x97192),f673(x97191,x97193,x97192)),f195(f935(x97192,a922)))))) % 188.18/188.26 [8857]~P107(f334(f334(f243(a1),f2(a1)),x88573))+P107(f334(f334(f242(a1),f2(a1)),x88571))+~P107(f334(f334(f243(a1),x88572),x88573))+~P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),f334(f334(f87(a1),x88573),x88571)),x88572))) % 188.18/188.26 [8876]~P109(x88761)+~P107(f334(f66(x88761),x88762))+E(f334(f334(f23(f935(x88761,a922)),x88762),f334(f334(f316(x88761),x88763),f195(f935(x88761,a922)))),f195(f935(x88761,a922)))+E(f334(f334(f246(x88761),x88763),f14(x88761,f334(f334(f23(f935(x88761,a922)),x88762),f334(f334(f316(x88761),x88763),f195(f935(x88761,a922)))))),f14(x88761,f334(f334(f316(x88761),x88763),x88762))) % 188.18/188.26 [8877]~P109(x88771)+~P107(f334(f66(x88771),x88772))+E(f334(f334(f23(f935(x88771,a922)),x88772),f334(f334(f316(x88771),x88773),f195(f935(x88771,a922)))),f195(f935(x88771,a922)))+E(f334(f334(f241(x88771),x88773),f15(x88771,f334(f334(f23(f935(x88771,a922)),x88772),f334(f334(f316(x88771),x88773),f195(f935(x88771,a922)))))),f15(x88771,f334(f334(f316(x88771),x88773),x88772))) % 188.18/188.26 [8878]~P99(x88781)+~P107(f334(f66(x88781),x88782))+E(f334(f334(f23(f935(x88781,a922)),x88782),f334(f334(f316(x88781),x88783),f195(f935(x88781,a922)))),f195(f935(x88781,a922)))+E(f334(f334(f109(x88781),x88783),f10(x88781,f334(f334(f23(f935(x88781,a922)),x88782),f334(f334(f316(x88781),x88783),f195(f935(x88781,a922)))))),f10(x88781,f334(f334(f316(x88781),x88783),x88782))) % 188.18/188.26 [8879]~P99(x88791)+~P107(f334(f66(x88791),x88792))+E(f334(f334(f23(f935(x88791,a922)),x88792),f334(f334(f316(x88791),x88793),f195(f935(x88791,a922)))),f195(f935(x88791,a922)))+E(f334(f334(f108(x88791),x88793),f13(x88791,f334(f334(f23(f935(x88791,a922)),x88792),f334(f334(f316(x88791),x88793),f195(f935(x88791,a922)))))),f13(x88791,f334(f334(f316(x88791),x88793),x88792))) % 188.18/188.26 [8949]~P109(x89491)+~P107(f334(f66(x89491),x89492))+E(f334(f334(f23(f935(x89491,a922)),x89492),f334(f334(f316(x89491),x89493),f195(f935(x89491,a922)))),f195(f935(x89491,a922)))+E(f334(f334(f246(x89491),x89493),f11(x89491,f246(x89491),f334(f334(f23(f935(x89491,a922)),x89492),f334(f334(f316(x89491),x89493),f195(f935(x89491,a922)))))),f11(x89491,f246(x89491),f334(f334(f316(x89491),x89493),x89492))) % 188.18/188.26 [8950]~P109(x89501)+~P107(f334(f66(x89501),x89502))+E(f334(f334(f23(f935(x89501,a922)),x89502),f334(f334(f316(x89501),x89503),f195(f935(x89501,a922)))),f195(f935(x89501,a922)))+E(f334(f334(f241(x89501),x89503),f12(x89501,f241(x89501),f334(f334(f23(f935(x89501,a922)),x89502),f334(f334(f316(x89501),x89503),f195(f935(x89501,a922)))))),f12(x89501,f241(x89501),f334(f334(f316(x89501),x89503),x89502))) % 188.18/188.26 [9533]E(x95331,x95332)+~E(f334(f149(f928(x95333),f928(x95333),f141(x95333),f120(x95333)),x95331),f334(f149(f928(x95333),f928(x95333),f141(x95333),f120(x95333)),x95332))+~E(f334(f196(f928(f928(x95333))),x95331),f334(f196(f928(f928(x95333))),x95332))+P107(f334(f334(f336(f934(f928(x95333),f928(x95333))),f717(x95332,x95331,x95333)),f334(f179(f934(f928(x95333),f928(x95333))),f334(f334(f188(f928(x95333),f928(x95333)),x95331),x95332)))) % 188.18/188.26 [9534]E(x95341,x95342)+~E(f334(f149(f928(x95343),f928(x95343),f141(x95343),f120(x95343)),x95341),f334(f149(f928(x95343),f928(x95343),f141(x95343),f120(x95343)),x95342))+~E(f334(f196(f928(f928(x95343))),x95341),f334(f196(f928(f928(x95343))),x95342))+P107(f334(f334(f336(f934(f928(x95343),f928(x95343))),f718(x95341,x95342,x95343)),f334(f179(f934(f928(x95343),f928(x95343))),f334(f334(f188(f928(x95343),f928(x95343)),x95342),x95341)))) % 188.18/188.26 [10411]~P78(x104112)+E(x104111,f195(f935(x104112,a922)))+~P107(f334(f66(x104112),x104111))+E(f14(x104112,f334(f270(x104112),f334(f334(f8(f935(x104112,a922),a922,x104112),f92(x104112)),f334(f334(f7(x104112,f935(x104112,a922),f935(x104112,a922)),f334(f334(f8(f935(x104112,f935(a922,a922)),f935(f935(x104112,a922),f935(x104112,a922)),x104112),f18(x104112,a922,a922)),f334(f334(f8(f935(x104112,a922),f935(x104112,f935(a922,a922)),x104112),f334(f8(a922,f935(a922,a922),x104112),a332)),f334(f334(f7(x104112,f935(x104112,x104112),f935(x104112,a922)),f334(f334(f8(f935(x104112,a922),f935(f935(x104112,x104112),f935(x104112,a922)),x104112),f8(x104112,a922,x104112)),a331)),f334(f86(x104112),x104113))))),f334(f334(f7(x104112,f935(x104112,a922),a922),f336(x104112)),x104111))))),f334(f334(f86(x104112),x104113),f14(x104112,x104111))) % 188.18/188.26 [10412]~P78(x104122)+E(x104121,f195(f935(x104122,a922)))+~P107(f334(f66(x104122),x104121))+E(f15(x104122,f334(f270(x104122),f334(f334(f8(f935(x104122,a922),a922,x104122),f92(x104122)),f334(f334(f7(x104122,f935(x104122,a922),f935(x104122,a922)),f334(f334(f8(f935(x104122,f935(a922,a922)),f935(f935(x104122,a922),f935(x104122,a922)),x104122),f18(x104122,a922,a922)),f334(f334(f8(f935(x104122,a922),f935(x104122,f935(a922,a922)),x104122),f334(f8(a922,f935(a922,a922),x104122),a332)),f334(f334(f7(x104122,f935(x104122,x104122),f935(x104122,a922)),f334(f334(f8(f935(x104122,a922),f935(f935(x104122,x104122),f935(x104122,a922)),x104122),f8(x104122,a922,x104122)),a331)),f334(f86(x104122),x104123))))),f334(f334(f7(x104122,f935(x104122,a922),a922),f336(x104122)),x104121))))),f334(f334(f86(x104122),x104123),f15(x104122,x104121))) % 188.18/188.26 [10413]~P103(x104132)+E(x104131,f195(f935(x104132,a922)))+~P107(f334(f66(x104132),x104131))+E(f10(x104132,f334(f270(x104132),f334(f334(f8(f935(x104132,a922),a922,x104132),f92(x104132)),f334(f334(f7(x104132,f935(x104132,a922),f935(x104132,a922)),f334(f334(f8(f935(x104132,f935(a922,a922)),f935(f935(x104132,a922),f935(x104132,a922)),x104132),f18(x104132,a922,a922)),f334(f334(f8(f935(x104132,a922),f935(x104132,f935(a922,a922)),x104132),f334(f8(a922,f935(a922,a922),x104132),a332)),f334(f334(f7(x104132,f935(x104132,x104132),f935(x104132,a922)),f334(f334(f8(f935(x104132,a922),f935(f935(x104132,x104132),f935(x104132,a922)),x104132),f8(x104132,a922,x104132)),a331)),f334(f108(x104132),x104133))))),f334(f334(f7(x104132,f935(x104132,a922),a922),f336(x104132)),x104131))))),f334(f334(f108(x104132),x104133),f10(x104132,x104131))) % 188.18/188.26 [10414]~P103(x104142)+E(x104141,f195(f935(x104142,a922)))+~P107(f334(f66(x104142),x104141))+E(f13(x104142,f334(f270(x104142),f334(f334(f8(f935(x104142,a922),a922,x104142),f92(x104142)),f334(f334(f7(x104142,f935(x104142,a922),f935(x104142,a922)),f334(f334(f8(f935(x104142,f935(a922,a922)),f935(f935(x104142,a922),f935(x104142,a922)),x104142),f18(x104142,a922,a922)),f334(f334(f8(f935(x104142,a922),f935(x104142,f935(a922,a922)),x104142),f334(f8(a922,f935(a922,a922),x104142),a332)),f334(f334(f7(x104142,f935(x104142,x104142),f935(x104142,a922)),f334(f334(f8(f935(x104142,a922),f935(f935(x104142,x104142),f935(x104142,a922)),x104142),f8(x104142,a922,x104142)),a331)),f334(f109(x104142),x104143))))),f334(f334(f7(x104142,f935(x104142,a922),a922),f336(x104142)),x104141))))),f334(f334(f109(x104142),x104143),f13(x104142,x104141))) % 188.18/188.26 [10415]~P109(x104152)+E(x104151,f195(f935(x104152,a922)))+~P107(f334(f66(x104152),x104151))+E(f12(x104152,f241(x104152),f334(f270(x104152),f334(f334(f8(f935(x104152,a922),a922,x104152),f92(x104152)),f334(f334(f7(x104152,f935(x104152,a922),f935(x104152,a922)),f334(f334(f8(f935(x104152,f935(a922,a922)),f935(f935(x104152,a922),f935(x104152,a922)),x104152),f18(x104152,a922,a922)),f334(f334(f8(f935(x104152,a922),f935(x104152,f935(a922,a922)),x104152),f334(f8(a922,f935(a922,a922),x104152),a332)),f334(f334(f7(x104152,f935(x104152,x104152),f935(x104152,a922)),f334(f334(f8(f935(x104152,a922),f935(f935(x104152,x104152),f935(x104152,a922)),x104152),f8(x104152,a922,x104152)),a331)),f334(f246(x104152),x104153))))),f334(f334(f7(x104152,f935(x104152,a922),a922),f336(x104152)),x104151))))),f334(f334(f246(x104152),x104153),f12(x104152,f241(x104152),x104151))) % 188.18/188.26 [10416]~P109(x104162)+E(x104161,f195(f935(x104162,a922)))+~P107(f334(f66(x104162),x104161))+E(f11(x104162,f246(x104162),f334(f270(x104162),f334(f334(f8(f935(x104162,a922),a922,x104162),f92(x104162)),f334(f334(f7(x104162,f935(x104162,a922),f935(x104162,a922)),f334(f334(f8(f935(x104162,f935(a922,a922)),f935(f935(x104162,a922),f935(x104162,a922)),x104162),f18(x104162,a922,a922)),f334(f334(f8(f935(x104162,a922),f935(x104162,f935(a922,a922)),x104162),f334(f8(a922,f935(a922,a922),x104162),a332)),f334(f334(f7(x104162,f935(x104162,x104162),f935(x104162,a922)),f334(f334(f8(f935(x104162,a922),f935(f935(x104162,x104162),f935(x104162,a922)),x104162),f8(x104162,a922,x104162)),a331)),f334(f241(x104162),x104163))))),f334(f334(f7(x104162,f935(x104162,a922),a922),f336(x104162)),x104161))))),f334(f334(f241(x104162),x104163),f11(x104162,f246(x104162),x104161))) % 188.18/188.26 [10345]~P124(x103451)+~E(x103453,f2(x103451))+~E(x103452,f2(x103451))+E(f334(f334(f86(x103451),f334(f334(f252(x103451),x103452),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x103451),x103453),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f2(x103451)) % 188.18/188.26 [10421]~P127(x104211)+~P107(f334(f334(f242(x104211),f2(x104211)),x104213))+P107(f334(f334(f242(x104211),x104212),x104213))+~P107(f334(f334(f242(x104211),f334(f334(f252(x104211),x104212),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104211),x104213),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))))) % 188.18/188.26 [10447]~P124(x104472)+~E(x104471,f2(x104472))+~E(x104473,f2(x104472))+~P107(f334(f334(f243(x104472),f2(x104472)),f334(f334(f86(x104472),f334(f334(f252(x104472),x104473),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))),f334(f334(f252(x104472),x104471),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))))) % 188.18/188.26 [6933]~P9(x69333,x69332)+~P107(f334(x69331,x69334))+~P107(f334(f334(f336(x69333),x69334),f278(x69333,x69332)))+P107(f334(x69331,f838(x69331,x69332,x69333))) % 188.18/188.26 [8792]P28(x87921,x87922,f778(x87923,x87922,x87924,x87921),x87924,x87923)+~E(f334(f40(x87921),x87924),f334(f40(x87922),x87923))+~P107(f334(f66(x87922),x87923))+~P107(f334(f66(x87921),x87924)) % 188.18/188.26 [9493]E(x94931,x94932)+~E(f669(x94931,x94932,x94934,x94933),f670(x94931,x94932,x94934,x94933))+P107(f334(f334(f336(f934(f928(x94933),f928(x94933))),f334(f334(f260(f928(x94933),f928(x94933)),x94932),x94931)),f154(x94933,x94934)))+P107(f334(f334(f336(f934(f928(x94933),f928(x94933))),f334(f334(f260(f928(x94933),f928(x94933)),x94931),x94932)),f154(x94933,x94934))) % 188.18/188.26 [5092]~P65(x50922)+~E(x50924,f2(x50922))+~E(x50921,f2(x50922))+E(x50921,f334(f334(f296(x50922),x50923),x50924)) % 188.18/188.26 [5093]~P65(x50931)+~E(x50933,f2(x50931))+~E(x50934,f2(x50931))+E(f334(f334(f296(x50931),x50932),x50933),x50934) % 188.18/188.26 [5209]~P65(x52092)+E(x52091,f2(x52092))+~E(x52093,f2(x52092))+~E(x52091,f334(f334(f296(x52092),x52094),x52093)) % 188.18/188.26 [5210]~P65(x52102)+E(x52101,f2(x52102))+~E(x52103,f2(x52102))+~E(f334(f334(f296(x52102),x52104),x52103),x52101) % 188.18/188.26 [5389]~P122(x53892)+E(x53891,f2(x53892))+~E(f334(f334(f296(x53892),x53893),x53891),x53894)+E(x53893,f334(f334(f87(x53892),x53894),x53891)) % 188.18/188.26 [5391]~P122(x53912)+E(x53911,f2(x53912))+~E(f334(f334(f87(x53912),x53913),x53911),x53914)+E(x53913,f334(f334(f296(x53912),x53914),x53911)) % 188.18/188.26 [5392]~P65(x53922)+E(x53921,f2(x53922))+~E(f334(f334(f296(x53922),x53923),x53921),x53924)+E(x53923,f334(f334(f87(x53922),x53924),x53921)) % 188.18/188.26 [5393]~P65(x53932)+E(x53931,f2(x53932))+~E(f334(f334(f87(x53932),x53933),x53931),x53934)+E(x53933,f334(f334(f296(x53932),x53934),x53931)) % 188.18/188.26 [5394]~P122(x53942)+E(x53941,f2(x53942))+~E(x53943,f334(f334(f296(x53942),x53944),x53941))+E(f334(f334(f87(x53942),x53943),x53941),x53944) % 188.18/188.26 [5396]~P122(x53962)+E(x53961,f2(x53962))+~E(x53963,f334(f334(f87(x53962),x53964),x53961))+E(f334(f334(f296(x53962),x53963),x53961),x53964) % 188.18/188.26 [5397]~P65(x53972)+E(x53971,f2(x53972))+~E(x53973,f334(f334(f296(x53972),x53974),x53971))+E(f334(f334(f87(x53972),x53973),x53971),x53974) % 188.18/188.26 [5398]~P65(x53982)+E(x53981,f2(x53982))+~E(x53983,f334(f334(f87(x53982),x53984),x53981))+E(f334(f334(f296(x53982),x53983),x53981),x53984) % 188.18/188.26 [5422]~P65(x54222)+~E(x54221,f2(x54222))+~E(f334(f334(f87(x54222),x54221),x54224),x54223)+E(x54221,f334(f334(f296(x54222),x54223),x54224)) % 188.18/188.26 [5423]~P65(x54231)+~E(x54234,f2(x54231))+~E(x54232,f334(f334(f87(x54231),x54234),x54233))+E(f334(f334(f296(x54231),x54232),x54233),x54234) % 188.18/188.26 [5498]~E(x54983,x54984)+~E(x54982,x54983)+~P111(x54981)+E(f311(x54981,x54982,x54983),f334(f334(f316(x54981),x54984),f195(f935(x54981,a922)))) % 188.18/188.26 [5702]~E(f121(x57022,x57021),x57023)+~E(f151(x57022,x57021),x57024)+E(x57021,f120(x57022))+E(f334(f334(f141(x57022),x57023),f334(f334(f158(x57022),x57024),f120(x57022))),x57021) % 188.18/188.26 [6334]~P127(x63343)+E(x63341,x63342)+~E(f334(f334(f252(x63343),x63344),x63341),f334(f334(f252(x63343),x63344),x63342))+~P107(f334(f334(f243(x63343),f84(x63343)),x63344)) % 188.18/188.26 [6335]E(x63351,x63352)+~E(f334(f334(f316(x63353),x63354),x63351),f334(f334(f316(x63353),x63354),x63352))+P107(f334(f334(f336(x63353),x63354),x63352))+P107(f334(f334(f336(x63353),x63354),x63351)) % 188.18/188.26 [6377]E(f334(x63771,x63772),f84(a927))+~E(f334(f334(f9(x63773,a927),x63771),x63774),f84(a927))+~P107(f334(f66(x63773),x63774))+~P107(f334(f334(f336(x63773),x63772),x63774)) % 188.18/188.26 [6378]E(f334(x63781,x63782),f2(a927))+~E(f334(f334(f6(x63783,a927),x63781),x63784),f2(a927))+~P107(f334(f66(x63783),x63784))+~P107(f334(f334(f336(x63783),x63782),x63784)) % 188.18/188.26 [6590]~P111(x65901)+~P107(f334(f334(f242(x65901),x65904),x65903))+P107(f334(f334(f242(x65901),x65902),x65903))+~P107(f334(f334(f242(x65901),x65902),x65904)) % 188.18/188.26 [6591]~P108(x65911)+~P107(f334(f334(f242(x65911),x65912),x65914))+P107(f334(f334(f242(x65911),x65912),x65913))+~P107(f334(f334(f242(x65911),x65914),x65913)) % 188.18/188.26 [6592]~P111(x65921)+~P107(f334(f334(f243(x65921),x65924),x65923))+P107(f334(f334(f243(x65921),x65922),x65923))+~P107(f334(f334(f242(x65921),x65922),x65924)) % 188.18/188.26 [6593]~P111(x65931)+~P107(f334(f334(f243(x65931),x65932),x65934))+P107(f334(f334(f243(x65931),x65932),x65933))+~P107(f334(f334(f242(x65931),x65934),x65933)) % 188.18/188.26 [6594]~P111(x65941)+~P107(f334(f334(f243(x65941),x65944),x65943))+P107(f334(f334(f243(x65941),x65942),x65943))+~P107(f334(f334(f243(x65941),x65942),x65944)) % 188.18/188.26 [6595]~P108(x65951)+~P107(f334(f334(f243(x65951),x65952),x65954))+P107(f334(f334(f243(x65951),x65952),x65953))+~P107(f334(f334(f242(x65951),x65954),x65953)) % 188.18/188.26 [6596]~P108(x65961)+~P107(f334(f334(f243(x65961),x65964),x65963))+P107(f334(f334(f243(x65961),x65962),x65963))+~P107(f334(f334(f242(x65961),x65962),x65964)) % 188.18/188.26 [6597]~P108(x65971)+~P107(f334(f334(f243(x65971),x65972),x65974))+P107(f334(f334(f243(x65971),x65972),x65973))+~P107(f334(f334(f243(x65971),x65974),x65973)) % 188.18/188.26 [6676]~P114(x66762)+P59(x66762,x66763,x66764)+E(x66761,f2(x66762))+~P59(x66762,f334(f334(f87(x66762),x66763),x66761),f334(f334(f87(x66762),x66764),x66761)) % 188.18/188.26 [6677]~P114(x66772)+P59(x66772,x66773,x66774)+E(x66771,f2(x66772))+~P59(x66772,f334(f334(f87(x66772),x66771),x66773),f334(f334(f87(x66772),x66771),x66774)) % 188.18/188.26 [6682]~P37(x66824,x66823,x66822)+E(x66821,f770(x66822,x66823,x66824))+~P107(f334(x66823,x66821))+~P107(f334(f334(f336(x66824),x66821),f334(f179(x66824),x66822))) % 188.18/188.26 [6683]~P37(x66834,x66833,x66832)+E(x66831,f782(x66832,x66833,x66834))+~P107(f334(x66833,x66831))+~P107(f334(f334(f336(x66834),x66831),f334(f179(x66834),x66832))) % 188.18/188.26 [6828]~P7(x68281)+~P107(f334(f334(f242(x68281),x68282),f43(x68281,x68284)))+P107(f334(f334(f242(x68281),x68282),x68283))+~P107(f334(f334(f336(x68281),x68283),x68284)) % 188.18/188.26 [6971]~P109(x69711)+~P15(x69711,f334(f334(f158(x69711),x69712),x69714))+~P107(f334(f334(f336(x69711),x69713),f334(f179(x69711),x69714)))+P107(f334(f334(f242(x69711),x69712),x69713)) % 188.18/188.26 [7055]~P7(x70551)+~P107(f334(f334(f242(x70551),f42(x70551,x70554)),x70553))+P107(f334(f334(f242(x70551),x70552),x70553))+~P107(f334(f334(f336(x70551),x70552),x70554)) % 188.18/188.26 [7453]~P109(x74531)+E(f334(f334(f108(f935(x74531,a922)),f334(f310(x74531,x74532),x74533)),f334(f310(x74531,x74533),x74534)),f334(f310(x74531,x74532),x74534))+~P107(f334(f334(f242(x74531),x74533),x74534))+~P107(f334(f334(f242(x74531),x74532),x74533)) % 188.18/188.26 [7500]P37(x75001,x75002,x75003)+~E(f784(x75003,x75002,x75001,x75004),x75004)+~P107(f334(x75002,x75004))+~P107(f334(f334(f336(x75001),x75004),f334(f179(x75001),x75003))) % 188.18/188.26 [7501]P37(x75011,x75012,x75013)+~E(f793(x75013,x75012,x75011,x75014),x75014)+~P107(f334(x75012,x75014))+~P107(f334(f334(f336(x75011),x75014),f334(f179(x75011),x75013))) % 188.18/188.26 [7565]~P109(x75651)+E(f334(f334(f108(f935(x75651,a922)),f334(f310(x75651,x75652),x75653)),f311(x75651,x75653,x75654)),f311(x75651,x75652,x75654))+~P107(f334(f334(f242(x75651),x75653),x75654))+~P107(f334(f334(f242(x75651),x75652),x75653)) % 188.18/188.26 [7624]~P109(x76241)+E(f334(f334(f108(f935(x76241,a922)),f313(x76241,x76242,x76243)),f334(f310(x76241,x76243),x76244)),f313(x76241,x76242,x76244))+~P107(f334(f334(f242(x76241),x76243),x76244))+~P107(f334(f334(f243(x76241),x76242),x76243)) % 188.18/188.26 [7641]~P109(x76411)+E(f334(f334(f108(f935(x76411,a922)),f311(x76411,x76412,x76413)),f313(x76411,x76413,x76414)),f334(f310(x76411,x76412),x76414))+~P107(f334(f334(f242(x76411),x76412),x76413))+~P107(f334(f334(f243(x76411),x76413),x76414)) % 188.18/188.26 [7672]~P109(x76721)+E(f334(f334(f108(f935(x76721,a922)),f313(x76721,x76722,x76723)),f311(x76721,x76723,x76724)),f312(x76721,x76722,x76724))+~P107(f334(f334(f242(x76721),x76723),x76724))+~P107(f334(f334(f243(x76721),x76722),x76723)) % 188.18/188.26 [7673]~P109(x76731)+E(f334(f334(f108(f935(x76731,a922)),f312(x76731,x76732,x76733)),f313(x76731,x76733,x76734)),f313(x76731,x76732,x76734))+~P107(f334(f334(f242(x76731),x76732),x76733))+~P107(f334(f334(f243(x76731),x76733),x76734)) % 188.18/188.26 [7674]~P109(x76741)+E(f334(f334(f108(f935(x76741,a922)),f312(x76741,x76742,x76743)),f312(x76741,x76743,x76744)),f312(x76741,x76742,x76744))+~P107(f334(f334(f242(x76741),x76743),x76744))+~P107(f334(f334(f242(x76741),x76742),x76743)) % 188.18/188.26 [7675]~P109(x76751)+E(f334(f334(f108(f935(x76751,a922)),f311(x76751,x76752,x76753)),f312(x76751,x76753,x76754)),f311(x76751,x76752,x76754))+~P107(f334(f334(f242(x76751),x76753),x76754))+~P107(f334(f334(f242(x76751),x76752),x76753)) % 188.18/188.26 [8442]P27(x84421,x84422,f786(x84423,x84422,x84424,x84421),x84424)+~P107(f334(f66(x84422),x84423))+~P107(f334(f66(x84421),x84424))+~P107(f334(f334(f242(a927),f334(f40(x84421),x84424)),f334(f40(x84422),x84423))) % 188.18/188.26 [8463]P37(x84631,x84632,x84633)+~P107(f334(x84632,x84634))+P107(f334(x84632,f784(x84633,x84632,x84631,x84634)))+~P107(f334(f334(f336(x84631),x84634),f334(f179(x84631),x84633))) % 188.18/188.26 [8464]P37(x84641,x84642,x84643)+~P107(f334(x84642,x84644))+P107(f334(x84642,f793(x84643,x84642,x84641,x84644)))+~P107(f334(f334(f336(x84641),x84644),f334(f179(x84641),x84643))) % 188.18/188.26 [8519]~P72(x85191)+~E(f334(x85193,f881(x85193,x85194,x85192,x85191)),f84(x85191))+E(f334(f334(f334(f70(x85191,x85192,f87(x85191)),x85193),f84(x85191)),x85194),f84(x85191))+~P107(f334(f66(x85192),x85194)) % 188.18/188.26 [8781]~P127(x87811)+~P107(f334(f334(f242(x87811),f2(x87811)),x87813))+P107(f334(f334(f242(x87811),x87812),x87813))+~P107(f334(f334(f242(x87811),f334(f334(f252(x87811),x87812),f334(a119,x87814))),f334(f334(f252(x87811),x87813),f334(a119,x87814)))) % 188.18/188.26 [9098]P37(x90981,x90982,x90983)+~P107(f334(x90982,x90984))+~P107(f334(f334(f336(x90981),x90984),f334(f179(x90981),x90983)))+P107(f334(f334(f336(x90981),f784(x90983,x90982,x90981,x90984)),f334(f179(x90981),x90983))) % 188.18/188.26 [9099]P37(x90991,x90992,x90993)+~P107(f334(x90992,x90994))+~P107(f334(f334(f336(x90991),x90994),f334(f179(x90991),x90993)))+P107(f334(f334(f336(x90991),f793(x90993,x90992,x90991,x90994)),f334(f179(x90991),x90993))) % 188.18/188.26 [9178]~P72(x91781)+E(f334(f334(f334(f70(x91781,x91782,f87(x91781)),x91783),f84(x91781)),x91784),f84(x91781))+~P107(f334(f66(x91782),x91784))+P107(f334(f334(f336(x91782),f881(x91783,x91784,x91782,x91781)),x91784)) % 188.18/188.26 [9661]~P107(f334(f334(f242(a1),x96614),f2(a1)))+P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f87(a1),x96611),f50(a1,x96612,x96613))),x96614)),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x96613))+~P107(f334(f334(f243(a1),x96611),x96614)) % 188.18/188.26 [10125]~P107(f334(f66(x101251),x101252))+~P107(f334(f334(f336(x101251),x101254),x101252))+~P107(f334(f334(f336(x101251),x101253),x101252))+P107(f334(f334(f243(a927),f334(f40(x101251),f334(f334(f23(f935(x101251,a922)),f334(f334(f23(f935(x101251,a922)),x101252),f334(f334(f316(x101251),x101253),f195(f935(x101251,a922))))),f334(f334(f316(x101251),x101254),f195(f935(x101251,a922)))))),f334(f40(x101251),x101252))) % 188.18/188.26 [7109]~P148(x71093)+~P121(x71093)+P107(f334(x71091,f871(x71092,x71091,x71093)))+~P107(f334(x71091,f334(f334(f87(x71093),x71092),x71094))) % 188.18/188.26 [7166]~P109(x71661)+~P107(f334(f334(f242(x71661),x71662),x71664))+~P107(f334(f334(f242(x71661),x71662),x71663))+P107(f334(f334(f242(x71661),x71662),f334(f334(f246(x71661),x71663),x71664))) % 188.18/188.26 [7169]~P104(x71691)+~P107(f334(f334(f242(x71691),x71692),x71694))+~P107(f334(f334(f242(x71691),x71692),x71693))+P107(f334(f334(f242(x71691),x71692),f334(f334(f109(x71691),x71693),x71694))) % 188.18/188.26 [7170]~P109(x71701)+~P107(f334(f334(f243(x71701),x71702),x71704))+~P107(f334(f334(f243(x71701),x71702),x71703))+P107(f334(f334(f243(x71701),x71702),f334(f334(f246(x71701),x71703),x71704))) % 188.18/188.26 [7190]~P66(x71902)+E(x71901,f2(x71902))+E(f334(f334(f296(x71902),f334(f334(f252(x71902),x71901),x71903)),f334(f334(f252(x71902),x71901),x71904)),f334(f334(f252(x71902),x71901),f334(f334(f23(a927),x71903),x71904)))+~P107(f334(f334(f242(a927),x71904),x71903)) % 188.18/188.26 [7235]~P109(x72351)+~P15(x72351,f334(f334(f158(x72351),x72353),x72354))+P15(x72351,f334(f334(f158(x72351),x72352),f334(f334(f158(x72351),x72353),x72354)))+~P107(f334(f334(f242(x72351),x72352),x72353)) % 188.18/188.26 [7271]~P88(x72711)+~P107(f334(f334(f242(x72711),f2(x72711)),x72714))+~P107(f334(f334(f242(x72711),x72712),x72713))+P107(f334(f334(f242(x72711),x72712),f334(f334(f86(x72711),x72713),x72714))) % 188.18/188.26 [7272]~P88(x72721)+~P107(f334(f334(f242(x72721),f2(x72721)),x72723))+~P107(f334(f334(f242(x72721),x72722),x72724))+P107(f334(f334(f242(x72721),x72722),f334(f334(f86(x72721),x72723),x72724))) % 188.18/188.26 [7273]~P127(x72731)+~P107(f334(f334(f243(x72731),f2(x72731)),x72733))+~P107(f334(f334(f243(x72731),x72732),x72734))+P107(f334(f334(f243(x72731),x72732),f334(f334(f86(x72731),x72733),x72734))) % 188.18/188.26 [7274]~P88(x72741)+~P107(f334(f334(f242(x72741),x72742),x72744))+~P107(f334(f334(f243(x72741),f2(x72741)),x72743))+P107(f334(f334(f243(x72741),x72742),f334(f334(f86(x72741),x72743),x72744))) % 188.18/188.26 [7275]~P88(x72751)+~P107(f334(f334(f242(x72751),f2(x72751)),x72753))+~P107(f334(f334(f243(x72751),x72752),x72754))+P107(f334(f334(f243(x72751),x72752),f334(f334(f86(x72751),x72753),x72754))) % 188.18/188.26 [7315]~P109(x73151)+P107(f334(f334(f242(x73151),x73152),x73153))+P107(f334(f334(f242(x73151),x73152),x73154))+~P107(f334(f334(f242(x73151),x73152),f334(f334(f241(x73151),x73154),x73153))) % 188.18/188.26 [7316]~P109(x73161)+P107(f334(f334(f243(x73161),x73162),x73163))+P107(f334(f334(f243(x73161),x73162),x73164))+~P107(f334(f334(f243(x73161),x73162),f334(f334(f241(x73161),x73164),x73163))) % 188.18/188.26 [7598]~P111(x75982)+~P64(x75981)+~P107(f334(f334(f243(f935(x75981,x75982)),x75983),x75984))+P107(f334(f334(f242(f935(x75981,x75982)),x75983),x75984)) % 188.18/188.26 [7930]~P148(x79301)+~P121(x79301)+P59(x79301,x79302,f334(f334(f86(x79301),f871(x79302,x79303,x79301)),f2(x79301)))+~P107(f334(x79303,f334(f334(f87(x79301),x79302),x79304))) % 188.18/188.26 [7953]~P68(x79531)+~P107(f334(f334(f243(x79531),x79534),f2(x79531)))+~P107(f334(f334(f242(x79531),x79533),f334(f334(f296(x79531),x79532),x79534)))+P107(f334(f334(f242(x79531),x79532),f334(f334(f87(x79531),x79533),x79534))) % 188.18/188.26 [7954]~P68(x79541)+~P107(f334(f334(f243(x79541),x79544),f2(x79541)))+~P107(f334(f334(f242(x79541),x79543),f334(f334(f87(x79541),x79542),x79544)))+P107(f334(f334(f242(x79541),x79542),f334(f334(f296(x79541),x79543),x79544))) % 188.18/188.26 [7955]~P68(x79551)+~P107(f334(f334(f243(x79551),x79554),f2(x79551)))+~P107(f334(f334(f243(x79551),x79553),f334(f334(f296(x79551),x79552),x79554)))+P107(f334(f334(f243(x79551),x79552),f334(f334(f87(x79551),x79553),x79554))) % 188.18/188.26 [7956]~P68(x79561)+~P107(f334(f334(f243(x79561),x79564),f2(x79561)))+~P107(f334(f334(f243(x79561),x79563),f334(f334(f87(x79561),x79562),x79564)))+P107(f334(f334(f243(x79561),x79562),f334(f334(f296(x79561),x79563),x79564))) % 188.18/188.26 [8064]~P130(x80641)+~P107(f334(f334(f242(x80641),x80642),f2(x80641)))+~P107(f334(f334(f242(x80641),x80644),x80643))+P107(f334(f334(f242(x80641),f334(f334(f87(x80641),x80642),x80643)),f334(f334(f87(x80641),x80642),x80644))) % 188.18/188.26 [8065]~P129(x80651)+~P107(f334(f334(f243(x80651),x80652),f2(x80651)))+~P107(f334(f334(f242(x80651),x80654),x80653))+P107(f334(f334(f242(x80651),f334(f334(f87(x80651),x80652),x80653)),f334(f334(f87(x80651),x80652),x80654))) % 188.18/188.26 [8066]~P130(x80661)+~P107(f334(f334(f242(x80661),x80663),f2(x80661)))+~P107(f334(f334(f242(x80661),x80664),x80662))+P107(f334(f334(f242(x80661),f334(f334(f87(x80661),x80662),x80663)),f334(f334(f87(x80661),x80664),x80663))) % 188.18/188.26 [8067]~P67(x80671)+~P107(f334(f334(f242(x80671),x80673),f2(x80671)))+~P107(f334(f334(f242(x80671),x80674),x80672))+P107(f334(f334(f242(x80671),f334(f334(f296(x80671),x80672),x80673)),f334(f334(f296(x80671),x80674),x80673))) % 188.18/188.26 [8071]~P129(x80711)+~P107(f334(f334(f243(x80711),x80713),f2(x80711)))+~P107(f334(f334(f243(x80711),x80714),x80712))+P107(f334(f334(f243(x80711),f334(f334(f87(x80711),x80712),x80713)),f334(f334(f87(x80711),x80714),x80713))) % 188.18/188.26 [8072]~P129(x80721)+~P107(f334(f334(f243(x80721),x80722),f2(x80721)))+~P107(f334(f334(f243(x80721),x80724),x80723))+P107(f334(f334(f243(x80721),f334(f334(f87(x80721),x80722),x80723)),f334(f334(f87(x80721),x80722),x80724))) % 188.18/188.26 [8073]~P68(x80731)+~P107(f334(f334(f243(x80731),x80733),f2(x80731)))+~P107(f334(f334(f243(x80731),x80734),x80732))+P107(f334(f334(f243(x80731),f334(f334(f296(x80731),x80732),x80733)),f334(f334(f296(x80731),x80734),x80733))) % 188.18/188.26 [8074]~P127(x80741)+~P107(f334(f334(f243(x80741),f84(x80741)),x80742))+~P107(f334(f334(f242(a927),x80743),x80744))+P107(f334(f334(f242(x80741),f334(f334(f252(x80741),x80742),x80743)),f334(f334(f252(x80741),x80742),x80744))) % 188.18/188.26 [8075]~P127(x80751)+~P107(f334(f334(f242(x80751),f84(x80751)),x80752))+~P107(f334(f334(f242(a927),x80753),x80754))+P107(f334(f334(f242(x80751),f334(f334(f252(x80751),x80752),x80753)),f334(f334(f252(x80751),x80752),x80754))) % 188.18/188.26 [8077]~P127(x80771)+~P107(f334(f334(f243(x80771),f84(x80771)),x80772))+~P107(f334(f334(f243(a927),x80773),x80774))+P107(f334(f334(f243(x80771),f334(f334(f252(x80771),x80772),x80773)),f334(f334(f252(x80771),x80772),x80774))) % 188.18/188.26 [8100]P107(f334(f334(f243(a927),f2(a927)),f334(x81001,x81002)))+~P107(f334(f66(x81003),x81004))+~P107(f334(f334(f336(x81003),x81002),x81004))+~P107(f334(f334(f243(a927),f2(a927)),f334(f334(f9(x81003,a927),x81001),x81004))) % 188.18/188.26 [8108]~P129(x81081)+~P107(f334(f334(f243(x81081),f2(x81081)),x81082))+~P107(f334(f334(f242(x81081),x81083),x81084))+P107(f334(f334(f242(x81081),f334(f334(f87(x81081),x81082),x81083)),f334(f334(f87(x81081),x81082),x81084))) % 188.18/188.26 [8109]~P139(x81091)+~P107(f334(f334(f242(x81091),x81093),x81094))+~P107(f334(f334(f242(x81091),f2(x81091)),x81092))+P107(f334(f334(f242(x81091),f334(f334(f87(x81091),x81092),x81093)),f334(f334(f87(x81091),x81092),x81094))) % 188.18/188.26 [8110]~P138(x81101)+~P107(f334(f334(f242(x81101),x81103),x81104))+~P107(f334(f334(f242(x81101),f2(x81101)),x81102))+P107(f334(f334(f242(x81101),f334(f334(f87(x81101),x81102),x81103)),f334(f334(f87(x81101),x81102),x81104))) % 188.18/188.26 [8111]~P139(x81111)+~P107(f334(f334(f242(x81111),x81112),x81114))+~P107(f334(f334(f242(x81111),f2(x81111)),x81113))+P107(f334(f334(f242(x81111),f334(f334(f87(x81111),x81112),x81113)),f334(f334(f87(x81111),x81114),x81113))) % 188.18/188.26 [8112]~P127(x81121)+~P107(f334(f334(f242(x81121),x81122),x81124))+~P107(f334(f334(f242(x81121),f2(x81121)),x81122))+P107(f334(f334(f242(x81121),f334(f334(f252(x81121),x81122),x81123)),f334(f334(f252(x81121),x81124),x81123))) % 188.18/188.26 [8113]~P67(x81131)+~P107(f334(f334(f242(x81131),x81132),x81134))+~P107(f334(f334(f242(x81131),f2(x81131)),x81133))+P107(f334(f334(f242(x81131),f334(f334(f296(x81131),x81132),x81133)),f334(f334(f296(x81131),x81134),x81133))) % 188.18/188.26 [8115]~P125(x81151)+~P107(f334(f334(f243(x81151),x81153),x81154))+~P107(f334(f334(f243(x81151),f2(x81151)),x81152))+P107(f334(f334(f243(x81151),f334(f334(f87(x81151),x81152),x81153)),f334(f334(f87(x81151),x81152),x81154))) % 188.18/188.26 [8116]~P135(x81161)+~P107(f334(f334(f243(x81161),x81163),x81164))+~P107(f334(f334(f243(x81161),f2(x81161)),x81162))+P107(f334(f334(f243(x81161),f334(f334(f87(x81161),x81162),x81163)),f334(f334(f87(x81161),x81162),x81164))) % 188.18/188.26 [8117]~P129(x81171)+~P107(f334(f334(f243(x81171),x81172),x81174))+~P107(f334(f334(f243(x81171),f2(x81171)),x81173))+P107(f334(f334(f243(x81171),f334(f334(f87(x81171),x81172),x81173)),f334(f334(f87(x81171),x81174),x81173))) % 188.18/188.26 [8118]~P135(x81181)+~P107(f334(f334(f243(x81181),x81182),x81184))+~P107(f334(f334(f243(x81181),f2(x81181)),x81183))+P107(f334(f334(f243(x81181),f334(f334(f87(x81181),x81182),x81183)),f334(f334(f87(x81181),x81184),x81183))) % 188.18/188.26 [8119]~P129(x81191)+~P107(f334(f334(f243(x81191),x81193),x81194))+~P107(f334(f334(f243(x81191),f2(x81191)),x81192))+P107(f334(f334(f243(x81191),f334(f334(f87(x81191),x81192),x81193)),f334(f334(f87(x81191),x81192),x81194))) % 188.18/188.26 [8120]~P68(x81201)+~P107(f334(f334(f243(x81201),x81202),x81204))+~P107(f334(f334(f243(x81201),f2(x81201)),x81203))+P107(f334(f334(f243(x81201),f334(f334(f296(x81201),x81202),x81203)),f334(f334(f296(x81201),x81204),x81203))) % 188.18/188.26 [8158]~P110(x81582)+P107(f334(f334(f243(f935(x81581,x81582)),x81584),x81583))+~P107(f334(f334(f242(f935(x81581,x81582)),x81584),x81583))+P107(f334(f334(f242(f935(x81581,x81582)),x81583),x81584)) % 188.18/188.26 [8197]P107(f334(f334(f336(x81971),x81972),x81973))+P107(f334(f334(f336(x81971),x81972),x81974))+~P107(f334(f334(f242(f935(x81971,a922)),x81974),x81973))+P107(f334(f334(f243(f935(x81971,a922)),x81974),f334(f334(f316(x81971),x81972),x81973))) % 188.18/188.26 [8356]P107(f334(f334(f336(x83561),x83562),x83563))+P107(f334(f334(f336(x83561),x83562),x83564))+~P107(f334(f334(f243(f935(x83561,a922)),x83564),f334(f334(f316(x83561),x83562),x83563)))+P107(f334(f334(f242(f935(x83561,a922)),x83564),x83563)) % 188.18/188.26 [8422]~P129(x84221)+P107(f334(f334(f243(x84221),x84223),x84222))+P107(f334(f334(f243(x84221),x84222),x84223))+~P107(f334(f334(f243(x84221),f334(f334(f87(x84221),x84224),x84222)),f334(f334(f87(x84221),x84224),x84223))) % 188.18/188.26 [8423]~P129(x84231)+P107(f334(f334(f243(x84231),x84233),x84232))+P107(f334(f334(f243(x84231),x84232),x84233))+~P107(f334(f334(f243(x84231),f334(f334(f87(x84231),x84232),x84234)),f334(f334(f87(x84231),x84233),x84234))) % 188.18/188.26 [8432]~P129(x84321)+P107(f334(f334(f243(x84321),x84324),f2(x84321)))+P107(f334(f334(f243(x84321),x84322),x84323))+~P107(f334(f334(f243(x84321),f334(f334(f87(x84321),x84322),x84324)),f334(f334(f87(x84321),x84323),x84324))) % 188.18/188.26 [8433]~P129(x84331)+P107(f334(f334(f243(x84331),x84334),f2(x84331)))+P107(f334(f334(f243(x84331),x84332),x84333))+~P107(f334(f334(f243(x84331),f334(f334(f87(x84331),x84334),x84332)),f334(f334(f87(x84331),x84334),x84333))) % 188.18/188.26 [8437]~P129(x84371)+P107(f334(f334(f243(x84371),x84372),x84373))+P107(f334(f334(f243(x84371),f2(x84371)),x84374))+~P107(f334(f334(f243(x84371),f334(f334(f87(x84371),x84374),x84373)),f334(f334(f87(x84371),x84374),x84372))) % 188.18/188.26 [8438]~P129(x84381)+P107(f334(f334(f243(x84381),x84382),x84383))+P107(f334(f334(f243(x84381),f2(x84381)),x84384))+~P107(f334(f334(f243(x84381),f334(f334(f87(x84381),x84383),x84384)),f334(f334(f87(x84381),x84382),x84384))) % 188.18/188.26 [8450]~P129(x84501)+P107(f334(f334(f243(x84501),x84502),f2(x84501)))+P107(f334(f334(f243(x84501),f2(x84501)),x84502))+~P107(f334(f334(f243(x84501),f334(f334(f87(x84501),x84503),x84502)),f334(f334(f87(x84501),x84504),x84502))) % 188.18/188.26 [8451]~P129(x84511)+P107(f334(f334(f243(x84511),x84512),f2(x84511)))+P107(f334(f334(f243(x84511),f2(x84511)),x84512))+~P107(f334(f334(f243(x84511),f334(f334(f87(x84511),x84512),x84513)),f334(f334(f87(x84511),x84512),x84514))) % 188.18/188.26 [8481]~P129(x84811)+~P107(f334(f334(f243(x84811),x84814),f2(x84811)))+P107(f334(f334(f242(x84811),x84812),x84813))+~P107(f334(f334(f242(x84811),f334(f334(f87(x84811),x84814),x84813)),f334(f334(f87(x84811),x84814),x84812))) % 188.18/188.26 [8482]~P129(x84821)+~P107(f334(f334(f243(x84821),x84824),f2(x84821)))+P107(f334(f334(f243(x84821),x84822),x84823))+~P107(f334(f334(f243(x84821),f334(f334(f87(x84821),x84824),x84823)),f334(f334(f87(x84821),x84824),x84822))) % 188.18/188.26 [8493]~P127(x84933)+~P107(f334(f334(f243(x84933),f84(x84933)),x84934))+P107(f334(f334(f242(a927),x84931),x84932))+~P107(f334(f334(f242(x84933),f334(f334(f252(x84933),x84934),x84931)),f334(f334(f252(x84933),x84934),x84932))) % 188.18/188.26 [8495]~P127(x84953)+~P107(f334(f334(f243(x84953),f84(x84953)),x84954))+P107(f334(f334(f243(a927),x84951),x84952))+~P107(f334(f334(f243(x84953),f334(f334(f252(x84953),x84954),x84951)),f334(f334(f252(x84953),x84954),x84952))) % 188.18/188.26 [8505]~P129(x85051)+P107(f334(f334(f242(x85051),x85052),x85053))+~P107(f334(f334(f243(x85051),f2(x85051)),x85054))+~P107(f334(f334(f242(x85051),f334(f334(f87(x85051),x85054),x85052)),f334(f334(f87(x85051),x85054),x85053))) % 188.18/188.26 [8506]~P135(x85061)+P107(f334(f334(f242(x85061),x85062),x85063))+~P107(f334(f334(f243(x85061),f2(x85061)),x85064))+~P107(f334(f334(f242(x85061),f334(f334(f87(x85061),x85064),x85062)),f334(f334(f87(x85061),x85064),x85063))) % 188.18/188.26 [8507]~P135(x85071)+P107(f334(f334(f242(x85071),x85072),x85073))+~P107(f334(f334(f243(x85071),f2(x85071)),x85074))+~P107(f334(f334(f242(x85071),f334(f334(f87(x85071),x85072),x85074)),f334(f334(f87(x85071),x85073),x85074))) % 188.18/188.26 [8508]~P129(x85081)+P107(f334(f334(f243(x85081),x85082),x85083))+~P107(f334(f334(f243(x85081),f2(x85081)),x85084))+~P107(f334(f334(f243(x85081),f334(f334(f87(x85081),x85084),x85082)),f334(f334(f87(x85081),x85084),x85083))) % 188.18/188.26 [8509]~P135(x85091)+P107(f334(f334(f243(x85091),x85092),x85093))+~P107(f334(f334(f242(x85091),f2(x85091)),x85094))+~P107(f334(f334(f243(x85091),f334(f334(f87(x85091),x85094),x85092)),f334(f334(f87(x85091),x85094),x85093))) % 188.18/188.26 [8510]~P132(x85101)+P107(f334(f334(f243(x85101),x85102),x85103))+~P107(f334(f334(f242(x85101),f2(x85101)),x85104))+~P107(f334(f334(f243(x85101),f334(f334(f87(x85101),x85104),x85102)),f334(f334(f87(x85101),x85104),x85103))) % 188.18/188.26 [8511]~P127(x85111)+~P107(f334(f334(f242(x85111),f2(x85111)),x85113))+P107(f334(f334(f243(x85111),x85112),x85113))+~P107(f334(f334(f243(x85111),f334(f334(f252(x85111),x85112),x85114)),f334(f334(f252(x85111),x85113),x85114))) % 188.18/188.26 [8512]~P135(x85121)+P107(f334(f334(f243(x85121),x85122),x85123))+~P107(f334(f334(f242(x85121),f2(x85121)),x85124))+~P107(f334(f334(f243(x85121),f334(f334(f87(x85121),x85122),x85124)),f334(f334(f87(x85121),x85123),x85124))) % 188.18/188.26 [8513]~P132(x85131)+P107(f334(f334(f243(x85131),x85132),x85133))+~P107(f334(f334(f242(x85131),f2(x85131)),x85134))+~P107(f334(f334(f243(x85131),f334(f334(f87(x85131),x85132),x85134)),f334(f334(f87(x85131),x85133),x85134))) % 188.18/188.26 [8553]P107(f334(f334(f336(x85531),x85532),x85533))+~P107(f334(f334(f242(f935(x85531,a922)),x85533),x85534))+~P107(f334(f334(f243(f935(x85531,a922)),x85533),x85534))+P107(f334(f334(f243(f935(x85531,a922)),x85533),f334(f334(f316(x85531),x85532),x85534))) % 188.18/188.26 [8924]E(f334(f334(f23(a1),f437(x89241,x89242,x89243,x89244)),f438(x89241,x89242,x89243,x89244)),x89244)+~P107(f334(f334(f243(a1),f2(a1)),x89243))+~P107(f334(f334(f242(a1),x89241),x89244))+P107(f334(f334(f242(a1),x89241),f334(f334(f86(a1),x89244),x89243))) % 188.18/188.26 [8925]E(f334(f334(f23(a1),f444(x89251,x89252,x89253,x89254)),f445(x89251,x89252,x89253,x89254)),x89254)+~P107(f334(f334(f243(a1),f2(a1)),x89253))+~P107(f334(f334(f243(a1),x89251),x89254))+P107(f334(f334(f243(a1),x89251),f334(f334(f86(a1),x89254),x89253))) % 188.18/188.26 [9080]~E(f334(f334(f171(x90801),x90803),f691(x90804,x90803,x90801,x90802)),f334(f334(f171(x90801),x90804),f691(x90804,x90803,x90801,x90802)))+E(f334(f334(f182(x90801),x90802),x90803),f334(f334(f182(x90801),x90802),x90804))+~P107(f334(f334(f242(a927),x90802),f334(f196(f928(x90801)),x90803)))+~P107(f334(f334(f242(a927),x90802),f334(f196(f928(x90801)),x90804))) % 188.18/188.26 [9146]~P107(f334(f334(f243(a1),f2(a1)),x91463))+~P107(f334(f334(f242(a1),x91461),x91464))+P107(f334(f334(f336(a1),f437(x91461,x91462,x91463,x91464)),x91462))+P107(f334(f334(f242(a1),x91461),f334(f334(f86(a1),x91464),x91463))) % 188.18/188.26 [9147]~P107(f334(f334(f243(a1),f2(a1)),x91473))+~P107(f334(f334(f243(a1),x91471),x91474))+P107(f334(f334(f336(a1),f444(x91471,x91472,x91473,x91474)),x91472))+P107(f334(f334(f243(a1),x91471),f334(f334(f86(a1),x91474),x91473))) % 188.18/188.26 [9187]~P109(x91871)+~P107(f334(f66(x91871),x91873))+~P107(f334(f334(f336(x91871),x91874),x91873))+P107(f334(f334(f242(x91871),f334(f334(f69(x91871,x91871,f246(x91871)),x91872),x91873)),f334(f334(f246(x91871),x91874),x91872))) % 188.18/188.26 [9188]~P104(x91881)+~P107(f334(f66(x91881),x91883))+~P107(f334(f334(f336(x91881),x91884),x91883))+P107(f334(f334(f242(x91881),f334(f334(f69(x91881,x91881,f109(x91881)),x91882),x91883)),f334(f334(f109(x91881),x91884),x91882))) % 188.18/188.26 [9231]E(f334(f334(f182(x92311),x92312),x92313),f334(f334(f182(x92311),x92312),x92314))+P107(f334(f334(f243(a927),f691(x92313,x92314,x92311,x92312)),x92312))+~P107(f334(f334(f242(a927),x92312),f334(f196(f928(x92311)),x92313)))+~P107(f334(f334(f242(a927),x92312),f334(f196(f928(x92311)),x92314))) % 188.18/188.26 [9236]~P107(f334(f334(f243(a1),f2(a1)),x92363))+~P107(f334(f334(f242(a1),x92361),x92362))+P107(f334(f334(f336(a1),f438(x92361,x92364,x92363,x92362)),f311(a1,f84(a1),x92363)))+P107(f334(f334(f242(a1),x92361),f334(f334(f86(a1),x92362),x92363))) % 188.18/188.26 [9237]~P107(f334(f334(f243(a1),f2(a1)),x92373))+~P107(f334(f334(f243(a1),x92371),x92372))+P107(f334(f334(f336(a1),f445(x92371,x92374,x92373,x92372)),f311(a1,f84(a1),x92373)))+P107(f334(f334(f243(a1),x92371),f334(f334(f86(a1),x92372),x92373))) % 188.18/188.26 [9554]~P109(x95541)+~P107(f334(f66(x95541),x95544))+P107(f334(f334(f336(x95541),f605(x95542,x95543,x95544,x95541)),x95544))+P107(f334(f334(f242(x95541),f334(f334(f69(x95541,x95541,f241(x95541)),x95542),x95544)),f334(f334(f241(x95541),x95543),x95542))) % 188.18/188.26 [9555]~P98(x95551)+~P107(f334(f66(x95551),x95554))+P107(f334(f334(f336(x95551),f615(x95552,x95553,x95554,x95551)),x95554))+P107(f334(f334(f242(x95551),f334(f334(f69(x95551,x95551,f108(x95551)),x95552),x95554)),f334(f334(f108(x95551),x95553),x95552))) % 188.18/188.26 [9675]~P109(x96751)+~P107(f334(f66(x96751),x96753))+~P107(f334(f334(f242(x96751),f605(x96752,x96754,x96753,x96751)),x96754))+P107(f334(f334(f242(x96751),f334(f334(f69(x96751,x96751,f241(x96751)),x96752),x96753)),f334(f334(f241(x96751),x96754),x96752))) % 188.18/188.26 [9676]~P98(x96761)+~P107(f334(f66(x96761),x96763))+~P107(f334(f334(f242(x96761),f615(x96762,x96764,x96763,x96761)),x96764))+P107(f334(f334(f242(x96761),f334(f334(f69(x96761,x96761,f108(x96761)),x96762),x96763)),f334(f334(f108(x96761),x96764),x96762))) % 188.18/188.26 [9678]~P107(f334(f334(f242(a1),f2(a1)),x96784))+~P107(f334(f334(f243(a1),f2(a1)),x96783))+~P107(f334(f334(f243(a1),x96784),x96781))+P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f87(a1),x96781),f50(a1,x96782,x96783))),x96784)),f334(f334(f87(a1),x96781),x96783))) % 188.18/188.26 [10097]E(x100971,x100972)+P107(f334(f334(f336(f934(f928(x100973),f928(x100973))),f334(f334(f260(f928(x100973),f928(x100973)),x100972),x100971)),f154(x100973,x100974)))+P107(f334(f334(f336(f934(f928(x100973),f928(x100973))),f334(f334(f260(f928(x100973),f928(x100973)),x100971),x100972)),f154(x100973,x100974)))+~P107(f334(f334(f336(f934(x100973,x100973)),f334(f334(f260(x100973,x100973),f669(x100971,x100972,x100974,x100973)),f670(x100971,x100972,x100974,x100973))),x100974)) % 188.18/188.26 [10098]E(x100981,x100982)+P107(f334(f334(f336(f934(f928(x100983),f928(x100983))),f334(f334(f260(f928(x100983),f928(x100983)),x100982),x100981)),f154(x100983,x100984)))+P107(f334(f334(f336(f934(f928(x100983),f928(x100983))),f334(f334(f260(f928(x100983),f928(x100983)),x100981),x100982)),f154(x100983,x100984)))+~P107(f334(f334(f336(f934(x100983,x100983)),f334(f334(f260(x100983,x100983),f670(x100981,x100982,x100984,x100983)),f669(x100981,x100982,x100984,x100983))),x100984)) % 188.18/188.26 [7663]~P109(x76631)+~P107(f334(f334(f242(x76631),x76633),x76634))+~P107(f334(f334(f242(x76631),x76632),x76634))+P107(f334(f334(f242(x76631),f334(f334(f241(x76631),x76632),x76633)),x76634)) % 188.18/188.26 [7666]~P98(x76661)+~P107(f334(f334(f242(x76661),x76663),x76664))+~P107(f334(f334(f242(x76661),x76662),x76664))+P107(f334(f334(f242(x76661),f334(f334(f108(x76661),x76662),x76663)),x76664)) % 188.18/188.26 [7667]~P109(x76671)+~P107(f334(f334(f243(x76671),x76673),x76674))+~P107(f334(f334(f243(x76671),x76672),x76674))+P107(f334(f334(f243(x76671),f334(f334(f241(x76671),x76672),x76673)),x76674)) % 188.18/188.26 [7978]~E(x79781,x79783)+E(f146(a927,f334(f310(a927,x79781),x79782)),f334(f334(f158(a927),x79783),x79784))+~E(f146(a927,f334(f310(a927,f334(f334(f86(a927),x79781),f84(a927))),x79782)),x79784)+~P107(f334(f334(f243(a927),x79781),x79782)) % 188.18/188.26 [7987]~P109(x79871)+P107(f334(f334(f242(x79871),x79872),x79873))+P107(f334(f334(f242(x79871),x79874),x79873))+~P107(f334(f334(f242(x79871),f334(f334(f246(x79871),x79874),x79872)),x79873)) % 188.18/188.26 [7988]~P109(x79881)+P107(f334(f334(f243(x79881),x79882),x79883))+P107(f334(f334(f243(x79881),x79884),x79883))+~P107(f334(f334(f243(x79881),f334(f334(f246(x79881),x79884),x79882)),x79883)) % 188.18/188.26 [8255]~P67(x82551)+~P107(f334(f334(f243(x82551),f2(x82551)),x82553))+~P107(f334(f334(f242(x82551),x82552),f334(f334(f296(x82551),x82554),x82553)))+P107(f334(f334(f242(x82551),f334(f334(f87(x82551),x82552),x82553)),x82554)) % 188.18/188.26 [8256]~P68(x82561)+~P107(f334(f334(f243(x82561),f2(x82561)),x82563))+~P107(f334(f334(f242(x82561),x82562),f334(f334(f296(x82561),x82564),x82563)))+P107(f334(f334(f242(x82561),f334(f334(f87(x82561),x82562),x82563)),x82564)) % 188.18/188.26 [8257]~P67(x82571)+~P107(f334(f334(f243(x82571),f2(x82571)),x82573))+~P107(f334(f334(f242(x82571),x82572),f334(f334(f87(x82571),x82574),x82573)))+P107(f334(f334(f242(x82571),f334(f334(f296(x82571),x82572),x82573)),x82574)) % 188.18/188.26 [8259]~P68(x82591)+~P107(f334(f334(f243(x82591),f2(x82591)),x82593))+~P107(f334(f334(f242(x82591),x82592),f334(f334(f87(x82591),x82594),x82593)))+P107(f334(f334(f242(x82591),f334(f334(f296(x82591),x82592),x82593)),x82594)) % 188.18/188.26 [8260]~P67(x82601)+~P107(f334(f334(f243(x82601),f2(x82601)),x82603))+~P107(f334(f334(f243(x82601),x82602),f334(f334(f296(x82601),x82604),x82603)))+P107(f334(f334(f243(x82601),f334(f334(f87(x82601),x82602),x82603)),x82604)) % 188.18/188.26 [8261]~P68(x82611)+~P107(f334(f334(f243(x82611),f2(x82611)),x82613))+~P107(f334(f334(f243(x82611),x82612),f334(f334(f296(x82611),x82614),x82613)))+P107(f334(f334(f243(x82611),f334(f334(f87(x82611),x82612),x82613)),x82614)) % 188.18/188.26 [8262]~P67(x82621)+~P107(f334(f334(f243(x82621),f2(x82621)),x82623))+~P107(f334(f334(f243(x82621),x82622),f334(f334(f87(x82621),x82624),x82623)))+P107(f334(f334(f243(x82621),f334(f334(f296(x82621),x82622),x82623)),x82624)) % 188.18/188.26 [8264]~P68(x82641)+~P107(f334(f334(f243(x82641),f2(x82641)),x82643))+~P107(f334(f334(f243(x82641),x82642),f334(f334(f87(x82641),x82644),x82643)))+P107(f334(f334(f243(x82641),f334(f334(f296(x82641),x82642),x82643)),x82644)) % 188.18/188.26 [8391]~P67(x83911)+~P107(f334(f334(f243(x83911),f2(x83911)),x83914))+P107(f334(f334(f242(x83911),x83912),f334(f334(f87(x83911),x83913),x83914)))+~P107(f334(f334(f242(x83911),f334(f334(f296(x83911),x83912),x83914)),x83913)) % 188.18/188.26 [8392]~P67(x83921)+~P107(f334(f334(f243(x83921),f2(x83921)),x83924))+P107(f334(f334(f242(x83921),x83922),f334(f334(f296(x83921),x83923),x83924)))+~P107(f334(f334(f242(x83921),f334(f334(f87(x83921),x83922),x83924)),x83923)) % 188.18/188.26 [8394]~P68(x83941)+~P107(f334(f334(f243(x83941),f2(x83941)),x83944))+P107(f334(f334(f242(x83941),x83942),f334(f334(f87(x83941),x83943),x83944)))+~P107(f334(f334(f242(x83941),f334(f334(f296(x83941),x83942),x83944)),x83943)) % 188.18/188.26 [8395]~P68(x83951)+~P107(f334(f334(f243(x83951),f2(x83951)),x83954))+P107(f334(f334(f242(x83951),x83952),f334(f334(f296(x83951),x83953),x83954)))+~P107(f334(f334(f242(x83951),f334(f334(f87(x83951),x83952),x83954)),x83953)) % 188.18/188.26 [8396]~P67(x83961)+~P107(f334(f334(f243(x83961),f2(x83961)),x83964))+P107(f334(f334(f243(x83961),x83962),f334(f334(f87(x83961),x83963),x83964)))+~P107(f334(f334(f243(x83961),f334(f334(f296(x83961),x83962),x83964)),x83963)) % 188.18/188.26 [8397]~P67(x83971)+~P107(f334(f334(f243(x83971),f2(x83971)),x83974))+P107(f334(f334(f243(x83971),x83972),f334(f334(f296(x83971),x83973),x83974)))+~P107(f334(f334(f243(x83971),f334(f334(f87(x83971),x83972),x83974)),x83973)) % 188.18/188.26 [8399]~P68(x83991)+~P107(f334(f334(f243(x83991),f2(x83991)),x83994))+P107(f334(f334(f243(x83991),x83992),f334(f334(f87(x83991),x83993),x83994)))+~P107(f334(f334(f243(x83991),f334(f334(f296(x83991),x83992),x83994)),x83993)) % 188.18/188.26 [8400]~P68(x84001)+~P107(f334(f334(f243(x84001),f2(x84001)),x84004))+P107(f334(f334(f243(x84001),x84002),f334(f334(f296(x84001),x84003),x84004)))+~P107(f334(f334(f243(x84001),f334(f334(f87(x84001),x84002),x84004)),x84003)) % 188.18/188.26 [8556]~P68(x85561)+~P107(f334(f334(f243(x85561),x85563),f2(x85561)))+~P107(f334(f334(f242(x85561),f334(f334(f296(x85561),x85564),x85563)),x85562))+P107(f334(f334(f242(x85561),f334(f334(f87(x85561),x85562),x85563)),x85564)) % 188.18/188.26 [8557]~P68(x85571)+~P107(f334(f334(f243(x85571),x85573),f2(x85571)))+~P107(f334(f334(f242(x85571),f334(f334(f87(x85571),x85574),x85573)),x85572))+P107(f334(f334(f242(x85571),f334(f334(f296(x85571),x85572),x85573)),x85574)) % 188.18/188.26 [8558]~P68(x85581)+~P107(f334(f334(f243(x85581),x85583),f2(x85581)))+~P107(f334(f334(f243(x85581),f334(f334(f296(x85581),x85584),x85583)),x85582))+P107(f334(f334(f243(x85581),f334(f334(f87(x85581),x85582),x85583)),x85584)) % 188.18/188.26 [8559]~P68(x85591)+~P107(f334(f334(f243(x85591),x85593),f2(x85591)))+~P107(f334(f334(f243(x85591),f334(f334(f87(x85591),x85594),x85593)),x85592))+P107(f334(f334(f243(x85591),f334(f334(f296(x85591),x85592),x85593)),x85594)) % 188.18/188.26 [8571]~P107(f334(x85711,x85714))+~P107(f334(f334(f243(a927),x85712),f334(f334(f87(a927),x85713),f334(a119,x85714))))+P107(f334(x85711,f334(f334(f41(a927),x85712),x85713)))+~P107(f334(f334(f242(a927),f334(f334(f87(a927),x85713),x85714)),x85712)) % 188.18/188.26 [8779]~P109(x87791)+~P107(f334(f66(x87791),x87794))+~P107(f334(f334(f336(x87791),x87792),x87794))+P107(f334(f334(f242(x87791),f334(f334(f241(x87791),x87792),x87793)),f334(f334(f69(x87791,x87791,f241(x87791)),x87793),x87794))) % 188.18/188.26 [8780]~P98(x87801)+~P107(f334(f66(x87801),x87804))+~P107(f334(f334(f336(x87801),x87802),x87804))+P107(f334(f334(f242(x87801),f334(f334(f108(x87801),x87802),x87803)),f334(f334(f69(x87801,x87801,f108(x87801)),x87803),x87804))) % 188.18/188.26 [8926]~P107(f334(f66(x89261),x89262))+E(f334(f40(x89261),f334(f334(f23(f935(x89261,a922)),x89262),f334(f334(f316(x89261),x89263),x89264))),f334(f334(f23(a927),f334(f40(x89261),f334(f334(f23(f935(x89261,a922)),x89262),x89264))),f84(a927)))+P107(f334(f334(f336(x89261),x89263),x89264))+~P107(f334(f334(f336(x89261),x89263),x89262)) % 188.18/188.26 [9002]E(f334(f334(f86(a1),f439(x90021,x90022,x90023,x90024)),f440(x90021,x90022,x90023,x90024)),x90024)+~P107(f334(f334(f243(a1),f2(a1)),x90023))+~P107(f334(f334(f242(a1),x90024),x90021))+P107(f334(f334(f242(a1),f334(f334(f23(a1),x90024),x90023)),x90021)) % 188.18/188.26 [9003]E(f334(f334(f86(a1),f446(x90031,x90032,x90033,x90034)),f447(x90031,x90032,x90033,x90034)),x90034)+~P107(f334(f334(f243(a1),f2(a1)),x90033))+~P107(f334(f334(f243(a1),x90034),x90031))+P107(f334(f334(f243(a1),f334(f334(f23(a1),x90034),x90033)),x90031)) % 188.18/188.26 [9216]~P107(f334(f334(f243(a1),f2(a1)),x92163))+~P107(f334(f334(f242(a1),x92164),x92161))+P107(f334(f334(f336(a1),f439(x92161,x92162,x92163,x92164)),x92162))+P107(f334(f334(f242(a1),f334(f334(f23(a1),x92164),x92163)),x92161)) % 188.18/188.26 [9217]~P107(f334(f334(f243(a1),f2(a1)),x92173))+~P107(f334(f334(f243(a1),x92174),x92171))+P107(f334(f334(f336(a1),f446(x92171,x92172,x92173,x92174)),x92172))+P107(f334(f334(f243(a1),f334(f334(f23(a1),x92174),x92173)),x92171)) % 188.18/188.26 [9293]~P107(f334(f334(f243(a1),f2(a1)),x92932))+~P107(f334(f334(f242(a1),x92931),x92933))+P107(f334(f334(f336(a1),f440(x92933,x92934,x92932,x92931)),f311(a1,f84(a1),x92932)))+P107(f334(f334(f242(a1),f334(f334(f23(a1),x92931),x92932)),x92933)) % 188.18/188.26 [9294]~P107(f334(f334(f243(a1),f2(a1)),x92942))+~P107(f334(f334(f243(a1),x92941),x92943))+P107(f334(f334(f336(a1),f447(x92943,x92944,x92942,x92941)),f311(a1,f84(a1),x92942)))+P107(f334(f334(f243(a1),f334(f334(f23(a1),x92941),x92942)),x92943)) % 188.18/188.26 [9311]~P107(f334(f334(f242(a1),f2(a1)),x93114))+~P107(f334(f334(f243(a1),f2(a1)),x93113))+~P107(f334(f334(f243(a1),x93114),x93111))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),f334(f334(f87(a1),x93111),f50(a1,x93112,x93113))),x93114))) % 188.18/188.26 [9345]E(x93451,x93452)+~P41(x93453,x93454)+~P107(f334(f334(f336(f934(x93453,x93453)),f334(f334(f260(x93453,x93453),x93452),x93451)),x93454))+~P107(f334(f334(f336(f934(x93453,x93453)),f334(f334(f260(x93453,x93453),x93451),x93452)),x93454)) % 188.18/188.26 [9381]~P109(x93811)+~P107(f334(f66(x93811),x93814))+~P107(f334(f334(f242(x93811),x93812),f604(x93813,x93812,x93814,x93811)))+P107(f334(f334(f242(x93811),f334(f334(f246(x93811),x93812),x93813)),f334(f334(f69(x93811,x93811,f246(x93811)),x93813),x93814))) % 188.18/188.26 [9382]~P104(x93821)+~P107(f334(f66(x93821),x93824))+~P107(f334(f334(f242(x93821),x93822),f614(x93823,x93822,x93824,x93821)))+P107(f334(f334(f242(x93821),f334(f334(f109(x93821),x93822),x93823)),f334(f334(f69(x93821,x93821,f109(x93821)),x93823),x93824))) % 188.18/188.26 [9396]~P107(f334(f334(f242(a1),x93964),f2(a1)))+~P107(f334(f334(f243(a1),f2(a1)),x93962))+~P107(f334(f334(f243(a1),x93961),x93964))+P107(f334(f334(f243(a1),f334(f334(f87(a1),x93961),x93962)),f334(f334(f86(a1),f334(f334(f87(a1),x93961),f50(a1,x93963,x93962))),x93964))) % 188.18/188.26 [9421]P107(f334(f66(x94211),x94212))+~P107(f334(f66(x94211),x94213))+~P107(f334(f334(f336(f935(x94211,a922)),x94212),f334(f334(f65(x94211),x94213),x94214)))+~P107(f334(f334(f242(f935(f934(x94211,x94211),a922)),x94214),f334(f334(f262(x94211,x94211),x94213),f334(f16(f935(x94211,a922),x94211),x94213)))) % 188.18/188.26 [9443]~P109(x94431)+~P107(f334(f66(x94431),x94434))+P107(f334(f334(f336(x94431),f604(x94432,x94433,x94434,x94431)),x94434))+P107(f334(f334(f242(x94431),f334(f334(f246(x94431),x94433),x94432)),f334(f334(f69(x94431,x94431,f246(x94431)),x94432),x94434))) % 188.18/188.26 [9444]~P104(x94441)+~P107(f334(f66(x94441),x94444))+P107(f334(f334(f336(x94441),f614(x94442,x94443,x94444,x94441)),x94444))+P107(f334(f334(f242(x94441),f334(f334(f109(x94441),x94443),x94442)),f334(f334(f69(x94441,x94441,f109(x94441)),x94442),x94444))) % 188.18/188.26 [9864]~P107(f334(f66(x98642),x98644))+~P107(f334(f66(x98641),x98643))+~P107(f334(f334(f242(a927),f334(f40(x98642),x98644)),f334(f40(x98641),x98643)))+P107(f334(f334(f242(f935(x98641,a922)),f334(f317(x98642,x98641,f786(x98643,x98641,x98644,x98642)),x98644)),x98643)) % 188.18/188.26 [9492]~P107(f334(f334(f336(x94921),x94922),x94924))+P107(f334(f334(f336(x94921),x94922),x94923))+~P107(f334(f334(f243(f935(x94921,a922)),x94924),f334(f334(f316(x94921),x94922),x94923)))+P107(f334(f334(f243(f935(x94921,a922)),f334(f334(f23(f935(x94921,a922)),x94924),f334(f334(f316(x94921),x94922),f195(f935(x94921,a922))))),x94923)) % 188.18/188.26 [9658]~P107(f334(f334(f336(x96581),x96582),x96584))+P107(f334(f334(f336(x96581),x96582),x96583))+P107(f334(f334(f243(f935(x96581,a922)),x96584),f334(f334(f316(x96581),x96582),x96583)))+~P107(f334(f334(f243(f935(x96581,a922)),f334(f334(f23(f935(x96581,a922)),x96584),f334(f334(f316(x96581),x96582),f195(f935(x96581,a922))))),x96583)) % 188.18/188.26 [9681]P107(f334(f334(f336(x96811),x96812),x96813))+~P107(f334(f334(f242(f935(x96811,a922)),x96814),x96813))+P107(f334(f334(f243(f935(x96811,a922)),x96814),f334(f334(f316(x96811),x96812),x96813)))+~P107(f334(f334(f243(f935(x96811,a922)),f334(f334(f23(f935(x96811,a922)),x96814),f334(f334(f316(x96811),x96812),f195(f935(x96811,a922))))),x96813)) % 188.18/188.26 [9686]~P107(f334(f334(f336(x96861),x96863),x96862))+~P107(f334(f334(f243(f935(x96861,a922)),x96862),x96864))+P107(f334(f334(f243(f935(x96861,a922)),x96862),f334(f334(f316(x96861),x96863),x96864)))+~P107(f334(f334(f243(f935(x96861,a922)),f334(f334(f23(f935(x96861,a922)),x96862),f334(f334(f316(x96861),x96863),f195(f935(x96861,a922))))),x96864)) % 188.18/188.26 [9702]~P107(f334(f334(f242(f935(x97021,a922)),x97022),x97024))+~P107(f334(f334(f243(f935(x97021,a922)),x97022),x97024))+P107(f334(f334(f243(f935(x97021,a922)),x97022),f334(f334(f316(x97021),x97023),x97024)))+~P107(f334(f334(f243(f935(x97021,a922)),f334(f334(f23(f935(x97021,a922)),x97022),f334(f334(f316(x97021),x97023),f195(f935(x97021,a922))))),x97024)) % 188.18/188.26 [9760]~P111(x97602)+~P64(x97601)+~P107(f334(f334(f242(f935(x97601,x97602)),x97603),x97604))+P107(f334(f62(x97601),f334(f334(f18(x97601,x97602,a922),f334(f334(f8(x97602,f935(x97602,a922),x97601),f242(x97602)),x97603)),x97604))) % 188.18/188.26 [9914]~P111(x99142)+~P64(x99141)+P107(f334(f334(f242(f935(x99141,x99142)),x99143),x99144))+~P107(f334(f62(x99141),f334(f334(f18(x99141,x99142,a922),f334(f334(f8(x99142,f935(x99142,a922),x99141),f242(x99142)),x99143)),x99144))) % 188.18/188.26 [10088]E(f334(f334(f171(x100881),f334(f334(f171(f928(x100881)),f186(x100881,x100882)),x100883)),x100884),f334(f334(f171(x100881),f334(f334(f171(f928(x100881)),x100882),x100884)),x100883))+~P107(f334(f334(f243(a927),x100883),f334(f196(f928(f928(x100881))),f186(x100881,x100882))))+~P15(a927,f334(f175(a927),f334(f334(f161(f928(x100881),a927),f196(f928(x100881))),x100882)))+~P107(f334(f334(f243(a927),x100884),f334(f196(f928(f928(x100881))),f334(f143(f928(x100881),f334(f334(f8(a927,a922,f928(x100881)),f334(f243(a927),x100883)),f196(f928(x100881)))),x100882)))) % 188.18/188.26 [10110]~P107(f334(f334(f336(f934(a927,a927)),x101104),x101101))+~P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),x101104),x101102)),a38))+~P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x101101),x101103)),a74))+P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x101101),f334(f334(f316(f934(a927,a927)),x101102),x101103))),a74)) % 188.18/188.26 [10111]~P107(f334(f334(f336(f934(a927,a927)),x101114),x101111))+~P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),x101114),x101112)),a76))+~P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x101111),x101113)),a77))+P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x101111),f334(f334(f316(f934(a927,a927)),x101112),x101113))),a77)) % 188.18/188.26 [10003]~P111(x100032)+~P64(x100031)+~P107(f334(f334(f243(f935(x100031,x100032)),x100033),x100034))+P107(f334(f61(x100031),f334(f334(f8(a922,a922,x100031),a329),f334(f334(f18(x100031,x100032,a922),f334(f334(f8(x100032,f935(x100032,a922),x100031),a331),x100033)),x100034)))) % 188.18/188.26 [10121]~P107(f334(f334(f336(f934(a927,a927)),x101214),x101213))+~P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),x101211),x101214)),a38))+~P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x101212),x101213)),a39))+P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),f334(f334(f316(f934(a927,a927)),x101211),x101212)),x101213)),a39)) % 188.18/188.26 [10122]~P107(f334(f334(f336(f934(a927,a927)),x101224),x101223))+~P107(f334(f334(f336(f934(f934(a927,a927),f934(a927,a927))),f334(f334(f260(f934(a927,a927),f934(a927,a927)),x101221),x101224)),a76))+~P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),x101222),x101223)),a75))+P107(f334(f334(f336(f934(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922))),f334(f334(f260(f935(f934(a927,a927),a922),f935(f934(a927,a927),a922)),f334(f334(f316(f934(a927,a927)),x101221),x101222)),x101223)),a75)) % 188.18/188.26 [6287]~P9(x62874,x62871)+~P107(f334(f334(x62871,x62872),x62875))+P107(f334(f334(x62871,x62872),x62873))+~P107(f334(f334(x62871,x62875),x62873)) % 188.18/188.26 [6288]~P52(x62884,x62881)+~P107(f334(f334(x62881,x62882),x62885))+P107(f334(f334(x62881,x62882),x62883))+~P107(f334(f334(x62881,x62885),x62883)) % 188.18/188.26 [6289]~P17(x62894,x62891)+~P107(f334(f334(x62891,x62892),x62895))+P107(f334(f334(x62891,x62892),x62893))+~P107(f334(f334(x62891,x62895),x62893)) % 188.18/188.26 [8911]~P9(x89114,x89113)+~P107(f334(x89111,x89115))+P107(f334(x89112,f845(x89112,x89111,x89113,x89114)))+P107(f334(x89111,f843(x89112,x89111,x89113,x89114))) % 188.18/188.26 [9154]~P9(x91544,x91543)+~P107(f334(x91542,x91545))+~P107(f334(x91541,f843(x91541,x91542,x91543,x91544)))+P107(f334(x91541,f845(x91541,x91542,x91543,x91544))) % 188.18/188.26 [9324]~P9(x93244,x93243)+~P107(f334(x93241,x93245))+P107(f334(f334(f336(x93244),f845(x93242,x93241,x93243,x93244)),f278(x93244,x93243)))+P107(f334(x93241,f843(x93242,x93241,x93243,x93244))) % 188.18/188.26 [9450]~P9(x94501,x94504)+~P107(f334(x94503,x94505))+~P107(f334(x94502,f843(x94502,x94503,x94504,x94501)))+P107(f334(f334(f336(x94501),f845(x94502,x94503,x94504,x94501)),f278(x94501,x94504))) % 188.18/188.26 [9748]~P40(x97481,x97484)+P107(f334(f334(f336(f934(f928(x97481),f928(x97481))),f334(f334(f260(f928(x97481),f928(x97481)),x97482),x97483)),f154(x97481,x97484)))+~P107(f334(f334(f336(f934(f928(x97481),f928(x97481))),f334(f334(f260(f928(x97481),f928(x97481)),x97482),x97485)),f154(x97481,x97484)))+~P107(f334(f334(f336(f934(f928(x97481),f928(x97481))),f334(f334(f260(f928(x97481),f928(x97481)),x97485),x97483)),f154(x97481,x97484))) % 188.18/188.26 [5527]~P3(x55275)+E(x55271,x55272)+~E(x55273,x55274)+~E(f334(f334(f23(x55275),x55273),x55274),f334(f334(f23(x55275),x55271),x55272)) % 188.18/188.26 [6400]~P19(x64005,x64001,x64003)+E(f334(f334(x64001,x64002),f334(x64003,x64004)),f334(x64003,x64004))+~P107(f334(f66(x64005),x64004))+~P107(f334(f334(f336(x64005),x64002),x64004)) % 188.18/188.26 [6568]~P119(x65681)+~P59(x65681,x65683,x65685)+~P59(x65681,x65682,x65684)+P59(x65681,f334(f334(f87(x65681),x65682),x65683),f334(f334(f87(x65681),x65684),x65685)) % 188.18/188.26 [6581]~P79(x65811)+~E(f334(f334(f23(x65811),x65814),x65815),f334(f334(f23(x65811),x65812),x65813))+~P107(f334(f334(f242(x65811),x65814),x65815))+P107(f334(f334(f242(x65811),x65812),x65813)) % 188.18/188.26 [6583]~P79(x65831)+~E(f334(f334(f23(x65831),x65834),x65835),f334(f334(f23(x65831),x65832),x65833))+~P107(f334(f334(f243(x65831),x65834),x65835))+P107(f334(f334(f243(x65831),x65832),x65833)) % 188.18/188.26 [7538]~E(x75382,f334(f334(f158(x75381),x75384),x75385))+P107(f334(f334(f336(f928(x75381)),x75382),f168(x75381,x75383)))+~P107(f334(f334(f336(f928(x75381)),x75385),f168(x75381,x75383)))+~P107(f334(f334(f336(x75381),x75384),x75383)) % 188.18/188.26 [7925]~E(f334(f196(f928(x79251)),x79253),f334(f196(f928(x79252)),x79254))+~E(f334(f334(f161(f934(x79251,x79252),x79252),f264(x79251,x79252)),x79255),x79254)+~E(f334(f334(f161(f934(x79251,x79252),x79251),f259(x79251,x79252)),x79255),x79253)+E(f334(f334(f188(x79251,x79252),x79253),x79254),x79255) % 188.18/188.26 [8251]~P111(x82511)+P107(f334(f334(f243(f935(x82511,a922)),f311(x82511,x82512,x82513)),f311(x82511,x82514,x82515)))+~P107(f334(f334(f242(x82511),x82514),x82515))+P107(f334(f334(f242(x82511),x82512),x82513)) % 188.18/188.26 [8349]~P111(x83491)+P107(f334(f334(f242(f935(x83491,a922)),f311(x83491,x83492,x83493)),f311(x83491,x83494,x83495)))+~P107(f334(f334(f242(x83491),x83493),x83495))+~P107(f334(f334(f242(x83491),x83494),x83492)) % 188.18/188.26 [8466]~P109(x84661)+P107(f334(f334(f242(x84661),x84662),x84663))+P107(f334(f334(f242(x84661),x84664),x84663))+~P107(f334(f334(f242(f935(x84661,a922)),f334(f310(x84661,x84663),x84662)),f334(f310(x84661,x84664),x84665))) % 188.18/188.26 [8467]~P109(x84671)+P107(f334(f334(f242(x84671),x84672),x84673))+P107(f334(f334(f242(x84671),x84672),x84674))+~P107(f334(f334(f242(f935(x84671,a922)),f334(f310(x84671,x84673),x84672)),f334(f310(x84671,x84675),x84674))) % 188.18/188.26 [8694]~P111(x86941)+~P107(f334(f334(f242(f935(x86941,a922)),f311(x86941,x86944,x86942)),f311(x86941,x86945,x86943)))+P107(f334(f334(f242(x86941),x86942),x86943))+~P107(f334(f334(f242(x86941),x86944),x86942)) % 188.18/188.26 [8695]~P111(x86951)+~P107(f334(f334(f243(f935(x86951,a922)),f311(x86951,x86954,x86952)),f311(x86951,x86955,x86953)))+P107(f334(f334(f242(x86951),x86952),x86953))+~P107(f334(f334(f242(x86951),x86954),x86952)) % 188.18/188.26 [8696]~P111(x86961)+~P107(f334(f334(f242(f935(x86961,a922)),f311(x86961,x86963,x86964)),f311(x86961,x86962,x86965)))+P107(f334(f334(f242(x86961),x86962),x86963))+~P107(f334(f334(f242(x86961),x86963),x86964)) % 188.18/188.26 [8697]~P111(x86971)+~P107(f334(f334(f243(f935(x86971,a922)),f311(x86971,x86973,x86974)),f311(x86971,x86972,x86975)))+P107(f334(f334(f242(x86971),x86972),x86973))+~P107(f334(f334(f242(x86971),x86973),x86974)) % 188.18/188.26 [6286]~P19(x62862,x62865,x62863)+E(x62861,f195(f935(x62862,a922)))+~P107(f334(f66(x62862),x62861))+E(f334(x62863,f334(f334(f316(x62862),x62864),x62861)),f334(f334(x62865,x62864),f334(x62863,x62861))) % 188.18/188.26 [7044]~E(x70441,x70442)+~E(f334(f334(f109(f935(x70443,a922)),x70444),x70445),f195(f935(x70443,a922)))+~P107(f334(f334(f336(x70443),x70442),x70445))+~P107(f334(f334(f336(x70443),x70441),x70444)) % 188.18/188.26 [7121]~P20(x71212,x71215,x71211)+~P107(f334(f66(x71212),x71214))+E(f334(x71211,f334(f334(f316(x71212),x71213),x71214)),f334(f334(f69(x71212,x71212,x71215),x71213),x71214))+P107(f334(f334(f336(x71212),x71213),x71214)) % 188.18/188.27 [7186]~P72(x71862)+~P107(f334(f66(x71861),x71865))+E(f334(f334(f9(x71861,x71862),x71863),f334(f334(f316(x71861),x71864),x71865)),f334(f334(f87(x71862),f334(x71863,x71864)),f334(f334(f9(x71861,x71862),x71863),x71865)))+P107(f334(f334(f336(x71861),x71864),x71865)) % 188.18/188.27 [7188]~P76(x71882)+~P107(f334(f66(x71881),x71885))+E(f334(f334(f6(x71881,x71882),x71883),f334(f334(f316(x71881),x71884),x71885)),f334(f334(f86(x71882),f334(x71883,x71884)),f334(f334(f6(x71881,x71882),x71883),x71885)))+P107(f334(f334(f336(x71881),x71884),x71885)) % 188.18/188.27 [7676]~P20(x76762,x76765,x76761)+~P107(f334(f66(x76762),x76764))+E(f334(x76761,f334(f334(f316(x76762),x76763),x76764)),x76763)+~E(f334(f334(f23(f935(x76762,a922)),x76764),f334(f334(f316(x76762),x76763),f195(f935(x76762,a922)))),f195(f935(x76762,a922))) % 188.18/188.27 [7745]~P5(x77451)+~P59(x77451,x77455,x77453)+~P59(x77451,x77454,x77452)+E(f334(f334(f41(x77451),f334(f334(f87(x77451),x77452),x77453)),f334(f334(f87(x77451),x77454),x77455)),f334(f334(f87(x77451),f334(f334(f41(x77451),x77452),x77454)),f334(f334(f41(x77451),x77453),x77455))) % 188.18/188.27 [8032]~P85(x80321)+~P107(f334(f334(f242(x80321),x80323),x80325))+~P107(f334(f334(f242(x80321),x80322),x80324))+P107(f334(f334(f242(x80321),f334(f334(f86(x80321),x80322),x80323)),f334(f334(f86(x80321),x80324),x80325))) % 188.18/188.27 [8033]~P109(x80331)+~P107(f334(f334(f242(x80331),x80333),x80335))+~P107(f334(f334(f242(x80331),x80332),x80334))+P107(f334(f334(f242(x80331),f334(f334(f246(x80331),x80332),x80333)),f334(f334(f246(x80331),x80334),x80335))) % 188.18/188.27 [8034]~P109(x80341)+~P107(f334(f334(f242(x80341),x80343),x80345))+~P107(f334(f334(f242(x80341),x80342),x80344))+P107(f334(f334(f242(x80341),f334(f334(f241(x80341),x80342),x80343)),f334(f334(f241(x80341),x80344),x80345))) % 188.18/188.27 [8035]~P98(x80351)+~P107(f334(f334(f242(x80351),x80353),x80355))+~P107(f334(f334(f242(x80351),x80352),x80354))+P107(f334(f334(f242(x80351),f334(f334(f108(x80351),x80352),x80353)),f334(f334(f108(x80351),x80354),x80355))) % 188.18/188.27 [8036]~P104(x80361)+~P107(f334(f334(f242(x80361),x80363),x80365))+~P107(f334(f334(f242(x80361),x80362),x80364))+P107(f334(f334(f242(x80361),f334(f334(f109(x80361),x80362),x80363)),f334(f334(f109(x80361),x80364),x80365))) % 188.18/188.27 [8037]~P87(x80371)+~P107(f334(f334(f242(x80371),x80373),x80375))+~P107(f334(f334(f243(x80371),x80372),x80374))+P107(f334(f334(f243(x80371),f334(f334(f86(x80371),x80372),x80373)),f334(f334(f86(x80371),x80374),x80375))) % 188.18/188.27 [8038]~P87(x80381)+~P107(f334(f334(f242(x80381),x80382),x80384))+~P107(f334(f334(f243(x80381),x80383),x80385))+P107(f334(f334(f243(x80381),f334(f334(f86(x80381),x80382),x80383)),f334(f334(f86(x80381),x80384),x80385))) % 188.18/188.27 [8039]~P87(x80391)+~P107(f334(f334(f243(x80391),x80393),x80395))+~P107(f334(f334(f243(x80391),x80392),x80394))+P107(f334(f334(f243(x80391),f334(f334(f86(x80391),x80392),x80393)),f334(f334(f86(x80391),x80394),x80395))) % 188.18/188.27 [8169]~P143(x81695)+E(x81691,x81692)+E(x81693,x81694)+~E(f334(f334(f86(x81695),f334(f334(f87(x81695),x81693),x81691)),f334(f334(f87(x81695),x81694),x81692)),f334(f334(f86(x81695),f334(f334(f87(x81695),x81693),x81692)),f334(f334(f87(x81695),x81694),x81691))) % 188.18/188.27 [8369]~P109(x83694)+~P107(f334(f144(x83691),x83693))+P107(f334(f334(f336(x83691),x83692),f334(f179(x83691),x83693)))+P107(f334(f144(x83691),f334(f334(f155(x83691,x83694,x83695),x83692),x83693))) % 188.18/188.27 [8514]~P3(x85141)+E(f334(f334(f23(x85141),f334(f334(f6(a927,x85141),x85142),f334(f310(a927,x85143),x85144))),f334(f334(f6(a927,x85141),x85142),f334(f310(a927,x85143),x85145))),f334(f334(f6(a927,x85141),x85142),f334(f310(a927,x85145),x85144)))+~P107(f334(f334(f242(a927),x85145),x85144))+~P107(f334(f334(f242(a927),x85143),x85145)) % 188.18/188.27 [8515]~P76(x85151)+E(f334(f334(f86(x85151),f334(f334(f6(a927,x85151),x85152),f334(f310(a927,x85153),x85154))),f334(f334(f6(a927,x85151),x85152),f334(f310(a927,x85154),x85155))),f334(f334(f6(a927,x85151),x85152),f334(f310(a927,x85153),x85155)))+~P107(f334(f334(f242(a927),x85154),x85155))+~P107(f334(f334(f242(a927),x85153),x85154)) % 188.18/188.27 [8839]~P66(x88392)+E(x88391,f2(x88392))+E(x88393,f2(x88392))+E(f334(f334(f296(x88392),f334(f334(f23(x88392),f334(f334(f87(x88392),x88394),x88391)),f334(f334(f87(x88392),x88395),x88393))),f334(f334(f87(x88392),x88393),x88391)),f334(f334(f23(x88392),f334(f334(f296(x88392),x88394),x88393)),f334(f334(f296(x88392),x88395),x88391))) % 188.18/188.27 [8840]~P66(x88402)+E(x88401,f2(x88402))+E(x88403,f2(x88402))+E(f334(f334(f296(x88402),f334(f334(f86(x88402),f334(f334(f87(x88402),x88404),x88401)),f334(f334(f87(x88402),x88405),x88403))),f334(f334(f87(x88402),x88403),x88401)),f334(f334(f86(x88402),f334(f334(f296(x88402),x88404),x88403)),f334(f334(f296(x88402),x88405),x88401))) % 188.18/188.27 [8849]~E(x88492,f334(x88493,x88491))+E(x88491,f461(x88492,x88493,x88494,x88495))+~P27(x88495,x88494,x88493,f250(f935(x88495,a922)))+~P107(f334(f334(f336(x88494),x88492),f334(f317(x88495,x88494,x88493),f250(f935(x88495,a922))))) % 188.18/188.27 [9063]~P124(x90631)+~P107(f334(f334(f243(x90631),f334(f81(x90631),x90632)),x90634))+P107(f334(f334(f243(x90631),f334(f334(f87(x90631),f334(f81(x90631),x90632)),f334(f81(x90631),x90633))),f334(f334(f87(x90631),x90634),x90635)))+~P107(f334(f334(f243(x90631),f334(f81(x90631),x90633)),x90635)) % 188.18/188.27 [9179]~P27(x91791,x91793,x91795,x91792)+~P107(f334(f66(x91793),x91794))+P107(f334(f334(f242(a927),f334(f40(x91791),x91792)),f334(f40(x91793),x91794)))+~P107(f334(f334(f242(f935(x91793,a922)),f334(f317(x91791,x91793,x91795),x91792)),x91794)) % 188.18/188.27 [9245]~P72(x92452)+~P27(x92451,x92451,x92454,x92455)+~P107(f334(f66(x92451),x92455))+E(f334(f334(f9(x92451,x92452),f334(f78(x92451,x92452,x92451,x92453),x92454)),x92455),f334(f334(f9(x92451,x92452),x92453),f334(f317(x92451,x92451,x92454),x92455))) % 188.18/188.27 [9246]~P76(x92462)+~P27(x92461,x92461,x92464,x92465)+~P107(f334(f66(x92461),x92465))+E(f334(f334(f6(x92461,x92462),f334(f78(x92461,x92462,x92461,x92463),x92464)),x92465),f334(f334(f6(x92461,x92462),x92463),f334(f317(x92461,x92461,x92464),x92465))) % 188.18/188.27 [9353]~P39(x93531,x93532)+~P107(f334(f334(f336(x93531),x93533),x93534))+~P107(f334(f334(f336(x93531),x93535),x93534))+~P107(f334(f334(f336(f934(x93531,x93531)),f334(f334(f260(x93531,x93531),x93535),f627(x93532,x93531,x93534))),x93532)) % 188.18/188.27 [9395]~P27(x93952,x93953,x93955,x93951)+E(x93951,f195(f935(x93952,a922)))+E(f334(f317(x93953,x93952,f497(x93954,x93953,x93952,x93951)),x93954),x93951)+~P107(f334(f334(f242(f935(x93953,a922)),f334(f317(x93952,x93953,x93955),x93951)),x93954)) % 188.18/188.27 [9895]~P109(x98955)+~P7(x98955)+P107(f334(f334(f336(x98951),f406(x98952,x98953,x98951,x98954,x98955)),x98953))+~P107(f334(f334(f243(x98955),x98954),f334(f334(f44(x98951,x98955),x98953),x98952))) % 188.18/188.27 [9900]~P109(x99001)+~P7(x99001)+P107(f334(f334(f243(x99001),x99002),f334(x99003,f406(x99003,x99004,x99005,x99002,x99001))))+~P107(f334(f334(f243(x99001),x99002),f334(f334(f44(x99005,x99001),x99004),x99003))) % 188.18/188.27 [9984]~P70(x99841)+~P107(f334(f71(x99841,x99841,f87(x99841),x99842,x99843),x99845))+P107(f334(f334(f336(x99841),x99842),x99843))+P107(f334(f71(x99841,x99841,f87(x99841),x99844,f334(f334(f316(x99841),x99842),x99843)),f334(f334(f87(x99841),x99844),x99845))) % 188.18/188.27 [10176]~P72(x101762)+~P107(f334(f66(x101761),x101765))+E(f334(f334(f9(x101761,x101762),f334(f334(f7(x101761,x101762,x101762),f334(f334(f18(x101761,x101762,f935(x101762,x101762)),f334(f334(f8(a922,f935(x101762,f935(x101762,x101762)),x101761),f103(x101762)),f334(a331,x101763))),x101764)),f84(x101762))),x101765),f84(x101762))+P107(f334(f334(f336(x101761),x101763),x101765)) % 188.18/188.27 [10177]~P76(x101772)+~P107(f334(f66(x101771),x101775))+E(f334(f334(f6(x101771,x101772),f334(f334(f7(x101771,x101772,x101772),f334(f334(f18(x101771,x101772,f935(x101772,x101772)),f334(f334(f8(a922,f935(x101772,f935(x101772,x101772)),x101771),f103(x101772)),f334(a331,x101773))),x101774)),f2(x101772))),x101775),f2(x101772))+P107(f334(f334(f336(x101771),x101773),x101775)) % 188.18/188.27 [10178]~P72(x101782)+~P107(f334(f66(x101781),x101785))+E(f334(f334(f9(x101781,x101782),f334(f334(f7(x101781,x101782,x101782),f334(f334(f18(x101781,x101782,f935(x101782,x101782)),f334(f334(f8(a922,f935(x101782,f935(x101782,x101782)),x101781),f103(x101782)),f334(a331,x101783))),x101784)),f84(x101782))),x101785),f334(x101784,x101783))+~P107(f334(f334(f336(x101781),x101783),x101785)) % 188.18/188.27 [10179]~P76(x101792)+~P107(f334(f66(x101791),x101795))+E(f334(f334(f6(x101791,x101792),f334(f334(f7(x101791,x101792,x101792),f334(f334(f18(x101791,x101792,f935(x101792,x101792)),f334(f334(f8(a922,f935(x101792,f935(x101792,x101792)),x101791),f103(x101792)),f334(a331,x101793))),x101794)),f2(x101792))),x101795),f334(x101794,x101793))+~P107(f334(f334(f336(x101791),x101793),x101795)) % 188.18/188.27 [10228]~P72(x102282)+~P107(f334(f66(x102281),x102285))+E(f334(f334(f9(x102281,x102282),f334(f334(f7(x102281,x102282,x102282),f334(f334(f18(x102281,x102282,f935(x102282,x102282)),f334(f334(f8(a922,f935(x102282,f935(x102282,x102282)),x102281),f103(x102282)),f334(f334(f7(x102281,x102281,a922),a331),x102283))),x102284)),f84(x102282))),x102285),f84(x102282))+P107(f334(f334(f336(x102281),x102283),x102285)) % 188.18/188.27 [10229]~P76(x102292)+~P107(f334(f66(x102291),x102295))+E(f334(f334(f6(x102291,x102292),f334(f334(f7(x102291,x102292,x102292),f334(f334(f18(x102291,x102292,f935(x102292,x102292)),f334(f334(f8(a922,f935(x102292,f935(x102292,x102292)),x102291),f103(x102292)),f334(f334(f7(x102291,x102291,a922),a331),x102293))),x102294)),f2(x102292))),x102295),f2(x102292))+P107(f334(f334(f336(x102291),x102293),x102295)) % 188.18/188.27 [10231]~P72(x102312)+~P107(f334(f66(x102311),x102315))+E(f334(f334(f9(x102311,x102312),f334(f334(f7(x102311,x102312,x102312),f334(f334(f18(x102311,x102312,f935(x102312,x102312)),f334(f334(f8(a922,f935(x102312,f935(x102312,x102312)),x102311),f103(x102312)),f334(f334(f7(x102311,x102311,a922),a331),x102313))),x102314)),f84(x102312))),x102315),f334(x102314,x102313))+~P107(f334(f334(f336(x102311),x102313),x102315)) % 188.18/188.27 [10232]~P76(x102322)+~P107(f334(f66(x102321),x102325))+E(f334(f334(f6(x102321,x102322),f334(f334(f7(x102321,x102322,x102322),f334(f334(f18(x102321,x102322,f935(x102322,x102322)),f334(f334(f8(a922,f935(x102322,f935(x102322,x102322)),x102321),f103(x102322)),f334(f334(f7(x102321,x102321,a922),a331),x102323))),x102324)),f2(x102322))),x102325),f334(x102324,x102323))+~P107(f334(f334(f336(x102321),x102323),x102325)) % 188.18/188.27 [8031]~P3(x80312)+~P107(f334(f66(x80311),x80314))+E(f334(f334(f6(x80311,x80312),x80313),f334(f334(f23(f935(x80311,a922)),x80314),f334(f334(f316(x80311),x80315),f195(f935(x80311,a922))))),f334(f334(f6(x80311,x80312),x80313),x80314))+P107(f334(f334(f336(x80311),x80315),x80314)) % 188.18/188.27 [8522]~P113(x85222)+~P107(f334(f66(x85221),x85224))+E(f334(f334(f6(x85221,x85222),x85223),f334(f334(f23(f935(x85221,a922)),x85224),f334(f334(f316(x85221),x85225),f195(f935(x85221,a922))))),f334(f334(f23(x85222),f334(f334(f6(x85221,x85222),x85223),x85224)),f334(x85223,x85225)))+~P107(f334(f334(f336(x85221),x85225),x85224)) % 188.18/188.27 [8523]~P3(x85232)+~P107(f334(f66(x85231),x85234))+E(f334(f334(f6(x85231,x85232),x85233),f334(f334(f23(f935(x85231,a922)),x85234),f334(f334(f316(x85231),x85235),f195(f935(x85231,a922))))),f334(f334(f23(x85232),f334(f334(f6(x85231,x85232),x85233),x85234)),f334(x85233,x85235)))+~P107(f334(f334(f336(x85231),x85235),x85234)) % 188.18/188.27 [8549]~P3(x85491)+~P107(f334(f66(x85492),x85494))+E(f334(f334(f23(x85491),f334(f334(f6(x85492,x85491),x85493),x85494)),f334(f334(f6(x85492,x85491),x85493),x85495)),f334(f334(f6(x85492,x85491),x85493),f334(f334(f23(f935(x85492,a922)),x85494),x85495)))+~P107(f334(f334(f242(f935(x85492,a922)),x85495),x85494)) % 188.18/188.27 [8568]P107(f334(f66(x85681),f334(x85682,x85683)))+~P107(f334(f66(x85684),x85685))+~P107(f334(f334(f336(x85684),x85683),x85685))+~P107(f334(f66(x85681),f334(f334(f44(x85684,f935(x85681,a922)),x85685),x85682))) % 188.18/188.27 [9014]~P10(x90141,x90145,x90144)+~E(f334(f292(x90141,x90141,x90144),f334(f334(f316(x90141),x90142),f195(f935(x90141,a922)))),f334(f292(x90141,x90141,x90144),f334(f334(f316(x90141),x90143),f195(f935(x90141,a922)))))+~P107(f334(f334(f336(x90141),x90143),x90145))+P107(f334(f334(f336(f934(x90141,x90141)),f334(f334(f260(x90141,x90141),x90142),x90143)),x90144)) % 188.18/188.27 [9309]~P107(f334(x93091,x93095))+P107(f334(x93091,f379(x93091,x93092,x93093,x93094)))+P107(f334(x93091,f378(x93091,x93092,x93093,x93094)))+~P107(f334(f334(f336(x93094),x93095),f334(f334(f108(f935(x93094,a922)),x93093),x93092))) % 188.18/188.27 [9497]~P107(f334(x94971,x94975))+P107(f334(x94971,f378(x94971,x94972,x94973,x94974)))+P107(f334(f334(f336(x94974),f379(x94971,x94972,x94973,x94974)),x94972))+~P107(f334(f334(f336(x94974),x94975),f334(f334(f108(f935(x94974,a922)),x94973),x94972))) % 188.18/188.27 [9498]~P107(f334(x94981,x94985))+P107(f334(x94981,f379(x94981,x94982,x94983,x94984)))+P107(f334(f334(f336(x94984),f378(x94981,x94982,x94983,x94984)),x94983))+~P107(f334(f334(f336(x94984),x94985),f334(f334(f108(f935(x94984,a922)),x94983),x94982))) % 188.18/188.27 [9504]P107(f334(x95041,x95042))+~P107(f334(x95041,f383(x95041,x95043,x95044,x95045)))+~P107(f334(x95041,f382(x95041,x95043,x95044,x95045)))+~P107(f334(f334(f336(x95045),x95042),f334(f334(f108(f935(x95045,a922)),x95044),x95043))) % 188.18/188.27 [9510]~P40(x95101,x95104)+~P107(f334(f334(f336(f934(x95101,x95101)),f334(f334(f260(x95101,x95101),x95102),x95105)),x95104))+P107(f334(f334(f336(f934(x95101,x95101)),f334(f334(f260(x95101,x95101),x95102),x95103)),x95104))+~P107(f334(f334(f336(f934(x95101,x95101)),f334(f334(f260(x95101,x95101),x95105),x95103)),x95104)) % 188.18/188.27 [9549]E(x95491,x95492)+~P107(f334(f334(f336(f934(x95493,x95493)),f334(f334(f260(x95493,x95493),x95491),x95492)),f314(x95493,x95495)))+P107(f334(f334(f336(x95493),x95491),x95494))+~P107(f334(f334(f242(f935(f934(x95493,x95493),a922)),x95495),f334(f334(f262(x95493,x95493),x95494),f334(f16(f935(x95493,a922),x95493),x95494)))) % 188.18/188.27 [9567]P107(f334(x95671,x95672))+~P107(f334(x95671,f382(x95671,x95674,x95675,x95673)))+P107(f334(f334(f336(x95673),f383(x95671,x95674,x95675,x95673)),x95674))+~P107(f334(f334(f336(x95673),x95672),f334(f334(f108(f935(x95673,a922)),x95675),x95674))) % 188.18/188.27 [9568]P107(f334(x95681,x95682))+~P107(f334(x95681,f383(x95681,x95684,x95685,x95683)))+P107(f334(f334(f336(x95683),f382(x95681,x95684,x95685,x95683)),x95685))+~P107(f334(f334(f336(x95683),x95682),f334(f334(f108(f935(x95683,a922)),x95685),x95684))) % 188.18/188.27 [9631]P107(f334(x96311,x96312))+P107(f334(f334(f336(x96313),f383(x96311,x96314,x96315,x96313)),x96314))+P107(f334(f334(f336(x96313),f382(x96311,x96314,x96315,x96313)),x96315))+~P107(f334(f334(f336(x96313),x96312),f334(f334(f108(f935(x96313,a922)),x96315),x96314))) % 188.18/188.27 [9632]~P107(f334(x96322,x96325))+P107(f334(f334(f336(x96321),f379(x96322,x96323,x96324,x96321)),x96323))+P107(f334(f334(f336(x96321),f378(x96322,x96323,x96324,x96321)),x96324))+~P107(f334(f334(f336(x96321),x96325),f334(f334(f108(f935(x96321,a922)),x96324),x96323))) % 188.18/188.27 [9791]~P10(x97911,x97915,x97914)+~P107(f334(f334(f336(x97911),x97913),x97915))+P107(f334(f334(f336(f934(x97911,x97911)),f334(f334(f260(x97911,x97911),x97912),x97913)),x97914))+~P107(f334(f334(f242(f935(x97911,a922)),f334(f292(x97911,x97911,x97914),f334(f334(f316(x97911),x97913),f195(f935(x97911,a922))))),f334(f292(x97911,x97911,x97914),f334(f334(f316(x97911),x97912),f195(f935(x97911,a922)))))) % 188.18/188.27 [9931]~P109(x99315)+~P7(x99315)+P107(f334(f334(f336(x99311),f504(x99312,x99313,x99314,x99311,x99315)),x99314))+~P107(f334(f334(f243(x99315),f334(f334(f45(x99311,x99315),x99314),x99313)),x99312)) % 188.18/188.27 [9963]~P85(x99635)+~P82(x99635)+P107(f334(f334(f336(x99631),f709(x99632,x99633,x99634,x99631,x99635)),f334(f179(x99631),x99634)))+P107(f334(f334(f242(x99635),f334(f172(x99635),f334(f334(f161(x99631,x99635),x99633),x99634))),f334(f172(x99635),f334(f334(f161(x99631,x99635),x99632),x99634)))) % 188.18/188.27 [10087]~P109(x100871)+~P7(x100871)+P107(f334(f334(f243(x100871),f334(x100872,f504(x100873,x100872,x100874,x100875,x100871))),x100873))+~P107(f334(f334(f243(x100871),f334(f334(f45(x100875,x100871),x100874),x100872)),x100873)) % 188.18/188.27 [10192]~P85(x101921)+~P82(x101921)+~P107(f334(f334(f242(x101921),f334(x101923,f709(x101925,x101923,x101924,x101922,x101921))),f334(x101925,f709(x101925,x101923,x101924,x101922,x101921))))+P107(f334(f334(f242(x101921),f334(f172(x101921),f334(f334(f161(x101922,x101921),x101923),x101924))),f334(f172(x101921),f334(f334(f161(x101922,x101921),x101925),x101924)))) % 188.18/188.27 [8861]~P72(x88611)+~P107(f334(f66(x88614),x88615))+~P107(f334(f334(f336(x88614),x88613),x88615))+E(f334(f334(f87(x88611),f334(x88612,x88613)),f334(f334(f9(x88614,x88611),x88612),f334(f334(f23(f935(x88614,a922)),x88615),f334(f334(f316(x88614),x88613),f195(f935(x88614,a922)))))),f334(f334(f9(x88614,x88611),x88612),x88615)) % 188.18/188.27 [8863]~P76(x88631)+~P107(f334(f66(x88634),x88635))+~P107(f334(f334(f336(x88634),x88633),x88635))+E(f334(f334(f86(x88631),f334(x88632,x88633)),f334(f334(f6(x88634,x88631),x88632),f334(f334(f23(f935(x88634,a922)),x88635),f334(f334(f316(x88634),x88633),f195(f935(x88634,a922)))))),f334(f334(f6(x88634,x88631),x88632),x88635)) % 188.18/188.27 [8916]~P20(x89161,x89164,x89165)+~P107(f334(f66(x89161),x89162))+E(f334(f334(f23(f935(x89161,a922)),x89162),f334(f334(f316(x89161),x89163),f195(f935(x89161,a922)))),f195(f935(x89161,a922)))+E(f334(f334(x89164,x89163),f334(x89165,f334(f334(f23(f935(x89161,a922)),x89162),f334(f334(f316(x89161),x89163),f195(f935(x89161,a922)))))),f334(x89165,f334(f334(f316(x89161),x89163),x89162))) % 188.18/188.27 [9289]~P72(x92891)+~P107(f334(f66(x92892),x92895))+~P107(f334(f66(x92892),x92894))+E(f334(f334(f87(x92891),f334(f334(f9(x92892,x92891),x92893),f334(f334(f108(f935(x92892,a922)),x92894),x92895))),f334(f334(f9(x92892,x92891),x92893),f334(f334(f109(f935(x92892,a922)),x92894),x92895))),f334(f334(f87(x92891),f334(f334(f9(x92892,x92891),x92893),x92894)),f334(f334(f9(x92892,x92891),x92893),x92895))) % 188.18/188.27 [9290]~P76(x92901)+~P107(f334(f66(x92902),x92905))+~P107(f334(f66(x92902),x92904))+E(f334(f334(f86(x92901),f334(f334(f6(x92902,x92901),x92903),f334(f334(f108(f935(x92902,a922)),x92904),x92905))),f334(f334(f6(x92902,x92901),x92903),f334(f334(f109(f935(x92902,a922)),x92904),x92905))),f334(f334(f86(x92901),f334(f334(f6(x92902,x92901),x92903),x92904)),f334(f334(f6(x92902,x92901),x92903),x92905))) % 188.18/188.27 [9432]~P3(x94321)+~P107(f334(f66(x94322),x94325))+~P107(f334(f66(x94322),x94324))+E(f334(f334(f23(x94321),f334(f334(f86(x94321),f334(f334(f6(x94322,x94321),x94323),x94324)),f334(f334(f6(x94322,x94321),x94323),x94325))),f334(f334(f6(x94322,x94321),x94323),f334(f334(f109(f935(x94322,a922)),x94324),x94325))),f334(f334(f6(x94322,x94321),x94323),f334(f334(f108(f935(x94322,a922)),x94324),x94325))) % 188.18/188.27 [9642]~P27(x96421,x96422,x96423,x96425)+~P27(x96421,x96422,x96423,x96424)+P27(x96421,x96422,x96423,f334(f334(f108(f935(x96421,a922)),x96424),x96425))+~E(f334(f334(f109(f935(x96422,a922)),f334(f317(x96421,x96422,x96423),f334(f334(f23(f935(x96421,a922)),x96424),x96425))),f334(f317(x96421,x96422,x96423),f334(f334(f23(f935(x96421,a922)),x96425),x96424))),f195(f935(x96422,a922))) % 188.18/188.27 [9766]E(x97661,f2(a1))+~P107(f334(f334(f243(a1),f2(a1)),x97663))+~P107(f334(f54(x97662,x97661),f334(f334(f260(a1,a1),x97664),x97665)))+P107(f334(f54(x97662,f334(f334(f87(a1),x97661),x97663)),f334(f334(f260(a1,a1),f334(f334(f41(a1),x97664),x97663)),f334(f334(f86(a1),f334(f334(f87(a1),x97661),f50(a1,x97664,x97663))),x97665)))) % 188.18/188.27 [9774]~P107(f334(f334(f243(a927),f2(a927)),x97743))+~P107(f334(f334(f243(a927),f2(a927)),x97742))+~P107(f334(f53(x97741,x97742),f334(f334(f260(a927,a927),x97744),x97745)))+P107(f334(f53(x97741,f334(f334(f87(a927),x97742),x97743)),f334(f334(f260(a927,a927),f334(f334(f41(a927),x97744),x97743)),f334(f334(f86(a927),f334(f334(f87(a927),x97742),f50(a927,x97744,x97743))),x97745)))) % 188.18/188.27 [9828]~P72(x98281)+~P107(f334(f66(x98282),x98285))+~P107(f334(f66(x98282),x98284))+E(f334(f334(f87(x98281),f334(f334(f334(f70(x98281,x98282,f87(x98281)),x98283),f84(x98281)),f334(f334(f108(f935(x98282,a922)),x98284),x98285))),f334(f334(f334(f70(x98281,x98282,f87(x98281)),x98283),f84(x98281)),f334(f334(f109(f935(x98282,a922)),x98284),x98285))),f334(f334(f87(x98281),f334(f334(f334(f70(x98281,x98282,f87(x98281)),x98283),f84(x98281)),x98284)),f334(f334(f334(f70(x98281,x98282,f87(x98281)),x98283),f84(x98281)),x98285))) % 188.18/188.27 [9830]~E(f334(f334(f182(x98301),x98305),x98302),f334(f334(f182(x98301),x98305),x98303))+P107(f334(f334(f336(f934(f928(x98301),f928(x98301))),f334(f334(f260(f928(x98301),f928(x98301)),x98302),x98303)),f154(x98301,x98304)))+~P107(f334(f334(f243(a927),x98305),f334(f334(f246(a927),f334(f196(f928(x98301)),x98302)),f334(f196(f928(x98301)),x98303))))+~P107(f334(f334(f336(f934(x98301,x98301)),f334(f334(f260(x98301,x98301),f334(f334(f171(x98301),x98302),x98305)),f334(f334(f171(x98301),x98303),x98305))),x98304)) % 188.18/188.27 [9952]~P85(x99525)+~P147(x99525)+P107(f334(f334(f336(x99521),f465(x99522,x99523,x99524,x99521,x99525)),x99524))+P107(f334(f334(f242(x99525),f334(f334(f6(x99521,x99525),x99523),x99524)),f334(f334(f87(x99525),f334(f107(x99525),f334(f40(x99521),x99524))),x99522))) % 188.18/188.27 [10134]~P85(x101341)+~P147(x101341)+~P107(f334(f334(f242(x101341),f334(x101343,f465(x101345,x101343,x101344,x101342,x101341))),x101345))+P107(f334(f334(f242(x101341),f334(f334(f6(x101342,x101341),x101343),x101344)),f334(f334(f87(x101341),f334(f107(x101341),f334(f40(x101342),x101344))),x101345))) % 188.18/188.27 [8886]E(f334(f334(f141(x88861),x88862),x88863),f334(f334(f141(x88861),x88864),x88865))+~E(f334(f334(f182(x88861),f334(f196(f928(x88861)),x88862)),x88864),x88862)+~E(f334(f334(f141(x88861),f334(f334(f145(x88861),f334(f196(f928(x88861)),x88862)),x88864)),x88865),x88863)+P107(f334(f334(f242(a927),f334(f196(f928(x88861)),x88864)),f334(f196(f928(x88861)),x88862))) % 188.18/188.27 [9013]E(f334(f334(f141(x90131),x90132),x90133),f334(f334(f141(x90131),x90134),x90135))+~E(f334(f334(f182(x90131),f334(f196(f928(x90131)),x90132)),x90134),x90132)+~E(x90133,f334(f334(f141(x90131),f334(f334(f145(x90131),f334(f196(f928(x90131)),x90132)),x90134)),x90135))+~P107(f334(f334(f242(a927),f334(f196(f928(x90131)),x90132)),f334(f196(f928(x90131)),x90134))) % 188.18/188.27 [10252]~P107(f334(x102525,x102524))+~P107(f334(f66(x102522),f334(f270(x102522),x102525)))+P107(f334(f66(x102521),f334(f270(x102521),f334(f334(f7(x102521,x102522,a922),x102523),x102524))))+~P107(f334(f66(x102521),f334(f270(x102521),f334(f334(f8(f935(x102522,a922),a922,x102521),f92(x102522)),f334(f334(f8(f935(x102522,a922),f935(x102522,a922),x102521),f334(f18(x102522,a922,a922),f334(f334(f8(a922,f935(a922,a922),x102522),a332),x102525))),x102523))))) % 188.18/188.27 [10325]~P107(f334(f66(x103252),x103255))+~P107(f334(f334(f336(x103252),x103254),x103255))+P107(f334(f66(x103251),f334(f270(x103251),f334(f334(f7(x103251,x103252,a922),x103253),x103254))))+~P107(f334(f66(x103251),f334(f270(x103251),f334(f334(f8(f935(x103252,a922),a922,x103251),f92(x103252)),f334(f334(f8(f935(x103252,a922),f935(x103252,a922),x103251),f334(f18(x103252,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103252),a332),f334(f334(f7(x103252,f935(x103252,a922),a922),f336(x103252)),x103255)))),x103253))))) % 188.18/188.27 [8676]~P21(x86765,x86761,x86766,x86762)+E(f334(f78(x86761,x86761,x86761,f334(x86762,x86763)),f334(x86762,x86764)),f334(f78(x86761,x86761,x86761,f334(x86762,x86764)),f334(x86762,x86763)))+~P107(f334(f66(x86765),x86764))+~P107(f334(f66(x86765),x86763)) % 188.18/188.27 [8088]~P27(x80881,x80882,x80884,x80883)+~E(f334(x80884,x80886),x80885)+E(f334(f83(x80881,x80882,x80883,x80884),x80885),x80886)+~P107(f334(f334(f336(x80881),x80886),x80883)) % 188.18/188.27 [8089]~P27(x80891,x80892,x80894,x80893)+~E(f334(x80894,x80896),x80895)+E(f334(f97(x80891,x80892,x80893,x80894),x80895),x80896)+~P107(f334(f334(f336(x80891),x80896),x80893)) % 188.18/188.27 [8273]~P22(x82736,x82731,x82734,x82732)+E(f334(f78(x82731,x82731,x82731,f334(x82732,x82733)),f334(x82734,x82735)),f334(x82732,x82733))+~P107(f334(f66(x82736),x82733))+~P107(f334(f334(f336(x82736),x82735),x82733)) % 188.18/188.27 [9387]E(x93871,x93872)+~E(f334(f97(x93873,x93874,x93875,x93876),x93871),f334(f97(x93873,x93874,x93875,x93876),x93872))+~P107(f334(f334(f336(x93874),x93872),f334(f317(x93873,x93874,x93876),x93875)))+~P107(f334(f334(f336(x93874),x93871),f334(f317(x93873,x93874,x93876),x93875))) % 188.18/188.27 [9481]~P21(x94813,x94811,x94816,x94812)+E(f334(f78(x94811,x94811,x94811,f334(x94812,f334(f334(f23(f935(x94813,a922)),x94814),f334(f334(f316(x94813),x94815),f195(f935(x94813,a922)))))),f334(x94816,x94815)),f334(x94812,x94814))+~P107(f334(f66(x94813),x94814))+~P107(f334(f334(f336(x94813),x94815),x94814)) % 188.18/188.27 [7192]~P6(x71921)+~E(f50(x71921,x71923,x71924),f50(x71921,x71926,x71924))+~E(f50(x71921,x71922,x71924),f50(x71921,x71925,x71924))+E(f50(x71921,f334(f334(f23(x71921),x71922),x71923),x71924),f50(x71921,f334(f334(f23(x71921),x71925),x71926),x71924)) % 188.18/188.27 [7193]~P5(x71931)+~E(f50(x71931,x71933,x71934),f50(x71931,x71936,x71934))+~E(f50(x71931,x71932,x71934),f50(x71931,x71935,x71934))+E(f50(x71931,f334(f334(f87(x71931),x71932),x71933),x71934),f50(x71931,f334(f334(f87(x71931),x71935),x71936),x71934)) % 188.18/188.27 [7194]~P5(x71941)+~E(f50(x71941,x71943,x71944),f50(x71941,x71946,x71944))+~E(f50(x71941,x71942,x71944),f50(x71941,x71945,x71944))+E(f50(x71941,f334(f334(f86(x71941),x71942),x71943),x71944),f50(x71941,f334(f334(f86(x71941),x71945),x71946),x71944)) % 188.18/188.27 [7982]~P18(x79821,x79822,x79823)+~P107(f334(f66(x79821),x79826))+E(f334(f334(f69(x79821,x79822,x79823),x79824),f334(f334(f316(x79821),x79825),x79826)),f334(f334(f69(x79821,x79822,x79823),f334(f334(x79823,x79825),x79824)),x79826))+P107(f334(f334(f336(x79821),x79825),x79826)) % 188.18/188.27 [8046]~P7(x80461)+P107(f334(f334(f242(x80461),x80462),f334(x80463,x80464)))+~P107(f334(f334(f336(x80465),x80464),x80466))+~P107(f334(f334(f242(x80461),x80462),f334(f334(f45(x80465,x80461),x80466),x80463))) % 188.18/188.27 [8194]~P18(x81941,x81942,x81943)+~P107(f334(f66(x81941),x81946))+E(f334(f334(f69(x81941,x81942,x81943),x81944),f334(f334(f316(x81941),x81945),x81946)),f334(f334(x81943,x81945),f334(f334(f69(x81941,x81942,x81943),x81944),x81946)))+P107(f334(f334(f336(x81941),x81945),x81946)) % 188.18/188.27 [8292]~P109(x82923)+~P107(f334(x82922,x82925))+~P15(x82923,f334(f334(f161(x82921,x82923),x82924),x82926))+E(f334(f143(x82921,x82922),f334(f334(f155(x82921,x82923,x82924),x82925),x82926)),f334(f334(f155(x82921,x82923,x82924),x82925),f334(f143(x82921,x82922),x82926))) % 188.18/188.27 [8313]E(x83131,x83132)+E(x83133,f2(a1))+~P107(f334(f54(x83134,x83133),f334(f334(f260(a1,a1),x83135),x83132)))+~P107(f334(f54(x83134,x83133),f334(f334(f260(a1,a1),x83136),x83131))) % 188.18/188.27 [8314]E(x83141,x83142)+E(x83143,f2(a1))+~P107(f334(f54(x83144,x83143),f334(f334(f260(a1,a1),x83142),x83145)))+~P107(f334(f54(x83144,x83143),f334(f334(f260(a1,a1),x83141),x83146))) % 188.18/188.27 [8335]~P21(x83352,x83355,x83356,x83351)+~P107(f334(f66(x83352),x83354))+E(f334(x83351,f334(f334(f316(x83352),x83353),x83354)),f334(f78(x83355,x83355,x83355,f334(x83351,x83354)),f334(x83356,x83353)))+P107(f334(f334(f336(x83352),x83353),x83354)) % 188.18/188.27 [8552]~P22(x85525,x85521,x85526,x85522)+E(f334(f78(x85521,x85521,x85521,f334(x85522,x85523)),f334(x85522,x85524)),f334(x85522,x85523))+~P107(f334(f66(x85525),x85523))+~P107(f334(f334(f242(f935(x85525,a922)),x85524),x85523)) % 188.18/188.27 [9683]~P27(x96831,x96832,x96834,x96833)+~P107(f334(f334(f336(x96832),x96835),f334(f317(x96831,x96832,x96834),x96833)))+P107(f334(f334(f336(x96831),f334(f83(x96831,x96832,x96833,x96834),x96835)),x96836))+~P107(f334(f334(f242(f935(x96831,a922)),x96833),x96836)) % 188.18/188.27 [10089]~P76(x100892)+~E(f469(x100891,x100893,x100895,x100896,x100894,x100892),f470(x100891,x100893,x100895,x100896,x100894,x100892))+~P107(f334(f66(x100894),x100896))+E(f334(f334(f6(x100891,x100892),x100893),f334(f317(x100894,x100891,x100895),x100896)),f334(f334(f6(x100894,x100892),f334(f78(x100891,x100892,x100894,x100893),x100895)),x100896)) % 188.18/188.27 [10117]~P76(x101176)+E(f334(x101171,f469(x101172,x101173,x101171,x101174,x101175,x101176)),f334(x101171,f470(x101172,x101173,x101171,x101174,x101175,x101176)))+E(f334(f334(f6(x101172,x101176),x101173),f334(f317(x101175,x101172,x101171),x101174)),f334(f334(f6(x101175,x101176),f334(f78(x101172,x101176,x101175,x101173),x101171)),x101174))+~P107(f334(f66(x101175),x101174)) % 188.18/188.27 [10152]~P76(x101522)+~E(f334(x101523,f334(x101525,f470(x101521,x101523,x101525,x101526,x101524,x101522))),f2(x101522))+~P107(f334(f66(x101524),x101526))+E(f334(f334(f6(x101521,x101522),x101523),f334(f317(x101524,x101521,x101525),x101526)),f334(f334(f6(x101524,x101522),f334(f78(x101521,x101522,x101524,x101523),x101525)),x101526)) % 188.18/188.27 [10198]~P76(x101982)+~P107(f334(f66(x101984),x101986))+E(f334(f334(f6(x101981,x101982),x101983),f334(f317(x101984,x101981,x101985),x101986)),f334(f334(f6(x101984,x101982),f334(f78(x101981,x101982,x101984,x101983),x101985)),x101986))+P107(f334(f334(f336(x101984),f470(x101981,x101983,x101985,x101986,x101984,x101982)),x101986)) % 188.18/188.27 [10199]~P76(x101992)+~P107(f334(f66(x101994),x101996))+E(f334(f334(f6(x101991,x101992),x101993),f334(f317(x101994,x101991,x101995),x101996)),f334(f334(f6(x101994,x101992),f334(f78(x101991,x101992,x101994,x101993),x101995)),x101996))+P107(f334(f334(f336(x101994),f469(x101991,x101993,x101995,x101996,x101994,x101992)),x101996)) % 188.18/188.27 [10324]~P72(x103241)+~P107(f334(f66(x103242),x103246))+E(f334(f334(f334(f70(x103241,x103242,f87(x103241)),f334(f334(f18(x103242,f935(x103243,a922),x103241),f334(f334(f7(x103242,x103241,f935(f935(x103243,a922),x103241)),f334(f334(f8(f935(x103243,x103241),f935(x103241,f935(f935(x103243,a922),x103241)),x103242),f70(x103241,x103243,f87(x103241))),x103244)),f84(x103241))),x103245)),f84(x103241)),x103246),f334(f334(f334(f70(x103241,f934(x103242,x103243),f87(x103241)),f334(f265(x103242,x103243,x103241),x103244)),f84(x103241)),f334(f334(f262(x103242,x103243),x103246),x103245)))+P107(f334(f334(f336(x103242),f557(x103244,x103245,x103243,x103246,x103242,x103241)),x103246)) % 188.18/188.27 [10346]~P72(x103461)+~P107(f334(f66(x103462),x103466))+E(f334(f334(f334(f70(x103461,x103462,f87(x103461)),f334(f334(f18(x103462,f935(x103463,a922),x103461),f334(f334(f7(x103462,x103461,f935(f935(x103463,a922),x103461)),f334(f334(f8(f935(x103463,x103461),f935(x103461,f935(f935(x103463,a922),x103461)),x103462),f70(x103461,x103463,f87(x103461))),x103464)),f84(x103461))),x103465)),f84(x103461)),x103466),f334(f334(f334(f70(x103461,f934(x103462,x103463),f87(x103461)),f334(f265(x103462,x103463,x103461),x103464)),f84(x103461)),f334(f334(f262(x103462,x103463),x103466),x103465)))+~P107(f334(f66(x103463),f334(x103465,f557(x103464,x103465,x103463,x103466,x103462,x103461)))) % 188.18/188.27 [8465]~P22(x84652,x84655,x84656,x84651)+~P107(f334(f66(x84652),x84654))+~P107(f334(f66(x84652),x84653))+E(f334(x84651,f334(f334(f108(f935(x84652,a922)),x84653),x84654)),f334(f78(x84655,x84655,x84655,f334(x84651,x84653)),f334(x84651,x84654))) % 188.18/188.27 [8677]~P7(x86771)+P107(f334(f334(f242(x86771),f334(x86772,x86773)),x86774))+~P107(f334(f334(f336(x86775),x86773),x86776))+~P107(f334(f334(f242(x86771),f334(f334(f44(x86775,x86771),x86776),x86772)),x86774)) % 188.18/188.27 [9107]~P27(x91072,x91071,x91073,x91076)+E(f334(f334(f23(f935(x91071,a922)),f334(f317(x91072,x91071,x91073),x91074)),f334(f317(x91072,x91071,x91073),x91075)),f334(f317(x91072,x91071,x91073),f334(f334(f23(f935(x91072,a922)),x91074),x91075)))+~P107(f334(f334(f242(f935(x91072,a922)),x91075),x91076))+~P107(f334(f334(f242(f935(x91072,a922)),x91074),x91076)) % 188.18/188.27 [9108]~P27(x91082,x91081,x91083,x91086)+E(f334(f334(f109(f935(x91081,a922)),f334(f317(x91082,x91081,x91083),x91084)),f334(f317(x91082,x91081,x91083),x91085)),f334(f317(x91082,x91081,x91083),f334(f334(f109(f935(x91082,a922)),x91084),x91085)))+~P107(f334(f334(f242(f935(x91082,a922)),x91085),x91086))+~P107(f334(f334(f242(f935(x91082,a922)),x91084),x91086)) % 188.18/188.27 [9355]E(x93551,x93552)+~P57(x93553,x93554,x93555)+~P107(f334(f334(f336(f934(x93553,x93554)),f334(f334(f260(x93553,x93554),x93556),x93552)),x93555))+~P107(f334(f334(f336(f934(x93553,x93554)),f334(f334(f260(x93553,x93554),x93556),x93551)),x93555)) % 188.18/188.27 [10149]~P70(x101491)+~E(f334(x101493,f882(x101494,x101496,x101493,x101495,x101492,x101491)),f334(x101496,f882(x101494,x101496,x101493,x101495,x101492,x101491)))+~P107(f334(f66(x101492),x101495))+E(f334(f334(f334(f70(x101491,x101492,f87(x101491)),x101493),x101494),x101495),f334(f334(f334(f70(x101491,x101492,f87(x101491)),x101496),x101494),x101495)) % 188.18/188.27 [10196]~P70(x101961)+~P107(f334(f66(x101962),x101965))+E(f334(f334(f334(f70(x101961,x101962,f87(x101961)),x101963),x101964),x101965),f334(f334(f334(f70(x101961,x101962,f87(x101961)),x101966),x101964),x101965))+P107(f334(f334(f336(x101962),f882(x101964,x101963,x101966,x101965,x101962,x101961)),x101965)) % 188.18/188.27 [8898]~P70(x88981)+~P107(f334(f66(x88982),x88986))+P107(f334(f334(f336(x88982),x88985),x88986))+E(f334(f334(f334(f70(x88981,x88982,f87(x88981)),x88983),x88984),f334(f334(f316(x88982),x88985),x88986)),f334(f334(f87(x88981),f334(x88983,x88985)),f334(f334(f334(f70(x88981,x88982,f87(x88981)),x88983),x88984),x88986))) % 188.18/188.27 [8951]~P10(x89511,x89516,x89513)+~P13(x89511,f935(x89512,a922),x89513,x89515)+~P107(f334(f334(f336(x89511),x89514),x89516))+E(f334(f334(f44(x89511,f935(x89512,a922)),f334(f292(x89511,x89511,x89513),f334(f334(f316(x89511),x89514),f195(f935(x89511,a922))))),x89515),f334(x89515,x89514)) % 188.18/188.27 [9082]~P18(x90823,x90824,x90821)+~P107(f334(f66(x90823),x90826))+~P107(f334(f334(f336(x90823),x90822),x90826))+E(f334(f334(x90821,x90822),f334(f334(f69(x90823,x90824,x90821),x90825),f334(f334(f23(f935(x90823,a922)),x90826),f334(f334(f316(x90823),x90822),f195(f935(x90823,a922)))))),f334(f334(f69(x90823,x90824,x90821),x90825),x90826)) % 188.18/188.27 [9371]~P21(x93713,x93711,x93716,x93712)+~P107(f334(f66(x93713),x93715))+~P107(f334(f66(x93713),x93714))+E(f334(f78(x93711,x93711,x93711,f334(x93712,f334(f334(f108(f935(x93713,a922)),x93714),x93715))),f334(x93712,f334(f334(f109(f935(x93713,a922)),x93714),x93715))),f334(f78(x93711,x93711,x93711,f334(x93712,x93714)),f334(x93712,x93715))) % 188.18/188.27 [9706]~E(x97063,f334(f334(f166(x97061,x97062),x97065),x97066))+P107(f334(f334(f336(f934(f928(x97061),f928(x97061))),f334(f334(f260(f928(x97061),f928(x97061)),x97062),x97063)),f164(x97061,x97064)))+~P107(f334(f334(f243(a927),x97065),f334(f196(f928(x97061)),x97062)))+~P107(f334(f334(f336(f934(x97061,x97061)),f334(f334(f260(x97061,x97061),f334(f334(f171(x97061),x97062),x97065)),x97066)),x97064)) % 188.18/188.27 [10207]~P72(x102072)+~P107(f334(f66(x102071),x102076))+P107(f334(f334(f336(x102071),f556(x102074,x102075,x102073,x102076,x102071,x102072)),x102076))+E(f334(f334(f9(x102071,x102072),f334(f334(f18(x102071,f935(x102073,a922),x102072),f334(f334(f8(f935(x102073,x102072),f935(f935(x102073,a922),x102072),x102071),f9(x102073,x102072)),x102074)),x102075)),x102076),f334(f334(f9(f934(x102071,x102073),x102072),f334(f265(x102071,x102073,x102072),x102074)),f334(f334(f262(x102071,x102073),x102076),x102075))) % 188.18/188.27 [10208]~P76(x102082)+~P107(f334(f66(x102081),x102086))+P107(f334(f334(f336(x102081),f558(x102084,x102085,x102083,x102086,x102081,x102082)),x102086))+E(f334(f334(f6(x102081,x102082),f334(f334(f18(x102081,f935(x102083,a922),x102082),f334(f334(f8(f935(x102083,x102082),f935(f935(x102083,a922),x102082),x102081),f6(x102083,x102082)),x102084)),x102085)),x102086),f334(f334(f6(f934(x102081,x102083),x102082),f334(f265(x102081,x102083,x102082),x102084)),f334(f334(f262(x102081,x102083),x102086),x102085))) % 188.18/188.27 [10250]~P72(x102502)+~P107(f334(f66(x102501),x102506))+~P107(f334(f66(x102503),f334(x102505,f556(x102504,x102505,x102503,x102506,x102501,x102502))))+E(f334(f334(f9(x102501,x102502),f334(f334(f18(x102501,f935(x102503,a922),x102502),f334(f334(f8(f935(x102503,x102502),f935(f935(x102503,a922),x102502),x102501),f9(x102503,x102502)),x102504)),x102505)),x102506),f334(f334(f9(f934(x102501,x102503),x102502),f334(f265(x102501,x102503,x102502),x102504)),f334(f334(f262(x102501,x102503),x102506),x102505))) % 188.18/188.27 [10251]~P76(x102512)+~P107(f334(f66(x102511),x102516))+~P107(f334(f66(x102513),f334(x102515,f558(x102514,x102515,x102513,x102516,x102511,x102512))))+E(f334(f334(f6(x102511,x102512),f334(f334(f18(x102511,f935(x102513,a922),x102512),f334(f334(f8(f935(x102513,x102512),f935(f935(x102513,a922),x102512),x102511),f6(x102513,x102512)),x102514)),x102515)),x102516),f334(f334(f6(f934(x102511,x102513),x102512),f334(f265(x102511,x102513,x102512),x102514)),f334(f334(f262(x102511,x102513),x102516),x102515))) % 188.18/188.27 [10230]~P72(x102302)+~P107(f334(f66(x102301),x102306))+P107(f334(f334(f336(x102301),x102303),x102306))+E(f334(f334(f9(x102301,x102302),f334(f334(f7(x102301,x102302,x102302),f334(f334(f18(x102301,x102302,f935(x102302,x102302)),f334(f334(f8(a922,f935(x102302,f935(x102302,x102302)),x102301),f103(x102302)),f334(f334(f7(x102301,x102301,a922),a331),x102303))),x102304)),x102305)),x102306),f334(f334(f252(x102302),x102305),f334(f40(x102301),x102306))) % 188.18/188.27 [10233]~P72(x102332)+~P107(f334(f66(x102331),x102336))+~P107(f334(f334(f336(x102331),x102333),x102336))+E(f334(f334(f9(x102331,x102332),f334(f334(f7(x102331,x102332,x102332),f334(f334(f18(x102331,x102332,f935(x102332,x102332)),f334(f334(f8(a922,f935(x102332,f935(x102332,x102332)),x102331),f103(x102332)),f334(f334(f7(x102331,x102331,a922),a331),x102333))),x102334)),x102335)),x102336),f334(f334(f87(x102332),f334(x102334,x102333)),f334(f334(f252(x102332),x102335),f334(f334(f23(a927),f334(f40(x102331),x102336)),f84(a927))))) % 188.18/188.27 [10316]~P107(f334(f66(x103161),x103165))+~P107(f334(f66(x103162),x103163))+P107(f334(f334(f336(x103162),f467(x103166,x103164,x103163,x103162,x103165,x103161)),x103163))+E(f334(f334(f6(x103161,a927),f334(f334(f8(f935(x103162,a922),a927,x103161),f40(x103162)),f334(f334(f8(f935(x103162,a922),f935(x103162,a922),x103161),f270(x103162)),f334(f334(f8(f935(x103162,a922),f935(x103162,a922),x103161),f334(f18(x103162,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103162),a332),f334(f334(f7(x103162,f935(x103162,a922),a922),f336(x103162)),x103163)))),x103164)))),x103165),f334(f334(f87(a927),x103166),f334(f40(x103162),x103163))) % 188.18/188.27 [10317]~P107(f334(f66(x103171),x103175))+~P107(f334(f66(x103172),x103173))+P107(f334(f334(f336(x103172),f471(x103176,x103174,x103173,x103172,x103175,x103171)),x103173))+E(f334(f334(f6(x103171,a927),f334(f334(f8(f935(x103172,a922),a927,x103171),f40(x103172)),f334(f334(f8(f935(x103172,a922),f935(x103172,a922),x103171),f270(x103172)),f334(f334(f8(f935(x103172,a922),f935(x103172,a922),x103171),f334(f18(x103172,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103172),a332),f334(f334(f7(x103172,f935(x103172,a922),a922),f336(x103172)),x103173)))),x103174)))),x103175),f334(f334(f6(x103172,a927),x103176),x103173)) % 188.18/188.27 [10365]~P107(f334(f66(x103652),x103653))+~P107(f334(f66(x103651),x103655))+~E(f334(f40(x103651),f334(f270(x103651),f334(f334(f18(x103651,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103651),a332),f334(f334(f7(x103651,f935(x103651,a922),a922),f336(x103651)),x103655))),f334(f334(f7(x103651,x103652,a922),x103654),f467(x103656,x103654,x103653,x103652,x103655,x103651))))),x103656)+E(f334(f334(f6(x103651,a927),f334(f334(f8(f935(x103652,a922),a927,x103651),f40(x103652)),f334(f334(f8(f935(x103652,a922),f935(x103652,a922),x103651),f270(x103652)),f334(f334(f8(f935(x103652,a922),f935(x103652,a922),x103651),f334(f18(x103652,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103652),a332),f334(f334(f7(x103652,f935(x103652,a922),a922),f336(x103652)),x103653)))),x103654)))),x103655),f334(f334(f87(a927),x103656),f334(f40(x103652),x103653))) % 188.18/188.27 [10384]~P107(f334(f66(x103842),x103843))+~P107(f334(f66(x103841),x103845))+~E(f334(f40(x103841),f334(f270(x103841),f334(f334(f18(x103841,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103841),a332),f334(f334(f7(x103841,f935(x103841,a922),a922),f336(x103841)),x103845))),f334(f334(f7(x103841,x103842,a922),x103844),f471(x103846,x103844,x103843,x103842,x103845,x103841))))),f334(x103846,f471(x103846,x103844,x103843,x103842,x103845,x103841)))+E(f334(f334(f6(x103841,a927),f334(f334(f8(f935(x103842,a922),a927,x103841),f40(x103842)),f334(f334(f8(f935(x103842,a922),f935(x103842,a922),x103841),f270(x103842)),f334(f334(f8(f935(x103842,a922),f935(x103842,a922),x103841),f334(f18(x103842,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103842),a332),f334(f334(f7(x103842,f935(x103842,a922),a922),f336(x103842)),x103843)))),x103844)))),x103845),f334(f334(f6(x103842,a927),x103846),x103843)) % 188.18/188.27 [10022]E(x100221,x100222)+~P18(x100223,x100224,x100225)+~P107(f334(f71(x100223,x100224,x100225,x100226,x100227),x100222))+~P107(f334(f71(x100223,x100224,x100225,x100226,x100227),x100221)) % 188.18/188.27 [9795]P107(f334(x97951,x97952))+~P107(f334(f334(f336(x97957),x97952),f334(x97956,x97954)))+~P107(f334(x97951,f400(x97951,x97956,x97955,x97953,x97957)))+~P107(f334(f334(f336(x97953),x97954),x97955)) % 188.18/188.27 [10222]~P18(x102227,x102226,x102221)+E(f334(f334(x102221,x102222),f893(x102222,x102223,x102224,x102225,x102221,x102226,x102227)),x102223)+~P107(f334(f71(x102227,x102226,x102221,x102225,x102224),x102223))+~P107(f334(f334(f336(x102227),x102222),x102224)) % 188.18/188.27 [10284]~P18(x102841,x102842,x102843)+~P107(f334(f71(x102841,x102842,x102843,x102844,x102845),x102847))+P107(f334(f71(x102841,x102842,x102843,x102844,f334(f334(f23(f935(x102841,a922)),x102845),f334(f334(f316(x102841),x102846),f195(f935(x102841,a922))))),f893(x102846,x102847,x102845,x102844,x102843,x102842,x102841)))+~P107(f334(f334(f336(x102841),x102846),x102845)) % 188.18/188.27 [9439]P28(x94391,x94392,x94393,x94394,x94395)+~P28(x94391,x94392,x94393,x94396,x94397)+~E(f334(f317(x94391,x94392,x94393),x94394),x94395)+~P107(f334(f334(f242(f935(x94391,a922)),x94394),x94396)) % 188.18/188.27 [9674]~P28(x96741,x96742,x96743,x96745,x96747)+~P28(x96741,x96742,x96743,x96744,x96746)+P28(x96741,x96742,x96743,f334(f334(f108(f935(x96741,a922)),x96744),x96745),f334(f334(f108(f935(x96742,a922)),x96746),x96747))+~E(f334(f334(f109(f935(x96742,a922)),x96746),x96747),f195(f935(x96742,a922))) % 188.18/188.27 [9679]~P70(x96791)+~P27(x96795,x96792,x96796,x96797)+~P107(f334(f66(x96795),x96797))+E(f334(f334(f334(f70(x96791,x96792,f87(x96791)),x96793),x96794),f334(f317(x96795,x96792,x96796),x96797)),f334(f334(f334(f70(x96791,x96795,f87(x96791)),f334(f78(x96792,x96791,x96795,x96793),x96796)),x96794),x96797)) % 188.18/188.27 [9816]~E(f334(f334(f316(x98161),x98165),x98166),f334(f334(f316(x98161),x98162),x98163))+~P107(f334(f71(x98161,x98161,x98164,x98162,x98163),x98167))+P107(f334(f334(f336(x98161),x98162),x98163))+P107(f334(f67(x98161,x98164,f334(f334(f316(x98161),x98165),x98166)),x98167)) % 188.18/188.27 [9913]P107(f334(x99131,x99132))+~P107(f334(f334(f336(x99133),x99132),f334(x99134,x99137)))+~P107(f334(f334(f336(x99136),x99137),x99135))+P107(f334(f334(f336(x99133),f400(x99131,x99134,x99135,x99136,x99133)),f334(f334(f44(x99136,f935(x99133,a922)),x99135),x99134))) % 188.18/188.27 [9932]~P27(x99322,x99321,x99325,x99324)+~P27(x99321,x99323,x99326,f334(f317(x99322,x99321,x99325),x99324))+E(f334(f334(f78(x99321,x99322,x99323,f83(x99322,x99321,x99324,x99325)),f83(x99321,x99323,f334(f317(x99322,x99321,x99325),x99324),x99326)),x99327),f334(f83(x99322,x99323,x99324,f334(f78(x99321,x99323,x99322,x99326),x99325)),x99327))+~P107(f334(f334(f336(x99323),x99327),f334(f317(x99321,x99323,x99326),f334(f317(x99322,x99321,x99325),x99324)))) % 188.18/188.27 [9933]~P27(x99332,x99331,x99335,x99334)+~P27(x99331,x99333,x99336,f334(f317(x99332,x99331,x99335),x99334))+E(f334(f334(f78(x99331,x99332,x99333,f97(x99332,x99331,x99334,x99335)),f97(x99331,x99333,f334(f317(x99332,x99331,x99335),x99334),x99336)),x99337),f334(f97(x99332,x99333,x99334,f334(f78(x99331,x99333,x99332,x99336),x99335)),x99337))+~P107(f334(f334(f336(x99333),x99337),f334(f317(x99331,x99333,x99336),f334(f317(x99332,x99331,x99335),x99334)))) % 188.18/188.27 [10223]~P18(x102237,x102236,x102231)+E(f334(f334(x102231,x102232),f576(x102233,x102234,x102232,x102235,x102231,x102236,x102237)),x102233)+P107(f334(f334(f336(x102237),x102232),x102234))+~P107(f334(f71(x102237,x102236,x102231,x102235,f334(f334(f316(x102237),x102232),x102234)),x102233)) % 188.18/188.27 [10283]~P18(x102831,x102834,x102835)+P107(f334(f71(x102831,x102834,x102835,x102836,x102833),f576(x102837,x102833,x102832,x102836,x102835,x102834,x102831)))+P107(f334(f334(f336(x102831),x102832),x102833))+~P107(f334(f71(x102831,x102834,x102835,x102836,f334(f334(f316(x102831),x102832),x102833)),x102837)) % 188.18/188.27 [10000]E(x100001,f2(a1))+~P107(f334(f54(x100003,x100001),f334(f334(f260(a1,a1),x100005),x100007)))+~P107(f334(f54(x100002,x100001),f334(f334(f260(a1,a1),x100004),x100006)))+P107(f334(f54(f334(f334(f86(a1),x100002),x100003),x100001),f334(f334(f260(a1,a1),f334(f334(f86(a1),f334(f334(f86(a1),x100004),x100005)),f334(f334(f41(a1),f334(f334(f86(a1),x100006),x100007)),x100001))),f50(a1,f334(f334(f86(a1),x100006),x100007),x100001)))) % 188.18/188.27 [10002]~P107(f334(f334(f243(a927),f2(a927)),x100023))+~P107(f334(f53(x100022,x100023),f334(f334(f260(a927,a927),x100025),x100027)))+~P107(f334(f53(x100021,x100023),f334(f334(f260(a927,a927),x100024),x100026)))+P107(f334(f53(f334(f334(f86(a927),x100021),x100022),x100023),f334(f334(f260(a927,a927),f334(f334(f86(a927),f334(f334(f86(a927),x100024),x100025)),f334(f334(f41(a927),f334(f334(f86(a927),x100026),x100027)),x100023))),f50(a927,f334(f334(f86(a927),x100026),x100027),x100023)))) % 188.18/188.27 [10364]~P76(x103642)+~P107(f334(f66(x103643),x103645))+~P107(f334(f66(x103641),x103647))+E(f334(f334(f6(x103641,x103642),f334(f334(f18(x103641,f935(x103643,a922),x103642),f334(f334(f8(f935(x103643,x103642),f935(f935(x103643,a922),x103642),x103641),f6(x103643,x103642)),x103644)),f334(f334(f8(f935(x103643,a922),f935(x103643,a922),x103641),f270(x103643)),f334(f334(f8(f935(x103643,a922),f935(x103643,a922),x103641),f334(f18(x103643,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103643),a332),f334(f334(f7(x103643,f935(x103643,a922),a922),f336(x103643)),x103645)))),x103646)))),x103647),f334(f334(f6(x103643,x103642),f334(f334(f18(x103643,f935(x103641,a922),x103642),f334(f334(f8(f935(x103641,x103642),f935(f935(x103641,a922),x103642),x103643),f6(x103641,x103642)),f334(f7(x103641,x103643,x103642),x103644))),f334(f334(f8(f935(x103641,a922),f935(x103641,a922),x103643),f270(x103641)),f334(f334(f8(f935(x103641,a922),f935(x103641,a922),x103643),f334(f18(x103641,a922,a922),f334(f334(f8(a922,f935(a922,a922),x103641),a332),f334(f334(f7(x103641,f935(x103641,a922),a922),f336(x103641)),x103647)))),f334(f7(x103641,x103643,a922),x103646))))),x103645)) % 188.18/188.27 [10315]~P23(x103158,x103157,x103156,x103155,x103151)+~E(f334(x103152,f870(x103154,x103152,x103153,x103151,x103155,x103156,x103157)),f334(x103154,f870(x103154,x103152,x103153,x103151,x103155,x103156,x103157)))+E(f334(f334(x103151,x103152),x103153),f334(f334(x103151,x103154),x103153))+~P107(f334(f66(x103157),x103153)) % 188.18/188.27 [9863]~P24(x98637,x98636,x98631,x98638,x98632,x98634)+E(f334(f334(x98631,f334(x98632,x98633)),f334(x98634,x98635)),f334(x98634,x98635))+~P107(f334(f66(x98636),x98635))+~P107(f334(f334(f336(x98636),x98633),x98635)) % 188.18/188.27 [9868]~P14(x98686,x98681,x98682,x98688,x98683,x98684)+~P10(x98686,x98687,x98688)+P13(x98681,x98682,x98683,f334(x98684,x98685))+~P107(f334(f334(f336(x98686),x98685),x98687)) % 188.18/188.27 [10332]~P23(x103328,x103325,x103327,x103326,x103321)+E(f334(f334(x103321,x103322),x103323),f334(f334(x103321,x103324),x103323))+~P107(f334(f66(x103325),x103323))+P107(f334(f334(f336(x103325),f870(x103322,x103324,x103323,x103321,x103326,x103327,x103325)),x103323)) % 188.18/188.27 [10450]~P107(f334(f334(x104501,x104506),x104505))+P107(f334(f334(x104501,f855(x104501,x104504,x104505,x104506,x104503,x104502,x104507,x104508)),f856(x104501,x104504,x104505,x104506,x104503,x104502,x104507,x104508)))+P107(f334(f334(x104501,x104502),x104503))+~P107(f334(f334(f336(f934(f934(x104508,x104507),f934(x104508,x104507))),f334(f334(f260(f934(x104508,x104507),f934(x104508,x104507)),f334(f334(f260(x104508,x104507),x104502),x104503)),f334(f334(f260(x104508,x104507),x104506),x104505))),f314(f934(x104508,x104507),x104504))) % 188.18/188.27 [10451]~P107(f334(f334(x104511,x104516),x104515))+P107(f334(f334(x104511,f857(x104511,x104514,x104513,x104512,x104515,x104516,x104517,x104518)),f858(x104511,x104514,x104513,x104512,x104515,x104516,x104517,x104518)))+P107(f334(f334(x104511,x104512),x104513))+~P107(f334(f334(f336(f934(f934(x104518,x104517),f934(x104518,x104517))),f334(f334(f260(f934(x104518,x104517),f934(x104518,x104517)),f334(f334(f260(x104518,x104517),x104516),x104515)),f334(f334(f260(x104518,x104517),x104512),x104513))),f314(f934(x104518,x104517),x104514))) % 188.18/188.27 [10464]~P107(f334(f334(x104641,f851(x104641,x104646,x104645,x104644,x104643,x104642,x104647,x104648)),f854(x104641,x104646,x104645,x104644,x104643,x104642,x104647,x104648)))+P107(f334(f334(x104641,x104642),x104643))+~P107(f334(f334(x104641,x104644),x104645))+~P107(f334(f334(f336(f934(f934(x104648,x104647),f934(x104648,x104647))),f334(f334(f260(f934(x104648,x104647),f934(x104648,x104647)),f334(f334(f260(x104648,x104647),x104642),x104643)),f334(f334(f260(x104648,x104647),x104644),x104645))),f314(f934(x104648,x104647),x104646))) % 188.18/188.27 [10465]~P107(f334(f334(x104651,f859(x104651,x104656,x104653,x104652,x104655,x104654,x104657,x104658)),f860(x104651,x104656,x104653,x104652,x104655,x104654,x104657,x104658)))+P107(f334(f334(x104651,x104652),x104653))+~P107(f334(f334(x104651,x104654),x104655))+~P107(f334(f334(f336(f934(f934(x104658,x104657),f934(x104658,x104657))),f334(f334(f260(f934(x104658,x104657),f934(x104658,x104657)),f334(f334(f260(x104658,x104657),x104654),x104655)),f334(f334(f260(x104658,x104657),x104652),x104653))),f314(f934(x104658,x104657),x104656))) % 188.18/188.27 [10481]~P107(f334(f334(x104811,x104816),x104817))+P107(f334(f334(x104811,x104812),x104813))+P107(f334(f334(f336(f934(f934(x104814,x104815),f934(x104814,x104815))),f334(f334(f260(f934(x104814,x104815),f934(x104814,x104815)),f334(f334(f260(x104814,x104815),x104816),x104817)),f334(f334(f260(x104814,x104815),f857(x104811,x104818,x104813,x104812,x104817,x104816,x104815,x104814)),f858(x104811,x104818,x104813,x104812,x104817,x104816,x104815,x104814)))),f314(f934(x104814,x104815),x104818)))+~P107(f334(f334(f336(f934(f934(x104814,x104815),f934(x104814,x104815))),f334(f334(f260(f934(x104814,x104815),f934(x104814,x104815)),f334(f334(f260(x104814,x104815),x104816),x104817)),f334(f334(f260(x104814,x104815),x104812),x104813))),f314(f934(x104814,x104815),x104818))) % 188.18/188.27 [10483]~P107(f334(f334(x104831,x104838),x104837))+P107(f334(f334(x104831,x104832),x104833))+P107(f334(f334(f336(f934(f934(x104834,x104835),f934(x104834,x104835))),f334(f334(f260(f934(x104834,x104835),f934(x104834,x104835)),f334(f334(f260(x104834,x104835),f855(x104831,x104836,x104837,x104838,x104833,x104832,x104835,x104834)),f856(x104831,x104836,x104837,x104838,x104833,x104832,x104835,x104834))),f334(f334(f260(x104834,x104835),x104838),x104837))),f314(f934(x104834,x104835),x104836)))+~P107(f334(f334(f336(f934(f934(x104834,x104835),f934(x104834,x104835))),f334(f334(f260(f934(x104834,x104835),f934(x104834,x104835)),f334(f334(f260(x104834,x104835),x104832),x104833)),f334(f334(f260(x104834,x104835),x104838),x104837))),f314(f934(x104834,x104835),x104836))) % 188.18/188.27 [9464]~P21(x94647,x94641,x94648,x94643)+~P107(f334(f66(x94647),x94645))+~P107(f334(f66(x94647),x94644))+E(f334(f78(x94641,x94641,x94642,f334(x94643,x94644)),f334(f78(x94641,x94641,x94642,f334(x94643,x94645)),x94646)),f334(f78(x94641,x94641,x94642,f334(x94643,x94645)),f334(f78(x94641,x94641,x94642,f334(x94643,x94644)),x94646))) % 188.18/188.27 [9473]~P36(x94731,x94732,x94733,x94734,x94737)+P36(x94731,x94732,x94733,f334(f334(f166(x94731,x94734),x94735),x94736),f334(f334(f166(x94732,x94737),x94735),x94738))+~P107(f334(f334(x94733,x94736),x94738))+~P107(f334(f334(f243(a927),x94735),f334(f196(f928(x94731)),x94734))) % 188.18/188.27 [9474]~P36(x94741,x94742,x94743,x94744,x94747)+P36(x94741,x94742,x94743,f334(f334(f166(x94741,x94744),x94745),x94746),f334(f334(f166(x94742,x94747),x94745),x94748))+~P107(f334(f334(x94743,x94746),x94748))+~P107(f334(f334(f243(a927),x94745),f334(f196(f928(x94742)),x94747))) % 188.18/188.27 [9556]~P27(x95562,x95562,x95565,x95566)+~P23(x95563,x95562,x95567,x95568,x95561)+~P107(f334(f66(x95562),x95566))+E(f334(f334(x95561,f334(f78(x95562,x95563,x95562,x95564),x95565)),x95566),f334(f334(x95561,x95564),f334(f317(x95562,x95562,x95565),x95566))) % 188.18/188.27 [9817]P28(x98171,x98172,x98173,x98174,x98175)+~P28(x98172,x98176,x98177,x98175,x98178)+~P28(x98171,x98176,f334(f78(x98172,x98176,x98171,x98177),x98173),x98174,x98178)+~P107(f334(f334(f242(f935(x98172,a922)),f334(f317(x98171,x98172,x98173),x98174)),x98175)) % 188.18/188.27 [9865]~P25(x98657,x98652,x98655,x98658,x98656,x98651)+~P107(f334(f66(x98652),x98654))+E(f334(x98651,f334(f334(f316(x98652),x98653),x98654)),f334(f334(x98655,f334(x98656,x98653)),f334(x98651,x98654)))+P107(f334(f334(f336(x98652),x98653),x98654)) % 188.18/188.27 [9881]~P24(x98816,x98815,x98811,x98817,x98818,x98812)+E(f334(f334(x98811,f334(x98812,x98813)),f334(x98812,x98814)),f334(x98812,x98814))+~P107(f334(f66(x98815),x98814))+~P107(f334(f334(f242(f935(x98815,a922)),x98813),x98814)) % 188.18/188.27 [10360]P26(x103608,x103607,f334(f334(f316(f926(x103608)),f98(x103608,x103604,x103605,x103603)),f195(f935(f926(x103608),a922))))+~P26(x103608,x103607,f334(f334(f316(f926(x103608)),f98(x103608,x103606,x103605,x103601)),f195(f935(f926(x103608),a922))))+~P107(f334(f334(x103606,x103602),f920(x103603,x103604,x103601,x103605,x103606,x103607,x103608)))+P107(f334(f334(x103601,x103602),f355(x103603,x103604,x103601,x103605,x103606,x103607,x103608))) % 188.18/188.27 [9451]P107(f334(f334(f336(f934(f928(x94511),f928(x94511))),f334(f334(f260(f928(x94511),f928(x94511)),x94512),x94513)),f164(x94511,x94514)))+~E(x94513,f334(f334(f141(x94511),x94515),f334(f334(f158(x94511),x94516),x94517)))+~E(x94512,f334(f334(f141(x94511),x94515),f334(f334(f158(x94511),x94518),x94517)))+~P107(f334(f334(f336(f934(x94511,x94511)),f334(f334(f260(x94511,x94511),x94518),x94516)),x94514)) % 188.18/188.27 [9875]~P24(x98756,x98752,x98755,x98757,x98758,x98751)+~P107(f334(f66(x98752),x98754))+~P107(f334(f66(x98752),x98753))+E(f334(x98751,f334(f334(f108(f935(x98752,a922)),x98753),x98754)),f334(f334(x98755,f334(x98751,x98753)),f334(x98751,x98754))) % 188.18/188.27 [10437]~P27(x104374,x104372,x104375,x104378)+E(f334(f334(f45(x104371,f935(x104372,a922)),x104373),f334(f334(f8(f935(x104374,a922),f935(x104372,a922),x104371),f317(x104374,x104372,x104375)),x104376)),f334(f317(x104374,x104372,x104375),f334(f334(f45(x104371,f935(x104374,a922)),x104373),x104376)))+~P107(f334(f334(f336(x104371),x104377),x104373))+P107(f334(f334(f336(x104371),f511(x104377,x104376,x104373,x104371,x104378,x104375,x104372,x104374)),x104373)) % 188.18/188.27 [10472]~P27(x104724,x104722,x104725,x104727)+E(f334(f334(f45(x104721,f935(x104722,a922)),x104723),f334(f334(f8(f935(x104724,a922),f935(x104722,a922),x104721),f317(x104724,x104722,x104725)),x104726)),f334(f317(x104724,x104722,x104725),f334(f334(f45(x104721,f935(x104724,a922)),x104723),x104726)))+~P107(f334(f334(f336(x104721),x104728),x104723))+~P107(f334(f334(f242(f935(x104724,a922)),f334(x104726,f511(x104728,x104726,x104723,x104721,x104727,x104725,x104722,x104724))),x104727)) % 188.18/188.27 [10484]~P107(f334(f334(x104841,x104848),x104847))+P107(f334(f334(x104841,x104842),x104843))+~P107(f334(f334(f336(f934(f934(x104844,x104845),f934(x104844,x104845))),f334(f334(f260(f934(x104844,x104845),f934(x104844,x104845)),f334(f334(f260(x104844,x104845),x104842),x104843)),f334(f334(f260(x104844,x104845),x104848),x104847))),f314(f934(x104844,x104845),x104846)))+P107(f334(f334(f336(f934(f934(x104844,x104845),f934(x104844,x104845))),f334(f334(f260(f934(x104844,x104845),f934(x104844,x104845)),f334(f334(f260(x104844,x104845),f851(x104841,x104846,x104847,x104848,x104843,x104842,x104845,x104844)),f854(x104841,x104846,x104847,x104848,x104843,x104842,x104845,x104844))),f334(f334(f260(x104844,x104845),f855(x104841,x104846,x104847,x104848,x104843,x104842,x104845,x104844)),f856(x104841,x104846,x104847,x104848,x104843,x104842,x104845,x104844)))),x104846)) % 188.18/188.27 [10485]~P107(f334(f334(x104851,x104858),x104857))+P107(f334(f334(x104851,x104852),x104853))+~P107(f334(f334(f336(f934(f934(x104854,x104855),f934(x104854,x104855))),f334(f334(f260(f934(x104854,x104855),f934(x104854,x104855)),f334(f334(f260(x104854,x104855),x104858),x104857)),f334(f334(f260(x104854,x104855),x104852),x104853))),f314(f934(x104854,x104855),x104856)))+P107(f334(f334(f336(f934(f934(x104854,x104855),f934(x104854,x104855))),f334(f334(f260(f934(x104854,x104855),f934(x104854,x104855)),f334(f334(f260(x104854,x104855),f857(x104851,x104856,x104853,x104852,x104857,x104858,x104855,x104854)),f858(x104851,x104856,x104853,x104852,x104857,x104858,x104855,x104854))),f334(f334(f260(x104854,x104855),f859(x104851,x104856,x104853,x104852,x104857,x104858,x104855,x104854)),f860(x104851,x104856,x104853,x104852,x104857,x104858,x104855,x104854)))),x104856)) % 188.18/188.27 [9942]~P25(x99427,x99425,x99421,x99428,x99422,x99424)+~P107(f334(f66(x99425),x99426))+~P107(f334(f334(f336(x99425),x99423),x99426))+E(f334(f334(x99421,f334(x99422,x99423)),f334(x99424,f334(f334(f23(f935(x99425,a922)),x99426),f334(f334(f316(x99425),x99423),f195(f935(x99425,a922)))))),f334(x99424,x99426)) % 188.18/188.27 [9950]~P25(x99506,x99503,x99501,x99507,x99508,x99502)+~P107(f334(f66(x99503),x99505))+~P107(f334(f66(x99503),x99504))+E(f334(f334(x99501,f334(x99502,f334(f334(f108(f935(x99503,a922)),x99504),x99505))),f334(x99502,f334(f334(f109(f935(x99503,a922)),x99504),x99505))),f334(f334(x99501,f334(x99502,x99504)),f334(x99502,x99505))) % 188.18/188.27 [10043]P44(x100431,x100432,x100433,x100434,x100435,f334(f334(x100433,x100436),x100437))+~P44(x100431,x100432,x100433,x100434,f334(f334(f23(f935(x100431,a922)),x100435),f334(f334(f316(x100431),x100438),f195(f935(x100431,a922)))),x100439)+~E(f334(f334(x100433,x100436),x100437),f334(f334(x100433,x100438),x100439))+~P107(f334(f334(f336(x100431),x100438),x100435)) % 188.18/188.27 [9974]~P14(x99746,x99747,x99748,x99749,x997410,x99741)+E(f334(f334(x99741,x99742),x99743),f334(f334(x99741,x99744),x99745))+~P107(f334(f334(f336(f934(x99747,x99747)),f334(f334(f260(x99747,x99747),x99743),x99745)),x997410))+~P107(f334(f334(f336(f934(x99746,x99746)),f334(f334(f260(x99746,x99746),x99742),x99744)),x99749)) % 188.18/188.27 [9560]~P99(x95602)+E(x95601,f195(f935(x95602,a922)))+~P107(f334(f66(x95602),x95601))+P107(f334(f334(f336(x95602),f10(x95602,x95601)),x95601))+~P107(f334(f334(f336(x95602),f334(f334(f109(x95602),f484(x95601,x95602)),f485(x95601,x95602))),f334(f334(f316(x95602),f484(x95601,x95602)),f334(f334(f316(x95602),f485(x95601,x95602)),f195(f935(x95602,a922)))))) % 188.18/188.27 [9561]~P99(x95612)+E(x95611,f195(f935(x95612,a922)))+~P107(f334(f66(x95612),x95611))+P107(f334(f334(f336(x95612),f13(x95612,x95611)),x95611))+~P107(f334(f334(f336(x95612),f334(f334(f108(x95612),f390(x95611,x95612)),f391(x95611,x95612))),f334(f334(f316(x95612),f390(x95611,x95612)),f334(f334(f316(x95612),f391(x95611,x95612)),f195(f935(x95612,a922)))))) % 188.18/188.27 [9593]~P70(x95932)+E(x95931,f195(f935(x95932,a922)))+~P107(f334(f66(x95932),x95931))+P107(f334(f334(f336(x95932),f334(f68(x95932,f87(x95932)),x95931)),x95931))+~P107(f334(f334(f336(x95932),f334(f334(f87(x95932),f816(x95931,x95932)),f825(x95931,x95932))),f334(f334(f316(x95932),f816(x95931,x95932)),f334(f334(f316(x95932),f825(x95931,x95932)),f195(f935(x95932,a922)))))) % 188.18/188.27 [9598]~P109(x95982)+E(x95981,f195(f935(x95982,a922)))+~P107(f334(f66(x95982),x95981))+P107(f334(f334(f336(x95982),f11(x95982,f246(x95982),x95981)),x95981))+~P107(f334(f334(f336(x95982),f334(f334(f246(x95982),f346(x95981,x95982)),f347(x95981,x95982))),f334(f334(f316(x95982),f346(x95981,x95982)),f334(f334(f316(x95982),f347(x95981,x95982)),f195(f935(x95982,a922)))))) % 188.18/188.27 [9599]~P109(x95992)+E(x95991,f195(f935(x95992,a922)))+~P107(f334(f66(x95992),x95991))+P107(f334(f334(f336(x95992),f12(x95992,f241(x95992),x95991)),x95991))+~P107(f334(f334(f336(x95992),f334(f334(f241(x95992),f354(x95991,x95992)),f356(x95991,x95992))),f334(f334(f316(x95992),f354(x95991,x95992)),f334(f334(f316(x95992),f356(x95991,x95992)),f195(f935(x95992,a922)))))) % 188.18/188.27 [6770]~P88(x67702)+E(x67701,f2(x67702))+~E(f334(f334(f86(x67702),x67703),x67701),f2(x67702))+~P107(f334(f334(f242(x67702),f2(x67702)),x67703))+~P107(f334(f334(f242(x67702),f2(x67702)),x67701)) % 188.18/188.27 [6771]~P88(x67712)+E(x67711,f2(x67712))+~E(f334(f334(f86(x67712),x67711),x67713),f2(x67712))+~P107(f334(f334(f242(x67712),f2(x67712)),x67713))+~P107(f334(f334(f242(x67712),f2(x67712)),x67711)) % 188.18/188.27 [7291]~P109(x72912)+~P15(x72912,x72911)+E(x72911,f120(x72912))+~P107(f334(f334(f336(x72912),x72913),f334(f179(x72912),f721(x72911,x72912))))+P107(f334(f334(f242(x72912),f740(x72911,x72912)),x72913)) % 188.18/188.27 [7458]~P109(x74581)+E(f14(x74581,x74582),x74583)+~P107(f334(f66(x74581),x74582))+~P107(f334(f334(f242(x74581),x74583),f610(x74583,x74582,x74581)))+~P107(f334(f334(f336(x74581),x74583),x74582)) % 188.18/188.27 [7491]~P109(x74911)+~P15(x74911,x74912)+~P15(x74911,x74913)+P15(x74911,f334(f334(f141(x74911),x74912),x74913))+P107(f334(f334(f336(x74911),f727(x74913,x74912,x74911)),f334(f179(x74911),x74912))) % 188.18/188.27 [7492]~P109(x74921)+~P15(x74921,x74922)+~P15(x74921,x74923)+P15(x74921,f334(f334(f141(x74921),x74922),x74923))+P107(f334(f334(f336(x74921),f728(x74923,x74922,x74921)),f334(f179(x74921),x74923))) % 188.18/188.27 [7551]~P109(x75511)+E(f14(x75511,x75512),x75513)+~P107(f334(f66(x75511),x75512))+P107(f334(f334(f336(x75511),f610(x75513,x75512,x75511)),x75512))+~P107(f334(f334(f336(x75511),x75513),x75512)) % 188.18/188.27 [7552]~P109(x75521)+E(f15(x75521,x75522),x75523)+~P107(f334(f66(x75521),x75522))+P107(f334(f334(f336(x75521),f611(x75523,x75522,x75521)),x75522))+~P107(f334(f334(f336(x75521),x75523),x75522)) % 188.18/188.27 [8103]~P109(x81031)+E(f15(x81031,x81032),x81033)+~P107(f334(f66(x81031),x81032))+~P107(f334(f334(f336(x81031),x81033),x81032))+~P107(f334(f334(f242(x81031),f611(x81033,x81032,x81031)),x81033)) % 188.18/188.27 [8415]~P109(x84151)+~P15(x84151,x84152)+~P15(x84151,x84153)+P15(x84151,f334(f334(f141(x84151),x84152),x84153))+~P107(f334(f334(f242(x84151),f727(x84153,x84152,x84151)),f728(x84153,x84152,x84151))) % 188.18/188.27 [9202]~P109(x92022)+E(x92021,f195(f935(x92022,a922)))+~E(f334(f334(f246(x92022),f334(x92023,f384(x92021,x92023,x92022))),f334(x92023,f388(x92021,x92023,x92022))),f334(x92023,f334(f334(f246(x92022),f384(x92021,x92023,x92022)),f388(x92021,x92023,x92022))))+E(f14(x92022,f334(f317(x92022,x92022,x92023),x92021)),f334(x92023,f14(x92022,x92021)))+~P107(f334(f66(x92022),x92021)) % 188.18/188.27 [9203]~P109(x92032)+E(x92031,f195(f935(x92032,a922)))+~E(f334(f334(f241(x92032),f334(x92033,f385(x92031,x92033,x92032))),f334(x92033,f386(x92031,x92033,x92032))),f334(x92033,f334(f334(f241(x92032),f385(x92031,x92033,x92032)),f386(x92031,x92033,x92032))))+E(f15(x92032,f334(f317(x92032,x92032,x92033),x92031)),f334(x92033,f15(x92032,x92031)))+~P107(f334(f66(x92032),x92031)) % 188.18/188.27 [9204]~P99(x92042)+E(x92041,f195(f935(x92042,a922)))+~E(f334(f334(f109(x92042),f334(x92043,f501(x92041,x92043,x92042))),f334(x92043,f505(x92041,x92043,x92042))),f334(x92043,f334(f334(f109(x92042),f501(x92041,x92043,x92042)),f505(x92041,x92043,x92042))))+E(f10(x92042,f334(f317(x92042,x92042,x92043),x92041)),f334(x92043,f10(x92042,x92041)))+~P107(f334(f66(x92042),x92041)) % 188.18/188.27 [9205]~P99(x92052)+E(x92051,f195(f935(x92052,a922)))+~E(f334(f334(f108(x92052),f334(x92053,f389(x92051,x92053,x92052))),f334(x92053,f392(x92051,x92053,x92052))),f334(x92053,f334(f334(f108(x92052),f389(x92051,x92053,x92052)),f392(x92051,x92053,x92052))))+E(f13(x92052,f334(f317(x92052,x92052,x92053),x92051)),f334(x92053,f13(x92052,x92051)))+~P107(f334(f66(x92052),x92051)) % 188.18/188.27 [9268]~P109(x92682)+E(x92681,f195(f935(x92682,a922)))+~E(f334(f334(f246(x92682),f334(x92683,f369(x92681,x92683,x92682))),f334(x92683,f372(x92681,x92683,x92682))),f334(x92683,f334(f334(f246(x92682),f369(x92681,x92683,x92682)),f372(x92681,x92683,x92682))))+E(f11(x92682,f246(x92682),f334(f317(x92682,x92682,x92683),x92681)),f334(x92683,f11(x92682,f246(x92682),x92681)))+~P107(f334(f66(x92682),x92681)) % 188.18/188.27 [9269]~P109(x92692)+E(x92691,f195(f935(x92692,a922)))+~E(f334(f334(f241(x92692),f334(x92693,f370(x92691,x92693,x92692))),f334(x92693,f371(x92691,x92693,x92692))),f334(x92693,f334(f334(f241(x92692),f370(x92691,x92693,x92692)),f371(x92691,x92693,x92692))))+E(f12(x92692,f241(x92692),f334(f317(x92692,x92692,x92693),x92691)),f334(x92693,f12(x92692,f241(x92692),x92691)))+~P107(f334(f66(x92692),x92691)) % 188.18/188.27 [6788]~P70(x67882)+E(x67881,f195(f935(x67882,a922)))+~P107(f334(f66(x67882),x67881))+E(f334(f68(x67882,f87(x67882)),f334(f334(f316(x67882),x67883),x67881)),f334(f334(f87(x67882),x67883),f334(f68(x67882,f87(x67882)),x67881)))+P107(f334(f334(f336(x67882),x67883),x67881)) % 188.18/188.27 [7297]~P109(x72972)+E(f334(f334(f246(x72972),f14(x72972,x72971)),f14(x72972,x72973)),f14(x72972,x72973))+E(x72971,f195(f935(x72972,a922)))+~P107(f334(f66(x72972),x72973))+~P107(f334(f334(f242(f935(x72972,a922)),x72971),x72973)) % 188.18/188.27 [7298]~P109(x72982)+E(f334(f334(f241(x72982),f15(x72982,x72981)),f15(x72982,x72983)),f15(x72982,x72983))+E(x72981,f195(f935(x72982,a922)))+~P107(f334(f66(x72982),x72983))+~P107(f334(f334(f242(f935(x72982,a922)),x72981),x72983)) % 188.18/188.27 [7299]~P99(x72992)+E(f334(f334(f108(x72992),f13(x72992,x72991)),f13(x72992,x72993)),f13(x72992,x72993))+E(x72991,f195(f935(x72992,a922)))+~P107(f334(f66(x72992),x72993))+~P107(f334(f334(f242(f935(x72992,a922)),x72991),x72993)) % 188.18/188.27 [7300]~P99(x73002)+E(f334(f334(f109(x73002),f10(x73002,x73001)),f10(x73002,x73003)),f10(x73002,x73003))+E(x73001,f195(f935(x73002,a922)))+~P107(f334(f66(x73002),x73003))+~P107(f334(f334(f242(f935(x73002,a922)),x73001),x73003)) % 188.18/188.27 [7592]~P109(x75922)+E(x75921,f195(f935(x75922,a922)))+~P107(f334(f66(x75922),x75923))+P107(f334(f334(f242(x75922),f14(x75922,x75923)),f14(x75922,x75921)))+~P107(f334(f334(f242(f935(x75922,a922)),x75921),x75923)) % 188.18/188.27 [7593]~P109(x75932)+E(x75931,f195(f935(x75932,a922)))+~P107(f334(f66(x75932),x75933))+P107(f334(f334(f242(x75932),f15(x75932,x75931)),f15(x75932,x75933)))+~P107(f334(f334(f242(f935(x75932,a922)),x75931),x75933)) % 188.18/188.27 [7645]~P109(x76451)+E(f14(x76451,x76452),x76453)+~P107(f334(f66(x76451),x76452))+~E(f334(f334(f23(f935(x76451,a922)),x76452),f334(f334(f316(x76451),x76453),f195(f935(x76451,a922)))),f195(f935(x76451,a922)))+~P107(f334(f334(f336(x76451),x76453),x76452)) % 188.18/188.27 [7646]~P109(x76461)+E(f15(x76461,x76462),x76463)+~P107(f334(f66(x76461),x76462))+~E(f334(f334(f23(f935(x76461,a922)),x76462),f334(f334(f316(x76461),x76463),f195(f935(x76461,a922)))),f195(f935(x76461,a922)))+~P107(f334(f334(f336(x76461),x76463),x76462)) % 188.18/188.27 [7647]~P99(x76471)+E(f10(x76471,x76472),x76473)+~P107(f334(f66(x76471),x76472))+~E(f334(f334(f23(f935(x76471,a922)),x76472),f334(f334(f316(x76471),x76473),f195(f935(x76471,a922)))),f195(f935(x76471,a922)))+~P107(f334(f334(f336(x76471),x76473),x76472)) % 188.18/188.27 [7648]~P99(x76481)+E(f13(x76481,x76482),x76483)+~P107(f334(f66(x76481),x76482))+~E(f334(f334(f23(f935(x76481,a922)),x76482),f334(f334(f316(x76481),x76483),f195(f935(x76481,a922)))),f195(f935(x76481,a922)))+~P107(f334(f334(f336(x76481),x76483),x76482)) % 188.18/188.27 [7740]~P109(x77401)+E(f11(x77401,f246(x77401),x77402),x77403)+~P107(f334(f66(x77401),x77402))+~E(f334(f334(f23(f935(x77401,a922)),x77402),f334(f334(f316(x77401),x77403),f195(f935(x77401,a922)))),f195(f935(x77401,a922)))+~P107(f334(f334(f336(x77401),x77403),x77402)) % 188.18/188.27 [7741]~P109(x77411)+E(f12(x77411,f241(x77411),x77412),x77413)+~P107(f334(f66(x77411),x77412))+~E(f334(f334(f23(f935(x77411,a922)),x77412),f334(f334(f316(x77411),x77413),f195(f935(x77411,a922)))),f195(f935(x77411,a922)))+~P107(f334(f334(f336(x77411),x77413),x77412)) % 188.18/188.27 [7777]~P109(x77772)+E(x77771,f195(f935(x77772,a922)))+~P107(f334(f66(x77772),x77771))+~P107(f334(f334(f242(x77772),x77773),f344(x77773,x77771,x77772)))+P107(f334(f334(f242(x77772),x77773),f334(f68(x77772,f246(x77772)),x77771))) % 188.18/188.27 [7778]~P104(x77782)+E(x77781,f195(f935(x77782,a922)))+~P107(f334(f66(x77782),x77781))+~P107(f334(f334(f242(x77782),x77783),f474(x77783,x77781,x77782)))+P107(f334(f334(f242(x77782),x77783),f334(f68(x77782,f109(x77782)),x77781))) % 188.18/188.27 [7779]~P109(x77792)+E(x77791,f195(f935(x77792,a922)))+~P107(f334(f66(x77792),x77791))+~P107(f334(f334(f243(x77792),x77793),f917(x77793,x77791,x77792)))+P107(f334(f334(f243(x77792),x77793),f334(f68(x77792,f246(x77792)),x77791))) % 188.18/188.27 [7861]~P109(x78612)+E(x78611,f195(f935(x78612,a922)))+~P107(f334(f66(x78612),x78611))+P107(f334(f334(f336(x78612),f917(x78613,x78611,x78612)),x78611))+P107(f334(f334(f243(x78612),x78613),f334(f68(x78612,f246(x78612)),x78611))) % 188.18/188.27 [7862]~P109(x78622)+E(x78621,f195(f935(x78622,a922)))+~P107(f334(f66(x78622),x78621))+P107(f334(f334(f336(x78622),f344(x78623,x78621,x78622)),x78621))+P107(f334(f334(f242(x78622),x78623),f334(f68(x78622,f246(x78622)),x78621))) % 188.18/188.27 [7863]~P104(x78632)+E(x78631,f195(f935(x78632,a922)))+~P107(f334(f66(x78632),x78631))+P107(f334(f334(f336(x78632),f474(x78633,x78631,x78632)),x78631))+P107(f334(f334(f242(x78632),x78633),f334(f68(x78632,f109(x78632)),x78631))) % 188.18/188.27 [7984]~P109(x79842)+E(x79841,f195(f935(x79842,a922)))+E(f334(f334(f246(x79842),f11(x79842,f246(x79842),x79841)),f11(x79842,f246(x79842),x79843)),f11(x79842,f246(x79842),x79843))+~P107(f334(f66(x79842),x79843))+~P107(f334(f334(f242(f935(x79842,a922)),x79841),x79843)) % 188.18/188.27 [7985]~P109(x79852)+E(x79851,f195(f935(x79852,a922)))+E(f334(f334(f241(x79852),f12(x79852,f241(x79852),x79851)),f12(x79852,f241(x79852),x79853)),f12(x79852,f241(x79852),x79853))+~P107(f334(f66(x79852),x79853))+~P107(f334(f334(f242(f935(x79852,a922)),x79851),x79853)) % 188.18/188.27 [8177]~E(f537(x81771,x81773,x81772),f538(x81771,x81773,x81772))+~E(f334(f40(x81772),f539(x81771,x81773,x81772)),x81771)+E(f334(f334(f87(a927),x81771),f334(f40(f935(x81772,a922)),x81773)),f334(f40(x81772),f42(f935(x81772,a922),x81773)))+~P107(f334(f66(x81772),f42(f935(x81772,a922),x81773)))+~P107(f334(f66(f935(x81772,a922)),x81773)) % 188.18/188.27 [8354]~P109(x83542)+E(x83541,f195(f935(x83542,a922)))+~P107(f334(f66(x83542),x83543))+P107(f334(f334(f242(x83542),f334(f68(x83542,f246(x83542)),x83543)),f334(f68(x83542,f246(x83542)),x83541)))+~P107(f334(f334(f242(f935(x83542,a922)),x83541),x83543)) % 188.18/188.27 [8646]~E(f537(x86461,x86463,x86462),f538(x86461,x86463,x86462))+E(f334(f334(f87(a927),x86461),f334(f40(f935(x86462,a922)),x86463)),f334(f40(x86462),f42(f935(x86462,a922),x86463)))+P107(f334(f334(f336(f935(x86462,a922)),f539(x86461,x86463,x86462)),x86463))+~P107(f334(f66(x86462),f42(f935(x86462,a922),x86463)))+~P107(f334(f66(f935(x86462,a922)),x86463)) % 188.18/188.27 [8673]~E(f334(f40(x86732),f539(x86731,x86733,x86732)),x86731)+E(f334(f334(f87(a927),x86731),f334(f40(f935(x86732,a922)),x86733)),f334(f40(x86732),f42(f935(x86732,a922),x86733)))+P107(f334(f334(f336(f935(x86732,a922)),f538(x86731,x86733,x86732)),x86733))+~P107(f334(f66(x86732),f42(f935(x86732,a922),x86733)))+~P107(f334(f66(f935(x86732,a922)),x86733)) % 188.18/188.27 [8674]~E(f334(f40(x86742),f539(x86741,x86743,x86742)),x86741)+E(f334(f334(f87(a927),x86741),f334(f40(f935(x86742,a922)),x86743)),f334(f40(x86742),f42(f935(x86742,a922),x86743)))+P107(f334(f334(f336(f935(x86742,a922)),f537(x86741,x86743,x86742)),x86743))+~P107(f334(f66(x86742),f42(f935(x86742,a922),x86743)))+~P107(f334(f66(f935(x86742,a922)),x86743)) % 188.18/188.27 [8698]~E(f334(f40(x86982),f539(x86981,x86983,x86982)),x86981)+~E(f334(f334(f109(f935(x86982,a922)),f538(x86981,x86983,x86982)),f537(x86981,x86983,x86982)),f195(f935(x86982,a922)))+E(f334(f334(f87(a927),x86981),f334(f40(f935(x86982,a922)),x86983)),f334(f40(x86982),f42(f935(x86982,a922),x86983)))+~P107(f334(f66(f935(x86982,a922)),x86983))+~P107(f334(f66(x86982),f42(f935(x86982,a922),x86983))) % 188.18/188.27 [8958]E(f334(f334(f87(a927),x89581),f334(f40(f935(x89582,a922)),x89583)),f334(f40(x89582),f42(f935(x89582,a922),x89583)))+P107(f334(f334(f336(f935(x89582,a922)),f539(x89581,x89583,x89582)),x89583))+P107(f334(f334(f336(f935(x89582,a922)),f538(x89581,x89583,x89582)),x89583))+~P107(f334(f66(f935(x89582,a922)),x89583))+~P107(f334(f66(x89582),f42(f935(x89582,a922),x89583))) % 188.18/188.27 [8959]E(f334(f334(f87(a927),x89591),f334(f40(f935(x89592,a922)),x89593)),f334(f40(x89592),f42(f935(x89592,a922),x89593)))+P107(f334(f334(f336(f935(x89592,a922)),f539(x89591,x89593,x89592)),x89593))+P107(f334(f334(f336(f935(x89592,a922)),f537(x89591,x89593,x89592)),x89593))+~P107(f334(f66(f935(x89592,a922)),x89593))+~P107(f334(f66(x89592),f42(f935(x89592,a922),x89593))) % 188.18/188.27 [8984]~E(f334(f334(f109(f935(x89842,a922)),f538(x89841,x89843,x89842)),f537(x89841,x89843,x89842)),f195(f935(x89842,a922)))+E(f334(f334(f87(a927),x89841),f334(f40(f935(x89842,a922)),x89843)),f334(f40(x89842),f42(f935(x89842,a922),x89843)))+~P107(f334(f66(f935(x89842,a922)),x89843))+P107(f334(f334(f336(f935(x89842,a922)),f539(x89841,x89843,x89842)),x89843))+~P107(f334(f66(x89842),f42(f935(x89842,a922),x89843))) % 188.18/188.27 [9247]~P96(x92472)+E(x92471,f195(f935(x92472,a922)))+~E(f334(f334(f87(x92472),f334(x92473,f844(x92471,x92473,x92472))),f334(x92473,f846(x92471,x92473,x92472))),f334(x92473,f334(f334(f87(x92472),f844(x92471,x92473,x92472)),f846(x92471,x92473,x92472))))+~P107(f334(f66(x92472),x92471))+E(f334(f68(x92472,f87(x92472)),f334(f317(x92472,x92472,x92473),x92471)),f334(x92473,f334(f68(x92472,f87(x92472)),x92471))) % 188.18/188.27 [10381]P107(f334(f334(x103811,x103812),x103813))+P107(f334(f334(f243(a1),f364(x103811,x103813,x103812)),f365(x103811,x103813,x103812)))+P107(f334(f334(f242(a1),f365(x103811,x103813,x103812)),f2(a1)))+P107(f334(f334(x103811,f364(x103811,x103813,x103812)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f365(x103811,x103813,x103812))))+~P107(f334(f322(f934(a1,a1),a63),f334(f334(f260(a1,a1),x103812),x103813))) % 188.18/188.27 [10382]P107(f334(f334(x103821,x103822),x103823))+P107(f334(f334(f242(a1),f362(x103821,x103823,x103822)),f2(a1)))+P107(f334(f334(x103821,f358(x103821,x103823,x103822)),f334(f334(f87(a1),f334(f111(a1),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f362(x103821,x103823,x103822))))+P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),f358(x103821,x103823,x103822)),f362(x103821,x103823,x103822))))+~P107(f334(f322(f934(a1,a1),a57),f334(f334(f260(a1,a1),x103822),x103823))) % 188.18/188.27 [8148]~P124(x81481)+~P107(f334(f334(f242(x81481),x81482),f84(x81481)))+~P107(f334(f334(f242(x81481),f2(x81481)),x81482))+~P107(f334(f334(f242(x81481),f2(x81481)),x81483))+P107(f334(f334(f242(x81481),f334(f334(f87(x81481),x81482),x81483)),x81483)) % 188.18/188.27 [8149]~P124(x81491)+~P107(f334(f334(f242(x81491),x81493),f84(x81491)))+~P107(f334(f334(f242(x81491),f2(x81491)),x81493))+~P107(f334(f334(f242(x81491),f2(x81491)),x81492))+P107(f334(f334(f242(x81491),f334(f334(f87(x81491),x81492),x81493)),x81492)) % 188.18/188.27 [8499]~P109(x84992)+E(x84991,f195(f935(x84992,a922)))+~P107(f334(f66(x84992),x84991))+P107(f334(f334(f336(x84992),f918(x84993,x84991,x84992)),x84991))+~P107(f334(f334(f243(x84992),f334(f68(x84992,f246(x84992)),x84991)),x84993)) % 188.18/188.27 [8500]~P109(x85002)+E(x85001,f195(f935(x85002,a922)))+~P107(f334(f66(x85002),x85001))+P107(f334(f334(f336(x85002),f919(x85003,x85001,x85002)),x85001))+~P107(f334(f334(f242(x85002),f334(f68(x85002,f246(x85002)),x85001)),x85003)) % 188.18/188.27 [8501]~P109(x85012)+E(x85011,f195(f935(x85012,a922)))+~P107(f334(f66(x85012),x85011))+P107(f334(f334(f242(x85012),f919(x85013,x85011,x85012)),x85013))+~P107(f334(f334(f242(x85012),f334(f68(x85012,f246(x85012)),x85011)),x85013)) % 188.18/188.27 [8502]~P109(x85022)+E(x85021,f195(f935(x85022,a922)))+~P107(f334(f66(x85022),x85021))+P107(f334(f334(f243(x85022),f918(x85023,x85021,x85022)),x85023))+~P107(f334(f334(f243(x85022),f334(f68(x85022,f246(x85022)),x85021)),x85023)) % 188.18/188.27 [8585]~P107(f334(x85851,x85853))+P107(f334(x85851,f441(x85851,x85852)))+P107(f334(x85851,f436(x85851,x85852)))+~P107(f334(f334(f243(a1),f2(a1)),x85852))+P107(f334(x85851,f334(f334(f23(a1),f436(x85851,x85852)),f334(f334(f87(a1),f442(x85851,x85852)),x85852)))) % 188.18/188.27 [8801]~P107(f334(x88011,x88013))+P107(f334(x88011,f436(x88011,x88012)))+~P107(f334(f334(f243(a1),f2(a1)),x88012))+P107(f334(f334(f336(a1),f441(x88011,x88012)),f311(a1,f84(a1),x88012)))+P107(f334(x88011,f334(f334(f23(a1),f436(x88011,x88012)),f334(f334(f87(a1),f442(x88011,x88012)),x88012)))) % 188.18/188.27 [9005]~P107(f334(x90051,x90053))+~P107(f334(x90051,f436(x90051,x90052)))+P107(f334(x90051,f441(x90051,x90052)))+~P107(f334(f334(f243(a1),f2(a1)),x90052))+~P107(f334(x90051,f334(f334(f23(a1),f436(x90051,x90052)),f334(f334(f87(a1),f442(x90051,x90052)),x90052)))) % 188.18/188.27 [9140]~P107(f334(x91401,x91403))+~P107(f334(x91401,f436(x91401,x91402)))+~P107(f334(f334(f243(a1),f2(a1)),x91402))+P107(f334(f334(f336(a1),f441(x91401,x91402)),f311(a1,f84(a1),x91402)))+~P107(f334(x91401,f334(f334(f23(a1),f436(x91401,x91402)),f334(f334(f87(a1),f442(x91401,x91402)),x91402)))) % 188.18/188.27 [8912]~P109(x89121)+~P107(f334(f66(x89121),x89122))+E(f334(f334(f23(f935(x89121,a922)),x89122),f334(f334(f316(x89121),x89123),f195(f935(x89121,a922)))),f195(f935(x89121,a922)))+~P107(f334(f334(f336(x89121),x89123),x89122))+E(f334(f334(f246(x89121),x89123),f14(x89121,f334(f334(f23(f935(x89121,a922)),x89122),f334(f334(f316(x89121),x89123),f195(f935(x89121,a922)))))),f14(x89121,x89122)) % 188.18/188.27 [8913]~P109(x89131)+~P107(f334(f66(x89131),x89132))+E(f334(f334(f23(f935(x89131,a922)),x89132),f334(f334(f316(x89131),x89133),f195(f935(x89131,a922)))),f195(f935(x89131,a922)))+~P107(f334(f334(f336(x89131),x89133),x89132))+E(f334(f334(f241(x89131),x89133),f15(x89131,f334(f334(f23(f935(x89131,a922)),x89132),f334(f334(f316(x89131),x89133),f195(f935(x89131,a922)))))),f15(x89131,x89132)) % 188.18/188.27 [8914]~P99(x89141)+~P107(f334(f66(x89141),x89142))+E(f334(f334(f23(f935(x89141,a922)),x89142),f334(f334(f316(x89141),x89143),f195(f935(x89141,a922)))),f195(f935(x89141,a922)))+~P107(f334(f334(f336(x89141),x89143),x89142))+E(f334(f334(f109(x89141),x89143),f10(x89141,f334(f334(f23(f935(x89141,a922)),x89142),f334(f334(f316(x89141),x89143),f195(f935(x89141,a922)))))),f10(x89141,x89142)) % 188.18/188.27 [8915]~P99(x89151)+~P107(f334(f66(x89151),x89152))+E(f334(f334(f23(f935(x89151,a922)),x89152),f334(f334(f316(x89151),x89153),f195(f935(x89151,a922)))),f195(f935(x89151,a922)))+~P107(f334(f334(f336(x89151),x89153),x89152))+E(f334(f334(f108(x89151),x89153),f13(x89151,f334(f334(f23(f935(x89151,a922)),x89152),f334(f334(f316(x89151),x89153),f195(f935(x89151,a922)))))),f13(x89151,x89152)) % 188.18/188.27 [8975]~P109(x89751)+~P107(f334(f66(x89751),x89752))+E(f334(f334(f23(f935(x89751,a922)),x89752),f334(f334(f316(x89751),x89753),f195(f935(x89751,a922)))),f195(f935(x89751,a922)))+~P107(f334(f334(f336(x89751),x89753),x89752))+E(f334(f334(f246(x89751),x89753),f11(x89751,f246(x89751),f334(f334(f23(f935(x89751,a922)),x89752),f334(f334(f316(x89751),x89753),f195(f935(x89751,a922)))))),f11(x89751,f246(x89751),x89752)) % 188.18/188.27 [8976]~P109(x89761)+~P107(f334(f66(x89761),x89762))+E(f334(f334(f23(f935(x89761,a922)),x89762),f334(f334(f316(x89761),x89763),f195(f935(x89761,a922)))),f195(f935(x89761,a922)))+~P107(f334(f334(f336(x89761),x89763),x89762))+E(f334(f334(f241(x89761),x89763),f12(x89761,f241(x89761),f334(f334(f23(f935(x89761,a922)),x89762),f334(f334(f316(x89761),x89763),f195(f935(x89761,a922)))))),f12(x89761,f241(x89761),x89762)) % 188.18/188.27 [8992]~P109(x89921)+~P107(f334(f66(x89921),x89923))+~P107(f334(f66(x89921),x89922))+E(f334(f334(f109(f935(x89921,a922)),x89922),x89923),f195(f935(x89921,a922)))+E(f334(f334(f246(x89921),f14(x89921,f334(f334(f108(f935(x89921,a922)),x89922),x89923))),f14(x89921,f334(f334(f109(f935(x89921,a922)),x89922),x89923))),f334(f334(f246(x89921),f14(x89921,x89922)),f14(x89921,x89923))) % 188.18/188.27 [8993]~P109(x89931)+~P107(f334(f66(x89931),x89933))+~P107(f334(f66(x89931),x89932))+E(f334(f334(f109(f935(x89931,a922)),x89932),x89933),f195(f935(x89931,a922)))+E(f334(f334(f241(x89931),f15(x89931,f334(f334(f108(f935(x89931,a922)),x89932),x89933))),f15(x89931,f334(f334(f109(f935(x89931,a922)),x89932),x89933))),f334(f334(f241(x89931),f15(x89931,x89932)),f15(x89931,x89933))) % 188.18/188.27 [8994]~P99(x89941)+~P107(f334(f66(x89941),x89943))+~P107(f334(f66(x89941),x89942))+E(f334(f334(f109(f935(x89941,a922)),x89942),x89943),f195(f935(x89941,a922)))+E(f334(f334(f108(x89941),f13(x89941,f334(f334(f108(f935(x89941,a922)),x89942),x89943))),f13(x89941,f334(f334(f109(f935(x89941,a922)),x89942),x89943))),f334(f334(f108(x89941),f13(x89941,x89942)),f13(x89941,x89943))) % 188.18/188.27 [8995]~P99(x89951)+~P107(f334(f66(x89951),x89953))+~P107(f334(f66(x89951),x89952))+E(f334(f334(f109(f935(x89951,a922)),x89952),x89953),f195(f935(x89951,a922)))+E(f334(f334(f109(x89951),f10(x89951,f334(f334(f108(f935(x89951,a922)),x89952),x89953))),f10(x89951,f334(f334(f109(f935(x89951,a922)),x89952),x89953))),f334(f334(f109(x89951),f10(x89951,x89952)),f10(x89951,x89953))) % 188.18/188.27 [9219]~P109(x92191)+~P107(f334(f66(x92191),x92193))+~P107(f334(f66(x92191),x92192))+E(f334(f334(f109(f935(x92191,a922)),x92192),x92193),f195(f935(x92191,a922)))+E(f334(f334(f246(x92191),f11(x92191,f246(x92191),f334(f334(f108(f935(x92191,a922)),x92192),x92193))),f11(x92191,f246(x92191),f334(f334(f109(f935(x92191,a922)),x92192),x92193))),f334(f334(f246(x92191),f11(x92191,f246(x92191),x92192)),f11(x92191,f246(x92191),x92193))) % 188.18/188.27 [9220]~P109(x92201)+~P107(f334(f66(x92201),x92203))+~P107(f334(f66(x92201),x92202))+E(f334(f334(f109(f935(x92201,a922)),x92202),x92203),f195(f935(x92201,a922)))+E(f334(f334(f241(x92201),f12(x92201,f241(x92201),f334(f334(f108(f935(x92201,a922)),x92202),x92203))),f12(x92201,f241(x92201),f334(f334(f109(f935(x92201,a922)),x92202),x92203))),f334(f334(f241(x92201),f12(x92201,f241(x92201),x92202)),f12(x92201,f241(x92201),x92203))) % 188.18/188.27 [10286]~P127(x102863)+E(x102861,x102862)+~P107(f334(f334(f242(x102863),f2(x102863)),x102862))+~P107(f334(f334(f242(x102863),f2(x102863)),x102861))+~E(f334(f334(f252(x102863),x102861),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104))),f334(f334(f252(x102863),x102862),f334(f111(a927),f334(f334(f86(a1),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),f334(f334(f86(a1),f334(f334(f86(a1),f84(a1)),a89)),a89))),a104)))) % 188.18/188.27 [5785]~P5(x57852)+~P59(x57852,x57851,x57853)+E(x57851,f2(x57852))+~E(f334(f334(f41(x57852),x57853),x57851),x57854)+E(x57853,f334(f334(f87(x57852),x57854),x57851)) % 188.18/188.27 [5786]~P5(x57862)+~P59(x57862,x57861,x57863)+E(x57861,f2(x57862))+~E(x57863,f334(f334(f87(x57862),x57864),x57861))+E(f334(f334(f41(x57862),x57863),x57861),x57864) % 188.18/188.27 [6585]E(f451(x65851,x65852,x65853),x65854)+E(f334(x65851,x65854),f2(a927))+~E(f334(f334(f6(x65853,a927),x65851),x65852),f84(a927))+~P107(f334(f66(x65853),x65852))+~P107(f334(f334(f336(x65853),x65854),x65852)) % 188.18/188.27 [6649]E(f456(x66491,x66492,x66493),x66494)+E(f334(x66491,x66494),f2(a927))+~E(f334(f334(f6(x66493,a927),x66491),x66492),f334(a119,f2(a927)))+~P107(f334(f66(x66493),x66492))+~P107(f334(f334(f336(x66493),x66494),x66492)) % 188.18/188.27 [6760]~P109(x67601)+~P7(x67601)+P107(f334(f334(f243(x67601),x67602),f42(x67601,x67603)))+~P107(f334(f334(f243(x67601),x67602),x67604))+~P107(f334(f334(f336(x67601),x67604),x67603)) % 188.18/188.27 [6929]~P109(x69291)+~P7(x69291)+~P107(f334(f334(f243(x69291),x69294),x69293))+P107(f334(f334(f243(x69291),f43(x69291,x69292)),x69293))+~P107(f334(f334(f336(x69291),x69294),x69292)) % 188.18/188.27 [7177]~P127(x71773)+E(x71771,x71772)+~E(f334(f334(f252(x71773),x71771),f334(a119,x71774)),f334(f334(f252(x71773),x71772),f334(a119,x71774)))+~P107(f334(f334(f242(x71773),f2(x71773)),x71772))+~P107(f334(f334(f242(x71773),f2(x71773)),x71771)) % 188.18/188.27 [7385]~E(f458(x73852,x73853,x73851,x73854),x73854)+~E(f334(x73852,x73854),f84(a927))+E(f334(f334(f6(x73851,a927),x73852),x73853),f84(a927))+~P107(f334(f66(x73851),x73853))+~P107(f334(f334(f336(x73851),x73854),x73853)) % 188.18/188.27 [7392]~P119(x73924)+~P136(x73924)+E(f334(x73921,f343(x73921,x73922,x73923,x73924)),f2(x73924))+~E(f334(f334(f9(x73923,x73924),x73921),x73922),f2(x73924))+~P107(f334(f66(x73923),x73922)) % 188.18/188.27 [7481]~E(f457(x74812,x74813,x74811,x74814),x74814)+~E(f334(x74812,x74814),f334(a119,f2(a927)))+E(f334(f334(f6(x74811,a927),x74812),x74813),f334(a119,f2(a927)))+~P107(f334(f66(x74811),x74813))+~P107(f334(f334(f336(x74811),x74814),x74813)) % 188.18/188.27 [7944]~P148(x79442)+~P121(x79442)+~P59(x79442,x79443,f334(f334(f86(x79442),x79444),f2(x79442)))+~P107(f334(x79441,x79444))+P107(f334(x79441,f334(f334(f87(x79442),x79443),f872(x79443,x79441,x79442)))) % 188.18/188.27 [8188]~E(f334(x81882,x81884),f84(a927))+~E(f334(x81882,f458(x81882,x81883,x81881,x81884)),f2(a927))+E(f334(f334(f6(x81881,a927),x81882),x81883),f84(a927))+~P107(f334(f66(x81881),x81883))+~P107(f334(f334(f336(x81881),x81884),x81883)) % 188.18/188.27 [8225]~E(f334(x82252,x82254),f334(a119,f2(a927)))+~E(f334(x82252,f457(x82252,x82253,x82251,x82254)),f2(a927))+E(f334(f334(f6(x82251,a927),x82252),x82253),f334(a119,f2(a927)))+~P107(f334(f66(x82251),x82253))+~P107(f334(f334(f336(x82251),x82254),x82253)) % 188.18/188.27 [8769]~P109(x87691)+~P15(x87691,x87694)+P15(x87691,x87692)+~E(x87692,f334(f334(f158(x87691),x87693),x87694))+~P107(f334(f334(f242(x87691),x87693),f742(x87692,x87691,x87694,x87693))) % 188.18/188.27 [8805]E(x88051,x88052)+E(f334(f334(f23(a1),f414(x88053,x88052,x88054,x88051)),f415(x88053,x88052,x88054,x88051)),x88051)+~E(f334(f334(f86(a1),x88051),x88054),x88052)+~P107(f334(f334(f243(a1),f2(a1)),x88054))+~P107(f334(f334(f336(a1),x88052),x88053)) % 188.18/188.27 [8806]E(x88061,x88062)+E(f334(f334(f86(a1),f421(x88063,x88062,x88064,x88061)),f420(x88063,x88062,x88064,x88061)),x88061)+~E(f334(f334(f23(a1),x88061),x88064),x88062)+~P107(f334(f334(f243(a1),f2(a1)),x88064))+~P107(f334(f334(f336(a1),x88062),x88063)) % 188.18/188.27 [8990]E(f334(x89901,f612(x89902,x89901,x89903,x89904)),x89902)+P107(f334(f334(f242(a927),x89904),f613(x89902,x89901,x89903,x89904)))+~P107(f334(f334(f242(a1),x89902),f334(x89901,x89903)))+~P107(f334(f334(f243(a927),x89904),x89903))+~P107(f334(f334(f242(a1),f334(x89901,x89904)),x89902)) % 188.18/188.27 [8991]~P109(x89911)+~P15(x89911,x89913)+P15(x89911,x89912)+~E(x89912,f334(f334(f158(x89911),x89914),x89913))+P107(f334(f334(f336(x89911),f742(x89912,x89911,x89913,x89914)),f334(f179(x89911),x89913))) % 188.18/188.27 [9009]~P119(x90094)+~P136(x90094)+~E(f334(f334(f9(x90091,x90094),x90092),x90093),f2(x90094))+~P107(f334(f66(x90091),x90093))+P107(f334(f334(f336(x90091),f343(x90092,x90093,x90091,x90094)),x90093)) % 188.18/188.27 [9049]~E(f334(x90492,x90494),f84(a927))+E(f334(f334(f6(x90491,a927),x90492),x90493),f84(a927))+~P107(f334(f66(x90491),x90493))+~P107(f334(f334(f336(x90491),x90494),x90493))+P107(f334(f334(f336(x90491),f458(x90492,x90493,x90491,x90494)),x90493)) % 188.18/188.27 [9064]E(x90641,x90642)+~E(f334(f334(f86(a1),x90642),x90644),x90641)+~P107(f334(f334(f243(a1),f2(a1)),x90644))+~P107(f334(f334(f336(a1),x90641),x90643))+P107(f334(f334(f336(a1),f414(x90643,x90641,x90644,x90642)),x90643)) % 188.18/188.27 [9065]E(x90651,x90652)+~E(f334(f334(f23(a1),x90652),x90654),x90651)+~P107(f334(f334(f243(a1),f2(a1)),x90654))+~P107(f334(f334(f336(a1),x90651),x90653))+P107(f334(f334(f336(a1),f421(x90653,x90651,x90654,x90652)),x90653)) % 188.18/188.27 [9067]~E(f334(x90672,x90674),f334(a119,f2(a927)))+E(f334(f334(f6(x90671,a927),x90672),x90673),f334(a119,f2(a927)))+~P107(f334(f66(x90671),x90673))+~P107(f334(f334(f336(x90671),x90674),x90673))+P107(f334(f334(f336(x90671),f457(x90672,x90673,x90671,x90674)),x90673)) % 188.18/188.27 [9073]P62(x90732,x90733,x90734,x90731)+E(x90731,f195(f935(x90732,a922)))+~P107(f334(f66(x90732),x90734))+~P107(f334(f66(x90732),x90731))+P107(f334(f334(f336(x90732),f813(x90733,x90731,x90734,x90732)),x90734)) % 188.18/188.27 [9074]P62(x90742,x90743,x90744,x90741)+E(x90741,f195(f935(x90742,a922)))+~P107(f334(f66(x90742),x90744))+~P107(f334(f66(x90742),x90741))+P107(f334(f334(f336(x90742),f523(x90741,x90744,x90743,x90742)),x90744)) % 188.18/188.27 [9075]P62(x90752,x90753,x90754,x90751)+E(x90751,f195(f935(x90752,a922)))+~P107(f334(f66(x90752),x90754))+~P107(f334(f66(x90752),x90751))+P107(f334(f334(f336(x90752),f814(x90751,x90754,x90753,x90752)),x90754)) % 188.18/188.27 [9152]E(x91521,x91522)+~E(f334(f334(f86(a1),x91522),x91524),x91521)+~P107(f334(f334(f243(a1),f2(a1)),x91524))+~P107(f334(f334(f336(a1),x91521),x91523))+P107(f334(f334(f336(a1),f415(x91523,x91521,x91524,x91522)),f311(a1,f84(a1),x91524))) % 188.18/188.27 [9153]E(x91531,x91532)+~E(f334(f334(f23(a1),x91532),x91534),x91531)+~P107(f334(f334(f243(a1),f2(a1)),x91534))+~P107(f334(f334(f336(a1),x91531),x91533))+P107(f334(f334(f336(a1),f420(x91533,x91531,x91534,x91532)),f311(a1,f84(a1),x91534))) % 188.18/188.27 [9225]P107(f334(f334(f242(a927),x92251),f612(x92252,x92253,x92254,x92251)))+~P107(f334(f334(f242(a1),x92252),f334(x92253,x92254)))+P107(f334(f334(f242(a927),x92251),f613(x92252,x92253,x92254,x92251)))+~P107(f334(f334(f243(a927),x92251),x92254))+~P107(f334(f334(f242(a1),f334(x92253,x92251)),x92252)) % 188.18/188.27 [9332]E(f334(x93321,f612(x93322,x93321,x93323,x93324)),x93322)+~P107(f334(f334(f242(a1),x93322),f334(x93321,x93323)))+P107(f334(f334(f243(a927),f613(x93322,x93321,x93323,x93324)),x93323))+~P107(f334(f334(f243(a927),x93324),x93323))+~P107(f334(f334(f242(a1),f334(x93321,x93324)),x93322)) % 188.18/188.27 [9461]~P107(f334(f334(f242(a1),x94612),f334(x94613,x94614)))+P107(f334(f334(f242(a927),x94611),f613(x94612,x94613,x94614,x94611)))+P107(f334(f334(f242(a927),f612(x94612,x94613,x94614,x94611)),x94614))+~P107(f334(f334(f243(a927),x94611),x94614))+~P107(f334(f334(f242(a1),f334(x94613,x94611)),x94612)) % 188.18/188.27 [9462]~P107(f334(f334(f242(a1),x94622),f334(x94623,x94624)))+P107(f334(f334(f242(a927),x94621),f612(x94622,x94623,x94624,x94621)))+P107(f334(f334(f243(a927),f613(x94622,x94623,x94624,x94621)),x94624))+~P107(f334(f334(f243(a927),x94621),x94624))+~P107(f334(f334(f242(a1),f334(x94623,x94621)),x94622)) % 188.18/188.27 [9573]~P107(f334(f334(f242(a1),x95731),f334(x95732,x95733)))+P107(f334(f334(f243(a927),f613(x95731,x95732,x95733,x95734)),x95733))+~P107(f334(f334(f243(a927),x95734),x95733))+~P107(f334(f334(f242(a1),f334(x95732,x95734)),x95731))+P107(f334(f334(f242(a927),f612(x95731,x95732,x95733,x95734)),x95733)) % 188.18/188.27 [9652]E(x96521,f195(f935(x96522,a922)))+~P107(f334(f66(x96522),x96524))+~P107(f334(f66(x96522),x96521))+P107(f334(f334(f336(f934(f935(x96522,a922),f935(x96522,a922))),f334(f334(f260(f935(x96522,a922),f935(x96522,a922)),x96524),x96521)),f325(x96522,x96523)))+P107(f334(f334(f336(x96522),f532(x96523,x96521,x96524,x96522)),x96524)) % 188.18/188.27 [9653]E(x96531,f195(f935(x96532,a922)))+~P107(f334(f66(x96532),x96534))+~P107(f334(f66(x96532),x96531))+P107(f334(f334(f336(f934(f935(x96532,a922),f935(x96532,a922))),f334(f334(f260(f935(x96532,a922),f935(x96532,a922)),x96534),x96531)),f325(x96532,x96533)))+P107(f334(f334(f336(x96532),f606(x96533,x96531,x96534,x96532)),x96534)) % 188.18/188.27 [10326]E(f334(x103261,f612(x103262,x103261,x103263,x103264)),x103262)+~P107(f334(f334(f242(a1),x103262),f334(x103261,x103263)))+~P107(f334(f334(f242(a1),f334(f81(a1),f334(f334(f23(a1),f334(x103261,f334(f334(f86(a927),f613(x103262,x103261,x103263,x103264)),f84(a927)))),f334(x103261,f613(x103262,x103261,x103263,x103264))))),f84(a1)))+~P107(f334(f334(f243(a927),x103264),x103263))+~P107(f334(f334(f242(a1),f334(x103261,x103264)),x103262)) % 188.18/188.27 [10327]~P107(f334(f334(f242(a1),x103272),f334(x103273,x103274)))+P107(f334(f334(f242(a927),x103271),f612(x103272,x103273,x103274,x103271)))+~P107(f334(f334(f242(a1),f334(f81(a1),f334(f334(f23(a1),f334(x103273,f334(f334(f86(a927),f613(x103272,x103273,x103274,x103271)),f84(a927)))),f334(x103273,f613(x103272,x103273,x103274,x103271))))),f84(a1)))+~P107(f334(f334(f243(a927),x103271),x103274))+~P107(f334(f334(f242(a1),f334(x103273,x103271)),x103272)) % 188.18/188.27 [10328]~P107(f334(f334(f242(a1),x103281),f334(x103282,x103283)))+~P107(f334(f334(f242(a1),f334(f81(a1),f334(f334(f23(a1),f334(x103282,f334(f334(f86(a927),f613(x103281,x103282,x103283,x103284)),f84(a927)))),f334(x103282,f613(x103281,x103282,x103283,x103284))))),f84(a1)))+~P107(f334(f334(f243(a927),x103284),x103283))+~P107(f334(f334(f242(a1),f334(x103282,x103284)),x103281))+P107(f334(f334(f242(a927),f612(x103281,x103282,x103283,x103284)),x103283)) % 188.18/188.27 [7444]~P67(x74441)+P107(f334(f334(f243(x74441),x74442),f2(x74441)))+~P107(f334(f334(f242(x74441),x74443),f2(x74441)))+P107(f334(f334(f243(x74441),f2(x74441)),x74442))+P107(f334(f334(f242(x74441),x74443),f334(f334(f296(x74441),x74444),x74442))) % 188.18/188.27 [7445]~P67(x74451)+P107(f334(f334(f243(x74451),x74452),f2(x74451)))+~P107(f334(f334(f243(x74451),x74453),f2(x74451)))+P107(f334(f334(f243(x74451),f2(x74451)),x74452))+P107(f334(f334(f243(x74451),x74453),f334(f334(f296(x74451),x74454),x74452))) % 188.18/188.27 [7682]~P67(x76821)+P107(f334(f334(f242(x76821),x76822),f2(x76821)))+P107(f334(f334(f243(x76821),x76823),f2(x76821)))+P107(f334(f334(f243(x76821),f2(x76821)),x76823))+~P107(f334(f334(f242(x76821),x76822),f334(f334(f296(x76821),x76824),x76823))) % 188.18/188.27 [7683]~P67(x76831)+P107(f334(f334(f243(x76831),x76832),f2(x76831)))+P107(f334(f334(f243(x76831),x76833),f2(x76831)))+P107(f334(f334(f243(x76831),f2(x76831)),x76833))+~P107(f334(f334(f243(x76831),x76832),f334(f334(f296(x76831),x76834),x76833))) % 188.18/188.27 [7797]E(x77971,x77972)+~E(f334(f334(f171(x77973),x77974),x77971),f334(f334(f171(x77973),x77974),x77972))+~P107(f334(f144(x77973),x77974))+~P107(f334(f334(f243(a927),x77972),f334(f196(f928(x77973)),x77974)))+~P107(f334(f334(f243(a927),x77971),f334(f196(f928(x77973)),x77974))) % 188.18/188.27 [8150]~P67(x81501)+~P107(f334(f334(f242(x81501),x81503),f2(x81501)))+P107(f334(f334(f243(x81501),f2(x81501)),x81502))+~P107(f334(f334(f242(x81501),x81504),f334(f334(f87(x81501),x81503),x81502)))+P107(f334(f334(f242(x81501),x81503),f334(f334(f296(x81501),x81504),x81502))) % 188.18/188.27 [8151]~P67(x81511)+~P107(f334(f334(f243(x81511),x81513),f2(x81511)))+P107(f334(f334(f243(x81511),f2(x81511)),x81512))+~P107(f334(f334(f243(x81511),x81514),f334(f334(f87(x81511),x81513),x81512)))+P107(f334(f334(f243(x81511),x81513),f334(f334(f296(x81511),x81514),x81512))) % 188.18/188.27 [8152]~P67(x81521)+~P107(f334(f334(f243(x81521),x81522),f2(x81521)))+P107(f334(f334(f243(x81521),f2(x81521)),x81522))+~P107(f334(f334(f242(x81521),x81524),f334(f334(f87(x81521),x81523),x81522)))+P107(f334(f334(f242(x81521),x81523),f334(f334(f296(x81521),x81524),x81522))) % 188.18/188.27 [8153]~P67(x81531)+~P107(f334(f334(f243(x81531),x81532),f2(x81531)))+P107(f334(f334(f243(x81531),f2(x81531)),x81532))+~P107(f334(f334(f242(x81531),x81534),f334(f334(f296(x81531),x81533),x81532)))+P107(f334(f334(f242(x81531),x81533),f334(f334(f87(x81531),x81534),x81532))) % 188.18/188.27 [8154]~P67(x81541)+~P107(f334(f334(f243(x81541),x81542),f2(x81541)))+P107(f334(f334(f243(x81541),f2(x81541)),x81542))+~P107(f334(f334(f243(x81541),x81544),f334(f334(f87(x81541),x81543),x81542)))+P107(f334(f334(f243(x81541),x81543),f334(f334(f296(x81541),x81544),x81542))) % 188.18/188.27 [8155]~P67(x81551)+~P107(f334(f334(f243(x81551),x81552),f2(x81551)))+P107(f334(f334(f243(x81551),f2(x81551)),x81552))+~P107(f334(f334(f243(x81551),x81554),f334(f334(f296(x81551),x81553),x81552)))+P107(f334(f334(f243(x81551),x81553),f334(f334(f87(x81551),x81554),x81552))) % 188.18/188.27 [8296]~P109(x82961)+~P15(x82961,x82962)+~P107(f334(f334(f242(a927),x82963),x82964))+P107(f334(f334(f242(x82961),f334(f334(f171(x82961),x82962),x82963)),f334(f334(f171(x82961),x82962),x82964)))+~P107(f334(f334(f243(a927),x82964),f334(f196(f928(x82961)),x82962))) % 188.18/188.27 [8345]~P127(x83451)+~P107(f334(f334(f242(x83451),x83452),f84(x83451)))+~P107(f334(f334(f242(x83451),f2(x83451)),x83452))+~P107(f334(f334(f242(a927),x83454),x83453))+P107(f334(f334(f242(x83451),f334(f334(f252(x83451),x83452),x83453)),f334(f334(f252(x83451),x83452),x83454))) % 188.18/188.27 [8346]~P127(x83461)+~P107(f334(f334(f243(x83461),x83462),f84(x83461)))+~P107(f334(f334(f243(x83461),f2(x83461)),x83462))+~P107(f334(f334(f243(a927),x83464),x83463))+P107(f334(f334(f243(x83461),f334(f334(f252(x83461),x83462),x83463)),f334(f334(f252(x83461),x83462),x83464))) % 188.18/188.27 [8347]~P127(x83471)+~P107(f334(f334(f242(x83471),f2(x83471)),x83472))+~P107(f334(f334(f243(a927),f2(a927)),x83473))+~P107(f334(f334(f243(x83471),x83472),x83474))+P107(f334(f334(f243(x83471),f334(f334(f252(x83471),x83472),x83473)),f334(f334(f252(x83471),x83474),x83473))) % 188.18/188.27 [8365]~P109(x83651)+~P15(x83651,f334(f175(x83651),x83652))+~P107(f334(f334(f242(a927),x83654),x83653))+P107(f334(f334(f242(x83651),f334(f334(f171(x83651),x83652),x83653)),f334(f334(f171(x83651),x83652),x83654)))+~P107(f334(f334(f243(a927),x83653),f334(f196(f928(x83651)),x83652))) % 188.18/188.27 [8605]~P67(x86051)+~P107(f334(f334(f242(x86051),x86052),f2(x86051)))+~P107(f334(f334(f242(x86051),x86053),x86054))+~P107(f334(f334(f243(x86051),f2(x86051)),f334(f334(f87(x86051),x86053),x86054)))+P107(f334(f334(f242(x86051),f334(f334(f296(x86051),x86052),x86053)),f334(f334(f296(x86051),x86052),x86054))) % 188.18/188.27 [8606]~P68(x86061)+~P107(f334(f334(f243(x86061),x86062),f2(x86061)))+~P107(f334(f334(f243(x86061),x86063),x86064))+~P107(f334(f334(f243(x86061),f2(x86061)),f334(f334(f87(x86061),x86063),x86064)))+P107(f334(f334(f243(x86061),f334(f334(f296(x86061),x86062),x86063)),f334(f334(f296(x86061),x86062),x86064))) % 188.18/188.27 [8615]~P68(x86151)+~P107(f334(f334(f242(x86151),x86154),x86153))+~P107(f334(f334(f242(x86151),f2(x86151)),x86152))+~P107(f334(f334(f243(x86151),f2(x86151)),f334(f334(f87(x86151),x86153),x86154)))+P107(f334(f334(f242(x86151),f334(f334(f296(x86151),x86152),x86153)),f334(f334(f296(x86151),x86152),x86154))) % 188.18/188.27 [8616]~P68(x86161)+~P107(f334(f334(f243(x86161),x86164),x86163))+~P107(f334(f334(f243(x86161),f2(x86161)),x86162))+~P107(f334(f334(f243(x86161),f2(x86161)),f334(f334(f87(x86161),x86163),x86164)))+P107(f334(f334(f243(x86161),f334(f334(f296(x86161),x86162),x86163)),f334(f334(f296(x86161),x86162),x86164))) % 188.18/188.27 [8713]P107(f334(x87131,x87132))+~P107(f334(f66(x87134),x87132))+P107(f334(x87131,f707(x87131,x87133,x87132,x87134)))+~P107(f334(x87131,f195(f935(x87134,a922))))+~P107(f334(f334(f242(f935(x87134,a922)),x87132),x87133)) % 188.18/188.27 [8722]P107(f334(x87221,x87222))+P107(f334(f66(x87223),f707(x87221,x87224,x87222,x87223)))+~P107(f334(f66(x87223),x87222))+~P107(f334(x87221,f195(f935(x87223,a922))))+~P107(f334(f334(f242(f935(x87223,a922)),x87222),x87224)) % 188.18/188.27 [8985]E(f334(f334(f86(a1),f431(x89851,x89852,x89853,x89854)),f432(x89851,x89852,x89853,x89854)),x89854)+~P107(f334(f334(f243(a1),f2(a1)),x89853))+~P107(f334(f334(f243(a1),x89852),x89854))+~P107(f334(f334(f336(a1),x89852),x89851))+P107(f334(f334(f243(a1),x89852),f334(f334(f23(a1),x89854),x89853))) % 188.18/188.27 [9208]~P107(f334(f334(f243(a1),f2(a1)),x92083))+~P107(f334(f334(f243(a1),x92082),x92084))+~P107(f334(f334(f336(a1),x92082),x92081))+P107(f334(f334(f336(a1),f431(x92081,x92082,x92083,x92084)),x92081))+P107(f334(f334(f243(a1),x92082),f334(f334(f23(a1),x92084),x92083))) % 188.18/188.27 [9218]P107(f334(x92181,x92182))+~P107(f334(f66(x92183),x92182))+P107(f334(f334(f336(x92183),f695(x92181,x92184,x92182,x92183)),x92184))+~P107(f334(x92181,f195(f935(x92183,a922))))+~P107(f334(f334(f242(f935(x92183,a922)),x92182),x92184)) % 188.18/188.27 [9235]E(f334(f334(f86(a1),f416(x92351,x92352,x92353,x92354)),f417(x92351,x92352,x92353,x92354)),x92354)+~P107(f334(f334(f243(a1),f2(a1)),x92353))+~P107(f334(f334(f242(a1),x92352),x92354))+P107(f334(f334(f242(a1),x92352),f334(f334(f23(a1),x92354),x92353)))+~P107(f334(f334(f336(a1),f334(f334(f23(a1),x92352),f84(a1))),x92351)) % 188.18/188.27 [9284]~P107(f334(f334(f243(a1),f2(a1)),x92843))+~P107(f334(f334(f243(a1),x92841),x92842))+~P107(f334(f334(f336(a1),x92841),x92844))+P107(f334(f334(f336(a1),f432(x92844,x92841,x92843,x92842)),f311(a1,f84(a1),x92843)))+P107(f334(f334(f243(a1),x92841),f334(f334(f23(a1),x92842),x92843))) % 188.18/188.27 [9304]~P76(x93042)+~E(f799(x93043,x93044,x93041,x93042),f800(x93043,x93044,x93041,x93042))+~P107(f334(f66(x93041),f796(x93043,x93044,x93041,x93042)))+E(f334(f334(f6(f935(x93041,a922),x93042),f334(f6(x93041,x93042),x93043)),x93044),f334(f334(f6(x93041,x93042),x93043),f42(f935(x93041,a922),x93044)))+~P107(f334(f66(f935(x93041,a922)),x93044)) % 188.18/188.27 [9308]~P76(x93082)+~E(f334(x93083,f801(x93083,x93084,x93081,x93082)),f2(x93082))+~P107(f334(f66(x93081),f796(x93083,x93084,x93081,x93082)))+E(f334(f334(f6(f935(x93081,a922),x93082),f334(f6(x93081,x93082),x93083)),x93084),f334(f334(f6(x93081,x93082),x93083),f42(f935(x93081,a922),x93084)))+~P107(f334(f66(f935(x93081,a922)),x93084)) % 188.18/188.27 [9378]~P107(f334(f334(f243(a1),f2(a1)),x93783))+~P107(f334(f334(f242(a1),x93782),x93784))+P107(f334(f334(f336(a1),f416(x93781,x93782,x93783,x93784)),x93781))+P107(f334(f334(f242(a1),x93782),f334(f334(f23(a1),x93784),x93783)))+~P107(f334(f334(f336(a1),f334(f334(f23(a1),x93782),f84(a1))),x93781)) % 188.18/188.27 [9422]~P107(f334(f334(f243(a1),f2(a1)),x94223))+~P107(f334(f334(f242(a1),x94221),x94222))+P107(f334(f334(f336(a1),f417(x94224,x94221,x94223,x94222)),f311(a1,f84(a1),x94223)))+P107(f334(f334(f242(a1),x94221),f334(f334(f23(a1),x94222),x94223)))+~P107(f334(f334(f336(a1),f334(f334(f23(a1),x94221),f84(a1))),x94224)) % 188.18/188.27 [9441]~P76(x94412)+~E(f799(x94413,x94414,x94411,x94412),f800(x94413,x94414,x94411,x94412))+E(f334(f334(f6(f935(x94411,a922),x94412),f334(f6(x94411,x94412),x94413)),x94414),f334(f334(f6(x94411,x94412),x94413),f42(f935(x94411,a922),x94414)))+P107(f334(f334(f336(f935(x94411,a922)),f796(x94413,x94414,x94411,x94412)),x94414))+~P107(f334(f66(f935(x94411,a922)),x94414)) % 188.18/188.27 [9446]~P76(x94462)+~E(f334(x94463,f801(x94463,x94464,x94461,x94462)),f2(x94462))+E(f334(f334(f6(f935(x94461,a922),x94462),f334(f6(x94461,x94462),x94463)),x94464),f334(f334(f6(x94461,x94462),x94463),f42(f935(x94461,a922),x94464)))+P107(f334(f334(f336(f935(x94461,a922)),f796(x94463,x94464,x94461,x94462)),x94464))+~P107(f334(f66(f935(x94461,a922)),x94464)) % 188.18/188.27 [9550]~P76(x95502)+~P107(f334(f66(x95501),f796(x95503,x95504,x95501,x95502)))+E(f334(f334(f6(f935(x95501,a922),x95502),f334(f6(x95501,x95502),x95503)),x95504),f334(f334(f6(x95501,x95502),x95503),f42(f935(x95501,a922),x95504)))+P107(f334(f334(f336(f935(x95501,a922)),f800(x95503,x95504,x95501,x95502)),x95504))+~P107(f334(f66(f935(x95501,a922)),x95504)) % 188.18/188.27 [9551]~P76(x95512)+~P107(f334(f66(x95511),f796(x95513,x95514,x95511,x95512)))+E(f334(f334(f6(f935(x95511,a922),x95512),f334(f6(x95511,x95512),x95513)),x95514),f334(f334(f6(x95511,x95512),x95513),f42(f935(x95511,a922),x95514)))+P107(f334(f334(f336(f935(x95511,a922)),f799(x95513,x95514,x95511,x95512)),x95514))+~P107(f334(f66(f935(x95511,a922)),x95514)) % 188.18/188.27 [9629]~P76(x96292)+E(f334(f334(f6(f935(x96291,a922),x96292),f334(f6(x96291,x96292),x96293)),x96294),f334(f334(f6(x96291,x96292),x96293),f42(f935(x96291,a922),x96294)))+P107(f334(f334(f336(f935(x96291,a922)),f796(x96293,x96294,x96291,x96292)),x96294))+P107(f334(f334(f336(f935(x96291,a922)),f800(x96293,x96294,x96291,x96292)),x96294))+~P107(f334(f66(f935(x96291,a922)),x96294)) % 188.18/188.27 [9630]~P76(x96302)+E(f334(f334(f6(f935(x96301,a922),x96302),f334(f6(x96301,x96302),x96303)),x96304),f334(f334(f6(x96301,x96302),x96303),f42(f935(x96301,a922),x96304)))+P107(f334(f334(f336(f935(x96301,a922)),f796(x96303,x96304,x96301,x96302)),x96304))+P107(f334(f334(f336(f935(x96301,a922)),f799(x96303,x96304,x96301,x96302)),x96304))+~P107(f334(f66(f935(x96301,a922)),x96304)) % 188.18/188.27 [9643]~P76(x96432)+P107(f334(f334(f336(x96431),f801(x96433,x96434,x96431,x96432)),f800(x96433,x96434,x96431,x96432)))+~P107(f334(f66(x96431),f796(x96433,x96434,x96431,x96432)))+E(f334(f334(f6(f935(x96431,a922),x96432),f334(f6(x96431,x96432),x96433)),x96434),f334(f334(f6(x96431,x96432),x96433),f42(f935(x96431,a922),x96434)))+~P107(f334(f66(f935(x96431,a922)),x96434)) % 188.18/188.27 [9644]~P76(x96442)+P107(f334(f334(f336(x96441),f801(x96443,x96444,x96441,x96442)),f799(x96443,x96444,x96441,x96442)))+~P107(f334(f66(x96441),f796(x96443,x96444,x96441,x96442)))+E(f334(f334(f6(f935(x96441,a922),x96442),f334(f6(x96441,x96442),x96443)),x96444),f334(f334(f6(x96441,x96442),x96443),f42(f935(x96441,a922),x96444)))+~P107(f334(f66(f935(x96441,a922)),x96444)) % 188.18/188.27 [9656]P107(f334(x96561,x96562))+~P107(f334(f334(f336(x96563),f695(x96561,x96564,x96562,x96563)),f707(x96561,x96564,x96562,x96563)))+~P107(f334(f66(x96563),x96562))+~P107(f334(x96561,f195(f935(x96563,a922))))+~P107(f334(f334(f242(f935(x96563,a922)),x96562),x96564)) % 188.18/188.27 [9692]~P76(x96922)+P107(f334(f334(f336(x96921),f801(x96923,x96924,x96921,x96922)),f800(x96923,x96924,x96921,x96922)))+E(f334(f334(f6(f935(x96921,a922),x96922),f334(f6(x96921,x96922),x96923)),x96924),f334(f334(f6(x96921,x96922),x96923),f42(f935(x96921,a922),x96924)))+P107(f334(f334(f336(f935(x96921,a922)),f796(x96923,x96924,x96921,x96922)),x96924))+~P107(f334(f66(f935(x96921,a922)),x96924)) % 188.18/188.27 [9693]~P76(x96932)+P107(f334(f334(f336(x96931),f801(x96933,x96934,x96931,x96932)),f799(x96933,x96934,x96931,x96932)))+E(f334(f334(f6(f935(x96931,a922),x96932),f334(f6(x96931,x96932),x96933)),x96934),f334(f334(f6(x96931,x96932),x96933),f42(f935(x96931,a922),x96934)))+P107(f334(f334(f336(f935(x96931,a922)),f796(x96933,x96934,x96931,x96932)),x96934))+~P107(f334(f66(f935(x96931,a922)),x96934)) % 188.18/188.27 [9894]P107(f334(x98941,x98942))+~P107(f334(f66(x98943),x98942))+~P107(f334(x98941,f334(f334(f316(x98943),f695(x98941,x98944,x98942,x98943)),f707(x98941,x98944,x98942,x98943))))+~P107(f334(x98941,f195(f935(x98943,a922))))+~P107(f334(f334(f242(f935(x98943,a922)),x98942),x98944)) % 188.18/188.27 [7926]~P67(x79261)+P107(f334(f334(f243(x79261),x79262),f2(x79261)))+~P107(f334(f334(f242(x79261),f2(x79261)),x79264))+P107(f334(f334(f243(x79261),f2(x79261)),x79262))+P107(f334(f334(f242(x79261),f334(f334(f296(x79261),x79263),x79262)),x79264)) % 188.18/188.27 [7927]~P67(x79271)+P107(f334(f334(f243(x79271),x79272),f2(x79271)))+P107(f334(f334(f243(x79271),f2(x79271)),x79272))+~P107(f334(f334(f243(x79271),f2(x79271)),x79274))+P107(f334(f334(f243(x79271),f334(f334(f296(x79271),x79273),x79272)),x79274)) % 188.18/188.27 [8200]~P107(f334(f334(f242(a1),x82004),f2(a1)))+~E(x82002,f334(f334(f86(a1),f334(f334(f87(a1),x82001),x82003)),x82004))+P107(f334(f334(f243(a1),f2(a1)),x82001))+~P107(f334(f334(f243(a1),x82001),x82004))+P107(f334(f54(x82002,x82001),f334(f334(f260(a1,a1),x82003),x82004))) % 188.18/188.27 [8234]~P107(f334(x82341,x82344))+P107(f334(x82341,f892(x82342,x82341,x82343)))+~P107(f334(f334(f242(a1),f2(a1)),x82342))+~P107(f334(f334(f243(a1),f2(a1)),x82343))+P107(f334(x82341,f334(f334(f23(a1),x82344),f334(f334(f87(a1),x82342),x82343)))) % 188.18/188.27 [8235]~P107(f334(x82351,x82354))+P107(f334(x82351,f894(x82352,x82351,x82353)))+~P107(f334(f334(f242(a1),f2(a1)),x82352))+~P107(f334(f334(f243(a1),f2(a1)),x82353))+P107(f334(x82351,f334(f334(f86(a1),x82354),f334(f334(f87(a1),x82352),x82353)))) % 188.18/188.27 [8236]~P67(x82361)+P107(f334(f334(f243(x82361),x82362),f2(x82361)))+P107(f334(f334(f243(x82361),f2(x82361)),x82362))+P107(f334(f334(f242(x82361),f2(x82361)),x82363))+~P107(f334(f334(f242(x82361),f334(f334(f296(x82361),x82364),x82362)),x82363)) % 188.18/188.27 [8237]~P67(x82371)+P107(f334(f334(f243(x82371),x82372),f2(x82371)))+P107(f334(f334(f243(x82371),f2(x82371)),x82372))+P107(f334(f334(f243(x82371),f2(x82371)),x82373))+~P107(f334(f334(f243(x82371),f334(f334(f296(x82371),x82374),x82372)),x82373)) % 188.18/188.27 [8291]~E(x82911,f334(f334(f86(a1),f334(f334(f87(a1),x82912),x82913)),x82914))+~P107(f334(f334(f242(a1),f2(a1)),x82914))+~P107(f334(f334(f243(a1),f2(a1)),x82912))+~P107(f334(f334(f243(a1),x82914),x82912))+P107(f334(f54(x82911,x82912),f334(f334(f260(a1,a1),x82913),x82914))) % 188.18/188.27 [8404]~P67(x84041)+P107(f334(f334(f243(x84041),x84042),f2(x84041)))+~P107(f334(f334(f242(x84041),f2(x84041)),x84044))+~P107(f334(f334(f242(x84041),x84043),f334(f334(f87(x84041),x84044),x84042)))+P107(f334(f334(f242(x84041),f334(f334(f296(x84041),x84043),x84042)),x84044)) % 188.18/188.27 [8405]~P67(x84051)+P107(f334(f334(f243(x84051),x84052),f2(x84051)))+~P107(f334(f334(f243(x84051),f2(x84051)),x84054))+~P107(f334(f334(f243(x84051),x84053),f334(f334(f87(x84051),x84054),x84052)))+P107(f334(f334(f243(x84051),f334(f334(f296(x84051),x84053),x84052)),x84054)) % 188.18/188.27 [8489]~P67(x84891)+P107(f334(f334(f243(x84891),x84892),f2(x84891)))+~P107(f334(f334(f242(x84891),x84893),f2(x84891)))+P107(f334(f334(f242(x84891),x84893),f334(f334(f296(x84891),x84894),x84892)))+~P107(f334(f334(f242(x84891),f334(f334(f87(x84891),x84893),x84892)),x84894)) % 188.18/188.27 [8490]~P67(x84901)+P107(f334(f334(f243(x84901),x84902),f2(x84901)))+~P107(f334(f334(f243(x84901),x84903),f2(x84901)))+P107(f334(f334(f243(x84901),x84903),f334(f334(f296(x84901),x84904),x84902)))+~P107(f334(f334(f243(x84901),f334(f334(f87(x84901),x84903),x84902)),x84904)) % 188.18/188.27 [8635]~P67(x86351)+~P107(f334(f334(f243(x86351),x86352),f2(x86351)))+P107(f334(f334(f243(x86351),f2(x86351)),x86352))+~P107(f334(f334(f242(x86351),f334(f334(f296(x86351),x86354),x86352)),x86353))+P107(f334(f334(f242(x86351),f334(f334(f87(x86351),x86353),x86352)),x86354)) % 188.18/188.27 [8636]~P67(x86361)+~P107(f334(f334(f243(x86361),x86362),f2(x86361)))+P107(f334(f334(f243(x86361),f2(x86361)),x86362))+~P107(f334(f334(f242(x86361),f334(f334(f87(x86361),x86364),x86362)),x86363))+P107(f334(f334(f242(x86361),f334(f334(f296(x86361),x86363),x86362)),x86364)) % 188.18/188.27 [8637]~P67(x86371)+~P107(f334(f334(f243(x86371),x86372),f2(x86371)))+P107(f334(f334(f243(x86371),f2(x86371)),x86372))+~P107(f334(f334(f243(x86371),f334(f334(f296(x86371),x86374),x86372)),x86373))+P107(f334(f334(f243(x86371),f334(f334(f87(x86371),x86373),x86372)),x86374)) % 188.18/188.27 [8638]~P67(x86381)+~P107(f334(f334(f243(x86381),x86382),f2(x86381)))+P107(f334(f334(f243(x86381),f2(x86381)),x86382))+~P107(f334(f334(f243(x86381),f334(f334(f87(x86381),x86384),x86382)),x86383))+P107(f334(f334(f243(x86381),f334(f334(f296(x86381),x86383),x86382)),x86384)) % 188.18/188.27 [8655]~P67(x86551)+~P107(f334(f334(f242(x86551),f2(x86551)),x86554))+P107(f334(f334(f243(x86551),f2(x86551)),x86552))+~P107(f334(f334(f242(x86551),f334(f334(f87(x86551),x86554),x86552)),x86553))+P107(f334(f334(f242(x86551),f334(f334(f296(x86551),x86553),x86552)),x86554)) % 188.18/188.27 [8656]~P67(x86561)+~P107(f334(f334(f243(x86561),f2(x86561)),x86564))+P107(f334(f334(f243(x86561),f2(x86561)),x86562))+~P107(f334(f334(f243(x86561),f334(f334(f87(x86561),x86564),x86562)),x86563))+P107(f334(f334(f243(x86561),f334(f334(f296(x86561),x86563),x86562)),x86564)) % 188.18/188.27 [8734]~P67(x87341)+~P107(f334(f334(f243(x87341),x87344),f2(x87341)))+~P107(f334(f334(f242(x87341),x87343),f334(f334(f87(x87341),x87342),x87344)))+P107(f334(f334(f242(x87341),x87342),f334(f334(f296(x87341),x87343),x87344)))+~P107(f334(f334(f242(x87341),f334(f334(f87(x87341),x87342),x87344)),x87343)) % 188.18/188.27 [8735]~P67(x87351)+~P107(f334(f334(f242(x87351),x87352),f2(x87351)))+~P107(f334(f334(f242(x87351),x87353),f334(f334(f87(x87351),x87352),x87354)))+P107(f334(f334(f242(x87351),x87352),f334(f334(f296(x87351),x87353),x87354)))+~P107(f334(f334(f242(x87351),f334(f334(f87(x87351),x87352),x87354)),x87353)) % 188.18/188.27 [8736]~P67(x87361)+~P107(f334(f334(f243(x87361),x87364),f2(x87361)))+~P107(f334(f334(f243(x87361),x87363),f334(f334(f87(x87361),x87362),x87364)))+P107(f334(f334(f243(x87361),x87362),f334(f334(f296(x87361),x87363),x87364)))+~P107(f334(f334(f243(x87361),f334(f334(f87(x87361),x87362),x87364)),x87363)) % 188.18/188.27 [8737]~P67(x87371)+~P107(f334(f334(f243(x87371),x87372),f2(x87371)))+~P107(f334(f334(f243(x87371),x87373),f334(f334(f87(x87371),x87372),x87374)))+P107(f334(f334(f243(x87371),x87372),f334(f334(f296(x87371),x87373),x87374)))+~P107(f334(f334(f243(x87371),f334(f334(f87(x87371),x87372),x87374)),x87373)) % 188.18/188.27 [8858]~P67(x88581)+~P107(f334(f334(f243(x88581),x88583),f2(x88581)))+~P107(f334(f334(f242(x88581),x88582),f334(f334(f87(x88581),x88584),x88583)))+~P107(f334(f334(f242(x88581),f334(f334(f87(x88581),x88584),x88583)),x88582))+P107(f334(f334(f242(x88581),f334(f334(f296(x88581),x88582),x88583)),x88584)) % 188.18/188.27 [8859]~P67(x88591)+~P107(f334(f334(f243(x88591),x88593),f2(x88591)))+~P107(f334(f334(f243(x88591),x88592),f334(f334(f87(x88591),x88594),x88593)))+~P107(f334(f334(f243(x88591),f334(f334(f87(x88591),x88594),x88593)),x88592))+P107(f334(f334(f243(x88591),f334(f334(f296(x88591),x88592),x88593)),x88594)) % 188.18/188.27 [8871]~P67(x88711)+~P107(f334(f334(f242(x88711),f2(x88711)),x88714))+~P107(f334(f334(f242(x88711),x88712),f334(f334(f87(x88711),x88714),x88713)))+~P107(f334(f334(f242(x88711),f334(f334(f87(x88711),x88714),x88713)),x88712))+P107(f334(f334(f242(x88711),f334(f334(f296(x88711),x88712),x88713)),x88714)) % 188.18/188.27 [8872]~P67(x88721)+~P107(f334(f334(f243(x88721),f2(x88721)),x88724))+~P107(f334(f334(f243(x88721),x88722),f334(f334(f87(x88721),x88724),x88723)))+~P107(f334(f334(f243(x88721),f334(f334(f87(x88721),x88724),x88723)),x88722))+P107(f334(f334(f243(x88721),f334(f334(f296(x88721),x88722),x88723)),x88724)) % 188.18/188.27 [9057]E(f334(f334(f23(a1),f433(x90571,x90572,x90573,x90574)),f434(x90571,x90572,x90573,x90574)),x90574)+~P107(f334(f334(f243(a1),f2(a1)),x90573))+~P107(f334(f334(f336(a1),x90572),x90571))+~P107(f334(f334(f243(a1),x90574),x90572))+P107(f334(f334(f243(a1),f334(f334(f86(a1),x90574),x90573)),x90572)) % 188.18/188.27 [9134]~P107(f334(x91341,x91342))+~P107(f334(f334(f242(a1),f2(a1)),x91343))+~P107(f334(f334(f243(a1),f2(a1)),x91344))+~P107(f334(x91341,f334(f334(f23(a1),f892(x91343,x91341,x91344)),x91344)))+P107(f334(x91341,f334(f334(f23(a1),x91342),f334(f334(f87(a1),x91343),x91344)))) % 188.18/188.27 [9135]~P107(f334(x91351,x91352))+~P107(f334(f334(f242(a1),f2(a1)),x91353))+~P107(f334(f334(f243(a1),f2(a1)),x91354))+~P107(f334(x91351,f334(f334(f86(a1),f894(x91353,x91351,x91354)),x91354)))+P107(f334(x91351,f334(f334(f86(a1),x91352),f334(f334(f87(a1),x91353),x91354)))) % 188.18/188.27 [9277]~P107(f334(f334(f243(a1),f2(a1)),x92773))+~P107(f334(f334(f336(a1),x92772),x92771))+~P107(f334(f334(f243(a1),x92774),x92772))+P107(f334(f334(f336(a1),f433(x92771,x92772,x92773,x92774)),x92771))+P107(f334(f334(f243(a1),f334(f334(f86(a1),x92774),x92773)),x92772)) % 188.18/188.27 [9292]E(f334(f334(f23(a1),f418(x92921,x92922,x92923,x92924)),f419(x92921,x92922,x92923,x92924)),x92924)+~P107(f334(f334(f243(a1),f2(a1)),x92923))+~P107(f334(f334(f242(a1),x92924),x92922))+~P107(f334(f334(f336(a1),f334(f334(f86(a1),x92922),f84(a1))),x92921))+P107(f334(f334(f242(a1),f334(f334(f86(a1),x92924),x92923)),x92922)) % 188.18/188.27 [9319]~P107(f334(f334(f243(a1),f2(a1)),x93192))+~P107(f334(f334(f336(a1),x93193),x93194))+~P107(f334(f334(f243(a1),x93191),x93193))+P107(f334(f334(f336(a1),f434(x93194,x93193,x93192,x93191)),f311(a1,f84(a1),x93192)))+P107(f334(f334(f243(a1),f334(f334(f86(a1),x93191),x93192)),x93193)) % 188.18/188.27 [9414]~P107(f334(f334(f243(a1),f2(a1)),x94143))+~P107(f334(f334(f242(a1),x94144),x94142))+P107(f334(f334(f336(a1),f418(x94141,x94142,x94143,x94144)),x94141))+~P107(f334(f334(f336(a1),f334(f334(f86(a1),x94142),f84(a1))),x94141))+P107(f334(f334(f242(a1),f334(f334(f86(a1),x94144),x94143)),x94142)) % 188.18/188.27 [9457]~P107(f334(f334(f243(a1),f2(a1)),x94572))+~P107(f334(f334(f242(a1),x94571),x94573))+P107(f334(f334(f336(a1),f419(x94574,x94573,x94572,x94571)),f311(a1,f84(a1),x94572)))+~P107(f334(f334(f336(a1),f334(f334(f86(a1),x94573),f84(a1))),x94574))+P107(f334(f334(f242(a1),f334(f334(f86(a1),x94571),x94572)),x94573)) % 188.18/188.27 [9759]~P39(x97591,x97593)+~P29(x97591,x97594)+P39(x97591,f334(f334(f108(f935(f934(x97591,x97591),a922)),x97592),x97593))+~P107(f334(f334(f242(f935(f934(x97591,x97591),a922)),x97592),f334(f259(f935(f934(x97591,x97591),a922),f935(f934(x97591,x97591),a922)),x97594)))+~P107(f334(f334(f242(f935(f934(x97591,x97591),a922)),x97593),f334(f264(f935(f934(x97591,x97591),a922),f935(f934(x97591,x97591),a922)),x97594))) % 188.18/188.27 [10151]~P20(x101512,x101514,x101513)+E(x101511,f195(f935(x101512,a922)))+~P107(f334(f66(x101512),x101511))+P107(f334(f334(f336(x101512),f334(x101513,x101511)),x101511))+~P107(f334(f334(f336(x101512),f334(f334(x101514,f652(x101511,x101513,x101514,x101512)),f664(x101511,x101513,x101514,x101512))),f334(f334(f316(x101512),f652(x101511,x101513,x101514,x101512)),f334(f334(f316(x101512),f664(x101511,x101513,x101514,x101512)),f195(f935(x101512,a922)))))) % 188.18/188.27 [10091]~P111(x100912)+~P64(x100911)+~P107(f334(f334(f242(f935(x100911,x100912)),x100913),x100914))+P107(f334(f334(f243(f935(x100911,x100912)),x100913),x100914))+~P107(f334(f61(x100911),f334(f334(f8(a922,a922,x100911),a329),f334(f334(f18(x100911,x100912,a922),f334(f334(f8(x100912,f935(x100912,a922),x100911),a331),x100913)),x100914)))) % 188.18/188.27 [9663]~P57(x96631,x96631,x96634)+P107(f334(f334(f336(f934(x96631,x96631)),f334(f334(f260(x96631,x96631),x96632),x96633)),f314(x96631,x96634)))+P107(f334(f334(f336(f934(x96631,x96631)),f334(f334(f260(x96631,x96631),x96633),x96632)),f314(x96631,x96634)))+~P107(f334(f334(f336(f934(x96631,x96631)),f334(f334(f260(x96631,x96631),x96635),x96632)),f314(x96631,x96634)))+~P107(f334(f334(f336(f934(x96631,x96631)),f334(f334(f260(x96631,x96631),x96635),x96633)),f314(x96631,x96634))) % 188.18/188.27 [5869]E(x58691,f2(a927))+~E(f334(f40(x58692),x58695),x58691)+E(f334(f40(x58692),x58693),f334(a119,x58691))+~E(x58693,f334(f334(f316(x58692),x58694),x58695))+P107(f334(f334(f336(x58692),x58694),x58695)) % 188.18/188.27 [5993]~P66(x59932)+E(x59931,f2(x59932))+E(x59933,f2(x59932))+~E(f334(f334(f296(x59932),x59934),x59933),f334(f334(f296(x59932),x59935),x59931))+E(f334(f334(f87(x59932),x59934),x59931),f334(f334(f87(x59932),x59935),x59933)) % 188.18/188.27 [5994]~P66(x59942)+E(x59941,f2(x59942))+E(x59943,f2(x59942))+~E(f334(f334(f87(x59942),x59944),x59943),f334(f334(f87(x59942),x59945),x59941))+E(f334(f334(f296(x59942),x59944),x59941),f334(f334(f296(x59942),x59945),x59943)) % 188.18/188.27 [6063]~E(f334(f40(x60631),x60635),x60633)+~E(x60635,f195(f935(x60631,a922)))+E(f334(f40(x60631),x60632),f334(a119,x60633))+~E(x60632,f334(f334(f316(x60631),x60634),x60635))+P107(f334(f334(f336(x60631),x60634),x60635)) % 188.18/188.27 [6298]~P119(x62982)+~E(f334(x62983,x62985),f2(x62982))+E(f334(f334(f9(x62981,x62982),x62983),x62984),f2(x62982))+~P107(f334(f66(x62981),x62984))+~P107(f334(f334(f336(x62981),x62985),x62984)) % 188.18/188.27 [6662]~P109(x66623)+E(x66621,x66622)+~E(f334(f310(x66623,x66624),x66621),f334(f310(x66623,x66625),x66622))+~P107(f334(f334(f243(x66623),x66625),x66622))+~P107(f334(f334(f243(x66623),x66624),x66621)) % 188.18/188.27 [6663]~P109(x66633)+E(x66631,x66632)+~E(f334(f310(x66633,x66631),x66634),f334(f310(x66633,x66632),x66635))+~P107(f334(f334(f243(x66633),x66632),x66635))+~P107(f334(f334(f243(x66633),x66631),x66634)) % 188.18/188.27 [7699]~P109(x76991)+~P15(x76991,f334(f334(f141(x76991),x76994),x76995))+~P107(f334(f334(f336(x76991),x76993),f334(f179(x76991),x76995)))+~P107(f334(f334(f336(x76991),x76992),f334(f179(x76991),x76994)))+P107(f334(f334(f242(x76991),x76992),x76993)) % 188.18/188.27 [8771]~P111(x87711)+~P107(f334(f334(f243(f935(x87711,a922)),f311(x87711,x87715,x87712)),f311(x87711,x87714,x87713)))+~P107(f334(f334(f242(x87711),x87715),x87712))+P107(f334(f334(f243(x87711),x87712),x87713))+P107(f334(f334(f243(x87711),x87714),x87715)) % 188.18/188.27 [10184]~P19(x101842,x101845,x101843)+E(x101841,f195(f935(x101842,a922)))+~E(f334(f334(x101845,f334(x101844,f861(x101841,x101844,x101843,x101845,x101842))),f334(x101844,f874(x101841,x101844,x101843,x101845,x101842))),f334(x101844,f334(f334(x101845,f861(x101841,x101844,x101843,x101845,x101842)),f874(x101841,x101844,x101843,x101845,x101842))))+E(f334(x101843,f334(f317(x101842,x101842,x101844),x101841)),f334(x101844,f334(x101843,x101841)))+~P107(f334(f66(x101842),x101841)) % 188.18/188.27 [6659]~P20(x66592,x66595,x66593)+E(x66591,f195(f935(x66592,a922)))+~P107(f334(f66(x66592),x66591))+E(f334(x66593,f334(f334(f316(x66592),x66594),x66591)),f334(f334(x66595,x66594),f334(x66593,x66591)))+P107(f334(f334(f336(x66592),x66594),x66591)) % 188.18/188.27 [7472]~P19(x74722,x74723,x74724)+E(f334(f334(x74723,f334(x74724,x74721)),f334(x74724,x74725)),f334(x74724,x74725))+E(x74721,f195(f935(x74722,a922)))+~P107(f334(f66(x74722),x74725))+~P107(f334(f334(f242(f935(x74722,a922)),x74721),x74725)) % 188.18/188.27 [7828]~P20(x78284,x78285,x78281)+E(f334(x78281,x78282),x78283)+~P107(f334(f66(x78284),x78282))+~E(f334(f334(f23(f935(x78284,a922)),x78282),f334(f334(f316(x78284),x78283),f195(f935(x78284,a922)))),f195(f935(x78284,a922)))+~P107(f334(f334(f336(x78284),x78283),x78282)) % 188.18/188.27 [8741]E(x87411,x87412)+~P10(x87413,x87414,x87415)+E(f334(f334(f109(f935(x87413,a922)),x87411),x87412),f195(f935(x87413,a922)))+~P107(f334(f334(f336(f935(x87413,a922)),x87412),f334(f334(f65(x87413),x87414),x87415)))+~P107(f334(f334(f336(f935(x87413,a922)),x87411),f334(f334(f65(x87413),x87414),x87415))) % 188.18/188.27 [9543]~P72(x95432)+~E(f334(x95433,f405(x95433,x95434,x95435,x95431,x95432)),f84(x95432))+E(f334(f334(f9(x95431,x95432),x95433),x95434),f334(f334(f9(x95431,x95432),x95433),x95435))+~P107(f334(f66(x95431),x95435))+~P107(f334(f334(f242(f935(x95431,a922)),x95434),x95435)) % 188.18/188.27 [9544]~P72(x95442)+~E(f334(x95443,f409(x95443,x95444,x95445,x95441,x95442)),f84(x95442))+E(f334(f334(f9(x95441,x95442),x95443),x95444),f334(f334(f9(x95441,x95442),x95443),x95445))+~P107(f334(f66(x95441),x95445))+~P107(f334(f334(f242(f935(x95441,a922)),x95444),x95445)) % 188.18/188.27 [9545]~P76(x95452)+~E(f334(x95453,f507(x95453,x95454,x95455,x95451,x95452)),f2(x95452))+E(f334(f334(f6(x95451,x95452),x95453),x95454),f334(f334(f6(x95451,x95452),x95453),x95455))+~P107(f334(f66(x95451),x95455))+~P107(f334(f334(f242(f935(x95451,a922)),x95454),x95455)) % 188.18/188.27 [9546]~P76(x95462)+~E(f334(x95463,f508(x95463,x95464,x95465,x95461,x95462)),f2(x95462))+E(f334(f334(f6(x95461,x95462),x95463),x95464),f334(f334(f6(x95461,x95462),x95463),x95465))+~P107(f334(f66(x95461),x95465))+~P107(f334(f334(f242(f935(x95461,a922)),x95464),x95465)) % 188.18/188.27 [10049]~P88(x100491)+~P107(f334(f66(x100492),x100495))+~P107(f334(f334(f242(x100491),f2(x100491)),f334(x100493,f466(x100493,x100494,x100495,x100492,x100491))))+P107(f334(f334(f242(x100491),f334(f334(f6(x100492,x100491),x100493),x100494)),f334(f334(f6(x100492,x100491),x100493),x100495)))+~P107(f334(f334(f242(f935(x100492,a922)),x100494),x100495)) % 188.18/188.27 [7696]E(x76961,f2(a927))+P107(f334(x76962,x76963))+~E(x76964,f334(f334(f86(a927),f334(f334(f87(a927),x76961),x76963)),x76965))+~P107(f334(f334(f243(a927),x76965),x76961))+~P107(f334(x76962,f334(f334(f41(a927),x76964),x76961))) % 188.18/188.27 [7771]E(x77711,f2(a927))+P107(f334(x77712,x77713))+~P107(f334(x77712,f50(a927,x77714,x77711)))+~E(x77714,f334(f334(f86(a927),f334(f334(f87(a927),x77711),x77715)),x77713))+~P107(f334(f334(f243(a927),x77713),x77711)) % 188.18/188.27 [8060]~P66(x80603)+E(f334(x80601,x80602),f2(x80603))+~P107(f334(f66(x80604),x80605))+E(f334(f334(f9(x80604,x80603),x80601),f334(f334(f23(f935(x80604,a922)),x80605),f334(f334(f316(x80604),x80602),f195(f935(x80604,a922))))),f334(f334(f9(x80604,x80603),x80601),x80605))+P107(f334(f334(f336(x80604),x80602),x80605)) % 188.18/188.27 [8444]~P72(x84441)+~P107(f334(f66(x84442),x84445))+~P107(f334(f66(x84442),x84444))+~E(f334(f334(f109(f935(x84442,a922)),x84444),x84445),f195(f935(x84442,a922)))+E(f334(f334(f87(x84441),f334(f334(f9(x84442,x84441),x84443),x84444)),f334(f334(f9(x84442,x84441),x84443),x84445)),f334(f334(f9(x84442,x84441),x84443),f334(f334(f108(f935(x84442,a922)),x84444),x84445))) % 188.18/188.27 [8445]~P76(x84451)+~P107(f334(f66(x84452),x84455))+~P107(f334(f66(x84452),x84454))+~E(f334(f334(f109(f935(x84452,a922)),x84454),x84455),f195(f935(x84452,a922)))+E(f334(f334(f86(x84451),f334(f334(f6(x84452,x84451),x84453),x84454)),f334(f334(f6(x84452,x84451),x84453),x84455)),f334(f334(f6(x84452,x84451),x84453),f334(f334(f108(f935(x84452,a922)),x84454),x84455))) % 188.18/188.27 [8544]~P66(x85443)+E(f334(x85441,x85442),f2(x85443))+~P107(f334(f66(x85444),x85445))+E(f334(f334(f9(x85444,x85443),x85441),f334(f334(f23(f935(x85444,a922)),x85445),f334(f334(f316(x85444),x85442),f195(f935(x85444,a922))))),f334(f334(f296(x85443),f334(f334(f9(x85444,x85443),x85441),x85445)),f334(x85441,x85442)))+~P107(f334(f334(f336(x85444),x85442),x85445)) % 188.18/188.27 [9260]~P10(x92601,x92605,x92604)+~E(f334(f334(f65(x92601),f334(f334(f316(x92601),x92602),f195(f935(x92601,a922)))),x92604),f334(f334(f65(x92601),f334(f334(f316(x92601),x92603),f195(f935(x92601,a922)))),x92604))+~P107(f334(f334(f336(x92601),x92603),x92605))+~P107(f334(f334(f336(x92601),x92602),x92605))+P107(f334(f334(f336(f934(x92601,x92601)),f334(f334(f260(x92601,x92601),x92602),x92603)),x92604)) % 188.18/188.27 [9276]~P10(x92761,x92765,x92763)+E(f334(f334(f65(x92761),f334(f334(f316(x92761),x92762),f195(f935(x92761,a922)))),x92763),f334(f334(f65(x92761),f334(f334(f316(x92761),x92764),f195(f935(x92761,a922)))),x92763))+~P107(f334(f334(f336(x92761),x92764),x92765))+~P107(f334(f334(f336(x92761),x92762),x92765))+~P107(f334(f334(f336(f934(x92761,x92761)),f334(f334(f260(x92761,x92761),x92762),x92764)),x92763)) % 188.18/188.27 [9572]~P72(x95721)+~P107(f334(f66(x95722),x95725))+~P107(f334(f66(x95722),x95724))+~E(f334(f334(f109(f935(x95722,a922)),x95724),x95725),f195(f935(x95722,a922)))+E(f334(f334(f87(x95721),f334(f334(f334(f70(x95721,x95722,f87(x95721)),x95723),f84(x95721)),x95724)),f334(f334(f334(f70(x95721,x95722,f87(x95721)),x95723),f84(x95721)),x95725)),f334(f334(f334(f70(x95721,x95722,f87(x95721)),x95723),f84(x95721)),f334(f334(f108(f935(x95722,a922)),x95724),x95725))) % 188.18/188.27 [9581]~P72(x95811)+~E(f334(x95813,f486(x95813,x95815,x95814,x95812,x95811)),f84(x95811))+~P107(f334(f66(x95812),x95814))+~P107(f334(f66(x95812),x95815))+E(f334(f334(f87(x95811),f334(f334(f9(x95812,x95811),x95813),x95814)),f334(f334(f9(x95812,x95811),x95813),x95815)),f334(f334(f9(x95812,x95811),x95813),f334(f334(f108(f935(x95812,a922)),x95814),x95815))) % 188.18/188.27 [9582]~P72(x95821)+~E(f334(x95823,f487(x95823,x95825,x95824,x95822,x95821)),f84(x95821))+~P107(f334(f66(x95822),x95824))+~P107(f334(f66(x95822),x95825))+E(f334(f334(f87(x95821),f334(f334(f9(x95822,x95821),x95823),x95824)),f334(f334(f9(x95822,x95821),x95823),x95825)),f334(f334(f9(x95822,x95821),x95823),f334(f334(f108(f935(x95822,a922)),x95824),x95825))) % 188.18/188.27 [9583]~P76(x95831)+~E(f334(x95833,f488(x95833,x95835,x95834,x95832,x95831)),f2(x95831))+~P107(f334(f66(x95832),x95834))+~P107(f334(f66(x95832),x95835))+E(f334(f334(f86(x95831),f334(f334(f6(x95832,x95831),x95833),x95834)),f334(f334(f6(x95832,x95831),x95833),x95835)),f334(f334(f6(x95832,x95831),x95833),f334(f334(f108(f935(x95832,a922)),x95834),x95835))) % 188.18/188.27 [9584]~P76(x95841)+~E(f334(x95843,f489(x95843,x95845,x95844,x95842,x95841)),f2(x95841))+~P107(f334(f66(x95842),x95844))+~P107(f334(f66(x95842),x95845))+E(f334(f334(f86(x95841),f334(f334(f6(x95842,x95841),x95843),x95844)),f334(f334(f6(x95842,x95841),x95843),x95845)),f334(f334(f6(x95842,x95841),x95843),f334(f334(f108(f935(x95842,a922)),x95844),x95845))) % 188.18/188.27 [9800]~P72(x98001)+~E(f334(x98003,f483(x98003,x98005,x98004,x98002,x98001)),f84(x98001))+~P107(f334(f66(x98002),x98004))+~P107(f334(f66(x98002),x98005))+E(f334(f334(f87(x98001),f334(f334(f334(f70(x98001,x98002,f87(x98001)),x98003),f84(x98001)),x98004)),f334(f334(f334(f70(x98001,x98002,f87(x98001)),x98003),f84(x98001)),x98005)),f334(f334(f334(f70(x98001,x98002,f87(x98001)),x98003),f84(x98001)),f334(f334(f108(f935(x98002,a922)),x98004),x98005))) % 188.18/188.27 [9924]~P72(x99242)+E(f334(f334(f9(x99241,x99242),x99243),x99244),f334(f334(f9(x99241,x99242),x99243),x99245))+~P107(f334(f66(x99241),x99245))+~P107(f334(f334(f242(f935(x99241,a922)),x99244),x99245))+P107(f334(f334(f336(x99241),f405(x99243,x99244,x99245,x99241,x99242)),f334(f334(f23(f935(x99241,a922)),x99245),x99244))) % 188.18/188.27 [9925]~P72(x99252)+E(f334(f334(f9(x99251,x99252),x99253),x99254),f334(f334(f9(x99251,x99252),x99253),x99255))+~P107(f334(f66(x99251),x99255))+~P107(f334(f334(f242(f935(x99251,a922)),x99254),x99255))+P107(f334(f334(f336(x99251),f409(x99253,x99254,x99255,x99251,x99252)),f334(f334(f23(f935(x99251,a922)),x99255),x99254))) % 188.18/188.27 [9926]~P76(x99262)+E(f334(f334(f6(x99261,x99262),x99263),x99264),f334(f334(f6(x99261,x99262),x99263),x99265))+~P107(f334(f66(x99261),x99265))+~P107(f334(f334(f242(f935(x99261,a922)),x99264),x99265))+P107(f334(f334(f336(x99261),f507(x99263,x99264,x99265,x99261,x99262)),f334(f334(f23(f935(x99261,a922)),x99265),x99264))) % 188.18/188.27 [9927]~P76(x99272)+E(f334(f334(f6(x99271,x99272),x99273),x99274),f334(f334(f6(x99271,x99272),x99273),x99275))+~P107(f334(f66(x99271),x99275))+~P107(f334(f334(f242(f935(x99271,a922)),x99274),x99275))+P107(f334(f334(f336(x99271),f508(x99273,x99274,x99275,x99271,x99272)),f334(f334(f23(f935(x99271,a922)),x99275),x99274))) % 188.18/188.27 [9946]~P72(x99461)+~P107(f334(f66(x99462),x99464))+~P107(f334(f66(x99462),x99465))+E(f334(f334(f87(x99461),f334(f334(f9(x99462,x99461),x99463),x99464)),f334(f334(f9(x99462,x99461),x99463),x99465)),f334(f334(f9(x99462,x99461),x99463),f334(f334(f108(f935(x99462,a922)),x99464),x99465)))+P107(f334(f334(f336(x99462),f486(x99463,x99465,x99464,x99462,x99461)),f334(f334(f109(f935(x99462,a922)),x99464),x99465))) % 188.18/188.27 [9947]~P72(x99471)+~P107(f334(f66(x99472),x99474))+~P107(f334(f66(x99472),x99475))+E(f334(f334(f87(x99471),f334(f334(f9(x99472,x99471),x99473),x99474)),f334(f334(f9(x99472,x99471),x99473),x99475)),f334(f334(f9(x99472,x99471),x99473),f334(f334(f108(f935(x99472,a922)),x99474),x99475)))+P107(f334(f334(f336(x99472),f487(x99473,x99475,x99474,x99472,x99471)),f334(f334(f109(f935(x99472,a922)),x99474),x99475))) % 188.18/188.27 [9948]~P76(x99481)+~P107(f334(f66(x99482),x99484))+~P107(f334(f66(x99482),x99485))+E(f334(f334(f86(x99481),f334(f334(f6(x99482,x99481),x99483),x99484)),f334(f334(f6(x99482,x99481),x99483),x99485)),f334(f334(f6(x99482,x99481),x99483),f334(f334(f108(f935(x99482,a922)),x99484),x99485)))+P107(f334(f334(f336(x99482),f488(x99483,x99485,x99484,x99482,x99481)),f334(f334(f109(f935(x99482,a922)),x99484),x99485))) % 188.18/188.27 [9949]~P76(x99491)+~P107(f334(f66(x99492),x99494))+~P107(f334(f66(x99492),x99495))+E(f334(f334(f86(x99491),f334(f334(f6(x99492,x99491),x99493),x99494)),f334(f334(f6(x99492,x99491),x99493),x99495)),f334(f334(f6(x99492,x99491),x99493),f334(f334(f108(f935(x99492,a922)),x99494),x99495)))+P107(f334(f334(f336(x99492),f489(x99493,x99495,x99494,x99492,x99491)),f334(f334(f109(f935(x99492,a922)),x99494),x99495))) % 188.18/188.27 [9955]~P88(x99555)+~P107(f334(f66(x99551),x99554))+P107(f334(f334(f242(x99555),f334(f334(f6(x99551,x99555),x99552),x99553)),f334(f334(f6(x99551,x99555),x99552),x99554)))+~P107(f334(f334(f242(f935(x99551,a922)),x99553),x99554))+P107(f334(f334(f336(x99551),f466(x99552,x99553,x99554,x99551,x99555)),f334(f334(f23(f935(x99551,a922)),x99554),x99553))) % 188.18/188.27 [10009]~P72(x100091)+~P107(f334(f66(x100092),x100094))+~P107(f334(f66(x100092),x100095))+E(f334(f334(f87(x100091),f334(f334(f334(f70(x100091,x100092,f87(x100091)),x100093),f84(x100091)),x100094)),f334(f334(f334(f70(x100091,x100092,f87(x100091)),x100093),f84(x100091)),x100095)),f334(f334(f334(f70(x100091,x100092,f87(x100091)),x100093),f84(x100091)),f334(f334(f108(f935(x100092,a922)),x100094),x100095)))+P107(f334(f334(f336(x100092),f483(x100093,x100095,x100094,x100092,x100091)),f334(f334(f109(f935(x100092,a922)),x100094),x100095))) % 188.18/188.27 [8942]~P20(x89421,x89424,x89425)+~P107(f334(f66(x89421),x89422))+E(f334(f334(f23(f935(x89421,a922)),x89422),f334(f334(f316(x89421),x89423),f195(f935(x89421,a922)))),f195(f935(x89421,a922)))+~P107(f334(f334(f336(x89421),x89423),x89422))+E(f334(f334(x89424,x89423),f334(x89425,f334(f334(f23(f935(x89421,a922)),x89422),f334(f334(f316(x89421),x89423),f195(f935(x89421,a922)))))),f334(x89425,x89422)) % 188.18/188.27 [9019]~P20(x90191,x90194,x90195)+~P107(f334(f66(x90191),x90193))+~P107(f334(f66(x90191),x90192))+E(f334(f334(f109(f935(x90191,a922)),x90192),x90193),f195(f935(x90191,a922)))+E(f334(f334(x90194,f334(x90195,f334(f334(f108(f935(x90191,a922)),x90192),x90193))),f334(x90195,f334(f334(f109(f935(x90191,a922)),x90192),x90193))),f334(f334(x90194,f334(x90195,x90192)),f334(x90195,x90193))) % 188.18/188.27 [9586]~P107(f334(f334(f242(a1),x95864),f2(a1)))+~P107(f334(f334(f243(a1),x95863),x95865))+P107(f334(f334(f242(a1),x95861),x95862))+~P107(f334(f334(f243(a1),x95863),x95864))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f87(a1),x95863),x95862)),x95865)),f334(f334(f86(a1),f334(f334(f87(a1),x95863),x95861)),x95864))) % 188.18/188.27 [9592]~P107(f334(f334(f242(a1),f2(a1)),x95925))+P107(f334(f334(f242(a1),x95921),x95922))+~P107(f334(f334(f243(a1),x95923),x95924))+~P107(f334(f334(f243(a1),x95925),x95924))+~P107(f334(f334(f242(a1),f334(f334(f86(a1),f334(f334(f87(a1),x95924),x95921)),x95925)),f334(f334(f86(a1),f334(f334(f87(a1),x95924),x95922)),x95923))) % 188.18/188.27 [9698]~P66(x96985)+E(f334(x96981,f482(x96981,x96982,x96983,x96984,x96985)),f2(x96985))+~P107(f334(f66(x96984),x96983))+~P107(f334(f66(x96984),x96982))+E(f334(f334(f296(x96985),f334(f334(f87(x96985),f334(f334(f9(x96984,x96985),x96981),x96983)),f334(f334(f9(x96984,x96985),x96981),x96982))),f334(f334(f9(x96984,x96985),x96981),f334(f334(f109(f935(x96984,a922)),x96983),x96982))),f334(f334(f9(x96984,x96985),x96981),f334(f334(f108(f935(x96984,a922)),x96983),x96982))) % 188.18/188.27 [10001]~P66(x100011)+~P107(f334(f66(x100012),x100014))+~P107(f334(f66(x100012),x100015))+E(f334(f334(f296(x100011),f334(f334(f87(x100011),f334(f334(f9(x100012,x100011),x100013),x100014)),f334(f334(f9(x100012,x100011),x100013),x100015))),f334(f334(f9(x100012,x100011),x100013),f334(f334(f109(f935(x100012,a922)),x100014),x100015))),f334(f334(f9(x100012,x100011),x100013),f334(f334(f108(f935(x100012,a922)),x100014),x100015)))+P107(f334(f334(f336(x100012),f482(x100013,x100015,x100014,x100012,x100011)),f334(f334(f109(f935(x100012,a922)),x100014),x100015))) % 188.18/188.27 [9291]E(f334(f334(f141(x92911),x92912),x92913),f334(f334(f141(x92911),x92914),x92915))+~E(f334(f334(f182(x92911),f334(f196(f928(x92911)),x92914)),x92912),x92914)+~E(f334(f334(f182(x92911),f334(f196(f928(x92911)),x92912)),x92914),x92912)+~E(x92915,f334(f334(f141(x92911),f334(f334(f145(x92911),f334(f196(f928(x92911)),x92914)),x92912)),x92913))+~E(f334(f334(f141(x92911),f334(f334(f145(x92911),f334(f196(f928(x92911)),x92912)),x92914)),x92915),x92913) % 188.18/188.27 [9696]~P109(x96962)+E(f334(f334(f155(x96961,x96962,x96963),x96964),f177(x96961,x96964,x96965)),x96965)+~P15(x96962,f334(f334(f161(x96961,x96962),x96963),x96965))+~P107(f334(f334(f336(x96961),x96964),f334(f179(x96961),x96965)))+~E(f334(f148(x96961),f334(f143(x96961,f334(f334(f8(x96962,a922,x96961),f334(a331,f334(x96963,x96964))),x96963)),x96965)),x96964) % 188.18/188.27 [10067]~P70(x100671)+~P107(f334(f71(x100671,x100671,f87(x100671),x100672,x100673),x100675))+~P107(f334(f334(f336(x100671),x100674),x100673))+P107(f334(f334(f336(x100671),x100672),x100673))+P107(f334(f71(x100671,x100671,f87(x100671),x100674,f334(f334(f316(x100671),x100672),f334(f334(f23(f935(x100671,a922)),x100673),f334(f334(f316(x100671),x100674),f195(f935(x100671,a922)))))),x100675)) % 188.18/188.27 [7480]E(x74801,x74802)+~P27(x74804,x74805,x74803,x74806)+~E(f334(x74803,x74801),f334(x74803,x74802))+~P107(f334(f334(f336(x74804),x74802),x74806))+~P107(f334(f334(f336(x74804),x74801),x74806)) % 188.18/188.27 [6753]~P143(x67534)+E(x67531,x67532)+~E(x67535,x67536)+E(x67533,f2(x67534))+~E(f334(f334(f86(x67534),x67535),f334(f334(f87(x67534),x67533),x67531)),f334(f334(f86(x67534),x67536),f334(f334(f87(x67534),x67533),x67532))) % 188.18/188.27 [7751]~P109(x77511)+~P7(x77511)+~P107(f334(f334(f243(x77511),x77512),f334(x77515,x77516)))+~P107(f334(f334(f336(x77513),x77516),x77514))+P107(f334(f334(f243(x77511),x77512),f334(f334(f44(x77513,x77511),x77514),x77515))) % 188.18/188.27 [10063]~P27(x100632,x100631,x100633,x100634)+~P27(x100631,x100632,x100636,x100635)+P28(x100631,x100632,f548(x100633,x100634,x100635,x100636,x100632,x100631),x100635,x100634)+~P107(f334(f334(f242(f935(x100632,a922)),f334(f317(x100631,x100632,x100636),x100635)),x100634))+~P107(f334(f334(f242(f935(x100631,a922)),f334(f317(x100632,x100631,x100633),x100634)),x100635)) % 188.18/188.27 [8416]~P109(x84161)+~P7(x84161)+~P107(f334(f334(f243(x84161),f334(x84164,x84166)),x84165))+~P107(f334(f334(f336(x84162),x84166),x84163))+P107(f334(f334(f243(x84161),f334(f334(f45(x84162,x84161),x84163),x84164)),x84165)) % 188.18/188.27 [8662]~P21(x86622,x86625,x86626,x86621)+~P107(f334(f66(x86622),x86624))+~P107(f334(f66(x86622),x86623))+~E(f334(f334(f109(f935(x86622,a922)),x86623),x86624),f195(f935(x86622,a922)))+E(f334(x86621,f334(f334(f108(f935(x86622,a922)),x86623),x86624)),f334(f78(x86625,x86625,x86625,f334(x86621,x86623)),f334(x86621,x86624))) % 188.18/188.27 [10239]~P72(x102391)+~E(f828(x102394,x102395,x102393,x102396,x102392,x102391),f829(x102394,x102395,x102393,x102396,x102392,x102391))+~P107(f334(f66(x102392),x102396))+E(f334(f334(f334(f70(x102391,x102392,f87(x102391)),f334(f334(f8(f935(x102393,a922),x102391,x102392),f334(f334(f70(x102391,x102393,f87(x102391)),x102394),f84(x102391))),x102395)),f84(x102391)),x102396),f334(f334(f334(f70(x102391,x102393,f87(x102391)),x102394),f84(x102391)),f334(f334(f44(x102392,f935(x102393,a922)),x102396),x102395)))+P107(f334(f334(f336(x102392),f827(x102394,x102395,x102393,x102396,x102392,x102391)),x102396)) % 188.18/188.27 [10265]~P72(x102651)+~E(f828(x102654,x102655,x102653,x102656,x102652,x102651),f829(x102654,x102655,x102653,x102656,x102652,x102651))+~P107(f334(f66(x102652),x102656))+E(f334(f334(f334(f70(x102651,x102652,f87(x102651)),f334(f334(f8(f935(x102653,a922),x102651,x102652),f334(f334(f70(x102651,x102653,f87(x102651)),x102654),f84(x102651))),x102655)),f84(x102651)),x102656),f334(f334(f334(f70(x102651,x102653,f87(x102651)),x102654),f84(x102651)),f334(f334(f44(x102652,f935(x102653,a922)),x102656),x102655)))+~P107(f334(f66(x102653),f334(x102655,f827(x102654,x102655,x102653,x102656,x102652,x102651)))) % 188.18/188.27 [10268]~P72(x102681)+~P107(f334(f66(x102682),x102686))+E(f334(f334(f334(f70(x102681,x102682,f87(x102681)),f334(f334(f8(f935(x102683,a922),x102681,x102682),f334(f334(f70(x102681,x102683,f87(x102681)),x102684),f84(x102681))),x102685)),f84(x102681)),x102686),f334(f334(f334(f70(x102681,x102683,f87(x102681)),x102684),f84(x102681)),f334(f334(f44(x102682,f935(x102683,a922)),x102686),x102685)))+P107(f334(f334(f336(x102682),f827(x102684,x102685,x102683,x102686,x102682,x102681)),x102686))+P107(f334(f334(f336(x102682),f829(x102684,x102685,x102683,x102686,x102682,x102681)),x102686)) % 188.18/188.27 [10269]~P72(x102691)+~P107(f334(f66(x102692),x102696))+E(f334(f334(f334(f70(x102691,x102692,f87(x102691)),f334(f334(f8(f935(x102693,a922),x102691,x102692),f334(f334(f70(x102691,x102693,f87(x102691)),x102694),f84(x102691))),x102695)),f84(x102691)),x102696),f334(f334(f334(f70(x102691,x102693,f87(x102691)),x102694),f84(x102691)),f334(f334(f44(x102692,f935(x102693,a922)),x102696),x102695)))+P107(f334(f334(f336(x102692),f827(x102694,x102695,x102693,x102696,x102692,x102691)),x102696))+P107(f334(f334(f336(x102692),f828(x102694,x102695,x102693,x102696,x102692,x102691)),x102696)) % 188.18/188.27 [10287]~P72(x102871)+~P107(f334(f66(x102872),x102876))+E(f334(f334(f334(f70(x102871,x102872,f87(x102871)),f334(f334(f8(f935(x102873,a922),x102871,x102872),f334(f334(f70(x102871,x102873,f87(x102871)),x102874),f84(x102871))),x102875)),f84(x102871)),x102876),f334(f334(f334(f70(x102871,x102873,f87(x102871)),x102874),f84(x102871)),f334(f334(f44(x102872,f935(x102873,a922)),x102876),x102875)))+P107(f334(f334(f336(x102872),f829(x102874,x102875,x102873,x102876,x102872,x102871)),x102876))+~P107(f334(f66(x102873),f334(x102875,f827(x102874,x102875,x102873,x102876,x102872,x102871)))) % 188.18/188.27 [10288]~P72(x102881)+~P107(f334(f66(x102882),x102886))+E(f334(f334(f334(f70(x102881,x102882,f87(x102881)),f334(f334(f8(f935(x102883,a922),x102881,x102882),f334(f334(f70(x102881,x102883,f87(x102881)),x102884),f84(x102881))),x102885)),f84(x102881)),x102886),f334(f334(f334(f70(x102881,x102883,f87(x102881)),x102884),f84(x102881)),f334(f334(f44(x102882,f935(x102883,a922)),x102886),x102885)))+P107(f334(f334(f336(x102882),f828(x102884,x102885,x102883,x102886,x102882,x102881)),x102886))+~P107(f334(f66(x102883),f334(x102885,f827(x102884,x102885,x102883,x102886,x102882,x102881)))) % 188.18/188.27 [10308]~P72(x103081)+~E(f334(f334(f109(f935(x103083,a922)),f334(x103085,f829(x103084,x103085,x103083,x103086,x103082,x103081))),f334(x103085,f828(x103084,x103085,x103083,x103086,x103082,x103081))),f195(f935(x103083,a922)))+~P107(f334(f66(x103082),x103086))+E(f334(f334(f334(f70(x103081,x103082,f87(x103081)),f334(f334(f8(f935(x103083,a922),x103081,x103082),f334(f334(f70(x103081,x103083,f87(x103081)),x103084),f84(x103081))),x103085)),f84(x103081)),x103086),f334(f334(f334(f70(x103081,x103083,f87(x103081)),x103084),f84(x103081)),f334(f334(f44(x103082,f935(x103083,a922)),x103086),x103085)))+P107(f334(f334(f336(x103082),f827(x103084,x103085,x103083,x103086,x103082,x103081)),x103086)) % 188.18/188.27 [10318]~P72(x103181)+~E(f334(f334(f109(f935(x103183,a922)),f334(x103185,f829(x103184,x103185,x103183,x103186,x103182,x103181))),f334(x103185,f828(x103184,x103185,x103183,x103186,x103182,x103181))),f195(f935(x103183,a922)))+~P107(f334(f66(x103182),x103186))+E(f334(f334(f334(f70(x103181,x103182,f87(x103181)),f334(f334(f8(f935(x103183,a922),x103181,x103182),f334(f334(f70(x103181,x103183,f87(x103181)),x103184),f84(x103181))),x103185)),f84(x103181)),x103186),f334(f334(f334(f70(x103181,x103183,f87(x103181)),x103184),f84(x103181)),f334(f334(f44(x103182,f935(x103183,a922)),x103186),x103185)))+~P107(f334(f66(x103183),f334(x103185,f827(x103184,x103185,x103183,x103186,x103182,x103181)))) % 188.18/188.27 [8689]~P118(x86891)+~P121(x86891)+~P59(x86891,x86892,x86895)+~P59(x86891,x86892,f334(f334(f86(x86891),x86893),x86896))+P59(x86891,x86892,f334(f334(f86(x86891),f334(f334(f23(x86891),x86893),f334(f334(f87(x86891),x86894),x86895))),x86896)) % 188.18/188.27 [9051]~P118(x90511)+~P121(x90511)+~P59(x90511,x90512,x90515)+P59(x90511,x90512,f334(f334(f86(x90511),x90513),x90514))+~P59(x90511,x90512,f334(f334(f86(x90511),f334(f334(f23(x90511),x90513),f334(f334(f87(x90511),x90516),x90515))),x90514)) % 188.18/188.27 [8989]E(x89891,x89892)+~P60(x89894,x89895,x89896,x89893,x89897)+~E(f334(x89893,x89891),f334(x89893,x89892))+~P107(f334(f334(f336(x89895),x89892),x89897))+~P107(f334(f334(f336(x89895),x89891),x89897)) % 188.18/188.27 [10278]~P107(f334(x102782,x102784))+~E(x102785,f334(f143(x102781,x102782),x102787))+E(f334(f143(x102781,x102782),x102783),f334(f334(f158(x102781),x102784),x102785))+~E(x102783,f334(f334(f141(x102781),x102786),f334(f334(f158(x102781),x102784),x102787)))+P107(f334(x102782,f760(x102785,x102784,x102783,x102782,x102781,x102786,x102787))) % 188.18/188.27 [10279]~P107(f334(x102794,x102792))+~E(x102793,f334(f143(x102791,x102794),x102797))+E(f334(f334(f158(x102791),x102792),x102793),f334(f143(x102791,x102794),x102795))+~E(x102795,f334(f334(f141(x102791),x102796),f334(f334(f158(x102791),x102792),x102797)))+P107(f334(x102794,f761(x102795,x102794,x102793,x102792,x102791,x102796,x102797))) % 188.18/188.27 [10329]~P107(f334(x103292,x103294))+~E(x103295,f334(f143(x103291,x103292),x103297))+E(f334(f143(x103291,x103292),x103293),f334(f334(f158(x103291),x103294),x103295))+~E(x103293,f334(f334(f141(x103291),x103296),f334(f334(f158(x103291),x103294),x103297)))+P107(f334(f334(f336(x103291),f760(x103295,x103294,x103293,x103292,x103291,x103296,x103297)),f334(f179(x103291),x103296))) % 188.18/188.27 [10330]~P107(f334(x103304,x103302))+~E(x103303,f334(f143(x103301,x103304),x103307))+E(f334(f334(f158(x103301),x103302),x103303),f334(f143(x103301,x103304),x103305))+~E(x103305,f334(f334(f141(x103301),x103306),f334(f334(f158(x103301),x103302),x103307)))+P107(f334(f334(f336(x103301),f761(x103305,x103304,x103303,x103302,x103301,x103306,x103307)),f334(f179(x103301),x103306))) % 188.18/188.27 [10335]~P10(x103351,x103357,x103356)+~P13(x103351,f935(x103355,a922),x103356,x103354)+P107(f334(f334(f336(x103351),f478(x103352,x103353,x103354,x103355,x103356,x103357,x103351)),x103357))+~P107(f334(f334(f336(f935(x103351,a922)),x103353),f334(f334(f65(x103351),x103357),x103356)))+P107(f334(f334(f336(f935(x103355,a922)),f334(f334(f44(x103351,f935(x103355,a922)),x103353),x103354)),x103352)) % 188.18/188.27 [10419]~P10(x104192,x104196,x104197)+~P13(x104192,f935(x104191,a922),x104197,x104194)+~P107(f334(f334(f336(f935(x104192,a922)),x104193),f334(f334(f65(x104192),x104196),x104197)))+~P107(f334(f334(f336(f935(x104191,a922)),f334(x104194,f478(x104195,x104193,x104194,x104191,x104197,x104196,x104192))),x104195))+P107(f334(f334(f336(f935(x104191,a922)),f334(f334(f44(x104192,f935(x104191,a922)),x104193),x104194)),x104195)) % 188.18/188.27 [8584]~P72(x85842)+~P27(x85841,x85845,x85848,x85844)+~E(x85843,f334(f78(x85845,x85842,x85841,x85846),x85848))+~E(x85847,f334(f317(x85841,x85845,x85848),x85844))+E(f334(f334(f9(x85841,x85842),x85843),x85844),f334(f334(f9(x85845,x85842),x85846),x85847)) % 188.18/188.27 [10428]~P72(x104282)+~P27(x104285,x104281,x104288,x104287)+~E(f334(x104286,f394(x104283,x104286,x104284,x104287,x104288,x104281,x104285,x104282)),f334(f334(f78(x104281,x104282,x104285,x104283),x104288),f394(x104283,x104286,x104284,x104287,x104288,x104281,x104285,x104282)))+~E(x104284,f334(f317(x104285,x104281,x104288),x104287))+E(f334(f334(f9(x104281,x104282),x104283),x104284),f334(f334(f9(x104285,x104282),x104286),x104287)) % 188.18/188.27 [10435]~P72(x104352)+~P27(x104351,x104355,x104358,x104354)+~E(x104357,f334(f317(x104351,x104355,x104358),x104354))+E(f334(f334(f9(x104351,x104352),x104353),x104354),f334(f334(f9(x104355,x104352),x104356),x104357))+P107(f334(f334(f336(x104351),f394(x104356,x104353,x104357,x104354,x104358,x104355,x104351,x104352)),x104354)) % 188.18/188.27 [10436]~P76(x104362)+~P27(x104361,x104365,x104368,x104364)+~E(x104367,f334(f317(x104361,x104365,x104368),x104364))+E(f334(f334(f6(x104361,x104362),x104363),x104364),f334(f334(f6(x104365,x104362),x104366),x104367))+P107(f334(f334(f336(x104361),f619(x104366,x104363,x104367,x104364,x104368,x104365,x104361,x104362)),x104364)) % 188.18/188.27 [10441]~P76(x104412)+~P27(x104415,x104411,x104418,x104417)+~E(x104414,f334(f317(x104415,x104411,x104418),x104417))+~E(f334(x104416,f619(x104413,x104416,x104414,x104417,x104418,x104411,x104415,x104412)),f334(x104413,f334(x104418,f619(x104413,x104416,x104414,x104417,x104418,x104411,x104415,x104412))))+E(f334(f334(f6(x104411,x104412),x104413),x104414),f334(f334(f6(x104415,x104412),x104416),x104417)) % 188.18/188.27 [9889]~P25(x98896,x98892,x98895,x98897,x98898,x98891)+~P107(f334(f66(x98892),x98894))+~P107(f334(f66(x98892),x98893))+~E(f334(f334(f109(f935(x98892,a922)),x98893),x98894),f195(f935(x98892,a922)))+E(f334(x98891,f334(f334(f108(f935(x98892,a922)),x98893),x98894)),f334(f334(x98895,f334(x98891,x98893)),f334(x98891,x98894))) % 188.18/188.27 [10264]~P25(x102648,x102642,x102645,x102647,x102646,x102641)+~E(f334(x102646,f577(x102644,x102643,x102641,x102646,x102647,x102645,x102642)),x102647)+~P107(f334(f66(x102642),x102643))+~P107(f334(f66(x102642),x102644))+E(f334(x102641,f334(f334(f108(f935(x102642,a922)),x102643),x102644)),f334(f334(x102645,f334(x102641,x102643)),f334(x102641,x102644))) % 188.18/188.27 [10342]~P25(x103428,x103422,x103425,x103427,x103426,x103421)+~P107(f334(f66(x103422),x103423))+~P107(f334(f66(x103422),x103424))+E(f334(x103421,f334(f334(f108(f935(x103422,a922)),x103423),x103424)),f334(f334(x103425,f334(x103421,x103423)),f334(x103421,x103424)))+P107(f334(f334(f336(x103422),f577(x103424,x103423,x103421,x103426,x103427,x103425,x103422)),f334(f334(f109(f935(x103422,a922)),x103423),x103424))) % 188.18/188.27 [10054]~P10(x100544,x100548,x100545)+~P10(x100541,x100549,x100543)+~P14(x100541,x100544,f935(x100542,a922),x100543,x100545,x100547)+P13(x100541,f935(x100542,a922),x100543,f334(f334(f8(f935(x100544,f935(x100542,a922)),f935(x100542,a922),x100541),f334(f44(x100544,f935(x100542,a922)),f334(f292(x100544,x100544,x100545),f334(f334(f316(x100544),x100546),f195(f935(x100544,a922)))))),x100547))+~P107(f334(f334(f336(x100544),x100546),x100548)) % 188.18/188.27 [5663]~P109(x56633)+~P15(x56633,x56631)+E(x56631,f738(x56632,x56633))+~E(f334(f179(x56633),x56631),x56632)+~P107(f334(f66(x56633),x56632))+~P107(f334(f144(x56633),x56631)) % 188.18/188.27 [7471]P17(x74711,x74712)+~E(f334(x74712,f822(x74712)),f334(x74712,f823(x74712)))+~P107(f334(f334(x74712,f822(x74712)),f822(x74712)))+~P107(f334(f334(x74712,f822(x74712)),f823(x74712)))+~P107(f334(f334(x74712,f823(x74712)),f823(x74712)))+~P107(f334(f334(x74712,x74713),x74713)) % 188.18/188.27 [5289]~P134(x52892)+~P136(x52892)+~P146(x52892)+~P116(x52892)+E(x52891,f2(x52892))+~E(f334(f334(f252(x52892),x52891),x52893),f2(x52892)) % 188.18/188.27 [5290]~P134(x52902)+~P136(x52902)+~P146(x52902)+~P116(x52902)+~E(x52901,f2(a927))+~E(f334(f334(f252(x52902),x52903),x52901),f2(x52902)) % 188.18/188.27 [6735]~P88(x67351)+~E(x67353,f2(x67351))+~E(x67352,f2(x67351))+E(f334(f334(f86(x67351),x67352),x67353),f2(x67351))+~P107(f334(f334(f242(x67351),f2(x67351)),x67353))+~P107(f334(f334(f242(x67351),f2(x67351)),x67352)) % 188.18/188.27 [9062]~E(f334(f259(a927,a927),x90623),f2(a927))+~E(x90621,f334(f334(f86(a927),f334(f334(f87(a927),f334(f259(a927,a927),x90623)),x90622)),f334(f264(a927,a927),x90623)))+P107(f334(f53(x90621,x90622),x90623))+~P107(f334(f334(f242(a927),f334(f264(a927,a927),x90623)),f2(a927)))+P107(f334(f334(f243(a927),f2(a927)),x90622))+~P107(f334(f334(f243(a927),x90622),f334(f264(a927,a927),x90623))) % 188.18/188.27 [9070]E(x90701,f2(a927))+~E(x90702,f334(f334(f86(a927),f334(f334(f87(a927),f334(f259(a927,a927),x90703)),x90701)),f334(f264(a927,a927),x90703)))+P107(f334(f53(x90702,x90701),x90703))+~P107(f334(f334(f243(a927),f2(a927)),x90701))+~P107(f334(f334(f242(a927),f2(a927)),f334(f264(a927,a927),x90703)))+~P107(f334(f334(f243(a927),f334(f264(a927,a927),x90703)),x90701)) % 188.18/188.27 [9088]~E(f334(f259(a927,a927),x90883),f2(a927))+~E(x90881,f334(f334(f86(a927),f334(f334(f87(a927),f334(f259(a927,a927),x90883)),x90882)),f334(f264(a927,a927),x90883)))+P107(f334(f53(x90881,x90882),x90883))+~P107(f334(f334(f243(a927),f2(a927)),x90882))+~P107(f334(f334(f242(a927),f2(a927)),f334(f264(a927,a927),x90883)))+~P107(f334(f334(f243(a927),f334(f264(a927,a927),x90883)),x90882)) % 188.18/188.27 [7103]~P109(x71032)+E(x71031,f195(f935(x71032,a922)))+E(x71033,f195(f935(x71032,a922)))+~P107(f334(f66(x71032),x71031))+~P107(f334(f66(x71032),x71033))+E(f14(x71032,f334(f334(f108(f935(x71032,a922)),x71033),x71031)),f334(f334(f246(x71032),f14(x71032,x71033)),f14(x71032,x71031))) % 188.18/188.27 [7104]~P109(x71042)+E(x71041,f195(f935(x71042,a922)))+E(x71043,f195(f935(x71042,a922)))+~P107(f334(f66(x71042),x71041))+~P107(f334(f66(x71042),x71043))+E(f15(x71042,f334(f334(f108(f935(x71042,a922)),x71043),x71041)),f334(f334(f241(x71042),f15(x71042,x71043)),f15(x71042,x71041))) % 188.18/188.27 [7105]~P99(x71052)+E(x71051,f195(f935(x71052,a922)))+E(x71053,f195(f935(x71052,a922)))+~P107(f334(f66(x71052),x71051))+~P107(f334(f66(x71052),x71053))+E(f10(x71052,f334(f334(f108(f935(x71052,a922)),x71053),x71051)),f334(f334(f109(x71052),f10(x71052,x71053)),f10(x71052,x71051))) % 188.18/188.27 [7106]~P99(x71062)+E(x71061,f195(f935(x71062,a922)))+E(x71063,f195(f935(x71062,a922)))+~P107(f334(f66(x71062),x71061))+~P107(f334(f66(x71062),x71063))+E(f13(x71062,f334(f334(f108(f935(x71062,a922)),x71063),x71061)),f334(f334(f108(x71062),f13(x71062,x71063)),f13(x71062,x71061))) % 188.18/188.27 [7727]~P96(x77272)+E(x77271,f195(f935(x77272,a922)))+E(x77273,f195(f935(x77272,a922)))+~P107(f334(f66(x77272),x77271))+~P107(f334(f66(x77272),x77273))+E(f334(f334(f87(x77272),f334(f68(x77272,f87(x77272)),x77273)),f334(f68(x77272,f87(x77272)),x77271)),f334(f68(x77272,f87(x77272)),f334(f334(f108(f935(x77272,a922)),x77273),x77271))) % 188.18/188.27 [7881]~P109(x78812)+E(x78811,f195(f935(x78812,a922)))+E(x78813,f195(f935(x78812,a922)))+~P107(f334(f66(x78812),x78811))+~P107(f334(f66(x78812),x78813))+E(f334(f334(f246(x78812),f11(x78812,f246(x78812),x78813)),f11(x78812,f246(x78812),x78811)),f11(x78812,f246(x78812),f334(f334(f108(f935(x78812,a922)),x78813),x78811))) % 188.18/188.27 [7882]~P109(x78822)+E(x78821,f195(f935(x78822,a922)))+E(x78823,f195(f935(x78822,a922)))+~P107(f334(f66(x78822),x78821))+~P107(f334(f66(x78822),x78823))+E(f334(f334(f241(x78822),f12(x78822,f241(x78822),x78823)),f12(x78822,f241(x78822),x78821)),f12(x78822,f241(x78822),f334(f334(f108(f935(x78822,a922)),x78823),x78821))) % 188.18/188.27 [8892]~P107(f334(x88921,x88923))+P107(f334(x88921,f443(x88921,x88922)))+P107(f334(x88921,f436(x88921,x88922)))+~P107(f334(f334(f243(a1),f2(a1)),x88922))+~P107(f334(f334(f336(a1),x88923),f311(a1,f84(a1),x88922)))+P107(f334(x88921,f334(f334(f23(a1),f436(x88921,x88922)),f334(f334(f87(a1),f442(x88921,x88922)),x88922)))) % 188.18/188.27 [9201]~P107(f334(x92011,x92013))+~P107(f334(x92011,f436(x92011,x92012)))+P107(f334(x92011,f443(x92011,x92012)))+~P107(f334(f334(f243(a1),f2(a1)),x92012))+~P107(f334(f334(f336(a1),x92013),f311(a1,f84(a1),x92012)))+~P107(f334(x92011,f334(f334(f23(a1),f436(x92011,x92012)),f334(f334(f87(a1),f442(x92011,x92012)),x92012)))) % 188.18/188.27 [10477]~P103(x104772)+E(x104771,f195(f935(x104772,a922)))+E(x104773,f195(f935(x104772,a922)))+~P107(f334(f66(x104772),x104771))+~P107(f334(f66(x104772),x104773))+E(f10(x104772,f334(f270(x104772),f334(f334(f8(f935(x104772,a922),a922,x104772),f92(x104772)),f334(f334(f8(f935(x104772,f935(x104772,a922)),f935(x104772,a922),x104772),f334(f8(f935(x104772,a922),a922,x104772),f92(x104772))),f334(f334(f7(x104772,f935(x104772,f935(x104772,a922)),f935(x104772,f935(x104772,a922))),f334(f334(f8(f935(x104772,f935(f935(x104772,a922),f935(x104772,a922))),f935(f935(x104772,f935(x104772,a922)),f935(x104772,f935(x104772,a922))),x104772),f18(x104772,f935(x104772,a922),f935(x104772,a922))),f334(f334(f8(f935(x104772,f935(x104772,f935(a922,a922))),f935(x104772,f935(f935(x104772,a922),f935(x104772,a922))),x104772),f334(f8(f935(x104772,f935(a922,a922)),f935(f935(x104772,a922),f935(x104772,a922)),x104772),f18(x104772,a922,a922))),f334(f334(f8(f935(x104772,f935(x104772,a922)),f935(x104772,f935(x104772,f935(a922,a922))),x104772),f334(f8(f935(x104772,a922),f935(x104772,f935(a922,a922)),x104772),f334(f8(a922,f935(a922,a922),x104772),a332))),f334(f334(f7(x104772,f935(x104772,f935(x104772,x104772)),f935(x104772,f935(x104772,a922))),f334(f334(f8(f935(f935(x104772,x104772),f935(x104772,a922)),f935(f935(x104772,f935(x104772,x104772)),f935(x104772,f935(x104772,a922))),x104772),f8(f935(x104772,x104772),f935(x104772,a922),x104772)),f334(f334(f8(f935(x104772,a922),f935(f935(x104772,x104772),f935(x104772,a922)),x104772),f8(x104772,a922,x104772)),a331))),f108(x104772)))))),f334(f334(f7(x104772,f935(x104772,a922),f935(x104772,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x104772,a922),f935(x104772,a922)),x104772),f8(a922,a922,x104772)),f334(f334(f8(a922,f935(a922,a922),x104772),a332),f334(f334(f7(x104772,f935(x104772,a922),a922),f336(x104772)),x104773)))),f334(f334(f7(x104772,f935(x104772,a922),a922),f336(x104772)),x104771))))))),f334(f334(f108(x104772),f10(x104772,x104773)),f10(x104772,x104771))) % 188.18/188.27 [10478]~P103(x104782)+E(x104781,f195(f935(x104782,a922)))+E(x104783,f195(f935(x104782,a922)))+~P107(f334(f66(x104782),x104781))+~P107(f334(f66(x104782),x104783))+E(f13(x104782,f334(f270(x104782),f334(f334(f8(f935(x104782,a922),a922,x104782),f92(x104782)),f334(f334(f8(f935(x104782,f935(x104782,a922)),f935(x104782,a922),x104782),f334(f8(f935(x104782,a922),a922,x104782),f92(x104782))),f334(f334(f7(x104782,f935(x104782,f935(x104782,a922)),f935(x104782,f935(x104782,a922))),f334(f334(f8(f935(x104782,f935(f935(x104782,a922),f935(x104782,a922))),f935(f935(x104782,f935(x104782,a922)),f935(x104782,f935(x104782,a922))),x104782),f18(x104782,f935(x104782,a922),f935(x104782,a922))),f334(f334(f8(f935(x104782,f935(x104782,f935(a922,a922))),f935(x104782,f935(f935(x104782,a922),f935(x104782,a922))),x104782),f334(f8(f935(x104782,f935(a922,a922)),f935(f935(x104782,a922),f935(x104782,a922)),x104782),f18(x104782,a922,a922))),f334(f334(f8(f935(x104782,f935(x104782,a922)),f935(x104782,f935(x104782,f935(a922,a922))),x104782),f334(f8(f935(x104782,a922),f935(x104782,f935(a922,a922)),x104782),f334(f8(a922,f935(a922,a922),x104782),a332))),f334(f334(f7(x104782,f935(x104782,f935(x104782,x104782)),f935(x104782,f935(x104782,a922))),f334(f334(f8(f935(f935(x104782,x104782),f935(x104782,a922)),f935(f935(x104782,f935(x104782,x104782)),f935(x104782,f935(x104782,a922))),x104782),f8(f935(x104782,x104782),f935(x104782,a922),x104782)),f334(f334(f8(f935(x104782,a922),f935(f935(x104782,x104782),f935(x104782,a922)),x104782),f8(x104782,a922,x104782)),a331))),f109(x104782)))))),f334(f334(f7(x104782,f935(x104782,a922),f935(x104782,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x104782,a922),f935(x104782,a922)),x104782),f8(a922,a922,x104782)),f334(f334(f8(a922,f935(a922,a922),x104782),a332),f334(f334(f7(x104782,f935(x104782,a922),a922),f336(x104782)),x104783)))),f334(f334(f7(x104782,f935(x104782,a922),a922),f336(x104782)),x104781))))))),f334(f334(f109(x104782),f13(x104782,x104783)),f13(x104782,x104781))) % 188.18/188.27 [10479]~P109(x104792)+E(x104791,f195(f935(x104792,a922)))+E(x104793,f195(f935(x104792,a922)))+~P107(f334(f66(x104792),x104791))+~P107(f334(f66(x104792),x104793))+E(f12(x104792,f241(x104792),f334(f270(x104792),f334(f334(f8(f935(x104792,a922),a922,x104792),f92(x104792)),f334(f334(f8(f935(x104792,f935(x104792,a922)),f935(x104792,a922),x104792),f334(f8(f935(x104792,a922),a922,x104792),f92(x104792))),f334(f334(f7(x104792,f935(x104792,f935(x104792,a922)),f935(x104792,f935(x104792,a922))),f334(f334(f8(f935(x104792,f935(f935(x104792,a922),f935(x104792,a922))),f935(f935(x104792,f935(x104792,a922)),f935(x104792,f935(x104792,a922))),x104792),f18(x104792,f935(x104792,a922),f935(x104792,a922))),f334(f334(f8(f935(x104792,f935(x104792,f935(a922,a922))),f935(x104792,f935(f935(x104792,a922),f935(x104792,a922))),x104792),f334(f8(f935(x104792,f935(a922,a922)),f935(f935(x104792,a922),f935(x104792,a922)),x104792),f18(x104792,a922,a922))),f334(f334(f8(f935(x104792,f935(x104792,a922)),f935(x104792,f935(x104792,f935(a922,a922))),x104792),f334(f8(f935(x104792,a922),f935(x104792,f935(a922,a922)),x104792),f334(f8(a922,f935(a922,a922),x104792),a332))),f334(f334(f7(x104792,f935(x104792,f935(x104792,x104792)),f935(x104792,f935(x104792,a922))),f334(f334(f8(f935(f935(x104792,x104792),f935(x104792,a922)),f935(f935(x104792,f935(x104792,x104792)),f935(x104792,f935(x104792,a922))),x104792),f8(f935(x104792,x104792),f935(x104792,a922),x104792)),f334(f334(f8(f935(x104792,a922),f935(f935(x104792,x104792),f935(x104792,a922)),x104792),f8(x104792,a922,x104792)),a331))),f246(x104792)))))),f334(f334(f7(x104792,f935(x104792,a922),f935(x104792,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x104792,a922),f935(x104792,a922)),x104792),f8(a922,a922,x104792)),f334(f334(f8(a922,f935(a922,a922),x104792),a332),f334(f334(f7(x104792,f935(x104792,a922),a922),f336(x104792)),x104793)))),f334(f334(f7(x104792,f935(x104792,a922),a922),f336(x104792)),x104791))))))),f334(f334(f246(x104792),f12(x104792,f241(x104792),x104793)),f12(x104792,f241(x104792),x104791))) % 188.18/188.27 [10480]~P109(x104802)+E(x104801,f195(f935(x104802,a922)))+E(x104803,f195(f935(x104802,a922)))+~P107(f334(f66(x104802),x104801))+~P107(f334(f66(x104802),x104803))+E(f11(x104802,f246(x104802),f334(f270(x104802),f334(f334(f8(f935(x104802,a922),a922,x104802),f92(x104802)),f334(f334(f8(f935(x104802,f935(x104802,a922)),f935(x104802,a922),x104802),f334(f8(f935(x104802,a922),a922,x104802),f92(x104802))),f334(f334(f7(x104802,f935(x104802,f935(x104802,a922)),f935(x104802,f935(x104802,a922))),f334(f334(f8(f935(x104802,f935(f935(x104802,a922),f935(x104802,a922))),f935(f935(x104802,f935(x104802,a922)),f935(x104802,f935(x104802,a922))),x104802),f18(x104802,f935(x104802,a922),f935(x104802,a922))),f334(f334(f8(f935(x104802,f935(x104802,f935(a922,a922))),f935(x104802,f935(f935(x104802,a922),f935(x104802,a922))),x104802),f334(f8(f935(x104802,f935(a922,a922)),f935(f935(x104802,a922),f935(x104802,a922)),x104802),f18(x104802,a922,a922))),f334(f334(f8(f935(x104802,f935(x104802,a922)),f935(x104802,f935(x104802,f935(a922,a922))),x104802),f334(f8(f935(x104802,a922),f935(x104802,f935(a922,a922)),x104802),f334(f8(a922,f935(a922,a922),x104802),a332))),f334(f334(f7(x104802,f935(x104802,f935(x104802,x104802)),f935(x104802,f935(x104802,a922))),f334(f334(f8(f935(f935(x104802,x104802),f935(x104802,a922)),f935(f935(x104802,f935(x104802,x104802)),f935(x104802,f935(x104802,a922))),x104802),f8(f935(x104802,x104802),f935(x104802,a922),x104802)),f334(f334(f8(f935(x104802,a922),f935(f935(x104802,x104802),f935(x104802,a922)),x104802),f8(x104802,a922,x104802)),a331))),f241(x104802)))))),f334(f334(f7(x104802,f935(x104802,a922),f935(x104802,a922)),f334(f334(f8(f935(a922,a922),f935(f935(x104802,a922),f935(x104802,a922)),x104802),f8(a922,a922,x104802)),f334(f334(f8(a922,f935(a922,a922),x104802),a332),f334(f334(f7(x104802,f935(x104802,a922),a922),f336(x104802)),x104803)))),f334(f334(f7(x104802,f935(x104802,a922),a922),f336(x104802)),x104801))))))),f334(f334(f241(x104802),f11(x104802,f246(x104802),x104803)),f11(x104802,f246(x104802),x104801))) % 188.18/188.27 [7427]~P127(x74273)+E(x74271,x74272)+~E(f334(f334(f252(x74273),x74271),x74274),f334(f334(f252(x74273),x74272),x74274))+~P107(f334(f334(f242(x74273),f2(x74273)),x74272))+~P107(f334(f334(f242(x74273),f2(x74273)),x74271))+~P107(f334(f334(f243(a927),f2(a927)),x74274)) % 188.18/188.27 [7688]~P109(x76882)+E(x76881,f195(f935(x76882,a922)))+~P107(f334(f66(x76882),x76881))+~P107(f334(f334(f336(x76882),x76884),x76881))+P107(f334(f334(f242(x76882),x76883),x76884))+~P107(f334(f334(f242(x76882),x76883),f334(f68(x76882,f246(x76882)),x76881))) % 188.18/188.27 [7689]~P104(x76892)+E(x76891,f195(f935(x76892,a922)))+~P107(f334(f66(x76892),x76891))+~P107(f334(f334(f336(x76892),x76894),x76891))+P107(f334(f334(f242(x76892),x76893),x76894))+~P107(f334(f334(f242(x76892),x76893),f334(f68(x76892,f109(x76892)),x76891))) % 188.18/188.27 [7690]~P109(x76902)+E(x76901,f195(f935(x76902,a922)))+~P107(f334(f66(x76902),x76901))+~P107(f334(f334(f336(x76902),x76904),x76901))+P107(f334(f334(f243(x76902),x76903),x76904))+~P107(f334(f334(f243(x76902),x76903),f334(f68(x76902,f246(x76902)),x76901))) % 188.18/188.27 [7596]E(x75961,f2(a1))+E(f334(f334(f41(a1),x75962),x75961),x75963)+~P107(f334(f334(f242(a1),x75964),f2(a1)))+~E(x75962,f334(f334(f86(a1),f334(f334(f87(a1),x75961),x75963)),x75964))+P107(f334(f334(f243(a1),f2(a1)),x75961))+~P107(f334(f334(f243(a1),x75961),x75964)) % 188.18/188.27 [7610]E(f50(a1,x76102,x76101),x76103)+E(x76101,f2(a1))+~P107(f334(f334(f242(a1),x76103),f2(a1)))+~E(x76102,f334(f334(f86(a1),f334(f334(f87(a1),x76101),x76104)),x76103))+P107(f334(f334(f243(a1),f2(a1)),x76101))+~P107(f334(f334(f243(a1),x76101),x76103)) % 188.18/188.27 [7726]E(x77261,f2(a1))+E(f334(f334(f41(a1),x77262),x77261),x77263)+~E(x77262,f334(f334(f86(a1),f334(f334(f87(a1),x77261),x77263)),x77264))+~P107(f334(f334(f242(a1),f2(a1)),x77264))+~P107(f334(f334(f243(a1),f2(a1)),x77261))+~P107(f334(f334(f243(a1),x77264),x77261)) % 188.18/188.27 [7747]E(f50(a1,x77472,x77471),x77473)+E(x77471,f2(a1))+~E(x77472,f334(f334(f86(a1),f334(f334(f87(a1),x77471),x77474)),x77473))+~P107(f334(f334(f242(a1),f2(a1)),x77473))+~P107(f334(f334(f243(a1),f2(a1)),x77471))+~P107(f334(f334(f243(a1),x77473),x77471)) % 188.18/188.27 [7885]~P109(x78852)+E(x78851,f195(f935(x78852,a922)))+~P107(f334(f66(x78852),x78851))+~P107(f334(f334(f242(x78852),x78854),x78853))+~P107(f334(f334(f336(x78852),x78854),x78851))+P107(f334(f334(f242(x78852),f334(f68(x78852,f246(x78852)),x78851)),x78853)) % 188.18/188.27 [7886]~P109(x78862)+E(x78861,f195(f935(x78862,a922)))+~P107(f334(f66(x78862),x78861))+~P107(f334(f334(f243(x78862),x78864),x78863))+~P107(f334(f334(f336(x78862),x78864),x78861))+P107(f334(f334(f243(x78862),f334(f68(x78862,f246(x78862)),x78861)),x78863)) % 188.18/188.27 [8439]~P107(f334(f334(f242(a1),x84394),f2(a1)))+~E(x84391,f334(f334(f86(a1),f334(f334(f87(a1),x84392),x84393)),x84394))+~P107(f334(f334(f242(a1),f2(a1)),x84394))+~P107(f334(f334(f243(a1),x84394),x84392))+~P107(f334(f334(f243(a1),x84392),x84394))+P107(f334(f54(x84391,x84392),f334(f334(f260(a1,a1),x84393),x84394))) % 188.18/188.27 [8602]~P111(x86021)+P107(f334(f334(f243(f935(x86021,a922)),f311(x86021,x86022,x86023)),f311(x86021,x86024,x86025)))+~P107(f334(f334(f242(x86021),x86024),x86022))+~P107(f334(f334(f242(x86021),x86024),x86025))+~P107(f334(f334(f242(x86021),x86023),x86025))+~P107(f334(f334(f243(x86021),x86023),x86025)) % 188.18/188.27 [8603]~P111(x86031)+P107(f334(f334(f243(f935(x86031,a922)),f311(x86031,x86032,x86033)),f311(x86031,x86034,x86035)))+~P107(f334(f334(f242(x86031),x86033),x86035))+~P107(f334(f334(f242(x86031),x86034),x86035))+~P107(f334(f334(f242(x86031),x86034),x86032))+~P107(f334(f334(f243(x86031),x86034),x86032)) % 188.18/188.27 [9453]P62(x94532,x94533,x94534,x94531)+E(x94531,f195(f935(x94532,a922)))+~P107(f334(f66(x94532),x94534))+~P107(f334(f66(x94532),x94531))+~P107(f334(f334(x94533,f523(x94531,x94534,x94533,x94532)),x94535))+~P107(f334(f334(f336(x94532),x94535),x94531)) % 188.18/188.27 [9454]P62(x94542,x94543,x94544,x94541)+E(x94541,f195(f935(x94542,a922)))+~P107(f334(f66(x94542),x94544))+~P107(f334(f66(x94542),x94541))+~P107(f334(f334(x94543,f813(x94543,x94541,x94544,x94542)),x94545))+~P107(f334(f334(f336(x94542),x94545),x94541)) % 188.18/188.27 [9455]P62(x94552,x94553,x94554,x94551)+E(x94551,f195(f935(x94552,a922)))+~P107(f334(f66(x94552),x94554))+~P107(f334(f66(x94552),x94551))+~P107(f334(f334(x94553,f814(x94551,x94554,x94553,x94552)),x94555))+~P107(f334(f334(f336(x94552),x94555),x94551)) % 188.18/188.27 [9608]~E(x96083,x96085)+~P72(x96081)+~P76(x96081)+~P42(x96083)+E(f334(f334(f9(a1,x96081),x96082),x96083),f334(f334(f9(a1,x96081),x96084),x96085))+P107(f334(f334(f242(a1),f2(a1)),f516(x96082,x96084,x96083,x96085,x96081))) % 188.18/188.27 [9609]~E(x96093,x96095)+~P72(x96091)+~P76(x96091)+~P42(x96093)+E(f334(f334(f6(a1,x96091),x96092),x96093),f334(f334(f6(a1,x96091),x96094),x96095))+P107(f334(f334(f242(a1),f2(a1)),f519(x96092,x96094,x96093,x96095,x96091))) % 188.18/188.27 [9785]~E(x97855,x97853)+~P72(x97851)+~P76(x97851)+~P42(x97855)+~E(f334(x97852,f516(x97854,x97852,x97855,x97853,x97851)),f334(x97854,f516(x97854,x97852,x97855,x97853,x97851)))+E(f334(f334(f9(a1,x97851),x97852),x97853),f334(f334(f9(a1,x97851),x97854),x97855)) % 188.18/188.27 [9786]~E(x97865,x97863)+~P72(x97861)+~P76(x97861)+~P42(x97865)+~E(f334(x97862,f519(x97864,x97862,x97865,x97863,x97861)),f334(x97864,f519(x97864,x97862,x97865,x97863,x97861)))+E(f334(f334(f6(a1,x97861),x97862),x97863),f334(f334(f6(a1,x97861),x97864),x97865)) % 188.18/188.27 [9887]~P79(x98873)+E(f334(x98871,x98872),f2(x98873))+~E(f334(f334(f6(x98874,x98873),x98871),x98875),f2(x98873))+~P107(f334(f66(x98874),x98875))+P107(f334(f334(f336(x98874),f490(x98872,x98871,x98875,x98874,x98873)),x98875))+~P107(f334(f334(f336(x98874),x98872),x98875)) % 188.18/188.27 [10026]~P79(x100263)+E(f334(x100261,x100262),f2(x100263))+~E(f334(f334(f6(x100264,x100263),x100261),x100265),f2(x100263))+~P107(f334(f66(x100264),x100265))+~P107(f334(f334(f336(x100264),x100262),x100265))+~P107(f334(f334(f242(x100263),f2(x100263)),f334(x100261,f490(x100262,x100261,x100265,x100264,x100263)))) % 188.18/188.27 [8524]~P139(x85241)+~P107(f334(f334(f242(x85241),x85243),x85245))+~P107(f334(f334(f242(x85241),x85242),x85244))+~P107(f334(f334(f242(x85241),f2(x85241)),x85243))+~P107(f334(f334(f242(x85241),f2(x85241)),x85244))+P107(f334(f334(f242(x85241),f334(f334(f87(x85241),x85242),x85243)),f334(f334(f87(x85241),x85244),x85245))) % 188.18/188.27 [8525]~P139(x85251)+~P107(f334(f334(f242(x85251),x85253),x85255))+~P107(f334(f334(f242(x85251),x85252),x85254))+~P107(f334(f334(f242(x85251),f2(x85251)),x85253))+~P107(f334(f334(f242(x85251),f2(x85251)),x85252))+P107(f334(f334(f242(x85251),f334(f334(f87(x85251),x85252),x85253)),f334(f334(f87(x85251),x85254),x85255))) % 188.18/188.27 [8526]~P68(x85261)+~P107(f334(f334(f243(x85261),f2(x85261)),x85265))+~P107(f334(f334(f242(x85261),x85265),x85263))+~P107(f334(f334(f242(x85261),x85262),x85264))+~P107(f334(f334(f242(x85261),f2(x85261)),x85262))+P107(f334(f334(f242(x85261),f334(f334(f296(x85261),x85262),x85263)),f334(f334(f296(x85261),x85264),x85265))) % 188.18/188.27 [8527]~P135(x85271)+~P107(f334(f334(f242(x85271),x85273),x85275))+~P107(f334(f334(f242(x85271),f2(x85271)),x85272))+~P107(f334(f334(f243(x85271),x85272),x85274))+~P107(f334(f334(f243(x85271),f2(x85271)),x85273))+P107(f334(f334(f243(x85271),f334(f334(f87(x85271),x85272),x85273)),f334(f334(f87(x85271),x85274),x85275))) % 188.18/188.27 [8528]~P135(x85281)+~P107(f334(f334(f242(x85281),x85282),x85284))+~P107(f334(f334(f242(x85281),f2(x85281)),x85283))+~P107(f334(f334(f243(x85281),x85283),x85285))+~P107(f334(f334(f243(x85281),f2(x85281)),x85282))+P107(f334(f334(f243(x85281),f334(f334(f87(x85281),x85282),x85283)),f334(f334(f87(x85281),x85284),x85285))) % 188.18/188.27 [8529]~P135(x85291)+~P107(f334(f334(f242(x85291),f2(x85291)),x85293))+~P107(f334(f334(f242(x85291),f2(x85291)),x85292))+~P107(f334(f334(f243(x85291),x85293),x85295))+~P107(f334(f334(f243(x85291),x85292),x85294))+P107(f334(f334(f243(x85291),f334(f334(f87(x85291),x85292),x85293)),f334(f334(f87(x85291),x85294),x85295))) % 188.18/188.27 [8530]~P135(x85301)+~P107(f334(f334(f242(x85301),f2(x85301)),x85303))+~P107(f334(f334(f243(x85301),x85303),x85305))+~P107(f334(f334(f243(x85301),x85302),x85304))+~P107(f334(f334(f243(x85301),f2(x85301)),x85304))+P107(f334(f334(f243(x85301),f334(f334(f87(x85301),x85302),x85303)),f334(f334(f87(x85301),x85304),x85305))) % 188.18/188.27 [8531]~P68(x85311)+~P107(f334(f334(f242(x85311),x85315),x85313))+~P107(f334(f334(f242(x85311),f2(x85311)),x85312))+~P107(f334(f334(f243(x85311),x85312),x85314))+~P107(f334(f334(f243(x85311),f2(x85311)),x85315))+P107(f334(f334(f243(x85311),f334(f334(f296(x85311),x85312),x85313)),f334(f334(f296(x85311),x85314),x85315))) % 188.18/188.27 [8532]~P68(x85321)+~P107(f334(f334(f242(x85321),x85322),x85324))+~P107(f334(f334(f243(x85321),x85325),x85323))+~P107(f334(f334(f243(x85321),f2(x85321)),x85325))+~P107(f334(f334(f243(x85321),f2(x85321)),x85322))+P107(f334(f334(f243(x85321),f334(f334(f296(x85321),x85322),x85323)),f334(f334(f296(x85321),x85324),x85325))) % 188.18/188.27 [9929]~P87(x99295)+~P76(x99295)+E(x99291,f195(f935(x99292,a922)))+~P107(f334(f66(x99292),x99291))+P107(f334(f334(f336(x99292),f512(x99293,x99294,x99291,x99292,x99295)),x99291))+P107(f334(f334(f243(x99295),f334(f334(f6(x99292,x99295),x99294),x99291)),f334(f334(f6(x99292,x99295),x99293),x99291))) % 188.18/188.27 [10050]~P85(x100501)+~P76(x100501)+~P107(f334(f66(x100502),x100505))+~P107(f334(f334(f242(x100501),f2(x100501)),f334(x100503,f468(x100503,x100504,x100505,x100502,x100501))))+P107(f334(f334(f242(x100501),f334(f334(f6(x100502,x100501),x100503),x100504)),f334(f334(f6(x100502,x100501),x100503),x100505)))+~P107(f334(f334(f242(f935(x100502,a922)),x100504),x100505)) % 188.18/188.27 [10189]~P87(x101893)+~P76(x101893)+E(x101891,f195(f935(x101892,a922)))+~P107(f334(f66(x101892),x101891))+~P107(f334(f334(f243(x101893),f334(x101894,f512(x101895,x101894,x101891,x101892,x101893))),f334(x101895,f512(x101895,x101894,x101891,x101892,x101893))))+P107(f334(f334(f243(x101893),f334(f334(f6(x101892,x101893),x101894),x101891)),f334(f334(f6(x101892,x101893),x101895),x101891))) % 188.18/188.27 [7285]~P19(x72852,x72855,x72854)+E(x72851,f195(f935(x72852,a922)))+E(x72853,f195(f935(x72852,a922)))+~P107(f334(f66(x72852),x72851))+~P107(f334(f66(x72852),x72853))+E(f334(x72854,f334(f334(f108(f935(x72852,a922)),x72853),x72851)),f334(f334(x72855,f334(x72854,x72853)),f334(x72854,x72851))) % 188.18/188.27 [7852]~P150(x78521,x78523,x78524)+P107(f334(x78521,x78522))+~P107(f334(f334(f243(a1),x78524),f2(a1)))+~P107(f334(f334(f242(a1),x78525),f2(a1)))+~E(x78523,f334(f334(f86(a1),f334(f334(f87(a1),x78524),x78522)),x78525))+~P107(f334(f334(f243(a1),x78524),x78525)) % 188.18/188.27 [7853]~P149(x78531,x78533,x78534)+P107(f334(x78531,x78532))+~P107(f334(f334(f243(a1),x78534),f2(a1)))+~P107(f334(f334(f242(a1),x78532),f2(a1)))+~E(x78533,f334(f334(f86(a1),f334(f334(f87(a1),x78534),x78535)),x78532))+~P107(f334(f334(f243(a1),x78534),x78532)) % 188.18/188.27 [7894]~P150(x78941,x78943,x78944)+P107(f334(x78941,x78942))+~E(x78943,f334(f334(f86(a1),f334(f334(f87(a1),x78944),x78942)),x78945))+~P107(f334(f334(f242(a1),f2(a1)),x78945))+~P107(f334(f334(f243(a1),f2(a1)),x78944))+~P107(f334(f334(f243(a1),x78945),x78944)) % 188.18/188.27 [7895]~P149(x78951,x78953,x78954)+P107(f334(x78951,x78952))+~E(x78953,f334(f334(f86(a1),f334(f334(f87(a1),x78954),x78955)),x78952))+~P107(f334(f334(f242(a1),f2(a1)),x78952))+~P107(f334(f334(f243(a1),f2(a1)),x78954))+~P107(f334(f334(f243(a1),x78952),x78954)) % 188.18/188.27 [8810]P107(f334(f334(x88101,x88102),x88103))+~P107(f334(f334(x88101,f334(f334(f41(a1),x88104),x88105)),f50(a1,x88104,x88105)))+~P107(f334(f334(f243(a1),x88105),f2(a1)))+~P107(f334(f334(f242(a1),x88103),f2(a1)))+~E(x88104,f334(f334(f86(a1),f334(f334(f87(a1),x88105),x88102)),x88103))+~P107(f334(f334(f243(a1),x88105),x88103)) % 188.18/188.27 [8819]P107(f334(f334(x88191,x88192),x88193))+~P107(f334(f334(x88191,f334(f334(f41(a1),x88194),x88195)),f50(a1,x88194,x88195)))+~E(x88194,f334(f334(f86(a1),f334(f334(f87(a1),x88195),x88192)),x88193))+~P107(f334(f334(f242(a1),f2(a1)),x88193))+~P107(f334(f334(f243(a1),f2(a1)),x88195))+~P107(f334(f334(f243(a1),x88193),x88195)) % 188.18/188.27 [9079]E(x90791,x90792)+~P58(x90793,x90795,x90794)+~P107(f334(f334(f336(x90793),x90792),x90795))+~P107(f334(f334(f336(x90793),x90791),x90795))+P107(f334(f334(f336(f934(x90793,x90793)),f334(f334(f260(x90793,x90793),x90791),x90792)),x90794))+P107(f334(f334(f336(f934(x90793,x90793)),f334(f334(f260(x90793,x90793),x90792),x90791)),x90794)) % 188.18/188.27 [9956]~P85(x99565)+~P76(x99565)+~P107(f334(f66(x99561),x99564))+P107(f334(f334(f242(x99565),f334(f334(f6(x99561,x99565),x99562),x99563)),f334(f334(f6(x99561,x99565),x99562),x99564)))+~P107(f334(f334(f242(f935(x99561,a922)),x99563),x99564))+P107(f334(f334(f336(x99561),f468(x99562,x99563,x99564,x99561,x99565)),f334(f334(f23(f935(x99561,a922)),x99564),x99563))) % 188.18/188.27 [10058]E(x100581,f195(f935(x100582,a922)))+~P107(f334(f66(x100582),x100583))+~P107(f334(f66(x100582),x100581))+P107(f334(f334(f336(f934(f935(x100582,a922),f935(x100582,a922))),f334(f334(f260(f935(x100582,a922),f935(x100582,a922)),x100583),x100581)),f325(x100582,x100584)))+~P107(f334(f334(f336(x100582),x100585),x100581))+~P107(f334(f334(f336(f934(x100582,x100582)),f334(f334(f260(x100582,x100582),f532(x100584,x100581,x100583,x100582)),x100585)),x100584)) % 188.18/188.27 [10059]E(x100591,f195(f935(x100592,a922)))+~P107(f334(f66(x100592),x100593))+~P107(f334(f66(x100592),x100591))+P107(f334(f334(f336(f934(f935(x100592,a922),f935(x100592,a922))),f334(f334(f260(f935(x100592,a922),f935(x100592,a922)),x100593),x100591)),f325(x100592,x100594)))+~P107(f334(f334(f336(x100592),x100595),x100591))+~P107(f334(f334(f336(f934(x100592,x100592)),f334(f334(f260(x100592,x100592),f606(x100594,x100591,x100593,x100592)),x100595)),x100594)) % 188.18/188.27 [10193]~P79(x101931)+~E(f334(f334(f6(x101935,x101931),x101932),x101936),x101934)+~P107(f334(f66(x101935),x101936))+P107(f334(f334(f336(x101935),f498(x101933,x101934,x101932,x101936,x101935,x101931)),x101936))+P107(f334(f334(f242(x101931),f334(x101932,x101933)),x101934))+~P107(f334(f334(f336(x101935),x101933),x101936)) % 188.18/188.27 [10234]~P79(x102341)+~E(f334(f334(f6(x102345,x102341),x102342),x102346),x102344)+~P107(f334(f66(x102345),x102346))+~P107(f334(f334(f336(x102345),x102343),x102346))+~P107(f334(f334(f242(x102341),f2(x102341)),f334(x102342,f498(x102343,x102344,x102342,x102346,x102345,x102341))))+P107(f334(f334(f242(x102341),f334(x102342,x102343)),x102344)) % 188.18/188.27 [10404]~E(x104045,x104048)+~E(x104044,x104047)+~P110(x104041)+~P76(x104042)+E(f334(f334(f6(x104041,x104042),x104043),f334(f310(x104041,x104044),x104045)),f334(f334(f6(x104041,x104042),x104046),f334(f310(x104041,x104047),x104048)))+P107(f334(f334(f242(x104041),x104044),f618(x104043,x104046,x104045,x104048,x104044,x104047,x104041,x104042))) % 188.18/188.27 [10427]~E(x104277,x104274)+~E(x104278,x104275)+~P110(x104271)+~P76(x104272)+~E(f334(x104273,f618(x104276,x104273,x104278,x104275,x104277,x104274,x104271,x104272)),f334(x104276,f618(x104276,x104273,x104278,x104275,x104277,x104274,x104271,x104272)))+E(f334(f334(f6(x104271,x104272),x104273),f334(f310(x104271,x104274),x104275)),f334(f334(f6(x104271,x104272),x104276),f334(f310(x104271,x104277),x104278))) % 188.18/188.27 [10434]~E(x104344,x104347)+~E(x104345,x104348)+~P110(x104341)+~P76(x104342)+E(f334(f334(f6(x104341,x104342),x104343),f334(f310(x104341,x104344),x104345)),f334(f334(f6(x104341,x104342),x104346),f334(f310(x104341,x104347),x104348)))+P107(f334(f334(f243(x104341),f618(x104343,x104346,x104345,x104348,x104344,x104347,x104341,x104342)),x104345)) % 188.18/188.27 [10065]~P10(x100655,x100659,x100656)+~P10(x100651,x1006510,x100653)+~P14(x100651,x100655,f935(x100652,a922),x100653,x100656,x100658)+~P107(f334(f334(f336(x100655),x100657),x100659))+~P107(f334(f334(f336(x100651),x100654),x1006510))+E(f334(f334(f44(x100651,f935(x100652,a922)),f334(f292(x100651,x100651,x100653),f334(f334(f316(x100651),x100654),f195(f935(x100651,a922))))),f334(f334(f8(f935(x100655,f935(x100652,a922)),f935(x100652,a922),x100651),f334(f44(x100655,f935(x100652,a922)),f334(f292(x100655,x100655,x100656),f334(f334(f316(x100655),x100657),f195(f935(x100655,a922)))))),x100658)),f334(f334(x100658,x100654),x100657)) % 188.18/188.27 [5838]~P109(x58383)+~P15(x58383,x58382)+~P15(x58383,x58381)+E(x58381,x58382)+~E(f334(f179(x58383),x58381),f334(f179(x58383),x58382))+~P107(f334(f144(x58383),x58382))+~P107(f334(f144(x58383),x58381)) % 188.18/188.27 [5169]~P134(x51692)+~P136(x51692)+~P146(x51692)+~P116(x51692)+~E(x51693,f2(x51692))+E(x51691,f2(a927))+E(f334(f334(f252(x51692),x51693),x51691),f2(x51692)) % 188.18/188.27 [9326]E(x93261,f2(a927))+~E(x93262,f334(f334(f86(a927),f334(f334(f87(a927),f334(f259(a927,a927),x93263)),x93261)),f334(f264(a927,a927),x93263)))+P107(f334(f53(x93262,x93261),x93263))+~P107(f334(f334(f242(a927),f334(f264(a927,a927),x93263)),f2(a927)))+~P107(f334(f334(f242(a927),f2(a927)),f334(f264(a927,a927),x93263)))+~P107(f334(f334(f243(a927),x93261),f334(f264(a927,a927),x93263)))+~P107(f334(f334(f243(a927),f334(f264(a927,a927),x93263)),x93261)) % 188.18/188.27 [9339]~E(f334(f259(a927,a927),x93393),f2(a927))+~E(x93391,f334(f334(f86(a927),f334(f334(f87(a927),f334(f259(a927,a927),x93393)),x93392)),f334(f264(a927,a927),x93393)))+P107(f334(f53(x93391,x93392),x93393))+~P107(f334(f334(f242(a927),f334(f264(a927,a927),x93393)),f2(a927)))+~P107(f334(f334(f242(a927),f2(a927)),f334(f264(a927,a927),x93393)))+~P107(f334(f334(f243(a927),x93392),f334(f264(a927,a927),x93393)))+~P107(f334(f334(f243(a927),f334(f264(a927,a927),x93393)),x93392)) % 188.18/188.27 [8196]~P70(x81962)+E(x81961,f195(f935(x81962,a922)))+E(x81963,f195(f935(x81962,a922)))+~P107(f334(f66(x81962),x81961))+~P107(f334(f66(x81962),x81963))+~E(f334(f334(f109(f935(x81962,a922)),x81963),x81961),f195(f935(x81962,a922)))+E(f334(f334(f87(x81962),f334(f68(x81962,f87(x81962)),x81963)),f334(f68(x81962,f87(x81962)),x81961)),f334(f68(x81962,f87(x81962)),f334(f334(f108(f935(x81962,a922)),x81963),x81961))) % 188.18/188.27 [7990]E(x79901,f2(a1))+E(f334(f334(f41(a1),x79902),x79901),x79903)+~P107(f334(f334(f242(a1),x79904),f2(a1)))+~E(x79902,f334(f334(f86(a1),f334(f334(f87(a1),x79901),x79903)),x79904))+~P107(f334(f334(f242(a1),f2(a1)),x79904))+~P107(f334(f334(f243(a1),x79904),x79901))+~P107(f334(f334(f243(a1),x79901),x79904)) % 188.18/188.27 [7998]E(f50(a1,x79982,x79981),x79983)+E(x79981,f2(a1))+~P107(f334(f334(f242(a1),x79983),f2(a1)))+~E(x79982,f334(f334(f86(a1),f334(f334(f87(a1),x79981),x79984)),x79983))+~P107(f334(f334(f242(a1),f2(a1)),x79983))+~P107(f334(f334(f243(a1),x79983),x79981))+~P107(f334(f334(f243(a1),x79981),x79983)) % 188.18/188.27 [6627]~P5(x66272)+~P59(x66272,x66271,x66275)+~P59(x66272,x66273,x66274)+E(x66271,f2(x66272))+E(x66273,f2(x66272))+~E(f334(f334(f41(x66272),x66274),x66273),f334(f334(f41(x66272),x66275),x66271))+E(f334(f334(f87(x66272),x66274),x66271),f334(f334(f87(x66272),x66273),x66275)) % 188.18/188.27 [6628]~P5(x66282)+~P59(x66282,x66281,x66284)+~P59(x66282,x66283,x66285)+E(x66281,f2(x66282))+E(x66283,f2(x66282))+~E(f334(f334(f87(x66282),x66284),x66283),f334(f334(f87(x66282),x66281),x66285))+E(f334(f334(f41(x66282),x66284),x66281),f334(f334(f41(x66282),x66285),x66283)) % 188.18/188.27 [7903]~P20(x79032,x79035,x79034)+E(x79031,f195(f935(x79032,a922)))+E(x79033,f195(f935(x79032,a922)))+~P107(f334(f66(x79032),x79031))+~P107(f334(f66(x79032),x79033))+~E(f334(f334(f109(f935(x79032,a922)),x79033),x79031),f195(f935(x79032,a922)))+E(f334(x79034,f334(f334(f108(f935(x79032,a922)),x79033),x79031)),f334(f334(x79035,f334(x79034,x79033)),f334(x79034,x79031))) % 188.18/188.27 [9577]~P27(x95773,x95771,x95775,x95774)+~P27(x95771,x95773,x95776,x95772)+E(f334(f40(x95771),x95772),f334(f40(x95773),x95774))+~P107(f334(f66(x95773),x95774))+~P107(f334(f66(x95771),x95772))+~P107(f334(f334(f242(f935(x95773,a922)),f334(f317(x95771,x95773,x95776),x95772)),x95774))+~P107(f334(f334(f242(f935(x95771,a922)),f334(f317(x95773,x95771,x95775),x95774)),x95772)) % 188.18/188.27 [9525]~P107(f334(f334(f243(a1),f334(f334(f86(a1),f334(f334(f87(a1),x95255),x95251)),x95256)),f2(a1)))+~E(f334(f334(f86(a1),f334(f334(f87(a1),x95253),x95252)),x95254),f334(f334(f86(a1),f334(f334(f87(a1),x95255),x95251)),x95256))+~P107(f334(f334(f242(a1),f2(a1)),x95256))+~P107(f334(f334(f243(a1),f2(a1)),x95255))+~P107(f334(f334(f242(a1),x95255),x95253))+~P107(f334(f334(f243(a1),x95254),x95253))+P107(f334(f334(f242(a1),x95251),x95252)) % 188.18/188.27 [9283]~E(f334(f334(f86(a1),f334(f334(f87(a1),x92833),x92831)),x92834),f334(f334(f86(a1),f334(f334(f87(a1),x92835),x92832)),x92836))+~P107(f334(f334(f242(a1),f2(a1)),x92834))+~P107(f334(f334(f243(a1),f2(a1)),x92835))+~P107(f334(f334(f242(a1),x92835),x92833))+~P107(f334(f334(f243(a1),x92836),x92835))+P107(f334(f334(f242(a1),x92831),x92832))+~P107(f334(f334(f242(a1),f2(a1)),f334(f334(f86(a1),f334(f334(f87(a1),x92835),x92832)),x92836))) % 188.18/188.27 [9458]~P133(x94581)+~E(f334(f334(f86(x94581),x94582),x94584),f84(x94581))+~P107(f334(f334(f242(x94581),x94585),x94586))+~P107(f334(f334(f242(x94581),x94583),x94586))+~P107(f334(f334(f242(x94581),f2(x94581)),x94584))+~P107(f334(f334(f242(x94581),f2(x94581)),x94582))+P107(f334(f334(f242(x94581),f334(f334(f86(x94581),f334(f334(f87(x94581),x94582),x94583)),f334(f334(f87(x94581),x94584),x94585))),x94586)) % 188.18/188.27 [9459]~P131(x94591)+~E(f334(f334(f86(x94591),x94592),x94594),f84(x94591))+~P107(f334(f334(f242(x94591),f2(x94591)),x94594))+~P107(f334(f334(f242(x94591),f2(x94591)),x94592))+~P107(f334(f334(f243(x94591),x94595),x94596))+~P107(f334(f334(f243(x94591),x94593),x94596))+P107(f334(f334(f243(x94591),f334(f334(f86(x94591),f334(f334(f87(x94591),x94592),x94593)),f334(f334(f87(x94591),x94594),x94595))),x94596)) % 188.18/188.27 [10281]~P10(x102817,x102816,x102815)+E(x102811,x102812)+~P13(x102817,f935(x102814,a922),x102815,x102813)+E(f334(x102813,f476(x102811,x102812,x102813,x102814,x102815,x102816,x102817)),f334(x102813,f477(x102811,x102812,x102813,x102814,x102815,x102816,x102817)))+~E(f334(f334(f44(x102817,f935(x102814,a922)),x102811),x102813),f334(f334(f44(x102817,f935(x102814,a922)),x102812),x102813))+~P107(f334(f334(f336(f935(x102817,a922)),x102812),f334(f334(f65(x102817),x102816),x102815)))+~P107(f334(f334(f336(f935(x102817,a922)),x102811),f334(f334(f65(x102817),x102816),x102815))) % 188.18/188.27 [10333]~P10(x103333,x103337,x103336)+E(x103331,x103332)+~P13(x103333,f935(x103335,a922),x103336,x103334)+~E(f334(f334(f44(x103333,f935(x103335,a922)),x103331),x103334),f334(f334(f44(x103333,f935(x103335,a922)),x103332),x103334))+P107(f334(f334(f336(x103333),f477(x103331,x103332,x103334,x103335,x103336,x103337,x103333)),x103337))+~P107(f334(f334(f336(f935(x103333,a922)),x103332),f334(f334(f65(x103333),x103337),x103336)))+~P107(f334(f334(f336(f935(x103333,a922)),x103331),f334(f334(f65(x103333),x103337),x103336))) % 188.18/188.27 [10334]~P10(x103343,x103347,x103346)+E(x103341,x103342)+~P13(x103343,f935(x103345,a922),x103346,x103344)+~E(f334(f334(f44(x103343,f935(x103345,a922)),x103341),x103344),f334(f334(f44(x103343,f935(x103345,a922)),x103342),x103344))+P107(f334(f334(f336(x103343),f476(x103341,x103342,x103344,x103345,x103346,x103347,x103343)),x103347))+~P107(f334(f334(f336(f935(x103343,a922)),x103342),f334(f334(f65(x103343),x103347),x103346)))+~P107(f334(f334(f336(f935(x103343,a922)),x103341),f334(f334(f65(x103343),x103347),x103346))) % 188.18/188.27 [10455]E(x104551,x104552)+~P10(x104553,x104556,x104557)+~P13(x104553,f935(x104554,a922),x104557,x104555)+~E(f334(f334(f44(x104553,f935(x104554,a922)),x104551),x104555),f334(f334(f44(x104553,f935(x104554,a922)),x104552),x104555))+~P107(f334(f334(f336(f934(x104553,x104553)),f334(f334(f260(x104553,x104553),f477(x104551,x104552,x104555,x104554,x104557,x104556,x104553)),f476(x104551,x104552,x104555,x104554,x104557,x104556,x104553))),x104557))+~P107(f334(f334(f336(f935(x104553,a922)),x104552),f334(f334(f65(x104553),x104556),x104557)))+~P107(f334(f334(f336(f935(x104553,a922)),x104551),f334(f334(f65(x104553),x104556),x104557))) % 188.18/188.27 [9282]~P10(x92821,x92827,x92824)+~E(x92825,x92826)+~P107(f334(f334(f336(x92821),x92823),x92826))+~P107(f334(f334(f336(x92821),x92822),x92825))+~P107(f334(f334(f336(f935(x92821,a922)),x92826),f334(f334(f65(x92821),x92827),x92824)))+~P107(f334(f334(f336(f935(x92821,a922)),x92825),f334(f334(f65(x92821),x92827),x92824)))+P107(f334(f334(f336(f934(x92821,x92821)),f334(f334(f260(x92821,x92821),x92822),x92823)),x92824)) % 188.18/188.27 [9419]E(x94191,x94192)+~P10(x94193,x94194,x94195)+~P107(f334(f334(f336(x94193),x94196),x94192))+~P107(f334(f334(f336(x94193),x94197),x94191))+~P107(f334(f334(f336(f935(x94193,a922)),x94192),f334(f334(f65(x94193),x94194),x94195)))+~P107(f334(f334(f336(f935(x94193,a922)),x94191),f334(f334(f65(x94193),x94194),x94195)))+~P107(f334(f334(f336(f934(x94193,x94193)),f334(f334(f260(x94193,x94193),x94197),x94196)),x94195)) % 188.18/188.27 [10486]~P10(x104869,x104868,x104867)+~P10(x104861,x1048611,x1048610)+~P14(x104861,x104869,f935(x104866,a922),x1048610,x104867,x104865)+P107(f334(f334(f336(x104861),f479(x104862,x104863,x104864,x104865,x104866,x104867,x104868,x104869,x1048610,x1048611,x104861)),x1048611))+~P107(f334(f334(f336(f935(x104869,a922)),x104863),f334(f334(f65(x104869),x104868),x104867)))+~P107(f334(f334(f336(f935(x104861,a922)),x104864),f334(f334(f65(x104861),x1048611),x1048610)))+P107(f334(f334(f336(f935(x104866,a922)),f334(f334(f44(x104861,f935(x104866,a922)),x104864),f334(f334(f8(f935(x104869,f935(x104866,a922)),f935(x104866,a922),x104861),f334(f44(x104869,f935(x104866,a922)),x104863)),x104865))),x104862)) % 188.18/188.27 [10487]~P10(x1048711,x1048710,x104879)+~P10(x104871,x104878,x104877)+~P14(x1048711,x104871,f935(x104876,a922),x104879,x104877,x104875)+P107(f334(f334(f336(x104871),f480(x104872,x104873,x104874,x104875,x104876,x104877,x104878,x104871,x104879,x1048710,x1048711)),x104878))+~P107(f334(f334(f336(f935(x1048711,a922)),x104874),f334(f334(f65(x1048711),x1048710),x104879)))+~P107(f334(f334(f336(f935(x104871,a922)),x104873),f334(f334(f65(x104871),x104878),x104877)))+P107(f334(f334(f336(f935(x104876,a922)),f334(f334(f44(x1048711,f935(x104876,a922)),x104874),f334(f334(f8(f935(x104871,f935(x104876,a922)),f935(x104876,a922),x1048711),f334(f44(x104871,f935(x104876,a922)),x104873)),x104875))),x104872)) % 188.18/188.27 [10488]~P10(x104882,x104888,x104889)+~P10(x104884,x1048810,x1048811)+~P14(x104882,x104884,f935(x104881,a922),x104889,x1048811,x104886)+~P107(f334(f334(f336(f935(x104882,a922)),x104883),f334(f334(f65(x104882),x104888),x104889)))+~P107(f334(f334(f336(f935(x104884,a922)),x104885),f334(f334(f65(x104884),x1048810),x1048811)))+~P107(f334(f334(f336(f935(x104881,a922)),f334(f334(x104886,f479(x104887,x104885,x104883,x104886,x104881,x1048811,x1048810,x104884,x104889,x104888,x104882)),f480(x104887,x104885,x104883,x104886,x104881,x1048811,x1048810,x104884,x104889,x104888,x104882))),x104887))+P107(f334(f334(f336(f935(x104881,a922)),f334(f334(f44(x104882,f935(x104881,a922)),x104883),f334(f334(f8(f935(x104884,f935(x104881,a922)),f935(x104881,a922),x104882),f334(f44(x104884,f935(x104881,a922)),x104885)),x104886))),x104887)) % 188.18/188.27 [9312]E(x93121,x93122)+~P109(x93124)+~P27(x93123,x93124,x93125,f334(f334(f108(f935(x93123,a922)),f334(f179(x93123),x93121)),f334(f179(x93123),x93122)))+~E(f334(f179(x93123),x93121),f334(f179(x93123),x93122))+~P15(x93124,f334(f334(f161(x93123,x93124),x93125),x93122))+~P15(x93124,f334(f334(f161(x93123,x93124),x93125),x93121))+~P107(f334(f144(x93124),f334(f334(f161(x93123,x93124),x93125),x93122)))+~P107(f334(f144(x93124),f334(f334(f161(x93123,x93124),x93125),x93121))) % 188.18/188.27 %EqnAxiom % 188.18/188.27 [1]E(x11,x11) % 188.18/188.27 [2]E(x22,x21)+~E(x21,x22) % 188.18/188.27 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 188.18/188.27 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 188.18/188.27 [5]~E(x51,x52)+E(f107(x51),f107(x52)) % 188.18/188.27 [6]~E(x61,x62)+E(f23(x61),f23(x62)) % 188.18/188.27 [7]~E(x71,x72)+E(f195(x71),f195(x72)) % 188.18/188.27 [8]~E(x81,x82)+E(f334(x81,x83),f334(x82,x83)) % 188.18/188.27 [9]~E(x91,x92)+E(f334(x93,x91),f334(x93,x92)) % 188.18/188.27 [10]~E(x101,x102)+E(f29(x101),f29(x102)) % 188.18/188.27 [11]~E(x111,x112)+E(f336(x111),f336(x112)) % 188.18/188.27 [12]~E(x121,x122)+E(f241(x121),f241(x122)) % 188.18/188.27 [13]~E(x131,x132)+E(f108(x131),f108(x132)) % 188.18/188.27 [14]~E(x141,x142)+E(f246(x141),f246(x142)) % 188.18/188.27 [15]~E(x151,x152)+E(f109(x151),f109(x152)) % 188.18/188.27 [16]~E(x161,x162)+E(f110(x161),f110(x162)) % 188.18/188.27 [17]~E(x171,x172)+E(f32(x171),f32(x172)) % 188.18/188.27 [18]~E(x181,x182)+E(f90(x181),f90(x182)) % 188.18/188.27 [19]~E(x191,x192)+E(f7(x191,x193,x194),f7(x192,x193,x194)) % 188.18/188.27 [20]~E(x201,x202)+E(f7(x203,x201,x204),f7(x203,x202,x204)) % 188.18/188.27 [21]~E(x211,x212)+E(f7(x213,x214,x211),f7(x213,x214,x212)) % 188.18/188.27 [22]~E(x221,x222)+E(f69(x221,x223,x224),f69(x222,x223,x224)) % 188.18/188.27 [23]~E(x231,x232)+E(f69(x233,x231,x234),f69(x233,x232,x234)) % 188.18/188.27 [24]~E(x241,x242)+E(f69(x243,x244,x241),f69(x243,x244,x242)) % 188.18/188.27 [25]~E(x251,x252)+E(f480(x251,x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f480(x252,x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 188.18/188.27 [26]~E(x261,x262)+E(f480(x263,x261,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612),f480(x263,x262,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612)) % 188.18/188.27 [27]~E(x271,x272)+E(f480(x273,x274,x271,x275,x276,x277,x278,x279,x2710,x2711,x2712),f480(x273,x274,x272,x275,x276,x277,x278,x279,x2710,x2711,x2712)) % 188.18/188.27 [28]~E(x281,x282)+E(f480(x283,x284,x285,x281,x286,x287,x288,x289,x2810,x2811,x2812),f480(x283,x284,x285,x282,x286,x287,x288,x289,x2810,x2811,x2812)) % 188.18/188.27 [29]~E(x291,x292)+E(f480(x293,x294,x295,x296,x291,x297,x298,x299,x2910,x2911,x2912),f480(x293,x294,x295,x296,x292,x297,x298,x299,x2910,x2911,x2912)) % 188.18/188.27 [30]~E(x301,x302)+E(f480(x303,x304,x305,x306,x307,x301,x308,x309,x3010,x3011,x3012),f480(x303,x304,x305,x306,x307,x302,x308,x309,x3010,x3011,x3012)) % 188.18/188.27 [31]~E(x311,x312)+E(f480(x313,x314,x315,x316,x317,x318,x311,x319,x3110,x3111,x3112),f480(x313,x314,x315,x316,x317,x318,x312,x319,x3110,x3111,x3112)) % 188.18/188.27 [32]~E(x321,x322)+E(f480(x323,x324,x325,x326,x327,x328,x329,x321,x3210,x3211,x3212),f480(x323,x324,x325,x326,x327,x328,x329,x322,x3210,x3211,x3212)) % 188.18/188.27 [33]~E(x331,x332)+E(f480(x333,x334,x335,x336,x337,x338,x339,x3310,x331,x3311,x3312),f480(x333,x334,x335,x336,x337,x338,x339,x3310,x332,x3311,x3312)) % 188.18/188.27 [34]~E(x341,x342)+E(f480(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x341,x3412),f480(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x342,x3412)) % 188.18/188.27 [35]~E(x351,x352)+E(f480(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512,x351),f480(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512,x352)) % 188.18/188.27 [36]~E(x361,x362)+E(f84(x361),f84(x362)) % 188.18/188.27 [37]~E(x371,x372)+E(f935(x371,x373),f935(x372,x373)) % 188.18/188.27 [38]~E(x381,x382)+E(f935(x383,x381),f935(x383,x382)) % 188.18/188.27 [39]~E(x391,x392)+E(f479(x391,x393,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912),f479(x392,x393,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 188.18/188.27 [40]~E(x401,x402)+E(f479(x403,x401,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012),f479(x403,x402,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012)) % 188.18/188.27 [41]~E(x411,x412)+E(f479(x413,x414,x411,x415,x416,x417,x418,x419,x4110,x4111,x4112),f479(x413,x414,x412,x415,x416,x417,x418,x419,x4110,x4111,x4112)) % 188.18/188.27 [42]~E(x421,x422)+E(f479(x423,x424,x425,x421,x426,x427,x428,x429,x4210,x4211,x4212),f479(x423,x424,x425,x422,x426,x427,x428,x429,x4210,x4211,x4212)) % 188.18/188.27 [43]~E(x431,x432)+E(f479(x433,x434,x435,x436,x431,x437,x438,x439,x4310,x4311,x4312),f479(x433,x434,x435,x436,x432,x437,x438,x439,x4310,x4311,x4312)) % 188.18/188.27 [44]~E(x441,x442)+E(f479(x443,x444,x445,x446,x447,x441,x448,x449,x4410,x4411,x4412),f479(x443,x444,x445,x446,x447,x442,x448,x449,x4410,x4411,x4412)) % 188.18/188.27 [45]~E(x451,x452)+E(f479(x453,x454,x455,x456,x457,x458,x451,x459,x4510,x4511,x4512),f479(x453,x454,x455,x456,x457,x458,x452,x459,x4510,x4511,x4512)) % 188.18/188.27 [46]~E(x461,x462)+E(f479(x463,x464,x465,x466,x467,x468,x469,x461,x4610,x4611,x4612),f479(x463,x464,x465,x466,x467,x468,x469,x462,x4610,x4611,x4612)) % 188.18/188.27 [47]~E(x471,x472)+E(f479(x473,x474,x475,x476,x477,x478,x479,x4710,x471,x4711,x4712),f479(x473,x474,x475,x476,x477,x478,x479,x4710,x472,x4711,x4712)) % 188.18/188.27 [48]~E(x481,x482)+E(f479(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x481,x4812),f479(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x482,x4812)) % 188.18/188.27 [49]~E(x491,x492)+E(f479(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x4912,x491),f479(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x4912,x492)) % 188.18/188.27 [50]~E(x501,x502)+E(f4(x501),f4(x502)) % 188.18/188.27 [51]~E(x511,x512)+E(f242(x511),f242(x512)) % 188.18/188.27 [52]~E(x521,x522)+E(f45(x521,x523),f45(x522,x523)) % 188.18/188.27 [53]~E(x531,x532)+E(f45(x533,x531),f45(x533,x532)) % 188.18/188.27 [54]~E(x541,x542)+E(f118(x541),f118(x542)) % 188.18/188.27 [55]~E(x551,x552)+E(f243(x551),f243(x552)) % 188.18/188.27 [56]~E(x561,x562)+E(f926(x561),f926(x562)) % 188.18/188.27 [57]~E(x571,x572)+E(f931(x571),f931(x572)) % 188.18/188.27 [58]~E(x581,x582)+E(f928(x581),f928(x582)) % 188.18/188.27 [59]~E(x591,x592)+E(f929(x591),f929(x592)) % 188.18/188.27 [60]~E(x601,x602)+E(f33(x601),f33(x602)) % 188.18/188.27 [61]~E(x611,x612)+E(f35(x611),f35(x612)) % 188.18/188.27 [62]~E(x621,x622)+E(f8(x621,x623,x624),f8(x622,x623,x624)) % 188.18/188.27 [63]~E(x631,x632)+E(f8(x633,x631,x634),f8(x633,x632,x634)) % 188.18/188.27 [64]~E(x641,x642)+E(f8(x643,x644,x641),f8(x643,x644,x642)) % 188.18/188.27 [65]~E(x651,x652)+E(f34(x651),f34(x652)) % 188.18/188.27 [66]~E(x661,x662)+E(f158(x661),f158(x662)) % 188.18/188.27 [67]~E(x671,x672)+E(f196(x671),f196(x672)) % 188.18/188.27 [68]~E(x681,x682)+E(f85(x681),f85(x682)) % 188.18/188.27 [69]~E(x691,x692)+E(f311(x691,x693,x694),f311(x692,x693,x694)) % 188.18/188.27 [70]~E(x701,x702)+E(f311(x703,x701,x704),f311(x703,x702,x704)) % 188.18/188.27 [71]~E(x711,x712)+E(f311(x713,x714,x711),f311(x713,x714,x712)) % 188.18/188.27 [72]~E(x721,x722)+E(f934(x721,x723),f934(x722,x723)) % 188.18/188.27 [73]~E(x731,x732)+E(f934(x733,x731),f934(x733,x732)) % 188.18/188.27 [74]~E(x741,x742)+E(f144(x741),f144(x742)) % 188.18/188.27 [75]~E(x751,x752)+E(f111(x751),f111(x752)) % 188.18/188.27 [76]~E(x761,x762)+E(f13(x761,x763),f13(x762,x763)) % 188.18/188.27 [77]~E(x771,x772)+E(f13(x773,x771),f13(x773,x772)) % 188.18/188.27 [78]~E(x781,x782)+E(f65(x781),f65(x782)) % 188.18/188.27 [79]~E(x791,x792)+E(f260(x791,x793),f260(x792,x793)) % 188.18/188.27 [80]~E(x801,x802)+E(f260(x803,x801),f260(x803,x802)) % 188.18/188.27 [81]~E(x811,x812)+E(f120(x811),f120(x812)) % 188.18/188.27 [82]~E(x821,x822)+E(f40(x821),f40(x822)) % 188.18/188.27 [83]~E(x831,x832)+E(f316(x831),f316(x832)) % 188.18/188.27 [84]~E(x841,x842)+E(f66(x841),f66(x842)) % 188.18/188.27 [85]~E(x851,x852)+E(f184(x851,x853,x854),f184(x852,x853,x854)) % 188.18/188.27 [86]~E(x861,x862)+E(f184(x863,x861,x864),f184(x863,x862,x864)) % 188.18/188.27 [87]~E(x871,x872)+E(f184(x873,x874,x871),f184(x873,x874,x872)) % 188.18/188.27 [88]~E(x881,x882)+E(f190(x881,x883),f190(x882,x883)) % 188.18/188.27 [89]~E(x891,x892)+E(f190(x893,x891),f190(x893,x892)) % 188.18/188.27 [90]~E(x901,x902)+E(f11(x901,x903,x904),f11(x902,x903,x904)) % 188.18/188.27 [91]~E(x911,x912)+E(f11(x913,x911,x914),f11(x913,x912,x914)) % 188.18/188.27 [92]~E(x921,x922)+E(f11(x923,x924,x921),f11(x923,x924,x922)) % 188.18/188.27 [93]~E(x931,x932)+E(f250(x931),f250(x932)) % 188.18/188.27 [94]~E(x941,x942)+E(f86(x941),f86(x942)) % 188.18/188.27 [95]~E(x951,x952)+E(f174(x951),f174(x952)) % 188.18/188.27 [96]~E(x961,x962)+E(f454(x961,x963,x964),f454(x962,x963,x964)) % 188.18/188.27 [97]~E(x971,x972)+E(f454(x973,x971,x974),f454(x973,x972,x974)) % 188.18/188.27 [98]~E(x981,x982)+E(f454(x983,x984,x981),f454(x983,x984,x982)) % 188.18/188.27 [99]~E(x991,x992)+E(f310(x991,x993),f310(x992,x993)) % 188.18/188.27 [100]~E(x1001,x1002)+E(f310(x1003,x1001),f310(x1003,x1002)) % 188.18/188.27 [101]~E(x1011,x1012)+E(f141(x1011),f141(x1012)) % 188.18/188.27 [102]~E(x1021,x1022)+E(f50(x1021,x1023,x1024),f50(x1022,x1023,x1024)) % 188.18/188.27 [103]~E(x1031,x1032)+E(f50(x1033,x1031,x1034),f50(x1033,x1032,x1034)) % 188.18/188.27 [104]~E(x1041,x1042)+E(f50(x1043,x1044,x1041),f50(x1043,x1044,x1042)) % 188.18/188.27 [105]~E(x1051,x1052)+E(f192(x1051,x1053,x1054,x1055),f192(x1052,x1053,x1054,x1055)) % 188.18/188.27 [106]~E(x1061,x1062)+E(f192(x1063,x1061,x1064,x1065),f192(x1063,x1062,x1064,x1065)) % 188.18/188.27 [107]~E(x1071,x1072)+E(f192(x1073,x1074,x1071,x1075),f192(x1073,x1074,x1072,x1075)) % 188.18/188.27 [108]~E(x1081,x1082)+E(f192(x1083,x1084,x1085,x1081),f192(x1083,x1084,x1085,x1082)) % 188.18/188.27 [109]~E(x1091,x1092)+E(f159(x1091,x1093),f159(x1092,x1093)) % 188.18/188.27 [110]~E(x1101,x1102)+E(f159(x1103,x1101),f159(x1103,x1102)) % 188.18/188.27 [111]~E(x1111,x1112)+E(f87(x1111),f87(x1112)) % 188.18/188.27 [112]~E(x1121,x1122)+E(f317(x1121,x1123,x1124),f317(x1122,x1123,x1124)) % 188.18/188.27 [113]~E(x1131,x1132)+E(f317(x1133,x1131,x1134),f317(x1133,x1132,x1134)) % 188.18/188.27 [114]~E(x1141,x1142)+E(f317(x1143,x1144,x1141),f317(x1143,x1144,x1142)) % 188.18/188.27 [115]~E(x1151,x1152)+E(f18(x1151,x1153,x1154),f18(x1152,x1153,x1154)) % 188.18/188.27 [116]~E(x1161,x1162)+E(f18(x1163,x1161,x1164),f18(x1163,x1162,x1164)) % 188.18/188.27 [117]~E(x1171,x1172)+E(f18(x1173,x1174,x1171),f18(x1173,x1174,x1172)) % 188.18/188.27 [118]~E(x1181,x1182)+E(f259(x1181,x1183),f259(x1182,x1183)) % 188.18/188.27 [119]~E(x1191,x1192)+E(f259(x1193,x1191),f259(x1193,x1192)) % 188.18/188.27 [120]~E(x1201,x1202)+E(f876(x1201,x1203,x1204),f876(x1202,x1203,x1204)) % 188.18/188.27 [121]~E(x1211,x1212)+E(f876(x1213,x1211,x1214),f876(x1213,x1212,x1214)) % 188.18/188.27 [122]~E(x1221,x1222)+E(f876(x1223,x1224,x1221),f876(x1223,x1224,x1222)) % 188.18/188.27 [123]~E(x1231,x1232)+E(f103(x1231),f103(x1232)) % 188.18/188.27 [124]~E(x1241,x1242)+E(f135(x1241,x1243),f135(x1242,x1243)) % 188.18/188.27 [125]~E(x1251,x1252)+E(f135(x1253,x1251),f135(x1253,x1252)) % 188.18/188.27 [126]~E(x1261,x1262)+E(f867(x1261,x1263,x1264),f867(x1262,x1263,x1264)) % 188.18/188.27 [127]~E(x1271,x1272)+E(f867(x1273,x1271,x1274),f867(x1273,x1272,x1274)) % 188.18/188.27 [128]~E(x1281,x1282)+E(f867(x1283,x1284,x1281),f867(x1283,x1284,x1282)) % 188.18/188.27 [129]~E(x1291,x1292)+E(f307(x1291),f307(x1292)) % 188.18/188.27 [130]~E(x1301,x1302)+E(f270(x1301),f270(x1302)) % 188.18/188.27 [131]~E(x1311,x1312)+E(f436(x1311,x1313),f436(x1312,x1313)) % 188.18/188.27 [132]~E(x1321,x1322)+E(f436(x1323,x1321),f436(x1323,x1322)) % 188.18/188.27 [133]~E(x1331,x1332)+E(f70(x1331,x1333,x1334),f70(x1332,x1333,x1334)) % 188.18/188.27 [134]~E(x1341,x1342)+E(f70(x1343,x1341,x1344),f70(x1343,x1342,x1344)) % 188.18/188.27 [135]~E(x1351,x1352)+E(f70(x1353,x1354,x1351),f70(x1353,x1354,x1352)) % 188.18/188.27 [136]~E(x1361,x1362)+E(f442(x1361,x1363),f442(x1362,x1363)) % 188.18/188.27 [137]~E(x1371,x1372)+E(f442(x1373,x1371),f442(x1373,x1372)) % 188.18/188.27 [138]~E(x1381,x1382)+E(f9(x1381,x1383),f9(x1382,x1383)) % 188.18/188.27 [139]~E(x1391,x1392)+E(f9(x1393,x1391),f9(x1393,x1392)) % 188.18/188.27 [140]~E(x1401,x1402)+E(f162(x1401,x1403,x1404),f162(x1402,x1403,x1404)) % 188.18/188.27 [141]~E(x1411,x1412)+E(f162(x1413,x1411,x1414),f162(x1413,x1412,x1414)) % 188.18/188.27 [142]~E(x1421,x1422)+E(f162(x1423,x1424,x1421),f162(x1423,x1424,x1422)) % 188.18/188.27 [143]~E(x1431,x1432)+E(f92(x1431),f92(x1432)) % 188.18/188.27 [144]~E(x1441,x1442)+E(f182(x1441),f182(x1442)) % 188.18/188.27 [145]~E(x1451,x1452)+E(f44(x1451,x1453),f44(x1452,x1453)) % 188.18/188.27 [146]~E(x1461,x1462)+E(f44(x1463,x1461),f44(x1463,x1462)) % 188.18/188.27 [147]~E(x1471,x1472)+E(f292(x1471,x1473,x1474),f292(x1472,x1473,x1474)) % 188.18/188.27 [148]~E(x1481,x1482)+E(f292(x1483,x1481,x1484),f292(x1483,x1482,x1484)) % 188.18/188.27 [149]~E(x1491,x1492)+E(f292(x1493,x1494,x1491),f292(x1493,x1494,x1492)) % 188.18/188.27 [150]~E(x1501,x1502)+E(f252(x1501),f252(x1502)) % 188.18/188.27 [151]~E(x1511,x1512)+E(f296(x1511),f296(x1512)) % 188.18/188.27 [152]~E(x1521,x1522)+E(f113(x1521),f113(x1522)) % 188.18/188.27 [153]~E(x1531,x1532)+E(f114(x1531),f114(x1532)) % 188.18/188.27 [154]~E(x1541,x1542)+E(f335(x1541),f335(x1542)) % 188.18/188.27 [155]~E(x1551,x1552)+E(f907(x1551,x1553,x1554),f907(x1552,x1553,x1554)) % 188.18/188.27 [156]~E(x1561,x1562)+E(f907(x1563,x1561,x1564),f907(x1563,x1562,x1564)) % 188.18/188.27 [157]~E(x1571,x1572)+E(f907(x1573,x1574,x1571),f907(x1573,x1574,x1572)) % 188.18/188.27 [158]~E(x1581,x1582)+E(f579(x1581),f579(x1582)) % 188.18/188.27 [159]~E(x1591,x1592)+E(f186(x1591,x1593),f186(x1592,x1593)) % 188.18/188.27 [160]~E(x1601,x1602)+E(f186(x1603,x1601),f186(x1603,x1602)) % 188.18/188.27 [161]~E(x1611,x1612)+E(f262(x1611,x1613),f262(x1612,x1613)) % 188.18/188.27 [162]~E(x1621,x1622)+E(f262(x1623,x1621),f262(x1623,x1622)) % 188.18/188.27 [163]~E(x1631,x1632)+E(f249(x1631,x1633),f249(x1632,x1633)) % 188.18/188.27 [164]~E(x1641,x1642)+E(f249(x1643,x1641),f249(x1643,x1642)) % 188.18/188.27 [165]~E(x1651,x1652)+E(f143(x1651,x1653),f143(x1652,x1653)) % 188.18/188.27 [166]~E(x1661,x1662)+E(f143(x1663,x1661),f143(x1663,x1662)) % 188.18/188.27 [167]~E(x1671,x1672)+E(f171(x1671),f171(x1672)) % 188.18/188.27 [168]~E(x1681,x1682)+E(f873(x1681,x1683,x1684),f873(x1682,x1683,x1684)) % 188.18/188.27 [169]~E(x1691,x1692)+E(f873(x1693,x1691,x1694),f873(x1693,x1692,x1694)) % 188.18/188.27 [170]~E(x1701,x1702)+E(f873(x1703,x1704,x1701),f873(x1703,x1704,x1702)) % 188.18/188.27 [171]~E(x1711,x1712)+E(f161(x1711,x1713),f161(x1712,x1713)) % 188.18/188.27 [172]~E(x1721,x1722)+E(f161(x1723,x1721),f161(x1723,x1722)) % 188.18/188.27 [173]~E(x1731,x1732)+E(f149(x1731,x1733,x1734,x1735),f149(x1732,x1733,x1734,x1735)) % 188.18/188.27 [174]~E(x1741,x1742)+E(f149(x1743,x1741,x1744,x1745),f149(x1743,x1742,x1744,x1745)) % 188.18/188.27 [175]~E(x1751,x1752)+E(f149(x1753,x1754,x1751,x1755),f149(x1753,x1754,x1752,x1755)) % 188.18/188.27 [176]~E(x1761,x1762)+E(f149(x1763,x1764,x1765,x1761),f149(x1763,x1764,x1765,x1762)) % 188.18/188.27 [177]~E(x1771,x1772)+E(f295(x1771,x1773,x1774),f295(x1772,x1773,x1774)) % 188.18/188.27 [178]~E(x1781,x1782)+E(f295(x1783,x1781,x1784),f295(x1783,x1782,x1784)) % 188.18/188.27 [179]~E(x1791,x1792)+E(f295(x1793,x1794,x1791),f295(x1793,x1794,x1792)) % 188.18/188.27 [180]~E(x1801,x1802)+E(f5(x1801),f5(x1802)) % 188.18/188.27 [181]~E(x1811,x1812)+E(f10(x1811,x1813),f10(x1812,x1813)) % 188.18/188.27 [182]~E(x1821,x1822)+E(f10(x1823,x1821),f10(x1823,x1822)) % 188.18/188.27 [183]~E(x1831,x1832)+E(f750(x1831,x1833,x1834,x1835,x1836),f750(x1832,x1833,x1834,x1835,x1836)) % 188.18/188.27 [184]~E(x1841,x1842)+E(f750(x1843,x1841,x1844,x1845,x1846),f750(x1843,x1842,x1844,x1845,x1846)) % 188.18/188.27 [185]~E(x1851,x1852)+E(f750(x1853,x1854,x1851,x1855,x1856),f750(x1853,x1854,x1852,x1855,x1856)) % 188.18/188.27 [186]~E(x1861,x1862)+E(f750(x1863,x1864,x1865,x1861,x1866),f750(x1863,x1864,x1865,x1862,x1866)) % 188.18/188.27 [187]~E(x1871,x1872)+E(f750(x1873,x1874,x1875,x1876,x1871),f750(x1873,x1874,x1875,x1876,x1872)) % 188.18/188.27 [188]~E(x1881,x1882)+E(f41(x1881),f41(x1882)) % 188.18/188.27 [189]~E(x1891,x1892)+E(f123(x1891,x1893,x1894),f123(x1892,x1893,x1894)) % 188.18/188.27 [190]~E(x1901,x1902)+E(f123(x1903,x1901,x1904),f123(x1903,x1902,x1904)) % 188.18/188.27 [191]~E(x1911,x1912)+E(f123(x1913,x1914,x1911),f123(x1913,x1914,x1912)) % 188.18/188.27 [192]~E(x1921,x1922)+E(f185(x1921,x1923),f185(x1922,x1923)) % 188.18/188.27 [193]~E(x1931,x1932)+E(f185(x1933,x1931),f185(x1933,x1932)) % 188.18/188.27 [194]~E(x1941,x1942)+E(f485(x1941,x1943),f485(x1942,x1943)) % 188.18/188.27 [195]~E(x1951,x1952)+E(f485(x1953,x1951),f485(x1953,x1952)) % 188.18/188.27 [196]~E(x1961,x1962)+E(f382(x1961,x1963,x1964,x1965),f382(x1962,x1963,x1964,x1965)) % 188.18/188.27 [197]~E(x1971,x1972)+E(f382(x1973,x1971,x1974,x1975),f382(x1973,x1972,x1974,x1975)) % 188.18/188.27 [198]~E(x1981,x1982)+E(f382(x1983,x1984,x1981,x1985),f382(x1983,x1984,x1982,x1985)) % 188.18/188.27 [199]~E(x1991,x1992)+E(f382(x1993,x1994,x1995,x1991),f382(x1993,x1994,x1995,x1992)) % 188.18/188.27 [200]~E(x2001,x2002)+E(f12(x2001,x2003,x2004),f12(x2002,x2003,x2004)) % 188.18/188.27 [201]~E(x2011,x2012)+E(f12(x2013,x2011,x2014),f12(x2013,x2012,x2014)) % 188.18/188.27 [202]~E(x2021,x2022)+E(f12(x2023,x2024,x2021),f12(x2023,x2024,x2022)) % 188.18/188.27 [203]~E(x2031,x2032)+E(f732(x2031,x2033,x2034),f732(x2032,x2033,x2034)) % 188.18/188.27 [204]~E(x2041,x2042)+E(f732(x2043,x2041,x2044),f732(x2043,x2042,x2044)) % 188.18/188.27 [205]~E(x2051,x2052)+E(f732(x2053,x2054,x2051),f732(x2053,x2054,x2052)) % 188.18/188.27 [206]~E(x2061,x2062)+E(f172(x2061),f172(x2062)) % 188.18/188.27 [207]~E(x2071,x2072)+E(f14(x2071,x2073),f14(x2072,x2073)) % 188.18/188.27 [208]~E(x2081,x2082)+E(f14(x2083,x2081),f14(x2083,x2082)) % 188.18/188.27 [209]~E(x2091,x2092)+E(f175(x2091),f175(x2092)) % 188.18/188.27 [210]~E(x2101,x2102)+E(f769(x2101,x2103,x2104),f769(x2102,x2103,x2104)) % 188.18/188.27 [211]~E(x2111,x2112)+E(f769(x2113,x2111,x2114),f769(x2113,x2112,x2114)) % 188.18/188.27 [212]~E(x2121,x2122)+E(f769(x2123,x2124,x2121),f769(x2123,x2124,x2122)) % 188.18/188.27 [213]~E(x2131,x2132)+E(f81(x2131),f81(x2132)) % 188.18/188.27 [214]~E(x2141,x2142)+E(f179(x2141),f179(x2142)) % 188.18/188.27 [215]~E(x2151,x2152)+E(f6(x2151,x2153),f6(x2152,x2153)) % 188.18/188.27 [216]~E(x2161,x2162)+E(f6(x2163,x2161),f6(x2163,x2162)) % 188.18/188.27 [217]~E(x2171,x2172)+E(f838(x2171,x2173,x2174),f838(x2172,x2173,x2174)) % 188.18/188.27 [218]~E(x2181,x2182)+E(f838(x2183,x2181,x2184),f838(x2183,x2182,x2184)) % 188.18/188.27 [219]~E(x2191,x2192)+E(f838(x2193,x2194,x2191),f838(x2193,x2194,x2192)) % 188.18/188.27 [220]~E(x2201,x2202)+E(f636(x2201,x2203,x2204,x2205,x2206),f636(x2202,x2203,x2204,x2205,x2206)) % 188.18/188.27 [221]~E(x2211,x2212)+E(f636(x2213,x2211,x2214,x2215,x2216),f636(x2213,x2212,x2214,x2215,x2216)) % 188.18/188.27 [222]~E(x2221,x2222)+E(f636(x2223,x2224,x2221,x2225,x2226),f636(x2223,x2224,x2222,x2225,x2226)) % 188.18/188.27 [223]~E(x2231,x2232)+E(f636(x2233,x2234,x2235,x2231,x2236),f636(x2233,x2234,x2235,x2232,x2236)) % 188.18/188.27 [224]~E(x2241,x2242)+E(f636(x2243,x2244,x2245,x2246,x2241),f636(x2243,x2244,x2245,x2246,x2242)) % 188.18/188.27 [225]~E(x2251,x2252)+E(f563(x2251,x2253,x2254),f563(x2252,x2253,x2254)) % 188.18/188.27 [226]~E(x2261,x2262)+E(f563(x2263,x2261,x2264),f563(x2263,x2262,x2264)) % 188.18/188.27 [227]~E(x2271,x2272)+E(f563(x2273,x2274,x2271),f563(x2273,x2274,x2272)) % 188.18/188.27 [228]~E(x2281,x2282)+E(f15(x2281,x2283),f15(x2282,x2283)) % 188.18/188.27 [229]~E(x2291,x2292)+E(f15(x2293,x2291),f15(x2293,x2292)) % 188.18/188.27 [230]~E(x2301,x2302)+E(f265(x2301,x2303,x2304),f265(x2302,x2303,x2304)) % 188.18/188.27 [231]~E(x2311,x2312)+E(f265(x2313,x2311,x2314),f265(x2313,x2312,x2314)) % 188.18/188.27 [232]~E(x2321,x2322)+E(f265(x2323,x2324,x2321),f265(x2323,x2324,x2322)) % 188.18/188.27 [233]~E(x2331,x2332)+E(f152(x2331,x2333),f152(x2332,x2333)) % 188.18/188.27 [234]~E(x2341,x2342)+E(f152(x2343,x2341),f152(x2343,x2342)) % 188.18/188.27 [235]~E(x2351,x2352)+E(f52(x2351,x2353),f52(x2352,x2353)) % 188.18/188.27 [236]~E(x2361,x2362)+E(f52(x2363,x2361),f52(x2363,x2362)) % 188.18/188.27 [237]~E(x2371,x2372)+E(f164(x2371,x2373),f164(x2372,x2373)) % 188.18/188.27 [238]~E(x2381,x2382)+E(f164(x2383,x2381),f164(x2383,x2382)) % 188.18/188.27 [239]~E(x2391,x2392)+E(f124(x2391,x2393,x2394),f124(x2392,x2393,x2394)) % 188.18/188.27 [240]~E(x2401,x2402)+E(f124(x2403,x2401,x2404),f124(x2403,x2402,x2404)) % 188.18/188.27 [241]~E(x2411,x2412)+E(f124(x2413,x2414,x2411),f124(x2413,x2414,x2412)) % 188.18/188.27 [242]~E(x2421,x2422)+E(f293(x2421,x2423),f293(x2422,x2423)) % 188.18/188.27 [243]~E(x2431,x2432)+E(f293(x2433,x2431),f293(x2433,x2432)) % 188.18/188.27 [244]~E(x2441,x2442)+E(f46(x2441),f46(x2442)) % 188.18/188.27 [245]~E(x2451,x2452)+E(f153(x2451,x2453),f153(x2452,x2453)) % 188.18/188.27 [246]~E(x2461,x2462)+E(f153(x2463,x2461),f153(x2463,x2462)) % 188.18/188.27 [247]~E(x2471,x2472)+E(f526(x2471,x2473,x2474),f526(x2472,x2473,x2474)) % 188.18/188.27 [248]~E(x2481,x2482)+E(f526(x2483,x2481,x2484),f526(x2483,x2482,x2484)) % 188.18/188.27 [249]~E(x2491,x2492)+E(f526(x2493,x2494,x2491),f526(x2493,x2494,x2492)) % 188.18/188.27 [250]~E(x2501,x2502)+E(f264(x2501,x2503),f264(x2502,x2503)) % 188.18/188.27 [251]~E(x2511,x2512)+E(f264(x2513,x2511),f264(x2513,x2512)) % 188.18/188.27 [252]~E(x2521,x2522)+E(f397(x2521,x2523,x2524),f397(x2522,x2523,x2524)) % 188.18/188.27 [253]~E(x2531,x2532)+E(f397(x2533,x2531,x2534),f397(x2533,x2532,x2534)) % 188.18/188.27 [254]~E(x2541,x2542)+E(f397(x2543,x2544,x2541),f397(x2543,x2544,x2542)) % 188.18/188.27 [255]~E(x2551,x2552)+E(f572(x2551,x2553,x2554),f572(x2552,x2553,x2554)) % 188.18/188.27 [256]~E(x2561,x2562)+E(f572(x2563,x2561,x2564),f572(x2563,x2562,x2564)) % 188.18/188.27 [257]~E(x2571,x2572)+E(f572(x2573,x2574,x2571),f572(x2573,x2574,x2572)) % 188.18/188.27 [258]~E(x2581,x2582)+E(f673(x2581,x2583,x2584),f673(x2582,x2583,x2584)) % 188.18/188.27 [259]~E(x2591,x2592)+E(f673(x2593,x2591,x2594),f673(x2593,x2592,x2594)) % 188.18/188.27 [260]~E(x2601,x2602)+E(f673(x2603,x2604,x2601),f673(x2603,x2604,x2602)) % 188.18/188.27 [261]~E(x2611,x2612)+E(f494(x2611,x2613,x2614,x2615),f494(x2612,x2613,x2614,x2615)) % 188.18/188.27 [262]~E(x2621,x2622)+E(f494(x2623,x2621,x2624,x2625),f494(x2623,x2622,x2624,x2625)) % 188.18/188.27 [263]~E(x2631,x2632)+E(f494(x2633,x2634,x2631,x2635),f494(x2633,x2634,x2632,x2635)) % 188.18/188.27 [264]~E(x2641,x2642)+E(f494(x2643,x2644,x2645,x2641),f494(x2643,x2644,x2645,x2642)) % 188.18/188.27 [265]~E(x2651,x2652)+E(f121(x2651,x2653),f121(x2652,x2653)) % 188.18/188.27 [266]~E(x2661,x2662)+E(f121(x2663,x2661),f121(x2663,x2662)) % 188.18/188.27 [267]~E(x2671,x2672)+E(f88(x2671,x2673),f88(x2672,x2673)) % 188.18/188.27 [268]~E(x2681,x2682)+E(f88(x2683,x2681),f88(x2683,x2682)) % 188.18/188.27 [269]~E(x2691,x2692)+E(f289(x2691),f289(x2692)) % 188.18/188.27 [270]~E(x2701,x2702)+E(f68(x2701,x2703),f68(x2702,x2703)) % 188.18/188.27 [271]~E(x2711,x2712)+E(f68(x2713,x2711),f68(x2713,x2712)) % 188.18/188.27 [272]~E(x2721,x2722)+E(f606(x2721,x2723,x2724,x2725),f606(x2722,x2723,x2724,x2725)) % 188.18/188.27 [273]~E(x2731,x2732)+E(f606(x2733,x2731,x2734,x2735),f606(x2733,x2732,x2734,x2735)) % 188.18/188.27 [274]~E(x2741,x2742)+E(f606(x2743,x2744,x2741,x2745),f606(x2743,x2744,x2742,x2745)) % 188.18/188.27 [275]~E(x2751,x2752)+E(f606(x2753,x2754,x2755,x2751),f606(x2753,x2754,x2755,x2752)) % 188.18/188.27 [276]~E(x2761,x2762)+E(f198(x2761),f198(x2762)) % 188.18/188.27 [277]~E(x2771,x2772)+E(f856(x2771,x2773,x2774,x2775,x2776,x2777,x2778,x2779),f856(x2772,x2773,x2774,x2775,x2776,x2777,x2778,x2779)) % 188.18/188.27 [278]~E(x2781,x2782)+E(f856(x2783,x2781,x2784,x2785,x2786,x2787,x2788,x2789),f856(x2783,x2782,x2784,x2785,x2786,x2787,x2788,x2789)) % 188.18/188.27 [279]~E(x2791,x2792)+E(f856(x2793,x2794,x2791,x2795,x2796,x2797,x2798,x2799),f856(x2793,x2794,x2792,x2795,x2796,x2797,x2798,x2799)) % 188.18/188.27 [280]~E(x2801,x2802)+E(f856(x2803,x2804,x2805,x2801,x2806,x2807,x2808,x2809),f856(x2803,x2804,x2805,x2802,x2806,x2807,x2808,x2809)) % 188.18/188.27 [281]~E(x2811,x2812)+E(f856(x2813,x2814,x2815,x2816,x2811,x2817,x2818,x2819),f856(x2813,x2814,x2815,x2816,x2812,x2817,x2818,x2819)) % 188.18/188.27 [282]~E(x2821,x2822)+E(f856(x2823,x2824,x2825,x2826,x2827,x2821,x2828,x2829),f856(x2823,x2824,x2825,x2826,x2827,x2822,x2828,x2829)) % 188.18/188.27 [283]~E(x2831,x2832)+E(f856(x2833,x2834,x2835,x2836,x2837,x2838,x2831,x2839),f856(x2833,x2834,x2835,x2836,x2837,x2838,x2832,x2839)) % 188.18/188.27 [284]~E(x2841,x2842)+E(f856(x2843,x2844,x2845,x2846,x2847,x2848,x2849,x2841),f856(x2843,x2844,x2845,x2846,x2847,x2848,x2849,x2842)) % 188.18/188.27 [285]~E(x2851,x2852)+E(f122(x2851),f122(x2852)) % 188.18/188.27 [286]~E(x2861,x2862)+E(f785(x2861,x2863,x2864,x2865),f785(x2862,x2863,x2864,x2865)) % 188.18/188.27 [287]~E(x2871,x2872)+E(f785(x2873,x2871,x2874,x2875),f785(x2873,x2872,x2874,x2875)) % 188.18/188.27 [288]~E(x2881,x2882)+E(f785(x2883,x2884,x2881,x2885),f785(x2883,x2884,x2882,x2885)) % 188.18/188.27 [289]~E(x2891,x2892)+E(f785(x2893,x2894,x2895,x2891),f785(x2893,x2894,x2895,x2892)) % 188.18/188.27 [290]~E(x2901,x2902)+E(f314(x2901,x2903),f314(x2902,x2903)) % 188.18/188.27 [291]~E(x2911,x2912)+E(f314(x2913,x2911),f314(x2913,x2912)) % 188.18/188.27 [292]~E(x2921,x2922)+E(f167(x2921,x2923),f167(x2922,x2923)) % 188.18/188.27 [293]~E(x2931,x2932)+E(f167(x2933,x2931),f167(x2933,x2932)) % 188.18/188.27 [294]~E(x2941,x2942)+E(f285(x2941,x2943,x2944,x2945),f285(x2942,x2943,x2944,x2945)) % 188.18/188.27 [295]~E(x2951,x2952)+E(f285(x2953,x2951,x2954,x2955),f285(x2953,x2952,x2954,x2955)) % 188.18/188.27 [296]~E(x2961,x2962)+E(f285(x2963,x2964,x2961,x2965),f285(x2963,x2964,x2962,x2965)) % 188.18/188.27 [297]~E(x2971,x2972)+E(f285(x2973,x2974,x2975,x2971),f285(x2973,x2974,x2975,x2972)) % 188.18/188.27 [298]~E(x2981,x2982)+E(f736(x2981,x2983,x2984,x2985),f736(x2982,x2983,x2984,x2985)) % 188.18/188.27 [299]~E(x2991,x2992)+E(f736(x2993,x2991,x2994,x2995),f736(x2993,x2992,x2994,x2995)) % 188.18/188.27 [300]~E(x3001,x3002)+E(f736(x3003,x3004,x3001,x3005),f736(x3003,x3004,x3002,x3005)) % 188.18/188.27 [301]~E(x3011,x3012)+E(f736(x3013,x3014,x3015,x3011),f736(x3013,x3014,x3015,x3012)) % 188.18/188.27 [302]~E(x3021,x3022)+E(f315(x3021),f315(x3022)) % 188.18/188.27 [303]~E(x3031,x3032)+E(f176(x3031,x3033,x3034),f176(x3032,x3033,x3034)) % 188.18/188.27 [304]~E(x3041,x3042)+E(f176(x3043,x3041,x3044),f176(x3043,x3042,x3044)) % 188.18/188.27 [305]~E(x3051,x3052)+E(f176(x3053,x3054,x3051),f176(x3053,x3054,x3052)) % 188.18/188.27 [306]~E(x3061,x3062)+E(f875(x3061,x3063,x3064),f875(x3062,x3063,x3064)) % 188.18/188.27 [307]~E(x3071,x3072)+E(f875(x3073,x3071,x3074),f875(x3073,x3072,x3074)) % 188.18/188.27 [308]~E(x3081,x3082)+E(f875(x3083,x3084,x3081),f875(x3083,x3084,x3082)) % 188.18/188.27 [309]~E(x3091,x3092)+E(f933(x3091,x3093),f933(x3092,x3093)) % 188.18/188.27 [310]~E(x3101,x3102)+E(f933(x3103,x3101),f933(x3103,x3102)) % 188.18/188.27 [311]~E(x3111,x3112)+E(f151(x3111,x3113),f151(x3112,x3113)) % 188.18/188.27 [312]~E(x3121,x3122)+E(f151(x3123,x3121),f151(x3123,x3122)) % 188.18/188.27 [313]~E(x3131,x3132)+E(f932(x3131,x3133),f932(x3132,x3133)) % 188.18/188.27 [314]~E(x3141,x3142)+E(f932(x3143,x3141),f932(x3143,x3142)) % 188.18/188.27 [315]~E(x3151,x3152)+E(f154(x3151,x3153),f154(x3152,x3153)) % 188.18/188.27 [316]~E(x3161,x3162)+E(f154(x3163,x3161),f154(x3163,x3162)) % 188.18/188.27 [317]~E(x3171,x3172)+E(f687(x3171,x3173,x3174),f687(x3172,x3173,x3174)) % 188.18/188.27 [318]~E(x3181,x3182)+E(f687(x3183,x3181,x3184),f687(x3183,x3182,x3184)) % 188.18/188.27 [319]~E(x3191,x3192)+E(f687(x3193,x3194,x3191),f687(x3193,x3194,x3192)) % 188.18/188.27 [320]~E(x3201,x3202)+E(f218(x3201,x3203,x3204,x3205),f218(x3202,x3203,x3204,x3205)) % 188.18/188.27 [321]~E(x3211,x3212)+E(f218(x3213,x3211,x3214,x3215),f218(x3213,x3212,x3214,x3215)) % 188.18/188.27 [322]~E(x3221,x3222)+E(f218(x3223,x3224,x3221,x3225),f218(x3223,x3224,x3222,x3225)) % 188.18/188.27 [323]~E(x3231,x3232)+E(f218(x3233,x3234,x3235,x3231),f218(x3233,x3234,x3235,x3232)) % 188.18/188.27 [324]~E(x3241,x3242)+E(f42(x3241,x3243),f42(x3242,x3243)) % 188.18/188.27 [325]~E(x3251,x3252)+E(f42(x3253,x3251),f42(x3253,x3252)) % 188.18/188.27 [326]~E(x3261,x3262)+E(f178(x3261),f178(x3262)) % 188.18/188.27 [327]~E(x3271,x3272)+E(f266(x3271,x3273,x3274,x3275,x3276,x3277),f266(x3272,x3273,x3274,x3275,x3276,x3277)) % 188.18/188.27 [328]~E(x3281,x3282)+E(f266(x3283,x3281,x3284,x3285,x3286,x3287),f266(x3283,x3282,x3284,x3285,x3286,x3287)) % 188.18/188.27 [329]~E(x3291,x3292)+E(f266(x3293,x3294,x3291,x3295,x3296,x3297),f266(x3293,x3294,x3292,x3295,x3296,x3297)) % 188.18/188.27 [330]~E(x3301,x3302)+E(f266(x3303,x3304,x3305,x3301,x3306,x3307),f266(x3303,x3304,x3305,x3302,x3306,x3307)) % 188.18/188.27 [331]~E(x3311,x3312)+E(f266(x3313,x3314,x3315,x3316,x3311,x3317),f266(x3313,x3314,x3315,x3316,x3312,x3317)) % 188.18/188.27 [332]~E(x3321,x3322)+E(f266(x3323,x3324,x3325,x3326,x3327,x3321),f266(x3323,x3324,x3325,x3326,x3327,x3322)) % 188.18/188.27 [333]~E(x3331,x3332)+E(f767(x3331,x3333,x3334),f767(x3332,x3333,x3334)) % 188.18/188.27 [334]~E(x3341,x3342)+E(f767(x3343,x3341,x3344),f767(x3343,x3342,x3344)) % 188.18/188.27 [335]~E(x3351,x3352)+E(f767(x3353,x3354,x3351),f767(x3353,x3354,x3352)) % 188.18/188.27 [336]~E(x3361,x3362)+E(f274(x3361,x3363),f274(x3362,x3363)) % 188.18/188.27 [337]~E(x3371,x3372)+E(f274(x3373,x3371),f274(x3373,x3372)) % 188.18/188.27 [338]~E(x3381,x3382)+E(f610(x3381,x3383,x3384),f610(x3382,x3383,x3384)) % 188.18/188.27 [339]~E(x3391,x3392)+E(f610(x3393,x3391,x3394),f610(x3393,x3392,x3394)) % 188.18/188.27 [340]~E(x3401,x3402)+E(f610(x3403,x3404,x3401),f610(x3403,x3404,x3402)) % 188.18/188.27 [341]~E(x3411,x3412)+E(f877(x3411,x3413,x3414),f877(x3412,x3413,x3414)) % 188.18/188.27 [342]~E(x3421,x3422)+E(f877(x3423,x3421,x3424),f877(x3423,x3422,x3424)) % 188.18/188.27 [343]~E(x3431,x3432)+E(f877(x3433,x3434,x3431),f877(x3433,x3434,x3432)) % 188.18/188.27 [344]~E(x3441,x3442)+E(f632(x3441,x3443,x3444),f632(x3442,x3443,x3444)) % 188.18/188.27 [345]~E(x3451,x3452)+E(f632(x3453,x3451,x3454),f632(x3453,x3452,x3454)) % 188.18/188.27 [346]~E(x3461,x3462)+E(f632(x3463,x3464,x3461),f632(x3463,x3464,x3462)) % 188.18/188.27 [347]~E(x3471,x3472)+E(f51(x3471,x3473),f51(x3472,x3473)) % 188.18/188.27 [348]~E(x3481,x3482)+E(f51(x3483,x3481),f51(x3483,x3482)) % 188.18/188.27 [349]~E(x3491,x3492)+E(f206(x3491,x3493,x3494,x3495),f206(x3492,x3493,x3494,x3495)) % 188.18/188.27 [350]~E(x3501,x3502)+E(f206(x3503,x3501,x3504,x3505),f206(x3503,x3502,x3504,x3505)) % 188.18/188.27 [351]~E(x3511,x3512)+E(f206(x3513,x3514,x3511,x3515),f206(x3513,x3514,x3512,x3515)) % 188.18/188.27 [352]~E(x3521,x3522)+E(f206(x3523,x3524,x3525,x3521),f206(x3523,x3524,x3525,x3522)) % 188.18/188.27 [353]~E(x3531,x3532)+E(f224(x3531,x3533),f224(x3532,x3533)) % 188.18/188.27 [354]~E(x3541,x3542)+E(f224(x3543,x3541),f224(x3543,x3542)) % 188.18/188.27 [355]~E(x3551,x3552)+E(f263(x3551,x3553,x3554,x3555),f263(x3552,x3553,x3554,x3555)) % 188.18/188.27 [356]~E(x3561,x3562)+E(f263(x3563,x3561,x3564,x3565),f263(x3563,x3562,x3564,x3565)) % 188.18/188.27 [357]~E(x3571,x3572)+E(f263(x3573,x3574,x3571,x3575),f263(x3573,x3574,x3572,x3575)) % 188.18/188.27 [358]~E(x3581,x3582)+E(f263(x3583,x3584,x3585,x3581),f263(x3583,x3584,x3585,x3582)) % 188.18/188.27 [359]~E(x3591,x3592)+E(f188(x3591,x3593),f188(x3592,x3593)) % 188.18/188.27 [360]~E(x3601,x3602)+E(f188(x3603,x3601),f188(x3603,x3602)) % 188.18/188.27 [361]~E(x3611,x3612)+E(f26(x3611,x3613),f26(x3612,x3613)) % 188.18/188.27 [362]~E(x3621,x3622)+E(f26(x3623,x3621),f26(x3623,x3622)) % 188.18/188.27 [363]~E(x3631,x3632)+E(f496(x3631,x3633,x3634,x3635),f496(x3632,x3633,x3634,x3635)) % 188.18/188.27 [364]~E(x3641,x3642)+E(f496(x3643,x3641,x3644,x3645),f496(x3643,x3642,x3644,x3645)) % 188.18/188.27 [365]~E(x3651,x3652)+E(f496(x3653,x3654,x3651,x3655),f496(x3653,x3654,x3652,x3655)) % 188.18/188.27 [366]~E(x3661,x3662)+E(f496(x3663,x3664,x3665,x3661),f496(x3663,x3664,x3665,x3662)) % 188.18/188.27 [367]~E(x3671,x3672)+E(f573(x3671,x3673,x3674),f573(x3672,x3673,x3674)) % 188.18/188.27 [368]~E(x3681,x3682)+E(f573(x3683,x3681,x3684),f573(x3683,x3682,x3684)) % 188.18/188.27 [369]~E(x3691,x3692)+E(f573(x3693,x3694,x3691),f573(x3693,x3694,x3692)) % 188.18/188.27 [370]~E(x3701,x3702)+E(f403(x3701,x3703,x3704,x3705,x3706),f403(x3702,x3703,x3704,x3705,x3706)) % 188.18/188.27 [371]~E(x3711,x3712)+E(f403(x3713,x3711,x3714,x3715,x3716),f403(x3713,x3712,x3714,x3715,x3716)) % 188.18/188.27 [372]~E(x3721,x3722)+E(f403(x3723,x3724,x3721,x3725,x3726),f403(x3723,x3724,x3722,x3725,x3726)) % 188.18/188.27 [373]~E(x3731,x3732)+E(f403(x3733,x3734,x3735,x3731,x3736),f403(x3733,x3734,x3735,x3732,x3736)) % 188.18/188.27 [374]~E(x3741,x3742)+E(f403(x3743,x3744,x3745,x3746,x3741),f403(x3743,x3744,x3745,x3746,x3742)) % 188.18/188.27 [375]~E(x3751,x3752)+E(f325(x3751,x3753),f325(x3752,x3753)) % 188.18/188.27 [376]~E(x3761,x3762)+E(f325(x3763,x3761),f325(x3763,x3762)) % 188.18/188.27 [377]~E(x3771,x3772)+E(f668(x3771,x3773,x3774,x3775,x3776),f668(x3772,x3773,x3774,x3775,x3776)) % 188.18/188.27 [378]~E(x3781,x3782)+E(f668(x3783,x3781,x3784,x3785,x3786),f668(x3783,x3782,x3784,x3785,x3786)) % 188.18/188.27 [379]~E(x3791,x3792)+E(f668(x3793,x3794,x3791,x3795,x3796),f668(x3793,x3794,x3792,x3795,x3796)) % 188.18/188.27 [380]~E(x3801,x3802)+E(f668(x3803,x3804,x3805,x3801,x3806),f668(x3803,x3804,x3805,x3802,x3806)) % 188.18/188.27 [381]~E(x3811,x3812)+E(f668(x3813,x3814,x3815,x3816,x3811),f668(x3813,x3814,x3815,x3816,x3812)) % 188.18/188.27 [382]~E(x3821,x3822)+E(f327(x3821,x3823),f327(x3822,x3823)) % 188.18/188.27 [383]~E(x3831,x3832)+E(f327(x3833,x3831),f327(x3833,x3832)) % 188.18/188.27 [384]~E(x3841,x3842)+E(f318(x3841,x3843,x3844),f318(x3842,x3843,x3844)) % 188.18/188.27 [385]~E(x3851,x3852)+E(f318(x3853,x3851,x3854),f318(x3853,x3852,x3854)) % 188.18/188.27 [386]~E(x3861,x3862)+E(f318(x3863,x3864,x3861),f318(x3863,x3864,x3862)) % 188.18/188.27 [387]~E(x3871,x3872)+E(f165(x3871,x3873),f165(x3872,x3873)) % 188.18/188.27 [388]~E(x3881,x3882)+E(f165(x3883,x3881),f165(x3883,x3882)) % 188.18/188.27 [389]~E(x3891,x3892)+E(f566(x3891,x3893,x3894),f566(x3892,x3893,x3894)) % 188.18/188.27 [390]~E(x3901,x3902)+E(f566(x3903,x3901,x3904),f566(x3903,x3902,x3904)) % 188.18/188.27 [391]~E(x3911,x3912)+E(f566(x3913,x3914,x3911),f566(x3913,x3914,x3912)) % 188.18/188.27 [392]~E(x3921,x3922)+E(f136(x3921),f136(x3922)) % 188.18/188.27 [393]~E(x3931,x3932)+E(f383(x3931,x3933,x3934,x3935),f383(x3932,x3933,x3934,x3935)) % 188.18/188.27 [394]~E(x3941,x3942)+E(f383(x3943,x3941,x3944,x3945),f383(x3943,x3942,x3944,x3945)) % 188.18/188.27 [395]~E(x3951,x3952)+E(f383(x3953,x3954,x3951,x3955),f383(x3953,x3954,x3952,x3955)) % 188.18/188.27 [396]~E(x3961,x3962)+E(f383(x3963,x3964,x3965,x3961),f383(x3963,x3964,x3965,x3962)) % 188.18/188.27 [397]~E(x3971,x3972)+E(f97(x3971,x3973,x3974,x3975),f97(x3972,x3973,x3974,x3975)) % 188.18/188.27 [398]~E(x3981,x3982)+E(f97(x3983,x3981,x3984,x3985),f97(x3983,x3982,x3984,x3985)) % 188.18/188.27 [399]~E(x3991,x3992)+E(f97(x3993,x3994,x3991,x3995),f97(x3993,x3994,x3992,x3995)) % 188.18/188.27 [400]~E(x4001,x4002)+E(f97(x4003,x4004,x4005,x4001),f97(x4003,x4004,x4005,x4002)) % 188.18/188.27 [401]~E(x4011,x4012)+E(f913(x4011,x4013,x4014),f913(x4012,x4013,x4014)) % 188.18/188.27 [402]~E(x4021,x4022)+E(f913(x4023,x4021,x4024),f913(x4023,x4022,x4024)) % 188.18/188.27 [403]~E(x4031,x4032)+E(f913(x4033,x4034,x4031),f913(x4033,x4034,x4032)) % 188.18/188.27 [404]~E(x4041,x4042)+E(f745(x4041,x4043),f745(x4042,x4043)) % 188.18/188.27 [405]~E(x4051,x4052)+E(f745(x4053,x4051),f745(x4053,x4052)) % 188.18/188.27 [406]~E(x4061,x4062)+E(f96(x4061,x4063),f96(x4062,x4063)) % 188.18/188.27 [407]~E(x4071,x4072)+E(f96(x4073,x4071),f96(x4073,x4072)) % 188.18/188.27 [408]~E(x4081,x4082)+E(f58(x4081,x4083),f58(x4082,x4083)) % 188.18/188.27 [409]~E(x4091,x4092)+E(f58(x4093,x4091),f58(x4093,x4092)) % 188.18/188.27 [410]~E(x4101,x4102)+E(f91(x4101,x4103),f91(x4102,x4103)) % 188.18/188.27 [411]~E(x4111,x4112)+E(f91(x4113,x4111),f91(x4113,x4112)) % 188.18/188.27 [412]~E(x4121,x4122)+E(f739(x4121,x4123),f739(x4122,x4123)) % 188.18/188.27 [413]~E(x4131,x4132)+E(f739(x4133,x4131),f739(x4133,x4132)) % 188.18/188.27 [414]~E(x4141,x4142)+E(f261(x4141,x4143,x4144,x4145,x4146),f261(x4142,x4143,x4144,x4145,x4146)) % 188.18/188.27 [415]~E(x4151,x4152)+E(f261(x4153,x4151,x4154,x4155,x4156),f261(x4153,x4152,x4154,x4155,x4156)) % 188.18/188.27 [416]~E(x4161,x4162)+E(f261(x4163,x4164,x4161,x4165,x4166),f261(x4163,x4164,x4162,x4165,x4166)) % 188.18/188.27 [417]~E(x4171,x4172)+E(f261(x4173,x4174,x4175,x4171,x4176),f261(x4173,x4174,x4175,x4172,x4176)) % 188.18/188.27 [418]~E(x4181,x4182)+E(f261(x4183,x4184,x4185,x4186,x4181),f261(x4183,x4184,x4185,x4186,x4182)) % 188.18/188.27 [419]~E(x4191,x4192)+E(f354(x4191,x4193),f354(x4192,x4193)) % 188.18/188.27 [420]~E(x4201,x4202)+E(f354(x4203,x4201),f354(x4203,x4202)) % 188.18/188.27 [421]~E(x4211,x4212)+E(f126(x4211),f126(x4212)) % 188.18/188.27 [422]~E(x4221,x4222)+E(f127(x4221,x4223),f127(x4222,x4223)) % 188.18/188.27 [423]~E(x4231,x4232)+E(f127(x4233,x4231),f127(x4233,x4232)) % 188.18/188.27 [424]~E(x4241,x4242)+E(f16(x4241,x4243),f16(x4242,x4243)) % 188.18/188.27 [425]~E(x4251,x4252)+E(f16(x4253,x4251),f16(x4253,x4252)) % 188.18/188.27 [426]~E(x4261,x4262)+E(f267(x4261,x4263,x4264,x4265),f267(x4262,x4263,x4264,x4265)) % 188.18/188.27 [427]~E(x4271,x4272)+E(f267(x4273,x4271,x4274,x4275),f267(x4273,x4272,x4274,x4275)) % 188.18/188.27 [428]~E(x4281,x4282)+E(f267(x4283,x4284,x4281,x4285),f267(x4283,x4284,x4282,x4285)) % 188.18/188.27 [429]~E(x4291,x4292)+E(f267(x4293,x4294,x4295,x4291),f267(x4293,x4294,x4295,x4292)) % 188.18/188.27 [430]~E(x4301,x4302)+E(f763(x4301,x4303),f763(x4302,x4303)) % 188.18/188.27 [431]~E(x4311,x4312)+E(f763(x4313,x4311),f763(x4313,x4312)) % 188.18/188.27 [432]~E(x4321,x4322)+E(f823(x4321),f823(x4322)) % 188.18/188.27 [433]~E(x4331,x4332)+E(f43(x4331,x4333),f43(x4332,x4333)) % 188.18/188.27 [434]~E(x4341,x4342)+E(f43(x4343,x4341),f43(x4343,x4342)) % 188.18/188.27 [435]~E(x4351,x4352)+E(f291(x4351,x4353),f291(x4352,x4353)) % 188.18/188.27 [436]~E(x4361,x4362)+E(f291(x4363,x4361),f291(x4363,x4362)) % 188.18/188.27 [437]~E(x4371,x4372)+E(f866(x4371,x4373,x4374),f866(x4372,x4373,x4374)) % 188.18/188.27 [438]~E(x4381,x4382)+E(f866(x4383,x4381,x4384),f866(x4383,x4382,x4384)) % 188.18/188.27 [439]~E(x4391,x4392)+E(f866(x4393,x4394,x4391),f866(x4393,x4394,x4392)) % 188.18/188.27 [440]~E(x4401,x4402)+E(f811(x4401,x4403,x4404,x4405),f811(x4402,x4403,x4404,x4405)) % 188.18/188.27 [441]~E(x4411,x4412)+E(f811(x4413,x4411,x4414,x4415),f811(x4413,x4412,x4414,x4415)) % 188.18/188.27 [442]~E(x4421,x4422)+E(f811(x4423,x4424,x4421,x4425),f811(x4423,x4424,x4422,x4425)) % 188.18/188.27 [443]~E(x4431,x4432)+E(f811(x4433,x4434,x4435,x4431),f811(x4433,x4434,x4435,x4432)) % 188.18/188.27 [444]~E(x4441,x4442)+E(f160(x4441,x4443),f160(x4442,x4443)) % 188.18/188.27 [445]~E(x4451,x4452)+E(f160(x4453,x4451),f160(x4453,x4452)) % 188.18/188.27 [446]~E(x4461,x4462)+E(f271(x4461,x4463),f271(x4462,x4463)) % 188.18/188.27 [447]~E(x4471,x4472)+E(f271(x4473,x4471),f271(x4473,x4472)) % 188.18/188.27 [448]~E(x4481,x4482)+E(f747(x4481,x4483),f747(x4482,x4483)) % 188.18/188.27 [449]~E(x4491,x4492)+E(f747(x4493,x4491),f747(x4493,x4492)) % 188.18/188.27 [450]~E(x4501,x4502)+E(f773(x4501,x4503,x4504),f773(x4502,x4503,x4504)) % 188.18/188.27 [451]~E(x4511,x4512)+E(f773(x4513,x4511,x4514),f773(x4513,x4512,x4514)) % 188.18/188.27 [452]~E(x4521,x4522)+E(f773(x4523,x4524,x4521),f773(x4523,x4524,x4522)) % 188.18/188.27 [453]~E(x4531,x4532)+E(f458(x4531,x4533,x4534,x4535),f458(x4532,x4533,x4534,x4535)) % 188.18/188.27 [454]~E(x4541,x4542)+E(f458(x4543,x4541,x4544,x4545),f458(x4543,x4542,x4544,x4545)) % 188.18/188.27 [455]~E(x4551,x4552)+E(f458(x4553,x4554,x4551,x4555),f458(x4553,x4554,x4552,x4555)) % 188.18/188.27 [456]~E(x4561,x4562)+E(f458(x4563,x4564,x4565,x4561),f458(x4563,x4564,x4565,x4562)) % 188.18/188.27 [457]~E(x4571,x4572)+E(f221(x4571),f221(x4572)) % 188.18/188.27 [458]~E(x4581,x4582)+E(f746(x4581,x4583,x4584,x4585,x4586,x4587,x4588,x4589),f746(x4582,x4583,x4584,x4585,x4586,x4587,x4588,x4589)) % 188.18/188.27 [459]~E(x4591,x4592)+E(f746(x4593,x4591,x4594,x4595,x4596,x4597,x4598,x4599),f746(x4593,x4592,x4594,x4595,x4596,x4597,x4598,x4599)) % 188.18/188.27 [460]~E(x4601,x4602)+E(f746(x4603,x4604,x4601,x4605,x4606,x4607,x4608,x4609),f746(x4603,x4604,x4602,x4605,x4606,x4607,x4608,x4609)) % 188.18/188.27 [461]~E(x4611,x4612)+E(f746(x4613,x4614,x4615,x4611,x4616,x4617,x4618,x4619),f746(x4613,x4614,x4615,x4612,x4616,x4617,x4618,x4619)) % 188.18/188.27 [462]~E(x4621,x4622)+E(f746(x4623,x4624,x4625,x4626,x4621,x4627,x4628,x4629),f746(x4623,x4624,x4625,x4626,x4622,x4627,x4628,x4629)) % 188.18/188.27 [463]~E(x4631,x4632)+E(f746(x4633,x4634,x4635,x4636,x4637,x4631,x4638,x4639),f746(x4633,x4634,x4635,x4636,x4637,x4632,x4638,x4639)) % 188.18/188.27 [464]~E(x4641,x4642)+E(f746(x4643,x4644,x4645,x4646,x4647,x4648,x4641,x4649),f746(x4643,x4644,x4645,x4646,x4647,x4648,x4642,x4649)) % 188.18/188.27 [465]~E(x4651,x4652)+E(f746(x4653,x4654,x4655,x4656,x4657,x4658,x4659,x4651),f746(x4653,x4654,x4655,x4656,x4657,x4658,x4659,x4652)) % 188.18/188.27 [466]~E(x4661,x4662)+E(f145(x4661),f145(x4662)) % 188.18/188.27 [467]~E(x4671,x4672)+E(f653(x4671,x4673,x4674,x4675,x4676),f653(x4672,x4673,x4674,x4675,x4676)) % 188.18/188.27 [468]~E(x4681,x4682)+E(f653(x4683,x4681,x4684,x4685,x4686),f653(x4683,x4682,x4684,x4685,x4686)) % 188.18/188.27 [469]~E(x4691,x4692)+E(f653(x4693,x4694,x4691,x4695,x4696),f653(x4693,x4694,x4692,x4695,x4696)) % 188.18/188.27 [470]~E(x4701,x4702)+E(f653(x4703,x4704,x4705,x4701,x4706),f653(x4703,x4704,x4705,x4702,x4706)) % 188.18/188.27 [471]~E(x4711,x4712)+E(f653(x4713,x4714,x4715,x4716,x4711),f653(x4713,x4714,x4715,x4716,x4712)) % 188.18/188.27 [472]~E(x4721,x4722)+E(f872(x4721,x4723,x4724),f872(x4722,x4723,x4724)) % 188.18/188.27 [473]~E(x4731,x4732)+E(f872(x4733,x4731,x4734),f872(x4733,x4732,x4734)) % 188.18/188.27 [474]~E(x4741,x4742)+E(f872(x4743,x4744,x4741),f872(x4743,x4744,x4742)) % 188.18/188.27 [475]~E(x4751,x4752)+E(f712(x4751,x4753,x4754,x4755,x4756),f712(x4752,x4753,x4754,x4755,x4756)) % 188.18/188.27 [476]~E(x4761,x4762)+E(f712(x4763,x4761,x4764,x4765,x4766),f712(x4763,x4762,x4764,x4765,x4766)) % 188.18/188.27 [477]~E(x4771,x4772)+E(f712(x4773,x4774,x4771,x4775,x4776),f712(x4773,x4774,x4772,x4775,x4776)) % 188.18/188.27 [478]~E(x4781,x4782)+E(f712(x4783,x4784,x4785,x4781,x4786),f712(x4783,x4784,x4785,x4782,x4786)) % 188.18/188.27 [479]~E(x4791,x4792)+E(f712(x4793,x4794,x4795,x4796,x4791),f712(x4793,x4794,x4795,x4796,x4792)) % 188.18/188.27 [480]~E(x4801,x4802)+E(f71(x4801,x4803,x4804,x4805,x4806),f71(x4802,x4803,x4804,x4805,x4806)) % 188.18/188.27 [481]~E(x4811,x4812)+E(f71(x4813,x4811,x4814,x4815,x4816),f71(x4813,x4812,x4814,x4815,x4816)) % 188.18/188.27 [482]~E(x4821,x4822)+E(f71(x4823,x4824,x4821,x4825,x4826),f71(x4823,x4824,x4822,x4825,x4826)) % 188.18/188.27 [483]~E(x4831,x4832)+E(f71(x4833,x4834,x4835,x4831,x4836),f71(x4833,x4834,x4835,x4832,x4836)) % 188.18/188.27 [484]~E(x4841,x4842)+E(f71(x4843,x4844,x4845,x4846,x4841),f71(x4843,x4844,x4845,x4846,x4842)) % 188.18/188.27 [485]~E(x4851,x4852)+E(f94(x4851,x4853),f94(x4852,x4853)) % 188.18/188.27 [486]~E(x4861,x4862)+E(f94(x4863,x4861),f94(x4863,x4862)) % 188.18/188.27 [487]~E(x4871,x4872)+E(f166(x4871,x4873),f166(x4872,x4873)) % 188.18/188.27 [488]~E(x4881,x4882)+E(f166(x4883,x4881),f166(x4883,x4882)) % 188.18/188.27 [489]~E(x4891,x4892)+E(f827(x4891,x4893,x4894,x4895,x4896,x4897),f827(x4892,x4893,x4894,x4895,x4896,x4897)) % 188.18/188.27 [490]~E(x4901,x4902)+E(f827(x4903,x4901,x4904,x4905,x4906,x4907),f827(x4903,x4902,x4904,x4905,x4906,x4907)) % 188.18/188.27 [491]~E(x4911,x4912)+E(f827(x4913,x4914,x4911,x4915,x4916,x4917),f827(x4913,x4914,x4912,x4915,x4916,x4917)) % 188.18/188.27 [492]~E(x4921,x4922)+E(f827(x4923,x4924,x4925,x4921,x4926,x4927),f827(x4923,x4924,x4925,x4922,x4926,x4927)) % 188.18/188.27 [493]~E(x4931,x4932)+E(f827(x4933,x4934,x4935,x4936,x4931,x4937),f827(x4933,x4934,x4935,x4936,x4932,x4937)) % 188.18/188.27 [494]~E(x4941,x4942)+E(f827(x4943,x4944,x4945,x4946,x4947,x4941),f827(x4943,x4944,x4945,x4946,x4947,x4942)) % 188.18/188.27 [495]~E(x4951,x4952)+E(f407(x4951,x4953,x4954,x4955,x4956),f407(x4952,x4953,x4954,x4955,x4956)) % 188.18/188.27 [496]~E(x4961,x4962)+E(f407(x4963,x4961,x4964,x4965,x4966),f407(x4963,x4962,x4964,x4965,x4966)) % 188.18/188.27 [497]~E(x4971,x4972)+E(f407(x4973,x4974,x4971,x4975,x4976),f407(x4973,x4974,x4972,x4975,x4976)) % 188.18/188.27 [498]~E(x4981,x4982)+E(f407(x4983,x4984,x4985,x4981,x4986),f407(x4983,x4984,x4985,x4982,x4986)) % 188.18/188.27 [499]~E(x4991,x4992)+E(f407(x4993,x4994,x4995,x4996,x4991),f407(x4993,x4994,x4995,x4996,x4992)) % 188.18/188.27 [500]~E(x5001,x5002)+E(f565(x5001,x5003,x5004),f565(x5002,x5003,x5004)) % 188.18/188.27 [501]~E(x5011,x5012)+E(f565(x5013,x5011,x5014),f565(x5013,x5012,x5014)) % 188.18/188.27 [502]~E(x5021,x5022)+E(f565(x5023,x5024,x5021),f565(x5023,x5024,x5022)) % 188.18/188.27 [503]~E(x5031,x5032)+E(f308(x5031),f308(x5032)) % 188.18/188.27 [504]~E(x5041,x5042)+E(f720(x5041,x5043),f720(x5042,x5043)) % 188.18/188.27 [505]~E(x5051,x5052)+E(f720(x5053,x5051),f720(x5053,x5052)) % 188.18/188.27 [506]~E(x5061,x5062)+E(f323(x5061,x5063),f323(x5062,x5063)) % 188.18/188.27 [507]~E(x5071,x5072)+E(f323(x5073,x5071),f323(x5073,x5072)) % 188.18/188.27 [508]~E(x5081,x5082)+E(f373(x5081,x5083),f373(x5082,x5083)) % 188.18/188.27 [509]~E(x5091,x5092)+E(f373(x5093,x5091),f373(x5093,x5092)) % 188.18/188.27 [510]~E(x5101,x5102)+E(f83(x5101,x5103,x5104,x5105),f83(x5102,x5103,x5104,x5105)) % 188.18/188.27 [511]~E(x5111,x5112)+E(f83(x5113,x5111,x5114,x5115),f83(x5113,x5112,x5114,x5115)) % 188.18/188.27 [512]~E(x5121,x5122)+E(f83(x5123,x5124,x5121,x5125),f83(x5123,x5124,x5122,x5125)) % 188.18/188.27 [513]~E(x5131,x5132)+E(f83(x5133,x5134,x5135,x5131),f83(x5133,x5134,x5135,x5132)) % 188.18/188.27 [514]~E(x5141,x5142)+E(f320(x5141,x5143,x5144,x5145),f320(x5142,x5143,x5144,x5145)) % 188.18/188.27 [515]~E(x5151,x5152)+E(f320(x5153,x5151,x5154,x5155),f320(x5153,x5152,x5154,x5155)) % 188.18/188.27 [516]~E(x5161,x5162)+E(f320(x5163,x5164,x5161,x5165),f320(x5163,x5164,x5162,x5165)) % 188.18/188.27 [517]~E(x5171,x5172)+E(f320(x5173,x5174,x5175,x5171),f320(x5173,x5174,x5175,x5172)) % 188.18/188.27 [518]~E(x5181,x5182)+E(f98(x5181,x5183,x5184,x5185),f98(x5182,x5183,x5184,x5185)) % 188.18/188.27 [519]~E(x5191,x5192)+E(f98(x5193,x5191,x5194,x5195),f98(x5193,x5192,x5194,x5195)) % 188.18/188.27 [520]~E(x5201,x5202)+E(f98(x5203,x5204,x5201,x5205),f98(x5203,x5204,x5202,x5205)) % 188.18/188.27 [521]~E(x5211,x5212)+E(f98(x5213,x5214,x5215,x5211),f98(x5213,x5214,x5215,x5212)) % 188.18/188.27 [522]~E(x5221,x5222)+E(f908(x5221,x5223,x5224),f908(x5222,x5223,x5224)) % 188.18/188.27 [523]~E(x5231,x5232)+E(f908(x5233,x5231,x5234),f908(x5233,x5232,x5234)) % 188.18/188.27 [524]~E(x5241,x5242)+E(f908(x5243,x5244,x5241),f908(x5243,x5244,x5242)) % 188.18/188.27 [525]~E(x5251,x5252)+E(f800(x5251,x5253,x5254,x5255),f800(x5252,x5253,x5254,x5255)) % 188.18/188.27 [526]~E(x5261,x5262)+E(f800(x5263,x5261,x5264,x5265),f800(x5263,x5262,x5264,x5265)) % 188.18/188.27 [527]~E(x5271,x5272)+E(f800(x5273,x5274,x5271,x5275),f800(x5273,x5274,x5272,x5275)) % 188.18/188.27 [528]~E(x5281,x5282)+E(f800(x5283,x5284,x5285,x5281),f800(x5283,x5284,x5285,x5282)) % 188.18/188.27 [529]~E(x5291,x5292)+E(f741(x5291,x5293,x5294,x5295),f741(x5292,x5293,x5294,x5295)) % 188.18/188.27 [530]~E(x5301,x5302)+E(f741(x5303,x5301,x5304,x5305),f741(x5303,x5302,x5304,x5305)) % 188.18/188.27 [531]~E(x5311,x5312)+E(f741(x5313,x5314,x5311,x5315),f741(x5313,x5314,x5312,x5315)) % 188.18/188.27 [532]~E(x5321,x5322)+E(f741(x5323,x5324,x5325,x5321),f741(x5323,x5324,x5325,x5322)) % 188.18/188.27 [533]~E(x5331,x5332)+E(f321(x5331),f321(x5332)) % 188.18/188.27 [534]~E(x5341,x5342)+E(f193(x5341),f193(x5342)) % 188.18/188.27 [535]~E(x5351,x5352)+E(f664(x5351,x5353,x5354,x5355),f664(x5352,x5353,x5354,x5355)) % 188.18/188.27 [536]~E(x5361,x5362)+E(f664(x5363,x5361,x5364,x5365),f664(x5363,x5362,x5364,x5365)) % 188.18/188.27 [537]~E(x5371,x5372)+E(f664(x5373,x5374,x5371,x5375),f664(x5373,x5374,x5372,x5375)) % 188.18/188.27 [538]~E(x5381,x5382)+E(f664(x5383,x5384,x5385,x5381),f664(x5383,x5384,x5385,x5382)) % 188.18/188.27 [539]~E(x5391,x5392)+E(f476(x5391,x5393,x5394,x5395,x5396,x5397,x5398),f476(x5392,x5393,x5394,x5395,x5396,x5397,x5398)) % 188.18/188.27 [540]~E(x5401,x5402)+E(f476(x5403,x5401,x5404,x5405,x5406,x5407,x5408),f476(x5403,x5402,x5404,x5405,x5406,x5407,x5408)) % 188.18/188.27 [541]~E(x5411,x5412)+E(f476(x5413,x5414,x5411,x5415,x5416,x5417,x5418),f476(x5413,x5414,x5412,x5415,x5416,x5417,x5418)) % 188.18/188.27 [542]~E(x5421,x5422)+E(f476(x5423,x5424,x5425,x5421,x5426,x5427,x5428),f476(x5423,x5424,x5425,x5422,x5426,x5427,x5428)) % 188.18/188.27 [543]~E(x5431,x5432)+E(f476(x5433,x5434,x5435,x5436,x5431,x5437,x5438),f476(x5433,x5434,x5435,x5436,x5432,x5437,x5438)) % 188.18/188.27 [544]~E(x5441,x5442)+E(f476(x5443,x5444,x5445,x5446,x5447,x5441,x5448),f476(x5443,x5444,x5445,x5446,x5447,x5442,x5448)) % 188.18/188.27 [545]~E(x5451,x5452)+E(f476(x5453,x5454,x5455,x5456,x5457,x5458,x5451),f476(x5453,x5454,x5455,x5456,x5457,x5458,x5452)) % 188.18/188.27 [546]~E(x5461,x5462)+E(f635(x5461,x5463,x5464,x5465,x5466),f635(x5462,x5463,x5464,x5465,x5466)) % 188.18/188.27 [547]~E(x5471,x5472)+E(f635(x5473,x5471,x5474,x5475,x5476),f635(x5473,x5472,x5474,x5475,x5476)) % 188.18/188.27 [548]~E(x5481,x5482)+E(f635(x5483,x5484,x5481,x5485,x5486),f635(x5483,x5484,x5482,x5485,x5486)) % 188.18/188.27 [549]~E(x5491,x5492)+E(f635(x5493,x5494,x5495,x5491,x5496),f635(x5493,x5494,x5495,x5492,x5496)) % 188.18/188.27 [550]~E(x5501,x5502)+E(f635(x5503,x5504,x5505,x5506,x5501),f635(x5503,x5504,x5505,x5506,x5502)) % 188.18/188.27 [551]~E(x5511,x5512)+E(f674(x5511,x5513,x5514,x5515),f674(x5512,x5513,x5514,x5515)) % 188.18/188.27 [552]~E(x5521,x5522)+E(f674(x5523,x5521,x5524,x5525),f674(x5523,x5522,x5524,x5525)) % 188.18/188.27 [553]~E(x5531,x5532)+E(f674(x5533,x5534,x5531,x5535),f674(x5533,x5534,x5532,x5535)) % 188.18/188.27 [554]~E(x5541,x5542)+E(f674(x5543,x5544,x5545,x5541),f674(x5543,x5544,x5545,x5542)) % 188.18/188.27 [555]~E(x5551,x5552)+E(f53(x5551,x5553),f53(x5552,x5553)) % 188.18/188.27 [556]~E(x5561,x5562)+E(f53(x5563,x5561),f53(x5563,x5562)) % 188.18/188.27 [557]~E(x5571,x5572)+E(f305(x5571,x5573,x5574,x5575),f305(x5572,x5573,x5574,x5575)) % 188.18/188.27 [558]~E(x5581,x5582)+E(f305(x5583,x5581,x5584,x5585),f305(x5583,x5582,x5584,x5585)) % 188.18/188.27 [559]~E(x5591,x5592)+E(f305(x5593,x5594,x5591,x5595),f305(x5593,x5594,x5592,x5595)) % 188.18/188.27 [560]~E(x5601,x5602)+E(f305(x5603,x5604,x5605,x5601),f305(x5603,x5604,x5605,x5602)) % 188.18/188.27 [561]~E(x5611,x5612)+E(f915(x5611,x5613,x5614),f915(x5612,x5613,x5614)) % 188.18/188.27 [562]~E(x5621,x5622)+E(f915(x5623,x5621,x5624),f915(x5623,x5622,x5624)) % 188.18/188.27 [563]~E(x5631,x5632)+E(f915(x5633,x5634,x5631),f915(x5633,x5634,x5632)) % 188.18/188.27 [564]~E(x5641,x5642)+E(f290(x5641),f290(x5642)) % 188.18/188.27 [565]~E(x5651,x5652)+E(f648(x5651,x5653,x5654),f648(x5652,x5653,x5654)) % 188.18/188.27 [566]~E(x5661,x5662)+E(f648(x5663,x5661,x5664),f648(x5663,x5662,x5664)) % 188.18/188.27 [567]~E(x5671,x5672)+E(f648(x5673,x5674,x5671),f648(x5673,x5674,x5672)) % 188.18/188.27 [568]~E(x5681,x5682)+E(f183(x5681,x5683,x5684),f183(x5682,x5683,x5684)) % 188.18/188.27 [569]~E(x5691,x5692)+E(f183(x5693,x5691,x5694),f183(x5693,x5692,x5694)) % 188.18/188.27 [570]~E(x5701,x5702)+E(f183(x5703,x5704,x5701),f183(x5703,x5704,x5702)) % 188.18/188.27 [571]~E(x5711,x5712)+E(f735(x5711,x5713,x5714),f735(x5712,x5713,x5714)) % 188.18/188.27 [572]~E(x5721,x5722)+E(f735(x5723,x5721,x5724),f735(x5723,x5722,x5724)) % 188.18/188.27 [573]~E(x5731,x5732)+E(f735(x5733,x5734,x5731),f735(x5733,x5734,x5732)) % 188.18/188.27 [574]~E(x5741,x5742)+E(f814(x5741,x5743,x5744,x5745),f814(x5742,x5743,x5744,x5745)) % 188.18/188.27 [575]~E(x5751,x5752)+E(f814(x5753,x5751,x5754,x5755),f814(x5753,x5752,x5754,x5755)) % 188.18/188.27 [576]~E(x5761,x5762)+E(f814(x5763,x5764,x5761,x5765),f814(x5763,x5764,x5762,x5765)) % 188.18/188.27 [577]~E(x5771,x5772)+E(f814(x5773,x5774,x5775,x5771),f814(x5773,x5774,x5775,x5772)) % 188.18/188.27 [578]~E(x5781,x5782)+E(f168(x5781,x5783),f168(x5782,x5783)) % 188.18/188.27 [579]~E(x5791,x5792)+E(f168(x5793,x5791),f168(x5793,x5792)) % 188.18/188.27 [580]~E(x5801,x5802)+E(f78(x5801,x5803,x5804,x5805),f78(x5802,x5803,x5804,x5805)) % 188.18/188.27 [581]~E(x5811,x5812)+E(f78(x5813,x5811,x5814,x5815),f78(x5813,x5812,x5814,x5815)) % 188.18/188.27 [582]~E(x5821,x5822)+E(f78(x5823,x5824,x5821,x5825),f78(x5823,x5824,x5822,x5825)) % 188.18/188.27 [583]~E(x5831,x5832)+E(f78(x5833,x5834,x5835,x5831),f78(x5833,x5834,x5835,x5832)) % 188.18/188.27 [584]~E(x5841,x5842)+E(f191(x5841,x5843,x5844),f191(x5842,x5843,x5844)) % 188.18/188.27 [585]~E(x5851,x5852)+E(f191(x5853,x5851,x5854),f191(x5853,x5852,x5854)) % 188.18/188.27 [586]~E(x5861,x5862)+E(f191(x5863,x5864,x5861),f191(x5863,x5864,x5862)) % 188.18/188.27 [587]~E(x5871,x5872)+E(f581(x5871,x5873),f581(x5872,x5873)) % 188.18/188.27 [588]~E(x5881,x5882)+E(f581(x5883,x5881),f581(x5883,x5882)) % 188.18/188.27 [589]~E(x5891,x5892)+E(f613(x5891,x5893,x5894,x5895),f613(x5892,x5893,x5894,x5895)) % 188.18/188.27 [590]~E(x5901,x5902)+E(f613(x5903,x5901,x5904,x5905),f613(x5903,x5902,x5904,x5905)) % 188.18/188.27 [591]~E(x5911,x5912)+E(f613(x5913,x5914,x5911,x5915),f613(x5913,x5914,x5912,x5915)) % 188.18/188.27 [592]~E(x5921,x5922)+E(f613(x5923,x5924,x5925,x5921),f613(x5923,x5924,x5925,x5922)) % 188.18/188.27 [593]~E(x5931,x5932)+E(f322(x5931,x5933),f322(x5932,x5933)) % 188.18/188.27 [594]~E(x5941,x5942)+E(f322(x5943,x5941),f322(x5943,x5942)) % 188.18/188.27 [595]~E(x5951,x5952)+E(f411(x5951,x5953),f411(x5952,x5953)) % 188.18/188.27 [596]~E(x5961,x5962)+E(f411(x5963,x5961),f411(x5963,x5962)) % 188.18/188.27 [597]~E(x5971,x5972)+E(f470(x5971,x5973,x5974,x5975,x5976,x5977),f470(x5972,x5973,x5974,x5975,x5976,x5977)) % 188.18/188.27 [598]~E(x5981,x5982)+E(f470(x5983,x5981,x5984,x5985,x5986,x5987),f470(x5983,x5982,x5984,x5985,x5986,x5987)) % 188.18/188.27 [599]~E(x5991,x5992)+E(f470(x5993,x5994,x5991,x5995,x5996,x5997),f470(x5993,x5994,x5992,x5995,x5996,x5997)) % 188.18/188.27 [600]~E(x6001,x6002)+E(f470(x6003,x6004,x6005,x6001,x6006,x6007),f470(x6003,x6004,x6005,x6002,x6006,x6007)) % 188.18/188.27 [601]~E(x6011,x6012)+E(f470(x6013,x6014,x6015,x6016,x6011,x6017),f470(x6013,x6014,x6015,x6016,x6012,x6017)) % 188.18/188.27 [602]~E(x6021,x6022)+E(f470(x6023,x6024,x6025,x6026,x6027,x6021),f470(x6023,x6024,x6025,x6026,x6027,x6022)) % 188.18/188.27 [603]~E(x6031,x6032)+E(f280(x6031,x6033),f280(x6032,x6033)) % 188.18/188.27 [604]~E(x6041,x6042)+E(f280(x6043,x6041),f280(x6043,x6042)) % 188.18/188.27 [605]~E(x6051,x6052)+E(f650(x6051,x6053,x6054),f650(x6052,x6053,x6054)) % 188.18/188.27 [606]~E(x6061,x6062)+E(f650(x6063,x6061,x6064),f650(x6063,x6062,x6064)) % 188.18/188.27 [607]~E(x6071,x6072)+E(f650(x6073,x6074,x6071),f650(x6073,x6074,x6072)) % 188.18/188.27 [608]~E(x6081,x6082)+E(f309(x6081),f309(x6082)) % 188.18/188.27 [609]~E(x6091,x6092)+E(f240(x6091,x6093,x6094,x6095),f240(x6092,x6093,x6094,x6095)) % 188.18/188.27 [610]~E(x6101,x6102)+E(f240(x6103,x6101,x6104,x6105),f240(x6103,x6102,x6104,x6105)) % 188.18/188.27 [611]~E(x6111,x6112)+E(f240(x6113,x6114,x6111,x6115),f240(x6113,x6114,x6112,x6115)) % 188.18/188.27 [612]~E(x6121,x6122)+E(f240(x6123,x6124,x6125,x6121),f240(x6123,x6124,x6125,x6122)) % 188.18/188.27 [613]~E(x6131,x6132)+E(f725(x6131,x6133,x6134),f725(x6132,x6133,x6134)) % 188.18/188.27 [614]~E(x6141,x6142)+E(f725(x6143,x6141,x6144),f725(x6143,x6142,x6144)) % 188.18/188.27 [615]~E(x6151,x6152)+E(f725(x6153,x6154,x6151),f725(x6153,x6154,x6152)) % 188.18/188.27 [616]~E(x6161,x6162)+E(f30(x6161,x6163),f30(x6162,x6163)) % 188.18/188.27 [617]~E(x6171,x6172)+E(f30(x6173,x6171),f30(x6173,x6172)) % 188.18/188.27 [618]~E(x6181,x6182)+E(f690(x6181,x6183,x6184),f690(x6182,x6183,x6184)) % 188.18/188.27 [619]~E(x6191,x6192)+E(f690(x6193,x6191,x6194),f690(x6193,x6192,x6194)) % 188.18/188.27 [620]~E(x6201,x6202)+E(f690(x6203,x6204,x6201),f690(x6203,x6204,x6202)) % 188.18/188.27 [621]~E(x6211,x6212)+E(f536(x6211,x6213,x6214),f536(x6212,x6213,x6214)) % 188.18/188.27 [622]~E(x6221,x6222)+E(f536(x6223,x6221,x6224),f536(x6223,x6222,x6224)) % 188.18/188.27 [623]~E(x6231,x6232)+E(f536(x6233,x6234,x6231),f536(x6233,x6234,x6232)) % 188.18/188.27 [624]~E(x6241,x6242)+E(f862(x6241,x6243,x6244,x6245,x6246,x6247),f862(x6242,x6243,x6244,x6245,x6246,x6247)) % 188.18/188.27 [625]~E(x6251,x6252)+E(f862(x6253,x6251,x6254,x6255,x6256,x6257),f862(x6253,x6252,x6254,x6255,x6256,x6257)) % 188.18/188.27 [626]~E(x6261,x6262)+E(f862(x6263,x6264,x6261,x6265,x6266,x6267),f862(x6263,x6264,x6262,x6265,x6266,x6267)) % 188.18/188.27 [627]~E(x6271,x6272)+E(f862(x6273,x6274,x6275,x6271,x6276,x6277),f862(x6273,x6274,x6275,x6272,x6276,x6277)) % 188.18/188.27 [628]~E(x6281,x6282)+E(f862(x6283,x6284,x6285,x6286,x6281,x6287),f862(x6283,x6284,x6285,x6286,x6282,x6287)) % 188.18/188.27 [629]~E(x6291,x6292)+E(f862(x6293,x6294,x6295,x6296,x6297,x6291),f862(x6293,x6294,x6295,x6296,x6297,x6292)) % 188.18/188.27 [630]~E(x6301,x6302)+E(f326(x6301,x6303,x6304,x6305),f326(x6302,x6303,x6304,x6305)) % 188.18/188.27 [631]~E(x6311,x6312)+E(f326(x6313,x6311,x6314,x6315),f326(x6313,x6312,x6314,x6315)) % 188.18/188.27 [632]~E(x6321,x6322)+E(f326(x6323,x6324,x6321,x6325),f326(x6323,x6324,x6322,x6325)) % 188.18/188.27 [633]~E(x6331,x6332)+E(f326(x6333,x6334,x6335,x6331),f326(x6333,x6334,x6335,x6332)) % 188.18/188.27 [634]~E(x6341,x6342)+E(f132(x6341,x6343),f132(x6342,x6343)) % 188.18/188.27 [635]~E(x6351,x6352)+E(f132(x6353,x6351),f132(x6353,x6352)) % 188.18/188.27 [636]~E(x6361,x6362)+E(f844(x6361,x6363,x6364),f844(x6362,x6363,x6364)) % 188.18/188.27 [637]~E(x6371,x6372)+E(f844(x6373,x6371,x6374),f844(x6373,x6372,x6374)) % 188.18/188.27 [638]~E(x6381,x6382)+E(f844(x6383,x6384,x6381),f844(x6383,x6384,x6382)) % 188.18/188.27 [639]~E(x6391,x6392)+E(f451(x6391,x6393,x6394),f451(x6392,x6393,x6394)) % 188.18/188.27 [640]~E(x6401,x6402)+E(f451(x6403,x6401,x6404),f451(x6403,x6402,x6404)) % 188.18/188.27 [641]~E(x6411,x6412)+E(f451(x6413,x6414,x6411),f451(x6413,x6414,x6412)) % 188.18/188.27 [642]~E(x6421,x6422)+E(f556(x6421,x6423,x6424,x6425,x6426,x6427),f556(x6422,x6423,x6424,x6425,x6426,x6427)) % 188.18/188.27 [643]~E(x6431,x6432)+E(f556(x6433,x6431,x6434,x6435,x6436,x6437),f556(x6433,x6432,x6434,x6435,x6436,x6437)) % 188.18/188.27 [644]~E(x6441,x6442)+E(f556(x6443,x6444,x6441,x6445,x6446,x6447),f556(x6443,x6444,x6442,x6445,x6446,x6447)) % 188.18/188.27 [645]~E(x6451,x6452)+E(f556(x6453,x6454,x6455,x6451,x6456,x6457),f556(x6453,x6454,x6455,x6452,x6456,x6457)) % 188.18/188.27 [646]~E(x6461,x6462)+E(f556(x6463,x6464,x6465,x6466,x6461,x6467),f556(x6463,x6464,x6465,x6466,x6462,x6467)) % 188.18/188.27 [647]~E(x6471,x6472)+E(f556(x6473,x6474,x6475,x6476,x6477,x6471),f556(x6473,x6474,x6475,x6476,x6477,x6472)) % 188.18/188.27 [648]~E(x6481,x6482)+E(f177(x6481,x6483,x6484),f177(x6482,x6483,x6484)) % 188.18/188.27 [649]~E(x6491,x6492)+E(f177(x6493,x6491,x6494),f177(x6493,x6492,x6494)) % 188.18/188.27 [650]~E(x6501,x6502)+E(f177(x6503,x6504,x6501),f177(x6503,x6504,x6502)) % 188.18/188.27 [651]~E(x6511,x6512)+E(f173(x6511,x6513,x6514),f173(x6512,x6513,x6514)) % 188.18/188.27 [652]~E(x6521,x6522)+E(f173(x6523,x6521,x6524),f173(x6523,x6522,x6524)) % 188.18/188.27 [653]~E(x6531,x6532)+E(f173(x6533,x6534,x6531),f173(x6533,x6534,x6532)) % 188.18/188.27 [654]~E(x6541,x6542)+E(f133(x6541,x6543,x6544),f133(x6542,x6543,x6544)) % 188.18/188.27 [655]~E(x6551,x6552)+E(f133(x6553,x6551,x6554),f133(x6553,x6552,x6554)) % 188.18/188.27 [656]~E(x6561,x6562)+E(f133(x6563,x6564,x6561),f133(x6563,x6564,x6562)) % 188.18/188.27 [657]~E(x6571,x6572)+E(f54(x6571,x6573),f54(x6572,x6573)) % 188.18/188.27 [658]~E(x6581,x6582)+E(f54(x6583,x6581),f54(x6583,x6582)) % 188.18/188.27 [659]~E(x6591,x6592)+E(f448(x6591,x6593),f448(x6592,x6593)) % 188.18/188.27 [660]~E(x6601,x6602)+E(f448(x6603,x6601),f448(x6603,x6602)) % 188.18/188.27 [661]~E(x6611,x6612)+E(f455(x6611,x6613,x6614,x6615),f455(x6612,x6613,x6614,x6615)) % 188.18/188.27 [662]~E(x6621,x6622)+E(f455(x6623,x6621,x6624,x6625),f455(x6623,x6622,x6624,x6625)) % 188.18/188.27 [663]~E(x6631,x6632)+E(f455(x6633,x6634,x6631,x6635),f455(x6633,x6634,x6632,x6635)) % 188.18/188.27 [664]~E(x6641,x6642)+E(f455(x6643,x6644,x6645,x6641),f455(x6643,x6644,x6645,x6642)) % 188.18/188.27 [665]~E(x6651,x6652)+E(f617(x6651,x6653,x6654),f617(x6652,x6653,x6654)) % 188.18/188.27 [666]~E(x6661,x6662)+E(f617(x6663,x6661,x6664),f617(x6663,x6662,x6664)) % 188.18/188.27 [667]~E(x6671,x6672)+E(f617(x6673,x6674,x6671),f617(x6673,x6674,x6672)) % 188.18/188.27 [668]~E(x6681,x6682)+E(f822(x6681),f822(x6682)) % 188.18/188.27 [669]~E(x6691,x6692)+E(f799(x6691,x6693,x6694,x6695),f799(x6692,x6693,x6694,x6695)) % 188.18/188.27 [670]~E(x6701,x6702)+E(f799(x6703,x6701,x6704,x6705),f799(x6703,x6702,x6704,x6705)) % 188.18/188.27 [671]~E(x6711,x6712)+E(f799(x6713,x6714,x6711,x6715),f799(x6713,x6714,x6712,x6715)) % 188.18/188.27 [672]~E(x6721,x6722)+E(f799(x6723,x6724,x6725,x6721),f799(x6723,x6724,x6725,x6722)) % 188.18/188.27 [673]~E(x6731,x6732)+E(f574(x6731,x6733,x6734,x6735,x6736),f574(x6732,x6733,x6734,x6735,x6736)) % 188.18/188.27 [674]~E(x6741,x6742)+E(f574(x6743,x6741,x6744,x6745,x6746),f574(x6743,x6742,x6744,x6745,x6746)) % 188.18/188.27 [675]~E(x6751,x6752)+E(f574(x6753,x6754,x6751,x6755,x6756),f574(x6753,x6754,x6752,x6755,x6756)) % 188.18/188.27 [676]~E(x6761,x6762)+E(f574(x6763,x6764,x6765,x6761,x6766),f574(x6763,x6764,x6765,x6762,x6766)) % 188.18/188.27 [677]~E(x6771,x6772)+E(f574(x6773,x6774,x6775,x6776,x6771),f574(x6773,x6774,x6775,x6776,x6772)) % 188.18/188.27 [678]~E(x6781,x6782)+E(f743(x6781,x6783),f743(x6782,x6783)) % 188.18/188.27 [679]~E(x6791,x6792)+E(f743(x6793,x6791),f743(x6793,x6792)) % 188.18/188.27 [680]~E(x6801,x6802)+E(f139(x6801,x6803),f139(x6802,x6803)) % 188.18/188.27 [681]~E(x6811,x6812)+E(f139(x6813,x6811),f139(x6813,x6812)) % 188.18/188.27 [682]~E(x6821,x6822)+E(f55(x6821,x6823),f55(x6822,x6823)) % 188.18/188.27 [683]~E(x6831,x6832)+E(f55(x6833,x6831),f55(x6833,x6832)) % 188.18/188.27 [684]~E(x6841,x6842)+E(f434(x6841,x6843,x6844,x6845),f434(x6842,x6843,x6844,x6845)) % 188.18/188.27 [685]~E(x6851,x6852)+E(f434(x6853,x6851,x6854,x6855),f434(x6853,x6852,x6854,x6855)) % 188.18/188.27 [686]~E(x6861,x6862)+E(f434(x6863,x6864,x6861,x6865),f434(x6863,x6864,x6862,x6865)) % 188.18/188.27 [687]~E(x6871,x6872)+E(f434(x6873,x6874,x6875,x6871),f434(x6873,x6874,x6875,x6872)) % 188.18/188.27 [688]~E(x6881,x6882)+E(f772(x6881,x6883,x6884),f772(x6882,x6883,x6884)) % 188.18/188.27 [689]~E(x6891,x6892)+E(f772(x6893,x6891,x6894),f772(x6893,x6892,x6894)) % 188.18/188.27 [690]~E(x6901,x6902)+E(f772(x6903,x6904,x6901),f772(x6903,x6904,x6902)) % 188.18/188.27 [691]~E(x6911,x6912)+E(f547(x6911,x6913,x6914,x6915),f547(x6912,x6913,x6914,x6915)) % 188.18/188.27 [692]~E(x6921,x6922)+E(f547(x6923,x6921,x6924,x6925),f547(x6923,x6922,x6924,x6925)) % 188.18/188.27 [693]~E(x6931,x6932)+E(f547(x6933,x6934,x6931,x6935),f547(x6933,x6934,x6932,x6935)) % 188.18/188.27 [694]~E(x6941,x6942)+E(f547(x6943,x6944,x6945,x6941),f547(x6943,x6944,x6945,x6942)) % 188.18/188.27 [695]~E(x6951,x6952)+E(f170(x6951,x6953,x6954,x6955),f170(x6952,x6953,x6954,x6955)) % 188.18/188.27 [696]~E(x6961,x6962)+E(f170(x6963,x6961,x6964,x6965),f170(x6963,x6962,x6964,x6965)) % 188.18/188.27 [697]~E(x6971,x6972)+E(f170(x6973,x6974,x6971,x6975),f170(x6973,x6974,x6972,x6975)) % 188.18/188.27 [698]~E(x6981,x6982)+E(f170(x6983,x6984,x6985,x6981),f170(x6983,x6984,x6985,x6982)) % 188.18/188.27 [699]~E(x6991,x6992)+E(f729(x6991,x6993),f729(x6992,x6993)) % 188.18/188.27 [700]~E(x7001,x7002)+E(f729(x7003,x7001),f729(x7003,x7002)) % 188.18/188.27 [701]~E(x7011,x7012)+E(f163(x7011,x7013,x7014,x7015),f163(x7012,x7013,x7014,x7015)) % 188.18/188.27 [702]~E(x7021,x7022)+E(f163(x7023,x7021,x7024,x7025),f163(x7023,x7022,x7024,x7025)) % 188.18/188.27 [703]~E(x7031,x7032)+E(f163(x7033,x7034,x7031,x7035),f163(x7033,x7034,x7032,x7035)) % 188.18/188.27 [704]~E(x7041,x7042)+E(f163(x7043,x7044,x7045,x7041),f163(x7043,x7044,x7045,x7042)) % 188.18/188.27 [705]~E(x7051,x7052)+E(f642(x7051,x7053,x7054,x7055),f642(x7052,x7053,x7054,x7055)) % 188.18/188.27 [706]~E(x7061,x7062)+E(f642(x7063,x7061,x7064,x7065),f642(x7063,x7062,x7064,x7065)) % 188.18/188.27 [707]~E(x7071,x7072)+E(f642(x7073,x7074,x7071,x7075),f642(x7073,x7074,x7072,x7075)) % 188.18/188.27 [708]~E(x7081,x7082)+E(f642(x7083,x7084,x7085,x7081),f642(x7083,x7084,x7085,x7082)) % 188.18/188.27 [709]~E(x7091,x7092)+E(f590(x7091,x7093,x7094,x7095),f590(x7092,x7093,x7094,x7095)) % 188.18/188.27 [710]~E(x7101,x7102)+E(f590(x7103,x7101,x7104,x7105),f590(x7103,x7102,x7104,x7105)) % 188.18/188.27 [711]~E(x7111,x7112)+E(f590(x7113,x7114,x7111,x7115),f590(x7113,x7114,x7112,x7115)) % 188.18/188.27 [712]~E(x7121,x7122)+E(f590(x7123,x7124,x7125,x7121),f590(x7123,x7124,x7125,x7122)) % 188.18/188.27 [713]~E(x7131,x7132)+E(f155(x7131,x7133,x7134),f155(x7132,x7133,x7134)) % 188.18/188.27 [714]~E(x7141,x7142)+E(f155(x7143,x7141,x7144),f155(x7143,x7142,x7144)) % 188.18/188.27 [715]~E(x7151,x7152)+E(f155(x7153,x7154,x7151),f155(x7153,x7154,x7152)) % 188.18/188.27 [716]~E(x7161,x7162)+E(f489(x7161,x7163,x7164,x7165,x7166),f489(x7162,x7163,x7164,x7165,x7166)) % 188.18/188.27 [717]~E(x7171,x7172)+E(f489(x7173,x7171,x7174,x7175,x7176),f489(x7173,x7172,x7174,x7175,x7176)) % 188.18/188.27 [718]~E(x7181,x7182)+E(f489(x7183,x7184,x7181,x7185,x7186),f489(x7183,x7184,x7182,x7185,x7186)) % 188.18/188.27 [719]~E(x7191,x7192)+E(f489(x7193,x7194,x7195,x7191,x7196),f489(x7193,x7194,x7195,x7192,x7196)) % 188.18/188.27 [720]~E(x7201,x7202)+E(f489(x7203,x7204,x7205,x7206,x7201),f489(x7203,x7204,x7205,x7206,x7202)) % 188.18/188.27 [721]~E(x7211,x7212)+E(f677(x7211,x7213,x7214),f677(x7212,x7213,x7214)) % 188.18/188.27 [722]~E(x7221,x7222)+E(f677(x7223,x7221,x7224),f677(x7223,x7222,x7224)) % 188.18/188.27 [723]~E(x7231,x7232)+E(f677(x7233,x7234,x7231),f677(x7233,x7234,x7232)) % 188.18/188.27 [724]~E(x7241,x7242)+E(f719(x7241,x7243),f719(x7242,x7243)) % 188.18/188.27 [725]~E(x7251,x7252)+E(f719(x7253,x7251),f719(x7253,x7252)) % 188.18/188.27 [726]~E(x7261,x7262)+E(f380(x7261,x7263),f380(x7262,x7263)) % 188.18/188.27 [727]~E(x7271,x7272)+E(f380(x7273,x7271),f380(x7273,x7272)) % 188.18/188.27 [728]~E(x7281,x7282)+E(f420(x7281,x7283,x7284,x7285),f420(x7282,x7283,x7284,x7285)) % 188.18/188.27 [729]~E(x7291,x7292)+E(f420(x7293,x7291,x7294,x7295),f420(x7293,x7292,x7294,x7295)) % 188.18/188.27 [730]~E(x7301,x7302)+E(f420(x7303,x7304,x7301,x7305),f420(x7303,x7304,x7302,x7305)) % 188.18/188.27 [731]~E(x7311,x7312)+E(f420(x7313,x7314,x7315,x7311),f420(x7313,x7314,x7315,x7312)) % 188.18/188.27 [732]~E(x7321,x7322)+E(f146(x7321,x7323),f146(x7322,x7323)) % 188.18/188.27 [733]~E(x7331,x7332)+E(f146(x7333,x7331),f146(x7333,x7332)) % 188.18/188.27 [734]~E(x7341,x7342)+E(f428(x7341,x7343,x7344),f428(x7342,x7343,x7344)) % 188.18/188.27 [735]~E(x7351,x7352)+E(f428(x7353,x7351,x7354),f428(x7353,x7352,x7354)) % 188.18/188.27 [736]~E(x7361,x7362)+E(f428(x7363,x7364,x7361),f428(x7363,x7364,x7362)) % 188.18/188.27 [737]~E(x7371,x7372)+E(f477(x7371,x7373,x7374,x7375,x7376,x7377,x7378),f477(x7372,x7373,x7374,x7375,x7376,x7377,x7378)) % 188.18/188.27 [738]~E(x7381,x7382)+E(f477(x7383,x7381,x7384,x7385,x7386,x7387,x7388),f477(x7383,x7382,x7384,x7385,x7386,x7387,x7388)) % 188.18/188.27 [739]~E(x7391,x7392)+E(f477(x7393,x7394,x7391,x7395,x7396,x7397,x7398),f477(x7393,x7394,x7392,x7395,x7396,x7397,x7398)) % 188.18/188.27 [740]~E(x7401,x7402)+E(f477(x7403,x7404,x7405,x7401,x7406,x7407,x7408),f477(x7403,x7404,x7405,x7402,x7406,x7407,x7408)) % 188.18/188.27 [741]~E(x7411,x7412)+E(f477(x7413,x7414,x7415,x7416,x7411,x7417,x7418),f477(x7413,x7414,x7415,x7416,x7412,x7417,x7418)) % 188.18/188.27 [742]~E(x7421,x7422)+E(f477(x7423,x7424,x7425,x7426,x7427,x7421,x7428),f477(x7423,x7424,x7425,x7426,x7427,x7422,x7428)) % 188.18/188.27 [743]~E(x7431,x7432)+E(f477(x7433,x7434,x7435,x7436,x7437,x7438,x7431),f477(x7433,x7434,x7435,x7436,x7437,x7438,x7432)) % 188.18/188.27 [744]~E(x7441,x7442)+E(f425(x7441,x7443),f425(x7442,x7443)) % 188.18/188.27 [745]~E(x7451,x7452)+E(f425(x7453,x7451),f425(x7453,x7452)) % 188.18/188.27 [746]~E(x7461,x7462)+E(f483(x7461,x7463,x7464,x7465,x7466),f483(x7462,x7463,x7464,x7465,x7466)) % 188.18/188.27 [747]~E(x7471,x7472)+E(f483(x7473,x7471,x7474,x7475,x7476),f483(x7473,x7472,x7474,x7475,x7476)) % 188.18/188.27 [748]~E(x7481,x7482)+E(f483(x7483,x7484,x7481,x7485,x7486),f483(x7483,x7484,x7482,x7485,x7486)) % 188.18/188.27 [749]~E(x7491,x7492)+E(f483(x7493,x7494,x7495,x7491,x7496),f483(x7493,x7494,x7495,x7492,x7496)) % 188.18/188.27 [750]~E(x7501,x7502)+E(f483(x7503,x7504,x7505,x7506,x7501),f483(x7503,x7504,x7505,x7506,x7502)) % 188.18/188.27 [751]~E(x7511,x7512)+E(f80(x7511,x7513,x7514,x7515,x7516),f80(x7512,x7513,x7514,x7515,x7516)) % 188.18/188.27 [752]~E(x7521,x7522)+E(f80(x7523,x7521,x7524,x7525,x7526),f80(x7523,x7522,x7524,x7525,x7526)) % 188.18/188.27 [753]~E(x7531,x7532)+E(f80(x7533,x7534,x7531,x7535,x7536),f80(x7533,x7534,x7532,x7535,x7536)) % 188.18/188.27 [754]~E(x7541,x7542)+E(f80(x7543,x7544,x7545,x7541,x7546),f80(x7543,x7544,x7545,x7542,x7546)) % 188.18/188.27 [755]~E(x7551,x7552)+E(f80(x7553,x7554,x7555,x7556,x7551),f80(x7553,x7554,x7555,x7556,x7552)) % 188.18/188.27 [756]~E(x7561,x7562)+E(f156(x7561,x7563,x7564,x7565,x7566),f156(x7562,x7563,x7564,x7565,x7566)) % 188.18/188.27 [757]~E(x7571,x7572)+E(f156(x7573,x7571,x7574,x7575,x7576),f156(x7573,x7572,x7574,x7575,x7576)) % 188.18/188.27 [758]~E(x7581,x7582)+E(f156(x7583,x7584,x7581,x7585,x7586),f156(x7583,x7584,x7582,x7585,x7586)) % 188.18/188.27 [759]~E(x7591,x7592)+E(f156(x7593,x7594,x7595,x7591,x7596),f156(x7593,x7594,x7595,x7592,x7596)) % 188.18/188.27 [760]~E(x7601,x7602)+E(f156(x7603,x7604,x7605,x7606,x7601),f156(x7603,x7604,x7605,x7606,x7602)) % 188.18/188.27 [761]~E(x7611,x7612)+E(f552(x7611,x7613,x7614),f552(x7612,x7613,x7614)) % 188.18/188.27 [762]~E(x7621,x7622)+E(f552(x7623,x7621,x7624),f552(x7623,x7622,x7624)) % 188.18/188.27 [763]~E(x7631,x7632)+E(f552(x7633,x7634,x7631),f552(x7633,x7634,x7632)) % 188.18/188.27 [764]~E(x7641,x7642)+E(f463(x7641,x7643,x7644),f463(x7642,x7643,x7644)) % 188.18/188.27 [765]~E(x7651,x7652)+E(f463(x7653,x7651,x7654),f463(x7653,x7652,x7654)) % 188.18/188.27 [766]~E(x7661,x7662)+E(f463(x7663,x7664,x7661),f463(x7663,x7664,x7662)) % 188.18/188.27 [767]~E(x7671,x7672)+E(f312(x7671,x7673,x7674),f312(x7672,x7673,x7674)) % 188.18/188.27 [768]~E(x7681,x7682)+E(f312(x7683,x7681,x7684),f312(x7683,x7682,x7684)) % 188.18/188.27 [769]~E(x7691,x7692)+E(f312(x7693,x7694,x7691),f312(x7693,x7694,x7692)) % 188.18/188.27 [770]~E(x7701,x7702)+E(f238(x7701,x7703,x7704,x7705),f238(x7702,x7703,x7704,x7705)) % 188.18/188.27 [771]~E(x7711,x7712)+E(f238(x7713,x7711,x7714,x7715),f238(x7713,x7712,x7714,x7715)) % 188.18/188.27 [772]~E(x7721,x7722)+E(f238(x7723,x7724,x7721,x7725),f238(x7723,x7724,x7722,x7725)) % 188.18/188.27 [773]~E(x7731,x7732)+E(f238(x7733,x7734,x7735,x7731),f238(x7733,x7734,x7735,x7732)) % 188.18/188.27 [774]~E(x7741,x7742)+E(f539(x7741,x7743,x7744),f539(x7742,x7743,x7744)) % 188.18/188.27 [775]~E(x7751,x7752)+E(f539(x7753,x7751,x7754),f539(x7753,x7752,x7754)) % 188.18/188.27 [776]~E(x7761,x7762)+E(f539(x7763,x7764,x7761),f539(x7763,x7764,x7762)) % 188.18/188.27 [777]~E(x7771,x7772)+E(f615(x7771,x7773,x7774,x7775),f615(x7772,x7773,x7774,x7775)) % 188.18/188.27 [778]~E(x7781,x7782)+E(f615(x7783,x7781,x7784,x7785),f615(x7783,x7782,x7784,x7785)) % 188.18/188.27 [779]~E(x7791,x7792)+E(f615(x7793,x7794,x7791,x7795),f615(x7793,x7794,x7792,x7795)) % 188.18/188.27 [780]~E(x7801,x7802)+E(f615(x7803,x7804,x7805,x7801),f615(x7803,x7804,x7805,x7802)) % 188.18/188.27 [781]~E(x7811,x7812)+E(f681(x7811,x7813,x7814),f681(x7812,x7813,x7814)) % 188.18/188.27 [782]~E(x7821,x7822)+E(f681(x7823,x7821,x7824),f681(x7823,x7822,x7824)) % 188.18/188.27 [783]~E(x7831,x7832)+E(f681(x7833,x7834,x7831),f681(x7833,x7834,x7832)) % 188.18/188.27 [784]~E(x7841,x7842)+E(f313(x7841,x7843,x7844),f313(x7842,x7843,x7844)) % 188.18/188.27 [785]~E(x7851,x7852)+E(f313(x7853,x7851,x7854),f313(x7853,x7852,x7854)) % 188.18/188.27 [786]~E(x7861,x7862)+E(f313(x7863,x7864,x7861),f313(x7863,x7864,x7862)) % 188.18/188.27 [787]~E(x7871,x7872)+E(f439(x7871,x7873,x7874,x7875),f439(x7872,x7873,x7874,x7875)) % 188.18/188.27 [788]~E(x7881,x7882)+E(f439(x7883,x7881,x7884,x7885),f439(x7883,x7882,x7884,x7885)) % 188.18/188.27 [789]~E(x7891,x7892)+E(f439(x7893,x7894,x7891,x7895),f439(x7893,x7894,x7892,x7895)) % 188.18/188.27 [790]~E(x7901,x7902)+E(f439(x7903,x7904,x7905,x7901),f439(x7903,x7904,x7905,x7902)) % 188.18/188.27 [791]~E(x7911,x7912)+E(f524(x7911,x7913,x7914,x7915,x7916),f524(x7912,x7913,x7914,x7915,x7916)) % 188.18/188.27 [792]~E(x7921,x7922)+E(f524(x7923,x7921,x7924,x7925,x7926),f524(x7923,x7922,x7924,x7925,x7926)) % 188.18/188.27 [793]~E(x7931,x7932)+E(f524(x7933,x7934,x7931,x7935,x7936),f524(x7933,x7934,x7932,x7935,x7936)) % 188.18/188.27 [794]~E(x7941,x7942)+E(f524(x7943,x7944,x7945,x7941,x7946),f524(x7943,x7944,x7945,x7942,x7946)) % 188.18/188.27 [795]~E(x7951,x7952)+E(f524(x7953,x7954,x7955,x7956,x7951),f524(x7953,x7954,x7955,x7956,x7952)) % 188.18/188.27 [796]~E(x7961,x7962)+E(f357(x7961,x7963),f357(x7962,x7963)) % 188.18/188.27 [797]~E(x7971,x7972)+E(f357(x7973,x7971),f357(x7973,x7972)) % 188.18/188.27 [798]~E(x7981,x7982)+E(f709(x7981,x7983,x7984,x7985,x7986),f709(x7982,x7983,x7984,x7985,x7986)) % 188.18/188.27 [799]~E(x7991,x7992)+E(f709(x7993,x7991,x7994,x7995,x7996),f709(x7993,x7992,x7994,x7995,x7996)) % 188.18/188.27 [800]~E(x8001,x8002)+E(f709(x8003,x8004,x8001,x8005,x8006),f709(x8003,x8004,x8002,x8005,x8006)) % 188.18/188.27 [801]~E(x8011,x8012)+E(f709(x8013,x8014,x8015,x8011,x8016),f709(x8013,x8014,x8015,x8012,x8016)) % 188.18/188.27 [802]~E(x8021,x8022)+E(f709(x8023,x8024,x8025,x8026,x8021),f709(x8023,x8024,x8025,x8026,x8022)) % 188.18/188.27 [803]~E(x8031,x8032)+E(f229(x8031,x8033,x8034,x8035),f229(x8032,x8033,x8034,x8035)) % 188.18/188.27 [804]~E(x8041,x8042)+E(f229(x8043,x8041,x8044,x8045),f229(x8043,x8042,x8044,x8045)) % 188.18/188.27 [805]~E(x8051,x8052)+E(f229(x8053,x8054,x8051,x8055),f229(x8053,x8054,x8052,x8055)) % 188.18/188.27 [806]~E(x8061,x8062)+E(f229(x8063,x8064,x8065,x8061),f229(x8063,x8064,x8065,x8062)) % 188.18/188.27 [807]~E(x8071,x8072)+E(f696(x8071,x8073,x8074,x8075,x8076),f696(x8072,x8073,x8074,x8075,x8076)) % 188.18/188.27 [808]~E(x8081,x8082)+E(f696(x8083,x8081,x8084,x8085,x8086),f696(x8083,x8082,x8084,x8085,x8086)) % 188.18/188.27 [809]~E(x8091,x8092)+E(f696(x8093,x8094,x8091,x8095,x8096),f696(x8093,x8094,x8092,x8095,x8096)) % 188.18/188.27 [810]~E(x8101,x8102)+E(f696(x8103,x8104,x8105,x8101,x8106),f696(x8103,x8104,x8105,x8102,x8106)) % 188.18/188.27 [811]~E(x8111,x8112)+E(f696(x8113,x8114,x8115,x8116,x8111),f696(x8113,x8114,x8115,x8116,x8112)) % 188.18/188.27 [812]~E(x8121,x8122)+E(f464(x8121,x8123,x8124,x8125),f464(x8122,x8123,x8124,x8125)) % 188.18/188.27 [813]~E(x8131,x8132)+E(f464(x8133,x8131,x8134,x8135),f464(x8133,x8132,x8134,x8135)) % 188.18/188.27 [814]~E(x8141,x8142)+E(f464(x8143,x8144,x8141,x8145),f464(x8143,x8144,x8142,x8145)) % 188.18/188.27 [815]~E(x8151,x8152)+E(f464(x8153,x8154,x8155,x8151),f464(x8153,x8154,x8155,x8152)) % 188.18/188.27 [816]~E(x8161,x8162)+E(f294(x8161,x8163),f294(x8162,x8163)) % 188.18/188.27 [817]~E(x8171,x8172)+E(f294(x8173,x8171),f294(x8173,x8172)) % 188.18/188.27 [818]~E(x8181,x8182)+E(f812(x8181,x8183,x8184),f812(x8182,x8183,x8184)) % 188.18/188.27 [819]~E(x8191,x8192)+E(f812(x8193,x8191,x8194),f812(x8193,x8192,x8194)) % 188.18/188.27 [820]~E(x8201,x8202)+E(f812(x8203,x8204,x8201),f812(x8203,x8204,x8202)) % 188.18/188.27 [821]~E(x8211,x8212)+E(f716(x8211,x8213),f716(x8212,x8213)) % 188.18/188.27 [822]~E(x8221,x8222)+E(f716(x8223,x8221),f716(x8223,x8222)) % 188.18/188.27 [823]~E(x8231,x8232)+E(f278(x8231,x8233),f278(x8232,x8233)) % 188.18/188.27 [824]~E(x8241,x8242)+E(f278(x8243,x8241),f278(x8243,x8242)) % 188.18/188.27 [825]~E(x8251,x8252)+E(f582(x8251,x8253),f582(x8252,x8253)) % 188.18/188.27 [826]~E(x8261,x8262)+E(f582(x8263,x8261),f582(x8263,x8262)) % 188.18/188.27 [827]~E(x8271,x8272)+E(f850(x8271,x8273,x8274,x8275,x8276,x8277),f850(x8272,x8273,x8274,x8275,x8276,x8277)) % 188.18/188.27 [828]~E(x8281,x8282)+E(f850(x8283,x8281,x8284,x8285,x8286,x8287),f850(x8283,x8282,x8284,x8285,x8286,x8287)) % 188.18/188.27 [829]~E(x8291,x8292)+E(f850(x8293,x8294,x8291,x8295,x8296,x8297),f850(x8293,x8294,x8292,x8295,x8296,x8297)) % 188.18/188.27 [830]~E(x8301,x8302)+E(f850(x8303,x8304,x8305,x8301,x8306,x8307),f850(x8303,x8304,x8305,x8302,x8306,x8307)) % 188.18/188.27 [831]~E(x8311,x8312)+E(f850(x8313,x8314,x8315,x8316,x8311,x8317),f850(x8313,x8314,x8315,x8316,x8312,x8317)) % 188.18/188.27 [832]~E(x8321,x8322)+E(f850(x8323,x8324,x8325,x8326,x8327,x8321),f850(x8323,x8324,x8325,x8326,x8327,x8322)) % 188.18/188.27 [833]~E(x8331,x8332)+E(f791(x8331,x8333,x8334,x8335,x8336),f791(x8332,x8333,x8334,x8335,x8336)) % 188.18/188.27 [834]~E(x8341,x8342)+E(f791(x8343,x8341,x8344,x8345,x8346),f791(x8343,x8342,x8344,x8345,x8346)) % 188.18/188.27 [835]~E(x8351,x8352)+E(f791(x8353,x8354,x8351,x8355,x8356),f791(x8353,x8354,x8352,x8355,x8356)) % 188.18/188.27 [836]~E(x8361,x8362)+E(f791(x8363,x8364,x8365,x8361,x8366),f791(x8363,x8364,x8365,x8362,x8366)) % 188.18/188.27 [837]~E(x8371,x8372)+E(f791(x8373,x8374,x8375,x8376,x8371),f791(x8373,x8374,x8375,x8376,x8372)) % 188.18/188.27 [838]~E(x8381,x8382)+E(f562(x8381,x8383,x8384,x8385,x8386,x8387,x8388,x8389),f562(x8382,x8383,x8384,x8385,x8386,x8387,x8388,x8389)) % 188.18/188.27 [839]~E(x8391,x8392)+E(f562(x8393,x8391,x8394,x8395,x8396,x8397,x8398,x8399),f562(x8393,x8392,x8394,x8395,x8396,x8397,x8398,x8399)) % 188.18/188.27 [840]~E(x8401,x8402)+E(f562(x8403,x8404,x8401,x8405,x8406,x8407,x8408,x8409),f562(x8403,x8404,x8402,x8405,x8406,x8407,x8408,x8409)) % 188.18/188.27 [841]~E(x8411,x8412)+E(f562(x8413,x8414,x8415,x8411,x8416,x8417,x8418,x8419),f562(x8413,x8414,x8415,x8412,x8416,x8417,x8418,x8419)) % 188.18/188.27 [842]~E(x8421,x8422)+E(f562(x8423,x8424,x8425,x8426,x8421,x8427,x8428,x8429),f562(x8423,x8424,x8425,x8426,x8422,x8427,x8428,x8429)) % 188.18/188.27 [843]~E(x8431,x8432)+E(f562(x8433,x8434,x8435,x8436,x8437,x8431,x8438,x8439),f562(x8433,x8434,x8435,x8436,x8437,x8432,x8438,x8439)) % 188.18/188.27 [844]~E(x8441,x8442)+E(f562(x8443,x8444,x8445,x8446,x8447,x8448,x8441,x8449),f562(x8443,x8444,x8445,x8446,x8447,x8448,x8442,x8449)) % 188.18/188.27 [845]~E(x8451,x8452)+E(f562(x8453,x8454,x8455,x8456,x8457,x8458,x8459,x8451),f562(x8453,x8454,x8455,x8456,x8457,x8458,x8459,x8452)) % 188.18/188.27 [846]~E(x8461,x8462)+E(f857(x8461,x8463,x8464,x8465,x8466,x8467,x8468,x8469),f857(x8462,x8463,x8464,x8465,x8466,x8467,x8468,x8469)) % 188.18/188.27 [847]~E(x8471,x8472)+E(f857(x8473,x8471,x8474,x8475,x8476,x8477,x8478,x8479),f857(x8473,x8472,x8474,x8475,x8476,x8477,x8478,x8479)) % 188.18/188.27 [848]~E(x8481,x8482)+E(f857(x8483,x8484,x8481,x8485,x8486,x8487,x8488,x8489),f857(x8483,x8484,x8482,x8485,x8486,x8487,x8488,x8489)) % 188.18/188.27 [849]~E(x8491,x8492)+E(f857(x8493,x8494,x8495,x8491,x8496,x8497,x8498,x8499),f857(x8493,x8494,x8495,x8492,x8496,x8497,x8498,x8499)) % 188.18/188.27 [850]~E(x8501,x8502)+E(f857(x8503,x8504,x8505,x8506,x8501,x8507,x8508,x8509),f857(x8503,x8504,x8505,x8506,x8502,x8507,x8508,x8509)) % 188.18/188.27 [851]~E(x8511,x8512)+E(f857(x8513,x8514,x8515,x8516,x8517,x8511,x8518,x8519),f857(x8513,x8514,x8515,x8516,x8517,x8512,x8518,x8519)) % 188.18/188.27 [852]~E(x8521,x8522)+E(f857(x8523,x8524,x8525,x8526,x8527,x8528,x8521,x8529),f857(x8523,x8524,x8525,x8526,x8527,x8528,x8522,x8529)) % 188.18/188.27 [853]~E(x8531,x8532)+E(f857(x8533,x8534,x8535,x8536,x8537,x8538,x8539,x8531),f857(x8533,x8534,x8535,x8536,x8537,x8538,x8539,x8532)) % 188.18/188.27 [854]~E(x8541,x8542)+E(f272(x8541,x8543),f272(x8542,x8543)) % 188.18/188.27 [855]~E(x8551,x8552)+E(f272(x8553,x8551),f272(x8553,x8552)) % 188.18/188.27 [856]~E(x8561,x8562)+E(f28(x8561,x8563,x8564),f28(x8562,x8563,x8564)) % 188.18/188.27 [857]~E(x8571,x8572)+E(f28(x8573,x8571,x8574),f28(x8573,x8572,x8574)) % 188.18/188.27 [858]~E(x8581,x8582)+E(f28(x8583,x8584,x8581),f28(x8583,x8584,x8582)) % 188.18/188.27 [859]~E(x8591,x8592)+E(f797(x8591,x8593,x8594),f797(x8592,x8593,x8594)) % 188.18/188.27 [860]~E(x8601,x8602)+E(f797(x8603,x8601,x8604),f797(x8603,x8602,x8604)) % 188.18/188.27 [861]~E(x8611,x8612)+E(f797(x8613,x8614,x8611),f797(x8613,x8614,x8612)) % 188.18/188.27 [862]~E(x8621,x8622)+E(f853(x8621,x8623,x8624,x8625,x8626,x8627,x8628),f853(x8622,x8623,x8624,x8625,x8626,x8627,x8628)) % 188.18/188.27 [863]~E(x8631,x8632)+E(f853(x8633,x8631,x8634,x8635,x8636,x8637,x8638),f853(x8633,x8632,x8634,x8635,x8636,x8637,x8638)) % 188.18/188.27 [864]~E(x8641,x8642)+E(f853(x8643,x8644,x8641,x8645,x8646,x8647,x8648),f853(x8643,x8644,x8642,x8645,x8646,x8647,x8648)) % 188.18/188.27 [865]~E(x8651,x8652)+E(f853(x8653,x8654,x8655,x8651,x8656,x8657,x8658),f853(x8653,x8654,x8655,x8652,x8656,x8657,x8658)) % 188.18/188.27 [866]~E(x8661,x8662)+E(f853(x8663,x8664,x8665,x8666,x8661,x8667,x8668),f853(x8663,x8664,x8665,x8666,x8662,x8667,x8668)) % 188.18/188.27 [867]~E(x8671,x8672)+E(f853(x8673,x8674,x8675,x8676,x8677,x8671,x8678),f853(x8673,x8674,x8675,x8676,x8677,x8672,x8678)) % 188.18/188.27 [868]~E(x8681,x8682)+E(f853(x8683,x8684,x8685,x8686,x8687,x8688,x8681),f853(x8683,x8684,x8685,x8686,x8687,x8688,x8682)) % 188.18/188.27 [869]~E(x8691,x8692)+E(f251(x8691,x8693,x8694),f251(x8692,x8693,x8694)) % 188.18/188.27 [870]~E(x8701,x8702)+E(f251(x8703,x8701,x8704),f251(x8703,x8702,x8704)) % 188.18/188.27 [871]~E(x8711,x8712)+E(f251(x8713,x8714,x8711),f251(x8713,x8714,x8712)) % 188.18/188.27 [872]~E(x8721,x8722)+E(f490(x8721,x8723,x8724,x8725,x8726),f490(x8722,x8723,x8724,x8725,x8726)) % 188.18/188.27 [873]~E(x8731,x8732)+E(f490(x8733,x8731,x8734,x8735,x8736),f490(x8733,x8732,x8734,x8735,x8736)) % 188.18/188.27 [874]~E(x8741,x8742)+E(f490(x8743,x8744,x8741,x8745,x8746),f490(x8743,x8744,x8742,x8745,x8746)) % 188.18/188.27 [875]~E(x8751,x8752)+E(f490(x8753,x8754,x8755,x8751,x8756),f490(x8753,x8754,x8755,x8752,x8756)) % 188.18/188.27 [876]~E(x8761,x8762)+E(f490(x8763,x8764,x8765,x8766,x8761),f490(x8763,x8764,x8765,x8766,x8762)) % 188.18/188.27 [877]~E(x8771,x8772)+E(f781(x8771,x8773,x8774),f781(x8772,x8773,x8774)) % 188.18/188.27 [878]~E(x8781,x8782)+E(f781(x8783,x8781,x8784),f781(x8783,x8782,x8784)) % 188.18/188.27 [879]~E(x8791,x8792)+E(f781(x8793,x8794,x8791),f781(x8793,x8794,x8792)) % 188.18/188.27 [880]~E(x8801,x8802)+E(f542(x8801,x8803,x8804,x8805),f542(x8802,x8803,x8804,x8805)) % 188.18/188.27 [881]~E(x8811,x8812)+E(f542(x8813,x8811,x8814,x8815),f542(x8813,x8812,x8814,x8815)) % 188.18/188.27 [882]~E(x8821,x8822)+E(f542(x8823,x8824,x8821,x8825),f542(x8823,x8824,x8822,x8825)) % 188.18/188.27 [883]~E(x8831,x8832)+E(f542(x8833,x8834,x8835,x8831),f542(x8833,x8834,x8835,x8832)) % 188.18/188.27 [884]~E(x8841,x8842)+E(f513(x8841,x8843,x8844),f513(x8842,x8843,x8844)) % 188.18/188.27 [885]~E(x8851,x8852)+E(f513(x8853,x8851,x8854),f513(x8853,x8852,x8854)) % 188.18/188.27 [886]~E(x8861,x8862)+E(f513(x8863,x8864,x8861),f513(x8863,x8864,x8862)) % 188.18/188.27 [887]~E(x8871,x8872)+E(f150(x8871,x8873),f150(x8872,x8873)) % 188.18/188.27 [888]~E(x8881,x8882)+E(f150(x8883,x8881),f150(x8883,x8882)) % 188.18/188.27 [889]~E(x8891,x8892)+E(f589(x8891,x8893,x8894),f589(x8892,x8893,x8894)) % 188.18/188.27 [890]~E(x8901,x8902)+E(f589(x8903,x8901,x8904),f589(x8903,x8902,x8904)) % 188.18/188.27 [891]~E(x8911,x8912)+E(f589(x8913,x8914,x8911),f589(x8913,x8914,x8912)) % 188.18/188.27 [892]~E(x8921,x8922)+E(f658(x8921,x8923,x8924,x8925,x8926,x8927),f658(x8922,x8923,x8924,x8925,x8926,x8927)) % 188.18/188.27 [893]~E(x8931,x8932)+E(f658(x8933,x8931,x8934,x8935,x8936,x8937),f658(x8933,x8932,x8934,x8935,x8936,x8937)) % 188.18/188.27 [894]~E(x8941,x8942)+E(f658(x8943,x8944,x8941,x8945,x8946,x8947),f658(x8943,x8944,x8942,x8945,x8946,x8947)) % 188.18/188.27 [895]~E(x8951,x8952)+E(f658(x8953,x8954,x8955,x8951,x8956,x8957),f658(x8953,x8954,x8955,x8952,x8956,x8957)) % 188.18/188.27 [896]~E(x8961,x8962)+E(f658(x8963,x8964,x8965,x8966,x8961,x8967),f658(x8963,x8964,x8965,x8966,x8962,x8967)) % 188.18/188.27 [897]~E(x8971,x8972)+E(f658(x8973,x8974,x8975,x8976,x8977,x8971),f658(x8973,x8974,x8975,x8976,x8977,x8972)) % 188.18/188.27 [898]~E(x8981,x8982)+E(f849(x8981,x8983,x8984),f849(x8982,x8983,x8984)) % 188.18/188.27 [899]~E(x8991,x8992)+E(f849(x8993,x8991,x8994),f849(x8993,x8992,x8994)) % 188.18/188.27 [900]~E(x9001,x9002)+E(f849(x9003,x9004,x9001),f849(x9003,x9004,x9002)) % 188.18/188.27 [901]~E(x9011,x9012)+E(f599(x9011,x9013,x9014),f599(x9012,x9013,x9014)) % 188.18/188.27 [902]~E(x9021,x9022)+E(f599(x9023,x9021,x9024),f599(x9023,x9022,x9024)) % 188.18/188.27 [903]~E(x9031,x9032)+E(f599(x9033,x9034,x9031),f599(x9033,x9034,x9032)) % 188.18/188.27 [904]~E(x9041,x9042)+E(f537(x9041,x9043,x9044),f537(x9042,x9043,x9044)) % 188.18/188.27 [905]~E(x9051,x9052)+E(f537(x9053,x9051,x9054),f537(x9053,x9052,x9054)) % 188.18/188.27 [906]~E(x9061,x9062)+E(f537(x9063,x9064,x9061),f537(x9063,x9064,x9062)) % 188.18/188.27 [907]~E(x9071,x9072)+E(f301(x9071,x9073,x9074),f301(x9072,x9073,x9074)) % 188.18/188.27 [908]~E(x9081,x9082)+E(f301(x9083,x9081,x9084),f301(x9083,x9082,x9084)) % 188.18/188.27 [909]~E(x9091,x9092)+E(f301(x9093,x9094,x9091),f301(x9093,x9094,x9092)) % 188.18/188.27 [910]~E(x9101,x9102)+E(f99(x9101,x9103,x9104),f99(x9102,x9103,x9104)) % 188.18/188.27 [911]~E(x9111,x9112)+E(f99(x9113,x9111,x9114),f99(x9113,x9112,x9114)) % 188.18/188.27 [912]~E(x9121,x9122)+E(f99(x9123,x9124,x9121),f99(x9123,x9124,x9122)) % 188.18/188.27 [913]~E(x9131,x9132)+E(f726(x9131,x9133,x9134),f726(x9132,x9133,x9134)) % 188.18/188.27 [914]~E(x9141,x9142)+E(f726(x9143,x9141,x9144),f726(x9143,x9142,x9144)) % 188.18/188.27 [915]~E(x9151,x9152)+E(f726(x9153,x9154,x9151),f726(x9153,x9154,x9152)) % 188.18/188.27 [916]~E(x9161,x9162)+E(f665(x9161,x9163,x9164,x9165,x9166),f665(x9162,x9163,x9164,x9165,x9166)) % 188.18/188.27 [917]~E(x9171,x9172)+E(f665(x9173,x9171,x9174,x9175,x9176),f665(x9173,x9172,x9174,x9175,x9176)) % 188.18/188.27 [918]~E(x9181,x9182)+E(f665(x9183,x9184,x9181,x9185,x9186),f665(x9183,x9184,x9182,x9185,x9186)) % 188.18/188.27 [919]~E(x9191,x9192)+E(f665(x9193,x9194,x9195,x9191,x9196),f665(x9193,x9194,x9195,x9192,x9196)) % 188.18/188.27 [920]~E(x9201,x9202)+E(f665(x9203,x9204,x9205,x9206,x9201),f665(x9203,x9204,x9205,x9206,x9202)) % 188.18/188.27 [921]~E(x9211,x9212)+E(f440(x9211,x9213,x9214,x9215),f440(x9212,x9213,x9214,x9215)) % 188.18/188.27 [922]~E(x9221,x9222)+E(f440(x9223,x9221,x9224,x9225),f440(x9223,x9222,x9224,x9225)) % 188.18/188.27 [923]~E(x9231,x9232)+E(f440(x9233,x9234,x9231,x9235),f440(x9233,x9234,x9232,x9235)) % 188.18/188.27 [924]~E(x9241,x9242)+E(f440(x9243,x9244,x9245,x9241),f440(x9243,x9244,x9245,x9242)) % 188.18/188.27 [925]~E(x9251,x9252)+E(f258(x9251,x9253,x9254),f258(x9252,x9253,x9254)) % 188.18/188.27 [926]~E(x9261,x9262)+E(f258(x9263,x9261,x9264),f258(x9263,x9262,x9264)) % 188.18/188.27 [927]~E(x9271,x9272)+E(f258(x9273,x9274,x9271),f258(x9273,x9274,x9272)) % 188.18/188.27 [928]~E(x9281,x9282)+E(f67(x9281,x9283,x9284),f67(x9282,x9283,x9284)) % 188.18/188.27 [929]~E(x9291,x9292)+E(f67(x9293,x9291,x9294),f67(x9293,x9292,x9294)) % 188.18/188.27 [930]~E(x9301,x9302)+E(f67(x9303,x9304,x9301),f67(x9303,x9304,x9302)) % 188.18/188.27 [931]~E(x9311,x9312)+E(f548(x9311,x9313,x9314,x9315,x9316,x9317),f548(x9312,x9313,x9314,x9315,x9316,x9317)) % 188.18/188.27 [932]~E(x9321,x9322)+E(f548(x9323,x9321,x9324,x9325,x9326,x9327),f548(x9323,x9322,x9324,x9325,x9326,x9327)) % 188.18/188.27 [933]~E(x9331,x9332)+E(f548(x9333,x9334,x9331,x9335,x9336,x9337),f548(x9333,x9334,x9332,x9335,x9336,x9337)) % 188.18/188.27 [934]~E(x9341,x9342)+E(f548(x9343,x9344,x9345,x9341,x9346,x9347),f548(x9343,x9344,x9345,x9342,x9346,x9347)) % 188.18/188.27 [935]~E(x9351,x9352)+E(f548(x9353,x9354,x9355,x9356,x9351,x9357),f548(x9353,x9354,x9355,x9356,x9352,x9357)) % 188.18/188.27 [936]~E(x9361,x9362)+E(f548(x9363,x9364,x9365,x9366,x9367,x9361),f548(x9363,x9364,x9365,x9366,x9367,x9362)) % 188.18/188.27 [937]~E(x9371,x9372)+E(f753(x9371,x9373),f753(x9372,x9373)) % 188.18/188.27 [938]~E(x9381,x9382)+E(f753(x9383,x9381),f753(x9383,x9382)) % 188.18/188.27 [939]~E(x9391,x9392)+E(f31(x9391,x9393),f31(x9392,x9393)) % 188.18/188.27 [940]~E(x9401,x9402)+E(f31(x9403,x9401),f31(x9403,x9402)) % 188.18/188.27 [941]~E(x9411,x9412)+E(f352(x9411,x9413,x9414),f352(x9412,x9413,x9414)) % 188.18/188.27 [942]~E(x9421,x9422)+E(f352(x9423,x9421,x9424),f352(x9423,x9422,x9424)) % 188.18/188.27 [943]~E(x9431,x9432)+E(f352(x9433,x9434,x9431),f352(x9433,x9434,x9432)) % 188.18/188.27 [944]~E(x9441,x9442)+E(f148(x9441),f148(x9442)) % 188.18/188.27 [945]~E(x9451,x9452)+E(f488(x9451,x9453,x9454,x9455,x9456),f488(x9452,x9453,x9454,x9455,x9456)) % 188.18/188.27 [946]~E(x9461,x9462)+E(f488(x9463,x9461,x9464,x9465,x9466),f488(x9463,x9462,x9464,x9465,x9466)) % 188.18/188.27 [947]~E(x9471,x9472)+E(f488(x9473,x9474,x9471,x9475,x9476),f488(x9473,x9474,x9472,x9475,x9476)) % 188.18/188.27 [948]~E(x9481,x9482)+E(f488(x9483,x9484,x9485,x9481,x9486),f488(x9483,x9484,x9485,x9482,x9486)) % 188.18/188.27 [949]~E(x9491,x9492)+E(f488(x9493,x9494,x9495,x9496,x9491),f488(x9493,x9494,x9495,x9496,x9492)) % 188.18/188.27 [950]~E(x9501,x9502)+E(f421(x9501,x9503,x9504,x9505),f421(x9502,x9503,x9504,x9505)) % 188.18/188.27 [951]~E(x9511,x9512)+E(f421(x9513,x9511,x9514,x9515),f421(x9513,x9512,x9514,x9515)) % 188.18/188.27 [952]~E(x9521,x9522)+E(f421(x9523,x9524,x9521,x9525),f421(x9523,x9524,x9522,x9525)) % 188.18/188.27 [953]~E(x9531,x9532)+E(f421(x9533,x9534,x9535,x9531),f421(x9533,x9534,x9535,x9532)) % 188.18/188.27 [954]~E(x9541,x9542)+E(f858(x9541,x9543,x9544,x9545,x9546,x9547,x9548,x9549),f858(x9542,x9543,x9544,x9545,x9546,x9547,x9548,x9549)) % 188.18/188.27 [955]~E(x9551,x9552)+E(f858(x9553,x9551,x9554,x9555,x9556,x9557,x9558,x9559),f858(x9553,x9552,x9554,x9555,x9556,x9557,x9558,x9559)) % 188.18/188.27 [956]~E(x9561,x9562)+E(f858(x9563,x9564,x9561,x9565,x9566,x9567,x9568,x9569),f858(x9563,x9564,x9562,x9565,x9566,x9567,x9568,x9569)) % 188.18/188.27 [957]~E(x9571,x9572)+E(f858(x9573,x9574,x9575,x9571,x9576,x9577,x9578,x9579),f858(x9573,x9574,x9575,x9572,x9576,x9577,x9578,x9579)) % 188.18/188.27 [958]~E(x9581,x9582)+E(f858(x9583,x9584,x9585,x9586,x9581,x9587,x9588,x9589),f858(x9583,x9584,x9585,x9586,x9582,x9587,x9588,x9589)) % 188.18/188.27 [959]~E(x9591,x9592)+E(f858(x9593,x9594,x9595,x9596,x9597,x9591,x9598,x9599),f858(x9593,x9594,x9595,x9596,x9597,x9592,x9598,x9599)) % 188.18/188.27 [960]~E(x9601,x9602)+E(f858(x9603,x9604,x9605,x9606,x9607,x9608,x9601,x9609),f858(x9603,x9604,x9605,x9606,x9607,x9608,x9602,x9609)) % 188.18/188.27 [961]~E(x9611,x9612)+E(f858(x9613,x9614,x9615,x9616,x9617,x9618,x9619,x9611),f858(x9613,x9614,x9615,x9616,x9617,x9618,x9619,x9612)) % 188.18/188.27 [962]~E(x9621,x9622)+E(f62(x9621),f62(x9622)) % 188.18/188.27 [963]~E(x9631,x9632)+E(f760(x9631,x9633,x9634,x9635,x9636,x9637,x9638),f760(x9632,x9633,x9634,x9635,x9636,x9637,x9638)) % 188.18/188.27 [964]~E(x9641,x9642)+E(f760(x9643,x9641,x9644,x9645,x9646,x9647,x9648),f760(x9643,x9642,x9644,x9645,x9646,x9647,x9648)) % 188.18/188.27 [965]~E(x9651,x9652)+E(f760(x9653,x9654,x9651,x9655,x9656,x9657,x9658),f760(x9653,x9654,x9652,x9655,x9656,x9657,x9658)) % 188.18/188.27 [966]~E(x9661,x9662)+E(f760(x9663,x9664,x9665,x9661,x9666,x9667,x9668),f760(x9663,x9664,x9665,x9662,x9666,x9667,x9668)) % 188.18/188.27 [967]~E(x9671,x9672)+E(f760(x9673,x9674,x9675,x9676,x9671,x9677,x9678),f760(x9673,x9674,x9675,x9676,x9672,x9677,x9678)) % 188.18/188.27 [968]~E(x9681,x9682)+E(f760(x9683,x9684,x9685,x9686,x9687,x9681,x9688),f760(x9683,x9684,x9685,x9686,x9687,x9682,x9688)) % 188.18/188.27 [969]~E(x9691,x9692)+E(f760(x9693,x9694,x9695,x9696,x9697,x9698,x9691),f760(x9693,x9694,x9695,x9696,x9697,x9698,x9692)) % 188.18/188.27 [970]~E(x9701,x9702)+E(f533(x9701,x9703,x9704,x9705),f533(x9702,x9703,x9704,x9705)) % 188.18/188.27 [971]~E(x9711,x9712)+E(f533(x9713,x9711,x9714,x9715),f533(x9713,x9712,x9714,x9715)) % 188.18/188.27 [972]~E(x9721,x9722)+E(f533(x9723,x9724,x9721,x9725),f533(x9723,x9724,x9722,x9725)) % 188.18/188.27 [973]~E(x9731,x9732)+E(f533(x9733,x9734,x9735,x9731),f533(x9733,x9734,x9735,x9732)) % 188.18/188.27 [974]~E(x9741,x9742)+E(f621(x9741,x9743,x9744),f621(x9742,x9743,x9744)) % 188.18/188.27 [975]~E(x9751,x9752)+E(f621(x9753,x9751,x9754),f621(x9753,x9752,x9754)) % 188.18/188.27 [976]~E(x9761,x9762)+E(f621(x9763,x9764,x9761),f621(x9763,x9764,x9762)) % 188.18/188.27 [977]~E(x9771,x9772)+E(f453(x9771,x9773,x9774,x9775,x9776),f453(x9772,x9773,x9774,x9775,x9776)) % 188.18/188.27 [978]~E(x9781,x9782)+E(f453(x9783,x9781,x9784,x9785,x9786),f453(x9783,x9782,x9784,x9785,x9786)) % 188.18/188.27 [979]~E(x9791,x9792)+E(f453(x9793,x9794,x9791,x9795,x9796),f453(x9793,x9794,x9792,x9795,x9796)) % 188.18/188.27 [980]~E(x9801,x9802)+E(f453(x9803,x9804,x9805,x9801,x9806),f453(x9803,x9804,x9805,x9802,x9806)) % 188.18/188.27 [981]~E(x9811,x9812)+E(f453(x9813,x9814,x9815,x9816,x9811),f453(x9813,x9814,x9815,x9816,x9812)) % 188.18/188.27 [982]~E(x9821,x9822)+E(f783(x9821,x9823,x9824),f783(x9822,x9823,x9824)) % 188.18/188.27 [983]~E(x9831,x9832)+E(f783(x9833,x9831,x9834),f783(x9833,x9832,x9834)) % 188.18/188.27 [984]~E(x9841,x9842)+E(f783(x9843,x9844,x9841),f783(x9843,x9844,x9842)) % 188.18/188.27 [985]~E(x9851,x9852)+E(f199(x9851,x9853),f199(x9852,x9853)) % 188.18/188.27 [986]~E(x9861,x9862)+E(f199(x9863,x9861),f199(x9863,x9862)) % 188.18/188.27 [987]~E(x9871,x9872)+E(f543(x9871,x9873,x9874,x9875),f543(x9872,x9873,x9874,x9875)) % 188.18/188.27 [988]~E(x9881,x9882)+E(f543(x9883,x9881,x9884,x9885),f543(x9883,x9882,x9884,x9885)) % 188.18/188.27 [989]~E(x9891,x9892)+E(f543(x9893,x9894,x9891,x9895),f543(x9893,x9894,x9892,x9895)) % 188.18/188.27 [990]~E(x9901,x9902)+E(f543(x9903,x9904,x9905,x9901),f543(x9903,x9904,x9905,x9902)) % 188.18/188.27 [991]~E(x9911,x9912)+E(f128(x9911,x9913),f128(x9912,x9913)) % 188.18/188.27 [992]~E(x9921,x9922)+E(f128(x9923,x9921),f128(x9923,x9922)) % 188.18/188.27 [993]~E(x9931,x9932)+E(f612(x9931,x9933,x9934,x9935),f612(x9932,x9933,x9934,x9935)) % 188.18/188.27 [994]~E(x9941,x9942)+E(f612(x9943,x9941,x9944,x9945),f612(x9943,x9942,x9944,x9945)) % 188.18/188.27 [995]~E(x9951,x9952)+E(f612(x9953,x9954,x9951,x9955),f612(x9953,x9954,x9952,x9955)) % 188.18/188.27 [996]~E(x9961,x9962)+E(f612(x9963,x9964,x9965,x9961),f612(x9963,x9964,x9965,x9962)) % 188.18/188.27 [997]~E(x9971,x9972)+E(f591(x9971,x9973,x9974,x9975,x9976,x9977),f591(x9972,x9973,x9974,x9975,x9976,x9977)) % 188.18/188.27 [998]~E(x9981,x9982)+E(f591(x9983,x9981,x9984,x9985,x9986,x9987),f591(x9983,x9982,x9984,x9985,x9986,x9987)) % 188.18/188.27 [999]~E(x9991,x9992)+E(f591(x9993,x9994,x9991,x9995,x9996,x9997),f591(x9993,x9994,x9992,x9995,x9996,x9997)) % 188.18/188.27 [1000]~E(x10001,x10002)+E(f591(x10003,x10004,x10005,x10001,x10006,x10007),f591(x10003,x10004,x10005,x10002,x10006,x10007)) % 188.18/188.27 [1001]~E(x10011,x10012)+E(f591(x10013,x10014,x10015,x10016,x10011,x10017),f591(x10013,x10014,x10015,x10016,x10012,x10017)) % 188.18/188.27 [1002]~E(x10021,x10022)+E(f591(x10023,x10024,x10025,x10026,x10027,x10021),f591(x10023,x10024,x10025,x10026,x10027,x10022)) % 188.18/188.27 [1003]~E(x10031,x10032)+E(f851(x10031,x10033,x10034,x10035,x10036,x10037,x10038,x10039),f851(x10032,x10033,x10034,x10035,x10036,x10037,x10038,x10039)) % 188.18/188.27 [1004]~E(x10041,x10042)+E(f851(x10043,x10041,x10044,x10045,x10046,x10047,x10048,x10049),f851(x10043,x10042,x10044,x10045,x10046,x10047,x10048,x10049)) % 188.18/188.27 [1005]~E(x10051,x10052)+E(f851(x10053,x10054,x10051,x10055,x10056,x10057,x10058,x10059),f851(x10053,x10054,x10052,x10055,x10056,x10057,x10058,x10059)) % 188.18/188.27 [1006]~E(x10061,x10062)+E(f851(x10063,x10064,x10065,x10061,x10066,x10067,x10068,x10069),f851(x10063,x10064,x10065,x10062,x10066,x10067,x10068,x10069)) % 188.18/188.27 [1007]~E(x10071,x10072)+E(f851(x10073,x10074,x10075,x10076,x10071,x10077,x10078,x10079),f851(x10073,x10074,x10075,x10076,x10072,x10077,x10078,x10079)) % 188.18/188.27 [1008]~E(x10081,x10082)+E(f851(x10083,x10084,x10085,x10086,x10087,x10081,x10088,x10089),f851(x10083,x10084,x10085,x10086,x10087,x10082,x10088,x10089)) % 188.18/188.27 [1009]~E(x10091,x10092)+E(f851(x10093,x10094,x10095,x10096,x10097,x10098,x10091,x10099),f851(x10093,x10094,x10095,x10096,x10097,x10098,x10092,x10099)) % 188.18/188.27 [1010]~E(x10101,x10102)+E(f851(x10103,x10104,x10105,x10106,x10107,x10108,x10109,x10101),f851(x10103,x10104,x10105,x10106,x10107,x10108,x10109,x10102)) % 188.18/188.27 [1011]~E(x10111,x10112)+E(f236(x10111,x10113),f236(x10112,x10113)) % 188.18/188.27 [1012]~E(x10121,x10122)+E(f236(x10123,x10121),f236(x10123,x10122)) % 188.18/188.27 [1013]~E(x10131,x10132)+E(f779(x10131,x10133,x10134),f779(x10132,x10133,x10134)) % 188.18/188.27 [1014]~E(x10141,x10142)+E(f779(x10143,x10141,x10144),f779(x10143,x10142,x10144)) % 188.18/188.27 [1015]~E(x10151,x10152)+E(f779(x10153,x10154,x10151),f779(x10153,x10154,x10152)) % 188.18/188.27 [1016]~E(x10161,x10162)+E(f286(x10161),f286(x10162)) % 188.18/188.27 [1017]~E(x10171,x10172)+E(f569(x10171,x10173,x10174),f569(x10172,x10173,x10174)) % 188.18/188.27 [1018]~E(x10181,x10182)+E(f569(x10183,x10181,x10184),f569(x10183,x10182,x10184)) % 188.18/188.27 [1019]~E(x10191,x10192)+E(f569(x10193,x10194,x10191),f569(x10193,x10194,x10192)) % 188.18/188.27 [1020]~E(x10201,x10202)+E(f253(x10201,x10203,x10204),f253(x10202,x10203,x10204)) % 188.18/188.27 [1021]~E(x10211,x10212)+E(f253(x10213,x10211,x10214),f253(x10213,x10212,x10214)) % 188.18/188.27 [1022]~E(x10221,x10222)+E(f253(x10223,x10224,x10221),f253(x10223,x10224,x10222)) % 188.18/188.27 [1023]~E(x10231,x10232)+E(f187(x10231),f187(x10232)) % 188.18/188.27 [1024]~E(x10241,x10242)+E(f721(x10241,x10243),f721(x10242,x10243)) % 188.18/188.27 [1025]~E(x10251,x10252)+E(f721(x10253,x10251),f721(x10253,x10252)) % 188.18/188.27 [1026]~E(x10261,x10262)+E(f233(x10261,x10263,x10264,x10265,x10266),f233(x10262,x10263,x10264,x10265,x10266)) % 188.18/188.27 [1027]~E(x10271,x10272)+E(f233(x10273,x10271,x10274,x10275,x10276),f233(x10273,x10272,x10274,x10275,x10276)) % 188.18/188.27 [1028]~E(x10281,x10282)+E(f233(x10283,x10284,x10281,x10285,x10286),f233(x10283,x10284,x10282,x10285,x10286)) % 188.18/188.27 [1029]~E(x10291,x10292)+E(f233(x10293,x10294,x10295,x10291,x10296),f233(x10293,x10294,x10295,x10292,x10296)) % 188.18/188.27 [1030]~E(x10301,x10302)+E(f233(x10303,x10304,x10305,x10306,x10301),f233(x10303,x10304,x10305,x10306,x10302)) % 188.18/188.27 [1031]~E(x10311,x10312)+E(f657(x10311,x10313,x10314,x10315,x10316,x10317),f657(x10312,x10313,x10314,x10315,x10316,x10317)) % 188.18/188.27 [1032]~E(x10321,x10322)+E(f657(x10323,x10321,x10324,x10325,x10326,x10327),f657(x10323,x10322,x10324,x10325,x10326,x10327)) % 188.18/188.27 [1033]~E(x10331,x10332)+E(f657(x10333,x10334,x10331,x10335,x10336,x10337),f657(x10333,x10334,x10332,x10335,x10336,x10337)) % 188.18/188.27 [1034]~E(x10341,x10342)+E(f657(x10343,x10344,x10345,x10341,x10346,x10347),f657(x10343,x10344,x10345,x10342,x10346,x10347)) % 188.18/188.27 [1035]~E(x10351,x10352)+E(f657(x10353,x10354,x10355,x10356,x10351,x10357),f657(x10353,x10354,x10355,x10356,x10352,x10357)) % 188.18/188.27 [1036]~E(x10361,x10362)+E(f657(x10363,x10364,x10365,x10366,x10367,x10361),f657(x10363,x10364,x10365,x10366,x10367,x10362)) % 188.18/188.27 [1037]~E(x10371,x10372)+E(f868(x10371,x10373,x10374),f868(x10372,x10373,x10374)) % 188.18/188.27 [1038]~E(x10381,x10382)+E(f868(x10383,x10381,x10384),f868(x10383,x10382,x10384)) % 188.18/188.27 [1039]~E(x10391,x10392)+E(f868(x10393,x10394,x10391),f868(x10393,x10394,x10392)) % 188.18/188.27 [1040]~E(x10401,x10402)+E(f608(x10401,x10403,x10404,x10405,x10406),f608(x10402,x10403,x10404,x10405,x10406)) % 188.18/188.27 [1041]~E(x10411,x10412)+E(f608(x10413,x10411,x10414,x10415,x10416),f608(x10413,x10412,x10414,x10415,x10416)) % 188.18/188.27 [1042]~E(x10421,x10422)+E(f608(x10423,x10424,x10421,x10425,x10426),f608(x10423,x10424,x10422,x10425,x10426)) % 188.18/188.27 [1043]~E(x10431,x10432)+E(f608(x10433,x10434,x10435,x10431,x10436),f608(x10433,x10434,x10435,x10432,x10436)) % 188.18/188.27 [1044]~E(x10441,x10442)+E(f608(x10443,x10444,x10445,x10446,x10441),f608(x10443,x10444,x10445,x10446,x10442)) % 188.18/188.27 [1045]~E(x10451,x10452)+E(f384(x10451,x10453,x10454),f384(x10452,x10453,x10454)) % 188.18/188.27 [1046]~E(x10461,x10462)+E(f384(x10463,x10461,x10464),f384(x10463,x10462,x10464)) % 188.18/188.27 [1047]~E(x10471,x10472)+E(f384(x10473,x10474,x10471),f384(x10473,x10474,x10472)) % 188.18/188.27 [1048]~E(x10481,x10482)+E(f578(x10481,x10483,x10484,x10485),f578(x10482,x10483,x10484,x10485)) % 188.18/188.27 [1049]~E(x10491,x10492)+E(f578(x10493,x10491,x10494,x10495),f578(x10493,x10492,x10494,x10495)) % 188.18/188.27 [1050]~E(x10501,x10502)+E(f578(x10503,x10504,x10501,x10505),f578(x10503,x10504,x10502,x10505)) % 188.18/188.27 [1051]~E(x10511,x10512)+E(f578(x10513,x10514,x10515,x10511),f578(x10513,x10514,x10515,x10512)) % 188.18/188.27 [1052]~E(x10521,x10522)+E(f831(x10521,x10523),f831(x10522,x10523)) % 188.18/188.27 [1053]~E(x10531,x10532)+E(f831(x10533,x10531),f831(x10533,x10532)) % 188.18/188.27 [1054]~E(x10541,x10542)+E(f784(x10541,x10543,x10544,x10545),f784(x10542,x10543,x10544,x10545)) % 188.18/188.27 [1055]~E(x10551,x10552)+E(f784(x10553,x10551,x10554,x10555),f784(x10553,x10552,x10554,x10555)) % 188.18/188.27 [1056]~E(x10561,x10562)+E(f784(x10563,x10564,x10561,x10565),f784(x10563,x10564,x10562,x10565)) % 188.18/188.27 [1057]~E(x10571,x10572)+E(f784(x10573,x10574,x10575,x10571),f784(x10573,x10574,x10575,x10572)) % 188.18/188.27 [1058]~E(x10581,x10582)+E(f394(x10581,x10583,x10584,x10585,x10586,x10587,x10588,x10589),f394(x10582,x10583,x10584,x10585,x10586,x10587,x10588,x10589)) % 188.18/188.27 [1059]~E(x10591,x10592)+E(f394(x10593,x10591,x10594,x10595,x10596,x10597,x10598,x10599),f394(x10593,x10592,x10594,x10595,x10596,x10597,x10598,x10599)) % 188.18/188.27 [1060]~E(x10601,x10602)+E(f394(x10603,x10604,x10601,x10605,x10606,x10607,x10608,x10609),f394(x10603,x10604,x10602,x10605,x10606,x10607,x10608,x10609)) % 188.18/188.27 [1061]~E(x10611,x10612)+E(f394(x10613,x10614,x10615,x10611,x10616,x10617,x10618,x10619),f394(x10613,x10614,x10615,x10612,x10616,x10617,x10618,x10619)) % 188.18/188.27 [1062]~E(x10621,x10622)+E(f394(x10623,x10624,x10625,x10626,x10621,x10627,x10628,x10629),f394(x10623,x10624,x10625,x10626,x10622,x10627,x10628,x10629)) % 188.18/188.27 [1063]~E(x10631,x10632)+E(f394(x10633,x10634,x10635,x10636,x10637,x10631,x10638,x10639),f394(x10633,x10634,x10635,x10636,x10637,x10632,x10638,x10639)) % 188.18/188.27 [1064]~E(x10641,x10642)+E(f394(x10643,x10644,x10645,x10646,x10647,x10648,x10641,x10649),f394(x10643,x10644,x10645,x10646,x10647,x10648,x10642,x10649)) % 188.18/188.27 [1065]~E(x10651,x10652)+E(f394(x10653,x10654,x10655,x10656,x10657,x10658,x10659,x10651),f394(x10653,x10654,x10655,x10656,x10657,x10658,x10659,x10652)) % 188.18/188.27 [1066]~E(x10661,x10662)+E(f519(x10661,x10663,x10664,x10665,x10666),f519(x10662,x10663,x10664,x10665,x10666)) % 188.18/188.27 [1067]~E(x10671,x10672)+E(f519(x10673,x10671,x10674,x10675,x10676),f519(x10673,x10672,x10674,x10675,x10676)) % 188.18/188.27 [1068]~E(x10681,x10682)+E(f519(x10683,x10684,x10681,x10685,x10686),f519(x10683,x10684,x10682,x10685,x10686)) % 188.18/188.27 [1069]~E(x10691,x10692)+E(f519(x10693,x10694,x10695,x10691,x10696),f519(x10693,x10694,x10695,x10692,x10696)) % 188.18/188.27 [1070]~E(x10701,x10702)+E(f519(x10703,x10704,x10705,x10706,x10701),f519(x10703,x10704,x10705,x10706,x10702)) % 188.18/188.27 [1071]~E(x10711,x10712)+E(f443(x10711,x10713),f443(x10712,x10713)) % 188.18/188.27 [1072]~E(x10721,x10722)+E(f443(x10723,x10721),f443(x10723,x10722)) % 188.18/188.27 [1073]~E(x10731,x10732)+E(f60(x10731,x10733,x10734),f60(x10732,x10733,x10734)) % 188.18/188.27 [1074]~E(x10741,x10742)+E(f60(x10743,x10741,x10744),f60(x10743,x10742,x10744)) % 188.18/188.27 [1075]~E(x10751,x10752)+E(f60(x10753,x10754,x10751),f60(x10753,x10754,x10752)) % 188.18/188.27 [1076]~E(x10761,x10762)+E(f399(x10761,x10763,x10764,x10765),f399(x10762,x10763,x10764,x10765)) % 188.18/188.27 [1077]~E(x10771,x10772)+E(f399(x10773,x10771,x10774,x10775),f399(x10773,x10772,x10774,x10775)) % 188.18/188.27 [1078]~E(x10781,x10782)+E(f399(x10783,x10784,x10781,x10785),f399(x10783,x10784,x10782,x10785)) % 188.18/188.27 [1079]~E(x10791,x10792)+E(f399(x10793,x10794,x10795,x10791),f399(x10793,x10794,x10795,x10792)) % 188.18/188.27 [1080]~E(x10801,x10802)+E(f762(x10801,x10803),f762(x10802,x10803)) % 188.18/188.27 [1081]~E(x10811,x10812)+E(f762(x10813,x10811),f762(x10813,x10812)) % 188.18/188.27 [1082]~E(x10821,x10822)+E(f231(x10821,x10823,x10824),f231(x10822,x10823,x10824)) % 188.18/188.27 [1083]~E(x10831,x10832)+E(f231(x10833,x10831,x10834),f231(x10833,x10832,x10834)) % 188.18/188.27 [1084]~E(x10841,x10842)+E(f231(x10843,x10844,x10841),f231(x10843,x10844,x10842)) % 188.18/188.27 [1085]~E(x10851,x10852)+E(f426(x10851,x10853,x10854,x10855),f426(x10852,x10853,x10854,x10855)) % 188.18/188.27 [1086]~E(x10861,x10862)+E(f426(x10863,x10861,x10864,x10865),f426(x10863,x10862,x10864,x10865)) % 188.18/188.27 [1087]~E(x10871,x10872)+E(f426(x10873,x10874,x10871,x10875),f426(x10873,x10874,x10872,x10875)) % 188.18/188.27 [1088]~E(x10881,x10882)+E(f426(x10883,x10884,x10885,x10881),f426(x10883,x10884,x10885,x10882)) % 188.18/188.27 [1089]~E(x10891,x10892)+E(f350(x10891,x10893,x10894),f350(x10892,x10893,x10894)) % 188.18/188.27 [1090]~E(x10901,x10902)+E(f350(x10903,x10901,x10904),f350(x10903,x10902,x10904)) % 188.18/188.27 [1091]~E(x10911,x10912)+E(f350(x10913,x10914,x10911),f350(x10913,x10914,x10912)) % 188.18/188.27 [1092]~E(x10921,x10922)+E(f592(x10921,x10923,x10924,x10925,x10926,x10927),f592(x10922,x10923,x10924,x10925,x10926,x10927)) % 188.18/188.27 [1093]~E(x10931,x10932)+E(f592(x10933,x10931,x10934,x10935,x10936,x10937),f592(x10933,x10932,x10934,x10935,x10936,x10937)) % 188.18/188.27 [1094]~E(x10941,x10942)+E(f592(x10943,x10944,x10941,x10945,x10946,x10947),f592(x10943,x10944,x10942,x10945,x10946,x10947)) % 188.18/188.27 [1095]~E(x10951,x10952)+E(f592(x10953,x10954,x10955,x10951,x10956,x10957),f592(x10953,x10954,x10955,x10952,x10956,x10957)) % 188.18/188.27 [1096]~E(x10961,x10962)+E(f592(x10963,x10964,x10965,x10966,x10961,x10967),f592(x10963,x10964,x10965,x10966,x10962,x10967)) % 188.18/188.27 [1097]~E(x10971,x10972)+E(f592(x10973,x10974,x10975,x10976,x10977,x10971),f592(x10973,x10974,x10975,x10976,x10977,x10972)) % 188.18/188.27 [1098]~E(x10981,x10982)+E(f512(x10981,x10983,x10984,x10985,x10986),f512(x10982,x10983,x10984,x10985,x10986)) % 188.18/188.27 [1099]~E(x10991,x10992)+E(f512(x10993,x10991,x10994,x10995,x10996),f512(x10993,x10992,x10994,x10995,x10996)) % 188.18/188.27 [1100]~E(x11001,x11002)+E(f512(x11003,x11004,x11001,x11005,x11006),f512(x11003,x11004,x11002,x11005,x11006)) % 188.18/188.27 [1101]~E(x11011,x11012)+E(f512(x11013,x11014,x11015,x11011,x11016),f512(x11013,x11014,x11015,x11012,x11016)) % 188.18/188.27 [1102]~E(x11021,x11022)+E(f512(x11023,x11024,x11025,x11026,x11021),f512(x11023,x11024,x11025,x11026,x11022)) % 188.18/188.27 [1103]~E(x11031,x11032)+E(f594(x11031,x11033,x11034,x11035,x11036,x11037),f594(x11032,x11033,x11034,x11035,x11036,x11037)) % 188.18/188.27 [1104]~E(x11041,x11042)+E(f594(x11043,x11041,x11044,x11045,x11046,x11047),f594(x11043,x11042,x11044,x11045,x11046,x11047)) % 188.18/188.27 [1105]~E(x11051,x11052)+E(f594(x11053,x11054,x11051,x11055,x11056,x11057),f594(x11053,x11054,x11052,x11055,x11056,x11057)) % 188.18/188.27 [1106]~E(x11061,x11062)+E(f594(x11063,x11064,x11065,x11061,x11066,x11067),f594(x11063,x11064,x11065,x11062,x11066,x11067)) % 188.18/188.27 [1107]~E(x11071,x11072)+E(f594(x11073,x11074,x11075,x11076,x11071,x11077),f594(x11073,x11074,x11075,x11076,x11072,x11077)) % 188.18/188.27 [1108]~E(x11081,x11082)+E(f594(x11083,x11084,x11085,x11086,x11087,x11081),f594(x11083,x11084,x11085,x11086,x11087,x11082)) % 188.18/188.27 [1109]~E(x11091,x11092)+E(f618(x11091,x11093,x11094,x11095,x11096,x11097,x11098,x11099),f618(x11092,x11093,x11094,x11095,x11096,x11097,x11098,x11099)) % 188.18/188.27 [1110]~E(x11101,x11102)+E(f618(x11103,x11101,x11104,x11105,x11106,x11107,x11108,x11109),f618(x11103,x11102,x11104,x11105,x11106,x11107,x11108,x11109)) % 188.18/188.27 [1111]~E(x11111,x11112)+E(f618(x11113,x11114,x11111,x11115,x11116,x11117,x11118,x11119),f618(x11113,x11114,x11112,x11115,x11116,x11117,x11118,x11119)) % 188.18/188.27 [1112]~E(x11121,x11122)+E(f618(x11123,x11124,x11125,x11121,x11126,x11127,x11128,x11129),f618(x11123,x11124,x11125,x11122,x11126,x11127,x11128,x11129)) % 188.18/188.27 [1113]~E(x11131,x11132)+E(f618(x11133,x11134,x11135,x11136,x11131,x11137,x11138,x11139),f618(x11133,x11134,x11135,x11136,x11132,x11137,x11138,x11139)) % 188.18/188.27 [1114]~E(x11141,x11142)+E(f618(x11143,x11144,x11145,x11146,x11147,x11141,x11148,x11149),f618(x11143,x11144,x11145,x11146,x11147,x11142,x11148,x11149)) % 188.18/188.27 [1115]~E(x11151,x11152)+E(f618(x11153,x11154,x11155,x11156,x11157,x11158,x11151,x11159),f618(x11153,x11154,x11155,x11156,x11157,x11158,x11152,x11159)) % 188.18/188.27 [1116]~E(x11161,x11162)+E(f618(x11163,x11164,x11165,x11166,x11167,x11168,x11169,x11161),f618(x11163,x11164,x11165,x11166,x11167,x11168,x11169,x11162)) % 188.18/188.27 [1117]~E(x11171,x11172)+E(f202(x11171,x11173,x11174,x11175),f202(x11172,x11173,x11174,x11175)) % 188.18/188.27 [1118]~E(x11181,x11182)+E(f202(x11183,x11181,x11184,x11185),f202(x11183,x11182,x11184,x11185)) % 188.18/188.27 [1119]~E(x11191,x11192)+E(f202(x11193,x11194,x11191,x11195),f202(x11193,x11194,x11192,x11195)) % 188.18/188.27 [1120]~E(x11201,x11202)+E(f202(x11203,x11204,x11205,x11201),f202(x11203,x11204,x11205,x11202)) % 188.18/188.27 [1121]~E(x11211,x11212)+E(f511(x11211,x11213,x11214,x11215,x11216,x11217,x11218,x11219),f511(x11212,x11213,x11214,x11215,x11216,x11217,x11218,x11219)) % 188.18/188.27 [1122]~E(x11221,x11222)+E(f511(x11223,x11221,x11224,x11225,x11226,x11227,x11228,x11229),f511(x11223,x11222,x11224,x11225,x11226,x11227,x11228,x11229)) % 188.18/188.27 [1123]~E(x11231,x11232)+E(f511(x11233,x11234,x11231,x11235,x11236,x11237,x11238,x11239),f511(x11233,x11234,x11232,x11235,x11236,x11237,x11238,x11239)) % 188.18/188.27 [1124]~E(x11241,x11242)+E(f511(x11243,x11244,x11245,x11241,x11246,x11247,x11248,x11249),f511(x11243,x11244,x11245,x11242,x11246,x11247,x11248,x11249)) % 188.18/188.27 [1125]~E(x11251,x11252)+E(f511(x11253,x11254,x11255,x11256,x11251,x11257,x11258,x11259),f511(x11253,x11254,x11255,x11256,x11252,x11257,x11258,x11259)) % 188.18/188.27 [1126]~E(x11261,x11262)+E(f511(x11263,x11264,x11265,x11266,x11267,x11261,x11268,x11269),f511(x11263,x11264,x11265,x11266,x11267,x11262,x11268,x11269)) % 188.18/188.27 [1127]~E(x11271,x11272)+E(f511(x11273,x11274,x11275,x11276,x11277,x11278,x11271,x11279),f511(x11273,x11274,x11275,x11276,x11277,x11278,x11272,x11279)) % 188.18/188.27 [1128]~E(x11281,x11282)+E(f511(x11283,x11284,x11285,x11286,x11287,x11288,x11289,x11281),f511(x11283,x11284,x11285,x11286,x11287,x11288,x11289,x11282)) % 188.18/188.27 [1129]~E(x11291,x11292)+E(f461(x11291,x11293,x11294,x11295),f461(x11292,x11293,x11294,x11295)) % 188.18/188.27 [1130]~E(x11301,x11302)+E(f461(x11303,x11301,x11304,x11305),f461(x11303,x11302,x11304,x11305)) % 188.18/188.27 [1131]~E(x11311,x11312)+E(f461(x11313,x11314,x11311,x11315),f461(x11313,x11314,x11312,x11315)) % 188.18/188.27 [1132]~E(x11321,x11322)+E(f461(x11323,x11324,x11325,x11321),f461(x11323,x11324,x11325,x11322)) % 188.18/188.27 [1133]~E(x11331,x11332)+E(f833(x11331,x11333,x11334),f833(x11332,x11333,x11334)) % 188.18/188.27 [1134]~E(x11341,x11342)+E(f833(x11343,x11341,x11344),f833(x11343,x11342,x11344)) % 188.18/188.27 [1135]~E(x11351,x11352)+E(f833(x11353,x11354,x11351),f833(x11353,x11354,x11352)) % 188.18/188.27 [1136]~E(x11361,x11362)+E(f656(x11361,x11363,x11364,x11365),f656(x11362,x11363,x11364,x11365)) % 188.18/188.27 [1137]~E(x11371,x11372)+E(f656(x11373,x11371,x11374,x11375),f656(x11373,x11372,x11374,x11375)) % 188.18/188.27 [1138]~E(x11381,x11382)+E(f656(x11383,x11384,x11381,x11385),f656(x11383,x11384,x11382,x11385)) % 188.18/188.27 [1139]~E(x11391,x11392)+E(f656(x11393,x11394,x11395,x11391),f656(x11393,x11394,x11395,x11392)) % 188.18/188.27 [1140]~E(x11401,x11402)+E(f885(x11401,x11403,x11404),f885(x11402,x11403,x11404)) % 188.18/188.27 [1141]~E(x11411,x11412)+E(f885(x11413,x11411,x11414),f885(x11413,x11412,x11414)) % 188.18/188.27 [1142]~E(x11421,x11422)+E(f885(x11423,x11424,x11421),f885(x11423,x11424,x11422)) % 188.18/188.27 [1143]~E(x11431,x11432)+E(f117(x11431),f117(x11432)) % 188.18/188.27 [1144]~E(x11441,x11442)+E(f374(x11441),f374(x11442)) % 188.18/188.27 [1145]~E(x11451,x11452)+E(f129(x11451,x11453,x11454,x11455),f129(x11452,x11453,x11454,x11455)) % 188.18/188.27 [1146]~E(x11461,x11462)+E(f129(x11463,x11461,x11464,x11465),f129(x11463,x11462,x11464,x11465)) % 188.18/188.27 [1147]~E(x11471,x11472)+E(f129(x11473,x11474,x11471,x11475),f129(x11473,x11474,x11472,x11475)) % 188.18/188.27 [1148]~E(x11481,x11482)+E(f129(x11483,x11484,x11485,x11481),f129(x11483,x11484,x11485,x11482)) % 188.18/188.27 [1149]~E(x11491,x11492)+E(f82(x11491,x11493,x11494,x11495,x11496),f82(x11492,x11493,x11494,x11495,x11496)) % 188.18/188.27 [1150]~E(x11501,x11502)+E(f82(x11503,x11501,x11504,x11505,x11506),f82(x11503,x11502,x11504,x11505,x11506)) % 188.18/188.27 [1151]~E(x11511,x11512)+E(f82(x11513,x11514,x11511,x11515,x11516),f82(x11513,x11514,x11512,x11515,x11516)) % 188.18/188.27 [1152]~E(x11521,x11522)+E(f82(x11523,x11524,x11525,x11521,x11526),f82(x11523,x11524,x11525,x11522,x11526)) % 188.18/188.27 [1153]~E(x11531,x11532)+E(f82(x11533,x11534,x11535,x11536,x11531),f82(x11533,x11534,x11535,x11536,x11532)) % 188.18/188.27 [1154]~E(x11541,x11542)+E(f467(x11541,x11543,x11544,x11545,x11546,x11547),f467(x11542,x11543,x11544,x11545,x11546,x11547)) % 188.18/188.27 [1155]~E(x11551,x11552)+E(f467(x11553,x11551,x11554,x11555,x11556,x11557),f467(x11553,x11552,x11554,x11555,x11556,x11557)) % 188.18/188.27 [1156]~E(x11561,x11562)+E(f467(x11563,x11564,x11561,x11565,x11566,x11567),f467(x11563,x11564,x11562,x11565,x11566,x11567)) % 188.18/188.27 [1157]~E(x11571,x11572)+E(f467(x11573,x11574,x11575,x11571,x11576,x11577),f467(x11573,x11574,x11575,x11572,x11576,x11577)) % 188.18/188.27 [1158]~E(x11581,x11582)+E(f467(x11583,x11584,x11585,x11586,x11581,x11587),f467(x11583,x11584,x11585,x11586,x11582,x11587)) % 188.18/188.27 [1159]~E(x11591,x11592)+E(f467(x11593,x11594,x11595,x11596,x11597,x11591),f467(x11593,x11594,x11595,x11596,x11597,x11592)) % 188.18/188.27 [1160]~E(x11601,x11602)+E(f588(x11601,x11603,x11604),f588(x11602,x11603,x11604)) % 188.18/188.27 [1161]~E(x11611,x11612)+E(f588(x11613,x11611,x11614),f588(x11613,x11612,x11614)) % 188.18/188.27 [1162]~E(x11621,x11622)+E(f588(x11623,x11624,x11621),f588(x11623,x11624,x11622)) % 188.18/188.27 [1163]~E(x11631,x11632)+E(f864(x11631,x11633,x11634,x11635,x11636,x11637),f864(x11632,x11633,x11634,x11635,x11636,x11637)) % 188.18/188.27 [1164]~E(x11641,x11642)+E(f864(x11643,x11641,x11644,x11645,x11646,x11647),f864(x11643,x11642,x11644,x11645,x11646,x11647)) % 188.18/188.27 [1165]~E(x11651,x11652)+E(f864(x11653,x11654,x11651,x11655,x11656,x11657),f864(x11653,x11654,x11652,x11655,x11656,x11657)) % 188.18/188.27 [1166]~E(x11661,x11662)+E(f864(x11663,x11664,x11665,x11661,x11666,x11667),f864(x11663,x11664,x11665,x11662,x11666,x11667)) % 188.18/188.27 [1167]~E(x11671,x11672)+E(f864(x11673,x11674,x11675,x11676,x11671,x11677),f864(x11673,x11674,x11675,x11676,x11672,x11677)) % 188.18/188.27 [1168]~E(x11681,x11682)+E(f864(x11683,x11684,x11685,x11686,x11687,x11681),f864(x11683,x11684,x11685,x11686,x11687,x11682)) % 188.18/188.27 [1169]~E(x11691,x11692)+E(f558(x11691,x11693,x11694,x11695,x11696,x11697),f558(x11692,x11693,x11694,x11695,x11696,x11697)) % 188.18/188.27 [1170]~E(x11701,x11702)+E(f558(x11703,x11701,x11704,x11705,x11706,x11707),f558(x11703,x11702,x11704,x11705,x11706,x11707)) % 188.18/188.27 [1171]~E(x11711,x11712)+E(f558(x11713,x11714,x11711,x11715,x11716,x11717),f558(x11713,x11714,x11712,x11715,x11716,x11717)) % 188.18/188.27 [1172]~E(x11721,x11722)+E(f558(x11723,x11724,x11725,x11721,x11726,x11727),f558(x11723,x11724,x11725,x11722,x11726,x11727)) % 188.18/188.27 [1173]~E(x11731,x11732)+E(f558(x11733,x11734,x11735,x11736,x11731,x11737),f558(x11733,x11734,x11735,x11736,x11732,x11737)) % 188.18/188.27 [1174]~E(x11741,x11742)+E(f558(x11743,x11744,x11745,x11746,x11747,x11741),f558(x11743,x11744,x11745,x11746,x11747,x11742)) % 188.18/188.27 [1175]~E(x11751,x11752)+E(f457(x11751,x11753,x11754,x11755),f457(x11752,x11753,x11754,x11755)) % 188.18/188.27 [1176]~E(x11761,x11762)+E(f457(x11763,x11761,x11764,x11765),f457(x11763,x11762,x11764,x11765)) % 188.18/188.27 [1177]~E(x11771,x11772)+E(f457(x11773,x11774,x11771,x11775),f457(x11773,x11774,x11772,x11775)) % 188.18/188.27 [1178]~E(x11781,x11782)+E(f457(x11783,x11784,x11785,x11781),f457(x11783,x11784,x11785,x11782)) % 188.18/188.27 [1179]~E(x11791,x11792)+E(f523(x11791,x11793,x11794,x11795),f523(x11792,x11793,x11794,x11795)) % 188.18/188.27 [1180]~E(x11801,x11802)+E(f523(x11803,x11801,x11804,x11805),f523(x11803,x11802,x11804,x11805)) % 188.18/188.27 [1181]~E(x11811,x11812)+E(f523(x11813,x11814,x11811,x11815),f523(x11813,x11814,x11812,x11815)) % 188.18/188.27 [1182]~E(x11821,x11822)+E(f523(x11823,x11824,x11825,x11821),f523(x11823,x11824,x11825,x11822)) % 188.18/188.27 [1183]~E(x11831,x11832)+E(f319(x11831,x11833),f319(x11832,x11833)) % 188.18/188.27 [1184]~E(x11841,x11842)+E(f319(x11843,x11841),f319(x11843,x11842)) % 188.18/188.27 [1185]~E(x11851,x11852)+E(f742(x11851,x11853,x11854,x11855),f742(x11852,x11853,x11854,x11855)) % 188.18/188.27 [1186]~E(x11861,x11862)+E(f742(x11863,x11861,x11864,x11865),f742(x11863,x11862,x11864,x11865)) % 188.18/188.27 [1187]~E(x11871,x11872)+E(f742(x11873,x11874,x11871,x11875),f742(x11873,x11874,x11872,x11875)) % 188.18/188.27 [1188]~E(x11881,x11882)+E(f742(x11883,x11884,x11885,x11881),f742(x11883,x11884,x11885,x11882)) % 188.18/188.27 [1189]~E(x11891,x11892)+E(f666(x11891,x11893,x11894,x11895,x11896),f666(x11892,x11893,x11894,x11895,x11896)) % 188.18/188.27 [1190]~E(x11901,x11902)+E(f666(x11903,x11901,x11904,x11905,x11906),f666(x11903,x11902,x11904,x11905,x11906)) % 188.18/188.27 [1191]~E(x11911,x11912)+E(f666(x11913,x11914,x11911,x11915,x11916),f666(x11913,x11914,x11912,x11915,x11916)) % 188.18/188.27 [1192]~E(x11921,x11922)+E(f666(x11923,x11924,x11925,x11921,x11926),f666(x11923,x11924,x11925,x11922,x11926)) % 188.18/188.27 [1193]~E(x11931,x11932)+E(f666(x11933,x11934,x11935,x11936,x11931),f666(x11933,x11934,x11935,x11936,x11932)) % 188.18/188.27 [1194]~E(x11941,x11942)+E(f796(x11941,x11943,x11944,x11945),f796(x11942,x11943,x11944,x11945)) % 188.18/188.27 [1195]~E(x11951,x11952)+E(f796(x11953,x11951,x11954,x11955),f796(x11953,x11952,x11954,x11955)) % 188.18/188.27 [1196]~E(x11961,x11962)+E(f796(x11963,x11964,x11961,x11965),f796(x11963,x11964,x11962,x11965)) % 188.18/188.27 [1197]~E(x11971,x11972)+E(f796(x11973,x11974,x11975,x11971),f796(x11973,x11974,x11975,x11972)) % 188.18/188.27 [1198]~E(x11981,x11982)+E(f803(x11981,x11983,x11984,x11985,x11986,x11987,x11988),f803(x11982,x11983,x11984,x11985,x11986,x11987,x11988)) % 188.18/188.27 [1199]~E(x11991,x11992)+E(f803(x11993,x11991,x11994,x11995,x11996,x11997,x11998),f803(x11993,x11992,x11994,x11995,x11996,x11997,x11998)) % 188.18/188.27 [1200]~E(x12001,x12002)+E(f803(x12003,x12004,x12001,x12005,x12006,x12007,x12008),f803(x12003,x12004,x12002,x12005,x12006,x12007,x12008)) % 188.18/188.27 [1201]~E(x12011,x12012)+E(f803(x12013,x12014,x12015,x12011,x12016,x12017,x12018),f803(x12013,x12014,x12015,x12012,x12016,x12017,x12018)) % 188.18/188.27 [1202]~E(x12021,x12022)+E(f803(x12023,x12024,x12025,x12026,x12021,x12027,x12028),f803(x12023,x12024,x12025,x12026,x12022,x12027,x12028)) % 188.18/188.27 [1203]~E(x12031,x12032)+E(f803(x12033,x12034,x12035,x12036,x12037,x12031,x12038),f803(x12033,x12034,x12035,x12036,x12037,x12032,x12038)) % 188.18/188.27 [1204]~E(x12041,x12042)+E(f803(x12043,x12044,x12045,x12046,x12047,x12048,x12041),f803(x12043,x12044,x12045,x12046,x12047,x12048,x12042)) % 188.18/188.27 [1205]~E(x12051,x12052)+E(f61(x12051),f61(x12052)) % 188.18/188.27 [1206]~E(x12061,x12062)+E(f634(x12061,x12063,x12064,x12065,x12066),f634(x12062,x12063,x12064,x12065,x12066)) % 188.18/188.27 [1207]~E(x12071,x12072)+E(f634(x12073,x12071,x12074,x12075,x12076),f634(x12073,x12072,x12074,x12075,x12076)) % 188.18/188.27 [1208]~E(x12081,x12082)+E(f634(x12083,x12084,x12081,x12085,x12086),f634(x12083,x12084,x12082,x12085,x12086)) % 188.18/188.27 [1209]~E(x12091,x12092)+E(f634(x12093,x12094,x12095,x12091,x12096),f634(x12093,x12094,x12095,x12092,x12096)) % 188.18/188.27 [1210]~E(x12101,x12102)+E(f634(x12103,x12104,x12105,x12106,x12101),f634(x12103,x12104,x12105,x12106,x12102)) % 188.18/188.27 [1211]~E(x12111,x12112)+E(f522(x12111,x12113,x12114),f522(x12112,x12113,x12114)) % 188.18/188.27 [1212]~E(x12121,x12122)+E(f522(x12123,x12121,x12124),f522(x12123,x12122,x12124)) % 188.18/188.27 [1213]~E(x12131,x12132)+E(f522(x12133,x12134,x12131),f522(x12133,x12134,x12132)) % 188.18/188.27 [1214]~E(x12141,x12142)+E(f683(x12141,x12143,x12144,x12145),f683(x12142,x12143,x12144,x12145)) % 188.18/188.27 [1215]~E(x12151,x12152)+E(f683(x12153,x12151,x12154,x12155),f683(x12153,x12152,x12154,x12155)) % 188.18/188.27 [1216]~E(x12161,x12162)+E(f683(x12163,x12164,x12161,x12165),f683(x12163,x12164,x12162,x12165)) % 188.18/188.27 [1217]~E(x12171,x12172)+E(f683(x12173,x12174,x12175,x12171),f683(x12173,x12174,x12175,x12172)) % 188.18/188.27 [1218]~E(x12181,x12182)+E(f568(x12181,x12183),f568(x12182,x12183)) % 188.18/188.27 [1219]~E(x12191,x12192)+E(f568(x12193,x12191),f568(x12193,x12192)) % 188.18/188.27 [1220]~E(x12201,x12202)+E(f138(x12201,x12203,x12204,x12205),f138(x12202,x12203,x12204,x12205)) % 188.18/188.27 [1221]~E(x12211,x12212)+E(f138(x12213,x12211,x12214,x12215),f138(x12213,x12212,x12214,x12215)) % 188.18/188.27 [1222]~E(x12221,x12222)+E(f138(x12223,x12224,x12221,x12225),f138(x12223,x12224,x12222,x12225)) % 188.18/188.27 [1223]~E(x12231,x12232)+E(f138(x12233,x12234,x12235,x12231),f138(x12233,x12234,x12235,x12232)) % 188.18/188.27 [1224]~E(x12241,x12242)+E(f600(x12241,x12243,x12244),f600(x12242,x12243,x12244)) % 188.18/188.27 [1225]~E(x12251,x12252)+E(f600(x12253,x12251,x12254),f600(x12253,x12252,x12254)) % 188.18/188.27 [1226]~E(x12261,x12262)+E(f600(x12263,x12264,x12261),f600(x12263,x12264,x12262)) % 188.18/188.27 [1227]~E(x12271,x12272)+E(f520(x12271,x12273,x12274,x12275,x12276,x12277,x12278),f520(x12272,x12273,x12274,x12275,x12276,x12277,x12278)) % 188.18/188.27 [1228]~E(x12281,x12282)+E(f520(x12283,x12281,x12284,x12285,x12286,x12287,x12288),f520(x12283,x12282,x12284,x12285,x12286,x12287,x12288)) % 188.18/188.27 [1229]~E(x12291,x12292)+E(f520(x12293,x12294,x12291,x12295,x12296,x12297,x12298),f520(x12293,x12294,x12292,x12295,x12296,x12297,x12298)) % 188.18/188.27 [1230]~E(x12301,x12302)+E(f520(x12303,x12304,x12305,x12301,x12306,x12307,x12308),f520(x12303,x12304,x12305,x12302,x12306,x12307,x12308)) % 188.18/188.27 [1231]~E(x12311,x12312)+E(f520(x12313,x12314,x12315,x12316,x12311,x12317,x12318),f520(x12313,x12314,x12315,x12316,x12312,x12317,x12318)) % 188.18/188.27 [1232]~E(x12321,x12322)+E(f520(x12323,x12324,x12325,x12326,x12327,x12321,x12328),f520(x12323,x12324,x12325,x12326,x12327,x12322,x12328)) % 188.18/188.27 [1233]~E(x12331,x12332)+E(f520(x12333,x12334,x12335,x12336,x12337,x12338,x12331),f520(x12333,x12334,x12335,x12336,x12337,x12338,x12332)) % 188.18/188.27 [1234]~E(x12341,x12342)+E(f487(x12341,x12343,x12344,x12345,x12346),f487(x12342,x12343,x12344,x12345,x12346)) % 188.18/188.27 [1235]~E(x12351,x12352)+E(f487(x12353,x12351,x12354,x12355,x12356),f487(x12353,x12352,x12354,x12355,x12356)) % 188.18/188.27 [1236]~E(x12361,x12362)+E(f487(x12363,x12364,x12361,x12365,x12366),f487(x12363,x12364,x12362,x12365,x12366)) % 188.18/188.27 [1237]~E(x12371,x12372)+E(f487(x12373,x12374,x12375,x12371,x12376),f487(x12373,x12374,x12375,x12372,x12376)) % 188.18/188.27 [1238]~E(x12381,x12382)+E(f487(x12383,x12384,x12385,x12386,x12381),f487(x12383,x12384,x12385,x12386,x12382)) % 188.18/188.27 [1239]~E(x12391,x12392)+E(f469(x12391,x12393,x12394,x12395,x12396,x12397),f469(x12392,x12393,x12394,x12395,x12396,x12397)) % 188.18/188.27 [1240]~E(x12401,x12402)+E(f469(x12403,x12401,x12404,x12405,x12406,x12407),f469(x12403,x12402,x12404,x12405,x12406,x12407)) % 188.18/188.27 [1241]~E(x12411,x12412)+E(f469(x12413,x12414,x12411,x12415,x12416,x12417),f469(x12413,x12414,x12412,x12415,x12416,x12417)) % 188.18/188.27 [1242]~E(x12421,x12422)+E(f469(x12423,x12424,x12425,x12421,x12426,x12427),f469(x12423,x12424,x12425,x12422,x12426,x12427)) % 188.18/188.27 [1243]~E(x12431,x12432)+E(f469(x12433,x12434,x12435,x12436,x12431,x12437),f469(x12433,x12434,x12435,x12436,x12432,x12437)) % 188.18/188.27 [1244]~E(x12441,x12442)+E(f469(x12443,x12444,x12445,x12446,x12447,x12441),f469(x12443,x12444,x12445,x12446,x12447,x12442)) % 188.18/188.27 [1245]~E(x12451,x12452)+E(f685(x12451,x12453),f685(x12452,x12453)) % 188.18/188.27 [1246]~E(x12461,x12462)+E(f685(x12463,x12461),f685(x12463,x12462)) % 188.18/188.27 [1247]~E(x12471,x12472)+E(f920(x12471,x12473,x12474,x12475,x12476,x12477,x12478),f920(x12472,x12473,x12474,x12475,x12476,x12477,x12478)) % 188.18/188.27 [1248]~E(x12481,x12482)+E(f920(x12483,x12481,x12484,x12485,x12486,x12487,x12488),f920(x12483,x12482,x12484,x12485,x12486,x12487,x12488)) % 188.18/188.27 [1249]~E(x12491,x12492)+E(f920(x12493,x12494,x12491,x12495,x12496,x12497,x12498),f920(x12493,x12494,x12492,x12495,x12496,x12497,x12498)) % 188.18/188.27 [1250]~E(x12501,x12502)+E(f920(x12503,x12504,x12505,x12501,x12506,x12507,x12508),f920(x12503,x12504,x12505,x12502,x12506,x12507,x12508)) % 188.18/188.27 [1251]~E(x12511,x12512)+E(f920(x12513,x12514,x12515,x12516,x12511,x12517,x12518),f920(x12513,x12514,x12515,x12516,x12512,x12517,x12518)) % 188.18/188.27 [1252]~E(x12521,x12522)+E(f920(x12523,x12524,x12525,x12526,x12527,x12521,x12528),f920(x12523,x12524,x12525,x12526,x12527,x12522,x12528)) % 188.18/188.27 [1253]~E(x12531,x12532)+E(f920(x12533,x12534,x12535,x12536,x12537,x12538,x12531),f920(x12533,x12534,x12535,x12536,x12537,x12538,x12532)) % 188.18/188.27 [1254]~E(x12541,x12542)+E(f757(x12541,x12543,x12544,x12545,x12546),f757(x12542,x12543,x12544,x12545,x12546)) % 188.18/188.27 [1255]~E(x12551,x12552)+E(f757(x12553,x12551,x12554,x12555,x12556),f757(x12553,x12552,x12554,x12555,x12556)) % 188.18/188.27 [1256]~E(x12561,x12562)+E(f757(x12563,x12564,x12561,x12565,x12566),f757(x12563,x12564,x12562,x12565,x12566)) % 188.18/188.27 [1257]~E(x12571,x12572)+E(f757(x12573,x12574,x12575,x12571,x12576),f757(x12573,x12574,x12575,x12572,x12576)) % 188.18/188.27 [1258]~E(x12581,x12582)+E(f757(x12583,x12584,x12585,x12586,x12581),f757(x12583,x12584,x12585,x12586,x12582)) % 188.18/188.27 [1259]~E(x12591,x12592)+E(f644(x12591,x12593,x12594,x12595,x12596),f644(x12592,x12593,x12594,x12595,x12596)) % 188.18/188.27 [1260]~E(x12601,x12602)+E(f644(x12603,x12601,x12604,x12605,x12606),f644(x12603,x12602,x12604,x12605,x12606)) % 188.18/188.27 [1261]~E(x12611,x12612)+E(f644(x12613,x12614,x12611,x12615,x12616),f644(x12613,x12614,x12612,x12615,x12616)) % 188.18/188.27 [1262]~E(x12621,x12622)+E(f644(x12623,x12624,x12625,x12621,x12626),f644(x12623,x12624,x12625,x12622,x12626)) % 188.18/188.27 [1263]~E(x12631,x12632)+E(f644(x12633,x12634,x12635,x12636,x12631),f644(x12633,x12634,x12635,x12636,x12632)) % 188.18/188.27 [1264]~E(x12641,x12642)+E(f788(x12641,x12643,x12644,x12645,x12646,x12647),f788(x12642,x12643,x12644,x12645,x12646,x12647)) % 188.18/188.27 [1265]~E(x12651,x12652)+E(f788(x12653,x12651,x12654,x12655,x12656,x12657),f788(x12653,x12652,x12654,x12655,x12656,x12657)) % 188.18/188.27 [1266]~E(x12661,x12662)+E(f788(x12663,x12664,x12661,x12665,x12666,x12667),f788(x12663,x12664,x12662,x12665,x12666,x12667)) % 188.18/188.27 [1267]~E(x12671,x12672)+E(f788(x12673,x12674,x12675,x12671,x12676,x12677),f788(x12673,x12674,x12675,x12672,x12676,x12677)) % 188.18/188.27 [1268]~E(x12681,x12682)+E(f788(x12683,x12684,x12685,x12686,x12681,x12687),f788(x12683,x12684,x12685,x12686,x12682,x12687)) % 188.18/188.27 [1269]~E(x12691,x12692)+E(f788(x12693,x12694,x12695,x12696,x12697,x12691),f788(x12693,x12694,x12695,x12696,x12697,x12692)) % 188.18/188.27 [1270]~E(x12701,x12702)+E(f832(x12701),f832(x12702)) % 188.18/188.27 [1271]~E(x12711,x12712)+E(f541(x12711,x12713,x12714),f541(x12712,x12713,x12714)) % 188.18/188.27 [1272]~E(x12721,x12722)+E(f541(x12723,x12721,x12724),f541(x12723,x12722,x12724)) % 188.18/188.27 [1273]~E(x12731,x12732)+E(f541(x12733,x12734,x12731),f541(x12733,x12734,x12732)) % 188.18/188.27 [1274]~E(x12741,x12742)+E(f508(x12741,x12743,x12744,x12745,x12746),f508(x12742,x12743,x12744,x12745,x12746)) % 188.18/188.27 [1275]~E(x12751,x12752)+E(f508(x12753,x12751,x12754,x12755,x12756),f508(x12753,x12752,x12754,x12755,x12756)) % 188.18/188.27 [1276]~E(x12761,x12762)+E(f508(x12763,x12764,x12761,x12765,x12766),f508(x12763,x12764,x12762,x12765,x12766)) % 188.18/188.27 [1277]~E(x12771,x12772)+E(f508(x12773,x12774,x12775,x12771,x12776),f508(x12773,x12774,x12775,x12772,x12776)) % 188.18/188.27 [1278]~E(x12781,x12782)+E(f508(x12783,x12784,x12785,x12786,x12781),f508(x12783,x12784,x12785,x12786,x12782)) % 188.18/188.27 [1279]~E(x12791,x12792)+E(f388(x12791,x12793,x12794),f388(x12792,x12793,x12794)) % 188.18/188.27 [1280]~E(x12801,x12802)+E(f388(x12803,x12801,x12804),f388(x12803,x12802,x12804)) % 188.18/188.27 [1281]~E(x12811,x12812)+E(f388(x12813,x12814,x12811),f388(x12813,x12814,x12812)) % 188.18/188.27 [1282]~E(x12821,x12822)+E(f422(x12821,x12823),f422(x12822,x12823)) % 188.18/188.27 [1283]~E(x12831,x12832)+E(f422(x12833,x12831),f422(x12833,x12832)) % 188.18/188.27 [1284]~E(x12841,x12842)+E(f699(x12841,x12843,x12844,x12845),f699(x12842,x12843,x12844,x12845)) % 188.18/188.27 [1285]~E(x12851,x12852)+E(f699(x12853,x12851,x12854,x12855),f699(x12853,x12852,x12854,x12855)) % 188.18/188.27 [1286]~E(x12861,x12862)+E(f699(x12863,x12864,x12861,x12865),f699(x12863,x12864,x12862,x12865)) % 188.18/188.27 [1287]~E(x12871,x12872)+E(f699(x12873,x12874,x12875,x12871),f699(x12873,x12874,x12875,x12872)) % 188.18/188.27 [1288]~E(x12881,x12882)+E(f828(x12881,x12883,x12884,x12885,x12886,x12887),f828(x12882,x12883,x12884,x12885,x12886,x12887)) % 188.18/188.27 [1289]~E(x12891,x12892)+E(f828(x12893,x12891,x12894,x12895,x12896,x12897),f828(x12893,x12892,x12894,x12895,x12896,x12897)) % 188.18/188.27 [1290]~E(x12901,x12902)+E(f828(x12903,x12904,x12901,x12905,x12906,x12907),f828(x12903,x12904,x12902,x12905,x12906,x12907)) % 188.18/188.27 [1291]~E(x12911,x12912)+E(f828(x12913,x12914,x12915,x12911,x12916,x12917),f828(x12913,x12914,x12915,x12912,x12916,x12917)) % 188.18/188.27 [1292]~E(x12921,x12922)+E(f828(x12923,x12924,x12925,x12926,x12921,x12927),f828(x12923,x12924,x12925,x12926,x12922,x12927)) % 188.18/188.27 [1293]~E(x12931,x12932)+E(f828(x12933,x12934,x12935,x12936,x12937,x12931),f828(x12933,x12934,x12935,x12936,x12937,x12932)) % 188.18/188.27 [1294]~E(x12941,x12942)+E(f391(x12941,x12943),f391(x12942,x12943)) % 188.18/188.27 [1295]~E(x12951,x12952)+E(f391(x12953,x12951),f391(x12953,x12952)) % 188.18/188.27 [1296]~E(x12961,x12962)+E(f101(x12961,x12963,x12964,x12965),f101(x12962,x12963,x12964,x12965)) % 188.18/188.27 [1297]~E(x12971,x12972)+E(f101(x12973,x12971,x12974,x12975),f101(x12973,x12972,x12974,x12975)) % 188.18/188.27 [1298]~E(x12981,x12982)+E(f101(x12983,x12984,x12981,x12985),f101(x12983,x12984,x12982,x12985)) % 188.18/188.27 [1299]~E(x12991,x12992)+E(f101(x12993,x12994,x12995,x12991),f101(x12993,x12994,x12995,x12992)) % 188.18/188.27 [1300]~E(x13001,x13002)+E(f899(x13001,x13003),f899(x13002,x13003)) % 188.18/188.27 [1301]~E(x13011,x13012)+E(f899(x13013,x13011),f899(x13013,x13012)) % 188.18/188.27 [1302]~E(x13021,x13022)+E(f208(x13021,x13023),f208(x13022,x13023)) % 188.18/188.27 [1303]~E(x13031,x13032)+E(f208(x13033,x13031),f208(x13033,x13032)) % 188.18/188.27 [1304]~E(x13041,x13042)+E(f484(x13041,x13043),f484(x13042,x13043)) % 188.18/188.27 [1305]~E(x13051,x13052)+E(f484(x13053,x13051),f484(x13053,x13052)) % 188.18/188.27 [1306]~E(x13061,x13062)+E(f462(x13061),f462(x13062)) % 188.18/188.27 [1307]~E(x13071,x13072)+E(f516(x13071,x13073,x13074,x13075,x13076),f516(x13072,x13073,x13074,x13075,x13076)) % 188.18/188.27 [1308]~E(x13081,x13082)+E(f516(x13083,x13081,x13084,x13085,x13086),f516(x13083,x13082,x13084,x13085,x13086)) % 188.18/188.27 [1309]~E(x13091,x13092)+E(f516(x13093,x13094,x13091,x13095,x13096),f516(x13093,x13094,x13092,x13095,x13096)) % 188.18/188.27 [1310]~E(x13101,x13102)+E(f516(x13103,x13104,x13105,x13101,x13106),f516(x13103,x13104,x13105,x13102,x13106)) % 188.18/188.27 [1311]~E(x13111,x13112)+E(f516(x13113,x13114,x13115,x13116,x13111),f516(x13113,x13114,x13115,x13116,x13112)) % 188.18/188.27 [1312]~E(x13121,x13122)+E(f287(x13121,x13123,x13124,x13125),f287(x13122,x13123,x13124,x13125)) % 188.18/188.27 [1313]~E(x13131,x13132)+E(f287(x13133,x13131,x13134,x13135),f287(x13133,x13132,x13134,x13135)) % 188.18/188.27 [1314]~E(x13141,x13142)+E(f287(x13143,x13144,x13141,x13145),f287(x13143,x13144,x13142,x13145)) % 188.18/188.27 [1315]~E(x13151,x13152)+E(f287(x13153,x13154,x13155,x13151),f287(x13153,x13154,x13155,x13152)) % 188.18/188.27 [1316]~E(x13161,x13162)+E(f256(x13161,x13163),f256(x13162,x13163)) % 188.18/188.27 [1317]~E(x13171,x13172)+E(f256(x13173,x13171),f256(x13173,x13172)) % 188.18/188.27 [1318]~E(x13181,x13182)+E(f398(x13181,x13183,x13184,x13185),f398(x13182,x13183,x13184,x13185)) % 188.18/188.27 [1319]~E(x13191,x13192)+E(f398(x13193,x13191,x13194,x13195),f398(x13193,x13192,x13194,x13195)) % 188.18/188.27 [1320]~E(x13201,x13202)+E(f398(x13203,x13204,x13201,x13205),f398(x13203,x13204,x13202,x13205)) % 188.18/188.27 [1321]~E(x13211,x13212)+E(f398(x13213,x13214,x13215,x13211),f398(x13213,x13214,x13215,x13212)) % 188.18/188.27 [1322]~E(x13221,x13222)+E(f201(x13221,x13223),f201(x13222,x13223)) % 188.18/188.27 [1323]~E(x13231,x13232)+E(f201(x13233,x13231),f201(x13233,x13232)) % 188.18/188.27 [1324]~E(x13241,x13242)+E(f281(x13241,x13243,x13244,x13245),f281(x13242,x13243,x13244,x13245)) % 188.18/188.27 [1325]~E(x13251,x13252)+E(f281(x13253,x13251,x13254,x13255),f281(x13253,x13252,x13254,x13255)) % 188.18/188.27 [1326]~E(x13261,x13262)+E(f281(x13263,x13264,x13261,x13265),f281(x13263,x13264,x13262,x13265)) % 188.18/188.27 [1327]~E(x13271,x13272)+E(f281(x13273,x13274,x13275,x13271),f281(x13273,x13274,x13275,x13272)) % 188.18/188.27 [1328]~E(x13281,x13282)+E(f738(x13281,x13283),f738(x13282,x13283)) % 188.18/188.27 [1329]~E(x13291,x13292)+E(f738(x13293,x13291),f738(x13293,x13292)) % 188.18/188.27 [1330]~E(x13301,x13302)+E(f774(x13301,x13303,x13304),f774(x13302,x13303,x13304)) % 188.18/188.27 [1331]~E(x13311,x13312)+E(f774(x13313,x13311,x13314),f774(x13313,x13312,x13314)) % 188.18/188.27 [1332]~E(x13321,x13322)+E(f774(x13323,x13324,x13321),f774(x13323,x13324,x13322)) % 188.18/188.27 [1333]~E(x13331,x13332)+E(f571(x13331,x13333),f571(x13332,x13333)) % 188.18/188.27 [1334]~E(x13341,x13342)+E(f571(x13343,x13341),f571(x13343,x13342)) % 188.18/188.27 [1335]~E(x13351,x13352)+E(f694(x13351,x13353,x13354,x13355,x13356),f694(x13352,x13353,x13354,x13355,x13356)) % 188.18/188.27 [1336]~E(x13361,x13362)+E(f694(x13363,x13361,x13364,x13365,x13366),f694(x13363,x13362,x13364,x13365,x13366)) % 188.18/188.27 [1337]~E(x13371,x13372)+E(f694(x13373,x13374,x13371,x13375,x13376),f694(x13373,x13374,x13372,x13375,x13376)) % 188.18/188.27 [1338]~E(x13381,x13382)+E(f694(x13383,x13384,x13385,x13381,x13386),f694(x13383,x13384,x13385,x13382,x13386)) % 188.18/188.27 [1339]~E(x13391,x13392)+E(f694(x13393,x13394,x13395,x13396,x13391),f694(x13393,x13394,x13395,x13396,x13392)) % 188.18/188.27 [1340]~E(x13401,x13402)+E(f688(x13401,x13403,x13404),f688(x13402,x13403,x13404)) % 188.18/188.27 [1341]~E(x13411,x13412)+E(f688(x13413,x13411,x13414),f688(x13413,x13412,x13414)) % 188.18/188.27 [1342]~E(x13421,x13422)+E(f688(x13423,x13424,x13421),f688(x13423,x13424,x13422)) % 188.18/188.27 [1343]~E(x13431,x13432)+E(f48(x13431),f48(x13432)) % 188.18/188.27 [1344]~E(x13441,x13442)+E(f809(x13441,x13443),f809(x13442,x13443)) % 188.18/188.27 [1345]~E(x13451,x13452)+E(f809(x13453,x13451),f809(x13453,x13452)) % 188.18/188.27 [1346]~E(x13461,x13462)+E(f180(x13461,x13463,x13464),f180(x13462,x13463,x13464)) % 188.18/188.27 [1347]~E(x13471,x13472)+E(f180(x13473,x13471,x13474),f180(x13473,x13472,x13474)) % 188.18/188.27 [1348]~E(x13481,x13482)+E(f180(x13483,x13484,x13481),f180(x13483,x13484,x13482)) % 188.18/188.27 [1349]~E(x13491,x13492)+E(f345(x13491,x13493),f345(x13492,x13493)) % 188.18/188.27 [1350]~E(x13501,x13502)+E(f345(x13503,x13501),f345(x13503,x13502)) % 188.18/188.27 [1351]~E(x13511,x13512)+E(f142(x13511),f142(x13512)) % 188.18/188.27 [1352]~E(x13521,x13522)+E(f895(x13521),f895(x13522)) % 188.18/188.27 [1353]~E(x13531,x13532)+E(f234(x13531,x13533,x13534,x13535,x13536),f234(x13532,x13533,x13534,x13535,x13536)) % 188.18/188.27 [1354]~E(x13541,x13542)+E(f234(x13543,x13541,x13544,x13545,x13546),f234(x13543,x13542,x13544,x13545,x13546)) % 188.18/188.27 [1355]~E(x13551,x13552)+E(f234(x13553,x13554,x13551,x13555,x13556),f234(x13553,x13554,x13552,x13555,x13556)) % 188.18/188.27 [1356]~E(x13561,x13562)+E(f234(x13563,x13564,x13565,x13561,x13566),f234(x13563,x13564,x13565,x13562,x13566)) % 188.18/188.27 [1357]~E(x13571,x13572)+E(f234(x13573,x13574,x13575,x13576,x13571),f234(x13573,x13574,x13575,x13576,x13572)) % 188.18/188.27 [1358]~E(x13581,x13582)+E(f906(x13581,x13583),f906(x13582,x13583)) % 188.18/188.27 [1359]~E(x13591,x13592)+E(f906(x13593,x13591),f906(x13593,x13592)) % 188.18/188.27 [1360]~E(x13601,x13602)+E(f225(x13601,x13603),f225(x13602,x13603)) % 188.18/188.27 [1361]~E(x13611,x13612)+E(f225(x13613,x13611),f225(x13613,x13612)) % 188.18/188.27 [1362]~E(x13621,x13622)+E(f213(x13621),f213(x13622)) % 188.18/188.27 [1363]~E(x13631,x13632)+E(f676(x13631,x13633,x13634),f676(x13632,x13633,x13634)) % 188.18/188.27 [1364]~E(x13641,x13642)+E(f676(x13643,x13641,x13644),f676(x13643,x13642,x13644)) % 188.18/188.27 [1365]~E(x13651,x13652)+E(f676(x13653,x13654,x13651),f676(x13653,x13654,x13652)) % 188.18/188.27 [1366]~E(x13661,x13662)+E(f659(x13661,x13663,x13664,x13665,x13666,x13667),f659(x13662,x13663,x13664,x13665,x13666,x13667)) % 188.18/188.27 [1367]~E(x13671,x13672)+E(f659(x13673,x13671,x13674,x13675,x13676,x13677),f659(x13673,x13672,x13674,x13675,x13676,x13677)) % 188.18/188.27 [1368]~E(x13681,x13682)+E(f659(x13683,x13684,x13681,x13685,x13686,x13687),f659(x13683,x13684,x13682,x13685,x13686,x13687)) % 188.18/188.27 [1369]~E(x13691,x13692)+E(f659(x13693,x13694,x13695,x13691,x13696,x13697),f659(x13693,x13694,x13695,x13692,x13696,x13697)) % 188.18/188.27 [1370]~E(x13701,x13702)+E(f659(x13703,x13704,x13705,x13706,x13701,x13707),f659(x13703,x13704,x13705,x13706,x13702,x13707)) % 188.18/188.27 [1371]~E(x13711,x13712)+E(f659(x13713,x13714,x13715,x13716,x13717,x13711),f659(x13713,x13714,x13715,x13716,x13717,x13712)) % 188.18/188.27 [1372]~E(x13721,x13722)+E(f801(x13721,x13723,x13724,x13725),f801(x13722,x13723,x13724,x13725)) % 188.18/188.27 [1373]~E(x13731,x13732)+E(f801(x13733,x13731,x13734,x13735),f801(x13733,x13732,x13734,x13735)) % 188.18/188.27 [1374]~E(x13741,x13742)+E(f801(x13743,x13744,x13741,x13745),f801(x13743,x13744,x13742,x13745)) % 188.18/188.27 [1375]~E(x13751,x13752)+E(f801(x13753,x13754,x13755,x13751),f801(x13753,x13754,x13755,x13752)) % 188.18/188.27 [1376]~E(x13761,x13762)+E(f557(x13761,x13763,x13764,x13765,x13766,x13767),f557(x13762,x13763,x13764,x13765,x13766,x13767)) % 188.18/188.27 [1377]~E(x13771,x13772)+E(f557(x13773,x13771,x13774,x13775,x13776,x13777),f557(x13773,x13772,x13774,x13775,x13776,x13777)) % 188.18/188.27 [1378]~E(x13781,x13782)+E(f557(x13783,x13784,x13781,x13785,x13786,x13787),f557(x13783,x13784,x13782,x13785,x13786,x13787)) % 188.18/188.27 [1379]~E(x13791,x13792)+E(f557(x13793,x13794,x13795,x13791,x13796,x13797),f557(x13793,x13794,x13795,x13792,x13796,x13797)) % 188.18/188.27 [1380]~E(x13801,x13802)+E(f557(x13803,x13804,x13805,x13806,x13801,x13807),f557(x13803,x13804,x13805,x13806,x13802,x13807)) % 188.18/188.27 [1381]~E(x13811,x13812)+E(f557(x13813,x13814,x13815,x13816,x13817,x13811),f557(x13813,x13814,x13815,x13816,x13817,x13812)) % 188.18/188.27 [1382]~E(x13821,x13822)+E(f692(x13821,x13823,x13824),f692(x13822,x13823,x13824)) % 188.18/188.27 [1383]~E(x13831,x13832)+E(f692(x13833,x13831,x13834),f692(x13833,x13832,x13834)) % 188.18/188.27 [1384]~E(x13841,x13842)+E(f692(x13843,x13844,x13841),f692(x13843,x13844,x13842)) % 188.18/188.27 [1385]~E(x13851,x13852)+E(f878(x13851,x13853,x13854),f878(x13852,x13853,x13854)) % 188.18/188.27 [1386]~E(x13861,x13862)+E(f878(x13863,x13861,x13864),f878(x13863,x13862,x13864)) % 188.18/188.27 [1387]~E(x13871,x13872)+E(f878(x13873,x13874,x13871),f878(x13873,x13874,x13872)) % 188.18/188.27 [1388]~E(x13881,x13882)+E(f232(x13881,x13883,x13884,x13885,x13886),f232(x13882,x13883,x13884,x13885,x13886)) % 188.18/188.27 [1389]~E(x13891,x13892)+E(f232(x13893,x13891,x13894,x13895,x13896),f232(x13893,x13892,x13894,x13895,x13896)) % 188.18/188.27 [1390]~E(x13901,x13902)+E(f232(x13903,x13904,x13901,x13905,x13906),f232(x13903,x13904,x13902,x13905,x13906)) % 188.18/188.27 [1391]~E(x13911,x13912)+E(f232(x13913,x13914,x13915,x13911,x13916),f232(x13913,x13914,x13915,x13912,x13916)) % 188.18/188.27 [1392]~E(x13921,x13922)+E(f232(x13923,x13924,x13925,x13926,x13921),f232(x13923,x13924,x13925,x13926,x13922)) % 188.18/188.27 [1393]~E(x13931,x13932)+E(f714(x13931,x13933,x13934,x13935,x13936),f714(x13932,x13933,x13934,x13935,x13936)) % 188.18/188.27 [1394]~E(x13941,x13942)+E(f714(x13943,x13941,x13944,x13945,x13946),f714(x13943,x13942,x13944,x13945,x13946)) % 188.18/188.27 [1395]~E(x13951,x13952)+E(f714(x13953,x13954,x13951,x13955,x13956),f714(x13953,x13954,x13952,x13955,x13956)) % 188.18/188.27 [1396]~E(x13961,x13962)+E(f714(x13963,x13964,x13965,x13961,x13966),f714(x13963,x13964,x13965,x13962,x13966)) % 188.18/188.27 [1397]~E(x13971,x13972)+E(f714(x13973,x13974,x13975,x13976,x13971),f714(x13973,x13974,x13975,x13976,x13972)) % 188.18/188.27 [1398]~E(x13981,x13982)+E(f880(x13981,x13983,x13984,x13985,x13986,x13987),f880(x13982,x13983,x13984,x13985,x13986,x13987)) % 188.18/188.27 [1399]~E(x13991,x13992)+E(f880(x13993,x13991,x13994,x13995,x13996,x13997),f880(x13993,x13992,x13994,x13995,x13996,x13997)) % 188.18/188.27 [1400]~E(x14001,x14002)+E(f880(x14003,x14004,x14001,x14005,x14006,x14007),f880(x14003,x14004,x14002,x14005,x14006,x14007)) % 188.18/188.27 [1401]~E(x14011,x14012)+E(f880(x14013,x14014,x14015,x14011,x14016,x14017),f880(x14013,x14014,x14015,x14012,x14016,x14017)) % 188.18/188.27 [1402]~E(x14021,x14022)+E(f880(x14023,x14024,x14025,x14026,x14021,x14027),f880(x14023,x14024,x14025,x14026,x14022,x14027)) % 188.18/188.27 [1403]~E(x14031,x14032)+E(f880(x14033,x14034,x14035,x14036,x14037,x14031),f880(x14033,x14034,x14035,x14036,x14037,x14032)) % 188.18/188.27 [1404]~E(x14041,x14042)+E(f393(x14041,x14043,x14044,x14045),f393(x14042,x14043,x14044,x14045)) % 188.18/188.27 [1405]~E(x14051,x14052)+E(f393(x14053,x14051,x14054,x14055),f393(x14053,x14052,x14054,x14055)) % 188.18/188.27 [1406]~E(x14061,x14062)+E(f393(x14063,x14064,x14061,x14065),f393(x14063,x14064,x14062,x14065)) % 188.18/188.27 [1407]~E(x14071,x14072)+E(f393(x14073,x14074,x14075,x14071),f393(x14073,x14074,x14075,x14072)) % 188.18/188.27 [1408]~E(x14081,x14082)+E(f27(x14081,x14083,x14084),f27(x14082,x14083,x14084)) % 188.18/188.27 [1409]~E(x14091,x14092)+E(f27(x14093,x14091,x14094),f27(x14093,x14092,x14094)) % 188.18/188.27 [1410]~E(x14101,x14102)+E(f27(x14103,x14104,x14101),f27(x14103,x14104,x14102)) % 188.18/188.27 [1411]~E(x14111,x14112)+E(f682(x14111,x14113,x14114,x14115),f682(x14112,x14113,x14114,x14115)) % 188.18/188.27 [1412]~E(x14121,x14122)+E(f682(x14123,x14121,x14124,x14125),f682(x14123,x14122,x14124,x14125)) % 188.18/188.27 [1413]~E(x14131,x14132)+E(f682(x14133,x14134,x14131,x14135),f682(x14133,x14134,x14132,x14135)) % 188.18/188.27 [1414]~E(x14141,x14142)+E(f682(x14143,x14144,x14145,x14141),f682(x14143,x14144,x14145,x14142)) % 188.18/188.27 [1415]~E(x14151,x14152)+E(f493(x14151,x14153,x14154),f493(x14152,x14153,x14154)) % 188.18/188.27 [1416]~E(x14161,x14162)+E(f493(x14163,x14161,x14164),f493(x14163,x14162,x14164)) % 188.18/188.27 [1417]~E(x14171,x14172)+E(f493(x14173,x14174,x14171),f493(x14173,x14174,x14172)) % 188.18/188.27 [1418]~E(x14181,x14182)+E(f220(x14181,x14183,x14184,x14185,x14186,x14187,x14188),f220(x14182,x14183,x14184,x14185,x14186,x14187,x14188)) % 188.18/188.27 [1419]~E(x14191,x14192)+E(f220(x14193,x14191,x14194,x14195,x14196,x14197,x14198),f220(x14193,x14192,x14194,x14195,x14196,x14197,x14198)) % 188.18/188.27 [1420]~E(x14201,x14202)+E(f220(x14203,x14204,x14201,x14205,x14206,x14207,x14208),f220(x14203,x14204,x14202,x14205,x14206,x14207,x14208)) % 188.18/188.27 [1421]~E(x14211,x14212)+E(f220(x14213,x14214,x14215,x14211,x14216,x14217,x14218),f220(x14213,x14214,x14215,x14212,x14216,x14217,x14218)) % 188.18/188.27 [1422]~E(x14221,x14222)+E(f220(x14223,x14224,x14225,x14226,x14221,x14227,x14228),f220(x14223,x14224,x14225,x14226,x14222,x14227,x14228)) % 188.18/188.27 [1423]~E(x14231,x14232)+E(f220(x14233,x14234,x14235,x14236,x14237,x14231,x14238),f220(x14233,x14234,x14235,x14236,x14237,x14232,x14238)) % 188.18/188.27 [1424]~E(x14241,x14242)+E(f220(x14243,x14244,x14245,x14246,x14247,x14248,x14241),f220(x14243,x14244,x14245,x14246,x14247,x14248,x14242)) % 188.18/188.27 [1425]~E(x14251,x14252)+E(f239(x14251,x14253,x14254),f239(x14252,x14253,x14254)) % 188.18/188.27 [1426]~E(x14261,x14262)+E(f239(x14263,x14261,x14264),f239(x14263,x14262,x14264)) % 188.18/188.27 [1427]~E(x14271,x14272)+E(f239(x14273,x14274,x14271),f239(x14273,x14274,x14272)) % 188.18/188.27 [1428]~E(x14281,x14282)+E(f381(x14281,x14283,x14284,x14285),f381(x14282,x14283,x14284,x14285)) % 188.18/188.27 [1429]~E(x14291,x14292)+E(f381(x14293,x14291,x14294,x14295),f381(x14293,x14292,x14294,x14295)) % 188.18/188.27 [1430]~E(x14301,x14302)+E(f381(x14303,x14304,x14301,x14305),f381(x14303,x14304,x14302,x14305)) % 188.18/188.27 [1431]~E(x14311,x14312)+E(f381(x14313,x14314,x14315,x14311),f381(x14313,x14314,x14315,x14312)) % 188.18/188.27 [1432]~E(x14321,x14322)+E(f638(x14321,x14323,x14324,x14325,x14326),f638(x14322,x14323,x14324,x14325,x14326)) % 188.18/188.27 [1433]~E(x14331,x14332)+E(f638(x14333,x14331,x14334,x14335,x14336),f638(x14333,x14332,x14334,x14335,x14336)) % 188.18/188.27 [1434]~E(x14341,x14342)+E(f638(x14343,x14344,x14341,x14345,x14346),f638(x14343,x14344,x14342,x14345,x14346)) % 188.18/188.27 [1435]~E(x14351,x14352)+E(f638(x14353,x14354,x14355,x14351,x14356),f638(x14353,x14354,x14355,x14352,x14356)) % 188.18/188.27 [1436]~E(x14361,x14362)+E(f638(x14363,x14364,x14365,x14366,x14361),f638(x14363,x14364,x14365,x14366,x14362)) % 188.18/188.27 [1437]~E(x14371,x14372)+E(f793(x14371,x14373,x14374,x14375),f793(x14372,x14373,x14374,x14375)) % 188.18/188.27 [1438]~E(x14381,x14382)+E(f793(x14383,x14381,x14384,x14385),f793(x14383,x14382,x14384,x14385)) % 188.18/188.27 [1439]~E(x14391,x14392)+E(f793(x14393,x14394,x14391,x14395),f793(x14393,x14394,x14392,x14395)) % 188.18/188.27 [1440]~E(x14401,x14402)+E(f793(x14403,x14404,x14405,x14401),f793(x14403,x14404,x14405,x14402)) % 188.18/188.27 [1441]~E(x14411,x14412)+E(f400(x14411,x14413,x14414,x14415,x14416),f400(x14412,x14413,x14414,x14415,x14416)) % 188.18/188.27 [1442]~E(x14421,x14422)+E(f400(x14423,x14421,x14424,x14425,x14426),f400(x14423,x14422,x14424,x14425,x14426)) % 188.18/188.27 [1443]~E(x14431,x14432)+E(f400(x14433,x14434,x14431,x14435,x14436),f400(x14433,x14434,x14432,x14435,x14436)) % 188.18/188.27 [1444]~E(x14441,x14442)+E(f400(x14443,x14444,x14445,x14441,x14446),f400(x14443,x14444,x14445,x14442,x14446)) % 188.18/188.27 [1445]~E(x14451,x14452)+E(f400(x14453,x14454,x14455,x14456,x14451),f400(x14453,x14454,x14455,x14456,x14452)) % 188.18/188.27 [1446]~E(x14461,x14462)+E(f678(x14461,x14463,x14464,x14465),f678(x14462,x14463,x14464,x14465)) % 188.18/188.27 [1447]~E(x14471,x14472)+E(f678(x14473,x14471,x14474,x14475),f678(x14473,x14472,x14474,x14475)) % 188.18/188.27 [1448]~E(x14481,x14482)+E(f678(x14483,x14484,x14481,x14485),f678(x14483,x14484,x14482,x14485)) % 188.18/188.27 [1449]~E(x14491,x14492)+E(f678(x14493,x14494,x14495,x14491),f678(x14493,x14494,x14495,x14492)) % 188.18/188.27 [1450]~E(x14501,x14502)+E(f535(x14501,x14503,x14504),f535(x14502,x14503,x14504)) % 188.18/188.27 [1451]~E(x14511,x14512)+E(f535(x14513,x14511,x14514),f535(x14513,x14512,x14514)) % 188.18/188.27 [1452]~E(x14521,x14522)+E(f535(x14523,x14524,x14521),f535(x14523,x14524,x14522)) % 188.18/188.27 [1453]~E(x14531,x14532)+E(f802(x14531,x14533,x14534,x14535,x14536,x14537,x14538),f802(x14532,x14533,x14534,x14535,x14536,x14537,x14538)) % 188.18/188.27 [1454]~E(x14541,x14542)+E(f802(x14543,x14541,x14544,x14545,x14546,x14547,x14548),f802(x14543,x14542,x14544,x14545,x14546,x14547,x14548)) % 188.18/188.27 [1455]~E(x14551,x14552)+E(f802(x14553,x14554,x14551,x14555,x14556,x14557,x14558),f802(x14553,x14554,x14552,x14555,x14556,x14557,x14558)) % 188.18/188.27 [1456]~E(x14561,x14562)+E(f802(x14563,x14564,x14565,x14561,x14566,x14567,x14568),f802(x14563,x14564,x14565,x14562,x14566,x14567,x14568)) % 188.18/188.27 [1457]~E(x14571,x14572)+E(f802(x14573,x14574,x14575,x14576,x14571,x14577,x14578),f802(x14573,x14574,x14575,x14576,x14572,x14577,x14578)) % 188.18/188.27 [1458]~E(x14581,x14582)+E(f802(x14583,x14584,x14585,x14586,x14587,x14581,x14588),f802(x14583,x14584,x14585,x14586,x14587,x14582,x14588)) % 188.18/188.27 [1459]~E(x14591,x14592)+E(f802(x14593,x14594,x14595,x14596,x14597,x14598,x14591),f802(x14593,x14594,x14595,x14596,x14597,x14598,x14592)) % 188.18/188.27 [1460]~E(x14601,x14602)+E(f901(x14601),f901(x14602)) % 188.18/188.27 [1461]~E(x14611,x14612)+E(f379(x14611,x14613,x14614,x14615),f379(x14612,x14613,x14614,x14615)) % 188.18/188.27 [1462]~E(x14621,x14622)+E(f379(x14623,x14621,x14624,x14625),f379(x14623,x14622,x14624,x14625)) % 188.18/188.27 [1463]~E(x14631,x14632)+E(f379(x14633,x14634,x14631,x14635),f379(x14633,x14634,x14632,x14635)) % 188.18/188.27 [1464]~E(x14641,x14642)+E(f379(x14643,x14644,x14645,x14641),f379(x14643,x14644,x14645,x14642)) % 188.18/188.27 [1465]~E(x14651,x14652)+E(f130(x14651),f130(x14652)) % 188.18/188.27 [1466]~E(x14661,x14662)+E(f367(x14661,x14663,x14664),f367(x14662,x14663,x14664)) % 188.18/188.27 [1467]~E(x14671,x14672)+E(f367(x14673,x14671,x14674),f367(x14673,x14672,x14674)) % 188.18/188.27 [1468]~E(x14681,x14682)+E(f367(x14683,x14684,x14681),f367(x14683,x14684,x14682)) % 188.18/188.27 [1469]~E(x14691,x14692)+E(f372(x14691,x14693,x14694),f372(x14692,x14693,x14694)) % 188.18/188.27 [1470]~E(x14701,x14702)+E(f372(x14703,x14701,x14704),f372(x14703,x14702,x14704)) % 188.18/188.27 [1471]~E(x14711,x14712)+E(f372(x14713,x14714,x14711),f372(x14713,x14714,x14712)) % 188.18/188.27 [1472]~E(x14721,x14722)+E(f836(x14721,x14723),f836(x14722,x14723)) % 188.18/188.27 [1473]~E(x14731,x14732)+E(f836(x14733,x14731),f836(x14733,x14732)) % 188.18/188.27 [1474]~E(x14741,x14742)+E(f446(x14741,x14743,x14744,x14745),f446(x14742,x14743,x14744,x14745)) % 188.18/188.27 [1475]~E(x14751,x14752)+E(f446(x14753,x14751,x14754,x14755),f446(x14753,x14752,x14754,x14755)) % 188.18/188.27 [1476]~E(x14761,x14762)+E(f446(x14763,x14764,x14761,x14765),f446(x14763,x14764,x14762,x14765)) % 188.18/188.27 [1477]~E(x14771,x14772)+E(f446(x14773,x14774,x14775,x14771),f446(x14773,x14774,x14775,x14772)) % 188.18/188.27 [1478]~E(x14781,x14782)+E(f387(x14781),f387(x14782)) % 188.18/188.27 [1479]~E(x14791,x14792)+E(f911(x14791,x14793,x14794,x14795,x14796,x14797,x14798),f911(x14792,x14793,x14794,x14795,x14796,x14797,x14798)) % 188.18/188.27 [1480]~E(x14801,x14802)+E(f911(x14803,x14801,x14804,x14805,x14806,x14807,x14808),f911(x14803,x14802,x14804,x14805,x14806,x14807,x14808)) % 188.18/188.27 [1481]~E(x14811,x14812)+E(f911(x14813,x14814,x14811,x14815,x14816,x14817,x14818),f911(x14813,x14814,x14812,x14815,x14816,x14817,x14818)) % 188.18/188.27 [1482]~E(x14821,x14822)+E(f911(x14823,x14824,x14825,x14821,x14826,x14827,x14828),f911(x14823,x14824,x14825,x14822,x14826,x14827,x14828)) % 188.18/188.27 [1483]~E(x14831,x14832)+E(f911(x14833,x14834,x14835,x14836,x14831,x14837,x14838),f911(x14833,x14834,x14835,x14836,x14832,x14837,x14838)) % 188.18/188.27 [1484]~E(x14841,x14842)+E(f911(x14843,x14844,x14845,x14846,x14847,x14841,x14848),f911(x14843,x14844,x14845,x14846,x14847,x14842,x14848)) % 188.18/188.27 [1485]~E(x14851,x14852)+E(f911(x14853,x14854,x14855,x14856,x14857,x14858,x14851),f911(x14853,x14854,x14855,x14856,x14857,x14858,x14852)) % 188.18/188.27 [1486]~E(x14861,x14862)+E(f874(x14861,x14863,x14864,x14865,x14866),f874(x14862,x14863,x14864,x14865,x14866)) % 188.18/188.27 [1487]~E(x14871,x14872)+E(f874(x14873,x14871,x14874,x14875,x14876),f874(x14873,x14872,x14874,x14875,x14876)) % 188.18/188.27 [1488]~E(x14881,x14882)+E(f874(x14883,x14884,x14881,x14885,x14886),f874(x14883,x14884,x14882,x14885,x14886)) % 188.18/188.27 [1489]~E(x14891,x14892)+E(f874(x14893,x14894,x14895,x14891,x14896),f874(x14893,x14894,x14895,x14892,x14896)) % 188.18/188.27 [1490]~E(x14901,x14902)+E(f874(x14903,x14904,x14905,x14906,x14901),f874(x14903,x14904,x14905,x14906,x14902)) % 188.18/188.27 [1491]~E(x14911,x14912)+E(f532(x14911,x14913,x14914,x14915),f532(x14912,x14913,x14914,x14915)) % 188.18/188.27 [1492]~E(x14921,x14922)+E(f532(x14923,x14921,x14924,x14925),f532(x14923,x14922,x14924,x14925)) % 188.18/188.27 [1493]~E(x14931,x14932)+E(f532(x14933,x14934,x14931,x14935),f532(x14933,x14934,x14932,x14935)) % 188.18/188.27 [1494]~E(x14941,x14942)+E(f532(x14943,x14944,x14945,x14941),f532(x14943,x14944,x14945,x14942)) % 188.18/188.27 [1495]~E(x14951,x14952)+E(f474(x14951,x14953,x14954),f474(x14952,x14953,x14954)) % 188.18/188.27 [1496]~E(x14961,x14962)+E(f474(x14963,x14961,x14964),f474(x14963,x14962,x14964)) % 188.18/188.27 [1497]~E(x14971,x14972)+E(f474(x14973,x14974,x14971),f474(x14973,x14974,x14972)) % 188.18/188.27 [1498]~E(x14981,x14982)+E(f47(x14981),f47(x14982)) % 188.18/188.27 [1499]~E(x14991,x14992)+E(f777(x14991,x14993,x14994),f777(x14992,x14993,x14994)) % 188.18/188.27 [1500]~E(x15001,x15002)+E(f777(x15003,x15001,x15004),f777(x15003,x15002,x15004)) % 188.18/188.27 [1501]~E(x15011,x15012)+E(f777(x15013,x15014,x15011),f777(x15013,x15014,x15012)) % 188.18/188.27 [1502]~E(x15021,x15022)+E(f806(x15021,x15023,x15024,x15025,x15026,x15027,x15028),f806(x15022,x15023,x15024,x15025,x15026,x15027,x15028)) % 188.18/188.27 [1503]~E(x15031,x15032)+E(f806(x15033,x15031,x15034,x15035,x15036,x15037,x15038),f806(x15033,x15032,x15034,x15035,x15036,x15037,x15038)) % 188.18/188.27 [1504]~E(x15041,x15042)+E(f806(x15043,x15044,x15041,x15045,x15046,x15047,x15048),f806(x15043,x15044,x15042,x15045,x15046,x15047,x15048)) % 188.18/188.27 [1505]~E(x15051,x15052)+E(f806(x15053,x15054,x15055,x15051,x15056,x15057,x15058),f806(x15053,x15054,x15055,x15052,x15056,x15057,x15058)) % 188.18/188.27 [1506]~E(x15061,x15062)+E(f806(x15063,x15064,x15065,x15066,x15061,x15067,x15068),f806(x15063,x15064,x15065,x15066,x15062,x15067,x15068)) % 188.18/188.27 [1507]~E(x15071,x15072)+E(f806(x15073,x15074,x15075,x15076,x15077,x15071,x15078),f806(x15073,x15074,x15075,x15076,x15077,x15072,x15078)) % 188.18/188.27 [1508]~E(x15081,x15082)+E(f806(x15083,x15084,x15085,x15086,x15087,x15088,x15081),f806(x15083,x15084,x15085,x15086,x15087,x15088,x15082)) % 188.18/188.27 [1509]~E(x15091,x15092)+E(f424(x15091,x15093),f424(x15092,x15093)) % 188.18/188.27 [1510]~E(x15101,x15102)+E(f424(x15103,x15101),f424(x15103,x15102)) % 188.18/188.27 [1511]~E(x15111,x15112)+E(f437(x15111,x15113,x15114,x15115),f437(x15112,x15113,x15114,x15115)) % 188.18/188.27 [1512]~E(x15121,x15122)+E(f437(x15123,x15121,x15124,x15125),f437(x15123,x15122,x15124,x15125)) % 188.18/188.27 [1513]~E(x15131,x15132)+E(f437(x15133,x15134,x15131,x15135),f437(x15133,x15134,x15132,x15135)) % 188.18/188.27 [1514]~E(x15141,x15142)+E(f437(x15143,x15144,x15145,x15141),f437(x15143,x15144,x15145,x15142)) % 188.18/188.27 [1515]~E(x15151,x15152)+E(f707(x15151,x15153,x15154,x15155),f707(x15152,x15153,x15154,x15155)) % 188.18/188.27 [1516]~E(x15161,x15162)+E(f707(x15163,x15161,x15164,x15165),f707(x15163,x15162,x15164,x15165)) % 188.18/188.27 [1517]~E(x15171,x15172)+E(f707(x15173,x15174,x15171,x15175),f707(x15173,x15174,x15172,x15175)) % 188.18/188.27 [1518]~E(x15181,x15182)+E(f707(x15183,x15184,x15185,x15181),f707(x15183,x15184,x15185,x15182)) % 188.18/188.27 [1519]~E(x15191,x15192)+E(f134(x15191,x15193,x15194,x15195,x15196),f134(x15192,x15193,x15194,x15195,x15196)) % 188.18/188.27 [1520]~E(x15201,x15202)+E(f134(x15203,x15201,x15204,x15205,x15206),f134(x15203,x15202,x15204,x15205,x15206)) % 188.18/188.27 [1521]~E(x15211,x15212)+E(f134(x15213,x15214,x15211,x15215,x15216),f134(x15213,x15214,x15212,x15215,x15216)) % 188.18/188.27 [1522]~E(x15221,x15222)+E(f134(x15223,x15224,x15225,x15221,x15226),f134(x15223,x15224,x15225,x15222,x15226)) % 188.18/188.27 [1523]~E(x15231,x15232)+E(f134(x15233,x15234,x15235,x15236,x15231),f134(x15233,x15234,x15235,x15236,x15232)) % 188.18/188.27 [1524]~E(x15241,x15242)+E(f441(x15241,x15243),f441(x15242,x15243)) % 188.18/188.27 [1525]~E(x15251,x15252)+E(f441(x15253,x15251),f441(x15253,x15252)) % 188.18/188.27 [1526]~E(x15261,x15262)+E(f406(x15261,x15263,x15264,x15265,x15266),f406(x15262,x15263,x15264,x15265,x15266)) % 188.18/188.27 [1527]~E(x15271,x15272)+E(f406(x15273,x15271,x15274,x15275,x15276),f406(x15273,x15272,x15274,x15275,x15276)) % 188.18/188.27 [1528]~E(x15281,x15282)+E(f406(x15283,x15284,x15281,x15285,x15286),f406(x15283,x15284,x15282,x15285,x15286)) % 188.18/188.27 [1529]~E(x15291,x15292)+E(f406(x15293,x15294,x15295,x15291,x15296),f406(x15293,x15294,x15295,x15292,x15296)) % 188.18/188.27 [1530]~E(x15301,x15302)+E(f406(x15303,x15304,x15305,x15306,x15301),f406(x15303,x15304,x15305,x15306,x15302)) % 188.18/188.27 [1531]~E(x15311,x15312)+E(f181(x15311,x15313,x15314),f181(x15312,x15313,x15314)) % 188.18/188.27 [1532]~E(x15321,x15322)+E(f181(x15323,x15321,x15324),f181(x15323,x15322,x15324)) % 188.18/188.27 [1533]~E(x15331,x15332)+E(f181(x15333,x15334,x15331),f181(x15333,x15334,x15332)) % 188.18/188.27 [1534]~E(x15341,x15342)+E(f447(x15341,x15343,x15344,x15345),f447(x15342,x15343,x15344,x15345)) % 188.18/188.27 [1535]~E(x15351,x15352)+E(f447(x15353,x15351,x15354,x15355),f447(x15353,x15352,x15354,x15355)) % 188.18/188.27 [1536]~E(x15361,x15362)+E(f447(x15363,x15364,x15361,x15365),f447(x15363,x15364,x15362,x15365)) % 188.18/188.27 [1537]~E(x15371,x15372)+E(f447(x15373,x15374,x15375,x15371),f447(x15373,x15374,x15375,x15372)) % 188.18/188.27 [1538]~E(x15381,x15382)+E(f787(x15381,x15383,x15384,x15385),f787(x15382,x15383,x15384,x15385)) % 188.18/188.27 [1539]~E(x15391,x15392)+E(f787(x15393,x15391,x15394,x15395),f787(x15393,x15392,x15394,x15395)) % 188.18/188.27 [1540]~E(x15401,x15402)+E(f787(x15403,x15404,x15401,x15405),f787(x15403,x15404,x15402,x15405)) % 188.18/188.27 [1541]~E(x15411,x15412)+E(f787(x15413,x15414,x15415,x15411),f787(x15413,x15414,x15415,x15412)) % 188.18/188.27 [1542]~E(x15421,x15422)+E(f596(x15421,x15423,x15424),f596(x15422,x15423,x15424)) % 188.18/188.27 [1543]~E(x15431,x15432)+E(f596(x15433,x15431,x15434),f596(x15433,x15432,x15434)) % 188.18/188.27 [1544]~E(x15441,x15442)+E(f596(x15443,x15444,x15441),f596(x15443,x15444,x15442)) % 188.18/188.27 [1545]~E(x15451,x15452)+E(f604(x15451,x15453,x15454,x15455),f604(x15452,x15453,x15454,x15455)) % 188.18/188.27 [1546]~E(x15461,x15462)+E(f604(x15463,x15461,x15464,x15465),f604(x15463,x15462,x15464,x15465)) % 188.18/188.27 [1547]~E(x15471,x15472)+E(f604(x15473,x15474,x15471,x15475),f604(x15473,x15474,x15472,x15475)) % 188.18/188.27 [1548]~E(x15481,x15482)+E(f604(x15483,x15484,x15485,x15481),f604(x15483,x15484,x15485,x15482)) % 188.18/188.27 [1549]~E(x15491,x15492)+E(f717(x15491,x15493,x15494),f717(x15492,x15493,x15494)) % 188.18/188.27 [1550]~E(x15501,x15502)+E(f717(x15503,x15501,x15504),f717(x15503,x15502,x15504)) % 188.18/188.27 [1551]~E(x15511,x15512)+E(f717(x15513,x15514,x15511),f717(x15513,x15514,x15512)) % 188.18/188.27 [1552]~E(x15521,x15522)+E(f404(x15521,x15523,x15524,x15525),f404(x15522,x15523,x15524,x15525)) % 188.18/188.27 [1553]~E(x15531,x15532)+E(f404(x15533,x15531,x15534,x15535),f404(x15533,x15532,x15534,x15535)) % 188.18/188.27 [1554]~E(x15541,x15542)+E(f404(x15543,x15544,x15541,x15545),f404(x15543,x15544,x15542,x15545)) % 188.18/188.27 [1555]~E(x15551,x15552)+E(f404(x15553,x15554,x15555,x15551),f404(x15553,x15554,x15555,x15552)) % 188.18/188.27 [1556]~E(x15561,x15562)+E(f645(x15561,x15563,x15564,x15565,x15566),f645(x15562,x15563,x15564,x15565,x15566)) % 188.18/188.27 [1557]~E(x15571,x15572)+E(f645(x15573,x15571,x15574,x15575,x15576),f645(x15573,x15572,x15574,x15575,x15576)) % 188.18/188.27 [1558]~E(x15581,x15582)+E(f645(x15583,x15584,x15581,x15585,x15586),f645(x15583,x15584,x15582,x15585,x15586)) % 188.18/188.27 [1559]~E(x15591,x15592)+E(f645(x15593,x15594,x15595,x15591,x15596),f645(x15593,x15594,x15595,x15592,x15596)) % 188.18/188.27 [1560]~E(x15601,x15602)+E(f645(x15603,x15604,x15605,x15606,x15601),f645(x15603,x15604,x15605,x15606,x15602)) % 188.18/188.27 [1561]~E(x15611,x15612)+E(f371(x15611,x15613,x15614),f371(x15612,x15613,x15614)) % 188.18/188.27 [1562]~E(x15621,x15622)+E(f371(x15623,x15621,x15624),f371(x15623,x15622,x15624)) % 188.18/188.27 [1563]~E(x15631,x15632)+E(f371(x15633,x15634,x15631),f371(x15633,x15634,x15632)) % 188.18/188.27 [1564]~E(x15641,x15642)+E(f641(x15641,x15643,x15644,x15645,x15646),f641(x15642,x15643,x15644,x15645,x15646)) % 188.18/188.27 [1565]~E(x15651,x15652)+E(f641(x15653,x15651,x15654,x15655,x15656),f641(x15653,x15652,x15654,x15655,x15656)) % 188.18/188.27 [1566]~E(x15661,x15662)+E(f641(x15663,x15664,x15661,x15665,x15666),f641(x15663,x15664,x15662,x15665,x15666)) % 188.18/188.27 [1567]~E(x15671,x15672)+E(f641(x15673,x15674,x15675,x15671,x15676),f641(x15673,x15674,x15675,x15672,x15676)) % 188.18/188.27 [1568]~E(x15681,x15682)+E(f641(x15683,x15684,x15685,x15686,x15681),f641(x15683,x15684,x15685,x15686,x15682)) % 188.18/188.27 [1569]~E(x15691,x15692)+E(f912(x15691,x15693,x15694),f912(x15692,x15693,x15694)) % 188.18/188.27 [1570]~E(x15701,x15702)+E(f912(x15703,x15701,x15704),f912(x15703,x15702,x15704)) % 188.18/188.27 [1571]~E(x15711,x15712)+E(f912(x15713,x15714,x15711),f912(x15713,x15714,x15712)) % 188.18/188.27 [1572]~E(x15721,x15722)+E(f584(x15721,x15723),f584(x15722,x15723)) % 188.18/188.27 [1573]~E(x15731,x15732)+E(f584(x15733,x15731),f584(x15733,x15732)) % 188.18/188.27 [1574]~E(x15741,x15742)+E(f518(x15741,x15743,x15744),f518(x15742,x15743,x15744)) % 188.18/188.27 [1575]~E(x15751,x15752)+E(f518(x15753,x15751,x15754),f518(x15753,x15752,x15754)) % 188.18/188.27 [1576]~E(x15761,x15762)+E(f518(x15763,x15764,x15761),f518(x15763,x15764,x15762)) % 188.18/188.27 [1577]~E(x15771,x15772)+E(f498(x15771,x15773,x15774,x15775,x15776,x15777),f498(x15772,x15773,x15774,x15775,x15776,x15777)) % 188.18/188.27 [1578]~E(x15781,x15782)+E(f498(x15783,x15781,x15784,x15785,x15786,x15787),f498(x15783,x15782,x15784,x15785,x15786,x15787)) % 188.18/188.27 [1579]~E(x15791,x15792)+E(f498(x15793,x15794,x15791,x15795,x15796,x15797),f498(x15793,x15794,x15792,x15795,x15796,x15797)) % 188.18/188.27 [1580]~E(x15801,x15802)+E(f498(x15803,x15804,x15805,x15801,x15806,x15807),f498(x15803,x15804,x15805,x15802,x15806,x15807)) % 188.18/188.27 [1581]~E(x15811,x15812)+E(f498(x15813,x15814,x15815,x15816,x15811,x15817),f498(x15813,x15814,x15815,x15816,x15812,x15817)) % 188.18/188.27 [1582]~E(x15821,x15822)+E(f498(x15823,x15824,x15825,x15826,x15827,x15821),f498(x15823,x15824,x15825,x15826,x15827,x15822)) % 188.18/188.27 [1583]~E(x15831,x15832)+E(f744(x15831,x15833),f744(x15832,x15833)) % 188.18/188.27 [1584]~E(x15841,x15842)+E(f744(x15843,x15841),f744(x15843,x15842)) % 188.18/188.27 [1585]~E(x15851,x15852)+E(f369(x15851,x15853,x15854),f369(x15852,x15853,x15854)) % 188.18/188.27 [1586]~E(x15861,x15862)+E(f369(x15863,x15861,x15864),f369(x15863,x15862,x15864)) % 188.18/188.27 [1587]~E(x15871,x15872)+E(f369(x15873,x15874,x15871),f369(x15873,x15874,x15872)) % 188.18/188.27 [1588]~E(x15881,x15882)+E(f456(x15881,x15883,x15884),f456(x15882,x15883,x15884)) % 188.18/188.27 [1589]~E(x15891,x15892)+E(f456(x15893,x15891,x15894),f456(x15893,x15892,x15894)) % 188.18/188.27 [1590]~E(x15901,x15902)+E(f456(x15903,x15904,x15901),f456(x15903,x15904,x15902)) % 188.18/188.27 [1591]~E(x15911,x15912)+E(f848(x15911,x15913,x15914),f848(x15912,x15913,x15914)) % 188.18/188.27 [1592]~E(x15921,x15922)+E(f848(x15923,x15921,x15924),f848(x15923,x15922,x15924)) % 188.18/188.27 [1593]~E(x15931,x15932)+E(f848(x15933,x15934,x15931),f848(x15933,x15934,x15932)) % 188.18/188.27 [1594]~E(x15941,x15942)+E(f553(x15941,x15943,x15944),f553(x15942,x15943,x15944)) % 188.18/188.27 [1595]~E(x15951,x15952)+E(f553(x15953,x15951,x15954),f553(x15953,x15952,x15954)) % 188.18/188.27 [1596]~E(x15961,x15962)+E(f553(x15963,x15964,x15961),f553(x15963,x15964,x15962)) % 188.18/188.27 [1597]~E(x15971,x15972)+E(f433(x15971,x15973,x15974,x15975),f433(x15972,x15973,x15974,x15975)) % 188.18/188.27 [1598]~E(x15981,x15982)+E(f433(x15983,x15981,x15984,x15985),f433(x15983,x15982,x15984,x15985)) % 188.18/188.27 [1599]~E(x15991,x15992)+E(f433(x15993,x15994,x15991,x15995),f433(x15993,x15994,x15992,x15995)) % 188.18/188.27 [1600]~E(x16001,x16002)+E(f433(x16003,x16004,x16005,x16001),f433(x16003,x16004,x16005,x16002)) % 188.18/188.27 [1601]~E(x16011,x16012)+E(f790(x16011,x16013,x16014),f790(x16012,x16013,x16014)) % 188.18/188.27 [1602]~E(x16021,x16022)+E(f790(x16023,x16021,x16024),f790(x16023,x16022,x16024)) % 188.18/188.27 [1603]~E(x16031,x16032)+E(f790(x16033,x16034,x16031),f790(x16033,x16034,x16032)) % 188.18/188.27 [1604]~E(x16041,x16042)+E(f651(x16041,x16043),f651(x16042,x16043)) % 188.18/188.27 [1605]~E(x16051,x16052)+E(f651(x16053,x16051),f651(x16053,x16052)) % 188.18/188.27 [1606]~E(x16061,x16062)+E(f49(x16061),f49(x16062)) % 188.18/188.27 [1607]~E(x16071,x16072)+E(f819(x16071,x16073),f819(x16072,x16073)) % 188.18/188.27 [1608]~E(x16081,x16082)+E(f819(x16083,x16081),f819(x16083,x16082)) % 188.18/188.27 [1609]~E(x16091,x16092)+E(f500(x16091,x16093,x16094,x16095,x16096),f500(x16092,x16093,x16094,x16095,x16096)) % 188.18/188.27 [1610]~E(x16101,x16102)+E(f500(x16103,x16101,x16104,x16105,x16106),f500(x16103,x16102,x16104,x16105,x16106)) % 188.18/188.27 [1611]~E(x16111,x16112)+E(f500(x16113,x16114,x16111,x16115,x16116),f500(x16113,x16114,x16112,x16115,x16116)) % 188.18/188.27 [1612]~E(x16121,x16122)+E(f500(x16123,x16124,x16125,x16121,x16126),f500(x16123,x16124,x16125,x16122,x16126)) % 188.18/188.27 [1613]~E(x16131,x16132)+E(f500(x16133,x16134,x16135,x16136,x16131),f500(x16133,x16134,x16135,x16136,x16132)) % 188.18/188.27 [1614]~E(x16141,x16142)+E(f93(x16141),f93(x16142)) % 188.18/188.27 [1615]~E(x16151,x16152)+E(f672(x16151,x16153,x16154),f672(x16152,x16153,x16154)) % 188.18/188.27 [1616]~E(x16161,x16162)+E(f672(x16163,x16161,x16164),f672(x16163,x16162,x16164)) % 188.18/188.27 [1617]~E(x16171,x16172)+E(f672(x16173,x16174,x16171),f672(x16173,x16174,x16172)) % 188.18/188.27 [1618]~E(x16181,x16182)+E(f577(x16181,x16183,x16184,x16185,x16186,x16187,x16188),f577(x16182,x16183,x16184,x16185,x16186,x16187,x16188)) % 188.18/188.27 [1619]~E(x16191,x16192)+E(f577(x16193,x16191,x16194,x16195,x16196,x16197,x16198),f577(x16193,x16192,x16194,x16195,x16196,x16197,x16198)) % 188.18/188.27 [1620]~E(x16201,x16202)+E(f577(x16203,x16204,x16201,x16205,x16206,x16207,x16208),f577(x16203,x16204,x16202,x16205,x16206,x16207,x16208)) % 188.18/188.27 [1621]~E(x16211,x16212)+E(f577(x16213,x16214,x16215,x16211,x16216,x16217,x16218),f577(x16213,x16214,x16215,x16212,x16216,x16217,x16218)) % 188.18/188.27 [1622]~E(x16221,x16222)+E(f577(x16223,x16224,x16225,x16226,x16221,x16227,x16228),f577(x16223,x16224,x16225,x16226,x16222,x16227,x16228)) % 188.18/188.27 [1623]~E(x16231,x16232)+E(f577(x16233,x16234,x16235,x16236,x16237,x16231,x16238),f577(x16233,x16234,x16235,x16236,x16237,x16232,x16238)) % 188.18/188.27 [1624]~E(x16241,x16242)+E(f577(x16243,x16244,x16245,x16246,x16247,x16248,x16241),f577(x16243,x16244,x16245,x16246,x16247,x16248,x16242)) % 188.18/188.27 [1625]~E(x16251,x16252)+E(f279(x16251,x16253,x16254,x16255),f279(x16252,x16253,x16254,x16255)) % 188.18/188.27 [1626]~E(x16261,x16262)+E(f279(x16263,x16261,x16264,x16265),f279(x16263,x16262,x16264,x16265)) % 188.18/188.27 [1627]~E(x16271,x16272)+E(f279(x16273,x16274,x16271,x16275),f279(x16273,x16274,x16272,x16275)) % 188.18/188.27 [1628]~E(x16281,x16282)+E(f279(x16283,x16284,x16285,x16281),f279(x16283,x16284,x16285,x16282)) % 188.18/188.27 [1629]~E(x16291,x16292)+E(f59(x16291,x16293),f59(x16292,x16293)) % 188.18/188.27 [1630]~E(x16301,x16302)+E(f59(x16303,x16301),f59(x16303,x16302)) % 188.18/188.27 [1631]~E(x16311,x16312)+E(f528(x16311,x16313),f528(x16312,x16313)) % 188.18/188.27 [1632]~E(x16321,x16322)+E(f528(x16323,x16321),f528(x16323,x16322)) % 188.18/188.27 [1633]~E(x16331,x16332)+E(f297(x16331,x16333),f297(x16332,x16333)) % 188.18/188.27 [1634]~E(x16341,x16342)+E(f297(x16343,x16341),f297(x16343,x16342)) % 188.18/188.27 [1635]~E(x16351,x16352)+E(f255(x16351,x16353,x16354),f255(x16352,x16353,x16354)) % 188.18/188.27 [1636]~E(x16361,x16362)+E(f255(x16363,x16361,x16364),f255(x16363,x16362,x16364)) % 188.18/188.27 [1637]~E(x16371,x16372)+E(f255(x16373,x16374,x16371),f255(x16373,x16374,x16372)) % 188.18/188.27 [1638]~E(x16381,x16382)+E(f554(x16381,x16383,x16384,x16385),f554(x16382,x16383,x16384,x16385)) % 188.18/188.27 [1639]~E(x16391,x16392)+E(f554(x16393,x16391,x16394,x16395),f554(x16393,x16392,x16394,x16395)) % 188.18/188.27 [1640]~E(x16401,x16402)+E(f554(x16403,x16404,x16401,x16405),f554(x16403,x16404,x16402,x16405)) % 188.18/188.27 [1641]~E(x16411,x16412)+E(f554(x16413,x16414,x16415,x16411),f554(x16413,x16414,x16415,x16412)) % 188.18/188.27 [1642]~E(x16421,x16422)+E(f205(x16421,x16423,x16424,x16425),f205(x16422,x16423,x16424,x16425)) % 188.18/188.27 [1643]~E(x16431,x16432)+E(f205(x16433,x16431,x16434,x16435),f205(x16433,x16432,x16434,x16435)) % 188.18/188.27 [1644]~E(x16441,x16442)+E(f205(x16443,x16444,x16441,x16445),f205(x16443,x16444,x16442,x16445)) % 188.18/188.27 [1645]~E(x16451,x16452)+E(f205(x16453,x16454,x16455,x16451),f205(x16453,x16454,x16455,x16452)) % 188.18/188.27 [1646]~E(x16461,x16462)+E(f517(x16461,x16463,x16464),f517(x16462,x16463,x16464)) % 188.18/188.27 [1647]~E(x16471,x16472)+E(f517(x16473,x16471,x16474),f517(x16473,x16472,x16474)) % 188.18/188.27 [1648]~E(x16481,x16482)+E(f517(x16483,x16484,x16481),f517(x16483,x16484,x16482)) % 188.18/188.27 [1649]~E(x16491,x16492)+E(f364(x16491,x16493,x16494),f364(x16492,x16493,x16494)) % 188.18/188.27 [1650]~E(x16501,x16502)+E(f364(x16503,x16501,x16504),f364(x16503,x16502,x16504)) % 188.18/188.27 [1651]~E(x16511,x16512)+E(f364(x16513,x16514,x16511),f364(x16513,x16514,x16512)) % 188.18/188.27 [1652]~E(x16521,x16522)+E(f197(x16521,x16523,x16524,x16525),f197(x16522,x16523,x16524,x16525)) % 188.18/188.27 [1653]~E(x16531,x16532)+E(f197(x16533,x16531,x16534,x16535),f197(x16533,x16532,x16534,x16535)) % 188.18/188.27 [1654]~E(x16541,x16542)+E(f197(x16543,x16544,x16541,x16545),f197(x16543,x16544,x16542,x16545)) % 188.18/188.27 [1655]~E(x16551,x16552)+E(f197(x16553,x16554,x16555,x16551),f197(x16553,x16554,x16555,x16552)) % 188.18/188.27 [1656]~E(x16561,x16562)+E(f593(x16561,x16563,x16564,x16565,x16566,x16567),f593(x16562,x16563,x16564,x16565,x16566,x16567)) % 188.18/188.27 [1657]~E(x16571,x16572)+E(f593(x16573,x16571,x16574,x16575,x16576,x16577),f593(x16573,x16572,x16574,x16575,x16576,x16577)) % 188.18/188.27 [1658]~E(x16581,x16582)+E(f593(x16583,x16584,x16581,x16585,x16586,x16587),f593(x16583,x16584,x16582,x16585,x16586,x16587)) % 188.18/188.27 [1659]~E(x16591,x16592)+E(f593(x16593,x16594,x16595,x16591,x16596,x16597),f593(x16593,x16594,x16595,x16592,x16596,x16597)) % 188.18/188.27 [1660]~E(x16601,x16602)+E(f593(x16603,x16604,x16605,x16606,x16601,x16607),f593(x16603,x16604,x16605,x16606,x16602,x16607)) % 188.18/188.27 [1661]~E(x16611,x16612)+E(f593(x16613,x16614,x16615,x16616,x16617,x16611),f593(x16613,x16614,x16615,x16616,x16617,x16612)) % 188.18/188.27 [1662]~E(x16621,x16622)+E(f466(x16621,x16623,x16624,x16625,x16626),f466(x16622,x16623,x16624,x16625,x16626)) % 188.18/188.27 [1663]~E(x16631,x16632)+E(f466(x16633,x16631,x16634,x16635,x16636),f466(x16633,x16632,x16634,x16635,x16636)) % 188.18/188.27 [1664]~E(x16641,x16642)+E(f466(x16643,x16644,x16641,x16645,x16646),f466(x16643,x16644,x16642,x16645,x16646)) % 188.18/188.27 [1665]~E(x16651,x16652)+E(f466(x16653,x16654,x16655,x16651,x16656),f466(x16653,x16654,x16655,x16652,x16656)) % 188.18/188.27 [1666]~E(x16661,x16662)+E(f466(x16663,x16664,x16665,x16666,x16661),f466(x16663,x16664,x16665,x16666,x16662)) % 188.18/188.27 [1667]~E(x16671,x16672)+E(f531(x16671,x16673,x16674),f531(x16672,x16673,x16674)) % 188.18/188.27 [1668]~E(x16681,x16682)+E(f531(x16683,x16681,x16684),f531(x16683,x16682,x16684)) % 188.18/188.27 [1669]~E(x16691,x16692)+E(f531(x16693,x16694,x16691),f531(x16693,x16694,x16692)) % 188.18/188.27 [1670]~E(x16701,x16702)+E(f587(x16701,x16703,x16704),f587(x16702,x16703,x16704)) % 188.18/188.27 [1671]~E(x16711,x16712)+E(f587(x16713,x16711,x16714),f587(x16713,x16712,x16714)) % 188.18/188.27 [1672]~E(x16721,x16722)+E(f587(x16723,x16724,x16721),f587(x16723,x16724,x16722)) % 188.18/188.27 [1673]~E(x16731,x16732)+E(f300(x16731,x16733,x16734),f300(x16732,x16733,x16734)) % 188.18/188.27 [1674]~E(x16741,x16742)+E(f300(x16743,x16741,x16744),f300(x16743,x16742,x16744)) % 188.18/188.27 [1675]~E(x16751,x16752)+E(f300(x16753,x16754,x16751),f300(x16753,x16754,x16752)) % 188.18/188.27 [1676]~E(x16761,x16762)+E(f529(x16761,x16763),f529(x16762,x16763)) % 188.18/188.27 [1677]~E(x16771,x16772)+E(f529(x16773,x16771),f529(x16773,x16772)) % 188.18/188.27 [1678]~E(x16781,x16782)+E(f749(x16781,x16783,x16784,x16785),f749(x16782,x16783,x16784,x16785)) % 188.18/188.27 [1679]~E(x16791,x16792)+E(f749(x16793,x16791,x16794,x16795),f749(x16793,x16792,x16794,x16795)) % 188.18/188.27 [1680]~E(x16801,x16802)+E(f749(x16803,x16804,x16801,x16805),f749(x16803,x16804,x16802,x16805)) % 188.18/188.27 [1681]~E(x16811,x16812)+E(f749(x16813,x16814,x16815,x16811),f749(x16813,x16814,x16815,x16812)) % 188.18/188.27 [1682]~E(x16821,x16822)+E(f647(x16821,x16823,x16824),f647(x16822,x16823,x16824)) % 188.18/188.27 [1683]~E(x16831,x16832)+E(f647(x16833,x16831,x16834),f647(x16833,x16832,x16834)) % 188.18/188.27 [1684]~E(x16841,x16842)+E(f647(x16843,x16844,x16841),f647(x16843,x16844,x16842)) % 188.18/188.27 [1685]~E(x16851,x16852)+E(f355(x16851,x16853,x16854,x16855,x16856,x16857,x16858),f355(x16852,x16853,x16854,x16855,x16856,x16857,x16858)) % 188.18/188.27 [1686]~E(x16861,x16862)+E(f355(x16863,x16861,x16864,x16865,x16866,x16867,x16868),f355(x16863,x16862,x16864,x16865,x16866,x16867,x16868)) % 188.18/188.27 [1687]~E(x16871,x16872)+E(f355(x16873,x16874,x16871,x16875,x16876,x16877,x16878),f355(x16873,x16874,x16872,x16875,x16876,x16877,x16878)) % 188.18/188.27 [1688]~E(x16881,x16882)+E(f355(x16883,x16884,x16885,x16881,x16886,x16887,x16888),f355(x16883,x16884,x16885,x16882,x16886,x16887,x16888)) % 188.18/188.27 [1689]~E(x16891,x16892)+E(f355(x16893,x16894,x16895,x16896,x16891,x16897,x16898),f355(x16893,x16894,x16895,x16896,x16892,x16897,x16898)) % 188.18/188.27 [1690]~E(x16901,x16902)+E(f355(x16903,x16904,x16905,x16906,x16907,x16901,x16908),f355(x16903,x16904,x16905,x16906,x16907,x16902,x16908)) % 188.18/188.27 [1691]~E(x16911,x16912)+E(f355(x16913,x16914,x16915,x16916,x16917,x16918,x16911),f355(x16913,x16914,x16915,x16916,x16917,x16918,x16912)) % 188.18/188.27 [1692]~E(x16921,x16922)+E(f669(x16921,x16923,x16924,x16925),f669(x16922,x16923,x16924,x16925)) % 188.18/188.27 [1693]~E(x16931,x16932)+E(f669(x16933,x16931,x16934,x16935),f669(x16933,x16932,x16934,x16935)) % 188.18/188.27 [1694]~E(x16941,x16942)+E(f669(x16943,x16944,x16941,x16945),f669(x16943,x16944,x16942,x16945)) % 188.18/188.27 [1695]~E(x16951,x16952)+E(f669(x16953,x16954,x16955,x16951),f669(x16953,x16954,x16955,x16952)) % 188.18/188.27 [1696]~E(x16961,x16962)+E(f869(x16961,x16963,x16964),f869(x16962,x16963,x16964)) % 188.18/188.27 [1697]~E(x16971,x16972)+E(f869(x16973,x16971,x16974),f869(x16973,x16972,x16974)) % 188.18/188.27 [1698]~E(x16981,x16982)+E(f869(x16983,x16984,x16981),f869(x16983,x16984,x16982)) % 188.18/188.27 [1699]~E(x16991,x16992)+E(f748(x16991),f748(x16992)) % 188.18/188.27 [1700]~E(x17001,x17002)+E(f813(x17001,x17003,x17004,x17005),f813(x17002,x17003,x17004,x17005)) % 188.18/188.27 [1701]~E(x17011,x17012)+E(f813(x17013,x17011,x17014,x17015),f813(x17013,x17012,x17014,x17015)) % 188.18/188.27 [1702]~E(x17021,x17022)+E(f813(x17023,x17024,x17021,x17025),f813(x17023,x17024,x17022,x17025)) % 188.18/188.27 [1703]~E(x17031,x17032)+E(f813(x17033,x17034,x17035,x17031),f813(x17033,x17034,x17035,x17032)) % 188.18/188.27 [1704]~E(x17041,x17042)+E(f514(x17041,x17043,x17044),f514(x17042,x17043,x17044)) % 188.18/188.27 [1705]~E(x17051,x17052)+E(f514(x17053,x17051,x17054),f514(x17053,x17052,x17054)) % 188.18/188.27 [1706]~E(x17061,x17062)+E(f514(x17063,x17064,x17061),f514(x17063,x17064,x17062)) % 188.18/188.27 [1707]~E(x17071,x17072)+E(f551(x17071,x17073,x17074),f551(x17072,x17073,x17074)) % 188.18/188.27 [1708]~E(x17081,x17082)+E(f551(x17083,x17081,x17084),f551(x17083,x17082,x17084)) % 188.18/188.27 [1709]~E(x17091,x17092)+E(f551(x17093,x17094,x17091),f551(x17093,x17094,x17092)) % 188.18/188.27 [1710]~E(x17101,x17102)+E(f643(x17101,x17103,x17104,x17105,x17106),f643(x17102,x17103,x17104,x17105,x17106)) % 188.18/188.27 [1711]~E(x17111,x17112)+E(f643(x17113,x17111,x17114,x17115,x17116),f643(x17113,x17112,x17114,x17115,x17116)) % 188.18/188.27 [1712]~E(x17121,x17122)+E(f643(x17123,x17124,x17121,x17125,x17126),f643(x17123,x17124,x17122,x17125,x17126)) % 188.18/188.27 [1713]~E(x17131,x17132)+E(f643(x17133,x17134,x17135,x17131,x17136),f643(x17133,x17134,x17135,x17132,x17136)) % 188.18/188.27 [1714]~E(x17141,x17142)+E(f643(x17143,x17144,x17145,x17146,x17141),f643(x17143,x17144,x17145,x17146,x17142)) % 188.18/188.27 [1715]~E(x17151,x17152)+E(f775(x17151,x17153,x17154),f775(x17152,x17153,x17154)) % 188.18/188.27 [1716]~E(x17161,x17162)+E(f775(x17163,x17161,x17164),f775(x17163,x17162,x17164)) % 188.18/188.27 [1717]~E(x17171,x17172)+E(f775(x17173,x17174,x17171),f775(x17173,x17174,x17172)) % 188.18/188.27 [1718]~E(x17181,x17182)+E(f815(x17181,x17183,x17184,x17185,x17186),f815(x17182,x17183,x17184,x17185,x17186)) % 188.18/188.27 [1719]~E(x17191,x17192)+E(f815(x17193,x17191,x17194,x17195,x17196),f815(x17193,x17192,x17194,x17195,x17196)) % 188.18/188.27 [1720]~E(x17201,x17202)+E(f815(x17203,x17204,x17201,x17205,x17206),f815(x17203,x17204,x17202,x17205,x17206)) % 188.18/188.27 [1721]~E(x17211,x17212)+E(f815(x17213,x17214,x17215,x17211,x17216),f815(x17213,x17214,x17215,x17212,x17216)) % 188.18/188.27 [1722]~E(x17221,x17222)+E(f815(x17223,x17224,x17225,x17226,x17221),f815(x17223,x17224,x17225,x17226,x17222)) % 188.18/188.27 [1723]~E(x17231,x17232)+E(f845(x17231,x17233,x17234,x17235),f845(x17232,x17233,x17234,x17235)) % 188.18/188.27 [1724]~E(x17241,x17242)+E(f845(x17243,x17241,x17244,x17245),f845(x17243,x17242,x17244,x17245)) % 188.18/188.27 [1725]~E(x17251,x17252)+E(f845(x17253,x17254,x17251,x17255),f845(x17253,x17254,x17252,x17255)) % 188.18/188.27 [1726]~E(x17261,x17262)+E(f845(x17263,x17264,x17265,x17261),f845(x17263,x17264,x17265,x17262)) % 188.18/188.27 [1727]~E(x17271,x17272)+E(f431(x17271,x17273,x17274,x17275),f431(x17272,x17273,x17274,x17275)) % 188.18/188.27 [1728]~E(x17281,x17282)+E(f431(x17283,x17281,x17284,x17285),f431(x17283,x17282,x17284,x17285)) % 188.18/188.27 [1729]~E(x17291,x17292)+E(f431(x17293,x17294,x17291,x17295),f431(x17293,x17294,x17292,x17295)) % 188.18/188.27 [1730]~E(x17301,x17302)+E(f431(x17303,x17304,x17305,x17301),f431(x17303,x17304,x17305,x17302)) % 188.18/188.27 [1731]~E(x17311,x17312)+E(f909(x17311,x17313,x17314),f909(x17312,x17313,x17314)) % 188.18/188.27 [1732]~E(x17321,x17322)+E(f909(x17323,x17321,x17324),f909(x17323,x17322,x17324)) % 188.18/188.27 [1733]~E(x17331,x17332)+E(f909(x17333,x17334,x17331),f909(x17333,x17334,x17332)) % 188.18/188.27 [1734]~E(x17341,x17342)+E(f684(x17341,x17343,x17344,x17345),f684(x17342,x17343,x17344,x17345)) % 188.18/188.27 [1735]~E(x17351,x17352)+E(f684(x17353,x17351,x17354,x17355),f684(x17353,x17352,x17354,x17355)) % 188.18/188.27 [1736]~E(x17361,x17362)+E(f684(x17363,x17364,x17361,x17365),f684(x17363,x17364,x17362,x17365)) % 188.18/188.27 [1737]~E(x17371,x17372)+E(f684(x17373,x17374,x17375,x17371),f684(x17373,x17374,x17375,x17372)) % 188.18/188.27 [1738]~E(x17381,x17382)+E(f691(x17381,x17383,x17384,x17385),f691(x17382,x17383,x17384,x17385)) % 188.18/188.27 [1739]~E(x17391,x17392)+E(f691(x17393,x17391,x17394,x17395),f691(x17393,x17392,x17394,x17395)) % 188.18/188.27 [1740]~E(x17401,x17402)+E(f691(x17403,x17404,x17401,x17405),f691(x17403,x17404,x17402,x17405)) % 188.18/188.27 [1741]~E(x17411,x17412)+E(f691(x17413,x17414,x17415,x17411),f691(x17413,x17414,x17415,x17412)) % 188.18/188.27 [1742]~E(x17421,x17422)+E(f883(x17421,x17423),f883(x17422,x17423)) % 188.18/188.27 [1743]~E(x17431,x17432)+E(f883(x17433,x17431),f883(x17433,x17432)) % 188.18/188.27 [1744]~E(x17441,x17442)+E(f438(x17441,x17443,x17444,x17445),f438(x17442,x17443,x17444,x17445)) % 188.18/188.27 [1745]~E(x17451,x17452)+E(f438(x17453,x17451,x17454,x17455),f438(x17453,x17452,x17454,x17455)) % 188.18/188.27 [1746]~E(x17461,x17462)+E(f438(x17463,x17464,x17461,x17465),f438(x17463,x17464,x17462,x17465)) % 188.18/188.27 [1747]~E(x17471,x17472)+E(f438(x17473,x17474,x17475,x17471),f438(x17473,x17474,x17475,x17472)) % 188.18/188.27 [1748]~E(x17481,x17482)+E(f465(x17481,x17483,x17484,x17485,x17486),f465(x17482,x17483,x17484,x17485,x17486)) % 188.18/188.27 [1749]~E(x17491,x17492)+E(f465(x17493,x17491,x17494,x17495,x17496),f465(x17493,x17492,x17494,x17495,x17496)) % 188.18/188.27 [1750]~E(x17501,x17502)+E(f465(x17503,x17504,x17501,x17505,x17506),f465(x17503,x17504,x17502,x17505,x17506)) % 188.18/188.27 [1751]~E(x17511,x17512)+E(f465(x17513,x17514,x17515,x17511,x17516),f465(x17513,x17514,x17515,x17512,x17516)) % 188.18/188.27 [1752]~E(x17521,x17522)+E(f465(x17523,x17524,x17525,x17526,x17521),f465(x17523,x17524,x17525,x17526,x17522)) % 188.18/188.27 [1753]~E(x17531,x17532)+E(f646(x17531,x17533,x17534,x17535),f646(x17532,x17533,x17534,x17535)) % 188.18/188.27 [1754]~E(x17541,x17542)+E(f646(x17543,x17541,x17544,x17545),f646(x17543,x17542,x17544,x17545)) % 188.18/188.27 [1755]~E(x17551,x17552)+E(f646(x17553,x17554,x17551,x17555),f646(x17553,x17554,x17552,x17555)) % 188.18/188.27 [1756]~E(x17561,x17562)+E(f646(x17563,x17564,x17565,x17561),f646(x17563,x17564,x17565,x17562)) % 188.18/188.27 [1757]~E(x17571,x17572)+E(f893(x17571,x17573,x17574,x17575,x17576,x17577,x17578),f893(x17572,x17573,x17574,x17575,x17576,x17577,x17578)) % 188.18/188.27 [1758]~E(x17581,x17582)+E(f893(x17583,x17581,x17584,x17585,x17586,x17587,x17588),f893(x17583,x17582,x17584,x17585,x17586,x17587,x17588)) % 188.18/188.27 [1759]~E(x17591,x17592)+E(f893(x17593,x17594,x17591,x17595,x17596,x17597,x17598),f893(x17593,x17594,x17592,x17595,x17596,x17597,x17598)) % 188.18/188.27 [1760]~E(x17601,x17602)+E(f893(x17603,x17604,x17605,x17601,x17606,x17607,x17608),f893(x17603,x17604,x17605,x17602,x17606,x17607,x17608)) % 188.18/188.27 [1761]~E(x17611,x17612)+E(f893(x17613,x17614,x17615,x17616,x17611,x17617,x17618),f893(x17613,x17614,x17615,x17616,x17612,x17617,x17618)) % 188.18/188.27 [1762]~E(x17621,x17622)+E(f893(x17623,x17624,x17625,x17626,x17627,x17621,x17628),f893(x17623,x17624,x17625,x17626,x17627,x17622,x17628)) % 188.18/188.27 [1763]~E(x17631,x17632)+E(f893(x17633,x17634,x17635,x17636,x17637,x17638,x17631),f893(x17633,x17634,x17635,x17636,x17637,x17638,x17632)) % 188.18/188.27 [1764]~E(x17641,x17642)+E(f754(x17641,x17643,x17644,x17645),f754(x17642,x17643,x17644,x17645)) % 188.18/188.27 [1765]~E(x17651,x17652)+E(f754(x17653,x17651,x17654,x17655),f754(x17653,x17652,x17654,x17655)) % 188.18/188.27 [1766]~E(x17661,x17662)+E(f754(x17663,x17664,x17661,x17665),f754(x17663,x17664,x17662,x17665)) % 188.18/188.27 [1767]~E(x17671,x17672)+E(f754(x17673,x17674,x17675,x17671),f754(x17673,x17674,x17675,x17672)) % 188.18/188.27 [1768]~E(x17681,x17682)+E(f362(x17681,x17683,x17684),f362(x17682,x17683,x17684)) % 188.18/188.27 [1769]~E(x17691,x17692)+E(f362(x17693,x17691,x17694),f362(x17693,x17692,x17694)) % 188.18/188.27 [1770]~E(x17701,x17702)+E(f362(x17703,x17704,x17701),f362(x17703,x17704,x17702)) % 188.18/188.27 [1771]~E(x17711,x17712)+E(f570(x17711),f570(x17712)) % 188.18/188.27 [1772]~E(x17721,x17722)+E(f416(x17721,x17723,x17724,x17725),f416(x17722,x17723,x17724,x17725)) % 188.18/188.27 [1773]~E(x17731,x17732)+E(f416(x17733,x17731,x17734,x17735),f416(x17733,x17732,x17734,x17735)) % 188.18/188.27 [1774]~E(x17741,x17742)+E(f416(x17743,x17744,x17741,x17745),f416(x17743,x17744,x17742,x17745)) % 188.18/188.27 [1775]~E(x17751,x17752)+E(f416(x17753,x17754,x17755,x17751),f416(x17753,x17754,x17755,x17752)) % 188.18/188.27 [1776]~E(x17761,x17762)+E(f276(x17761,x17763),f276(x17762,x17763)) % 188.18/188.27 [1777]~E(x17771,x17772)+E(f276(x17773,x17771),f276(x17773,x17772)) % 188.18/188.27 [1778]~E(x17781,x17782)+E(f623(x17781,x17783,x17784),f623(x17782,x17783,x17784)) % 188.18/188.27 [1779]~E(x17791,x17792)+E(f623(x17793,x17791,x17794),f623(x17793,x17792,x17794)) % 188.18/188.27 [1780]~E(x17801,x17802)+E(f623(x17803,x17804,x17801),f623(x17803,x17804,x17802)) % 188.18/188.27 [1781]~E(x17811,x17812)+E(f900(x17811,x17813,x17814,x17815,x17816,x17817),f900(x17812,x17813,x17814,x17815,x17816,x17817)) % 188.18/188.27 [1782]~E(x17821,x17822)+E(f900(x17823,x17821,x17824,x17825,x17826,x17827),f900(x17823,x17822,x17824,x17825,x17826,x17827)) % 188.18/188.27 [1783]~E(x17831,x17832)+E(f900(x17833,x17834,x17831,x17835,x17836,x17837),f900(x17833,x17834,x17832,x17835,x17836,x17837)) % 188.18/188.27 [1784]~E(x17841,x17842)+E(f900(x17843,x17844,x17845,x17841,x17846,x17847),f900(x17843,x17844,x17845,x17842,x17846,x17847)) % 188.18/188.27 [1785]~E(x17851,x17852)+E(f900(x17853,x17854,x17855,x17856,x17851,x17857),f900(x17853,x17854,x17855,x17856,x17852,x17857)) % 188.18/188.27 [1786]~E(x17861,x17862)+E(f900(x17863,x17864,x17865,x17866,x17867,x17861),f900(x17863,x17864,x17865,x17866,x17867,x17862)) % 188.18/188.27 [1787]~E(x17871,x17872)+E(f37(x17871,x17873,x17874,x17875),f37(x17872,x17873,x17874,x17875)) % 188.18/188.27 [1788]~E(x17881,x17882)+E(f37(x17883,x17881,x17884,x17885),f37(x17883,x17882,x17884,x17885)) % 188.18/188.27 [1789]~E(x17891,x17892)+E(f37(x17893,x17894,x17891,x17895),f37(x17893,x17894,x17892,x17895)) % 188.18/188.27 [1790]~E(x17901,x17902)+E(f37(x17903,x17904,x17905,x17901),f37(x17903,x17904,x17905,x17902)) % 188.18/188.27 [1791]~E(x17911,x17912)+E(f826(x17911,x17913),f826(x17912,x17913)) % 188.18/188.27 [1792]~E(x17921,x17922)+E(f826(x17923,x17921),f826(x17923,x17922)) % 188.18/188.27 [1793]~E(x17931,x17932)+E(f887(x17931),f887(x17932)) % 188.18/188.27 [1794]~E(x17941,x17942)+E(f649(x17941,x17943,x17944),f649(x17942,x17943,x17944)) % 188.18/188.27 [1795]~E(x17951,x17952)+E(f649(x17953,x17951,x17954),f649(x17953,x17952,x17954)) % 188.18/188.27 [1796]~E(x17961,x17962)+E(f649(x17963,x17964,x17961),f649(x17963,x17964,x17962)) % 188.18/188.27 [1797]~E(x17971,x17972)+E(f452(x17971,x17973,x17974),f452(x17972,x17973,x17974)) % 188.18/188.27 [1798]~E(x17981,x17982)+E(f452(x17983,x17981,x17984),f452(x17983,x17982,x17984)) % 188.18/188.27 [1799]~E(x17991,x17992)+E(f452(x17993,x17994,x17991),f452(x17993,x17994,x17992)) % 188.18/188.27 [1800]~E(x18001,x18002)+E(f614(x18001,x18003,x18004,x18005),f614(x18002,x18003,x18004,x18005)) % 188.18/188.27 [1801]~E(x18011,x18012)+E(f614(x18013,x18011,x18014,x18015),f614(x18013,x18012,x18014,x18015)) % 188.18/188.27 [1802]~E(x18021,x18022)+E(f614(x18023,x18024,x18021,x18025),f614(x18023,x18024,x18022,x18025)) % 188.18/188.27 [1803]~E(x18031,x18032)+E(f614(x18033,x18034,x18035,x18031),f614(x18033,x18034,x18035,x18032)) % 188.18/188.27 [1804]~E(x18041,x18042)+E(f395(x18041,x18043,x18044,x18045,x18046),f395(x18042,x18043,x18044,x18045,x18046)) % 188.18/188.27 [1805]~E(x18051,x18052)+E(f395(x18053,x18051,x18054,x18055,x18056),f395(x18053,x18052,x18054,x18055,x18056)) % 188.18/188.27 [1806]~E(x18061,x18062)+E(f395(x18063,x18064,x18061,x18065,x18066),f395(x18063,x18064,x18062,x18065,x18066)) % 188.18/188.27 [1807]~E(x18071,x18072)+E(f395(x18073,x18074,x18075,x18071,x18076),f395(x18073,x18074,x18075,x18072,x18076)) % 188.18/188.27 [1808]~E(x18081,x18082)+E(f395(x18083,x18084,x18085,x18086,x18081),f395(x18083,x18084,x18085,x18086,x18082)) % 188.18/188.27 [1809]~E(x18091,x18092)+E(f257(x18091,x18093,x18094),f257(x18092,x18093,x18094)) % 188.18/188.27 [1810]~E(x18101,x18102)+E(f257(x18103,x18101,x18104),f257(x18103,x18102,x18104)) % 188.18/188.27 [1811]~E(x18111,x18112)+E(f257(x18113,x18114,x18111),f257(x18113,x18114,x18112)) % 188.18/188.27 [1812]~E(x18121,x18122)+E(f217(x18121),f217(x18122)) % 188.18/188.27 [1813]~E(x18131,x18132)+E(f830(x18131,x18133),f830(x18132,x18133)) % 188.18/188.27 [1814]~E(x18141,x18142)+E(f830(x18143,x18141),f830(x18143,x18142)) % 188.18/188.27 [1815]~E(x18151,x18152)+E(f510(x18151,x18153,x18154,x18155,x18156,x18157,x18158),f510(x18152,x18153,x18154,x18155,x18156,x18157,x18158)) % 188.18/188.27 [1816]~E(x18161,x18162)+E(f510(x18163,x18161,x18164,x18165,x18166,x18167,x18168),f510(x18163,x18162,x18164,x18165,x18166,x18167,x18168)) % 188.18/188.27 [1817]~E(x18171,x18172)+E(f510(x18173,x18174,x18171,x18175,x18176,x18177,x18178),f510(x18173,x18174,x18172,x18175,x18176,x18177,x18178)) % 188.18/188.27 [1818]~E(x18181,x18182)+E(f510(x18183,x18184,x18185,x18181,x18186,x18187,x18188),f510(x18183,x18184,x18185,x18182,x18186,x18187,x18188)) % 188.18/188.27 [1819]~E(x18191,x18192)+E(f510(x18193,x18194,x18195,x18196,x18191,x18197,x18198),f510(x18193,x18194,x18195,x18196,x18192,x18197,x18198)) % 188.18/188.27 [1820]~E(x18201,x18202)+E(f510(x18203,x18204,x18205,x18206,x18207,x18201,x18208),f510(x18203,x18204,x18205,x18206,x18207,x18202,x18208)) % 188.18/188.27 [1821]~E(x18211,x18212)+E(f510(x18213,x18214,x18215,x18216,x18217,x18218,x18211),f510(x18213,x18214,x18215,x18216,x18217,x18218,x18212)) % 188.18/188.27 [1822]~E(x18221,x18222)+E(f840(x18221,x18223,x18224),f840(x18222,x18223,x18224)) % 188.18/188.27 [1823]~E(x18231,x18232)+E(f840(x18233,x18231,x18234),f840(x18233,x18232,x18234)) % 188.18/188.27 [1824]~E(x18241,x18242)+E(f840(x18243,x18244,x18241),f840(x18243,x18244,x18242)) % 188.18/188.27 [1825]~E(x18251,x18252)+E(f288(x18251,x18253,x18254,x18255),f288(x18252,x18253,x18254,x18255)) % 188.18/188.27 [1826]~E(x18261,x18262)+E(f288(x18263,x18261,x18264,x18265),f288(x18263,x18262,x18264,x18265)) % 188.18/188.27 [1827]~E(x18271,x18272)+E(f288(x18273,x18274,x18271,x18275),f288(x18273,x18274,x18272,x18275)) % 188.18/188.27 [1828]~E(x18281,x18282)+E(f288(x18283,x18284,x18285,x18281),f288(x18283,x18284,x18285,x18282)) % 188.18/188.27 [1829]~E(x18291,x18292)+E(f693(x18291,x18293,x18294,x18295,x18296),f693(x18292,x18293,x18294,x18295,x18296)) % 188.18/188.27 [1830]~E(x18301,x18302)+E(f693(x18303,x18301,x18304,x18305,x18306),f693(x18303,x18302,x18304,x18305,x18306)) % 188.18/188.27 [1831]~E(x18311,x18312)+E(f693(x18313,x18314,x18311,x18315,x18316),f693(x18313,x18314,x18312,x18315,x18316)) % 188.18/188.27 [1832]~E(x18321,x18322)+E(f693(x18323,x18324,x18325,x18321,x18326),f693(x18323,x18324,x18325,x18322,x18326)) % 188.18/188.27 [1833]~E(x18331,x18332)+E(f693(x18333,x18334,x18335,x18336,x18331),f693(x18333,x18334,x18335,x18336,x18332)) % 188.18/188.27 [1834]~E(x18341,x18342)+E(f640(x18341,x18343,x18344,x18345,x18346),f640(x18342,x18343,x18344,x18345,x18346)) % 188.18/188.27 [1835]~E(x18351,x18352)+E(f640(x18353,x18351,x18354,x18355,x18356),f640(x18353,x18352,x18354,x18355,x18356)) % 188.18/188.27 [1836]~E(x18361,x18362)+E(f640(x18363,x18364,x18361,x18365,x18366),f640(x18363,x18364,x18362,x18365,x18366)) % 188.18/188.27 [1837]~E(x18371,x18372)+E(f640(x18373,x18374,x18375,x18371,x18376),f640(x18373,x18374,x18375,x18372,x18376)) % 188.18/188.27 [1838]~E(x18381,x18382)+E(f640(x18383,x18384,x18385,x18386,x18381),f640(x18383,x18384,x18385,x18386,x18382)) % 188.18/188.27 [1839]~E(x18391,x18392)+E(f752(x18391,x18393,x18394),f752(x18392,x18393,x18394)) % 188.18/188.27 [1840]~E(x18401,x18402)+E(f752(x18403,x18401,x18404),f752(x18403,x18402,x18404)) % 188.18/188.27 [1841]~E(x18411,x18412)+E(f752(x18413,x18414,x18411),f752(x18413,x18414,x18412)) % 188.18/188.27 [1842]~E(x18421,x18422)+E(f715(x18421,x18423),f715(x18422,x18423)) % 188.18/188.27 [1843]~E(x18431,x18432)+E(f715(x18433,x18431),f715(x18433,x18432)) % 188.18/188.27 [1844]~E(x18441,x18442)+E(f891(x18441,x18443,x18444,x18445,x18446,x18447),f891(x18442,x18443,x18444,x18445,x18446,x18447)) % 188.18/188.27 [1845]~E(x18451,x18452)+E(f891(x18453,x18451,x18454,x18455,x18456,x18457),f891(x18453,x18452,x18454,x18455,x18456,x18457)) % 188.18/188.27 [1846]~E(x18461,x18462)+E(f891(x18463,x18464,x18461,x18465,x18466,x18467),f891(x18463,x18464,x18462,x18465,x18466,x18467)) % 188.18/188.27 [1847]~E(x18471,x18472)+E(f891(x18473,x18474,x18475,x18471,x18476,x18477),f891(x18473,x18474,x18475,x18472,x18476,x18477)) % 188.18/188.27 [1848]~E(x18481,x18482)+E(f891(x18483,x18484,x18485,x18486,x18481,x18487),f891(x18483,x18484,x18485,x18486,x18482,x18487)) % 188.18/188.27 [1849]~E(x18491,x18492)+E(f891(x18493,x18494,x18495,x18496,x18497,x18491),f891(x18493,x18494,x18495,x18496,x18497,x18492)) % 188.18/188.27 [1850]~E(x18501,x18502)+E(f356(x18501,x18503),f356(x18502,x18503)) % 188.18/188.27 [1851]~E(x18511,x18512)+E(f356(x18513,x18511),f356(x18513,x18512)) % 188.18/188.27 [1852]~E(x18521,x18522)+E(f771(x18521,x18523,x18524),f771(x18522,x18523,x18524)) % 188.18/188.27 [1853]~E(x18531,x18532)+E(f771(x18533,x18531,x18534),f771(x18533,x18532,x18534)) % 188.18/188.27 [1854]~E(x18541,x18542)+E(f771(x18543,x18544,x18541),f771(x18543,x18544,x18542)) % 188.18/188.27 [1855]~E(x18551,x18552)+E(f917(x18551,x18553,x18554),f917(x18552,x18553,x18554)) % 188.18/188.27 [1856]~E(x18561,x18562)+E(f917(x18563,x18561,x18564),f917(x18563,x18562,x18564)) % 188.18/188.27 [1857]~E(x18571,x18572)+E(f917(x18573,x18574,x18571),f917(x18573,x18574,x18572)) % 188.18/188.27 [1858]~E(x18581,x18582)+E(f545(x18581,x18583,x18584,x18585),f545(x18582,x18583,x18584,x18585)) % 188.18/188.27 [1859]~E(x18591,x18592)+E(f545(x18593,x18591,x18594,x18595),f545(x18593,x18592,x18594,x18595)) % 188.18/188.27 [1860]~E(x18601,x18602)+E(f545(x18603,x18604,x18601,x18605),f545(x18603,x18604,x18602,x18605)) % 188.18/188.27 [1861]~E(x18611,x18612)+E(f545(x18613,x18614,x18615,x18611),f545(x18613,x18614,x18615,x18612)) % 188.18/188.27 [1862]~E(x18621,x18622)+E(f860(x18621,x18623,x18624,x18625,x18626,x18627,x18628,x18629),f860(x18622,x18623,x18624,x18625,x18626,x18627,x18628,x18629)) % 188.18/188.27 [1863]~E(x18631,x18632)+E(f860(x18633,x18631,x18634,x18635,x18636,x18637,x18638,x18639),f860(x18633,x18632,x18634,x18635,x18636,x18637,x18638,x18639)) % 188.18/188.27 [1864]~E(x18641,x18642)+E(f860(x18643,x18644,x18641,x18645,x18646,x18647,x18648,x18649),f860(x18643,x18644,x18642,x18645,x18646,x18647,x18648,x18649)) % 188.18/188.27 [1865]~E(x18651,x18652)+E(f860(x18653,x18654,x18655,x18651,x18656,x18657,x18658,x18659),f860(x18653,x18654,x18655,x18652,x18656,x18657,x18658,x18659)) % 188.18/188.27 [1866]~E(x18661,x18662)+E(f860(x18663,x18664,x18665,x18666,x18661,x18667,x18668,x18669),f860(x18663,x18664,x18665,x18666,x18662,x18667,x18668,x18669)) % 188.18/188.27 [1867]~E(x18671,x18672)+E(f860(x18673,x18674,x18675,x18676,x18677,x18671,x18678,x18679),f860(x18673,x18674,x18675,x18676,x18677,x18672,x18678,x18679)) % 188.18/188.27 [1868]~E(x18681,x18682)+E(f860(x18683,x18684,x18685,x18686,x18687,x18688,x18681,x18689),f860(x18683,x18684,x18685,x18686,x18687,x18688,x18682,x18689)) % 188.18/188.27 [1869]~E(x18691,x18692)+E(f860(x18693,x18694,x18695,x18696,x18697,x18698,x18699,x18691),f860(x18693,x18694,x18695,x18696,x18697,x18698,x18699,x18692)) % 188.18/188.27 [1870]~E(x18701,x18702)+E(f897(x18701),f897(x18702)) % 188.18/188.27 [1871]~E(x18711,x18712)+E(f304(x18711,x18713,x18714),f304(x18712,x18713,x18714)) % 188.18/188.27 [1872]~E(x18721,x18722)+E(f304(x18723,x18721,x18724),f304(x18723,x18722,x18724)) % 188.18/188.27 [1873]~E(x18731,x18732)+E(f304(x18733,x18734,x18731),f304(x18733,x18734,x18732)) % 188.18/188.27 [1874]~E(x18741,x18742)+E(f432(x18741,x18743,x18744,x18745),f432(x18742,x18743,x18744,x18745)) % 188.18/188.27 [1875]~E(x18751,x18752)+E(f432(x18753,x18751,x18754,x18755),f432(x18753,x18752,x18754,x18755)) % 188.18/188.27 [1876]~E(x18761,x18762)+E(f432(x18763,x18764,x18761,x18765),f432(x18763,x18764,x18762,x18765)) % 188.18/188.27 [1877]~E(x18771,x18772)+E(f432(x18773,x18774,x18775,x18771),f432(x18773,x18774,x18775,x18772)) % 188.18/188.27 [1878]~E(x18781,x18782)+E(f377(x18781,x18783,x18784,x18785),f377(x18782,x18783,x18784,x18785)) % 188.18/188.27 [1879]~E(x18791,x18792)+E(f377(x18793,x18791,x18794,x18795),f377(x18793,x18792,x18794,x18795)) % 188.18/188.27 [1880]~E(x18801,x18802)+E(f377(x18803,x18804,x18801,x18805),f377(x18803,x18804,x18802,x18805)) % 188.18/188.27 [1881]~E(x18811,x18812)+E(f377(x18813,x18814,x18815,x18811),f377(x18813,x18814,x18815,x18812)) % 188.18/188.27 [1882]~E(x18821,x18822)+E(f829(x18821,x18823,x18824,x18825,x18826,x18827),f829(x18822,x18823,x18824,x18825,x18826,x18827)) % 188.18/188.27 [1883]~E(x18831,x18832)+E(f829(x18833,x18831,x18834,x18835,x18836,x18837),f829(x18833,x18832,x18834,x18835,x18836,x18837)) % 188.18/188.27 [1884]~E(x18841,x18842)+E(f829(x18843,x18844,x18841,x18845,x18846,x18847),f829(x18843,x18844,x18842,x18845,x18846,x18847)) % 188.18/188.27 [1885]~E(x18851,x18852)+E(f829(x18853,x18854,x18855,x18851,x18856,x18857),f829(x18853,x18854,x18855,x18852,x18856,x18857)) % 188.18/188.27 [1886]~E(x18861,x18862)+E(f829(x18863,x18864,x18865,x18866,x18861,x18867),f829(x18863,x18864,x18865,x18866,x18862,x18867)) % 188.18/188.27 [1887]~E(x18871,x18872)+E(f829(x18873,x18874,x18875,x18876,x18877,x18871),f829(x18873,x18874,x18875,x18876,x18877,x18872)) % 188.18/188.27 [1888]~E(x18881,x18882)+E(f157(x18881,x18883,x18884,x18885),f157(x18882,x18883,x18884,x18885)) % 188.18/188.27 [1889]~E(x18891,x18892)+E(f157(x18893,x18891,x18894,x18895),f157(x18893,x18892,x18894,x18895)) % 188.18/188.27 [1890]~E(x18901,x18902)+E(f157(x18903,x18904,x18901,x18905),f157(x18903,x18904,x18902,x18905)) % 188.18/188.27 [1891]~E(x18911,x18912)+E(f157(x18913,x18914,x18915,x18911),f157(x18913,x18914,x18915,x18912)) % 188.18/188.27 [1892]~E(x18921,x18922)+E(f597(x18921,x18923,x18924),f597(x18922,x18923,x18924)) % 188.18/188.27 [1893]~E(x18931,x18932)+E(f597(x18933,x18931,x18934),f597(x18933,x18932,x18934)) % 188.18/188.27 [1894]~E(x18941,x18942)+E(f597(x18943,x18944,x18941),f597(x18943,x18944,x18942)) % 188.18/188.27 [1895]~E(x18951,x18952)+E(f503(x18951,x18953,x18954,x18955,x18956),f503(x18952,x18953,x18954,x18955,x18956)) % 188.18/188.27 [1896]~E(x18961,x18962)+E(f503(x18963,x18961,x18964,x18965,x18966),f503(x18963,x18962,x18964,x18965,x18966)) % 188.18/188.27 [1897]~E(x18971,x18972)+E(f503(x18973,x18974,x18971,x18975,x18976),f503(x18973,x18974,x18972,x18975,x18976)) % 188.18/188.27 [1898]~E(x18981,x18982)+E(f503(x18983,x18984,x18985,x18981,x18986),f503(x18983,x18984,x18985,x18982,x18986)) % 188.18/188.27 [1899]~E(x18991,x18992)+E(f503(x18993,x18994,x18995,x18996,x18991),f503(x18993,x18994,x18995,x18996,x18992)) % 188.18/188.27 [1900]~E(x19001,x19002)+E(f555(x19001,x19003,x19004,x19005),f555(x19002,x19003,x19004,x19005)) % 188.18/188.27 [1901]~E(x19011,x19012)+E(f555(x19013,x19011,x19014,x19015),f555(x19013,x19012,x19014,x19015)) % 188.18/188.27 [1902]~E(x19021,x19022)+E(f555(x19023,x19024,x19021,x19025),f555(x19023,x19024,x19022,x19025)) % 188.18/188.27 [1903]~E(x19031,x19032)+E(f555(x19033,x19034,x19035,x19031),f555(x19033,x19034,x19035,x19032)) % 188.18/188.27 [1904]~E(x19041,x19042)+E(f347(x19041,x19043),f347(x19042,x19043)) % 188.18/188.27 [1905]~E(x19051,x19052)+E(f347(x19053,x19051),f347(x19053,x19052)) % 188.18/188.27 [1906]~E(x19061,x19062)+E(f595(x19061,x19063,x19064,x19065,x19066),f595(x19062,x19063,x19064,x19065,x19066)) % 188.18/188.27 [1907]~E(x19071,x19072)+E(f595(x19073,x19071,x19074,x19075,x19076),f595(x19073,x19072,x19074,x19075,x19076)) % 188.18/188.27 [1908]~E(x19081,x19082)+E(f595(x19083,x19084,x19081,x19085,x19086),f595(x19083,x19084,x19082,x19085,x19086)) % 188.18/188.27 [1909]~E(x19091,x19092)+E(f595(x19093,x19094,x19095,x19091,x19096),f595(x19093,x19094,x19095,x19092,x19096)) % 188.18/188.27 [1910]~E(x19101,x19102)+E(f595(x19103,x19104,x19105,x19106,x19101),f595(x19103,x19104,x19105,x19106,x19102)) % 188.18/188.27 [1911]~E(x19111,x19112)+E(f854(x19111,x19113,x19114,x19115,x19116,x19117,x19118,x19119),f854(x19112,x19113,x19114,x19115,x19116,x19117,x19118,x19119)) % 188.18/188.27 [1912]~E(x19121,x19122)+E(f854(x19123,x19121,x19124,x19125,x19126,x19127,x19128,x19129),f854(x19123,x19122,x19124,x19125,x19126,x19127,x19128,x19129)) % 188.18/188.27 [1913]~E(x19131,x19132)+E(f854(x19133,x19134,x19131,x19135,x19136,x19137,x19138,x19139),f854(x19133,x19134,x19132,x19135,x19136,x19137,x19138,x19139)) % 188.18/188.27 [1914]~E(x19141,x19142)+E(f854(x19143,x19144,x19145,x19141,x19146,x19147,x19148,x19149),f854(x19143,x19144,x19145,x19142,x19146,x19147,x19148,x19149)) % 188.18/188.27 [1915]~E(x19151,x19152)+E(f854(x19153,x19154,x19155,x19156,x19151,x19157,x19158,x19159),f854(x19153,x19154,x19155,x19156,x19152,x19157,x19158,x19159)) % 188.18/188.27 [1916]~E(x19161,x19162)+E(f854(x19163,x19164,x19165,x19166,x19167,x19161,x19168,x19169),f854(x19163,x19164,x19165,x19166,x19167,x19162,x19168,x19169)) % 188.18/188.27 [1917]~E(x19171,x19172)+E(f854(x19173,x19174,x19175,x19176,x19177,x19178,x19171,x19179),f854(x19173,x19174,x19175,x19176,x19177,x19178,x19172,x19179)) % 188.18/188.27 [1918]~E(x19181,x19182)+E(f854(x19183,x19184,x19185,x19186,x19187,x19188,x19189,x19181),f854(x19183,x19184,x19185,x19186,x19187,x19188,x19189,x19182)) % 188.18/188.27 [1919]~E(x19191,x19192)+E(f654(x19191,x19193,x19194,x19195),f654(x19192,x19193,x19194,x19195)) % 188.18/188.27 [1920]~E(x19201,x19202)+E(f654(x19203,x19201,x19204,x19205),f654(x19203,x19202,x19204,x19205)) % 188.18/188.27 [1921]~E(x19211,x19212)+E(f654(x19213,x19214,x19211,x19215),f654(x19213,x19214,x19212,x19215)) % 188.18/188.27 [1922]~E(x19221,x19222)+E(f654(x19223,x19224,x19225,x19221),f654(x19223,x19224,x19225,x19222)) % 188.18/188.27 [1923]~E(x19231,x19232)+E(f353(x19231,x19233),f353(x19232,x19233)) % 188.18/188.27 [1924]~E(x19241,x19242)+E(f353(x19243,x19241),f353(x19243,x19242)) % 188.18/188.27 [1925]~E(x19251,x19252)+E(f368(x19251,x19253,x19254),f368(x19252,x19253,x19254)) % 188.18/188.27 [1926]~E(x19261,x19262)+E(f368(x19263,x19261,x19264),f368(x19263,x19262,x19264)) % 188.18/188.27 [1927]~E(x19271,x19272)+E(f368(x19273,x19274,x19271),f368(x19273,x19274,x19272)) % 188.18/188.27 [1928]~E(x19281,x19282)+E(f894(x19281,x19283,x19284),f894(x19282,x19283,x19284)) % 188.18/188.27 [1929]~E(x19291,x19292)+E(f894(x19293,x19291,x19294),f894(x19293,x19292,x19294)) % 188.18/188.27 [1930]~E(x19301,x19302)+E(f894(x19303,x19304,x19301),f894(x19303,x19304,x19302)) % 188.18/188.27 [1931]~E(x19311,x19312)+E(f620(x19311,x19313),f620(x19312,x19313)) % 188.18/188.27 [1932]~E(x19321,x19322)+E(f620(x19323,x19321),f620(x19323,x19322)) % 188.18/188.27 [1933]~E(x19331,x19332)+E(f227(x19331,x19333),f227(x19332,x19333)) % 188.18/188.27 [1934]~E(x19341,x19342)+E(f227(x19343,x19341),f227(x19343,x19342)) % 188.18/188.27 [1935]~E(x19351,x19352)+E(f468(x19351,x19353,x19354,x19355,x19356),f468(x19352,x19353,x19354,x19355,x19356)) % 188.18/188.27 [1936]~E(x19361,x19362)+E(f468(x19363,x19361,x19364,x19365,x19366),f468(x19363,x19362,x19364,x19365,x19366)) % 188.18/188.27 [1937]~E(x19371,x19372)+E(f468(x19373,x19374,x19371,x19375,x19376),f468(x19373,x19374,x19372,x19375,x19376)) % 188.18/188.27 [1938]~E(x19381,x19382)+E(f468(x19383,x19384,x19385,x19381,x19386),f468(x19383,x19384,x19385,x19382,x19386)) % 188.18/188.27 [1939]~E(x19391,x19392)+E(f468(x19393,x19394,x19395,x19396,x19391),f468(x19393,x19394,x19395,x19396,x19392)) % 188.18/188.27 [1940]~E(x19401,x19402)+E(f794(x19401,x19403),f794(x19402,x19403)) % 188.18/188.27 [1941]~E(x19411,x19412)+E(f794(x19413,x19411),f794(x19413,x19412)) % 188.18/188.27 [1942]~E(x19421,x19422)+E(f370(x19421,x19423,x19424),f370(x19422,x19423,x19424)) % 188.18/188.27 [1943]~E(x19431,x19432)+E(f370(x19433,x19431,x19434),f370(x19433,x19432,x19434)) % 188.18/188.27 [1944]~E(x19441,x19442)+E(f370(x19443,x19444,x19441),f370(x19443,x19444,x19442)) % 188.18/188.27 [1945]~E(x19451,x19452)+E(f605(x19451,x19453,x19454,x19455),f605(x19452,x19453,x19454,x19455)) % 188.18/188.27 [1946]~E(x19461,x19462)+E(f605(x19463,x19461,x19464,x19465),f605(x19463,x19462,x19464,x19465)) % 188.18/188.27 [1947]~E(x19471,x19472)+E(f605(x19473,x19474,x19471,x19475),f605(x19473,x19474,x19472,x19475)) % 188.18/188.27 [1948]~E(x19481,x19482)+E(f605(x19483,x19484,x19485,x19481),f605(x19483,x19484,x19485,x19482)) % 188.18/188.27 [1949]~E(x19491,x19492)+E(f703(x19491,x19493,x19494),f703(x19492,x19493,x19494)) % 188.18/188.27 [1950]~E(x19501,x19502)+E(f703(x19503,x19501,x19504),f703(x19503,x19502,x19504)) % 188.18/188.27 [1951]~E(x19511,x19512)+E(f703(x19513,x19514,x19511),f703(x19513,x19514,x19512)) % 188.18/188.27 [1952]~E(x19521,x19522)+E(f427(x19521,x19523,x19524),f427(x19522,x19523,x19524)) % 188.18/188.27 [1953]~E(x19531,x19532)+E(f427(x19533,x19531,x19534),f427(x19533,x19532,x19534)) % 188.18/188.27 [1954]~E(x19541,x19542)+E(f427(x19543,x19544,x19541),f427(x19543,x19544,x19542)) % 188.18/188.27 [1955]~E(x19551,x19552)+E(f402(x19551,x19553,x19554,x19555,x19556),f402(x19552,x19553,x19554,x19555,x19556)) % 188.18/188.27 [1956]~E(x19561,x19562)+E(f402(x19563,x19561,x19564,x19565,x19566),f402(x19563,x19562,x19564,x19565,x19566)) % 188.18/188.27 [1957]~E(x19571,x19572)+E(f402(x19573,x19574,x19571,x19575,x19576),f402(x19573,x19574,x19572,x19575,x19576)) % 188.18/188.27 [1958]~E(x19581,x19582)+E(f402(x19583,x19584,x19585,x19581,x19586),f402(x19583,x19584,x19585,x19582,x19586)) % 188.18/188.27 [1959]~E(x19591,x19592)+E(f402(x19593,x19594,x19595,x19596,x19591),f402(x19593,x19594,x19595,x19596,x19592)) % 188.18/188.27 [1960]~E(x19601,x19602)+E(f385(x19601,x19603,x19604),f385(x19602,x19603,x19604)) % 188.18/188.27 [1961]~E(x19611,x19612)+E(f385(x19613,x19611,x19614),f385(x19613,x19612,x19614)) % 188.18/188.27 [1962]~E(x19621,x19622)+E(f385(x19623,x19624,x19621),f385(x19623,x19624,x19622)) % 188.18/188.27 [1963]~E(x19631,x19632)+E(f550(x19631,x19633,x19634),f550(x19632,x19633,x19634)) % 188.18/188.27 [1964]~E(x19641,x19642)+E(f550(x19643,x19641,x19644),f550(x19643,x19642,x19644)) % 188.18/188.27 [1965]~E(x19651,x19652)+E(f550(x19653,x19654,x19651),f550(x19653,x19654,x19652)) % 188.18/188.27 [1966]~E(x19661,x19662)+E(f910(x19661,x19663,x19664),f910(x19662,x19663,x19664)) % 188.18/188.27 [1967]~E(x19671,x19672)+E(f910(x19673,x19671,x19674),f910(x19673,x19672,x19674)) % 188.18/188.27 [1968]~E(x19681,x19682)+E(f910(x19683,x19684,x19681),f910(x19683,x19684,x19682)) % 188.18/188.27 [1969]~E(x19691,x19692)+E(f340(x19691),f340(x19692)) % 188.18/188.27 [1970]~E(x19701,x19702)+E(f782(x19701,x19703,x19704),f782(x19702,x19703,x19704)) % 188.18/188.27 [1971]~E(x19711,x19712)+E(f782(x19713,x19711,x19714),f782(x19713,x19712,x19714)) % 188.18/188.27 [1972]~E(x19721,x19722)+E(f782(x19723,x19724,x19721),f782(x19723,x19724,x19722)) % 188.18/188.27 [1973]~E(x19731,x19732)+E(f761(x19731,x19733,x19734,x19735,x19736,x19737,x19738),f761(x19732,x19733,x19734,x19735,x19736,x19737,x19738)) % 188.18/188.27 [1974]~E(x19741,x19742)+E(f761(x19743,x19741,x19744,x19745,x19746,x19747,x19748),f761(x19743,x19742,x19744,x19745,x19746,x19747,x19748)) % 188.18/188.27 [1975]~E(x19751,x19752)+E(f761(x19753,x19754,x19751,x19755,x19756,x19757,x19758),f761(x19753,x19754,x19752,x19755,x19756,x19757,x19758)) % 188.18/188.27 [1976]~E(x19761,x19762)+E(f761(x19763,x19764,x19765,x19761,x19766,x19767,x19768),f761(x19763,x19764,x19765,x19762,x19766,x19767,x19768)) % 188.18/188.27 [1977]~E(x19771,x19772)+E(f761(x19773,x19774,x19775,x19776,x19771,x19777,x19778),f761(x19773,x19774,x19775,x19776,x19772,x19777,x19778)) % 188.18/188.27 [1978]~E(x19781,x19782)+E(f761(x19783,x19784,x19785,x19786,x19787,x19781,x19788),f761(x19783,x19784,x19785,x19786,x19787,x19782,x19788)) % 188.18/188.27 [1979]~E(x19791,x19792)+E(f761(x19793,x19794,x19795,x19796,x19797,x19798,x19791),f761(x19793,x19794,x19795,x19796,x19797,x19798,x19792)) % 188.18/188.27 [1980]~E(x19801,x19802)+E(f147(x19801,x19803,x19804),f147(x19802,x19803,x19804)) % 188.18/188.27 [1981]~E(x19811,x19812)+E(f147(x19813,x19811,x19814),f147(x19813,x19812,x19814)) % 188.18/188.27 [1982]~E(x19821,x19822)+E(f147(x19823,x19824,x19821),f147(x19823,x19824,x19822)) % 188.18/188.27 [1983]~E(x19831,x19832)+E(f711(x19831,x19833,x19834,x19835),f711(x19832,x19833,x19834,x19835)) % 188.18/188.27 [1984]~E(x19841,x19842)+E(f711(x19843,x19841,x19844,x19845),f711(x19843,x19842,x19844,x19845)) % 188.18/188.27 [1985]~E(x19851,x19852)+E(f711(x19853,x19854,x19851,x19855),f711(x19853,x19854,x19852,x19855)) % 188.18/188.27 [1986]~E(x19861,x19862)+E(f711(x19863,x19864,x19865,x19861),f711(x19863,x19864,x19865,x19862)) % 188.18/188.27 [1987]~E(x19871,x19872)+E(f445(x19871,x19873,x19874,x19875),f445(x19872,x19873,x19874,x19875)) % 188.18/188.27 [1988]~E(x19881,x19882)+E(f445(x19883,x19881,x19884,x19885),f445(x19883,x19882,x19884,x19885)) % 188.18/188.27 [1989]~E(x19891,x19892)+E(f445(x19893,x19894,x19891,x19895),f445(x19893,x19894,x19892,x19895)) % 188.18/188.27 [1990]~E(x19901,x19902)+E(f445(x19903,x19904,x19905,x19901),f445(x19903,x19904,x19905,x19902)) % 188.18/188.27 [1991]~E(x19911,x19912)+E(f586(x19911,x19913,x19914,x19915),f586(x19912,x19913,x19914,x19915)) % 188.18/188.27 [1992]~E(x19921,x19922)+E(f586(x19923,x19921,x19924,x19925),f586(x19923,x19922,x19924,x19925)) % 188.18/188.27 [1993]~E(x19931,x19932)+E(f586(x19933,x19934,x19931,x19935),f586(x19933,x19934,x19932,x19935)) % 188.18/188.27 [1994]~E(x19941,x19942)+E(f586(x19943,x19944,x19945,x19941),f586(x19943,x19944,x19945,x19942)) % 188.18/188.27 [1995]~E(x19951,x19952)+E(f386(x19951,x19953,x19954),f386(x19952,x19953,x19954)) % 188.18/188.27 [1996]~E(x19961,x19962)+E(f386(x19963,x19961,x19964),f386(x19963,x19962,x19964)) % 188.18/188.27 [1997]~E(x19971,x19972)+E(f386(x19973,x19974,x19971),f386(x19973,x19974,x19972)) % 188.18/188.27 [1998]~E(x19981,x19982)+E(f472(x19981,x19983,x19984),f472(x19982,x19983,x19984)) % 188.18/188.27 [1999]~E(x19991,x19992)+E(f472(x19993,x19991,x19994),f472(x19993,x19992,x19994)) % 188.18/188.27 [2000]~E(x20001,x20002)+E(f472(x20003,x20004,x20001),f472(x20003,x20004,x20002)) % 188.18/188.27 [2001]~E(x20011,x20012)+E(f365(x20011,x20013,x20014),f365(x20012,x20013,x20014)) % 188.18/188.27 [2002]~E(x20021,x20022)+E(f365(x20023,x20021,x20024),f365(x20023,x20022,x20024)) % 188.18/188.27 [2003]~E(x20031,x20032)+E(f365(x20033,x20034,x20031),f365(x20033,x20034,x20032)) % 188.18/188.27 [2004]~E(x20041,x20042)+E(f730(x20041,x20043),f730(x20042,x20043)) % 188.18/188.27 [2005]~E(x20051,x20052)+E(f730(x20053,x20051),f730(x20053,x20052)) % 188.18/188.27 [2006]~E(x20061,x20062)+E(f509(x20061,x20063,x20064,x20065,x20066),f509(x20062,x20063,x20064,x20065,x20066)) % 188.18/188.27 [2007]~E(x20071,x20072)+E(f509(x20073,x20071,x20074,x20075,x20076),f509(x20073,x20072,x20074,x20075,x20076)) % 188.18/188.27 [2008]~E(x20081,x20082)+E(f509(x20083,x20084,x20081,x20085,x20086),f509(x20083,x20084,x20082,x20085,x20086)) % 188.18/188.27 [2009]~E(x20091,x20092)+E(f509(x20093,x20094,x20095,x20091,x20096),f509(x20093,x20094,x20095,x20092,x20096)) % 188.18/188.27 [2010]~E(x20101,x20102)+E(f509(x20103,x20104,x20105,x20106,x20101),f509(x20103,x20104,x20105,x20106,x20102)) % 188.18/188.27 [2011]~E(x20111,x20112)+E(f471(x20111,x20113,x20114,x20115,x20116,x20117),f471(x20112,x20113,x20114,x20115,x20116,x20117)) % 188.18/188.27 [2012]~E(x20121,x20122)+E(f471(x20123,x20121,x20124,x20125,x20126,x20127),f471(x20123,x20122,x20124,x20125,x20126,x20127)) % 188.18/188.27 [2013]~E(x20131,x20132)+E(f471(x20133,x20134,x20131,x20135,x20136,x20137),f471(x20133,x20134,x20132,x20135,x20136,x20137)) % 188.18/188.27 [2014]~E(x20141,x20142)+E(f471(x20143,x20144,x20145,x20141,x20146,x20147),f471(x20143,x20144,x20145,x20142,x20146,x20147)) % 188.18/188.27 [2015]~E(x20151,x20152)+E(f471(x20153,x20154,x20155,x20156,x20151,x20157),f471(x20153,x20154,x20155,x20156,x20152,x20157)) % 188.18/188.27 [2016]~E(x20161,x20162)+E(f471(x20163,x20164,x20165,x20166,x20167,x20161),f471(x20163,x20164,x20165,x20166,x20167,x20162)) % 188.18/188.27 [2017]~E(x20171,x20172)+E(f914(x20171,x20173,x20174),f914(x20172,x20173,x20174)) % 188.18/188.27 [2018]~E(x20181,x20182)+E(f914(x20183,x20181,x20184),f914(x20183,x20182,x20184)) % 188.18/188.27 [2019]~E(x20191,x20192)+E(f914(x20193,x20194,x20191),f914(x20193,x20194,x20192)) % 188.18/188.27 [2020]~E(x20201,x20202)+E(f210(x20201),f210(x20202)) % 188.18/188.27 [2021]~E(x20211,x20212)+E(f737(x20211,x20213,x20214,x20215),f737(x20212,x20213,x20214,x20215)) % 188.18/188.27 [2022]~E(x20221,x20222)+E(f737(x20223,x20221,x20224,x20225),f737(x20223,x20222,x20224,x20225)) % 188.18/188.27 [2023]~E(x20231,x20232)+E(f737(x20233,x20234,x20231,x20235),f737(x20233,x20234,x20232,x20235)) % 188.18/188.27 [2024]~E(x20241,x20242)+E(f737(x20243,x20244,x20245,x20241),f737(x20243,x20244,x20245,x20242)) % 188.18/188.27 [2025]~E(x20251,x20252)+E(f392(x20251,x20253,x20254),f392(x20252,x20253,x20254)) % 188.18/188.27 [2026]~E(x20261,x20262)+E(f392(x20263,x20261,x20264),f392(x20263,x20262,x20264)) % 188.18/188.27 [2027]~E(x20271,x20272)+E(f392(x20273,x20274,x20271),f392(x20273,x20274,x20272)) % 188.18/188.27 [2028]~E(x20281,x20282)+E(f616(x20281,x20283,x20284,x20285,x20286),f616(x20282,x20283,x20284,x20285,x20286)) % 188.18/188.27 [2029]~E(x20291,x20292)+E(f616(x20293,x20291,x20294,x20295,x20296),f616(x20293,x20292,x20294,x20295,x20296)) % 188.18/188.27 [2030]~E(x20301,x20302)+E(f616(x20303,x20304,x20301,x20305,x20306),f616(x20303,x20304,x20302,x20305,x20306)) % 188.18/188.27 [2031]~E(x20311,x20312)+E(f616(x20313,x20314,x20315,x20311,x20316),f616(x20313,x20314,x20315,x20312,x20316)) % 188.18/188.27 [2032]~E(x20321,x20322)+E(f616(x20323,x20324,x20325,x20326,x20321),f616(x20323,x20324,x20325,x20326,x20322)) % 188.18/188.27 [2033]~E(x20331,x20332)+E(f211(x20331,x20333),f211(x20332,x20333)) % 188.18/188.27 [2034]~E(x20341,x20342)+E(f211(x20343,x20341),f211(x20343,x20342)) % 188.18/188.27 [2035]~E(x20351,x20352)+E(f846(x20351,x20353,x20354),f846(x20352,x20353,x20354)) % 188.18/188.27 [2036]~E(x20361,x20362)+E(f846(x20363,x20361,x20364),f846(x20363,x20362,x20364)) % 188.18/188.27 [2037]~E(x20371,x20372)+E(f846(x20373,x20374,x20371),f846(x20373,x20374,x20372)) % 188.18/188.27 [2038]~E(x20381,x20382)+E(f538(x20381,x20383,x20384),f538(x20382,x20383,x20384)) % 188.18/188.27 [2039]~E(x20391,x20392)+E(f538(x20393,x20391,x20394),f538(x20393,x20392,x20394)) % 188.18/188.27 [2040]~E(x20401,x20402)+E(f538(x20403,x20404,x20401),f538(x20403,x20404,x20402)) % 188.18/188.27 [2041]~E(x20411,x20412)+E(f852(x20411,x20413,x20414,x20415,x20416,x20417,x20418),f852(x20412,x20413,x20414,x20415,x20416,x20417,x20418)) % 188.18/188.27 [2042]~E(x20421,x20422)+E(f852(x20423,x20421,x20424,x20425,x20426,x20427,x20428),f852(x20423,x20422,x20424,x20425,x20426,x20427,x20428)) % 188.18/188.27 [2043]~E(x20431,x20432)+E(f852(x20433,x20434,x20431,x20435,x20436,x20437,x20438),f852(x20433,x20434,x20432,x20435,x20436,x20437,x20438)) % 188.18/188.27 [2044]~E(x20441,x20442)+E(f852(x20443,x20444,x20445,x20441,x20446,x20447,x20448),f852(x20443,x20444,x20445,x20442,x20446,x20447,x20448)) % 188.18/188.27 [2045]~E(x20451,x20452)+E(f852(x20453,x20454,x20455,x20456,x20451,x20457,x20458),f852(x20453,x20454,x20455,x20456,x20452,x20457,x20458)) % 188.18/188.27 [2046]~E(x20461,x20462)+E(f852(x20463,x20464,x20465,x20466,x20467,x20461,x20468),f852(x20463,x20464,x20465,x20466,x20467,x20462,x20468)) % 188.18/188.27 [2047]~E(x20471,x20472)+E(f852(x20473,x20474,x20475,x20476,x20477,x20478,x20471),f852(x20473,x20474,x20475,x20476,x20477,x20478,x20472)) % 188.18/188.27 [2048]~E(x20481,x20482)+E(f303(x20481,x20483,x20484,x20485,x20486),f303(x20482,x20483,x20484,x20485,x20486)) % 188.18/188.27 [2049]~E(x20491,x20492)+E(f303(x20493,x20491,x20494,x20495,x20496),f303(x20493,x20492,x20494,x20495,x20496)) % 188.18/188.27 [2050]~E(x20501,x20502)+E(f303(x20503,x20504,x20501,x20505,x20506),f303(x20503,x20504,x20502,x20505,x20506)) % 188.18/188.27 [2051]~E(x20511,x20512)+E(f303(x20513,x20514,x20515,x20511,x20516),f303(x20513,x20514,x20515,x20512,x20516)) % 188.18/188.27 [2052]~E(x20521,x20522)+E(f303(x20523,x20524,x20525,x20526,x20521),f303(x20523,x20524,x20525,x20526,x20522)) % 188.18/188.27 [2053]~E(x20531,x20532)+E(f918(x20531,x20533,x20534),f918(x20532,x20533,x20534)) % 188.18/188.27 [2054]~E(x20541,x20542)+E(f918(x20543,x20541,x20544),f918(x20543,x20542,x20544)) % 188.18/188.27 [2055]~E(x20551,x20552)+E(f918(x20553,x20554,x20551),f918(x20553,x20554,x20552)) % 188.18/188.27 [2056]~E(x20561,x20562)+E(f344(x20561,x20563,x20564),f344(x20562,x20563,x20564)) % 188.18/188.27 [2057]~E(x20571,x20572)+E(f344(x20573,x20571,x20574),f344(x20573,x20572,x20574)) % 188.18/188.27 [2058]~E(x20581,x20582)+E(f344(x20583,x20584,x20581),f344(x20583,x20584,x20582)) % 188.18/188.27 [2059]~E(x20591,x20592)+E(f214(x20591,x20593,x20594,x20595),f214(x20592,x20593,x20594,x20595)) % 188.18/188.27 [2060]~E(x20601,x20602)+E(f214(x20603,x20601,x20604,x20605),f214(x20603,x20602,x20604,x20605)) % 188.18/188.27 [2061]~E(x20611,x20612)+E(f214(x20613,x20614,x20611,x20615),f214(x20613,x20614,x20612,x20615)) % 188.18/188.27 [2062]~E(x20621,x20622)+E(f214(x20623,x20624,x20625,x20621),f214(x20623,x20624,x20625,x20622)) % 188.18/188.27 [2063]~E(x20631,x20632)+E(f843(x20631,x20633,x20634,x20635),f843(x20632,x20633,x20634,x20635)) % 188.18/188.27 [2064]~E(x20641,x20642)+E(f843(x20643,x20641,x20644,x20645),f843(x20643,x20642,x20644,x20645)) % 188.18/188.27 [2065]~E(x20651,x20652)+E(f843(x20653,x20654,x20651,x20655),f843(x20653,x20654,x20652,x20655)) % 188.18/188.27 [2066]~E(x20661,x20662)+E(f843(x20663,x20664,x20665,x20661),f843(x20663,x20664,x20665,x20662)) % 188.18/188.27 [2067]~E(x20671,x20672)+E(f515(x20671,x20673,x20674),f515(x20672,x20673,x20674)) % 188.18/188.27 [2068]~E(x20681,x20682)+E(f515(x20683,x20681,x20684),f515(x20683,x20682,x20684)) % 188.18/188.27 [2069]~E(x20691,x20692)+E(f515(x20693,x20694,x20691),f515(x20693,x20694,x20692)) % 188.18/188.27 [2070]~E(x20701,x20702)+E(f611(x20701,x20703,x20704),f611(x20702,x20703,x20704)) % 188.18/188.27 [2071]~E(x20711,x20712)+E(f611(x20713,x20711,x20714),f611(x20713,x20712,x20714)) % 188.18/188.27 [2072]~E(x20721,x20722)+E(f611(x20723,x20724,x20721),f611(x20723,x20724,x20722)) % 188.18/188.27 [2073]~E(x20731,x20732)+E(f417(x20731,x20733,x20734,x20735),f417(x20732,x20733,x20734,x20735)) % 188.18/188.27 [2074]~E(x20741,x20742)+E(f417(x20743,x20741,x20744,x20745),f417(x20743,x20742,x20744,x20745)) % 188.18/188.27 [2075]~E(x20751,x20752)+E(f417(x20753,x20754,x20751,x20755),f417(x20753,x20754,x20752,x20755)) % 188.18/188.27 [2076]~E(x20761,x20762)+E(f417(x20763,x20764,x20765,x20761),f417(x20763,x20764,x20765,x20762)) % 188.18/188.27 [2077]~E(x20771,x20772)+E(f491(x20771),f491(x20772)) % 188.18/188.27 [2078]~E(x20781,x20782)+E(f601(x20781,x20783),f601(x20782,x20783)) % 188.18/188.27 [2079]~E(x20791,x20792)+E(f601(x20793,x20791),f601(x20793,x20792)) % 188.18/188.27 [2080]~E(x20801,x20802)+E(f697(x20801,x20803,x20804,x20805,x20806),f697(x20802,x20803,x20804,x20805,x20806)) % 188.18/188.27 [2081]~E(x20811,x20812)+E(f697(x20813,x20811,x20814,x20815,x20816),f697(x20813,x20812,x20814,x20815,x20816)) % 188.18/188.27 [2082]~E(x20821,x20822)+E(f697(x20823,x20824,x20821,x20825,x20826),f697(x20823,x20824,x20822,x20825,x20826)) % 188.18/188.27 [2083]~E(x20831,x20832)+E(f697(x20833,x20834,x20835,x20831,x20836),f697(x20833,x20834,x20835,x20832,x20836)) % 188.18/188.27 [2084]~E(x20841,x20842)+E(f697(x20843,x20844,x20845,x20846,x20841),f697(x20843,x20844,x20845,x20846,x20842)) % 188.18/188.27 [2085]~E(x20851,x20852)+E(f567(x20851,x20853,x20854),f567(x20852,x20853,x20854)) % 188.18/188.27 [2086]~E(x20861,x20862)+E(f567(x20863,x20861,x20864),f567(x20863,x20862,x20864)) % 188.18/188.27 [2087]~E(x20871,x20872)+E(f567(x20873,x20874,x20871),f567(x20873,x20874,x20872)) % 188.18/188.27 [2088]~E(x20881,x20882)+E(f768(x20881,x20883,x20884),f768(x20882,x20883,x20884)) % 188.18/188.27 [2089]~E(x20891,x20892)+E(f768(x20893,x20891,x20894),f768(x20893,x20892,x20894)) % 188.18/188.27 [2090]~E(x20901,x20902)+E(f768(x20903,x20904,x20901),f768(x20903,x20904,x20902)) % 188.18/188.27 [2091]~E(x20911,x20912)+E(f824(x20911),f824(x20912)) % 188.18/188.27 [2092]~E(x20921,x20922)+E(f435(x20921,x20923,x20924,x20925),f435(x20922,x20923,x20924,x20925)) % 188.18/188.27 [2093]~E(x20931,x20932)+E(f435(x20933,x20931,x20934,x20935),f435(x20933,x20932,x20934,x20935)) % 188.18/188.27 [2094]~E(x20941,x20942)+E(f435(x20943,x20944,x20941,x20945),f435(x20943,x20944,x20942,x20945)) % 188.18/188.27 [2095]~E(x20951,x20952)+E(f435(x20953,x20954,x20955,x20951),f435(x20953,x20954,x20955,x20952)) % 188.18/188.27 [2096]~E(x20961,x20962)+E(f879(x20961,x20963),f879(x20962,x20963)) % 188.18/188.27 [2097]~E(x20971,x20972)+E(f879(x20973,x20971),f879(x20973,x20972)) % 188.18/188.27 [2098]~E(x20981,x20982)+E(f619(x20981,x20983,x20984,x20985,x20986,x20987,x20988,x20989),f619(x20982,x20983,x20984,x20985,x20986,x20987,x20988,x20989)) % 188.18/188.27 [2099]~E(x20991,x20992)+E(f619(x20993,x20991,x20994,x20995,x20996,x20997,x20998,x20999),f619(x20993,x20992,x20994,x20995,x20996,x20997,x20998,x20999)) % 188.18/188.27 [2100]~E(x21001,x21002)+E(f619(x21003,x21004,x21001,x21005,x21006,x21007,x21008,x21009),f619(x21003,x21004,x21002,x21005,x21006,x21007,x21008,x21009)) % 188.18/188.27 [2101]~E(x21011,x21012)+E(f619(x21013,x21014,x21015,x21011,x21016,x21017,x21018,x21019),f619(x21013,x21014,x21015,x21012,x21016,x21017,x21018,x21019)) % 188.18/188.27 [2102]~E(x21021,x21022)+E(f619(x21023,x21024,x21025,x21026,x21021,x21027,x21028,x21029),f619(x21023,x21024,x21025,x21026,x21022,x21027,x21028,x21029)) % 188.18/188.27 [2103]~E(x21031,x21032)+E(f619(x21033,x21034,x21035,x21036,x21037,x21031,x21038,x21039),f619(x21033,x21034,x21035,x21036,x21037,x21032,x21038,x21039)) % 188.18/188.27 [2104]~E(x21041,x21042)+E(f619(x21043,x21044,x21045,x21046,x21047,x21048,x21041,x21049),f619(x21043,x21044,x21045,x21046,x21047,x21048,x21042,x21049)) % 188.18/188.27 [2105]~E(x21051,x21052)+E(f619(x21053,x21054,x21055,x21056,x21057,x21058,x21059,x21051),f619(x21053,x21054,x21055,x21056,x21057,x21058,x21059,x21052)) % 188.18/188.27 [2106]~E(x21061,x21062)+E(f486(x21061,x21063,x21064,x21065,x21066),f486(x21062,x21063,x21064,x21065,x21066)) % 188.18/188.27 [2107]~E(x21071,x21072)+E(f486(x21073,x21071,x21074,x21075,x21076),f486(x21073,x21072,x21074,x21075,x21076)) % 188.18/188.27 [2108]~E(x21081,x21082)+E(f486(x21083,x21084,x21081,x21085,x21086),f486(x21083,x21084,x21082,x21085,x21086)) % 188.18/188.27 [2109]~E(x21091,x21092)+E(f486(x21093,x21094,x21095,x21091,x21096),f486(x21093,x21094,x21095,x21092,x21096)) % 188.18/188.27 [2110]~E(x21101,x21102)+E(f486(x21103,x21104,x21105,x21106,x21101),f486(x21103,x21104,x21105,x21106,x21102)) % 188.18/188.27 [2111]~E(x21111,x21112)+E(f810(x21111,x21113,x21114),f810(x21112,x21113,x21114)) % 188.18/188.27 [2112]~E(x21121,x21122)+E(f810(x21123,x21121,x21124),f810(x21123,x21122,x21124)) % 188.18/188.27 [2113]~E(x21131,x21132)+E(f810(x21133,x21134,x21131),f810(x21133,x21134,x21132)) % 188.18/188.27 [2114]~E(x21141,x21142)+E(f602(x21141,x21143,x21144,x21145,x21146,x21147),f602(x21142,x21143,x21144,x21145,x21146,x21147)) % 188.18/188.27 [2115]~E(x21151,x21152)+E(f602(x21153,x21151,x21154,x21155,x21156,x21157),f602(x21153,x21152,x21154,x21155,x21156,x21157)) % 188.18/188.27 [2116]~E(x21161,x21162)+E(f602(x21163,x21164,x21161,x21165,x21166,x21167),f602(x21163,x21164,x21162,x21165,x21166,x21167)) % 188.18/188.27 [2117]~E(x21171,x21172)+E(f602(x21173,x21174,x21175,x21171,x21176,x21177),f602(x21173,x21174,x21175,x21172,x21176,x21177)) % 188.18/188.27 [2118]~E(x21181,x21182)+E(f602(x21183,x21184,x21185,x21186,x21181,x21187),f602(x21183,x21184,x21185,x21186,x21182,x21187)) % 188.18/188.27 [2119]~E(x21191,x21192)+E(f602(x21193,x21194,x21195,x21196,x21197,x21191),f602(x21193,x21194,x21195,x21196,x21197,x21192)) % 188.18/188.27 [2120]~E(x21201,x21202)+E(f125(x21201,x21203,x21204),f125(x21202,x21203,x21204)) % 188.18/188.27 [2121]~E(x21211,x21212)+E(f125(x21213,x21211,x21214),f125(x21213,x21212,x21214)) % 188.18/188.27 [2122]~E(x21221,x21222)+E(f125(x21223,x21224,x21221),f125(x21223,x21224,x21222)) % 188.18/188.27 [2123]~E(x21231,x21232)+E(f282(x21231,x21233,x21234),f282(x21232,x21233,x21234)) % 188.18/188.27 [2124]~E(x21241,x21242)+E(f282(x21243,x21241,x21244),f282(x21243,x21242,x21244)) % 188.18/188.27 [2125]~E(x21251,x21252)+E(f282(x21253,x21254,x21251),f282(x21253,x21254,x21252)) % 188.18/188.27 [2126]~E(x21261,x21262)+E(f904(x21261,x21263),f904(x21262,x21263)) % 188.18/188.27 [2127]~E(x21271,x21272)+E(f904(x21273,x21271),f904(x21273,x21272)) % 188.18/188.27 [2128]~E(x21281,x21282)+E(f449(x21281,x21283,x21284,x21285),f449(x21282,x21283,x21284,x21285)) % 188.18/188.27 [2129]~E(x21291,x21292)+E(f449(x21293,x21291,x21294,x21295),f449(x21293,x21292,x21294,x21295)) % 188.18/188.27 [2130]~E(x21301,x21302)+E(f449(x21303,x21304,x21301,x21305),f449(x21303,x21304,x21302,x21305)) % 188.18/188.27 [2131]~E(x21311,x21312)+E(f449(x21313,x21314,x21315,x21311),f449(x21313,x21314,x21315,x21312)) % 188.18/188.27 [2132]~E(x21321,x21322)+E(f401(x21321,x21323,x21324,x21325,x21326),f401(x21322,x21323,x21324,x21325,x21326)) % 188.18/188.27 [2133]~E(x21331,x21332)+E(f401(x21333,x21331,x21334,x21335,x21336),f401(x21333,x21332,x21334,x21335,x21336)) % 188.18/188.27 [2134]~E(x21341,x21342)+E(f401(x21343,x21344,x21341,x21345,x21346),f401(x21343,x21344,x21342,x21345,x21346)) % 188.18/188.27 [2135]~E(x21351,x21352)+E(f401(x21353,x21354,x21355,x21351,x21356),f401(x21353,x21354,x21355,x21352,x21356)) % 188.18/188.27 [2136]~E(x21361,x21362)+E(f401(x21363,x21364,x21365,x21366,x21361),f401(x21363,x21364,x21365,x21366,x21362)) % 188.18/188.27 [2137]~E(x21371,x21372)+E(f423(x21371,x21373),f423(x21372,x21373)) % 188.18/188.27 [2138]~E(x21381,x21382)+E(f423(x21383,x21381),f423(x21383,x21382)) % 188.18/188.27 [2139]~E(x21391,x21392)+E(f598(x21391,x21393,x21394),f598(x21392,x21393,x21394)) % 188.18/188.27 [2140]~E(x21401,x21402)+E(f598(x21403,x21401,x21404),f598(x21403,x21402,x21404)) % 188.18/188.27 [2141]~E(x21411,x21412)+E(f598(x21413,x21414,x21411),f598(x21413,x21414,x21412)) % 188.18/188.27 [2142]~E(x21421,x21422)+E(f708(x21421,x21423,x21424,x21425,x21426),f708(x21422,x21423,x21424,x21425,x21426)) % 188.18/188.27 [2143]~E(x21431,x21432)+E(f708(x21433,x21431,x21434,x21435,x21436),f708(x21433,x21432,x21434,x21435,x21436)) % 188.18/188.27 [2144]~E(x21441,x21442)+E(f708(x21443,x21444,x21441,x21445,x21446),f708(x21443,x21444,x21442,x21445,x21446)) % 188.18/188.27 [2145]~E(x21451,x21452)+E(f708(x21453,x21454,x21455,x21451,x21456),f708(x21453,x21454,x21455,x21452,x21456)) % 188.18/188.27 [2146]~E(x21461,x21462)+E(f708(x21463,x21464,x21465,x21466,x21461),f708(x21463,x21464,x21465,x21466,x21462)) % 188.18/188.27 [2147]~E(x21471,x21472)+E(f734(x21471,x21473),f734(x21472,x21473)) % 188.18/188.27 [2148]~E(x21481,x21482)+E(f734(x21483,x21481),f734(x21483,x21482)) % 188.18/188.27 [2149]~E(x21491,x21492)+E(f497(x21491,x21493,x21494,x21495),f497(x21492,x21493,x21494,x21495)) % 188.18/188.27 [2150]~E(x21501,x21502)+E(f497(x21503,x21501,x21504,x21505),f497(x21503,x21502,x21504,x21505)) % 188.18/188.27 [2151]~E(x21511,x21512)+E(f497(x21513,x21514,x21511,x21515),f497(x21513,x21514,x21512,x21515)) % 188.18/188.27 [2152]~E(x21521,x21522)+E(f497(x21523,x21524,x21525,x21521),f497(x21523,x21524,x21525,x21522)) % 188.18/188.27 [2153]~E(x21531,x21532)+E(f723(x21531,x21533),f723(x21532,x21533)) % 188.18/188.27 [2154]~E(x21541,x21542)+E(f723(x21543,x21541),f723(x21543,x21542)) % 188.18/188.27 [2155]~E(x21551,x21552)+E(f759(x21551,x21553,x21554,x21555,x21556),f759(x21552,x21553,x21554,x21555,x21556)) % 188.18/188.27 [2156]~E(x21561,x21562)+E(f759(x21563,x21561,x21564,x21565,x21566),f759(x21563,x21562,x21564,x21565,x21566)) % 188.18/188.27 [2157]~E(x21571,x21572)+E(f759(x21573,x21574,x21571,x21575,x21576),f759(x21573,x21574,x21572,x21575,x21576)) % 188.18/188.27 [2158]~E(x21581,x21582)+E(f759(x21583,x21584,x21585,x21581,x21586),f759(x21583,x21584,x21585,x21582,x21586)) % 188.18/188.27 [2159]~E(x21591,x21592)+E(f759(x21593,x21594,x21595,x21596,x21591),f759(x21593,x21594,x21595,x21596,x21592)) % 188.18/188.27 [2160]~E(x21601,x21602)+E(f859(x21601,x21603,x21604,x21605,x21606,x21607,x21608,x21609),f859(x21602,x21603,x21604,x21605,x21606,x21607,x21608,x21609)) % 188.18/188.27 [2161]~E(x21611,x21612)+E(f859(x21613,x21611,x21614,x21615,x21616,x21617,x21618,x21619),f859(x21613,x21612,x21614,x21615,x21616,x21617,x21618,x21619)) % 188.18/188.27 [2162]~E(x21621,x21622)+E(f859(x21623,x21624,x21621,x21625,x21626,x21627,x21628,x21629),f859(x21623,x21624,x21622,x21625,x21626,x21627,x21628,x21629)) % 188.18/188.27 [2163]~E(x21631,x21632)+E(f859(x21633,x21634,x21635,x21631,x21636,x21637,x21638,x21639),f859(x21633,x21634,x21635,x21632,x21636,x21637,x21638,x21639)) % 188.18/188.27 [2164]~E(x21641,x21642)+E(f859(x21643,x21644,x21645,x21646,x21641,x21647,x21648,x21649),f859(x21643,x21644,x21645,x21646,x21642,x21647,x21648,x21649)) % 188.18/188.27 [2165]~E(x21651,x21652)+E(f859(x21653,x21654,x21655,x21656,x21657,x21651,x21658,x21659),f859(x21653,x21654,x21655,x21656,x21657,x21652,x21658,x21659)) % 188.18/188.27 [2166]~E(x21661,x21662)+E(f859(x21663,x21664,x21665,x21666,x21667,x21668,x21661,x21669),f859(x21663,x21664,x21665,x21666,x21667,x21668,x21662,x21669)) % 188.18/188.27 [2167]~E(x21671,x21672)+E(f859(x21673,x21674,x21675,x21676,x21677,x21678,x21679,x21671),f859(x21673,x21674,x21675,x21676,x21677,x21678,x21679,x21672)) % 188.18/188.27 [2168]~E(x21681,x21682)+E(f888(x21681),f888(x21682)) % 188.18/188.27 [2169]~E(x21691,x21692)+E(f882(x21691,x21693,x21694,x21695,x21696,x21697),f882(x21692,x21693,x21694,x21695,x21696,x21697)) % 188.18/188.27 [2170]~E(x21701,x21702)+E(f882(x21703,x21701,x21704,x21705,x21706,x21707),f882(x21703,x21702,x21704,x21705,x21706,x21707)) % 188.18/188.27 [2171]~E(x21711,x21712)+E(f882(x21713,x21714,x21711,x21715,x21716,x21717),f882(x21713,x21714,x21712,x21715,x21716,x21717)) % 188.18/188.27 [2172]~E(x21721,x21722)+E(f882(x21723,x21724,x21725,x21721,x21726,x21727),f882(x21723,x21724,x21725,x21722,x21726,x21727)) % 188.18/188.27 [2173]~E(x21731,x21732)+E(f882(x21733,x21734,x21735,x21736,x21731,x21737),f882(x21733,x21734,x21735,x21736,x21732,x21737)) % 188.18/188.27 [2174]~E(x21741,x21742)+E(f882(x21743,x21744,x21745,x21746,x21747,x21741),f882(x21743,x21744,x21745,x21746,x21747,x21742)) % 188.18/188.27 [2175]~E(x21751,x21752)+E(f475(x21751,x21753,x21754),f475(x21752,x21753,x21754)) % 188.18/188.27 [2176]~E(x21761,x21762)+E(f475(x21763,x21761,x21764),f475(x21763,x21762,x21764)) % 188.18/188.27 [2177]~E(x21771,x21772)+E(f475(x21773,x21774,x21771),f475(x21773,x21774,x21772)) % 188.18/188.27 [2178]~E(x21781,x21782)+E(f525(x21781,x21783,x21784,x21785),f525(x21782,x21783,x21784,x21785)) % 188.18/188.27 [2179]~E(x21791,x21792)+E(f525(x21793,x21791,x21794,x21795),f525(x21793,x21792,x21794,x21795)) % 188.18/188.27 [2180]~E(x21801,x21802)+E(f525(x21803,x21804,x21801,x21805),f525(x21803,x21804,x21802,x21805)) % 188.18/188.27 [2181]~E(x21811,x21812)+E(f525(x21813,x21814,x21815,x21811),f525(x21813,x21814,x21815,x21812)) % 188.18/188.27 [2182]~E(x21821,x21822)+E(f700(x21821,x21823,x21824,x21825),f700(x21822,x21823,x21824,x21825)) % 188.18/188.27 [2183]~E(x21831,x21832)+E(f700(x21833,x21831,x21834,x21835),f700(x21833,x21832,x21834,x21835)) % 188.18/188.27 [2184]~E(x21841,x21842)+E(f700(x21843,x21844,x21841,x21845),f700(x21843,x21844,x21842,x21845)) % 188.18/188.27 [2185]~E(x21851,x21852)+E(f700(x21853,x21854,x21855,x21851),f700(x21853,x21854,x21855,x21852)) % 188.18/188.27 [2186]~E(x21861,x21862)+E(f339(x21861),f339(x21862)) % 188.18/188.27 [2187]~E(x21871,x21872)+E(f389(x21871,x21873,x21874),f389(x21872,x21873,x21874)) % 188.18/188.27 [2188]~E(x21881,x21882)+E(f389(x21883,x21881,x21884),f389(x21883,x21882,x21884)) % 188.18/188.27 [2189]~E(x21891,x21892)+E(f389(x21893,x21894,x21891),f389(x21893,x21894,x21892)) % 188.18/188.27 [2190]~E(x21901,x21902)+E(f626(x21901,x21903),f626(x21902,x21903)) % 188.18/188.27 [2191]~E(x21911,x21912)+E(f626(x21913,x21911),f626(x21913,x21912)) % 188.18/188.27 [2192]~E(x21921,x21922)+E(f275(x21921),f275(x21922)) % 188.18/188.27 [2193]~E(x21931,x21932)+E(f215(x21931,x21933,x21934,x21935),f215(x21932,x21933,x21934,x21935)) % 188.18/188.27 [2194]~E(x21941,x21942)+E(f215(x21943,x21941,x21944,x21945),f215(x21943,x21942,x21944,x21945)) % 188.18/188.27 [2195]~E(x21951,x21952)+E(f215(x21953,x21954,x21951,x21955),f215(x21953,x21954,x21952,x21955)) % 188.18/188.27 [2196]~E(x21961,x21962)+E(f215(x21963,x21964,x21965,x21961),f215(x21963,x21964,x21965,x21962)) % 188.18/188.27 [2197]~E(x21971,x21972)+E(f495(x21971,x21973,x21974,x21975),f495(x21972,x21973,x21974,x21975)) % 188.18/188.27 [2198]~E(x21981,x21982)+E(f495(x21983,x21981,x21984,x21985),f495(x21983,x21982,x21984,x21985)) % 188.18/188.27 [2199]~E(x21991,x21992)+E(f495(x21993,x21994,x21991,x21995),f495(x21993,x21994,x21992,x21995)) % 188.18/188.27 [2200]~E(x22001,x22002)+E(f495(x22003,x22004,x22005,x22001),f495(x22003,x22004,x22005,x22002)) % 188.18/188.27 [2201]~E(x22011,x22012)+E(f628(x22011,x22013),f628(x22012,x22013)) % 188.18/188.27 [2202]~E(x22021,x22022)+E(f628(x22023,x22021),f628(x22023,x22022)) % 188.18/188.27 [2203]~E(x22031,x22032)+E(f792(x22031,x22033,x22034,x22035),f792(x22032,x22033,x22034,x22035)) % 188.18/188.27 [2204]~E(x22041,x22042)+E(f792(x22043,x22041,x22044,x22045),f792(x22043,x22042,x22044,x22045)) % 188.18/188.27 [2205]~E(x22051,x22052)+E(f792(x22053,x22054,x22051,x22055),f792(x22053,x22054,x22052,x22055)) % 188.18/188.27 [2206]~E(x22061,x22062)+E(f792(x22063,x22064,x22065,x22061),f792(x22063,x22064,x22065,x22062)) % 188.18/188.27 [2207]~E(x22071,x22072)+E(f881(x22071,x22073,x22074,x22075),f881(x22072,x22073,x22074,x22075)) % 188.18/188.27 [2208]~E(x22081,x22082)+E(f881(x22083,x22081,x22084,x22085),f881(x22083,x22082,x22084,x22085)) % 188.18/188.27 [2209]~E(x22091,x22092)+E(f881(x22093,x22094,x22091,x22095),f881(x22093,x22094,x22092,x22095)) % 188.18/188.27 [2210]~E(x22101,x22102)+E(f881(x22103,x22104,x22105,x22101),f881(x22103,x22104,x22105,x22102)) % 188.18/188.27 [2211]~E(x22111,x22112)+E(f390(x22111,x22113),f390(x22112,x22113)) % 188.18/188.27 [2212]~E(x22121,x22122)+E(f390(x22123,x22121),f390(x22123,x22122)) % 188.18/188.27 [2213]~E(x22131,x22132)+E(f408(x22131,x22133,x22134,x22135,x22136),f408(x22132,x22133,x22134,x22135,x22136)) % 188.18/188.27 [2214]~E(x22141,x22142)+E(f408(x22143,x22141,x22144,x22145,x22146),f408(x22143,x22142,x22144,x22145,x22146)) % 188.18/188.27 [2215]~E(x22151,x22152)+E(f408(x22153,x22154,x22151,x22155,x22156),f408(x22153,x22154,x22152,x22155,x22156)) % 188.18/188.27 [2216]~E(x22161,x22162)+E(f408(x22163,x22164,x22165,x22161,x22166),f408(x22163,x22164,x22165,x22162,x22166)) % 188.18/188.27 [2217]~E(x22171,x22172)+E(f408(x22173,x22174,x22175,x22176,x22171),f408(x22173,x22174,x22175,x22176,x22172)) % 188.18/188.27 [2218]~E(x22181,x22182)+E(f660(x22181,x22183,x22184,x22185),f660(x22182,x22183,x22184,x22185)) % 188.18/188.27 [2219]~E(x22191,x22192)+E(f660(x22193,x22191,x22194,x22195),f660(x22193,x22192,x22194,x22195)) % 188.18/188.27 [2220]~E(x22201,x22202)+E(f660(x22203,x22204,x22201,x22205),f660(x22203,x22204,x22202,x22205)) % 188.18/188.27 [2221]~E(x22211,x22212)+E(f660(x22213,x22214,x22215,x22211),f660(x22213,x22214,x22215,x22212)) % 188.18/188.27 [2222]~E(x22221,x22222)+E(f639(x22221,x22223,x22224,x22225,x22226),f639(x22222,x22223,x22224,x22225,x22226)) % 188.18/188.27 [2223]~E(x22231,x22232)+E(f639(x22233,x22231,x22234,x22235,x22236),f639(x22233,x22232,x22234,x22235,x22236)) % 188.18/188.27 [2224]~E(x22241,x22242)+E(f639(x22243,x22244,x22241,x22245,x22246),f639(x22243,x22244,x22242,x22245,x22246)) % 188.18/188.27 [2225]~E(x22251,x22252)+E(f639(x22253,x22254,x22255,x22251,x22256),f639(x22253,x22254,x22255,x22252,x22256)) % 188.18/188.27 [2226]~E(x22261,x22262)+E(f639(x22263,x22264,x22265,x22266,x22261),f639(x22263,x22264,x22265,x22266,x22262)) % 188.18/188.27 [2227]~E(x22271,x22272)+E(f363(x22271,x22273,x22274),f363(x22272,x22273,x22274)) % 188.18/188.27 [2228]~E(x22281,x22282)+E(f363(x22283,x22281,x22284),f363(x22283,x22282,x22284)) % 188.18/188.27 [2229]~E(x22291,x22292)+E(f363(x22293,x22294,x22291),f363(x22293,x22294,x22292)) % 188.18/188.27 [2230]~E(x22301,x22302)+E(f343(x22301,x22303,x22304,x22305),f343(x22302,x22303,x22304,x22305)) % 188.18/188.27 [2231]~E(x22311,x22312)+E(f343(x22313,x22311,x22314,x22315),f343(x22313,x22312,x22314,x22315)) % 188.18/188.27 [2232]~E(x22321,x22322)+E(f343(x22323,x22324,x22321,x22325),f343(x22323,x22324,x22322,x22325)) % 188.18/188.27 [2233]~E(x22331,x22332)+E(f343(x22333,x22334,x22335,x22331),f343(x22333,x22334,x22335,x22332)) % 188.18/188.27 [2234]~E(x22341,x22342)+E(f460(x22341),f460(x22342)) % 188.18/188.27 [2235]~E(x22351,x22352)+E(f410(x22351,x22353),f410(x22352,x22353)) % 188.18/188.27 [2236]~E(x22361,x22362)+E(f410(x22363,x22361),f410(x22363,x22362)) % 188.18/188.27 [2237]~E(x22371,x22372)+E(f412(x22371,x22373),f412(x22372,x22373)) % 188.18/188.27 [2238]~E(x22381,x22382)+E(f412(x22383,x22381),f412(x22383,x22382)) % 188.18/188.27 [2239]~E(x22391,x22392)+E(f405(x22391,x22393,x22394,x22395,x22396),f405(x22392,x22393,x22394,x22395,x22396)) % 188.18/188.27 [2240]~E(x22401,x22402)+E(f405(x22403,x22401,x22404,x22405,x22406),f405(x22403,x22402,x22404,x22405,x22406)) % 188.18/188.27 [2241]~E(x22411,x22412)+E(f405(x22413,x22414,x22411,x22415,x22416),f405(x22413,x22414,x22412,x22415,x22416)) % 188.18/188.27 [2242]~E(x22421,x22422)+E(f405(x22423,x22424,x22425,x22421,x22426),f405(x22423,x22424,x22425,x22422,x22426)) % 188.18/188.27 [2243]~E(x22431,x22432)+E(f405(x22433,x22434,x22435,x22436,x22431),f405(x22433,x22434,x22435,x22436,x22432)) % 188.18/188.27 [2244]~E(x22441,x22442)+E(f137(x22441,x22443,x22444,x22445),f137(x22442,x22443,x22444,x22445)) % 188.18/188.27 [2245]~E(x22451,x22452)+E(f137(x22453,x22451,x22454,x22455),f137(x22453,x22452,x22454,x22455)) % 188.18/188.27 [2246]~E(x22461,x22462)+E(f137(x22463,x22464,x22461,x22465),f137(x22463,x22464,x22462,x22465)) % 188.18/188.27 [2247]~E(x22471,x22472)+E(f137(x22473,x22474,x22475,x22471),f137(x22473,x22474,x22475,x22472)) % 188.18/188.27 [2248]~E(x22481,x22482)+E(f820(x22481,x22483),f820(x22482,x22483)) % 188.18/188.27 [2249]~E(x22491,x22492)+E(f820(x22493,x22491),f820(x22493,x22492)) % 188.18/188.27 [2250]~E(x22501,x22502)+E(f429(x22501,x22503,x22504),f429(x22502,x22503,x22504)) % 188.18/188.27 [2251]~E(x22511,x22512)+E(f429(x22513,x22511,x22514),f429(x22513,x22512,x22514)) % 188.18/188.27 [2252]~E(x22521,x22522)+E(f429(x22523,x22524,x22521),f429(x22523,x22524,x22522)) % 188.18/188.27 [2253]~E(x22531,x22532)+E(f633(x22531,x22533,x22534,x22535,x22536),f633(x22532,x22533,x22534,x22535,x22536)) % 188.18/188.27 [2254]~E(x22541,x22542)+E(f633(x22543,x22541,x22544,x22545,x22546),f633(x22543,x22542,x22544,x22545,x22546)) % 188.18/188.27 [2255]~E(x22551,x22552)+E(f633(x22553,x22554,x22551,x22555,x22556),f633(x22553,x22554,x22552,x22555,x22556)) % 188.18/188.27 [2256]~E(x22561,x22562)+E(f633(x22563,x22564,x22565,x22561,x22566),f633(x22563,x22564,x22565,x22562,x22566)) % 188.18/188.27 [2257]~E(x22571,x22572)+E(f633(x22573,x22574,x22575,x22576,x22571),f633(x22573,x22574,x22575,x22576,x22572)) % 188.18/188.27 [2258]~E(x22581,x22582)+E(f713(x22581,x22583,x22584,x22585,x22586),f713(x22582,x22583,x22584,x22585,x22586)) % 188.18/188.27 [2259]~E(x22591,x22592)+E(f713(x22593,x22591,x22594,x22595,x22596),f713(x22593,x22592,x22594,x22595,x22596)) % 188.18/188.27 [2260]~E(x22601,x22602)+E(f713(x22603,x22604,x22601,x22605,x22606),f713(x22603,x22604,x22602,x22605,x22606)) % 188.18/188.27 [2261]~E(x22611,x22612)+E(f713(x22613,x22614,x22615,x22611,x22616),f713(x22613,x22614,x22615,x22612,x22616)) % 188.18/188.27 [2262]~E(x22621,x22622)+E(f713(x22623,x22624,x22625,x22626,x22621),f713(x22623,x22624,x22625,x22626,x22622)) % 188.18/188.27 [2263]~E(x22631,x22632)+E(f580(x22631),f580(x22632)) % 188.18/188.27 [2264]~E(x22641,x22642)+E(f346(x22641,x22643),f346(x22642,x22643)) % 188.18/188.27 [2265]~E(x22651,x22652)+E(f346(x22653,x22651),f346(x22653,x22652)) % 188.18/188.27 [2266]~E(x22661,x22662)+E(f298(x22661,x22663),f298(x22662,x22663)) % 188.18/188.27 [2267]~E(x22671,x22672)+E(f298(x22673,x22671),f298(x22673,x22672)) % 188.18/188.27 [2268]~E(x22681,x22682)+E(f561(x22681,x22683,x22684,x22685,x22686,x22687,x22688,x22689),f561(x22682,x22683,x22684,x22685,x22686,x22687,x22688,x22689)) % 188.18/188.27 [2269]~E(x22691,x22692)+E(f561(x22693,x22691,x22694,x22695,x22696,x22697,x22698,x22699),f561(x22693,x22692,x22694,x22695,x22696,x22697,x22698,x22699)) % 188.18/188.27 [2270]~E(x22701,x22702)+E(f561(x22703,x22704,x22701,x22705,x22706,x22707,x22708,x22709),f561(x22703,x22704,x22702,x22705,x22706,x22707,x22708,x22709)) % 188.18/188.27 [2271]~E(x22711,x22712)+E(f561(x22713,x22714,x22715,x22711,x22716,x22717,x22718,x22719),f561(x22713,x22714,x22715,x22712,x22716,x22717,x22718,x22719)) % 188.18/188.27 [2272]~E(x22721,x22722)+E(f561(x22723,x22724,x22725,x22726,x22721,x22727,x22728,x22729),f561(x22723,x22724,x22725,x22726,x22722,x22727,x22728,x22729)) % 188.18/188.27 [2273]~E(x22731,x22732)+E(f561(x22733,x22734,x22735,x22736,x22737,x22731,x22738,x22739),f561(x22733,x22734,x22735,x22736,x22737,x22732,x22738,x22739)) % 188.18/188.27 [2274]~E(x22741,x22742)+E(f561(x22743,x22744,x22745,x22746,x22747,x22748,x22741,x22749),f561(x22743,x22744,x22745,x22746,x22747,x22748,x22742,x22749)) % 188.18/188.27 [2275]~E(x22751,x22752)+E(f561(x22753,x22754,x22755,x22756,x22757,x22758,x22759,x22751),f561(x22753,x22754,x22755,x22756,x22757,x22758,x22759,x22752)) % 188.18/188.27 [2276]~E(x22761,x22762)+E(f459(x22761,x22763,x22764),f459(x22762,x22763,x22764)) % 188.18/188.27 [2277]~E(x22771,x22772)+E(f459(x22773,x22771,x22774),f459(x22773,x22772,x22774)) % 188.18/188.27 [2278]~E(x22781,x22782)+E(f459(x22783,x22784,x22781),f459(x22783,x22784,x22782)) % 188.18/188.27 [2279]~E(x22791,x22792)+E(f283(x22791,x22793),f283(x22792,x22793)) % 188.18/188.27 [2280]~E(x22801,x22802)+E(f283(x22803,x22801),f283(x22803,x22802)) % 188.18/188.27 [2281]~E(x22811,x22812)+E(f728(x22811,x22813,x22814),f728(x22812,x22813,x22814)) % 188.18/188.27 [2282]~E(x22821,x22822)+E(f728(x22823,x22821,x22824),f728(x22823,x22822,x22824)) % 188.18/188.27 [2283]~E(x22831,x22832)+E(f728(x22833,x22834,x22831),f728(x22833,x22834,x22832)) % 188.18/188.27 [2284]~E(x22841,x22842)+E(f430(x22841,x22843,x22844),f430(x22842,x22843,x22844)) % 188.18/188.27 [2285]~E(x22851,x22852)+E(f430(x22853,x22851,x22854),f430(x22853,x22852,x22854)) % 188.18/188.27 [2286]~E(x22861,x22862)+E(f430(x22863,x22864,x22861),f430(x22863,x22864,x22862)) % 188.18/188.27 [2287]~E(x22871,x22872)+E(f419(x22871,x22873,x22874,x22875),f419(x22872,x22873,x22874,x22875)) % 188.18/188.27 [2288]~E(x22881,x22882)+E(f419(x22883,x22881,x22884,x22885),f419(x22883,x22882,x22884,x22885)) % 188.18/188.27 [2289]~E(x22891,x22892)+E(f419(x22893,x22894,x22891,x22895),f419(x22893,x22894,x22892,x22895)) % 188.18/188.27 [2290]~E(x22901,x22902)+E(f419(x22903,x22904,x22905,x22901),f419(x22903,x22904,x22905,x22902)) % 188.18/188.27 [2291]~E(x22911,x22912)+E(f686(x22911,x22913,x22914),f686(x22912,x22913,x22914)) % 188.18/188.27 [2292]~E(x22921,x22922)+E(f686(x22923,x22921,x22924),f686(x22923,x22922,x22924)) % 188.18/188.27 [2293]~E(x22931,x22932)+E(f686(x22933,x22934,x22931),f686(x22933,x22934,x22932)) % 188.18/188.27 [2294]~E(x22941,x22942)+E(f73(x22941,x22943,x22944),f73(x22942,x22943,x22944)) % 188.18/188.27 [2295]~E(x22951,x22952)+E(f73(x22953,x22951,x22954),f73(x22953,x22952,x22954)) % 188.18/188.27 [2296]~E(x22961,x22962)+E(f73(x22963,x22964,x22961),f73(x22963,x22964,x22962)) % 188.18/188.27 [2297]~E(x22971,x22972)+E(f622(x22971,x22973,x22974,x22975,x22976),f622(x22972,x22973,x22974,x22975,x22976)) % 188.18/188.27 [2298]~E(x22981,x22982)+E(f622(x22983,x22981,x22984,x22985,x22986),f622(x22983,x22982,x22984,x22985,x22986)) % 188.18/188.27 [2299]~E(x22991,x22992)+E(f622(x22993,x22994,x22991,x22995,x22996),f622(x22993,x22994,x22992,x22995,x22996)) % 188.18/188.27 [2300]~E(x23001,x23002)+E(f622(x23003,x23004,x23005,x23001,x23006),f622(x23003,x23004,x23005,x23002,x23006)) % 188.18/188.27 [2301]~E(x23011,x23012)+E(f622(x23013,x23014,x23015,x23016,x23011),f622(x23013,x23014,x23015,x23016,x23012)) % 188.18/188.27 [2302]~E(x23021,x23022)+E(f670(x23021,x23023,x23024,x23025),f670(x23022,x23023,x23024,x23025)) % 188.18/188.27 [2303]~E(x23031,x23032)+E(f670(x23033,x23031,x23034,x23035),f670(x23033,x23032,x23034,x23035)) % 188.18/188.27 [2304]~E(x23041,x23042)+E(f670(x23043,x23044,x23041,x23045),f670(x23043,x23044,x23042,x23045)) % 188.18/188.27 [2305]~E(x23051,x23052)+E(f670(x23053,x23054,x23055,x23051),f670(x23053,x23054,x23055,x23052)) % 188.18/188.27 [2306]~E(x23061,x23062)+E(f871(x23061,x23063,x23064),f871(x23062,x23063,x23064)) % 188.18/188.27 [2307]~E(x23071,x23072)+E(f871(x23073,x23071,x23074),f871(x23073,x23072,x23074)) % 188.18/188.27 [2308]~E(x23081,x23082)+E(f871(x23083,x23084,x23081),f871(x23083,x23084,x23082)) % 188.18/188.27 [2309]~E(x23091,x23092)+E(f100(x23091,x23093,x23094),f100(x23092,x23093,x23094)) % 188.18/188.27 [2310]~E(x23101,x23102)+E(f100(x23103,x23101,x23104),f100(x23103,x23102,x23104)) % 188.18/188.27 [2311]~E(x23111,x23112)+E(f100(x23113,x23114,x23111),f100(x23113,x23114,x23112)) % 188.18/188.27 [2312]~E(x23121,x23122)+E(f378(x23121,x23123,x23124,x23125),f378(x23122,x23123,x23124,x23125)) % 188.18/188.27 [2313]~E(x23131,x23132)+E(f378(x23133,x23131,x23134,x23135),f378(x23133,x23132,x23134,x23135)) % 188.18/188.27 [2314]~E(x23141,x23142)+E(f378(x23143,x23144,x23141,x23145),f378(x23143,x23144,x23142,x23145)) % 188.18/188.27 [2315]~E(x23151,x23152)+E(f378(x23153,x23154,x23155,x23151),f378(x23153,x23154,x23155,x23152)) % 188.18/188.27 [2316]~E(x23161,x23162)+E(f576(x23161,x23163,x23164,x23165,x23166,x23167,x23168),f576(x23162,x23163,x23164,x23165,x23166,x23167,x23168)) % 188.18/188.27 [2317]~E(x23171,x23172)+E(f576(x23173,x23171,x23174,x23175,x23176,x23177,x23178),f576(x23173,x23172,x23174,x23175,x23176,x23177,x23178)) % 188.18/188.27 [2318]~E(x23181,x23182)+E(f576(x23183,x23184,x23181,x23185,x23186,x23187,x23188),f576(x23183,x23184,x23182,x23185,x23186,x23187,x23188)) % 188.18/188.27 [2319]~E(x23191,x23192)+E(f576(x23193,x23194,x23195,x23191,x23196,x23197,x23198),f576(x23193,x23194,x23195,x23192,x23196,x23197,x23198)) % 188.18/188.27 [2320]~E(x23201,x23202)+E(f576(x23203,x23204,x23205,x23206,x23201,x23207,x23208),f576(x23203,x23204,x23205,x23206,x23202,x23207,x23208)) % 188.18/188.27 [2321]~E(x23211,x23212)+E(f576(x23213,x23214,x23215,x23216,x23217,x23211,x23218),f576(x23213,x23214,x23215,x23216,x23217,x23212,x23218)) % 188.18/188.27 [2322]~E(x23221,x23222)+E(f576(x23223,x23224,x23225,x23226,x23227,x23228,x23221),f576(x23223,x23224,x23225,x23226,x23227,x23228,x23222)) % 188.18/188.27 [2323]~E(x23231,x23232)+E(f328(x23231,x23233,x23234),f328(x23232,x23233,x23234)) % 188.18/188.27 [2324]~E(x23241,x23242)+E(f328(x23243,x23241,x23244),f328(x23243,x23242,x23244)) % 188.18/188.27 [2325]~E(x23251,x23252)+E(f328(x23253,x23254,x23251),f328(x23253,x23254,x23252)) % 188.18/188.27 [2326]~E(x23261,x23262)+E(f886(x23261,x23263,x23264),f886(x23262,x23263,x23264)) % 188.18/188.27 [2327]~E(x23271,x23272)+E(f886(x23273,x23271,x23274),f886(x23273,x23272,x23274)) % 188.18/188.27 [2328]~E(x23281,x23282)+E(f886(x23283,x23284,x23281),f886(x23283,x23284,x23282)) % 188.18/188.27 [2329]~E(x23291,x23292)+E(f341(x23291),f341(x23292)) % 188.18/188.27 [2330]~E(x23301,x23302)+E(f764(x23301,x23303,x23304),f764(x23302,x23303,x23304)) % 188.18/188.27 [2331]~E(x23311,x23312)+E(f764(x23313,x23311,x23314),f764(x23313,x23312,x23314)) % 188.18/188.27 [2332]~E(x23321,x23322)+E(f764(x23323,x23324,x23321),f764(x23323,x23324,x23322)) % 188.18/188.27 [2333]~E(x23331,x23332)+E(f549(x23331,x23333),f549(x23332,x23333)) % 188.18/188.27 [2334]~E(x23341,x23342)+E(f549(x23343,x23341),f549(x23343,x23342)) % 188.18/188.27 [2335]~E(x23351,x23352)+E(f765(x23351,x23353,x23354),f765(x23352,x23353,x23354)) % 188.18/188.27 [2336]~E(x23361,x23362)+E(f765(x23363,x23361,x23364),f765(x23363,x23362,x23364)) % 188.18/188.27 [2337]~E(x23371,x23372)+E(f765(x23373,x23374,x23371),f765(x23373,x23374,x23372)) % 188.18/188.27 [2338]~E(x23381,x23382)+E(f169(x23381,x23383),f169(x23382,x23383)) % 188.18/188.27 [2339]~E(x23391,x23392)+E(f169(x23393,x23391),f169(x23393,x23392)) % 188.18/188.27 [2340]~E(x23401,x23402)+E(f652(x23401,x23403,x23404,x23405),f652(x23402,x23403,x23404,x23405)) % 188.18/188.27 [2341]~E(x23411,x23412)+E(f652(x23413,x23411,x23414,x23415),f652(x23413,x23412,x23414,x23415)) % 188.18/188.27 [2342]~E(x23421,x23422)+E(f652(x23423,x23424,x23421,x23425),f652(x23423,x23424,x23422,x23425)) % 188.18/188.27 [2343]~E(x23431,x23432)+E(f652(x23433,x23434,x23435,x23431),f652(x23433,x23434,x23435,x23432)) % 188.18/188.27 [2344]~E(x23441,x23442)+E(f870(x23441,x23443,x23444,x23445,x23446,x23447,x23448),f870(x23442,x23443,x23444,x23445,x23446,x23447,x23448)) % 188.18/188.27 [2345]~E(x23451,x23452)+E(f870(x23453,x23451,x23454,x23455,x23456,x23457,x23458),f870(x23453,x23452,x23454,x23455,x23456,x23457,x23458)) % 188.18/188.27 [2346]~E(x23461,x23462)+E(f870(x23463,x23464,x23461,x23465,x23466,x23467,x23468),f870(x23463,x23464,x23462,x23465,x23466,x23467,x23468)) % 188.18/188.27 [2347]~E(x23471,x23472)+E(f870(x23473,x23474,x23475,x23471,x23476,x23477,x23478),f870(x23473,x23474,x23475,x23472,x23476,x23477,x23478)) % 188.18/188.27 [2348]~E(x23481,x23482)+E(f870(x23483,x23484,x23485,x23486,x23481,x23487,x23488),f870(x23483,x23484,x23485,x23486,x23482,x23487,x23488)) % 188.18/188.27 [2349]~E(x23491,x23492)+E(f870(x23493,x23494,x23495,x23496,x23497,x23491,x23498),f870(x23493,x23494,x23495,x23496,x23497,x23492,x23498)) % 188.18/188.27 [2350]~E(x23501,x23502)+E(f870(x23503,x23504,x23505,x23506,x23507,x23508,x23501),f870(x23503,x23504,x23505,x23506,x23507,x23508,x23502)) % 188.18/188.27 [2351]~E(x23511,x23512)+E(f216(x23511,x23513,x23514,x23515,x23516,x23517,x23518),f216(x23512,x23513,x23514,x23515,x23516,x23517,x23518)) % 188.18/188.27 [2352]~E(x23521,x23522)+E(f216(x23523,x23521,x23524,x23525,x23526,x23527,x23528),f216(x23523,x23522,x23524,x23525,x23526,x23527,x23528)) % 188.18/188.27 [2353]~E(x23531,x23532)+E(f216(x23533,x23534,x23531,x23535,x23536,x23537,x23538),f216(x23533,x23534,x23532,x23535,x23536,x23537,x23538)) % 188.18/188.27 [2354]~E(x23541,x23542)+E(f216(x23543,x23544,x23545,x23541,x23546,x23547,x23548),f216(x23543,x23544,x23545,x23542,x23546,x23547,x23548)) % 188.18/188.27 [2355]~E(x23551,x23552)+E(f216(x23553,x23554,x23555,x23556,x23551,x23557,x23558),f216(x23553,x23554,x23555,x23556,x23552,x23557,x23558)) % 188.18/188.27 [2356]~E(x23561,x23562)+E(f216(x23563,x23564,x23565,x23566,x23567,x23561,x23568),f216(x23563,x23564,x23565,x23566,x23567,x23562,x23568)) % 188.18/188.27 [2357]~E(x23571,x23572)+E(f216(x23573,x23574,x23575,x23576,x23577,x23578,x23571),f216(x23573,x23574,x23575,x23576,x23577,x23578,x23572)) % 188.18/188.27 [2358]~E(x23581,x23582)+E(f375(x23581,x23583),f375(x23582,x23583)) % 188.18/188.27 [2359]~E(x23591,x23592)+E(f375(x23593,x23591),f375(x23593,x23592)) % 188.18/188.27 [2360]~E(x23601,x23602)+E(f727(x23601,x23603,x23604),f727(x23602,x23603,x23604)) % 188.18/188.27 [2361]~E(x23611,x23612)+E(f727(x23613,x23611,x23614),f727(x23613,x23612,x23614)) % 188.18/188.27 [2362]~E(x23621,x23622)+E(f727(x23623,x23624,x23621),f727(x23623,x23624,x23622)) % 188.18/188.27 [2363]~E(x23631,x23632)+E(f710(x23631,x23633),f710(x23632,x23633)) % 188.18/188.27 [2364]~E(x23641,x23642)+E(f710(x23643,x23641),f710(x23643,x23642)) % 188.18/188.27 [2365]~E(x23651,x23652)+E(f366(x23651,x23653,x23654),f366(x23652,x23653,x23654)) % 188.18/188.27 [2366]~E(x23661,x23662)+E(f366(x23663,x23661,x23664),f366(x23663,x23662,x23664)) % 188.18/188.27 [2367]~E(x23671,x23672)+E(f366(x23673,x23674,x23671),f366(x23673,x23674,x23672)) % 188.18/188.27 [2368]~E(x23681,x23682)+E(f689(x23681,x23683),f689(x23682,x23683)) % 188.18/188.27 [2369]~E(x23691,x23692)+E(f689(x23693,x23691),f689(x23693,x23692)) % 188.18/188.27 [2370]~E(x23701,x23702)+E(f839(x23701,x23703,x23704,x23705,x23706),f839(x23702,x23703,x23704,x23705,x23706)) % 188.18/188.27 [2371]~E(x23711,x23712)+E(f839(x23713,x23711,x23714,x23715,x23716),f839(x23713,x23712,x23714,x23715,x23716)) % 188.18/188.27 [2372]~E(x23721,x23722)+E(f839(x23723,x23724,x23721,x23725,x23726),f839(x23723,x23724,x23722,x23725,x23726)) % 188.18/188.27 [2373]~E(x23731,x23732)+E(f839(x23733,x23734,x23735,x23731,x23736),f839(x23733,x23734,x23735,x23732,x23736)) % 188.18/188.27 [2374]~E(x23741,x23742)+E(f839(x23743,x23744,x23745,x23746,x23741),f839(x23743,x23744,x23745,x23746,x23742)) % 188.18/188.27 [2375]~E(x23751,x23752)+E(f306(x23751,x23753,x23754,x23755,x23756),f306(x23752,x23753,x23754,x23755,x23756)) % 188.18/188.27 [2376]~E(x23761,x23762)+E(f306(x23763,x23761,x23764,x23765,x23766),f306(x23763,x23762,x23764,x23765,x23766)) % 188.18/188.27 [2377]~E(x23771,x23772)+E(f306(x23773,x23774,x23771,x23775,x23776),f306(x23773,x23774,x23772,x23775,x23776)) % 188.18/188.27 [2378]~E(x23781,x23782)+E(f306(x23783,x23784,x23785,x23781,x23786),f306(x23783,x23784,x23785,x23782,x23786)) % 188.18/188.27 [2379]~E(x23791,x23792)+E(f306(x23793,x23794,x23795,x23796,x23791),f306(x23793,x23794,x23795,x23796,x23792)) % 188.18/188.27 [2380]~E(x23801,x23802)+E(f359(x23801,x23803),f359(x23802,x23803)) % 188.18/188.27 [2381]~E(x23811,x23812)+E(f359(x23813,x23811),f359(x23813,x23812)) % 188.18/188.27 [2382]~E(x23821,x23822)+E(f789(x23821,x23823,x23824),f789(x23822,x23823,x23824)) % 188.18/188.27 [2383]~E(x23831,x23832)+E(f789(x23833,x23831,x23834),f789(x23833,x23832,x23834)) % 188.18/188.27 [2384]~E(x23841,x23842)+E(f789(x23843,x23844,x23841),f789(x23843,x23844,x23842)) % 188.18/188.27 [2385]~E(x23851,x23852)+E(f269(x23851,x23853,x23854,x23855,x23856),f269(x23852,x23853,x23854,x23855,x23856)) % 188.18/188.27 [2386]~E(x23861,x23862)+E(f269(x23863,x23861,x23864,x23865,x23866),f269(x23863,x23862,x23864,x23865,x23866)) % 188.18/188.27 [2387]~E(x23871,x23872)+E(f269(x23873,x23874,x23871,x23875,x23876),f269(x23873,x23874,x23872,x23875,x23876)) % 188.18/188.27 [2388]~E(x23881,x23882)+E(f269(x23883,x23884,x23885,x23881,x23886),f269(x23883,x23884,x23885,x23882,x23886)) % 188.18/188.27 [2389]~E(x23891,x23892)+E(f269(x23893,x23894,x23895,x23896,x23891),f269(x23893,x23894,x23895,x23896,x23892)) % 188.18/188.27 [2390]~E(x23901,x23902)+E(f837(x23901,x23903,x23904),f837(x23902,x23903,x23904)) % 188.18/188.27 [2391]~E(x23911,x23912)+E(f837(x23913,x23911,x23914),f837(x23913,x23912,x23914)) % 188.18/188.27 [2392]~E(x23921,x23922)+E(f837(x23923,x23924,x23921),f837(x23923,x23924,x23922)) % 188.18/188.27 [2393]~E(x23931,x23932)+E(f64(x23931,x23933,x23934,x23935),f64(x23932,x23933,x23934,x23935)) % 188.18/188.27 [2394]~E(x23941,x23942)+E(f64(x23943,x23941,x23944,x23945),f64(x23943,x23942,x23944,x23945)) % 188.18/188.27 [2395]~E(x23951,x23952)+E(f64(x23953,x23954,x23951,x23955),f64(x23953,x23954,x23952,x23955)) % 188.18/188.27 [2396]~E(x23961,x23962)+E(f64(x23963,x23964,x23965,x23961),f64(x23963,x23964,x23965,x23962)) % 188.18/188.27 [2397]~E(x23971,x23972)+E(f770(x23971,x23973,x23974),f770(x23972,x23973,x23974)) % 188.18/188.27 [2398]~E(x23981,x23982)+E(f770(x23983,x23981,x23984),f770(x23983,x23982,x23984)) % 188.18/188.27 [2399]~E(x23991,x23992)+E(f770(x23993,x23994,x23991),f770(x23993,x23994,x23992)) % 188.18/188.27 [2400]~E(x24001,x24002)+E(f396(x24001,x24003,x24004,x24005,x24006,x24007,x24008),f396(x24002,x24003,x24004,x24005,x24006,x24007,x24008)) % 188.18/188.27 [2401]~E(x24011,x24012)+E(f396(x24013,x24011,x24014,x24015,x24016,x24017,x24018),f396(x24013,x24012,x24014,x24015,x24016,x24017,x24018)) % 188.18/188.27 [2402]~E(x24021,x24022)+E(f396(x24023,x24024,x24021,x24025,x24026,x24027,x24028),f396(x24023,x24024,x24022,x24025,x24026,x24027,x24028)) % 188.18/188.27 [2403]~E(x24031,x24032)+E(f396(x24033,x24034,x24035,x24031,x24036,x24037,x24038),f396(x24033,x24034,x24035,x24032,x24036,x24037,x24038)) % 188.18/188.27 [2404]~E(x24041,x24042)+E(f396(x24043,x24044,x24045,x24046,x24041,x24047,x24048),f396(x24043,x24044,x24045,x24046,x24042,x24047,x24048)) % 188.18/188.27 [2405]~E(x24051,x24052)+E(f396(x24053,x24054,x24055,x24056,x24057,x24051,x24058),f396(x24053,x24054,x24055,x24056,x24057,x24052,x24058)) % 188.18/188.27 [2406]~E(x24061,x24062)+E(f396(x24063,x24064,x24065,x24066,x24067,x24068,x24061),f396(x24063,x24064,x24065,x24066,x24067,x24068,x24062)) % 188.18/188.27 [2407]~E(x24071,x24072)+E(f609(x24071,x24073,x24074),f609(x24072,x24073,x24074)) % 188.18/188.27 [2408]~E(x24081,x24082)+E(f609(x24083,x24081,x24084),f609(x24083,x24082,x24084)) % 188.18/188.27 [2409]~E(x24091,x24092)+E(f609(x24093,x24094,x24091),f609(x24093,x24094,x24092)) % 188.18/188.27 [2410]~E(x24101,x24102)+E(f358(x24101,x24103,x24104),f358(x24102,x24103,x24104)) % 188.18/188.27 [2411]~E(x24111,x24112)+E(f358(x24113,x24111,x24114),f358(x24113,x24112,x24114)) % 188.18/188.27 [2412]~E(x24121,x24122)+E(f358(x24123,x24124,x24121),f358(x24123,x24124,x24122)) % 188.18/188.27 [2413]~E(x24131,x24132)+E(f223(x24131,x24133),f223(x24132,x24133)) % 188.18/188.27 [2414]~E(x24141,x24142)+E(f223(x24143,x24141),f223(x24143,x24142)) % 188.18/188.27 [2415]~E(x24151,x24152)+E(f482(x24151,x24153,x24154,x24155,x24156),f482(x24152,x24153,x24154,x24155,x24156)) % 188.18/188.27 [2416]~E(x24161,x24162)+E(f482(x24163,x24161,x24164,x24165,x24166),f482(x24163,x24162,x24164,x24165,x24166)) % 188.18/188.27 [2417]~E(x24171,x24172)+E(f482(x24173,x24174,x24171,x24175,x24176),f482(x24173,x24174,x24172,x24175,x24176)) % 188.18/188.27 [2418]~E(x24181,x24182)+E(f482(x24183,x24184,x24185,x24181,x24186),f482(x24183,x24184,x24185,x24182,x24186)) % 188.18/188.27 [2419]~E(x24191,x24192)+E(f482(x24193,x24194,x24195,x24196,x24191),f482(x24193,x24194,x24195,x24196,x24192)) % 188.18/188.27 [2420]~E(x24201,x24202)+E(f585(x24201,x24203,x24204),f585(x24202,x24203,x24204)) % 188.18/188.27 [2421]~E(x24211,x24212)+E(f585(x24213,x24211,x24214),f585(x24213,x24212,x24214)) % 188.18/188.27 [2422]~E(x24221,x24222)+E(f585(x24223,x24224,x24221),f585(x24223,x24224,x24222)) % 188.18/188.27 [2423]~E(x24231,x24232)+E(f758(x24231,x24233,x24234,x24235,x24236),f758(x24232,x24233,x24234,x24235,x24236)) % 188.18/188.27 [2424]~E(x24241,x24242)+E(f758(x24243,x24241,x24244,x24245,x24246),f758(x24243,x24242,x24244,x24245,x24246)) % 188.18/188.27 [2425]~E(x24251,x24252)+E(f758(x24253,x24254,x24251,x24255,x24256),f758(x24253,x24254,x24252,x24255,x24256)) % 188.18/188.27 [2426]~E(x24261,x24262)+E(f758(x24263,x24264,x24265,x24261,x24266),f758(x24263,x24264,x24265,x24262,x24266)) % 188.18/188.27 [2427]~E(x24271,x24272)+E(f758(x24273,x24274,x24275,x24276,x24271),f758(x24273,x24274,x24275,x24276,x24272)) % 188.18/188.27 [2428]~E(x24281,x24282)+E(f338(x24281,x24283,x24284,x24285),f338(x24282,x24283,x24284,x24285)) % 188.18/188.27 [2429]~E(x24291,x24292)+E(f338(x24293,x24291,x24294,x24295),f338(x24293,x24292,x24294,x24295)) % 188.18/188.27 [2430]~E(x24301,x24302)+E(f338(x24303,x24304,x24301,x24305),f338(x24303,x24304,x24302,x24305)) % 188.18/188.27 [2431]~E(x24311,x24312)+E(f338(x24313,x24314,x24315,x24311),f338(x24313,x24314,x24315,x24312)) % 188.18/188.27 [2432]~E(x24321,x24322)+E(f821(x24321,x24323),f821(x24322,x24323)) % 188.18/188.27 [2433]~E(x24331,x24332)+E(f821(x24333,x24331),f821(x24333,x24332)) % 188.18/188.27 [2434]~E(x24341,x24342)+E(f661(x24341,x24343,x24344,x24345),f661(x24342,x24343,x24344,x24345)) % 188.18/188.27 [2435]~E(x24351,x24352)+E(f661(x24353,x24351,x24354,x24355),f661(x24353,x24352,x24354,x24355)) % 188.18/188.27 [2436]~E(x24361,x24362)+E(f661(x24363,x24364,x24361,x24365),f661(x24363,x24364,x24362,x24365)) % 188.18/188.27 [2437]~E(x24371,x24372)+E(f661(x24373,x24374,x24375,x24371),f661(x24373,x24374,x24375,x24372)) % 188.18/188.27 [2438]~E(x24381,x24382)+E(f861(x24381,x24383,x24384,x24385,x24386),f861(x24382,x24383,x24384,x24385,x24386)) % 188.18/188.27 [2439]~E(x24391,x24392)+E(f861(x24393,x24391,x24394,x24395,x24396),f861(x24393,x24392,x24394,x24395,x24396)) % 188.18/188.27 [2440]~E(x24401,x24402)+E(f861(x24403,x24404,x24401,x24405,x24406),f861(x24403,x24404,x24402,x24405,x24406)) % 188.18/188.27 [2441]~E(x24411,x24412)+E(f861(x24413,x24414,x24415,x24411,x24416),f861(x24413,x24414,x24415,x24412,x24416)) % 188.18/188.27 [2442]~E(x24421,x24422)+E(f861(x24423,x24424,x24425,x24426,x24421),f861(x24423,x24424,x24425,x24426,x24422)) % 188.18/188.27 [2443]~E(x24431,x24432)+E(f349(x24431,x24433,x24434),f349(x24432,x24433,x24434)) % 188.18/188.27 [2444]~E(x24441,x24442)+E(f349(x24443,x24441,x24444),f349(x24443,x24442,x24444)) % 188.18/188.27 [2445]~E(x24451,x24452)+E(f349(x24453,x24454,x24451),f349(x24453,x24454,x24452)) % 188.18/188.27 [2446]~E(x24461,x24462)+E(f905(x24461,x24463),f905(x24462,x24463)) % 188.18/188.27 [2447]~E(x24471,x24472)+E(f905(x24473,x24471),f905(x24473,x24472)) % 188.18/188.27 [2448]~E(x24481,x24482)+E(f505(x24481,x24483,x24484),f505(x24482,x24483,x24484)) % 188.18/188.27 [2449]~E(x24491,x24492)+E(f505(x24493,x24491,x24494),f505(x24493,x24492,x24494)) % 188.18/188.27 [2450]~E(x24501,x24502)+E(f505(x24503,x24504,x24501),f505(x24503,x24504,x24502)) % 188.18/188.27 [2451]~E(x24511,x24512)+E(f733(x24511,x24513,x24514,x24515,x24516),f733(x24512,x24513,x24514,x24515,x24516)) % 188.18/188.27 [2452]~E(x24521,x24522)+E(f733(x24523,x24521,x24524,x24525,x24526),f733(x24523,x24522,x24524,x24525,x24526)) % 188.18/188.27 [2453]~E(x24531,x24532)+E(f733(x24533,x24534,x24531,x24535,x24536),f733(x24533,x24534,x24532,x24535,x24536)) % 188.18/188.27 [2454]~E(x24541,x24542)+E(f733(x24543,x24544,x24545,x24541,x24546),f733(x24543,x24544,x24545,x24542,x24546)) % 188.18/188.27 [2455]~E(x24551,x24552)+E(f733(x24553,x24554,x24555,x24556,x24551),f733(x24553,x24554,x24555,x24556,x24552)) % 188.18/188.27 [2456]~E(x24561,x24562)+E(f718(x24561,x24563,x24564),f718(x24562,x24563,x24564)) % 188.18/188.27 [2457]~E(x24571,x24572)+E(f718(x24573,x24571,x24574),f718(x24573,x24572,x24574)) % 188.18/188.27 [2458]~E(x24581,x24582)+E(f718(x24583,x24584,x24581),f718(x24583,x24584,x24582)) % 188.18/188.27 [2459]~E(x24591,x24592)+E(f473(x24591,x24593,x24594,x24595,x24596),f473(x24592,x24593,x24594,x24595,x24596)) % 188.18/188.27 [2460]~E(x24601,x24602)+E(f473(x24603,x24601,x24604,x24605,x24606),f473(x24603,x24602,x24604,x24605,x24606)) % 188.18/188.27 [2461]~E(x24611,x24612)+E(f473(x24613,x24614,x24611,x24615,x24616),f473(x24613,x24614,x24612,x24615,x24616)) % 188.18/188.27 [2462]~E(x24621,x24622)+E(f473(x24623,x24624,x24625,x24621,x24626),f473(x24623,x24624,x24625,x24622,x24626)) % 188.18/188.27 [2463]~E(x24631,x24632)+E(f473(x24633,x24634,x24635,x24636,x24631),f473(x24633,x24634,x24635,x24636,x24632)) % 188.18/188.27 [2464]~E(x24641,x24642)+E(f302(x24641,x24643,x24644,x24645),f302(x24642,x24643,x24644,x24645)) % 188.18/188.27 [2465]~E(x24651,x24652)+E(f302(x24653,x24651,x24654,x24655),f302(x24653,x24652,x24654,x24655)) % 188.18/188.27 [2466]~E(x24661,x24662)+E(f302(x24663,x24664,x24661,x24665),f302(x24663,x24664,x24662,x24665)) % 188.18/188.27 [2467]~E(x24671,x24672)+E(f302(x24673,x24674,x24675,x24671),f302(x24673,x24674,x24675,x24672)) % 188.18/188.27 [2468]~E(x24681,x24682)+E(f706(x24681,x24683,x24684),f706(x24682,x24683,x24684)) % 188.18/188.27 [2469]~E(x24691,x24692)+E(f706(x24693,x24691,x24694),f706(x24693,x24692,x24694)) % 188.18/188.27 [2470]~E(x24701,x24702)+E(f706(x24703,x24704,x24701),f706(x24703,x24704,x24702)) % 188.18/188.27 [2471]~E(x24711,x24712)+E(f277(x24711,x24713),f277(x24712,x24713)) % 188.18/188.27 [2472]~E(x24721,x24722)+E(f277(x24723,x24721),f277(x24723,x24722)) % 188.18/188.27 [2473]~E(x24731,x24732)+E(f414(x24731,x24733,x24734,x24735),f414(x24732,x24733,x24734,x24735)) % 188.18/188.27 [2474]~E(x24741,x24742)+E(f414(x24743,x24741,x24744,x24745),f414(x24743,x24742,x24744,x24745)) % 188.18/188.27 [2475]~E(x24751,x24752)+E(f414(x24753,x24754,x24751,x24755),f414(x24753,x24754,x24752,x24755)) % 188.18/188.27 [2476]~E(x24761,x24762)+E(f414(x24763,x24764,x24765,x24761),f414(x24763,x24764,x24765,x24762)) % 188.18/188.27 [2477]~E(x24771,x24772)+E(f795(x24771),f795(x24772)) % 188.18/188.27 [2478]~E(x24781,x24782)+E(f834(x24781),f834(x24782)) % 188.18/188.27 [2479]~E(x24791,x24792)+E(f481(x24791,x24793,x24794,x24795,x24796),f481(x24792,x24793,x24794,x24795,x24796)) % 188.18/188.27 [2480]~E(x24801,x24802)+E(f481(x24803,x24801,x24804,x24805,x24806),f481(x24803,x24802,x24804,x24805,x24806)) % 188.18/188.27 [2481]~E(x24811,x24812)+E(f481(x24813,x24814,x24811,x24815,x24816),f481(x24813,x24814,x24812,x24815,x24816)) % 188.18/188.27 [2482]~E(x24821,x24822)+E(f481(x24823,x24824,x24825,x24821,x24826),f481(x24823,x24824,x24825,x24822,x24826)) % 188.18/188.27 [2483]~E(x24831,x24832)+E(f481(x24833,x24834,x24835,x24836,x24831),f481(x24833,x24834,x24835,x24836,x24832)) % 188.18/188.27 [2484]~E(x24841,x24842)+E(f72(x24841,x24843,x24844),f72(x24842,x24843,x24844)) % 188.18/188.27 [2485]~E(x24851,x24852)+E(f72(x24853,x24851,x24854),f72(x24853,x24852,x24854)) % 188.18/188.27 [2486]~E(x24861,x24862)+E(f72(x24863,x24864,x24861),f72(x24863,x24864,x24862)) % 188.18/188.27 [2487]~E(x24871,x24872)+E(f751(x24871,x24873),f751(x24872,x24873)) % 188.18/188.27 [2488]~E(x24881,x24882)+E(f751(x24883,x24881),f751(x24883,x24882)) % 188.18/188.27 [2489]~E(x24891,x24892)+E(f607(x24891,x24893,x24894,x24895,x24896),f607(x24892,x24893,x24894,x24895,x24896)) % 188.18/188.27 [2490]~E(x24901,x24902)+E(f607(x24903,x24901,x24904,x24905,x24906),f607(x24903,x24902,x24904,x24905,x24906)) % 188.18/188.27 [2491]~E(x24911,x24912)+E(f607(x24913,x24914,x24911,x24915,x24916),f607(x24913,x24914,x24912,x24915,x24916)) % 188.18/188.27 [2492]~E(x24921,x24922)+E(f607(x24923,x24924,x24925,x24921,x24926),f607(x24923,x24924,x24925,x24922,x24926)) % 188.18/188.27 [2493]~E(x24931,x24932)+E(f607(x24933,x24934,x24935,x24936,x24931),f607(x24933,x24934,x24935,x24936,x24932)) % 188.18/188.27 [2494]~E(x24941,x24942)+E(f903(x24941),f903(x24942)) % 188.18/188.27 [2495]~E(x24951,x24952)+E(f679(x24951,x24953),f679(x24952,x24953)) % 188.18/188.27 [2496]~E(x24961,x24962)+E(f679(x24963,x24961),f679(x24963,x24962)) % 188.18/188.27 [2497]~E(x24971,x24972)+E(f444(x24971,x24973,x24974,x24975),f444(x24972,x24973,x24974,x24975)) % 188.18/188.27 [2498]~E(x24981,x24982)+E(f444(x24983,x24981,x24984,x24985),f444(x24983,x24982,x24984,x24985)) % 188.18/188.27 [2499]~E(x24991,x24992)+E(f444(x24993,x24994,x24991,x24995),f444(x24993,x24994,x24992,x24995)) % 188.18/188.27 [2500]~E(x25001,x25002)+E(f444(x25003,x25004,x25005,x25001),f444(x25003,x25004,x25005,x25002)) % 188.18/188.27 [2501]~E(x25011,x25012)+E(f816(x25011,x25013),f816(x25012,x25013)) % 188.18/188.27 [2502]~E(x25021,x25022)+E(f816(x25023,x25021),f816(x25023,x25022)) % 188.18/188.27 [2503]~E(x25031,x25032)+E(f564(x25031,x25033,x25034,x25035,x25036),f564(x25032,x25033,x25034,x25035,x25036)) % 188.18/188.27 [2504]~E(x25041,x25042)+E(f564(x25043,x25041,x25044,x25045,x25046),f564(x25043,x25042,x25044,x25045,x25046)) % 188.18/188.27 [2505]~E(x25051,x25052)+E(f564(x25053,x25054,x25051,x25055,x25056),f564(x25053,x25054,x25052,x25055,x25056)) % 188.18/188.27 [2506]~E(x25061,x25062)+E(f564(x25063,x25064,x25065,x25061,x25066),f564(x25063,x25064,x25065,x25062,x25066)) % 188.18/188.27 [2507]~E(x25071,x25072)+E(f564(x25073,x25074,x25075,x25076,x25071),f564(x25073,x25074,x25075,x25076,x25072)) % 188.18/188.27 [2508]~E(x25081,x25082)+E(f212(x25081,x25083,x25084),f212(x25082,x25083,x25084)) % 188.18/188.27 [2509]~E(x25091,x25092)+E(f212(x25093,x25091,x25094),f212(x25093,x25092,x25094)) % 188.18/188.27 [2510]~E(x25101,x25102)+E(f212(x25103,x25104,x25101),f212(x25103,x25104,x25102)) % 188.18/188.27 [2511]~E(x25111,x25112)+E(f527(x25111,x25113,x25114,x25115,x25116,x25117,x25118),f527(x25112,x25113,x25114,x25115,x25116,x25117,x25118)) % 188.18/188.27 [2512]~E(x25121,x25122)+E(f527(x25123,x25121,x25124,x25125,x25126,x25127,x25128),f527(x25123,x25122,x25124,x25125,x25126,x25127,x25128)) % 188.18/188.27 [2513]~E(x25131,x25132)+E(f527(x25133,x25134,x25131,x25135,x25136,x25137,x25138),f527(x25133,x25134,x25132,x25135,x25136,x25137,x25138)) % 188.18/188.27 [2514]~E(x25141,x25142)+E(f527(x25143,x25144,x25145,x25141,x25146,x25147,x25148),f527(x25143,x25144,x25145,x25142,x25146,x25147,x25148)) % 188.18/188.27 [2515]~E(x25151,x25152)+E(f527(x25153,x25154,x25155,x25156,x25151,x25157,x25158),f527(x25153,x25154,x25155,x25156,x25152,x25157,x25158)) % 188.18/188.27 [2516]~E(x25161,x25162)+E(f527(x25163,x25164,x25165,x25166,x25167,x25161,x25168),f527(x25163,x25164,x25165,x25166,x25167,x25162,x25168)) % 188.18/188.27 [2517]~E(x25171,x25172)+E(f527(x25173,x25174,x25175,x25176,x25177,x25178,x25171),f527(x25173,x25174,x25175,x25176,x25177,x25178,x25172)) % 188.18/188.27 [2518]~E(x25181,x25182)+E(f695(x25181,x25183,x25184,x25185),f695(x25182,x25183,x25184,x25185)) % 188.18/188.27 [2519]~E(x25191,x25192)+E(f695(x25193,x25191,x25194,x25195),f695(x25193,x25192,x25194,x25195)) % 188.18/188.27 [2520]~E(x25201,x25202)+E(f695(x25203,x25204,x25201,x25205),f695(x25203,x25204,x25202,x25205)) % 188.18/188.27 [2521]~E(x25211,x25212)+E(f695(x25213,x25214,x25215,x25211),f695(x25213,x25214,x25215,x25212)) % 188.18/188.27 [2522]~E(x25221,x25222)+E(f478(x25221,x25223,x25224,x25225,x25226,x25227,x25228),f478(x25222,x25223,x25224,x25225,x25226,x25227,x25228)) % 188.18/188.27 [2523]~E(x25231,x25232)+E(f478(x25233,x25231,x25234,x25235,x25236,x25237,x25238),f478(x25233,x25232,x25234,x25235,x25236,x25237,x25238)) % 188.18/188.27 [2524]~E(x25241,x25242)+E(f478(x25243,x25244,x25241,x25245,x25246,x25247,x25248),f478(x25243,x25244,x25242,x25245,x25246,x25247,x25248)) % 188.18/188.27 [2525]~E(x25251,x25252)+E(f478(x25253,x25254,x25255,x25251,x25256,x25257,x25258),f478(x25253,x25254,x25255,x25252,x25256,x25257,x25258)) % 188.18/188.27 [2526]~E(x25261,x25262)+E(f478(x25263,x25264,x25265,x25266,x25261,x25267,x25268),f478(x25263,x25264,x25265,x25266,x25262,x25267,x25268)) % 188.18/188.27 [2527]~E(x25271,x25272)+E(f478(x25273,x25274,x25275,x25276,x25277,x25271,x25278),f478(x25273,x25274,x25275,x25276,x25277,x25272,x25278)) % 188.18/188.27 [2528]~E(x25281,x25282)+E(f478(x25283,x25284,x25285,x25286,x25287,x25288,x25281),f478(x25283,x25284,x25285,x25286,x25287,x25288,x25282)) % 188.18/188.27 [2529]~E(x25291,x25292)+E(f499(x25291,x25293,x25294),f499(x25292,x25293,x25294)) % 188.18/188.27 [2530]~E(x25301,x25302)+E(f499(x25303,x25301,x25304),f499(x25303,x25302,x25304)) % 188.18/188.27 [2531]~E(x25311,x25312)+E(f499(x25313,x25314,x25311),f499(x25313,x25314,x25312)) % 188.18/188.27 [2532]~E(x25321,x25322)+E(f804(x25321,x25323),f804(x25322,x25323)) % 188.18/188.27 [2533]~E(x25331,x25332)+E(f804(x25333,x25331),f804(x25333,x25332)) % 188.18/188.27 [2534]~E(x25341,x25342)+E(f766(x25341,x25343,x25344,x25345),f766(x25342,x25343,x25344,x25345)) % 188.18/188.27 [2535]~E(x25351,x25352)+E(f766(x25353,x25351,x25354,x25355),f766(x25353,x25352,x25354,x25355)) % 188.18/188.27 [2536]~E(x25361,x25362)+E(f766(x25363,x25364,x25361,x25365),f766(x25363,x25364,x25362,x25365)) % 188.18/188.27 [2537]~E(x25371,x25372)+E(f766(x25373,x25374,x25375,x25371),f766(x25373,x25374,x25375,x25372)) % 188.18/188.27 [2538]~E(x25381,x25382)+E(f902(x25381),f902(x25382)) % 188.18/188.27 [2539]~E(x25391,x25392)+E(f731(x25391,x25393,x25394),f731(x25392,x25393,x25394)) % 188.18/188.27 [2540]~E(x25401,x25402)+E(f731(x25403,x25401,x25404),f731(x25403,x25402,x25404)) % 188.18/188.27 [2541]~E(x25411,x25412)+E(f731(x25413,x25414,x25411),f731(x25413,x25414,x25412)) % 188.18/188.27 [2542]~E(x25421,x25422)+E(f102(x25421,x25423,x25424,x25425),f102(x25422,x25423,x25424,x25425)) % 188.18/188.27 [2543]~E(x25431,x25432)+E(f102(x25433,x25431,x25434,x25435),f102(x25433,x25432,x25434,x25435)) % 188.18/188.27 [2544]~E(x25441,x25442)+E(f102(x25443,x25444,x25441,x25445),f102(x25443,x25444,x25442,x25445)) % 188.18/188.27 [2545]~E(x25451,x25452)+E(f102(x25453,x25454,x25455,x25451),f102(x25453,x25454,x25455,x25452)) % 188.18/188.27 [2546]~E(x25461,x25462)+E(f786(x25461,x25463,x25464,x25465),f786(x25462,x25463,x25464,x25465)) % 188.18/188.27 [2547]~E(x25471,x25472)+E(f786(x25473,x25471,x25474,x25475),f786(x25473,x25472,x25474,x25475)) % 188.18/188.27 [2548]~E(x25481,x25482)+E(f786(x25483,x25484,x25481,x25485),f786(x25483,x25484,x25482,x25485)) % 188.18/188.27 [2549]~E(x25491,x25492)+E(f786(x25493,x25494,x25495,x25491),f786(x25493,x25494,x25495,x25492)) % 188.18/188.27 [2550]~E(x25501,x25502)+E(f863(x25501,x25503,x25504,x25505,x25506,x25507),f863(x25502,x25503,x25504,x25505,x25506,x25507)) % 188.18/188.27 [2551]~E(x25511,x25512)+E(f863(x25513,x25511,x25514,x25515,x25516,x25517),f863(x25513,x25512,x25514,x25515,x25516,x25517)) % 188.18/188.27 [2552]~E(x25521,x25522)+E(f863(x25523,x25524,x25521,x25525,x25526,x25527),f863(x25523,x25524,x25522,x25525,x25526,x25527)) % 188.18/188.27 [2553]~E(x25531,x25532)+E(f863(x25533,x25534,x25535,x25531,x25536,x25537),f863(x25533,x25534,x25535,x25532,x25536,x25537)) % 188.18/188.27 [2554]~E(x25541,x25542)+E(f863(x25543,x25544,x25545,x25546,x25541,x25547),f863(x25543,x25544,x25545,x25546,x25542,x25547)) % 188.18/188.27 [2555]~E(x25551,x25552)+E(f863(x25553,x25554,x25555,x25556,x25557,x25551),f863(x25553,x25554,x25555,x25556,x25557,x25552)) % 188.18/188.27 [2556]~E(x25561,x25562)+E(f842(x25561,x25563,x25564,x25565),f842(x25562,x25563,x25564,x25565)) % 188.18/188.27 [2557]~E(x25571,x25572)+E(f842(x25573,x25571,x25574,x25575),f842(x25573,x25572,x25574,x25575)) % 188.18/188.27 [2558]~E(x25581,x25582)+E(f842(x25583,x25584,x25581,x25585),f842(x25583,x25584,x25582,x25585)) % 188.18/188.27 [2559]~E(x25591,x25592)+E(f842(x25593,x25594,x25595,x25591),f842(x25593,x25594,x25595,x25592)) % 188.18/188.27 [2560]~E(x25601,x25602)+E(f245(x25601,x25603),f245(x25602,x25603)) % 188.18/188.27 [2561]~E(x25611,x25612)+E(f245(x25613,x25611),f245(x25613,x25612)) % 188.18/188.27 [2562]~E(x25621,x25622)+E(f631(x25621,x25623,x25624,x25625,x25626),f631(x25622,x25623,x25624,x25625,x25626)) % 188.18/188.27 [2563]~E(x25631,x25632)+E(f631(x25633,x25631,x25634,x25635,x25636),f631(x25633,x25632,x25634,x25635,x25636)) % 188.18/188.27 [2564]~E(x25641,x25642)+E(f631(x25643,x25644,x25641,x25645,x25646),f631(x25643,x25644,x25642,x25645,x25646)) % 188.18/188.27 [2565]~E(x25651,x25652)+E(f631(x25653,x25654,x25655,x25651,x25656),f631(x25653,x25654,x25655,x25652,x25656)) % 188.18/188.27 [2566]~E(x25661,x25662)+E(f631(x25663,x25664,x25665,x25666,x25661),f631(x25663,x25664,x25665,x25666,x25662)) % 188.18/188.27 [2567]~E(x25671,x25672)+E(f544(x25671,x25673,x25674,x25675),f544(x25672,x25673,x25674,x25675)) % 188.18/188.27 [2568]~E(x25681,x25682)+E(f544(x25683,x25681,x25684,x25685),f544(x25683,x25682,x25684,x25685)) % 188.18/188.27 [2569]~E(x25691,x25692)+E(f544(x25693,x25694,x25691,x25695),f544(x25693,x25694,x25692,x25695)) % 188.18/188.27 [2570]~E(x25701,x25702)+E(f544(x25703,x25704,x25705,x25701),f544(x25703,x25704,x25705,x25702)) % 188.18/188.27 [2571]~E(x25711,x25712)+E(f919(x25711,x25713,x25714),f919(x25712,x25713,x25714)) % 188.18/188.28 [2572]~E(x25721,x25722)+E(f919(x25723,x25721,x25724),f919(x25723,x25722,x25724)) % 188.18/188.28 [2573]~E(x25731,x25732)+E(f919(x25733,x25734,x25731),f919(x25733,x25734,x25732)) % 188.18/188.28 [2574]~E(x25741,x25742)+E(f418(x25741,x25743,x25744,x25745),f418(x25742,x25743,x25744,x25745)) % 188.18/188.28 [2575]~E(x25751,x25752)+E(f418(x25753,x25751,x25754,x25755),f418(x25753,x25752,x25754,x25755)) % 188.18/188.28 [2576]~E(x25761,x25762)+E(f418(x25763,x25764,x25761,x25765),f418(x25763,x25764,x25762,x25765)) % 188.18/188.28 [2577]~E(x25771,x25772)+E(f418(x25773,x25774,x25775,x25771),f418(x25773,x25774,x25775,x25772)) % 188.18/188.28 [2578]~E(x25781,x25782)+E(f413(x25781,x25783,x25784,x25785),f413(x25782,x25783,x25784,x25785)) % 188.18/188.28 [2579]~E(x25791,x25792)+E(f413(x25793,x25791,x25794,x25795),f413(x25793,x25792,x25794,x25795)) % 188.18/188.28 [2580]~E(x25801,x25802)+E(f413(x25803,x25804,x25801,x25805),f413(x25803,x25804,x25802,x25805)) % 188.18/188.28 [2581]~E(x25811,x25812)+E(f413(x25813,x25814,x25815,x25811),f413(x25813,x25814,x25815,x25812)) % 188.18/188.28 [2582]~E(x25821,x25822)+E(f818(x25821,x25823),f818(x25822,x25823)) % 188.18/188.28 [2583]~E(x25831,x25832)+E(f818(x25833,x25831),f818(x25833,x25832)) % 188.18/188.28 [2584]~E(x25841,x25842)+E(f627(x25841,x25843,x25844),f627(x25842,x25843,x25844)) % 188.18/188.28 [2585]~E(x25851,x25852)+E(f627(x25853,x25851,x25854),f627(x25853,x25852,x25854)) % 188.18/188.28 [2586]~E(x25861,x25862)+E(f627(x25863,x25864,x25861),f627(x25863,x25864,x25862)) % 188.18/188.28 [2587]~E(x25871,x25872)+E(f835(x25871,x25873),f835(x25872,x25873)) % 188.18/188.28 [2588]~E(x25881,x25882)+E(f835(x25883,x25881),f835(x25883,x25882)) % 188.18/188.28 [2589]~E(x25891,x25892)+E(f131(x25891),f131(x25892)) % 188.18/188.28 [2590]~E(x25901,x25902)+E(f778(x25901,x25903,x25904,x25905),f778(x25902,x25903,x25904,x25905)) % 188.18/188.28 [2591]~E(x25911,x25912)+E(f778(x25913,x25911,x25914,x25915),f778(x25913,x25912,x25914,x25915)) % 188.18/188.28 [2592]~E(x25921,x25922)+E(f778(x25923,x25924,x25921,x25925),f778(x25923,x25924,x25922,x25925)) % 188.18/188.28 [2593]~E(x25931,x25932)+E(f778(x25933,x25934,x25935,x25931),f778(x25933,x25934,x25935,x25932)) % 188.18/188.28 [2594]~E(x25941,x25942)+E(f655(x25941,x25943,x25944,x25945),f655(x25942,x25943,x25944,x25945)) % 188.18/188.28 [2595]~E(x25951,x25952)+E(f655(x25953,x25951,x25954,x25955),f655(x25953,x25952,x25954,x25955)) % 188.18/188.28 [2596]~E(x25961,x25962)+E(f655(x25963,x25964,x25961,x25965),f655(x25963,x25964,x25962,x25965)) % 188.18/188.28 [2597]~E(x25971,x25972)+E(f655(x25973,x25974,x25975,x25971),f655(x25973,x25974,x25975,x25972)) % 188.18/188.28 [2598]~E(x25981,x25982)+E(f724(x25981,x25983,x25984),f724(x25982,x25983,x25984)) % 188.18/188.28 [2599]~E(x25991,x25992)+E(f724(x25993,x25991,x25994),f724(x25993,x25992,x25994)) % 188.18/188.28 [2600]~E(x26001,x26002)+E(f724(x26003,x26004,x26001),f724(x26003,x26004,x26002)) % 188.18/188.28 [2601]~E(x26011,x26012)+E(f884(x26011,x26013,x26014),f884(x26012,x26013,x26014)) % 188.18/188.28 [2602]~E(x26021,x26022)+E(f884(x26023,x26021,x26024),f884(x26023,x26022,x26024)) % 188.18/188.28 [2603]~E(x26031,x26032)+E(f884(x26033,x26034,x26031),f884(x26033,x26034,x26032)) % 188.18/188.28 [2604]~E(x26041,x26042)+E(f740(x26041,x26043),f740(x26042,x26043)) % 188.18/188.28 [2605]~E(x26051,x26052)+E(f740(x26053,x26051),f740(x26053,x26052)) % 188.18/188.28 [2606]~E(x26061,x26062)+E(f667(x26061,x26063,x26064,x26065,x26066),f667(x26062,x26063,x26064,x26065,x26066)) % 188.18/188.28 [2607]~E(x26071,x26072)+E(f667(x26073,x26071,x26074,x26075,x26076),f667(x26073,x26072,x26074,x26075,x26076)) % 188.18/188.28 [2608]~E(x26081,x26082)+E(f667(x26083,x26084,x26081,x26085,x26086),f667(x26083,x26084,x26082,x26085,x26086)) % 188.18/188.28 [2609]~E(x26091,x26092)+E(f667(x26093,x26094,x26095,x26091,x26096),f667(x26093,x26094,x26095,x26092,x26096)) % 188.18/188.28 [2610]~E(x26101,x26102)+E(f667(x26103,x26104,x26105,x26106,x26101),f667(x26103,x26104,x26105,x26106,x26102)) % 188.18/188.28 [2611]~E(x26111,x26112)+E(f351(x26111,x26113,x26114,x26115),f351(x26112,x26113,x26114,x26115)) % 188.18/188.28 [2612]~E(x26121,x26122)+E(f351(x26123,x26121,x26124,x26125),f351(x26123,x26122,x26124,x26125)) % 188.18/188.28 [2613]~E(x26131,x26132)+E(f351(x26133,x26134,x26131,x26135),f351(x26133,x26134,x26132,x26135)) % 188.18/188.28 [2614]~E(x26141,x26142)+E(f351(x26143,x26144,x26145,x26141),f351(x26143,x26144,x26145,x26142)) % 188.18/188.28 [2615]~E(x26151,x26152)+E(f530(x26151,x26153),f530(x26152,x26153)) % 188.18/188.28 [2616]~E(x26161,x26162)+E(f530(x26163,x26161),f530(x26163,x26162)) % 188.18/188.28 [2617]~E(x26171,x26172)+E(f841(x26171,x26173,x26174,x26175),f841(x26172,x26173,x26174,x26175)) % 188.18/188.28 [2618]~E(x26181,x26182)+E(f841(x26183,x26181,x26184,x26185),f841(x26183,x26182,x26184,x26185)) % 188.18/188.28 [2619]~E(x26191,x26192)+E(f841(x26193,x26194,x26191,x26195),f841(x26193,x26194,x26192,x26195)) % 188.18/188.28 [2620]~E(x26201,x26202)+E(f841(x26203,x26204,x26205,x26201),f841(x26203,x26204,x26205,x26202)) % 188.18/188.28 [2621]~E(x26211,x26212)+E(f624(x26211,x26213,x26214),f624(x26212,x26213,x26214)) % 188.18/188.28 [2622]~E(x26221,x26222)+E(f624(x26223,x26221,x26224),f624(x26223,x26222,x26224)) % 188.18/188.28 [2623]~E(x26231,x26232)+E(f624(x26233,x26234,x26231),f624(x26233,x26234,x26232)) % 188.18/188.28 [2624]~E(x26241,x26242)+E(f889(x26241,x26243),f889(x26242,x26243)) % 188.18/188.28 [2625]~E(x26251,x26252)+E(f889(x26253,x26251),f889(x26253,x26252)) % 188.18/188.28 [2626]~E(x26261,x26262)+E(f805(x26261,x26263,x26264,x26265,x26266,x26267,x26268),f805(x26262,x26263,x26264,x26265,x26266,x26267,x26268)) % 188.18/188.28 [2627]~E(x26271,x26272)+E(f805(x26273,x26271,x26274,x26275,x26276,x26277,x26278),f805(x26273,x26272,x26274,x26275,x26276,x26277,x26278)) % 188.18/188.28 [2628]~E(x26281,x26282)+E(f805(x26283,x26284,x26281,x26285,x26286,x26287,x26288),f805(x26283,x26284,x26282,x26285,x26286,x26287,x26288)) % 188.18/188.28 [2629]~E(x26291,x26292)+E(f805(x26293,x26294,x26295,x26291,x26296,x26297,x26298),f805(x26293,x26294,x26295,x26292,x26296,x26297,x26298)) % 188.18/188.28 [2630]~E(x26301,x26302)+E(f805(x26303,x26304,x26305,x26306,x26301,x26307,x26308),f805(x26303,x26304,x26305,x26306,x26302,x26307,x26308)) % 188.18/188.28 [2631]~E(x26311,x26312)+E(f805(x26313,x26314,x26315,x26316,x26317,x26311,x26318),f805(x26313,x26314,x26315,x26316,x26317,x26312,x26318)) % 188.18/188.28 [2632]~E(x26321,x26322)+E(f805(x26323,x26324,x26325,x26326,x26327,x26328,x26321),f805(x26323,x26324,x26325,x26326,x26327,x26328,x26322)) % 188.18/188.28 [2633]~E(x26331,x26332)+E(f583(x26331,x26333),f583(x26332,x26333)) % 188.18/188.28 [2634]~E(x26341,x26342)+E(f583(x26343,x26341),f583(x26343,x26342)) % 188.18/188.28 [2635]~E(x26351,x26352)+E(f19(x26351,x26353,x26354,x26355),f19(x26352,x26353,x26354,x26355)) % 188.18/188.28 [2636]~E(x26361,x26362)+E(f19(x26363,x26361,x26364,x26365),f19(x26363,x26362,x26364,x26365)) % 188.18/188.28 [2637]~E(x26371,x26372)+E(f19(x26373,x26374,x26371,x26375),f19(x26373,x26374,x26372,x26375)) % 188.18/188.28 [2638]~E(x26381,x26382)+E(f19(x26383,x26384,x26385,x26381),f19(x26383,x26384,x26385,x26382)) % 188.18/188.28 [2639]~E(x26391,x26392)+E(f534(x26391,x26393),f534(x26392,x26393)) % 188.18/188.28 [2640]~E(x26401,x26402)+E(f534(x26403,x26401),f534(x26403,x26402)) % 188.18/188.28 [2641]~E(x26411,x26412)+E(f756(x26411,x26413,x26414,x26415,x26416),f756(x26412,x26413,x26414,x26415,x26416)) % 188.18/188.28 [2642]~E(x26421,x26422)+E(f756(x26423,x26421,x26424,x26425,x26426),f756(x26423,x26422,x26424,x26425,x26426)) % 188.18/188.28 [2643]~E(x26431,x26432)+E(f756(x26433,x26434,x26431,x26435,x26436),f756(x26433,x26434,x26432,x26435,x26436)) % 188.18/188.28 [2644]~E(x26441,x26442)+E(f756(x26443,x26444,x26445,x26441,x26446),f756(x26443,x26444,x26445,x26442,x26446)) % 188.18/188.28 [2645]~E(x26451,x26452)+E(f756(x26453,x26454,x26455,x26456,x26451),f756(x26453,x26454,x26455,x26456,x26452)) % 188.18/188.28 [2646]~E(x26461,x26462)+E(f207(x26461,x26463,x26464,x26465),f207(x26462,x26463,x26464,x26465)) % 188.18/188.28 [2647]~E(x26471,x26472)+E(f207(x26473,x26471,x26474,x26475),f207(x26473,x26472,x26474,x26475)) % 188.18/188.28 [2648]~E(x26481,x26482)+E(f207(x26483,x26484,x26481,x26485),f207(x26483,x26484,x26482,x26485)) % 188.18/188.28 [2649]~E(x26491,x26492)+E(f207(x26493,x26494,x26495,x26491),f207(x26493,x26494,x26495,x26492)) % 188.18/188.28 [2650]~E(x26501,x26502)+E(f671(x26501,x26503,x26504),f671(x26502,x26503,x26504)) % 188.18/188.28 [2651]~E(x26511,x26512)+E(f671(x26513,x26511,x26514),f671(x26513,x26512,x26514)) % 188.18/188.28 [2652]~E(x26521,x26522)+E(f671(x26523,x26524,x26521),f671(x26523,x26524,x26522)) % 188.18/188.28 [2653]~E(x26531,x26532)+E(f559(x26531,x26533,x26534,x26535,x26536),f559(x26532,x26533,x26534,x26535,x26536)) % 188.18/188.28 [2654]~E(x26541,x26542)+E(f559(x26543,x26541,x26544,x26545,x26546),f559(x26543,x26542,x26544,x26545,x26546)) % 188.18/188.28 [2655]~E(x26551,x26552)+E(f559(x26553,x26554,x26551,x26555,x26556),f559(x26553,x26554,x26552,x26555,x26556)) % 188.18/188.28 [2656]~E(x26561,x26562)+E(f559(x26563,x26564,x26565,x26561,x26566),f559(x26563,x26564,x26565,x26562,x26566)) % 188.18/188.28 [2657]~E(x26571,x26572)+E(f559(x26573,x26574,x26575,x26576,x26571),f559(x26573,x26574,x26575,x26576,x26572)) % 188.18/188.28 [2658]~E(x26581,x26582)+E(f898(x26581,x26583),f898(x26582,x26583)) % 188.18/188.28 [2659]~E(x26591,x26592)+E(f898(x26593,x26591),f898(x26593,x26592)) % 188.18/188.28 [2660]~E(x26601,x26602)+E(f865(x26601,x26603,x26604,x26605,x26606,x26607),f865(x26602,x26603,x26604,x26605,x26606,x26607)) % 188.18/188.28 [2661]~E(x26611,x26612)+E(f865(x26613,x26611,x26614,x26615,x26616,x26617),f865(x26613,x26612,x26614,x26615,x26616,x26617)) % 188.18/188.28 [2662]~E(x26621,x26622)+E(f865(x26623,x26624,x26621,x26625,x26626,x26627),f865(x26623,x26624,x26622,x26625,x26626,x26627)) % 188.18/188.28 [2663]~E(x26631,x26632)+E(f865(x26633,x26634,x26635,x26631,x26636,x26637),f865(x26633,x26634,x26635,x26632,x26636,x26637)) % 188.18/188.28 [2664]~E(x26641,x26642)+E(f865(x26643,x26644,x26645,x26646,x26641,x26647),f865(x26643,x26644,x26645,x26646,x26642,x26647)) % 188.18/188.28 [2665]~E(x26651,x26652)+E(f865(x26653,x26654,x26655,x26656,x26657,x26651),f865(x26653,x26654,x26655,x26656,x26657,x26652)) % 188.18/188.28 [2666]~E(x26661,x26662)+E(f629(x26661,x26663,x26664),f629(x26662,x26663,x26664)) % 188.18/188.28 [2667]~E(x26671,x26672)+E(f629(x26673,x26671,x26674),f629(x26673,x26672,x26674)) % 188.18/188.28 [2668]~E(x26681,x26682)+E(f629(x26683,x26684,x26681),f629(x26683,x26684,x26682)) % 188.18/188.28 [2669]~E(x26691,x26692)+E(f219(x26691,x26693,x26694,x26695),f219(x26692,x26693,x26694,x26695)) % 188.18/188.28 [2670]~E(x26701,x26702)+E(f219(x26703,x26701,x26704,x26705),f219(x26703,x26702,x26704,x26705)) % 188.18/188.28 [2671]~E(x26711,x26712)+E(f219(x26713,x26714,x26711,x26715),f219(x26713,x26714,x26712,x26715)) % 188.18/188.28 [2672]~E(x26721,x26722)+E(f219(x26723,x26724,x26725,x26721),f219(x26723,x26724,x26725,x26722)) % 188.18/188.28 [2673]~E(x26731,x26732)+E(f701(x26731,x26733,x26734,x26735),f701(x26732,x26733,x26734,x26735)) % 188.18/188.28 [2674]~E(x26741,x26742)+E(f701(x26743,x26741,x26744,x26745),f701(x26743,x26742,x26744,x26745)) % 188.18/188.28 [2675]~E(x26751,x26752)+E(f701(x26753,x26754,x26751,x26755),f701(x26753,x26754,x26752,x26755)) % 188.18/188.28 [2676]~E(x26761,x26762)+E(f701(x26763,x26764,x26765,x26761),f701(x26763,x26764,x26765,x26762)) % 188.18/188.28 [2677]~E(x26771,x26772)+E(f204(x26771,x26773),f204(x26772,x26773)) % 188.18/188.28 [2678]~E(x26781,x26782)+E(f204(x26783,x26781),f204(x26783,x26782)) % 188.18/188.28 [2679]~E(x26791,x26792)+E(f450(x26791,x26793,x26794,x26795),f450(x26792,x26793,x26794,x26795)) % 188.18/188.28 [2680]~E(x26801,x26802)+E(f450(x26803,x26801,x26804,x26805),f450(x26803,x26802,x26804,x26805)) % 188.18/188.28 [2681]~E(x26811,x26812)+E(f450(x26813,x26814,x26811,x26815),f450(x26813,x26814,x26812,x26815)) % 188.18/188.28 [2682]~E(x26821,x26822)+E(f450(x26823,x26824,x26825,x26821),f450(x26823,x26824,x26825,x26822)) % 188.18/188.28 [2683]~E(x26831,x26832)+E(f817(x26831),f817(x26832)) % 188.18/188.28 [2684]~E(x26841,x26842)+E(f698(x26841,x26843,x26844,x26845),f698(x26842,x26843,x26844,x26845)) % 188.18/188.28 [2685]~E(x26851,x26852)+E(f698(x26853,x26851,x26854,x26855),f698(x26853,x26852,x26854,x26855)) % 188.18/188.28 [2686]~E(x26861,x26862)+E(f698(x26863,x26864,x26861,x26865),f698(x26863,x26864,x26862,x26865)) % 188.18/188.28 [2687]~E(x26871,x26872)+E(f698(x26873,x26874,x26875,x26871),f698(x26873,x26874,x26875,x26872)) % 188.18/188.28 [2688]~E(x26881,x26882)+E(f890(x26881,x26883),f890(x26882,x26883)) % 188.18/188.28 [2689]~E(x26891,x26892)+E(f890(x26893,x26891),f890(x26893,x26892)) % 188.18/188.28 [2690]~E(x26901,x26902)+E(f521(x26901,x26903,x26904),f521(x26902,x26903,x26904)) % 188.18/188.28 [2691]~E(x26911,x26912)+E(f521(x26913,x26911,x26914),f521(x26913,x26912,x26914)) % 188.18/188.28 [2692]~E(x26921,x26922)+E(f521(x26923,x26924,x26921),f521(x26923,x26924,x26922)) % 188.18/188.28 [2693]~E(x26931,x26932)+E(f808(x26931,x26933),f808(x26932,x26933)) % 188.18/188.28 [2694]~E(x26941,x26942)+E(f808(x26943,x26941),f808(x26943,x26942)) % 188.18/188.28 [2695]~E(x26951,x26952)+E(f36(x26951,x26953,x26954,x26955),f36(x26952,x26953,x26954,x26955)) % 188.18/188.28 [2696]~E(x26961,x26962)+E(f36(x26963,x26961,x26964,x26965),f36(x26963,x26962,x26964,x26965)) % 188.18/188.28 [2697]~E(x26971,x26972)+E(f36(x26973,x26974,x26971,x26975),f36(x26973,x26974,x26972,x26975)) % 188.18/188.28 [2698]~E(x26981,x26982)+E(f36(x26983,x26984,x26985,x26981),f36(x26983,x26984,x26985,x26982)) % 188.18/188.28 [2699]~E(x26991,x26992)+E(f21(x26991,x26993),f21(x26992,x26993)) % 188.18/188.28 [2700]~E(x27001,x27002)+E(f21(x27003,x27001),f21(x27003,x27002)) % 188.18/188.28 [2701]~E(x27011,x27012)+E(f502(x27011,x27013,x27014,x27015,x27016),f502(x27012,x27013,x27014,x27015,x27016)) % 188.18/188.28 [2702]~E(x27021,x27022)+E(f502(x27023,x27021,x27024,x27025,x27026),f502(x27023,x27022,x27024,x27025,x27026)) % 188.18/188.28 [2703]~E(x27031,x27032)+E(f502(x27033,x27034,x27031,x27035,x27036),f502(x27033,x27034,x27032,x27035,x27036)) % 188.18/188.28 [2704]~E(x27041,x27042)+E(f502(x27043,x27044,x27045,x27041,x27046),f502(x27043,x27044,x27045,x27042,x27046)) % 188.18/188.28 [2705]~E(x27051,x27052)+E(f502(x27053,x27054,x27055,x27056,x27051),f502(x27053,x27054,x27055,x27056,x27052)) % 188.18/188.28 [2706]~E(x27061,x27062)+E(f722(x27061,x27063),f722(x27062,x27063)) % 188.18/188.28 [2707]~E(x27071,x27072)+E(f722(x27073,x27071),f722(x27073,x27072)) % 188.18/188.28 [2708]~E(x27081,x27082)+E(f776(x27081,x27083,x27084),f776(x27082,x27083,x27084)) % 188.18/188.28 [2709]~E(x27091,x27092)+E(f776(x27093,x27091,x27094),f776(x27093,x27092,x27094)) % 188.18/188.28 [2710]~E(x27101,x27102)+E(f776(x27103,x27104,x27101),f776(x27103,x27104,x27102)) % 188.18/188.28 [2711]~E(x27111,x27112)+E(f360(x27111,x27113,x27114),f360(x27112,x27113,x27114)) % 188.18/188.28 [2712]~E(x27121,x27122)+E(f360(x27123,x27121,x27124),f360(x27123,x27122,x27124)) % 188.18/188.28 [2713]~E(x27131,x27132)+E(f360(x27133,x27134,x27131),f360(x27133,x27134,x27132)) % 188.18/188.28 [2714]~E(x27141,x27142)+E(f680(x27141,x27143),f680(x27142,x27143)) % 188.18/188.28 [2715]~E(x27151,x27152)+E(f680(x27153,x27151),f680(x27153,x27152)) % 188.18/188.28 [2716]~E(x27161,x27162)+E(f79(x27161,x27163),f79(x27162,x27163)) % 188.18/188.28 [2717]~E(x27171,x27172)+E(f79(x27173,x27171),f79(x27173,x27172)) % 188.18/188.28 [2718]~E(x27181,x27182)+E(f702(x27181,x27183,x27184,x27185,x27186),f702(x27182,x27183,x27184,x27185,x27186)) % 188.18/188.28 [2719]~E(x27191,x27192)+E(f702(x27193,x27191,x27194,x27195,x27196),f702(x27193,x27192,x27194,x27195,x27196)) % 188.18/188.28 [2720]~E(x27201,x27202)+E(f702(x27203,x27204,x27201,x27205,x27206),f702(x27203,x27204,x27202,x27205,x27206)) % 188.18/188.28 [2721]~E(x27211,x27212)+E(f702(x27213,x27214,x27215,x27211,x27216),f702(x27213,x27214,x27215,x27212,x27216)) % 188.18/188.28 [2722]~E(x27221,x27222)+E(f702(x27223,x27224,x27225,x27226,x27221),f702(x27223,x27224,x27225,x27226,x27222)) % 188.18/188.28 [2723]~E(x27231,x27232)+E(f17(x27231,x27233,x27234,x27235),f17(x27232,x27233,x27234,x27235)) % 188.18/188.28 [2724]~E(x27241,x27242)+E(f17(x27243,x27241,x27244,x27245),f17(x27243,x27242,x27244,x27245)) % 188.18/188.28 [2725]~E(x27251,x27252)+E(f17(x27253,x27254,x27251,x27255),f17(x27253,x27254,x27252,x27255)) % 188.18/188.28 [2726]~E(x27261,x27262)+E(f17(x27263,x27264,x27265,x27261),f17(x27263,x27264,x27265,x27262)) % 188.18/188.28 [2727]~E(x27271,x27272)+E(f506(x27271,x27273,x27274,x27275,x27276),f506(x27272,x27273,x27274,x27275,x27276)) % 188.18/188.28 [2728]~E(x27281,x27282)+E(f506(x27283,x27281,x27284,x27285,x27286),f506(x27283,x27282,x27284,x27285,x27286)) % 188.18/188.28 [2729]~E(x27291,x27292)+E(f506(x27293,x27294,x27291,x27295,x27296),f506(x27293,x27294,x27292,x27295,x27296)) % 188.18/188.28 [2730]~E(x27301,x27302)+E(f506(x27303,x27304,x27305,x27301,x27306),f506(x27303,x27304,x27305,x27302,x27306)) % 188.18/188.28 [2731]~E(x27311,x27312)+E(f506(x27313,x27314,x27315,x27316,x27311),f506(x27313,x27314,x27315,x27316,x27312)) % 188.18/188.28 [2732]~E(x27321,x27322)+E(f637(x27321,x27323,x27324,x27325,x27326),f637(x27322,x27323,x27324,x27325,x27326)) % 188.18/188.28 [2733]~E(x27331,x27332)+E(f637(x27333,x27331,x27334,x27335,x27336),f637(x27333,x27332,x27334,x27335,x27336)) % 188.18/188.28 [2734]~E(x27341,x27342)+E(f637(x27343,x27344,x27341,x27345,x27346),f637(x27343,x27344,x27342,x27345,x27346)) % 188.18/188.28 [2735]~E(x27351,x27352)+E(f637(x27353,x27354,x27355,x27351,x27356),f637(x27353,x27354,x27355,x27352,x27356)) % 188.18/188.28 [2736]~E(x27361,x27362)+E(f637(x27363,x27364,x27365,x27366,x27361),f637(x27363,x27364,x27365,x27366,x27362)) % 188.18/188.28 [2737]~E(x27371,x27372)+E(f663(x27371,x27373),f663(x27372,x27373)) % 188.18/188.28 [2738]~E(x27381,x27382)+E(f663(x27383,x27381),f663(x27383,x27382)) % 188.18/188.28 [2739]~E(x27391,x27392)+E(f560(x27391,x27393,x27394,x27395,x27396),f560(x27392,x27393,x27394,x27395,x27396)) % 188.18/188.28 [2740]~E(x27401,x27402)+E(f560(x27403,x27401,x27404,x27405,x27406),f560(x27403,x27402,x27404,x27405,x27406)) % 188.18/188.28 [2741]~E(x27411,x27412)+E(f560(x27413,x27414,x27411,x27415,x27416),f560(x27413,x27414,x27412,x27415,x27416)) % 188.18/188.28 [2742]~E(x27421,x27422)+E(f560(x27423,x27424,x27425,x27421,x27426),f560(x27423,x27424,x27425,x27422,x27426)) % 188.18/188.28 [2743]~E(x27431,x27432)+E(f560(x27433,x27434,x27435,x27436,x27431),f560(x27433,x27434,x27435,x27436,x27432)) % 188.18/188.28 [2744]~E(x27441,x27442)+E(f348(x27441,x27443),f348(x27442,x27443)) % 188.18/188.28 [2745]~E(x27451,x27452)+E(f348(x27453,x27451),f348(x27453,x27452)) % 188.18/188.28 [2746]~E(x27461,x27462)+E(f268(x27461,x27463,x27464,x27465,x27466),f268(x27462,x27463,x27464,x27465,x27466)) % 188.18/188.28 [2747]~E(x27471,x27472)+E(f268(x27473,x27471,x27474,x27475,x27476),f268(x27473,x27472,x27474,x27475,x27476)) % 188.18/188.28 [2748]~E(x27481,x27482)+E(f268(x27483,x27484,x27481,x27485,x27486),f268(x27483,x27484,x27482,x27485,x27486)) % 188.18/188.28 [2749]~E(x27491,x27492)+E(f268(x27493,x27494,x27495,x27491,x27496),f268(x27493,x27494,x27495,x27492,x27496)) % 188.18/188.28 [2750]~E(x27501,x27502)+E(f268(x27503,x27504,x27505,x27506,x27501),f268(x27503,x27504,x27505,x27506,x27502)) % 188.18/188.28 [2751]~E(x27511,x27512)+E(f342(x27511,x27513,x27514),f342(x27512,x27513,x27514)) % 188.18/188.28 [2752]~E(x27521,x27522)+E(f342(x27523,x27521,x27524),f342(x27523,x27522,x27524)) % 188.18/188.28 [2753]~E(x27531,x27532)+E(f342(x27533,x27534,x27531),f342(x27533,x27534,x27532)) % 188.18/188.28 [2754]~E(x27541,x27542)+E(f501(x27541,x27543,x27544),f501(x27542,x27543,x27544)) % 188.18/188.28 [2755]~E(x27551,x27552)+E(f501(x27553,x27551,x27554),f501(x27553,x27552,x27554)) % 188.18/188.28 [2756]~E(x27561,x27562)+E(f501(x27563,x27564,x27561),f501(x27563,x27564,x27562)) % 188.18/188.28 [2757]~E(x27571,x27572)+E(f755(x27571,x27573,x27574,x27575,x27576),f755(x27572,x27573,x27574,x27575,x27576)) % 188.18/188.28 [2758]~E(x27581,x27582)+E(f755(x27583,x27581,x27584,x27585,x27586),f755(x27583,x27582,x27584,x27585,x27586)) % 188.18/188.28 [2759]~E(x27591,x27592)+E(f755(x27593,x27594,x27591,x27595,x27596),f755(x27593,x27594,x27592,x27595,x27596)) % 188.18/188.28 [2760]~E(x27601,x27602)+E(f755(x27603,x27604,x27605,x27601,x27606),f755(x27603,x27604,x27605,x27602,x27606)) % 188.18/188.28 [2761]~E(x27611,x27612)+E(f755(x27613,x27614,x27615,x27616,x27611),f755(x27613,x27614,x27615,x27616,x27612)) % 188.18/188.28 [2762]~E(x27621,x27622)+E(f603(x27621,x27623,x27624),f603(x27622,x27623,x27624)) % 188.18/188.28 [2763]~E(x27631,x27632)+E(f603(x27633,x27631,x27634),f603(x27633,x27632,x27634)) % 188.18/188.28 [2764]~E(x27641,x27642)+E(f603(x27643,x27644,x27641),f603(x27643,x27644,x27642)) % 188.18/188.28 [2765]~E(x27651,x27652)+E(f235(x27651,x27653,x27654,x27655,x27656),f235(x27652,x27653,x27654,x27655,x27656)) % 188.18/188.28 [2766]~E(x27661,x27662)+E(f235(x27663,x27661,x27664,x27665,x27666),f235(x27663,x27662,x27664,x27665,x27666)) % 188.18/188.28 [2767]~E(x27671,x27672)+E(f235(x27673,x27674,x27671,x27675,x27676),f235(x27673,x27674,x27672,x27675,x27676)) % 188.18/188.28 [2768]~E(x27681,x27682)+E(f235(x27683,x27684,x27685,x27681,x27686),f235(x27683,x27684,x27685,x27682,x27686)) % 188.18/188.28 [2769]~E(x27691,x27692)+E(f235(x27693,x27694,x27695,x27696,x27691),f235(x27693,x27694,x27695,x27696,x27692)) % 188.18/188.28 [2770]~E(x27701,x27702)+E(f507(x27701,x27703,x27704,x27705,x27706),f507(x27702,x27703,x27704,x27705,x27706)) % 188.18/188.28 [2771]~E(x27711,x27712)+E(f507(x27713,x27711,x27714,x27715,x27716),f507(x27713,x27712,x27714,x27715,x27716)) % 188.18/188.28 [2772]~E(x27721,x27722)+E(f507(x27723,x27724,x27721,x27725,x27726),f507(x27723,x27724,x27722,x27725,x27726)) % 188.18/188.28 [2773]~E(x27731,x27732)+E(f507(x27733,x27734,x27735,x27731,x27736),f507(x27733,x27734,x27735,x27732,x27736)) % 188.18/188.28 [2774]~E(x27741,x27742)+E(f507(x27743,x27744,x27745,x27746,x27741),f507(x27743,x27744,x27745,x27746,x27742)) % 188.18/188.28 [2775]~E(x27751,x27752)+E(f299(x27751,x27753,x27754),f299(x27752,x27753,x27754)) % 188.18/188.28 [2776]~E(x27761,x27762)+E(f299(x27763,x27761,x27764),f299(x27763,x27762,x27764)) % 188.18/188.28 [2777]~E(x27771,x27772)+E(f299(x27773,x27774,x27771),f299(x27773,x27774,x27772)) % 188.18/188.28 [2778]~E(x27781,x27782)+E(f675(x27781,x27783,x27784,x27785,x27786),f675(x27782,x27783,x27784,x27785,x27786)) % 188.18/188.28 [2779]~E(x27791,x27792)+E(f675(x27793,x27791,x27794,x27795,x27796),f675(x27793,x27792,x27794,x27795,x27796)) % 188.18/188.28 [2780]~E(x27801,x27802)+E(f675(x27803,x27804,x27801,x27805,x27806),f675(x27803,x27804,x27802,x27805,x27806)) % 188.18/188.28 [2781]~E(x27811,x27812)+E(f675(x27813,x27814,x27815,x27811,x27816),f675(x27813,x27814,x27815,x27812,x27816)) % 188.18/188.28 [2782]~E(x27821,x27822)+E(f675(x27823,x27824,x27825,x27826,x27821),f675(x27823,x27824,x27825,x27826,x27822)) % 188.18/188.28 [2783]~E(x27831,x27832)+E(f847(x27831,x27833,x27834,x27835,x27836),f847(x27832,x27833,x27834,x27835,x27836)) % 188.18/188.28 [2784]~E(x27841,x27842)+E(f847(x27843,x27841,x27844,x27845,x27846),f847(x27843,x27842,x27844,x27845,x27846)) % 188.18/188.28 [2785]~E(x27851,x27852)+E(f847(x27853,x27854,x27851,x27855,x27856),f847(x27853,x27854,x27852,x27855,x27856)) % 188.18/188.28 [2786]~E(x27861,x27862)+E(f847(x27863,x27864,x27865,x27861,x27866),f847(x27863,x27864,x27865,x27862,x27866)) % 188.18/188.28 [2787]~E(x27871,x27872)+E(f847(x27873,x27874,x27875,x27876,x27871),f847(x27873,x27874,x27875,x27876,x27872)) % 188.18/188.28 [2788]~E(x27881,x27882)+E(f896(x27881),f896(x27882)) % 188.18/188.28 [2789]~E(x27891,x27892)+E(f409(x27891,x27893,x27894,x27895,x27896),f409(x27892,x27893,x27894,x27895,x27896)) % 188.18/188.28 [2790]~E(x27901,x27902)+E(f409(x27903,x27901,x27904,x27905,x27906),f409(x27903,x27902,x27904,x27905,x27906)) % 188.18/188.28 [2791]~E(x27911,x27912)+E(f409(x27913,x27914,x27911,x27915,x27916),f409(x27913,x27914,x27912,x27915,x27916)) % 188.18/188.28 [2792]~E(x27921,x27922)+E(f409(x27923,x27924,x27925,x27921,x27926),f409(x27923,x27924,x27925,x27922,x27926)) % 188.18/188.28 [2793]~E(x27931,x27932)+E(f409(x27933,x27934,x27935,x27936,x27931),f409(x27933,x27934,x27935,x27936,x27932)) % 188.18/188.28 [2794]~E(x27941,x27942)+E(f376(x27941,x27943),f376(x27942,x27943)) % 188.18/188.28 [2795]~E(x27951,x27952)+E(f376(x27953,x27951),f376(x27953,x27952)) % 188.18/188.28 [2796]~E(x27961,x27962)+E(f361(x27961,x27963,x27964),f361(x27962,x27963,x27964)) % 188.18/188.28 [2797]~E(x27971,x27972)+E(f361(x27973,x27971,x27974),f361(x27973,x27972,x27974)) % 188.18/188.28 [2798]~E(x27981,x27982)+E(f361(x27983,x27984,x27981),f361(x27983,x27984,x27982)) % 188.18/188.28 [2799]~E(x27991,x27992)+E(f504(x27991,x27993,x27994,x27995,x27996),f504(x27992,x27993,x27994,x27995,x27996)) % 188.18/188.28 [2800]~E(x28001,x28002)+E(f504(x28003,x28001,x28004,x28005,x28006),f504(x28003,x28002,x28004,x28005,x28006)) % 188.18/188.28 [2801]~E(x28011,x28012)+E(f504(x28013,x28014,x28011,x28015,x28016),f504(x28013,x28014,x28012,x28015,x28016)) % 188.18/188.28 [2802]~E(x28021,x28022)+E(f504(x28023,x28024,x28025,x28021,x28026),f504(x28023,x28024,x28025,x28022,x28026)) % 188.18/188.28 [2803]~E(x28031,x28032)+E(f504(x28033,x28034,x28035,x28036,x28031),f504(x28033,x28034,x28035,x28036,x28032)) % 188.18/188.28 [2804]~E(x28041,x28042)+E(f825(x28041,x28043),f825(x28042,x28043)) % 188.18/188.28 [2805]~E(x28051,x28052)+E(f825(x28053,x28051),f825(x28053,x28052)) % 188.18/188.28 [2806]~E(x28061,x28062)+E(f916(x28061,x28063,x28064),f916(x28062,x28063,x28064)) % 188.18/188.28 [2807]~E(x28071,x28072)+E(f916(x28073,x28071,x28074),f916(x28073,x28072,x28074)) % 188.18/188.28 [2808]~E(x28081,x28082)+E(f916(x28083,x28084,x28081),f916(x28083,x28084,x28082)) % 188.18/188.28 [2809]~E(x28091,x28092)+E(f855(x28091,x28093,x28094,x28095,x28096,x28097,x28098,x28099),f855(x28092,x28093,x28094,x28095,x28096,x28097,x28098,x28099)) % 188.18/188.28 [2810]~E(x28101,x28102)+E(f855(x28103,x28101,x28104,x28105,x28106,x28107,x28108,x28109),f855(x28103,x28102,x28104,x28105,x28106,x28107,x28108,x28109)) % 188.18/188.28 [2811]~E(x28111,x28112)+E(f855(x28113,x28114,x28111,x28115,x28116,x28117,x28118,x28119),f855(x28113,x28114,x28112,x28115,x28116,x28117,x28118,x28119)) % 188.18/188.28 [2812]~E(x28121,x28122)+E(f855(x28123,x28124,x28125,x28121,x28126,x28127,x28128,x28129),f855(x28123,x28124,x28125,x28122,x28126,x28127,x28128,x28129)) % 188.18/188.28 [2813]~E(x28131,x28132)+E(f855(x28133,x28134,x28135,x28136,x28131,x28137,x28138,x28139),f855(x28133,x28134,x28135,x28136,x28132,x28137,x28138,x28139)) % 188.18/188.28 [2814]~E(x28141,x28142)+E(f855(x28143,x28144,x28145,x28146,x28147,x28141,x28148,x28149),f855(x28143,x28144,x28145,x28146,x28147,x28142,x28148,x28149)) % 188.18/188.28 [2815]~E(x28151,x28152)+E(f855(x28153,x28154,x28155,x28156,x28157,x28158,x28151,x28159),f855(x28153,x28154,x28155,x28156,x28157,x28158,x28152,x28159)) % 188.18/188.28 [2816]~E(x28161,x28162)+E(f855(x28163,x28164,x28165,x28166,x28167,x28168,x28169,x28161),f855(x28163,x28164,x28165,x28166,x28167,x28168,x28169,x28162)) % 188.18/188.28 [2817]~E(x28171,x28172)+E(f662(x28171,x28173,x28174),f662(x28172,x28173,x28174)) % 188.18/188.28 [2818]~E(x28181,x28182)+E(f662(x28183,x28181,x28184),f662(x28183,x28182,x28184)) % 188.18/188.28 [2819]~E(x28191,x28192)+E(f662(x28193,x28194,x28191),f662(x28193,x28194,x28192)) % 188.18/188.28 [2820]~E(x28201,x28202)+E(f625(x28201,x28203),f625(x28202,x28203)) % 188.18/188.28 [2821]~E(x28211,x28212)+E(f625(x28213,x28211),f625(x28213,x28212)) % 188.18/188.28 [2822]~E(x28221,x28222)+E(f807(x28221),f807(x28222)) % 188.18/188.28 [2823]~E(x28231,x28232)+E(f630(x28231,x28233),f630(x28232,x28233)) % 188.18/188.28 [2824]~E(x28241,x28242)+E(f630(x28243,x28241),f630(x28243,x28242)) % 188.18/188.28 [2825]~E(x28251,x28252)+E(f209(x28251),f209(x28252)) % 188.18/188.28 [2826]~E(x28261,x28262)+E(f244(x28261,x28263),f244(x28262,x28263)) % 188.18/188.28 [2827]~E(x28271,x28272)+E(f244(x28273,x28271),f244(x28273,x28272)) % 188.18/188.28 [2828]~E(x28281,x28282)+E(f705(x28281,x28283,x28284),f705(x28282,x28283,x28284)) % 188.18/188.28 [2829]~E(x28291,x28292)+E(f705(x28293,x28291,x28294),f705(x28293,x28292,x28294)) % 188.18/188.28 [2830]~E(x28301,x28302)+E(f705(x28303,x28304,x28301),f705(x28303,x28304,x28302)) % 188.18/188.28 [2831]~E(x28311,x28312)+E(f575(x28311,x28313,x28314,x28315,x28316,x28317),f575(x28312,x28313,x28314,x28315,x28316,x28317)) % 188.18/188.28 [2832]~E(x28321,x28322)+E(f575(x28323,x28321,x28324,x28325,x28326,x28327),f575(x28323,x28322,x28324,x28325,x28326,x28327)) % 188.18/188.28 [2833]~E(x28331,x28332)+E(f575(x28333,x28334,x28331,x28335,x28336,x28337),f575(x28333,x28334,x28332,x28335,x28336,x28337)) % 188.18/188.28 [2834]~E(x28341,x28342)+E(f575(x28343,x28344,x28345,x28341,x28346,x28347),f575(x28343,x28344,x28345,x28342,x28346,x28347)) % 188.18/188.28 [2835]~E(x28351,x28352)+E(f575(x28353,x28354,x28355,x28356,x28351,x28357),f575(x28353,x28354,x28355,x28356,x28352,x28357)) % 188.18/188.28 [2836]~E(x28361,x28362)+E(f575(x28363,x28364,x28365,x28366,x28367,x28361),f575(x28363,x28364,x28365,x28366,x28367,x28362)) % 188.18/188.28 [2837]~E(x28371,x28372)+E(f273(x28371,x28373,x28374),f273(x28372,x28373,x28374)) % 188.18/188.28 [2838]~E(x28381,x28382)+E(f273(x28383,x28381,x28384),f273(x28383,x28382,x28384)) % 188.18/188.28 [2839]~E(x28391,x28392)+E(f273(x28393,x28394,x28391),f273(x28393,x28394,x28392)) % 188.18/188.28 [2840]~E(x28401,x28402)+E(f254(x28401,x28403,x28404,x28405,x28406,x28407),f254(x28402,x28403,x28404,x28405,x28406,x28407)) % 188.18/188.28 [2841]~E(x28411,x28412)+E(f254(x28413,x28411,x28414,x28415,x28416,x28417),f254(x28413,x28412,x28414,x28415,x28416,x28417)) % 188.18/188.28 [2842]~E(x28421,x28422)+E(f254(x28423,x28424,x28421,x28425,x28426,x28427),f254(x28423,x28424,x28422,x28425,x28426,x28427)) % 188.18/188.28 [2843]~E(x28431,x28432)+E(f254(x28433,x28434,x28435,x28431,x28436,x28437),f254(x28433,x28434,x28435,x28432,x28436,x28437)) % 188.18/188.28 [2844]~E(x28441,x28442)+E(f254(x28443,x28444,x28445,x28446,x28441,x28447),f254(x28443,x28444,x28445,x28446,x28442,x28447)) % 188.18/188.28 [2845]~E(x28451,x28452)+E(f254(x28453,x28454,x28455,x28456,x28457,x28451),f254(x28453,x28454,x28455,x28456,x28457,x28452)) % 188.18/188.28 [2846]~E(x28461,x28462)+E(f798(x28461,x28463),f798(x28462,x28463)) % 188.18/188.28 [2847]~E(x28471,x28472)+E(f798(x28473,x28471),f798(x28473,x28472)) % 188.18/188.28 [2848]~E(x28481,x28482)+E(f492(x28481,x28483),f492(x28482,x28483)) % 188.18/188.28 [2849]~E(x28491,x28492)+E(f492(x28493,x28491),f492(x28493,x28492)) % 188.18/188.28 [2850]~E(x28501,x28502)+E(f704(x28501,x28503,x28504),f704(x28502,x28503,x28504)) % 188.18/188.28 [2851]~E(x28511,x28512)+E(f704(x28513,x28511,x28514),f704(x28513,x28512,x28514)) % 188.18/188.28 [2852]~E(x28521,x28522)+E(f704(x28523,x28524,x28521),f704(x28523,x28524,x28522)) % 188.18/188.28 [2853]~E(x28531,x28532)+E(f546(x28531,x28533,x28534,x28535),f546(x28532,x28533,x28534,x28535)) % 188.18/188.28 [2854]~E(x28541,x28542)+E(f546(x28543,x28541,x28544,x28545),f546(x28543,x28542,x28544,x28545)) % 188.18/188.28 [2855]~E(x28551,x28552)+E(f546(x28553,x28554,x28551,x28555),f546(x28553,x28554,x28552,x28555)) % 188.18/188.28 [2856]~E(x28561,x28562)+E(f546(x28563,x28564,x28565,x28561),f546(x28563,x28564,x28565,x28562)) % 188.18/188.28 [2857]~E(x28571,x28572)+E(f415(x28571,x28573,x28574,x28575),f415(x28572,x28573,x28574,x28575)) % 188.18/188.28 [2858]~E(x28581,x28582)+E(f415(x28583,x28581,x28584,x28585),f415(x28583,x28582,x28584,x28585)) % 188.18/188.28 [2859]~E(x28591,x28592)+E(f415(x28593,x28594,x28591,x28595),f415(x28593,x28594,x28592,x28595)) % 188.18/188.28 [2860]~E(x28601,x28602)+E(f415(x28603,x28604,x28605,x28601),f415(x28603,x28604,x28605,x28602)) % 188.18/188.28 [2861]~E(x28611,x28612)+E(f237(x28611,x28613,x28614),f237(x28612,x28613,x28614)) % 188.18/188.28 [2862]~E(x28621,x28622)+E(f237(x28623,x28621,x28624),f237(x28623,x28622,x28624)) % 188.18/188.28 [2863]~E(x28631,x28632)+E(f237(x28633,x28634,x28631),f237(x28633,x28634,x28632)) % 188.18/188.28 [2864]~E(x28641,x28642)+E(f780(x28641,x28643,x28644),f780(x28642,x28643,x28644)) % 188.18/188.28 [2865]~E(x28651,x28652)+E(f780(x28653,x28651,x28654),f780(x28653,x28652,x28654)) % 188.18/188.28 [2866]~E(x28661,x28662)+E(f780(x28663,x28664,x28661),f780(x28663,x28664,x28662)) % 188.18/188.28 [2867]~E(x28671,x28672)+E(f892(x28671,x28673,x28674),f892(x28672,x28673,x28674)) % 188.18/188.28 [2868]~E(x28681,x28682)+E(f892(x28683,x28681,x28684),f892(x28683,x28682,x28684)) % 188.18/188.28 [2869]~E(x28691,x28692)+E(f892(x28693,x28694,x28691),f892(x28693,x28694,x28692)) % 188.18/188.28 [2870]~E(x28701,x28702)+E(f540(x28701,x28703,x28704),f540(x28702,x28703,x28704)) % 188.18/188.28 [2871]~E(x28711,x28712)+E(f540(x28713,x28711,x28714),f540(x28713,x28712,x28714)) % 188.18/188.28 [2872]~E(x28721,x28722)+E(f540(x28723,x28724,x28721),f540(x28723,x28724,x28722)) % 188.18/188.28 [2873]~E(x28731,x28732)+E(f284(x28731,x28733,x28734,x28735),f284(x28732,x28733,x28734,x28735)) % 188.18/188.28 [2874]~E(x28741,x28742)+E(f284(x28743,x28741,x28744,x28745),f284(x28743,x28742,x28744,x28745)) % 188.18/188.28 [2875]~E(x28751,x28752)+E(f284(x28753,x28754,x28751,x28755),f284(x28753,x28754,x28752,x28755)) % 188.18/188.28 [2876]~E(x28761,x28762)+E(f284(x28763,x28764,x28765,x28761),f284(x28763,x28764,x28765,x28762)) % 188.18/188.28 [2877]~P1(x28771)+P1(x28772)+~E(x28771,x28772) % 188.18/188.28 [2878]~P107(x28781)+P107(x28782)+~E(x28781,x28782) % 188.18/188.28 [2879]P14(x28792,x28793,x28794,x28795,x28796,x28797)+~E(x28791,x28792)+~P14(x28791,x28793,x28794,x28795,x28796,x28797) % 188.18/188.28 [2880]P14(x28803,x28802,x28804,x28805,x28806,x28807)+~E(x28801,x28802)+~P14(x28803,x28801,x28804,x28805,x28806,x28807) % 188.18/188.28 [2881]P14(x28813,x28814,x28812,x28815,x28816,x28817)+~E(x28811,x28812)+~P14(x28813,x28814,x28811,x28815,x28816,x28817) % 188.18/188.28 [2882]P14(x28823,x28824,x28825,x28822,x28826,x28827)+~E(x28821,x28822)+~P14(x28823,x28824,x28825,x28821,x28826,x28827) % 188.18/188.28 [2883]P14(x28833,x28834,x28835,x28836,x28832,x28837)+~E(x28831,x28832)+~P14(x28833,x28834,x28835,x28836,x28831,x28837) % 188.18/188.28 [2884]P14(x28843,x28844,x28845,x28846,x28847,x28842)+~E(x28841,x28842)+~P14(x28843,x28844,x28845,x28846,x28847,x28841) % 188.18/188.28 [2885]~P2(x28851)+P2(x28852)+~E(x28851,x28852) % 188.18/188.28 [2886]~P103(x28861)+P103(x28862)+~E(x28861,x28862) % 188.18/188.28 [2887]~P122(x28871)+P122(x28872)+~E(x28871,x28872) % 188.18/188.28 [2888]~P127(x28881)+P127(x28882)+~E(x28881,x28882) % 188.18/188.28 [2889]~P3(x28891)+P3(x28892)+~E(x28891,x28892) % 188.18/188.28 [2890]~P108(x28901)+P108(x28902)+~E(x28901,x28902) % 188.18/188.28 [2891]~P109(x28911)+P109(x28912)+~E(x28911,x28912) % 188.18/188.28 [2892]~P140(x28921)+P140(x28922)+~E(x28921,x28922) % 188.18/188.28 [2893]P15(x28932,x28933)+~E(x28931,x28932)+~P15(x28931,x28933) % 188.18/188.28 [2894]P15(x28943,x28942)+~E(x28941,x28942)+~P15(x28943,x28941) % 188.18/188.28 [2895]~P135(x28951)+P135(x28952)+~E(x28951,x28952) % 188.18/188.28 [2896]~P104(x28961)+P104(x28962)+~E(x28961,x28962) % 188.18/188.28 [2897]~P111(x28971)+P111(x28972)+~E(x28971,x28972) % 188.18/188.28 [2898]~P110(x28981)+P110(x28982)+~E(x28981,x28982) % 188.18/188.28 [2899]P54(x28992,x28993)+~E(x28991,x28992)+~P54(x28991,x28993) % 188.18/188.28 [2900]P54(x29003,x29002)+~E(x29001,x29002)+~P54(x29003,x29001) % 188.18/188.28 [2901]~P79(x29011)+P79(x29012)+~E(x29011,x29012) % 188.18/188.28 [2902]~P68(x29021)+P68(x29022)+~E(x29021,x29022) % 188.18/188.28 [2903]~P66(x29031)+P66(x29032)+~E(x29031,x29032) % 188.18/188.28 [2904]P32(x29042,x29043,x29044)+~E(x29041,x29042)+~P32(x29041,x29043,x29044) % 188.18/188.28 [2905]P32(x29053,x29052,x29054)+~E(x29051,x29052)+~P32(x29053,x29051,x29054) % 188.18/188.28 [2906]P32(x29063,x29064,x29062)+~E(x29061,x29062)+~P32(x29063,x29064,x29061) % 188.18/188.28 [2907]~P65(x29071)+P65(x29072)+~E(x29071,x29072) % 188.18/188.28 [2908]P27(x29082,x29083,x29084,x29085)+~E(x29081,x29082)+~P27(x29081,x29083,x29084,x29085) % 188.18/188.28 [2909]P27(x29093,x29092,x29094,x29095)+~E(x29091,x29092)+~P27(x29093,x29091,x29094,x29095) % 188.18/188.28 [2910]P27(x29103,x29104,x29102,x29105)+~E(x29101,x29102)+~P27(x29103,x29104,x29101,x29105) % 188.18/188.28 [2911]P27(x29113,x29114,x29115,x29112)+~E(x29111,x29112)+~P27(x29113,x29114,x29115,x29111) % 188.18/188.28 [2912]~P112(x29121)+P112(x29122)+~E(x29121,x29122) % 188.18/188.28 [2913]~P147(x29131)+P147(x29132)+~E(x29131,x29132) % 188.18/188.28 [2914]~P83(x29141)+P83(x29142)+~E(x29141,x29142) % 188.18/188.28 [2915]~P76(x29151)+P76(x29152)+~E(x29151,x29152) % 188.18/188.28 [2916]~P69(x29161)+P69(x29162)+~E(x29161,x29162) % 188.18/188.28 [2917]~P91(x29171)+P91(x29172)+~E(x29171,x29172) % 188.18/188.28 [2918]~P70(x29181)+P70(x29182)+~E(x29181,x29182) % 188.18/188.28 [2919]P59(x29192,x29193,x29194)+~E(x29191,x29192)+~P59(x29191,x29193,x29194) % 188.18/188.28 [2920]P59(x29203,x29202,x29204)+~E(x29201,x29202)+~P59(x29203,x29201,x29204) % 188.18/188.28 [2921]P59(x29213,x29214,x29212)+~E(x29211,x29212)+~P59(x29213,x29214,x29211) % 188.18/188.28 [2922]~P5(x29221)+P5(x29222)+~E(x29221,x29222) % 188.18/188.28 [2923]~P113(x29231)+P113(x29232)+~E(x29231,x29232) % 188.18/188.28 [2924]~P114(x29241)+P114(x29242)+~E(x29241,x29242) % 188.18/188.28 [2925]~P4(x29251)+P4(x29252)+~E(x29251,x29252) % 188.18/188.28 [2926]~P67(x29261)+P67(x29262)+~E(x29261,x29262) % 188.18/188.28 [2927]~P124(x29271)+P124(x29272)+~E(x29271,x29272) % 188.18/188.28 [2928]~P80(x29281)+P80(x29282)+~E(x29281,x29282) % 188.18/188.28 [2929]P57(x29292,x29293,x29294)+~E(x29291,x29292)+~P57(x29291,x29293,x29294) % 188.18/188.28 [2930]P57(x29303,x29302,x29304)+~E(x29301,x29302)+~P57(x29303,x29301,x29304) % 188.18/188.28 [2931]P57(x29313,x29314,x29312)+~E(x29311,x29312)+~P57(x29313,x29314,x29311) % 188.18/188.28 [2932]P22(x29322,x29323,x29324,x29325)+~E(x29321,x29322)+~P22(x29321,x29323,x29324,x29325) % 188.18/188.28 [2933]P22(x29333,x29332,x29334,x29335)+~E(x29331,x29332)+~P22(x29333,x29331,x29334,x29335) % 188.18/188.28 [2934]P22(x29343,x29344,x29342,x29345)+~E(x29341,x29342)+~P22(x29343,x29344,x29341,x29345) % 188.18/188.28 [2935]P22(x29353,x29354,x29355,x29352)+~E(x29351,x29352)+~P22(x29353,x29354,x29355,x29351) % 188.18/188.28 [2936]~P81(x29361)+P81(x29362)+~E(x29361,x29362) % 188.18/188.28 [2937]P28(x29372,x29373,x29374,x29375,x29376)+~E(x29371,x29372)+~P28(x29371,x29373,x29374,x29375,x29376) % 188.18/188.28 [2938]P28(x29383,x29382,x29384,x29385,x29386)+~E(x29381,x29382)+~P28(x29383,x29381,x29384,x29385,x29386) % 188.18/188.28 [2939]P28(x29393,x29394,x29392,x29395,x29396)+~E(x29391,x29392)+~P28(x29393,x29394,x29391,x29395,x29396) % 188.18/188.28 [2940]P28(x29403,x29404,x29405,x29402,x29406)+~E(x29401,x29402)+~P28(x29403,x29404,x29405,x29401,x29406) % 188.18/188.28 [2941]P28(x29413,x29414,x29415,x29416,x29412)+~E(x29411,x29412)+~P28(x29413,x29414,x29415,x29416,x29411) % 188.18/188.28 [2942]~P99(x29421)+P99(x29422)+~E(x29421,x29422) % 188.18/188.28 [2943]~P72(x29431)+P72(x29432)+~E(x29431,x29432) % 188.18/188.28 [2944]P62(x29442,x29443,x29444,x29445)+~E(x29441,x29442)+~P62(x29441,x29443,x29444,x29445) % 188.18/188.28 [2945]P62(x29453,x29452,x29454,x29455)+~E(x29451,x29452)+~P62(x29453,x29451,x29454,x29455) % 188.18/188.28 [2946]P62(x29463,x29464,x29462,x29465)+~E(x29461,x29462)+~P62(x29463,x29464,x29461,x29465) % 188.18/188.28 [2947]P62(x29473,x29474,x29475,x29472)+~E(x29471,x29472)+~P62(x29473,x29474,x29475,x29471) % 188.18/188.28 [2948]~P94(x29481)+P94(x29482)+~E(x29481,x29482) % 188.18/188.28 [2949]P48(x29492,x29493)+~E(x29491,x29492)+~P48(x29491,x29493) % 188.18/188.28 [2950]P48(x29503,x29502)+~E(x29501,x29502)+~P48(x29503,x29501) % 188.18/188.28 [2951]P150(x29512,x29513,x29514)+~E(x29511,x29512)+~P150(x29511,x29513,x29514) % 188.18/188.28 [2952]P150(x29523,x29522,x29524)+~E(x29521,x29522)+~P150(x29523,x29521,x29524) % 188.18/188.28 [2953]P150(x29533,x29534,x29532)+~E(x29531,x29532)+~P150(x29533,x29534,x29531) % 188.18/188.28 [2954]P39(x29542,x29543)+~E(x29541,x29542)+~P39(x29541,x29543) % 188.18/188.28 [2955]P39(x29553,x29552)+~E(x29551,x29552)+~P39(x29553,x29551) % 188.18/188.28 [2956]~P141(x29561)+P141(x29562)+~E(x29561,x29562) % 188.18/188.28 [2957]~P115(x29571)+P115(x29572)+~E(x29571,x29572) % 188.18/188.28 [2958]~P119(x29581)+P119(x29582)+~E(x29581,x29582) % 188.18/188.28 [2959]~P133(x29591)+P133(x29592)+~E(x29591,x29592) % 188.18/188.28 [2960]~P131(x29601)+P131(x29602)+~E(x29601,x29602) % 188.18/188.28 [2961]~P73(x29611)+P73(x29612)+~E(x29611,x29612) % 188.18/188.28 [2962]~P75(x29621)+P75(x29622)+~E(x29621,x29622) % 188.18/188.28 [2963]P40(x29632,x29633)+~E(x29631,x29632)+~P40(x29631,x29633) % 188.18/188.28 [2964]P40(x29643,x29642)+~E(x29641,x29642)+~P40(x29643,x29641) % 188.18/188.28 [2965]~P74(x29651)+P74(x29652)+~E(x29651,x29652) % 188.18/188.28 [2966]~P42(x29661)+P42(x29662)+~E(x29661,x29662) % 188.18/188.28 [2967]~P95(x29671)+P95(x29672)+~E(x29671,x29672) % 188.18/188.28 [2968]~P71(x29681)+P71(x29682)+~E(x29681,x29682) % 188.18/188.28 [2969]~P129(x29691)+P129(x29692)+~E(x29691,x29692) % 188.18/188.28 [2970]~P86(x29701)+P86(x29702)+~E(x29701,x29702) % 188.18/188.28 [2971]~P143(x29711)+P143(x29712)+~E(x29711,x29712) % 188.18/188.28 [2972]P35(x29722,x29723,x29724)+~E(x29721,x29722)+~P35(x29721,x29723,x29724) % 188.18/188.28 [2973]P35(x29733,x29732,x29734)+~E(x29731,x29732)+~P35(x29733,x29731,x29734) % 188.18/188.28 [2974]P35(x29743,x29744,x29742)+~E(x29741,x29742)+~P35(x29743,x29744,x29741) % 188.18/188.28 [2975]~P84(x29751)+P84(x29752)+~E(x29751,x29752) % 188.18/188.28 [2976]~P77(x29761)+P77(x29762)+~E(x29761,x29762) % 188.18/188.28 [2977]P10(x29772,x29773,x29774)+~E(x29771,x29772)+~P10(x29771,x29773,x29774) % 188.18/188.28 [2978]P10(x29783,x29782,x29784)+~E(x29781,x29782)+~P10(x29783,x29781,x29784) % 188.18/188.28 [2979]P10(x29793,x29794,x29792)+~E(x29791,x29792)+~P10(x29793,x29794,x29791) % 188.18/188.28 [2980]~P85(x29801)+P85(x29802)+~E(x29801,x29802) % 188.18/188.28 [2981]P25(x29812,x29813,x29814,x29815,x29816,x29817)+~E(x29811,x29812)+~P25(x29811,x29813,x29814,x29815,x29816,x29817) % 188.18/188.28 [2982]P25(x29823,x29822,x29824,x29825,x29826,x29827)+~E(x29821,x29822)+~P25(x29823,x29821,x29824,x29825,x29826,x29827) % 188.18/188.28 [2983]P25(x29833,x29834,x29832,x29835,x29836,x29837)+~E(x29831,x29832)+~P25(x29833,x29834,x29831,x29835,x29836,x29837) % 188.18/188.28 [2984]P25(x29843,x29844,x29845,x29842,x29846,x29847)+~E(x29841,x29842)+~P25(x29843,x29844,x29845,x29841,x29846,x29847) % 188.18/188.28 [2985]P25(x29853,x29854,x29855,x29856,x29852,x29857)+~E(x29851,x29852)+~P25(x29853,x29854,x29855,x29856,x29851,x29857) % 188.18/188.28 [2986]P25(x29863,x29864,x29865,x29866,x29867,x29862)+~E(x29861,x29862)+~P25(x29863,x29864,x29865,x29866,x29867,x29861) % 188.18/188.28 [2987]~P7(x29871)+P7(x29872)+~E(x29871,x29872) % 188.18/188.28 [2988]~P87(x29881)+P87(x29882)+~E(x29881,x29882) % 188.18/188.28 [2989]~P8(x29891)+P8(x29892)+~E(x29891,x29892) % 188.18/188.28 [2990]~P125(x29901)+P125(x29902)+~E(x29901,x29902) % 188.18/188.28 [2991]~P120(x29911)+P120(x29912)+~E(x29911,x29912) % 188.18/188.28 [2992]P149(x29922,x29923,x29924)+~E(x29921,x29922)+~P149(x29921,x29923,x29924) % 188.18/188.28 [2993]P149(x29933,x29932,x29934)+~E(x29931,x29932)+~P149(x29933,x29931,x29934) % 188.18/188.28 [2994]P149(x29943,x29944,x29942)+~E(x29941,x29942)+~P149(x29943,x29944,x29941) % 188.18/188.28 [2995]~P82(x29951)+P82(x29952)+~E(x29951,x29952) % 188.18/188.28 [2996]~P144(x29961)+P144(x29962)+~E(x29961,x29962) % 188.18/188.28 [2997]P49(x29972,x29973,x29974)+~E(x29971,x29972)+~P49(x29971,x29973,x29974) % 188.18/188.28 [2998]P49(x29983,x29982,x29984)+~E(x29981,x29982)+~P49(x29983,x29981,x29984) % 188.18/188.28 [2999]P49(x29993,x29994,x29992)+~E(x29991,x29992)+~P49(x29993,x29994,x29991) % 188.18/188.28 [3000]P55(x30002,x30003,x30004)+~E(x30001,x30002)+~P55(x30001,x30003,x30004) % 188.18/188.28 [3001]P55(x30013,x30012,x30014)+~E(x30011,x30012)+~P55(x30013,x30011,x30014) % 188.18/188.28 [3002]P55(x30023,x30024,x30022)+~E(x30021,x30022)+~P55(x30023,x30024,x30021) % 188.18/188.28 [3003]~P130(x30031)+P130(x30032)+~E(x30031,x30032) % 188.18/188.28 [3004]~P38(x30041)+P38(x30042)+~E(x30041,x30042) % 188.18/188.28 [3005]~P92(x30051)+P92(x30052)+~E(x30051,x30052) % 188.18/188.28 [3006]P30(x30062,x30063)+~E(x30061,x30062)+~P30(x30061,x30063) % 188.18/188.28 [3007]P30(x30073,x30072)+~E(x30071,x30072)+~P30(x30073,x30071) % 188.18/188.28 [3008]P26(x30082,x30083,x30084)+~E(x30081,x30082)+~P26(x30081,x30083,x30084) % 188.18/188.28 [3009]P26(x30093,x30092,x30094)+~E(x30091,x30092)+~P26(x30093,x30091,x30094) % 188.18/188.28 [3010]P26(x30103,x30104,x30102)+~E(x30101,x30102)+~P26(x30103,x30104,x30101) % 188.18/188.28 [3011]P36(x30112,x30113,x30114,x30115,x30116)+~E(x30111,x30112)+~P36(x30111,x30113,x30114,x30115,x30116) % 188.18/188.28 [3012]P36(x30123,x30122,x30124,x30125,x30126)+~E(x30121,x30122)+~P36(x30123,x30121,x30124,x30125,x30126) % 188.18/188.28 [3013]P36(x30133,x30134,x30132,x30135,x30136)+~E(x30131,x30132)+~P36(x30133,x30134,x30131,x30135,x30136) % 188.18/188.28 [3014]P36(x30143,x30144,x30145,x30142,x30146)+~E(x30141,x30142)+~P36(x30143,x30144,x30145,x30141,x30146) % 188.18/188.28 [3015]P36(x30153,x30154,x30155,x30156,x30152)+~E(x30151,x30152)+~P36(x30153,x30154,x30155,x30156,x30151) % 188.18/188.28 [3016]P44(x30162,x30163,x30164,x30165,x30166,x30167)+~E(x30161,x30162)+~P44(x30161,x30163,x30164,x30165,x30166,x30167) % 188.18/188.28 [3017]P44(x30173,x30172,x30174,x30175,x30176,x30177)+~E(x30171,x30172)+~P44(x30173,x30171,x30174,x30175,x30176,x30177) % 188.18/188.28 [3018]P44(x30183,x30184,x30182,x30185,x30186,x30187)+~E(x30181,x30182)+~P44(x30183,x30184,x30181,x30185,x30186,x30187) % 188.18/188.28 [3019]P44(x30193,x30194,x30195,x30192,x30196,x30197)+~E(x30191,x30192)+~P44(x30193,x30194,x30195,x30191,x30196,x30197) % 188.18/188.28 [3020]P44(x30203,x30204,x30205,x30206,x30202,x30207)+~E(x30201,x30202)+~P44(x30203,x30204,x30205,x30206,x30201,x30207) % 188.18/188.28 [3021]P44(x30213,x30214,x30215,x30216,x30217,x30212)+~E(x30211,x30212)+~P44(x30213,x30214,x30215,x30216,x30217,x30211) % 188.18/188.28 [3022]~P121(x30221)+P121(x30222)+~E(x30221,x30222) % 188.18/188.28 [3023]P21(x30232,x30233,x30234,x30235)+~E(x30231,x30232)+~P21(x30231,x30233,x30234,x30235) % 188.18/188.28 [3024]P21(x30243,x30242,x30244,x30245)+~E(x30241,x30242)+~P21(x30243,x30241,x30244,x30245) % 188.18/188.28 [3025]P21(x30253,x30254,x30252,x30255)+~E(x30251,x30252)+~P21(x30253,x30254,x30251,x30255) % 188.18/188.28 [3026]P21(x30263,x30264,x30265,x30262)+~E(x30261,x30262)+~P21(x30263,x30264,x30265,x30261) % 188.18/188.28 [3027]P46(x30272,x30273)+~E(x30271,x30272)+~P46(x30271,x30273) % 188.18/188.28 [3028]P46(x30283,x30282)+~E(x30281,x30282)+~P46(x30283,x30281) % 188.18/188.28 [3029]P23(x30292,x30293,x30294,x30295,x30296)+~E(x30291,x30292)+~P23(x30291,x30293,x30294,x30295,x30296) % 188.18/188.28 [3030]P23(x30303,x30302,x30304,x30305,x30306)+~E(x30301,x30302)+~P23(x30303,x30301,x30304,x30305,x30306) % 188.18/188.28 [3031]P23(x30313,x30314,x30312,x30315,x30316)+~E(x30311,x30312)+~P23(x30313,x30314,x30311,x30315,x30316) % 188.18/188.28 [3032]P23(x30323,x30324,x30325,x30322,x30326)+~E(x30321,x30322)+~P23(x30323,x30324,x30325,x30321,x30326) % 188.18/188.28 [3033]P23(x30333,x30334,x30335,x30336,x30332)+~E(x30331,x30332)+~P23(x30333,x30334,x30335,x30336,x30331) % 188.18/188.28 [3034]~P89(x30341)+P89(x30342)+~E(x30341,x30342) % 188.18/188.28 [3035]~P134(x30351)+P134(x30352)+~E(x30351,x30352) % 188.18/188.28 [3036]P58(x30362,x30363,x30364)+~E(x30361,x30362)+~P58(x30361,x30363,x30364) % 188.18/188.28 [3037]P58(x30373,x30372,x30374)+~E(x30371,x30372)+~P58(x30373,x30371,x30374) % 188.18/188.28 [3038]P58(x30383,x30384,x30382)+~E(x30381,x30382)+~P58(x30383,x30384,x30381) % 188.18/188.28 [3039]~P142(x30391)+P142(x30392)+~E(x30391,x30392) % 188.18/188.28 [3040]~P145(x30401)+P145(x30402)+~E(x30401,x30402) % 188.18/188.28 [3041]~P136(x30411)+P136(x30412)+~E(x30411,x30412) % 188.18/188.28 [3042]~P101(x30421)+P101(x30422)+~E(x30421,x30422) % 188.18/188.28 [3043]~P100(x30431)+P100(x30432)+~E(x30431,x30432) % 188.18/188.28 [3044]~P146(x30441)+P146(x30442)+~E(x30441,x30442) % 188.18/188.28 [3045]~P137(x30451)+P137(x30452)+~E(x30451,x30452) % 188.18/188.28 [3046]P16(x30462,x30463,x30464)+~E(x30461,x30462)+~P16(x30461,x30463,x30464) % 188.18/188.28 [3047]P16(x30473,x30472,x30474)+~E(x30471,x30472)+~P16(x30473,x30471,x30474) % 188.18/188.28 [3048]P16(x30483,x30484,x30482)+~E(x30481,x30482)+~P16(x30483,x30484,x30481) % 188.18/188.28 [3049]~P88(x30491)+P88(x30492)+~E(x30491,x30492) % 188.18/188.28 [3050]P56(x30502,x30503)+~E(x30501,x30502)+~P56(x30501,x30503) % 188.18/188.28 [3051]P56(x30513,x30512)+~E(x30511,x30512)+~P56(x30513,x30511) % 188.18/188.28 [3052]P37(x30522,x30523,x30524)+~E(x30521,x30522)+~P37(x30521,x30523,x30524) % 188.18/188.28 [3053]P37(x30533,x30532,x30534)+~E(x30531,x30532)+~P37(x30533,x30531,x30534) % 188.18/188.28 [3054]P37(x30543,x30544,x30542)+~E(x30541,x30542)+~P37(x30543,x30544,x30541) % 188.18/188.28 [3055]~P128(x30551)+P128(x30552)+~E(x30551,x30552) % 188.18/188.28 [3056]P33(x30562,x30563,x30564)+~E(x30561,x30562)+~P33(x30561,x30563,x30564) % 188.18/188.28 [3057]P33(x30573,x30572,x30574)+~E(x30571,x30572)+~P33(x30573,x30571,x30574) % 188.18/188.28 [3058]P33(x30583,x30584,x30582)+~E(x30581,x30582)+~P33(x30583,x30584,x30581) % 188.18/188.28 [3059]~P123(x30591)+P123(x30592)+~E(x30591,x30592) % 188.18/188.28 [3060]~P96(x30601)+P96(x30602)+~E(x30601,x30602) % 188.18/188.28 [3061]P18(x30612,x30613,x30614)+~E(x30611,x30612)+~P18(x30611,x30613,x30614) % 188.18/188.28 [3062]P18(x30623,x30622,x30624)+~E(x30621,x30622)+~P18(x30623,x30621,x30624) % 188.18/188.28 [3063]P18(x30633,x30634,x30632)+~E(x30631,x30632)+~P18(x30633,x30634,x30631) % 188.18/188.28 [3064]~P139(x30641)+P139(x30642)+~E(x30641,x30642) % 188.18/188.28 [3065]~P98(x30651)+P98(x30652)+~E(x30651,x30652) % 188.18/188.28 [3066]~P64(x30661)+P64(x30662)+~E(x30661,x30662) % 188.18/188.28 [3067]~P138(x30671)+P138(x30672)+~E(x30671,x30672) % 188.18/188.28 [3068]P41(x30682,x30683)+~E(x30681,x30682)+~P41(x30681,x30683) % 188.18/188.28 [3069]P41(x30693,x30692)+~E(x30691,x30692)+~P41(x30693,x30691) % 188.18/188.28 [3070]~P105(x30701)+P105(x30702)+~E(x30701,x30702) % 188.18/188.28 [3071]P11(x30712,x30713,x30714)+~E(x30711,x30712)+~P11(x30711,x30713,x30714) % 188.18/188.28 [3072]P11(x30723,x30722,x30724)+~E(x30721,x30722)+~P11(x30723,x30721,x30724) % 188.18/188.28 [3073]P11(x30733,x30734,x30732)+~E(x30731,x30732)+~P11(x30733,x30734,x30731) % 188.18/188.28 [3074]P45(x30742,x30743)+~E(x30741,x30742)+~P45(x30741,x30743) % 188.18/188.28 [3075]P45(x30753,x30752)+~E(x30751,x30752)+~P45(x30753,x30751) % 188.18/188.28 [3076]P17(x30762,x30763)+~E(x30761,x30762)+~P17(x30761,x30763) % 188.18/188.28 [3077]P17(x30773,x30772)+~E(x30771,x30772)+~P17(x30773,x30771) % 188.18/188.28 [3078]P61(x30782,x30783)+~E(x30781,x30782)+~P61(x30781,x30783) % 188.18/188.28 [3079]P61(x30793,x30792)+~E(x30791,x30792)+~P61(x30793,x30791) % 188.18/188.28 [3080]~P47(x30801)+P47(x30802)+~E(x30801,x30802) % 188.18/188.28 [3081]~P93(x30811)+P93(x30812)+~E(x30811,x30812) % 188.18/188.28 [3082]~P132(x30821)+P132(x30822)+~E(x30821,x30822) % 188.18/188.28 [3083]P52(x30832,x30833)+~E(x30831,x30832)+~P52(x30831,x30833) % 188.18/188.28 [3084]P52(x30843,x30842)+~E(x30841,x30842)+~P52(x30843,x30841) % 188.18/188.28 [3085]~P6(x30851)+P6(x30852)+~E(x30851,x30852) % 188.18/188.28 [3086]~P97(x30861)+P97(x30862)+~E(x30861,x30862) % 188.18/188.28 [3087]P9(x30872,x30873)+~E(x30871,x30872)+~P9(x30871,x30873) % 188.18/188.28 [3088]P9(x30883,x30882)+~E(x30881,x30882)+~P9(x30883,x30881) % 188.18/188.28 [3089]~P148(x30891)+P148(x30892)+~E(x30891,x30892) % 188.18/188.28 [3090]P13(x30902,x30903,x30904,x30905)+~E(x30901,x30902)+~P13(x30901,x30903,x30904,x30905) % 188.18/188.28 [3091]P13(x30913,x30912,x30914,x30915)+~E(x30911,x30912)+~P13(x30913,x30911,x30914,x30915) % 188.18/188.28 [3092]P13(x30923,x30924,x30922,x30925)+~E(x30921,x30922)+~P13(x30923,x30924,x30921,x30925) % 188.18/188.28 [3093]P13(x30933,x30934,x30935,x30932)+~E(x30931,x30932)+~P13(x30933,x30934,x30935,x30931) % 188.18/188.28 [3094]P63(x30942,x30943)+~E(x30941,x30942)+~P63(x30941,x30943) % 188.18/188.28 [3095]P63(x30953,x30952)+~E(x30951,x30952)+~P63(x30953,x30951) % 188.18/188.28 [3096]~P118(x30961)+P118(x30962)+~E(x30961,x30962) % 188.18/188.28 [3097]P43(x30972,x30973,x30974,x30975)+~E(x30971,x30972)+~P43(x30971,x30973,x30974,x30975) % 188.18/188.28 [3098]P43(x30983,x30982,x30984,x30985)+~E(x30981,x30982)+~P43(x30983,x30981,x30984,x30985) % 188.18/188.28 [3099]P43(x30993,x30994,x30992,x30995)+~E(x30991,x30992)+~P43(x30993,x30994,x30991,x30995) % 188.18/188.28 [3100]P43(x31003,x31004,x31005,x31002)+~E(x31001,x31002)+~P43(x31003,x31004,x31005,x31001) % 188.18/188.28 [3101]~P116(x31011)+P116(x31012)+~E(x31011,x31012) % 188.18/188.28 [3102]P34(x31022,x31023,x31024,x31025)+~E(x31021,x31022)+~P34(x31021,x31023,x31024,x31025) % 188.18/188.28 [3103]P34(x31033,x31032,x31034,x31035)+~E(x31031,x31032)+~P34(x31033,x31031,x31034,x31035) % 188.18/188.28 [3104]P34(x31043,x31044,x31042,x31045)+~E(x31041,x31042)+~P34(x31043,x31044,x31041,x31045) % 188.18/188.28 [3105]P34(x31053,x31054,x31055,x31052)+~E(x31051,x31052)+~P34(x31053,x31054,x31055,x31051) % 188.18/188.28 [3106]P20(x31062,x31063,x31064)+~E(x31061,x31062)+~P20(x31061,x31063,x31064) % 188.18/188.28 [3107]P20(x31073,x31072,x31074)+~E(x31071,x31072)+~P20(x31073,x31071,x31074) % 188.18/188.28 [3108]P20(x31083,x31084,x31082)+~E(x31081,x31082)+~P20(x31083,x31084,x31081) % 188.18/188.28 [3109]P31(x31092,x31093,x31094)+~E(x31091,x31092)+~P31(x31091,x31093,x31094) % 188.18/188.28 [3110]P31(x31103,x31102,x31104)+~E(x31101,x31102)+~P31(x31103,x31101,x31104) % 188.18/188.28 [3111]P31(x31113,x31114,x31112)+~E(x31111,x31112)+~P31(x31113,x31114,x31111) % 188.18/188.28 [3112]P53(x31122,x31123)+~E(x31121,x31122)+~P53(x31121,x31123) % 188.18/188.28 [3113]P53(x31133,x31132)+~E(x31131,x31132)+~P53(x31133,x31131) % 188.18/188.28 [3114]P29(x31142,x31143)+~E(x31141,x31142)+~P29(x31141,x31143) % 188.18/188.28 [3115]P29(x31153,x31152)+~E(x31151,x31152)+~P29(x31153,x31151) % 188.18/188.28 [3116]P24(x31162,x31163,x31164,x31165,x31166,x31167)+~E(x31161,x31162)+~P24(x31161,x31163,x31164,x31165,x31166,x31167) % 188.18/188.28 [3117]P24(x31173,x31172,x31174,x31175,x31176,x31177)+~E(x31171,x31172)+~P24(x31173,x31171,x31174,x31175,x31176,x31177) % 188.18/188.28 [3118]P24(x31183,x31184,x31182,x31185,x31186,x31187)+~E(x31181,x31182)+~P24(x31183,x31184,x31181,x31185,x31186,x31187) % 188.18/188.28 [3119]P24(x31193,x31194,x31195,x31192,x31196,x31197)+~E(x31191,x31192)+~P24(x31193,x31194,x31195,x31191,x31196,x31197) % 188.18/188.28 [3120]P24(x31203,x31204,x31205,x31206,x31202,x31207)+~E(x31201,x31202)+~P24(x31203,x31204,x31205,x31206,x31201,x31207) % 188.18/188.28 [3121]P24(x31213,x31214,x31215,x31216,x31217,x31212)+~E(x31211,x31212)+~P24(x31213,x31214,x31215,x31216,x31217,x31211) % 188.18/188.28 [3122]P60(x31222,x31223,x31224,x31225,x31226)+~E(x31221,x31222)+~P60(x31221,x31223,x31224,x31225,x31226) % 188.18/188.28 [3123]P60(x31233,x31232,x31234,x31235,x31236)+~E(x31231,x31232)+~P60(x31233,x31231,x31234,x31235,x31236) % 188.18/188.28 [3124]P60(x31243,x31244,x31242,x31245,x31246)+~E(x31241,x31242)+~P60(x31243,x31244,x31241,x31245,x31246) % 188.18/188.28 [3125]P60(x31253,x31254,x31255,x31252,x31256)+~E(x31251,x31252)+~P60(x31253,x31254,x31255,x31251,x31256) % 188.18/188.28 [3126]P60(x31263,x31264,x31265,x31266,x31262)+~E(x31261,x31262)+~P60(x31263,x31264,x31265,x31266,x31261) % 188.18/188.28 [3127]~P102(x31271)+P102(x31272)+~E(x31271,x31272) % 188.18/188.28 [3128]P19(x31282,x31283,x31284)+~E(x31281,x31282)+~P19(x31281,x31283,x31284) % 188.18/188.28 [3129]P19(x31293,x31292,x31294)+~E(x31291,x31292)+~P19(x31293,x31291,x31294) % 188.18/188.28 [3130]P19(x31303,x31304,x31302)+~E(x31301,x31302)+~P19(x31303,x31304,x31301) % 188.18/188.28 [3131]~P106(x31311)+P106(x31312)+~E(x31311,x31312) % 188.18/188.28 [3132]P12(x31322,x31323,x31324,x31325,x31326)+~E(x31321,x31322)+~P12(x31321,x31323,x31324,x31325,x31326) % 188.18/188.28 [3133]P12(x31333,x31332,x31334,x31335,x31336)+~E(x31331,x31332)+~P12(x31333,x31331,x31334,x31335,x31336) % 188.18/188.28 [3134]P12(x31343,x31344,x31342,x31345,x31346)+~E(x31341,x31342)+~P12(x31343,x31344,x31341,x31345,x31346) % 188.18/188.28 [3135]P12(x31353,x31354,x31355,x31352,x31356)+~E(x31351,x31352)+~P12(x31353,x31354,x31355,x31351,x31356) % 188.18/188.28 [3136]P12(x31363,x31364,x31365,x31366,x31362)+~E(x31361,x31362)+~P12(x31363,x31364,x31365,x31366,x31361) % 188.18/188.28 [3137]~P90(x31371)+P90(x31372)+~E(x31371,x31372) % 188.18/188.28 [3138]~P78(x31381)+P78(x31382)+~E(x31381,x31382) % 188.18/188.28 [3139]P51(x31392,x31393,x31394,x31395)+~E(x31391,x31392)+~P51(x31391,x31393,x31394,x31395) % 188.18/188.28 [3140]P51(x31403,x31402,x31404,x31405)+~E(x31401,x31402)+~P51(x31403,x31401,x31404,x31405) % 188.18/188.28 [3141]P51(x31413,x31414,x31412,x31415)+~E(x31411,x31412)+~P51(x31413,x31414,x31411,x31415) % 188.18/188.28 [3142]P51(x31423,x31424,x31425,x31422)+~E(x31421,x31422)+~P51(x31423,x31424,x31425,x31421) % 188.18/188.28 [3143]P50(x31432,x31433,x31434)+~E(x31431,x31432)+~P50(x31431,x31433,x31434) % 188.18/188.28 [3144]P50(x31443,x31442,x31444)+~E(x31441,x31442)+~P50(x31443,x31441,x31444) % 188.18/188.28 [3145]P50(x31453,x31454,x31452)+~E(x31451,x31452)+~P50(x31453,x31454,x31451) % 188.18/188.28 [3146]~P126(x31461)+P126(x31462)+~E(x31461,x31462) % 188.18/188.28 [3147]~P117(x31471)+P117(x31472)+~E(x31471,x31472) % 188.18/188.28 % 188.18/188.28 %------------------------------------------- % 188.31/188.32 cnf(10492,plain, % 188.31/188.32 (~E(f334(a119,x104921),x104921)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10502,plain, % 188.31/188.32 (~E(f334(a119,x105021),x105021)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10515,plain, % 188.31/188.32 (~E(f334(a119,x105151),x105151)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10520,plain, % 188.31/188.32 (~P107(f334(f334(f179(x105201),f120(x105201)),x105202))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10523,plain, % 188.31/188.32 (~P107(f334(f334(f179(x105231),f120(x105231)),x105232))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10526,plain, % 188.31/188.32 (~E(f334(a119,x105261),x105261)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10529,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x105291),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(10532,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x105321),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(10549,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x105491)),x105491))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(10552,plain, % 188.31/188.32 (~E(f334(f334(f158(x105521),x105522),x105523),x105523)), % 188.31/188.32 inference(rename_variables,[],[4740])). % 188.31/188.32 cnf(10558,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x105581),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(10560,plain, % 188.31/188.32 (E(f50(a927,f334(f291(x105601,x105601),f271(x105601,f334(f334(f87(a927),x105602),x105603))),x105602),f2(a927))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,3342,3514,3385,3450,3382,3412,3394,4740,3538,4780,10529,10532,4777,4737,4785,10520,4786,4784,3531,4769,4800,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309])). % 188.31/188.32 cnf(10561,plain, % 188.31/188.32 (E(f334(f291(x105611,x105611),f271(x105611,x105612)),x105612)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(10564,plain, % 188.31/188.32 (E(f334(f291(x105641,x105641),f271(x105641,x105642)),x105642)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(10569,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x105691),x105691))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(10574,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x105741),x105742)),x105742))), % 188.31/188.32 inference(rename_variables,[],[4798])). % 188.31/188.32 cnf(10577,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x105771),x105772)),x105772))), % 188.31/188.32 inference(rename_variables,[],[4798])). % 188.31/188.32 cnf(10581,plain, % 188.31/188.32 (~E(x105811,f334(a119,x105811))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,3342,3514,10561,3385,3450,3382,3412,3394,4740,3621,3538,4780,10529,10532,4777,4737,4785,10520,4776,4786,4784,3531,4769,4800,4798,10574,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417])). % 188.31/188.32 cnf(10595,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x105951),x105951))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(10598,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f50(a927,x105981,x105982)),x105981))), % 188.31/188.32 inference(rename_variables,[],[4006])). % 188.31/188.32 cnf(10619,plain, % 188.31/188.32 (E(f334(f40(a927),f334(f307(a927),x106191)),x106191)), % 188.31/188.32 inference(rename_variables,[],[3448])). % 188.31/188.32 cnf(10627,plain, % 188.31/188.32 (~E(f334(a119,x106271),x106271)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10630,plain, % 188.31/188.32 (~E(f334(a119,x106301),x106301)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10633,plain, % 188.31/188.32 (~E(f334(a119,x106331),x106331)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10635,plain, % 188.31/188.32 (P107(f334(a200,a104))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,3342,3514,10561,3385,3450,3382,3412,3394,3484,4740,3448,4807,3469,3621,3538,4780,10529,10532,4132,3556,4777,4737,4785,10520,4776,10569,10595,3646,4069,4006,4786,10549,4784,4768,3531,4769,4800,4798,10574,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561])). % 188.31/188.32 cnf(10638,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x106381),f334(a119,x106381)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(10647,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x106471),x106471))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(10654,plain, % 188.31/188.32 (E(f334(f291(x106541,x106541),f271(x106541,x106542)),x106542)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(10657,plain, % 188.31/188.32 (E(f334(f291(x106571,x106571),f271(x106571,x106572)),x106572)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(10674,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x106741),x106741))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(10679,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x106791),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(10682,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x106821,a922)),x106822),f250(f935(x106821,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(10687,plain, % 188.31/188.32 (~P107(f334(f334(f179(x106871),f120(x106871)),x106872))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10716,plain, % 188.31/188.32 (~E(f334(f334(f158(x107161),x107162),x107163),x107163)), % 188.31/188.32 inference(rename_variables,[],[4740])). % 188.31/188.32 cnf(10719,plain, % 188.31/188.32 (~E(f334(a119,x107191),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[4729])). % 188.31/188.32 cnf(10730,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x107301),x107301))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(10735,plain, % 188.31/188.32 (~E(f334(a119,x107351),x107351)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10738,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x107381,f935(x107382,a922))),x107383),x107384))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(10745,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x107451),x107451))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(10758,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x107581),f334(a119,x107581)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(10779,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x107791,a922)),x107792),f250(f935(x107791,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(10782,plain, % 188.31/188.32 (~P107(f334(f334(f179(x107821),f120(x107821)),x107822))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10801,plain, % 188.31/188.32 (~P107(f334(f334(f179(x108011),f120(x108011)),x108012))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10808,plain, % 188.31/188.32 (~P107(f334(f334(f179(x108081),f120(x108081)),x108082))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10819,plain, % 188.31/188.32 (~E(f334(a119,x108191),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[4729])). % 188.31/188.32 cnf(10824,plain, % 188.31/188.32 (P107(f334(f334(f336(x108241),x108242),f250(f935(x108241,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(10831,plain, % 188.31/188.32 (~P107(f334(f334(f179(x108311),f120(x108311)),x108312))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10836,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x108361),f334(a119,x108361)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(10839,plain, % 188.31/188.32 (~P107(f334(f334(f179(x108391),f120(x108391)),x108392))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10842,plain, % 188.31/188.32 (~P107(f334(f334(f179(x108421),f120(x108421)),x108422))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10845,plain, % 188.31/188.32 (~P107(f334(f67(x108451,x108452,f195(f935(x108451,a922))),x108453))), % 188.31/188.32 inference(rename_variables,[],[4797])). % 188.31/188.32 cnf(10848,plain, % 188.31/188.32 (~P107(f334(f67(x108481,x108482,f195(f935(x108481,a922))),x108483))), % 188.31/188.32 inference(rename_variables,[],[4797])). % 188.31/188.32 cnf(10851,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x108511,f935(x108512,a922))),x108513),x108514))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(10854,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x108541),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(10859,plain, % 188.31/188.32 (~P107(f334(f334(f179(x108591),f120(x108591)),x108592))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(10870,plain, % 188.31/188.32 (~E(f334(a119,x108701),x108701)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(10888,plain, % 188.31/188.32 (P107(f334(f334(f243(a106),f334(a3,x108881)),f334(a3,f334(a119,x108881))))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,4729,10719,3342,3514,10561,10564,10654,3385,3450,3382,3412,3394,4022,3484,4740,10552,3448,4322,4807,3469,3916,3621,10638,10758,10836,3997,3538,4780,10529,10532,10558,10679,4791,3984,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,4274,3934,10682,3554,10647,10745,3555,10674,4776,10569,10595,3705,3646,4069,4006,10598,4786,10549,4784,4768,3531,3535,4770,4769,4797,10845,4800,4801,10738,4030,4798,10574,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342])). % 188.31/188.32 cnf(10895,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x108951),x108951))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(10898,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x108981),f334(f334(f87(a927),x108981),x108981)))), % 188.31/188.32 inference(rename_variables,[],[3815])). % 188.31/188.32 cnf(10901,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x109011),f334(f334(f87(a927),x109011),x109011)))), % 188.31/188.32 inference(rename_variables,[],[3815])). % 188.31/188.32 cnf(10904,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x109041),f334(a119,f334(f334(f86(a927),x109042),x109041))))), % 188.31/188.32 inference(rename_variables,[],[3995])). % 188.31/188.32 cnf(10909,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x109091),f334(a119,x109091)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(10912,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x109121),f334(a119,x109121)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(10915,plain, % 188.31/188.32 (P107(f334(f334(f336(x109151),x109152),f250(f935(x109151,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(10934,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x109341)),x109341))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(10937,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x109371)),x109371))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(10940,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x109401),x109402)),x109402))), % 188.31/188.32 inference(rename_variables,[],[4798])). % 188.31/188.32 cnf(10943,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x109431),x109432)),x109432))), % 188.31/188.32 inference(rename_variables,[],[4798])). % 188.31/188.32 cnf(10946,plain, % 188.31/188.32 (P107(f334(f250(f935(x109461,a922)),x109462))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(10949,plain, % 188.31/188.32 (E(f334(f40(a927),f334(f307(a927),x109491)),x109491)), % 188.31/188.32 inference(rename_variables,[],[3448])). % 188.31/188.32 cnf(10952,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x109521),f334(a119,x109521)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(10959,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x109591),x109591))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(10964,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x109641),x109641))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(10973,plain, % 188.31/188.32 (E(f334(f291(x109731,x109731),f271(x109731,x109732)),x109732)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(10976,plain, % 188.31/188.32 (P107(f334(f250(f935(x109761,a922)),x109762))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(10979,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x109791))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(10982,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x109821,a922)),f195(f935(x109821,a922))),x109822))), % 188.31/188.32 inference(rename_variables,[],[3994])). % 188.31/188.32 cnf(10985,plain, % 188.31/188.32 (P107(f334(f250(f935(x109851,a922)),x109852))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(10988,plain, % 188.31/188.32 (P107(f334(f250(f935(x109881,a922)),x109882))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(10991,plain, % 188.31/188.32 (P107(f334(f250(f935(x109911,a922)),x109912))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(10993,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(f334(f87(a927),f334(a119,x109931)),f334(a119,x109931))),x109931))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,4729,10719,3342,3514,10561,10564,10654,10657,3385,3450,3382,3412,3394,4022,3484,4740,10552,3448,10619,4322,4807,3469,3916,3853,3621,10638,10758,10836,10909,10912,3997,3538,4780,10529,10532,10558,10679,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,4274,3934,10682,3554,10647,10745,10895,3555,10674,10730,4776,10569,10595,3705,10824,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,3574,4784,4768,3531,3535,4770,4769,4797,10845,4806,3994,3815,10898,10901,4800,4801,10738,4030,4798,10574,10577,10940,3995,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575])). % 188.31/188.32 cnf(10994,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x109941),f334(f334(f87(a927),x109941),x109941)))), % 188.31/188.32 inference(rename_variables,[],[3815])). % 188.31/188.32 cnf(10998,plain, % 188.31/188.32 (E(f334(f175(x109981),f180(x109982,f334(f334(f141(x109981),f334(f175(x109981),x109983)),f334(f334(f158(x109981),x109984),f120(x109981))),f120(x109982))),f334(f334(f158(x109981),x109984),x109983))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,4729,10719,3342,3514,10561,10564,10654,10657,3491,3385,3450,3382,3412,3394,4022,3484,4740,10552,3448,10619,4322,4807,3469,3916,3853,3621,10638,10758,10836,10909,10912,3997,3538,4780,10529,10532,10558,10679,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,4274,3934,10682,3554,10647,10745,10895,3555,10674,10730,4776,10569,10595,3705,10824,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,3574,4784,4768,3531,3535,4770,4769,4797,10845,4806,3994,3815,10898,10901,4800,4801,10738,4030,4798,10574,10577,10940,3995,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611])). % 188.31/188.32 cnf(11003,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,f334(a119,f334(f334(f86(a927),x110031),x110032)))),f334(a119,x110032)))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,4729,10719,3342,3514,10561,10564,10654,10657,3491,3385,3450,3382,3412,3394,4022,3484,4740,10552,3448,10619,4322,4807,3469,3916,3853,3621,10638,10758,10836,10909,10912,10952,3997,3538,4780,10529,10532,10558,10679,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,4274,3934,10682,3554,10647,10745,10895,3555,10674,10730,4776,10569,10595,3705,10824,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,3574,4784,4768,3531,3535,4770,4769,4797,10845,4806,3994,3815,10898,10901,4800,4801,10738,4030,4798,10574,10577,10940,3995,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615])). % 188.31/188.32 cnf(11036,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x110361),x110361))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11047,plain, % 188.31/188.32 (~P107(f334(f334(f179(x110471),f120(x110471)),x110472))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(11056,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x110561),f334(a119,x110561)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(11059,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x110591),x110591))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(11064,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x110641),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(11077,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x110771),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(11080,plain, % 188.31/188.32 (~P107(f334(f334(f243(f935(x110801,a922)),x110802),f195(f935(x110801,a922))))), % 188.31/188.32 inference(rename_variables,[],[4795])). % 188.31/188.32 cnf(11083,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x110831),x110831))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11086,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x110861),x110861))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11101,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x111011),x111011))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(11110,plain, % 188.31/188.32 (~P107(f334(f334(f336(x111101),x111102),f195(f935(x111101,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11117,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x111171),x111171))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11120,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x111201,a922)),f334(f317(x111202,x111201,x111203),f334(f318(x111202,x111201,x111203),x111204))),x111204))), % 188.31/188.32 inference(rename_variables,[],[4414])). % 188.31/188.32 cnf(11129,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x111291,a922)),f334(f179(x111291),f334(f143(x111291,x111292),x111293))),f334(f179(x111291),x111293)))), % 188.31/188.32 inference(rename_variables,[],[4194])). % 188.31/188.32 cnf(11132,plain, % 188.31/188.32 (E(f334(f317(x111321,x111321,f5(x111321)),x111322),x111322)), % 188.31/188.32 inference(rename_variables,[],[3610])). % 188.31/188.32 cnf(11137,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x111371))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(11140,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x111401),x111401))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11143,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x111431),x111431))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(11145,plain, % 188.31/188.32 (~P35(x111451,f195(f935(x111452,a922)),x111453)), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,4729,10719,3342,3514,10561,10564,10654,10657,3491,3385,3450,3382,3412,3394,4022,3610,3484,4740,10552,3448,10619,4322,4186,4807,3469,3747,3916,3853,3621,10638,10758,10836,10909,10912,10952,11056,3997,3538,4780,10529,10532,10558,10679,10854,11064,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,4286,4194,4274,3934,10682,4795,3554,10647,10745,10895,10959,11036,11083,11086,11117,3555,10674,10730,10964,4776,10569,10595,11101,3705,10824,4789,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,3574,10979,4784,4768,4771,3531,3535,4770,4769,4797,10845,4806,3994,3815,10898,10901,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414])). % 188.31/188.32 cnf(11152,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x111521),x111521))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(11163,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x111631),f334(f334(f87(a927),x111631),x111631)))), % 188.31/188.32 inference(rename_variables,[],[3815])). % 188.31/188.32 cnf(11169,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x111691),f334(a119,f334(f334(f86(a927),x111692),x111691))))), % 188.31/188.32 inference(rename_variables,[],[3995])). % 188.31/188.32 cnf(11176,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x111761),x111761))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11179,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x111791),x111791))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(11182,plain, % 188.31/188.32 (~E(f334(a119,x111821),x111821)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11186,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x111861,x111861)),x111862),f314(x111861,f250(f935(f934(x111861,x111861),a922)))))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,4729,10719,3342,3514,10561,10564,10654,10657,3491,3385,3450,3382,3412,3394,4022,3610,3484,4740,10552,3448,10619,4322,4186,4807,3469,3747,3916,3853,3621,10638,10758,10836,10909,10912,10952,11056,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,4286,4194,4274,3934,10682,4795,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,4789,11110,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,3574,10979,4784,4768,4771,3531,3535,4770,4769,4797,10845,4806,3994,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670])). % 188.31/188.32 cnf(11187,plain, % 188.31/188.32 (P107(f334(f334(f336(x111871),x111872),f250(f935(x111871,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(11192,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x111921),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(11207,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x112071))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(11214,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x112141),x112141))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11223,plain, % 188.31/188.32 (~P107(f334(f334(f336(x112231),x112232),f195(f935(x112231,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11231,plain, % 188.31/188.32 (P107(f334(f334(f336(x112311),x112312),f250(f935(x112311,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(11234,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x112341),f928(x112341))),f334(f334(f260(f928(x112341),f928(x112341)),x112342),f120(x112341))),f152(x112341,x112343)))), % 188.31/188.32 inference(rename_variables,[],[4807])). % 188.31/188.32 cnf(11240,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(x112401,x112401)),x112402),f271(x112401,f195(f935(x112401,a922)))))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,4729,10719,3342,3514,10561,10564,10654,10657,3491,3385,3450,3382,3412,3394,4022,3610,3484,4740,10552,3448,10619,4322,4186,4807,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,4286,4194,11129,3917,4274,3934,10682,4795,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,11187,4789,11110,11223,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4797,10845,4806,3994,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133])). % 188.31/188.32 cnf(11241,plain, % 188.31/188.32 (~P107(f334(f334(f336(x112411),x112412),f195(f935(x112411,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11243,plain, % 188.31/188.32 (~P107(f334(f334(f336(x112431),x112432),f334(f318(x112431,x112433,x112434),f195(f935(x112433,a922)))))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,4729,10719,3342,3514,10561,10564,10654,10657,3491,3385,3450,3382,3412,3394,4022,3610,3484,4740,10552,3448,10619,4322,4186,4807,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,4286,4194,11129,3917,4274,3934,10682,4795,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,11187,4789,11110,11223,11241,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4797,10845,4806,3994,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161])). % 188.31/188.32 cnf(11244,plain, % 188.31/188.32 (~P107(f334(f334(f336(x112441),x112442),f195(f935(x112441,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11247,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x112471,a922)),x112472),f334(f334(f316(x112471),x112473),x112472)))), % 188.31/188.32 inference(rename_variables,[],[3992])). % 188.31/188.32 cnf(11250,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x112501),x112501))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(11253,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x112531,a922)),x112532),f334(f334(f316(x112531),x112533),x112532)))), % 188.31/188.32 inference(rename_variables,[],[3992])). % 188.31/188.32 cnf(11256,plain, % 188.31/188.32 (E(f334(f317(x112561,x112561,f5(x112561)),x112562),x112562)), % 188.31/188.32 inference(rename_variables,[],[3610])). % 188.31/188.32 cnf(11270,plain, % 188.31/188.32 (E(f334(x112701,f540(x112701,x112702,f334(x112701,x112703))),f334(x112701,x112703))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,4729,10719,3342,3396,3514,10561,10564,10654,10657,3491,3385,3450,3382,3412,3394,4022,3610,11132,3484,4740,10552,3448,10619,4322,4186,4807,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,4286,4194,11129,3917,4274,3934,10682,4795,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,11187,11231,4789,11110,11223,11241,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4797,10845,4806,4150,3992,11247,3994,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435])). % 188.31/188.32 cnf(11273,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x112731,a922)),x112732),f334(f334(f316(x112731),x112733),x112732)))), % 188.31/188.32 inference(rename_variables,[],[3992])). % 188.31/188.32 cnf(11286,plain, % 188.31/188.32 (~E(f334(a119,x112861),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[4729])). % 188.31/188.32 cnf(11289,plain, % 188.31/188.32 (~P107(f334(f334(f179(x112891),f120(x112891)),x112892))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(11302,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x113021),f334(a119,x113021)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(11312,plain, % 188.31/188.32 (~E(f334(f317(x113121,f935(x113121,a922),x113122),x113123),f334(f315(x113121),x113123))), % 188.31/188.32 inference(rename_variables,[],[4787])). % 188.31/188.32 cnf(11315,plain, % 188.31/188.32 (~P107(f334(f334(f336(x113151),x113152),f195(f935(x113151,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11318,plain, % 188.31/188.32 (~P107(f334(f334(f336(x113181),x113182),f195(f935(x113181,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11321,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(x113211,x113211)),f334(f334(f260(x113211,x113211),x113212),x113213)),f160(x113211,f120(f935(x113211,a927)))))), % 188.31/188.32 inference(rename_variables,[],[4806])). % 188.31/188.32 cnf(11324,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(x113241,x113241)),f334(f334(f260(x113241,x113241),x113242),x113243)),f160(x113241,f120(f935(x113241,a927)))))), % 188.31/188.32 inference(rename_variables,[],[4806])). % 188.31/188.32 cnf(11329,plain, % 188.31/188.32 (~P107(f334(f334(f336(x113291),x113292),f195(f935(x113291,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11332,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x113321,x113321)),f334(f334(f260(x113321,x113321),x113322),x113322)),f314(x113321,x113323)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(11335,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x113351,a922)),f334(f179(x113351),f183(x113351,x113352,x113353))),f334(f179(x113351),x113352)))), % 188.31/188.32 inference(rename_variables,[],[4241])). % 188.31/188.32 cnf(11338,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x113381,a922)),x113382),f250(f935(x113381,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(11354,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x113541,a922)),f195(f935(x113541,a922))),x113542))), % 188.31/188.32 inference(rename_variables,[],[3994])). % 188.31/188.32 cnf(11365,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x113651),f928(x113651))),f334(f334(f260(f928(x113651),f928(x113651)),x113652),f120(x113651))),f154(x113651,x113653)))), % 188.31/188.32 inference(rename_variables,[],[4808])). % 188.31/188.32 cnf(11376,plain, % 188.31/188.32 (~E(f334(a119,x113761),x113761)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11379,plain, % 188.31/188.32 (~E(f334(a119,x113791),x113791)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11383,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(f928(x113831),f928(x113831))),f334(f334(f260(f928(x113831),f928(x113831)),f120(x113831)),f120(x113831))),f334(f334(f295(f928(x113831),f928(x113831),f928(x113831)),f165(x113831,x113832)),f314(f928(x113831),f165(x113831,x113832)))))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,4729,10719,10819,3342,3396,3514,10561,10564,10654,10657,3491,4008,3385,3450,3382,3412,3394,4022,3610,11132,3484,4183,4740,10552,4787,3448,10619,4322,4186,11332,4807,11234,4808,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,11192,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,4286,4194,11129,4241,3917,4274,3934,10682,10779,4795,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,11187,11231,4789,11110,11223,11241,11244,11315,11318,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4797,10845,4806,11321,4150,3992,11247,11253,3994,10982,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807])). % 188.31/188.32 cnf(11386,plain, % 188.31/188.32 (~E(f334(a119,x113861),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[4729])). % 188.31/188.32 cnf(11391,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x113911,a922)),x113912),x113912))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(11398,plain, % 188.31/188.32 (~E(f334(a119,x113981),x113981)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11401,plain, % 188.31/188.32 (~E(f334(a119,x114011),x114011)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11403,plain, % 188.31/188.32 (~P28(x114031,f935(x114031,a922),x114032,x114033,f334(f315(x114031),x114033))), % 188.31/188.32 inference(scs_inference,[],[4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,4729,10719,10819,11286,3342,3396,3514,10561,10564,10654,10657,3491,4008,3385,3450,3382,3412,3394,4022,3610,11132,3484,4183,4740,10552,4787,11312,3448,10619,4322,4186,11332,4807,11234,4808,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,11192,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,4286,4194,11129,4241,3917,4274,3934,10682,10779,4795,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,11187,11231,4789,11110,11223,11241,11244,11315,11318,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4797,10845,4806,11321,4150,3992,11247,11253,3849,3994,10982,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860])). % 188.31/188.32 cnf(11406,plain, % 188.31/188.32 (P27(x114061,x114061,f5(x114061),x114062)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(11411,plain, % 188.31/188.32 (~E(f334(f317(x114111,f935(x114111,a922),x114112),x114113),f334(f315(x114111),x114113))), % 188.31/188.32 inference(rename_variables,[],[4787])). % 188.31/188.32 cnf(11416,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x114161,a922)),x114162),f250(f935(x114161,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(11432,plain, % 188.31/188.32 (~P107(f334(f334(f336(x114321),x114322),f195(f935(x114321,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11435,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x114351)),x114351))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(11440,plain, % 188.31/188.32 (~P107(f334(f334(f336(x114401),x114402),f195(f935(x114401,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11451,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x114511)),x114511))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(11454,plain, % 188.31/188.32 (~P107(f334(f334(f336(x114541),x114542),f195(f935(x114541,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11467,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x114671,x114671)),f334(f334(f260(x114671,x114671),x114672),x114672)),f314(x114671,x114673)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(11470,plain, % 188.31/188.32 (P107(f334(f334(f336(x114701),x114702),f250(f935(x114701,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(11473,plain, % 188.31/188.32 (P107(f334(f334(f336(x114731),x114732),f250(f935(x114731,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(11480,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x114801),f928(x114801))),f334(f334(f260(f928(x114801),f928(x114801)),x114802),f120(x114801))),f152(x114801,x114803)))), % 188.31/188.32 inference(rename_variables,[],[4807])). % 188.31/188.32 cnf(11483,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x114831),f928(x114831))),f334(f334(f260(f928(x114831),f928(x114831)),x114832),f120(x114831))),f154(x114831,x114833)))), % 188.31/188.32 inference(rename_variables,[],[4808])). % 188.31/188.32 cnf(11486,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x114861),f928(x114861))),f334(f334(f260(f928(x114861),f928(x114861)),x114862),f120(x114861))),f164(x114861,x114863)))), % 188.31/188.32 inference(rename_variables,[],[4809])). % 188.31/188.32 cnf(11491,plain, % 188.31/188.32 (~P107(f334(f334(f243(f935(x114911,a922)),x114912),f195(f935(x114911,a922))))), % 188.31/188.32 inference(rename_variables,[],[4795])). % 188.31/188.32 cnf(11494,plain, % 188.31/188.32 (~P107(f334(f334(f336(x114941),x114942),f195(f935(x114941,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11501,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x115011,a922)),x115012),f250(f935(x115011,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(11508,plain, % 188.31/188.32 (~P107(f334(f334(f179(x115081),f120(x115081)),x115082))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(11513,plain, % 188.31/188.32 (~P107(f334(f334(f336(x115131),x115132),f195(f935(x115131,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11516,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(x115161,x115161)),f334(f334(f260(x115161,x115161),x115162),x115163)),f160(x115161,f120(f935(x115161,a927)))))), % 188.31/188.32 inference(rename_variables,[],[4806])). % 188.31/188.32 cnf(11519,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x115191,a922)),x115192),x115192))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(11522,plain, % 188.31/188.32 (~P107(f334(f334(f336(x115221),x115222),f195(f935(x115221,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11525,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x115251,a922)),f195(f935(x115251,a922))),x115252))), % 188.31/188.32 inference(rename_variables,[],[3994])). % 188.31/188.32 cnf(11528,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x115281,x115281)),f334(f334(f260(x115281,x115281),x115282),x115282)),f314(x115281,x115283)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(11530,plain, % 188.31/188.32 (~P36(x115301,x115302,x115303,f334(f334(f161(x115304,x115301),x115305),f334(a119,f120(x115304))),f120(x115302))), % 188.31/188.32 inference(scs_inference,[],[3786,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,4729,10719,10819,11286,3342,3396,3514,10561,10564,10654,10657,3491,4008,3385,3450,3382,3412,3394,4022,3610,11132,3484,4183,4740,10552,4787,11312,3657,3448,10619,4322,4186,11332,11467,4807,11234,11480,4808,11365,4809,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,11302,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,11192,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,4286,4194,11129,4241,3917,4274,3934,10682,10779,11338,11416,4795,11080,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,11187,11231,11470,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,11435,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4797,10845,4806,11321,11324,4150,3992,11247,11253,3849,11391,3994,10982,11354,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487])). % 188.31/188.32 cnf(11534,plain, % 188.31/188.32 (P36(x115341,x115342,x115343,f334(f334(f161(x115344,x115341),x115345),f121(x115344,f120(x115344))),f120(x115342))), % 188.31/188.32 inference(scs_inference,[],[3786,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,4729,10719,10819,11286,3342,3396,3514,10561,10564,10654,10657,3491,4008,3385,3450,3382,3412,3394,4022,3610,11132,3484,4183,4740,10552,4787,11312,3657,3448,10619,4322,4186,11332,11467,4807,11234,11480,4808,11365,4809,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,11302,3997,3538,4780,10529,10532,10558,10679,10854,11064,11077,11192,4791,3984,3757,4132,3580,3582,3556,4777,4737,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,4286,4194,11129,4241,3917,4274,3934,10682,10779,11338,11416,4795,11080,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,3555,10674,10730,10964,11059,4776,10569,10595,11101,11143,3705,10824,10915,11187,11231,11470,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,3614,10946,10976,10985,10988,3646,4069,4006,10598,4786,10549,10934,10937,11435,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4797,10845,4806,11321,11324,4150,3992,11247,11253,3849,11391,3994,10982,11354,3815,10898,10901,10994,11163,4800,4801,10738,4414,4030,4798,10574,10577,10940,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513])). % 188.31/188.32 cnf(11539,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x115391),f928(x115391))),f334(f334(f260(f928(x115391),f928(x115391)),x115392),f120(x115391))),f164(x115391,x115393)))), % 188.31/188.32 inference(rename_variables,[],[4809])). % 188.31/188.32 cnf(11546,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x115461),f928(x115461))),f334(f334(f260(f928(x115461),f928(x115461)),f120(x115461)),x115462)),f152(x115461,x115463)))), % 188.31/188.32 inference(rename_variables,[],[4810])). % 188.31/188.32 cnf(11554,plain, % 188.31/188.32 (P107(f334(f334(f336(x115541),x115542),f250(f935(x115541,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(11559,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x115591,a922)),f195(f935(x115591,a922))),x115592))), % 188.31/188.32 inference(rename_variables,[],[3994])). % 188.31/188.32 cnf(11562,plain, % 188.31/188.32 (~P107(f334(f334(f336(x115621),x115622),f195(f935(x115621,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11565,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x115651,a922)),x115652),f250(f935(x115651,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(11570,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x115701,a922)),f195(f935(x115701,a922))),x115702))), % 188.31/188.32 inference(rename_variables,[],[3994])). % 188.31/188.32 cnf(11583,plain, % 188.31/188.32 (P107(f334(f250(f935(x115831,a922)),x115832))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(11591,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x115911),f928(x115911))),f334(f334(f260(f928(x115911),f928(x115911)),x115912),f120(x115911))),f152(x115911,x115913)))), % 188.31/188.32 inference(rename_variables,[],[4807])). % 188.31/188.32 cnf(11594,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x115941),f928(x115941))),f334(f334(f260(f928(x115941),f928(x115941)),x115942),f120(x115941))),f154(x115941,x115943)))), % 188.31/188.32 inference(rename_variables,[],[4808])). % 188.31/188.32 cnf(11597,plain, % 188.31/188.32 (~E(f334(f334(f158(x115971),x115972),x115973),x115973)), % 188.31/188.32 inference(rename_variables,[],[4740])). % 188.31/188.32 cnf(11600,plain, % 188.31/188.32 (~E(f334(a119,x116001),x116001)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11603,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116031),x116032),f195(f935(x116031,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11608,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116081),x116082),f195(f935(x116081,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11611,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116111),x116112),f195(f935(x116111,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11614,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(f928(x116141),f928(x116141))),f334(f334(f260(f928(x116141),f928(x116141)),x116142),x116142)),f165(x116141,f314(x116141,x116143))))), % 188.31/188.32 inference(rename_variables,[],[4315])). % 188.31/188.32 cnf(11617,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x116171),f928(x116171))),f334(f334(f260(f928(x116171),f928(x116171)),x116172),f120(x116171))),f152(x116171,x116173)))), % 188.31/188.32 inference(rename_variables,[],[4807])). % 188.31/188.32 cnf(11627,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(x116271,x116271)),f334(f334(f260(x116271,x116271),x116272),x116273)),f160(x116271,f120(f935(x116271,a927)))))), % 188.31/188.32 inference(rename_variables,[],[4806])). % 188.31/188.32 cnf(11630,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116301),x116302),f195(f935(x116301,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11633,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116331),x116332),f195(f935(x116331,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11636,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x116361,f935(x116362,a922))),x116363),x116364))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(11639,plain, % 188.31/188.32 (P107(f334(f334(f336(x116391),x116392),f250(f935(x116391,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(11642,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x116421),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(11647,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(x116471,x116471)),f334(f334(f260(x116471,x116471),x116472),x116473)),f160(x116471,f120(f935(x116471,a927)))))), % 188.31/188.32 inference(rename_variables,[],[4806])). % 188.31/188.32 cnf(11650,plain, % 188.31/188.32 (~E(f334(f317(x116501,f935(x116501,a922),x116502),x116503),f334(f315(x116501),x116503))), % 188.31/188.32 inference(rename_variables,[],[4787])). % 188.31/188.32 cnf(11653,plain, % 188.31/188.32 (~E(f334(f317(x116531,f935(x116531,a922),x116532),x116533),f334(f315(x116531),x116533))), % 188.31/188.32 inference(rename_variables,[],[4787])). % 188.31/188.32 cnf(11658,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x116581),f928(x116581))),f334(f334(f260(f928(x116581),f928(x116581)),x116582),f120(x116581))),f152(x116581,x116583)))), % 188.31/188.32 inference(rename_variables,[],[4807])). % 188.31/188.32 cnf(11664,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x116641),f928(x116641))),f334(f334(f260(f928(x116641),f928(x116641)),x116642),f120(x116641))),f152(x116641,x116643)))), % 188.31/188.32 inference(rename_variables,[],[4807])). % 188.31/188.32 cnf(11667,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116671),x116672),f195(f935(x116671,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11672,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116721),x116722),f195(f935(x116721,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11675,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116751),x116752),f195(f935(x116751,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11678,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116781),x116782),f195(f935(x116781,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11681,plain, % 188.31/188.32 (~P107(f334(f334(f336(x116811),x116812),f195(f935(x116811,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11684,plain, % 188.31/188.32 (P107(f334(f334(f336(x116841),f334(x116842,x116843)),f334(f317(x116844,x116841,x116842),f250(f935(x116844,a922)))))), % 188.31/188.32 inference(rename_variables,[],[4150])). % 188.31/188.32 cnf(11687,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(x116871,x116871)),f334(f334(f260(x116871,x116871),x116872),x116873)),f160(x116871,f120(f935(x116871,a927)))))), % 188.31/188.32 inference(rename_variables,[],[4806])). % 188.31/188.32 cnf(11695,plain, % 188.31/188.32 (E(f121(x116951,f120(x116951)),f120(x116951))), % 188.31/188.32 inference(rename_variables,[],[3396])). % 188.31/188.32 cnf(11698,plain, % 188.31/188.32 (~E(f334(a119,x116981),x116981)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11705,plain, % 188.31/188.32 (~E(f334(a119,x117051),x117051)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11710,plain, % 188.31/188.32 (E(f334(f291(x117101,x117101),f271(x117101,x117102)),x117102)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(11713,plain, % 188.31/188.32 (E(f334(f291(x117131,x117131),f271(x117131,x117132)),x117132)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(11719,plain, % 188.31/188.32 (~E(f334(a119,x117191),x117191)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11731,plain, % 188.31/188.32 (E(f334(f334(f23(a927),f2(a927)),x117311),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[3470])). % 188.31/188.32 cnf(11734,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x117341),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(11741,plain, % 188.31/188.32 (E(f334(f334(f86(a1),f334(f334(f87(a1),x117411),f334(f334(f41(a1),x117412),x117411))),f50(a1,x117412,x117411)),x117412)), % 188.31/188.32 inference(rename_variables,[],[4100])). % 188.31/188.32 cnf(11765,plain, % 188.31/188.32 (~E(f334(a119,x117651),x117651)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11768,plain, % 188.31/188.32 (~E(f334(a119,x117681),x117681)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11788,plain, % 188.31/188.32 (E(f334(f291(x117881,x117881),f271(x117881,x117882)),x117882)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(11797,plain, % 188.31/188.32 (~P107(f334(f334(f179(x117971),f120(x117971)),x117972))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(11803,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),f2(a927)),f334(a119,x118031)))), % 188.31/188.32 inference(rename_variables,[],[3633])). % 188.31/188.32 cnf(11804,plain, % 188.31/188.32 (~E(f334(a119,x118041),x118041)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11807,plain, % 188.31/188.32 (P107(f334(f334(f336(x118071),x118072),f250(f935(x118071,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(11819,plain, % 188.31/188.32 (~E(f334(a119,x118191),x118191)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11822,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x118221),x118221))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(11829,plain, % 188.31/188.32 (P107(f334(f71(x118291,x118292,x118293,x118294,f195(f935(x118291,a922))),x118294))), % 188.31/188.32 inference(rename_variables,[],[4461])). % 188.31/188.32 cnf(11830,plain, % 188.31/188.32 (E(f334(f291(x118301,x118301),f271(x118301,x118302)),x118302)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(11843,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x118431),x118432)),x118432))), % 188.31/188.32 inference(rename_variables,[],[4798])). % 188.31/188.32 cnf(11846,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x118461)),f2(a1)))), % 188.31/188.32 inference(rename_variables,[],[4791])). % 188.31/188.32 cnf(11860,plain, % 188.31/188.32 (~E(f334(f334(f246(a927),f334(a119,x118601)),x118601),f334(a119,x118601))), % 188.31/188.32 inference(scs_inference,[],[3786,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,3474,4729,10719,10819,11286,3161,3163,3171,3172,3178,3187,3194,3205,3214,3215,3236,3242,3279,3284,3285,3307,3320,3325,3338,3342,4713,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,3491,4008,3385,4100,11741,3450,3382,3412,3394,4022,3610,11132,3484,4183,4740,10552,10716,4787,11312,11411,11650,11653,3657,3447,3448,10619,10949,3363,3470,11731,4322,4186,11332,11467,11528,4807,11234,11480,11591,11617,11658,11664,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,3916,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,11302,3997,3538,3633,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,4791,3984,3757,4132,3580,3582,3556,4777,4737,3740,4794,4315,11614,3875,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,4286,4194,11129,4241,3917,4274,3934,10682,10779,11338,11416,11501,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,3555,10674,10730,10964,11059,11179,4776,10569,10595,11101,11143,3705,10824,10915,11187,11231,11470,11473,11554,11639,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,3614,10946,10976,10985,10988,10991,3646,4069,4006,10598,4786,10549,10934,10937,11435,11451,3574,10979,11137,4784,4077,4768,4771,3531,3535,4770,4769,4805,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,4150,3992,11247,11253,3849,11391,3994,10982,11354,11525,11559,3815,10898,10901,10994,11163,4800,4801,10738,10851,4414,4327,4030,4798,10574,10577,10940,10943,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607])). % 188.31/188.32 cnf(11869,plain, % 188.31/188.32 (E(f334(f291(x118691,x118691),f271(x118691,x118692)),x118692)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(11874,plain, % 188.31/188.32 (E(f334(f291(x118741,x118741),f271(x118741,x118742)),x118742)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(11877,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x118771)),f2(a1)))), % 188.31/188.32 inference(rename_variables,[],[4791])). % 188.31/188.32 cnf(11882,plain, % 188.31/188.32 (~E(f334(a119,x118821),x118821)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11891,plain, % 188.31/188.32 (~P107(f334(f334(f179(x118911),f120(x118911)),x118912))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(11912,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x119121)),f2(a1)))), % 188.31/188.32 inference(rename_variables,[],[4791])). % 188.31/188.32 cnf(11915,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x119151),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(11916,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x119161),f334(a119,x119161)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(11919,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x119191)),f2(a1)))), % 188.31/188.32 inference(rename_variables,[],[4791])). % 188.31/188.32 cnf(11922,plain, % 188.31/188.32 (~P107(f334(f334(f336(x119221),x119222),f195(f935(x119221,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(11923,plain, % 188.31/188.32 (P107(f334(f334(f336(f935(x119231,a922)),x119232),f334(f315(x119231),x119232)))), % 188.31/188.32 inference(rename_variables,[],[3917])). % 188.31/188.32 cnf(11938,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x119381)),x119381))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(11939,plain, % 188.31/188.32 (~E(f334(a119,x119391),x119391)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11949,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x119491),x119492)),x119491))), % 188.31/188.32 inference(rename_variables,[],[4799])). % 188.31/188.32 cnf(11952,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x119521)),f2(a1)))), % 188.31/188.32 inference(rename_variables,[],[4791])). % 188.31/188.32 cnf(11955,plain, % 188.31/188.32 (~E(f334(a119,x119551),x119551)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(11968,plain, % 188.31/188.32 (P107(f334(f334(f336(x119681),x119682),f334(f334(f316(x119681),x119682),x119683)))), % 188.31/188.32 inference(rename_variables,[],[3865])). % 188.31/188.32 cnf(11969,plain, % 188.31/188.32 (~P107(f334(f334(f242(a1),f2(a1)),f334(f85(a1),f334(f107(a1),f334(a119,x119691)))))), % 188.31/188.32 inference(rename_variables,[],[4800])). % 188.31/188.32 cnf(11972,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),f334(f334(f23(a927),x119721),x119722)),f334(a119,x119721)))), % 188.31/188.32 inference(rename_variables,[],[3997])). % 188.31/188.32 cnf(11975,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f50(a927,x119751,x119752)),x119751))), % 188.31/188.32 inference(rename_variables,[],[4006])). % 188.31/188.32 cnf(11981,plain, % 188.31/188.32 (E(f334(f291(x119811,x119811),f271(x119811,x119812)),x119812)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(11986,plain, % 188.31/188.32 (E(f334(f334(f141(x119861),f176(x119861,x119862,x119863)),f176(x119861,x119864,x119863)),f334(f334(f141(x119861),f176(x119861,x119864,x119863)),f176(x119861,x119862,x119863)))), % 188.31/188.32 inference(rename_variables,[],[4113])). % 188.31/188.32 cnf(11991,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x119911)),x119911))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12000,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x120001),x120001))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12003,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f50(a927,x120031,x120032)),x120031))), % 188.31/188.32 inference(rename_variables,[],[4006])). % 188.31/188.32 cnf(12004,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x120041))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(12006,plain, % 188.31/188.32 (~P107(f334(f334(f242(a1),f84(a1)),f2(a1)))), % 188.31/188.32 inference(scs_inference,[],[3786,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,3474,4729,10719,10819,11286,3160,3161,3163,3164,3171,3172,3178,3187,3194,3205,3214,3215,3236,3242,3279,3284,3285,3304,3305,3307,3316,3317,3318,3320,3325,3338,3342,4713,4113,11986,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,3491,4008,3385,3749,4100,11741,3450,3382,3412,3407,3394,3395,4022,3610,11132,3484,4183,4740,10552,10716,4787,11312,11411,11650,11653,3657,3447,3448,10619,10949,3709,3363,3470,11731,4322,4186,11332,11467,11528,4807,11234,11480,11591,11617,11658,11664,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,3916,4600,4601,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,3997,3538,3633,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,4791,11846,11877,11912,11919,3984,3757,4132,3580,3582,3556,4777,4737,3740,4794,4315,11614,3875,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,4286,4194,11129,4241,3917,4274,3934,10682,10779,11338,11416,11501,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,3555,10674,10730,10964,11059,11179,4776,10569,10595,11101,11143,11152,3705,10824,10915,11187,11231,11470,11473,11554,11639,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,3614,10946,10976,10985,10988,10991,3653,3646,4069,4006,10598,11975,4786,10549,10934,10937,11435,11451,11938,3574,10979,11137,11207,4784,4077,4768,4771,3531,3535,4770,4769,4805,3865,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,4150,3992,11247,11253,3849,11391,3994,10982,11354,11525,11559,3815,10898,10901,10994,11163,4800,4801,10738,10851,4414,4327,4030,4798,10574,10577,10940,10943,4799,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059])). % 188.31/188.32 cnf(12021,plain, % 188.31/188.32 (P59(a927,x120211,x120211)), % 188.31/188.32 inference(rename_variables,[],[3459])). % 188.31/188.32 cnf(12024,plain, % 188.31/188.32 (P59(a927,x120241,x120241)), % 188.31/188.32 inference(rename_variables,[],[3459])). % 188.31/188.32 cnf(12027,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x120271),x120271))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12030,plain, % 188.31/188.32 (P107(f334(f334(f336(x120301),f334(x120302,x120303)),f334(f317(x120304,x120301,x120302),f250(f935(x120304,a922)))))), % 188.31/188.32 inference(rename_variables,[],[4150])). % 188.31/188.32 cnf(12031,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x120311)),x120311))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12034,plain, % 188.31/188.32 (P107(f334(f334(f336(x120341),f334(x120342,x120343)),f334(f317(x120344,x120341,x120342),f250(f935(x120344,a922)))))), % 188.31/188.32 inference(rename_variables,[],[4150])). % 188.31/188.32 cnf(12035,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x120351),x120352)),x120352))), % 188.31/188.32 inference(rename_variables,[],[4798])). % 188.31/188.32 cnf(12040,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x120401),x120402)),x120401))), % 188.31/188.32 inference(rename_variables,[],[4799])). % 188.31/188.32 cnf(12043,plain, % 188.31/188.32 (~P107(f334(f334(f179(x120431),f120(x120431)),x120432))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(12046,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x120461),x120461))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12052,plain, % 188.31/188.32 (~P37(x120521,x120522,f120(x120521))), % 188.31/188.32 inference(rename_variables,[],[4751])). % 188.31/188.32 cnf(12055,plain, % 188.31/188.32 (P107(f334(f334(f336(x120551),x120552),f250(f935(x120551,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(12056,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x120561)),x120561))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12069,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x120691)),x120691))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12070,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x120701),f334(a119,x120701)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12073,plain, % 188.31/188.32 (~P107(f334(f334(f336(x120731),x120732),f195(f935(x120731,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12076,plain, % 188.31/188.32 (E(f334(f334(f16(x120761,x120762),x120763),x120764),x120763)), % 188.31/188.32 inference(rename_variables,[],[3545])). % 188.31/188.32 cnf(12079,plain, % 188.31/188.32 (E(f334(f334(f16(x120791,x120792),x120793),x120794),x120793)), % 188.31/188.32 inference(rename_variables,[],[3545])). % 188.31/188.32 cnf(12091,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),f2(a927)),f334(a119,x120911)))), % 188.31/188.32 inference(rename_variables,[],[3633])). % 188.31/188.32 cnf(12094,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x120941),x120941))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12097,plain, % 188.31/188.32 (P107(f334(f66(x120971),f334(f179(x120971),x120972)))), % 188.31/188.32 inference(rename_variables,[],[3593])). % 188.31/188.32 cnf(12100,plain, % 188.31/188.32 (P107(f334(f66(x121001),f334(f179(x121001),x121002)))), % 188.31/188.32 inference(rename_variables,[],[3593])). % 188.31/188.32 cnf(12103,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),f334(f85(a1),f334(f107(a1),x121031))),f334(f107(a1),x121032)))), % 188.31/188.32 inference(rename_variables,[],[4031])). % 188.31/188.32 cnf(12106,plain, % 188.31/188.32 (~P107(f334(f334(f336(x121061),x121062),f195(f935(x121061,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12122,plain, % 188.31/188.32 (~P107(f334(f334(f336(a927),x121221),f334(f307(a927),f2(a927))))), % 188.31/188.32 inference(scs_inference,[],[3786,3459,12021,4750,4751,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,3474,4729,10719,10819,11286,3160,3161,3163,3164,3167,3171,3172,3178,3187,3194,3202,3205,3214,3215,3236,3242,3279,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,3342,4713,4113,11986,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,3491,4008,3385,3749,4100,11741,3450,3382,3412,3407,3394,3395,4022,3610,11132,3484,4183,4740,10552,10716,3545,12076,4787,11312,11411,11650,11653,3657,3447,3448,10619,10949,3709,3363,3470,11731,4322,4186,11332,11467,11528,4807,11234,11480,11591,11617,11658,11664,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,3916,4600,4601,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,3997,11972,3538,3633,11803,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,4791,11846,11877,11912,11919,3984,3757,4132,3580,3582,3556,4777,4737,3740,4794,4315,11614,3875,3593,12097,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,4286,4194,11129,4241,3917,4274,3934,10682,10779,11338,11416,11501,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,3555,10674,10730,10964,11059,11179,3629,4776,10569,10595,11101,11143,11152,12000,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,3614,10946,10976,10985,10988,10991,3653,3646,4069,4006,10598,11975,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,3574,10979,11137,11207,4031,4784,4077,4768,4771,3531,3535,4770,4769,4805,3865,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,4150,11684,12030,3992,11247,11253,3849,11391,3994,10982,11354,11525,11559,3815,10898,10901,10994,11163,4800,11969,4801,10738,10851,4414,4327,4030,3971,4798,10574,10577,10940,10943,11843,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405])). % 188.31/188.32 cnf(12125,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x121251),x121251))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12128,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x121281),x121281))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12137,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x121371),x121371))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12140,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x121401),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12145,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x121451),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12154,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x121541))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(12155,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x121551)),x121551))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12158,plain, % 188.31/188.32 (~P107(f334(f334(f179(x121581),f120(x121581)),x121582))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(12161,plain, % 188.31/188.32 (~P107(f334(f334(f179(x121611),f120(x121611)),x121612))), % 188.31/188.32 inference(rename_variables,[],[4785])). % 188.31/188.32 cnf(12164,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x121641),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12165,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x121651),f334(a119,x121651)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12181,plain, % 188.31/188.32 (P107(f334(f334(f243(a1),f334(f85(a1),f84(a1))),f2(a1)))), % 188.31/188.32 inference(scs_inference,[],[3786,3459,12021,4750,4751,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,3474,4729,10719,10819,11286,3160,3161,3163,3164,3167,3171,3172,3175,3178,3187,3194,3197,3202,3205,3214,3215,3236,3242,3279,3283,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,3342,4713,4113,11986,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,3491,4008,3385,3749,4100,11741,3450,3382,3412,3407,3394,3395,4022,3610,11132,3484,4183,4740,10552,10716,3545,12076,4787,11312,11411,11650,11653,3657,3447,3448,10619,10949,3709,3363,3470,11731,4322,4186,11332,11467,11528,4807,11234,11480,11591,11617,11658,11664,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,3916,4600,4601,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,3997,11972,3538,3633,11803,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,4791,11846,11877,11912,11919,11952,3984,3757,4132,3580,3582,3556,4777,4737,3740,4794,4315,11614,3875,3593,12097,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,4286,4194,11129,4241,3917,4274,3934,10682,10779,11338,11416,11501,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,3555,10674,10730,10964,11059,11179,11822,12125,12128,3629,4776,10569,10595,11101,11143,11152,12000,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,3614,10946,10976,10985,10988,10991,3653,3646,4069,4006,10598,11975,12003,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,3574,10979,11137,11207,12004,4031,4784,4077,4768,4771,3531,3535,4770,4769,4805,3865,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,4150,11684,12030,3992,11247,11253,3849,11391,3994,10982,11354,11525,11559,3815,10898,10901,10994,11163,4800,11969,4801,10738,10851,4414,4327,4030,3971,4798,10574,10577,10940,10943,11843,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405,6431,6448,6500,6537,6538,6559,6560,6567,6572,6573,6576,6588,6603,6624,6625,6630,6633,6642,6657,6680,6686,6688,6703,6704])). % 188.31/188.32 cnf(12184,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x121841)),x121841))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12187,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x121871)),x121871))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12190,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x121901)),x121901))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12193,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x121931)),x121931))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12196,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x121961),x121961))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12199,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x121991),x121991))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12202,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x122021),x122021))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12205,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x122051),x122051))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12222,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x122221),x122221))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12225,plain, % 188.31/188.32 (P27(a927,a927,a119,x122251)), % 188.31/188.32 inference(rename_variables,[],[3755])). % 188.31/188.32 cnf(12228,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x122281),x122281))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12239,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x122391),x122391))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12242,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(f934(f928(x122421),f928(x122421)),a922)),f165(x122421,x122422)),f314(f928(x122421),f164(x122421,x122422))))), % 188.31/188.32 inference(rename_variables,[],[4246])). % 188.31/188.32 cnf(12249,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x122491),f334(a119,x122491)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12252,plain, % 188.31/188.32 (P107(f334(f334(f336(f935(x122521,a922)),x122522),f334(f315(x122521),x122522)))), % 188.31/188.32 inference(rename_variables,[],[3917])). % 188.31/188.32 cnf(12253,plain, % 188.31/188.32 (~E(f334(a119,x122531),x122531)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12258,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x122581),x122581))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12263,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x122631),x122631))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12270,plain, % 188.31/188.32 (P107(f334(f66(a927),f312(a927,x122701,x122702)))), % 188.31/188.32 inference(rename_variables,[],[3758])). % 188.31/188.32 cnf(12277,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x122771,a922)),x122772),f334(f334(f316(x122771),x122773),x122772)))), % 188.31/188.32 inference(rename_variables,[],[3992])). % 188.31/188.32 cnf(12280,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x122801),x122801))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12281,plain, % 188.31/188.32 (~E(f334(a119,x122811),x122811)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12292,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x122921),x122921))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12293,plain, % 188.31/188.32 (~E(f334(a119,x122931),x122931)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12296,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x122961),x122961))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12299,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x122991),x122991))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12302,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x123021),x123021))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12305,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x123051),x123051))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12308,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x123081),x123081))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12311,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123111),x123111))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12314,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123141),x123141))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12315,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x123151),f334(a119,x123151)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12322,plain, % 188.31/188.32 (~E(f334(a119,x123221),x123221)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12327,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123271),x123271))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12328,plain, % 188.31/188.32 (~E(f334(a119,x123281),x123281)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12331,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x123311),x123311))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12344,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x123441),f334(a119,x123441)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12351,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x123511),x123511))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(12356,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x123561))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(12370,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123701),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12373,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123731),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12376,plain, % 188.31/188.32 (~P107(f334(f334(f336(x123761),x123762),f195(f935(x123761,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12379,plain, % 188.31/188.32 (~P107(f334(f334(f336(x123791),x123792),f195(f935(x123791,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12382,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123821),x123821))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12384,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123841),f334(f334(f246(a927),x123841),x123842)))), % 188.31/188.32 inference(scs_inference,[],[3786,3459,12021,4750,4751,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,3755,3474,4729,10719,10819,11286,3160,3161,3163,3164,3167,3171,3172,3175,3178,3187,3194,3197,3202,3205,3214,3215,3236,3242,3279,3283,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,3342,4713,4113,11986,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,3491,3500,4008,4308,3385,3749,4100,11741,3450,3382,3412,3407,3394,3395,4022,3610,11132,3484,4183,4740,10552,10716,3545,12076,4787,11312,11411,11650,11653,3657,3447,3448,10619,10949,3709,3363,3470,11731,4322,4186,11332,11467,11528,4807,11234,11480,11591,11617,11658,11664,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,3916,4600,4601,3853,4065,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,3997,11972,3538,3633,11803,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,4791,11846,11877,11912,11919,11952,3984,3757,3758,4132,3580,3582,3556,4777,4737,3740,4794,4315,11614,3875,3593,12097,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,4286,4246,4194,11129,4241,3917,11923,4274,3934,10682,10779,11338,11416,11501,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,3629,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,3614,10946,10976,10985,10988,10991,3653,3646,4069,4006,10598,11975,12003,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,3574,10979,11137,11207,12004,12154,4031,4784,4043,4077,4768,4771,3531,3535,4770,4769,4805,3865,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,4150,11684,12030,3992,11247,11253,11273,3849,11391,3994,10982,11354,11525,11559,3815,10898,10901,10994,11163,4800,11969,4801,10738,10851,4414,4327,4030,3971,4798,10574,10577,10940,10943,11843,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405,6431,6448,6500,6537,6538,6559,6560,6567,6572,6573,6576,6588,6603,6624,6625,6630,6633,6642,6657,6680,6686,6688,6703,6704,6708,6710,6711,6712,6714,6716,6717,6718,6720,6726,6727,6729,6730,6736,6738,6779,6784,6800,6802,6803,6804,6837,6842,6844,6849,6850,6858,6862,6874,6897,6898,6900,6901,6912,6916,6919,6937,6940,6958,6989,6990,6991,6997,7006,7025,7027,7029,7031,7036,7042,7045,7057,7062,7063,7097,7098,7099,7114,7115,7117,7118,7119,7137,7139,7154,7180,7203,7214,7216,7218,7220,7221,7252,7253,7257,7258,7266,7268])). % 188.31/188.32 cnf(12385,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123851),x123851))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12388,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123881),x123881))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12391,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x123911),x123911))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12394,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x123941),f334(a119,x123941)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12401,plain, % 188.31/188.32 (P107(f334(f334(f336(f935(x124011,a922)),x124012),f334(f315(x124011),x124012)))), % 188.31/188.32 inference(rename_variables,[],[3917])). % 188.31/188.32 cnf(12406,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x124061,a922)),x124062),f334(f334(f316(x124061),x124063),x124062)))), % 188.31/188.32 inference(rename_variables,[],[3992])). % 188.31/188.32 cnf(12413,plain, % 188.31/188.32 (~P107(f334(f334(f336(x124131),x124132),f195(f935(x124131,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12422,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x124221,a922)),x124222),f250(f935(x124221,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(12423,plain, % 188.31/188.32 (~E(f334(a119,x124231),x124231)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12426,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x124261,a922)),f334(f179(x124261),f334(f143(x124261,x124262),x124263))),f334(f179(x124261),x124263)))), % 188.31/188.32 inference(rename_variables,[],[4194])). % 188.31/188.32 cnf(12432,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x124321),f334(a119,x124321)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12441,plain, % 188.31/188.32 (E(f334(f291(x124411,x124411),f271(x124411,x124412)),x124412)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12452,plain, % 188.31/188.32 (~P107(f334(f334(f242(a927),f334(a119,x124521)),x124521))), % 188.31/188.32 inference(rename_variables,[],[4786])). % 188.31/188.32 cnf(12453,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x124531),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12456,plain, % 188.31/188.32 (P107(f334(f66(x124561),f195(f935(x124561,a922))))), % 188.31/188.32 inference(rename_variables,[],[3629])). % 188.31/188.32 cnf(12457,plain, % 188.31/188.32 (~P107(f334(f334(f336(x124571),x124572),f195(f935(x124571,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12464,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x124641,a922)),f334(f179(x124641),f183(x124641,x124642,x124643))),f334(f179(x124641),x124642)))), % 188.31/188.32 inference(rename_variables,[],[4241])). % 188.31/188.32 cnf(12467,plain, % 188.31/188.32 (P27(x124671,x124671,f5(x124671),x124672)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12472,plain, % 188.31/188.32 (P107(f334(f334(f336(f935(x124721,a922)),x124722),f334(f315(x124721),x124722)))), % 188.31/188.32 inference(rename_variables,[],[3917])). % 188.31/188.32 cnf(12479,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x124791),x124791))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12482,plain, % 188.31/188.32 (~P107(f334(f334(f336(x124821),x124822),f195(f935(x124821,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12485,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x124851,a922)),x124852),f334(f334(f316(x124851),x124853),x124852)))), % 188.31/188.32 inference(rename_variables,[],[3992])). % 188.31/188.32 cnf(12486,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x124861,a922)),x124862),f250(f935(x124861,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(12493,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x124931),x124931))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12496,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x124961),x124961))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12499,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x124991),x124991))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12502,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x125021),x125021))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12505,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x125051),f334(a119,x125051)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12508,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x125081),f334(a119,x125081)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12511,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x125111,a922)),x125112),x125112))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(12518,plain, % 188.31/188.32 (P107(f334(f334(f336(f935(x125181,a922)),x125182),f334(f315(x125181),x125182)))), % 188.31/188.32 inference(rename_variables,[],[3917])). % 188.31/188.32 cnf(12527,plain, % 188.31/188.32 (~E(f334(a119,x125271),x125271)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12528,plain, % 188.31/188.32 (E(f334(f317(x125281,x125281,f5(x125281)),x125282),x125282)), % 188.31/188.32 inference(rename_variables,[],[3610])). % 188.31/188.32 cnf(12531,plain, % 188.31/188.32 (P34(x125311,x125312,f120(x125311),f120(x125311))), % 188.31/188.32 inference(rename_variables,[],[3796])). % 188.31/188.32 cnf(12534,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x125341,a922)),f334(f179(x125341),f183(x125341,x125342,x125343))),f334(f179(x125341),x125342)))), % 188.31/188.32 inference(rename_variables,[],[4241])). % 188.31/188.32 cnf(12535,plain, % 188.31/188.32 (P107(f334(f66(x125351),f334(f179(x125351),x125352)))), % 188.31/188.32 inference(rename_variables,[],[3593])). % 188.31/188.32 cnf(12546,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x125461),x125461))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12549,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x125491),x125491))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12554,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x125541))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(12561,plain, % 188.31/188.32 (P15(a927,f334(f175(a927),f334(f334(f161(f928(x125611),a927),f196(f928(x125611))),f186(x125611,x125612))))), % 188.31/188.32 inference(rename_variables,[],[4110])). % 188.31/188.32 cnf(12564,plain, % 188.31/188.32 (P27(x125641,x125641,f5(x125641),x125642)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12567,plain, % 188.31/188.32 (P27(x125671,x125671,f5(x125671),x125672)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12570,plain, % 188.31/188.32 (P107(f334(f334(f336(f928(x125701)),f120(x125701)),f168(x125701,x125702)))), % 188.31/188.32 inference(rename_variables,[],[3747])). % 188.31/188.32 cnf(12573,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x125731,f935(x125732,a922))),x125733),x125734))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(12578,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x125781),x125781))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12579,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x125791))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(12581,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),f2(a1)),f908(x125811,f195(f935(x125812,f935(x125813,a922))),f84(a1))))), % 188.31/188.32 inference(scs_inference,[],[3786,11406,12467,12564,3796,3459,12021,4750,4751,4749,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,3755,3474,4729,10719,10819,11286,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3187,3194,3197,3202,3205,3214,3215,3236,3242,3279,3283,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,3342,4713,4113,11986,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,3491,3500,4008,4308,3385,3749,4100,11741,3450,3382,3412,3407,3394,3395,4022,3431,3610,11132,11256,3484,4183,4740,10552,10716,3545,12076,4787,11312,11411,11650,11653,3657,3447,3448,10619,10949,3709,3363,3470,11731,4322,4186,11332,11467,11528,4807,11234,11480,11591,11617,11658,11664,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,3916,4600,4601,3853,4065,4110,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,4791,11846,11877,11912,11919,11952,3984,3757,3758,4132,3580,3582,3556,4777,4737,3740,4794,4315,11614,3875,3593,12097,12100,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,4286,4246,4194,11129,4241,11335,12464,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,3629,12456,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,3614,10946,10976,10985,10988,10991,3653,3646,4069,4006,10598,11975,12003,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,3574,10979,11137,11207,12004,12154,12356,12554,4031,4784,4043,4077,4768,4771,3531,3535,4770,4769,4805,3865,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,4150,11684,12030,3992,11247,11253,11273,12277,12406,3849,11391,11519,3994,10982,11354,11525,11559,3815,10898,10901,10994,11163,4800,11969,4801,10738,10851,11636,12573,4414,4327,4030,3971,4798,10574,10577,10940,10943,11843,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405,6431,6448,6500,6537,6538,6559,6560,6567,6572,6573,6576,6588,6603,6624,6625,6630,6633,6642,6657,6680,6686,6688,6703,6704,6708,6710,6711,6712,6714,6716,6717,6718,6720,6726,6727,6729,6730,6736,6738,6779,6784,6800,6802,6803,6804,6837,6842,6844,6849,6850,6858,6862,6874,6897,6898,6900,6901,6912,6916,6919,6937,6940,6958,6989,6990,6991,6997,7006,7025,7027,7029,7031,7036,7042,7045,7057,7062,7063,7097,7098,7099,7114,7115,7117,7118,7119,7137,7139,7154,7180,7203,7214,7216,7218,7220,7221,7252,7253,7257,7258,7266,7268,7269,7270,7292,7301,7302,7312,7322,7362,7372,7376,7383,7394,7399,7401,7408,7416,7429,7446,7467,7469,7488,7539,7540,7541,7543,7546,7550,7555,7609,7638,7653,7669,7700,7703,7725,7748,7766,7769,7770,7780,7799,7801,7803,7805,7806,7807,7830,7856,7857,7888,7890,7891,7892,7897,7917,7935,7940,7947,7949,7957,7969,7970,7972,7994,8000,8023,8091,8092,8093,8136,8142,8143,8163,8164])). % 188.31/188.32 cnf(12582,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x125821,f935(x125822,a922))),x125823),x125824))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(12585,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(f934(f928(x125851),f928(x125851)),a922)),f165(x125851,x125852)),f314(f928(x125851),f164(x125851,x125852))))), % 188.31/188.32 inference(rename_variables,[],[4246])). % 188.31/188.32 cnf(12591,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x125911,a922)),f334(f317(x125912,x125911,x125913),f334(f318(x125912,x125911,x125913),x125914))),x125914))), % 188.31/188.32 inference(rename_variables,[],[4414])). % 188.31/188.32 cnf(12594,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x125941,a922)),f334(f179(x125941),f183(x125941,x125942,x125943))),f334(f179(x125941),x125942)))), % 188.31/188.32 inference(rename_variables,[],[4241])). % 188.31/188.32 cnf(12595,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x125951,a922)),f334(f179(x125951),f334(f143(x125951,x125952),x125953))),f334(f179(x125951),x125953)))), % 188.31/188.32 inference(rename_variables,[],[4194])). % 188.31/188.32 cnf(12598,plain, % 188.31/188.32 (~P107(f334(f334(f243(f935(x125981,a922)),x125982),f195(f935(x125981,a922))))), % 188.31/188.32 inference(rename_variables,[],[4795])). % 188.31/188.32 cnf(12606,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x126061,a922)),f334(f317(x126062,x126061,x126063),f334(f318(x126062,x126061,x126063),x126064))),x126064))), % 188.31/188.32 inference(rename_variables,[],[4414])). % 188.31/188.32 cnf(12611,plain, % 188.31/188.32 (P107(f334(f334(f336(f928(x126111)),f120(x126111)),f168(x126111,x126112)))), % 188.31/188.32 inference(rename_variables,[],[3747])). % 188.31/188.32 cnf(12614,plain, % 188.31/188.32 (~P107(f334(f334(f336(f934(f928(x126141),f928(x126141))),f334(f334(f260(f928(x126141),f928(x126141)),x126142),f120(x126141))),f152(x126141,x126143)))), % 188.31/188.32 inference(rename_variables,[],[4807])). % 188.31/188.32 cnf(12617,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x126171),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12619,plain, % 188.31/188.32 (~P107(f334(f66(x126191),f250(f935(x126191,a922))))), % 188.31/188.32 inference(scs_inference,[],[3786,11406,12467,12564,3796,3804,3459,12021,3524,4750,4751,3422,3425,4749,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,3755,3474,4729,10719,10819,11286,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3187,3194,3197,3202,3205,3214,3215,3216,3236,3242,3279,3283,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,3342,4713,4113,11986,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,3491,3500,4008,4308,3385,3749,4100,11741,3450,3382,3412,3407,3394,3395,4022,3431,3610,11132,11256,3484,4183,4740,10552,10716,3545,12076,4787,11312,11411,11650,11653,3657,3447,3448,10619,10949,3709,3363,3470,11731,4322,4186,11332,11467,11528,4807,11234,11480,11591,11617,11658,11664,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,12570,12611,3916,4600,4601,3853,4065,4110,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,4791,11846,11877,11912,11919,11952,3984,3757,3758,4132,3580,3582,3556,4777,4737,3740,4794,4315,11614,3875,3593,12097,12100,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,4286,4246,12242,12585,4194,11129,12426,4241,11335,12464,12534,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,3629,12456,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,3614,10946,10976,10985,10988,10991,3653,3646,4069,4006,10598,11975,12003,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,3574,10979,11137,11207,12004,12154,12356,12554,4031,4784,4043,4077,4768,4771,3531,3535,4770,4769,4805,3865,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,4150,11684,12030,3992,11247,11253,11273,12277,12406,3849,11391,11519,12511,3994,10982,11354,11525,11559,3815,10898,10901,10994,11163,4800,11969,4801,10738,10851,11636,12573,4414,11120,12591,4327,4030,3971,4798,10574,10577,10940,10943,11843,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,92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% 188.31/188.32 cnf(12620,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x126201,a922)),x126202),x126202))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(12623,plain, % 188.31/188.32 (~P107(f334(f334(f336(x126231),x126232),f195(f935(x126231,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12626,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x126261,f935(x126262,a922))),x126263),x126264))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(12629,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x126291,a922)),f334(f317(x126292,x126291,x126293),f334(f318(x126292,x126291,x126293),x126294))),x126294))), % 188.31/188.32 inference(rename_variables,[],[4414])). % 188.31/188.32 cnf(12630,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x126301,a922)),x126302),x126302))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(12635,plain, % 188.31/188.32 (E(f334(f291(x126351,x126351),f271(x126351,x126352)),x126352)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12638,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x126381,a922)),f334(f179(x126381),f183(x126381,x126382,x126383))),f334(f179(x126381),x126382)))), % 188.31/188.32 inference(rename_variables,[],[4241])). % 188.31/188.32 cnf(12639,plain, % 188.31/188.32 (P107(f334(f66(x126391),f334(f179(x126391),x126392)))), % 188.31/188.32 inference(rename_variables,[],[3593])). % 188.31/188.32 cnf(12642,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x126421),x126421))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12645,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x126451),x126451))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12648,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x126481),x126481))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12659,plain, % 188.31/188.32 (P27(x126591,x126591,f5(x126591),x126592)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12667,plain, % 188.31/188.32 (~P107(f334(f334(f336(x126671),x126672),f195(f935(x126671,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12670,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x126701,x126701)),f334(f334(f260(x126701,x126701),x126702),x126702)),f314(x126701,x126703)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(12673,plain, % 188.31/188.32 (~P107(f334(f334(f336(x126731),x126732),f195(f935(x126731,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12676,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x126761,x126761)),f334(f334(f260(x126761,x126761),x126762),x126762)),f314(x126761,x126763)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(12683,plain, % 188.31/188.32 (~E(f334(f334(f158(x126831),x126832),x126833),x126833)), % 188.31/188.32 inference(rename_variables,[],[4740])). % 188.31/188.32 cnf(12690,plain, % 188.31/188.32 (P107(f334(f334(f336(x126901),x126902),f250(f935(x126901,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(12691,plain, % 188.31/188.32 (~E(f334(a119,x126911),x126911)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12694,plain, % 188.31/188.32 (P107(f334(f334(f336(f928(x126941)),f120(x126941)),f168(x126941,x126942)))), % 188.31/188.32 inference(rename_variables,[],[3747])). % 188.31/188.32 cnf(12695,plain, % 188.31/188.32 (~E(f334(f334(f158(x126951),x126952),x126953),f120(x126951))), % 188.31/188.32 inference(rename_variables,[],[4747])). % 188.31/188.32 cnf(12698,plain, % 188.31/188.32 (P27(x126981,x126981,f5(x126981),x126982)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12701,plain, % 188.31/188.32 (P107(f334(f334(f336(x127011),f334(x127012,x127013)),f334(f317(x127014,x127011,x127012),f250(f935(x127014,a922)))))), % 188.31/188.32 inference(rename_variables,[],[4150])). % 188.31/188.32 cnf(12702,plain, % 188.31/188.32 (P27(x127021,x127021,f5(x127021),x127022)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12705,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127051,a922)),f195(f935(x127051,a922))),x127052))), % 188.31/188.32 inference(rename_variables,[],[3994])). % 188.31/188.32 cnf(12706,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127061,a922)),x127062),x127062))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(12709,plain, % 188.31/188.32 (P107(f334(f334(f336(x127091),f334(x127092,x127093)),f334(f317(x127094,x127091,x127092),f250(f935(x127094,a922)))))), % 188.31/188.32 inference(rename_variables,[],[4150])). % 188.31/188.32 cnf(12710,plain, % 188.31/188.32 (P27(x127101,x127101,f5(x127101),x127102)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12713,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(f928(x127131),f928(x127131))),f334(f334(f260(f928(x127131),f928(x127131)),f120(x127131)),f120(x127131))),f165(x127131,x127132)))), % 188.31/188.32 inference(rename_variables,[],[4322])). % 188.31/188.32 cnf(12717,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x127171),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(12723,plain, % 188.31/188.32 (E(f334(f334(f141(x127231),x127232),f120(x127231)),x127232)), % 188.31/188.32 inference(rename_variables,[],[3485])). % 188.31/188.32 cnf(12724,plain, % 188.31/188.32 (~E(f334(f334(f158(x127241),x127242),x127243),x127243)), % 188.31/188.32 inference(rename_variables,[],[4740])). % 188.31/188.32 cnf(12727,plain, % 188.31/188.32 (E(f334(f334(f141(x127271),x127272),f120(x127271)),x127272)), % 188.31/188.32 inference(rename_variables,[],[3485])). % 188.31/188.32 cnf(12728,plain, % 188.31/188.32 (~E(f334(f334(f158(x127281),x127282),x127283),x127283)), % 188.31/188.32 inference(rename_variables,[],[4740])). % 188.31/188.32 cnf(12731,plain, % 188.31/188.32 (E(f334(f334(f141(x127311),x127312),f120(x127311)),x127312)), % 188.31/188.32 inference(rename_variables,[],[3485])). % 188.31/188.32 cnf(12738,plain, % 188.31/188.32 (P54(x127381,f271(x127381,x127382))), % 188.31/188.32 inference(rename_variables,[],[3426])). % 188.31/188.32 cnf(12741,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127411,a922)),f334(f179(x127411),f334(f143(x127411,x127412),x127413))),f334(f179(x127411),x127413)))), % 188.31/188.32 inference(rename_variables,[],[4194])). % 188.31/188.32 cnf(12742,plain, % 188.31/188.32 (E(f334(f317(x127421,x127421,f5(x127421)),x127422),x127422)), % 188.31/188.32 inference(rename_variables,[],[3610])). % 188.31/188.32 cnf(12747,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127471,a922)),x127472),f250(f935(x127471,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(12751,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x127511),x127511))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12752,plain, % 188.31/188.32 (~E(f334(a119,x127521),x127521)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12755,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127551,a922)),f195(f935(x127551,a922))),x127552))), % 188.31/188.32 inference(rename_variables,[],[3994])). % 188.31/188.32 cnf(12758,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x127581),x127581))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12761,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127611,a922)),x127612),x127612))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(12766,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127661,a922)),x127662),f334(f334(f316(x127661),x127663),x127662)))), % 188.31/188.32 inference(rename_variables,[],[3992])). % 188.31/188.32 cnf(12769,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x127691,a922)),x127692),x127692))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(12770,plain, % 188.31/188.32 (~P107(f334(f334(f336(x127701),x127702),f195(f935(x127701,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12773,plain, % 188.31/188.32 (~P107(f334(f334(f336(x127731),x127732),f195(f935(x127731,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12782,plain, % 188.31/188.32 (P27(x127821,x127821,f5(x127821),x127822)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12785,plain, % 188.31/188.32 (E(f334(f196(f928(x127851)),f176(x127851,x127852,x127853)),x127852)), % 188.31/188.32 inference(rename_variables,[],[3620])). % 188.31/188.32 cnf(12788,plain, % 188.31/188.32 (P28(x127881,x127881,f32(x127881),x127882,x127882)), % 188.31/188.32 inference(rename_variables,[],[4209])). % 188.31/188.32 cnf(12791,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x127911),x127911))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12792,plain, % 188.31/188.32 (P107(f334(f250(f935(x127921,a922)),x127922))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(12795,plain, % 188.31/188.32 (~P107(f334(f334(f336(x127951),x127952),f195(f935(x127951,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12798,plain, % 188.31/188.32 (P107(f334(f334(f336(x127981),f334(x127982,x127983)),f334(f317(x127984,x127981,x127982),f250(f935(x127984,a922)))))), % 188.31/188.32 inference(rename_variables,[],[4150])). % 188.31/188.32 cnf(12799,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x127991,x127991)),f334(f334(f260(x127991,x127991),x127992),x127992)),f314(x127991,x127993)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(12802,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x128021,x128021)),f334(f334(f260(x128021,x128021),x128022),x128022)),f314(x128021,x128023)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(12805,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x128051),x128051))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(12806,plain, % 188.31/188.32 (P107(f334(f250(f935(x128061,a922)),x128062))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(12809,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x128091,a922)),x128092),f250(f935(x128091,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(12810,plain, % 188.31/188.32 (P28(x128101,x128101,f32(x128101),x128102,x128102)), % 188.31/188.32 inference(rename_variables,[],[4209])). % 188.31/188.32 cnf(12813,plain, % 188.31/188.32 (P107(f334(f66(x128131),f334(f179(x128131),x128132)))), % 188.31/188.32 inference(rename_variables,[],[3593])). % 188.31/188.32 cnf(12823,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x128231,f935(x128232,a922))),x128233),x128234))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(12826,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x128261,f935(x128262,a922))),x128263),x128264))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(12829,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x128291,a922)),x128292),f250(f935(x128291,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(12832,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(x128321,x128321)),f334(f334(f260(x128321,x128321),x128322),x128322)),f314(x128321,x128323)))), % 188.31/188.32 inference(rename_variables,[],[4186])). % 188.31/188.32 cnf(12835,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),f334(f334(f86(a927),x128351),x128352)),x128352))), % 188.31/188.32 inference(rename_variables,[],[4798])). % 188.31/188.32 cnf(12836,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x128361),f334(a119,x128361)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(12839,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x128391,a922)),x128392),f250(f935(x128391,a922))))), % 188.31/188.32 inference(rename_variables,[],[3934])). % 188.31/188.32 cnf(12842,plain, % 188.31/188.32 (E(f334(f291(x128421,x128421),f271(x128421,x128422)),x128422)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12853,plain, % 188.31/188.32 (~P107(f334(f334(f336(x128531),x128532),f195(f935(x128531,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12854,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(f928(x128541),f928(x128541))),f334(f334(f260(f928(x128541),f928(x128541)),f120(x128541)),f120(x128541))),f165(x128541,x128542)))), % 188.31/188.32 inference(rename_variables,[],[4322])). % 188.31/188.32 cnf(12856,plain, % 188.31/188.32 (P107(f334(f334(f336(f934(a927,a927)),f334(f334(f260(a927,a927),f2(a927)),f334(a119,f2(a927)))),f334(f334(f295(a927,a927,a927),f314(a927,a324)),f314(a927,f314(a927,a324)))))), % 188.31/188.32 inference(scs_inference,[],[4209,12788,3786,11406,12467,12564,12567,12659,12698,12702,12710,3796,3804,3459,12021,3524,4750,4751,3422,3425,3426,4749,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,12527,12691,3609,3755,12225,3474,4729,10719,10819,11286,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3187,3194,3197,3202,3205,3214,3215,3216,3236,3242,3279,3283,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,3342,4713,3889,4113,11986,3396,11695,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,12441,12635,3485,12723,12727,12731,3491,3500,4008,4308,3620,3385,3749,4100,11741,3450,3382,3412,3870,3407,3394,3395,4022,3431,3610,11132,11256,12528,12742,3484,4183,4740,10552,10716,11597,12683,12724,4747,12695,3545,12076,4787,11312,11411,11650,11653,3657,4765,3447,3448,10619,10949,3709,3363,3470,11731,4322,12713,4186,11332,11467,11528,12670,12676,12799,12802,12832,4807,11234,11480,11591,11617,11658,11664,12614,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,12570,12611,12694,3916,3698,4600,4601,3853,4065,4110,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,12508,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,12617,4791,11846,11877,11912,11919,11952,3984,3757,3758,4132,3580,3582,3556,4777,4737,3942,3740,4794,4315,11614,3875,3593,12097,12100,12535,12639,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,12161,4286,4246,12242,12585,4194,11129,12426,12595,4241,11335,12464,12534,12594,12638,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,12486,12747,12809,12829,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,12578,12642,12758,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,3629,12456,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,12549,12645,12648,12751,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,12482,12623,12667,12673,12770,12773,12795,3614,10946,10976,10985,10988,10991,11583,12792,3653,3646,4069,4006,10598,11975,12003,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,3574,10979,11137,11207,12004,12154,12356,12554,4031,4784,4043,4077,4768,4771,3531,3535,4770,4769,4805,3865,4461,4797,10845,10848,4806,11321,11324,11516,11627,11647,11687,4150,11684,12030,12034,12701,12709,3992,11247,11253,11273,12277,12406,12485,3849,11391,11519,12511,12620,12630,12706,12761,4320,3994,10982,11354,11525,11559,11570,12705,3815,10898,10901,10994,11163,4800,11969,4801,10738,10851,11636,12573,12582,12626,12823,4414,11120,12591,12606,4327,4030,3971,4798,10574,10577,10940,10943,11843,12035,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405,6431,6448,6500,6537,6538,6559,6560,6567,6572,6573,6576,6588,6603,6624,6625,6630,6633,6642,6657,6680,6686,6688,6703,6704,6708,6710,6711,6712,6714,6716,6717,6718,6720,6726,6727,6729,6730,6736,6738,6779,6784,6800,6802,6803,6804,6837,6842,6844,6849,6850,6858,6862,6874,6897,6898,6900,6901,6912,6916,6919,6937,6940,6958,6989,6990,6991,6997,7006,7025,7027,7029,7031,7036,7042,7045,7057,7062,7063,7097,7098,7099,7114,7115,7117,7118,7119,7137,7139,7154,7180,7203,7214,7216,7218,7220,7221,7252,7253,7257,7258,7266,7268,7269,7270,7292,7301,7302,7312,7322,7362,7372,7376,7383,7394,7399,7401,7408,7416,7429,7446,7467,7469,7488,7539,7540,7541,7543,7546,7550,7555,7609,7638,7653,7669,7700,7703,7725,7748,7766,7769,7770,7780,7799,7801,7803,7805,7806,7807,7830,7856,7857,7888,7890,7891,7892,7897,7917,7935,7940,7947,7949,7957,7969,7970,7972,7994,8000,8023,8091,8092,8093,8136,8142,8143,8163,8164,8181,8182,8183,8238,8239,8269,8300,8309,8321,8333,8363,8367,8373,8385,8403,8409,8429,8474,8504,8518,8537,8540,8563,8589,8644,8645,8648,8649,8717,8755,8756,8757,8758,8815,8845,8853,8854,8889,8909,8955,8964,9015,9018,9035,9042,9087,9132,9133,9150,9151,9165,9275,9281,9285,9299,9310,9338,9340,9343,9349,9351,9352,9363,9364,9386,9392,9402,9409,9449,9467,9529,9530,9532,9571,9597,9603,9635,9645,9646,9647,9649,9650,9664,9685,9700,9713,9714,9715,9717,9756])). % 188.31/188.32 cnf(12859,plain, % 188.31/188.32 (~P107(f334(f334(f336(x128591),x128592),f195(f935(x128591,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12864,plain, % 188.31/188.32 (P33(x128641,x128642,f120(x128641))), % 188.31/188.32 inference(rename_variables,[],[3490])). % 188.31/188.32 cnf(12867,plain, % 188.31/188.32 (E(f334(f196(f928(x128671)),f176(x128671,x128672,x128673)),x128672)), % 188.31/188.32 inference(rename_variables,[],[3620])). % 188.31/188.32 cnf(12870,plain, % 188.31/188.32 (~P107(f334(f334(f336(x128701),x128702),f195(f935(x128701,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12876,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x128761),x128761))), % 188.31/188.32 inference(rename_variables,[],[4776])). % 188.31/188.32 cnf(12879,plain, % 188.31/188.32 (P107(f334(f334(f336(x128791),x128792),f250(f935(x128791,a922))))), % 188.31/188.32 inference(rename_variables,[],[3705])). % 188.31/188.32 cnf(12883,plain, % 188.31/188.32 (~P107(f334(f334(f195(f935(x128831,f935(x128832,a922))),x128833),x128834))), % 188.31/188.32 inference(rename_variables,[],[4801])). % 188.31/188.32 cnf(12888,plain, % 188.31/188.32 (P107(f334(f334(f242(f935(x128881,a922)),x128882),x128882))), % 188.31/188.32 inference(rename_variables,[],[3849])). % 188.31/188.32 cnf(12891,plain, % 188.31/188.32 (~P107(f334(f334(f336(x128911),x128912),f195(f935(x128911,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(12894,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),f2(a1)),f334(f334(f252(a1),f334(f81(a1),x128941)),x128942)))), % 188.31/188.32 inference(rename_variables,[],[4030])). % 188.31/188.32 cnf(12897,plain, % 188.31/188.32 (~E(f334(a119,x128971),x128971)), % 188.31/188.32 inference(rename_variables,[],[4717])). % 188.31/188.32 cnf(12899,plain, % 188.31/188.32 (E(f334(f291(x128991,x128991),f271(x128991,x128992)),x128992)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12903,plain, % 188.31/188.32 (E(f195(f935(f934(x129031,x129031),a922)),f271(x129031,f195(f935(x129031,a922))))), % 188.31/188.32 inference(rename_variables,[],[3624])). % 188.31/188.32 cnf(12905,plain, % 188.31/188.32 (E(f195(f935(f934(x129051,x129051),a922)),f271(x129051,f195(f935(x129051,a922))))), % 188.31/188.32 inference(rename_variables,[],[3624])). % 188.31/188.32 cnf(12907,plain, % 188.31/188.32 (E(f334(f291(x129071,x129071),f271(x129071,x129072)),x129072)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12911,plain, % 188.31/188.32 (P54(x129111,f271(x129111,x129112))), % 188.31/188.32 inference(rename_variables,[],[3426])). % 188.31/188.32 cnf(12916,plain, % 188.31/188.32 (E(f334(f291(x129161,x129161),f271(x129161,x129162)),x129162)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12918,plain, % 188.31/188.32 (P27(x129181,x129181,f5(x129181),x129182)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12920,plain, % 188.31/188.32 (P27(x129201,x129201,f5(x129201),x129202)), % 188.31/188.32 inference(rename_variables,[],[3786])). % 188.31/188.32 cnf(12927,plain, % 188.31/188.32 (E(f334(f291(x129271,x129271),f271(x129271,x129272)),x129272)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12929,plain, % 188.31/188.32 (E(f334(f291(x129291,x129291),f271(x129291,x129292)),x129292)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12933,plain, % 188.31/188.32 (E(f334(f291(x129331,x129331),f271(x129331,x129332)),x129332)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12935,plain, % 188.31/188.32 (E(f334(f291(x129351,x129351),f271(x129351,x129352)),x129352)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12937,plain, % 188.31/188.32 (P57(x129371,x129371,f271(x129371,x129372))), % 188.31/188.32 inference(rename_variables,[],[3524])). % 188.31/188.32 cnf(12943,plain, % 188.31/188.32 (P28(x129431,x129431,f32(x129431),x129432,x129432)), % 188.31/188.32 inference(rename_variables,[],[4209])). % 188.31/188.32 cnf(12945,plain, % 188.31/188.32 (P28(x129451,x129451,f32(x129451),x129452,x129452)), % 188.31/188.32 inference(rename_variables,[],[4209])). % 188.31/188.32 cnf(12947,plain, % 188.31/188.32 (P28(x129471,x129471,f32(x129471),x129472,x129472)), % 188.31/188.32 inference(rename_variables,[],[4209])). % 188.31/188.32 cnf(12949,plain, % 188.31/188.32 (E(f334(f310(a927,f2(a927)),x129491),f334(f307(a927),x129491))), % 188.31/188.32 inference(rename_variables,[],[3488])). % 188.31/188.32 cnf(12957,plain, % 188.31/188.32 (P39(x129571,f160(x129571,x129572))), % 188.31/188.32 inference(rename_variables,[],[3422])). % 188.31/188.32 cnf(12961,plain, % 188.31/188.32 (P40(x129611,f271(x129611,x129612))), % 188.31/188.32 inference(rename_variables,[],[3423])). % 188.31/188.32 cnf(12965,plain, % 188.31/188.32 (E(f334(f291(x129651,x129651),f271(x129651,x129652)),x129652)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12969,plain, % 188.31/188.32 (E(f195(f935(f934(x129691,x129691),a922)),f271(x129691,f195(f935(x129691,a922))))), % 188.31/188.32 inference(rename_variables,[],[3624])). % 188.31/188.32 cnf(12971,plain, % 188.31/188.32 (E(f334(f291(x129711,x129711),f271(x129711,x129712)),x129712)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12973,plain, % 188.31/188.32 (E(f334(f291(x129731,x129731),f271(x129731,x129732)),x129732)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(12978,plain, % 188.31/188.32 (P55(x129781,x129782,f271(x129781,x129782))), % 188.31/188.32 inference(rename_variables,[],[3523])). % 188.31/188.32 cnf(12980,plain, % 188.31/188.32 (P55(x129801,x129802,f271(x129801,x129802))), % 188.31/188.32 inference(rename_variables,[],[3523])). % 188.31/188.32 cnf(12982,plain, % 188.31/188.32 (P55(x129821,x129822,f271(x129821,x129822))), % 188.31/188.32 inference(rename_variables,[],[3523])). % 188.31/188.32 cnf(12985,plain, % 188.31/188.32 (P26(x129851,x129852,f195(f935(f926(x129851),a922)))), % 188.31/188.32 inference(rename_variables,[],[3608])). % 188.31/188.32 cnf(12995,plain, % 188.31/188.32 (P44(x129951,x129952,x129953,x129954,f195(f935(x129951,a922)),x129954)), % 188.31/188.32 inference(rename_variables,[],[4481])). % 188.31/188.32 cnf(13002,plain, % 188.31/188.32 (P58(x130021,f195(f935(x130021,a922)),x130022)), % 188.31/188.32 inference(rename_variables,[],[3572])). % 188.31/188.32 cnf(13006,plain, % 188.31/188.32 (P16(x130061,f935(x130061,a922),f316(x130061))), % 188.31/188.32 inference(rename_variables,[],[3528])). % 188.31/188.32 cnf(13031,plain, % 188.31/188.32 (P34(x130311,x130312,f120(x130311),f120(x130311))), % 188.31/188.32 inference(rename_variables,[],[3796])). % 188.31/188.32 cnf(13033,plain, % 188.31/188.32 (P34(x130331,x130332,f120(x130331),f120(x130331))), % 188.31/188.32 inference(rename_variables,[],[3796])). % 188.31/188.32 cnf(13041,plain, % 188.31/188.32 (E(f334(f291(x130411,x130411),f271(x130411,x130412)),x130412)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(13042,plain, % 188.31/188.32 (~E(f334(a119,x130421),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[4729])). % 188.31/188.32 cnf(13045,plain, % 188.31/188.32 (E(f334(f291(x130451,x130451),f271(x130451,x130452)),x130452)), % 188.31/188.32 inference(rename_variables,[],[3514])). % 188.31/188.32 cnf(13046,plain, % 188.31/188.32 (~E(f334(a119,x130461),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[4729])). % 188.31/188.32 cnf(13058,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x130581),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(13067,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x130671)),f334(f85(a1),f334(f107(a1),x130672))))), % 188.31/188.32 inference(rename_variables,[],[4796])). % 188.31/188.32 cnf(13077,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x130771),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(13080,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x130801),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(13083,plain, % 188.31/188.32 (P107(f334(f66(a927),f312(a927,x130831,x130832)))), % 188.31/188.32 inference(rename_variables,[],[3758])). % 188.31/188.32 cnf(13086,plain, % 188.31/188.32 (P107(f334(f66(a927),f312(a927,x130861,x130862)))), % 188.31/188.32 inference(rename_variables,[],[3758])). % 188.31/188.32 cnf(13089,plain, % 188.31/188.32 (P107(f334(f66(a927),f312(a927,x130891,x130892)))), % 188.31/188.32 inference(rename_variables,[],[3758])). % 188.31/188.32 cnf(13092,plain, % 188.31/188.32 (P107(f334(f66(a927),f312(a927,x130921,x130922)))), % 188.31/188.32 inference(rename_variables,[],[3758])). % 188.31/188.32 cnf(13099,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),f334(f85(a1),f334(f107(a1),x130991))),f334(f107(a1),x130992)))), % 188.31/188.32 inference(rename_variables,[],[4031])). % 188.31/188.32 cnf(13101,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),f2(a1)),f334(f111(a1),f2(a1))))), % 188.31/188.32 inference(scs_inference,[],[4812,4209,12788,12810,12943,12945,3786,11406,12467,12564,12567,12659,12698,12702,12710,12782,12918,3796,12531,13031,13033,3804,3459,12021,3523,12978,12980,12982,3524,12937,3490,12864,4750,4751,12052,4481,12995,3528,13006,3360,3422,12957,3423,12961,3424,3425,3426,12738,12911,4749,3851,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,12527,12691,12752,3609,3572,13002,3755,12225,3474,4729,10719,10819,11286,11386,13042,3158,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3187,3194,3197,3202,3205,3214,3215,3216,3236,3242,3277,3279,3283,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,4712,3342,3421,4713,3889,4113,11986,3396,11695,3536,3511,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,12441,12635,12842,12899,12907,12916,12927,12929,12933,12935,12965,12971,12973,13041,3485,12723,12727,12731,3491,3500,4008,4308,3620,12785,12867,3385,3749,4100,11741,3608,12985,3450,3382,3412,3870,3407,4219,4108,3932,4677,3394,3395,3366,3372,4022,3431,3610,11132,11256,12528,12742,3484,4183,4740,10552,10716,11597,12683,12724,12728,4747,12695,3545,12076,4140,4787,11312,11411,11650,11653,3951,3657,3876,4765,3624,12903,12905,12969,3447,3448,10619,10949,3709,3488,12949,3439,3363,3470,11731,4322,12713,12854,4186,11332,11467,11528,12670,12676,12799,12802,12832,4807,11234,11480,11591,11617,11658,11664,12614,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,12570,12611,12694,3916,3698,4600,4601,3768,3893,3853,4065,4110,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,12508,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,12617,12717,13058,13077,4791,11846,11877,11912,11919,11952,3984,3757,3758,12270,13083,13086,13089,4132,3580,3582,3556,4777,4737,3942,4247,3740,4794,4315,11614,3875,3593,12097,12100,12535,12639,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,12161,4286,4246,12242,12585,4194,11129,12426,12595,4241,11335,12464,12534,12594,12638,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,12486,12747,12809,12829,12839,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,12578,12642,12758,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,3629,12456,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,12549,12645,12648,12751,12791,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,12690,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,12482,12623,12667,12673,12770,12773,12795,12853,12859,12870,3614,10946,10976,10985,10988,10991,11583,12792,3653,3646,4069,4006,10598,11975,12003,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,3574,10979,11137,11207,12004,12154,12356,12554,4031,12103,4784,4043,4077,4768,4771,4772,3531,3535,4770,4769,4805,3865,4461,11829,4797,10845,10848,4806,11321,11324,11516,11627,11647,11687,4150,11684,12030,12034,12701,12709,3992,11247,11253,11273,12277,12406,12485,3849,11391,11519,12511,12620,12630,12706,12761,12769,4320,3994,10982,11354,11525,11559,11570,12705,3815,10898,10901,10994,11163,3817,4800,11969,4796,13067,4801,10738,10851,11636,12573,12582,12626,12823,12826,4414,11120,12591,12606,4327,4030,3971,3972,4798,10574,10577,10940,10943,11843,12035,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,65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% 188.31/188.32 cnf(13104,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x131041),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(13105,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x131051),x131051))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(13112,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x131121),f334(a119,x131121)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(13114,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),f2(a1)),a89))), % 188.31/188.32 inference(scs_inference,[],[4812,4209,12788,12810,12943,12945,3786,11406,12467,12564,12567,12659,12698,12702,12710,12782,12918,3796,12531,13031,13033,3804,3459,12021,3523,12978,12980,12982,3524,12937,3490,12864,4750,4751,12052,4481,12995,3528,13006,3360,3422,12957,3423,12961,3424,3425,3426,12738,12911,4749,3851,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,12527,12691,12752,3609,3572,13002,3755,12225,3474,4729,10719,10819,11286,11386,13042,3158,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3187,3194,3197,3202,3205,3214,3215,3216,3236,3242,3277,3279,3283,3284,3285,3304,3305,3307,3314,3316,3317,3318,3320,3325,3338,4712,3342,3421,4713,3889,4113,11986,3396,11695,3536,3511,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,12441,12635,12842,12899,12907,12916,12927,12929,12933,12935,12965,12971,12973,13041,3485,12723,12727,12731,3491,3500,4008,4308,3620,12785,12867,3385,3749,4100,11741,3608,12985,3450,3382,3412,3870,3407,4219,4108,3932,4677,3394,3395,3366,3372,4022,3431,3610,11132,11256,12528,12742,3484,4183,4740,10552,10716,11597,12683,12724,12728,4747,12695,3545,12076,4140,4787,11312,11411,11650,11653,3951,3657,3876,4765,3624,12903,12905,12969,3447,3448,10619,10949,3709,3488,12949,3439,3363,3470,11731,4322,12713,12854,4186,11332,11467,11528,12670,12676,12799,12802,12832,4807,11234,11480,11591,11617,11658,11664,12614,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,12570,12611,12694,3916,3698,4600,4601,3768,3893,3853,3895,4065,4110,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,12508,12836,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,12617,12717,13058,13077,13080,4791,11846,11877,11912,11919,11952,3984,3757,3758,12270,13083,13086,13089,4132,3580,3582,3556,4777,3446,4737,3942,4247,3740,4794,4315,11614,3875,3593,12097,12100,12535,12639,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,12161,4286,4246,12242,12585,4194,11129,12426,12595,4241,11335,12464,12534,12594,12638,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,12486,12747,12809,12829,12839,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,12578,12642,12758,12805,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,3629,12456,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,12549,12645,12648,12751,12791,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,12690,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,12482,12623,12667,12673,12770,12773,12795,12853,12859,12870,3614,10946,10976,10985,10988,10991,11583,12792,3653,3646,4069,4006,10598,11975,12003,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,3574,10979,11137,11207,12004,12154,12356,12554,4031,12103,3763,4784,4043,4077,4768,4771,4772,3531,3535,4770,4769,4805,3865,4461,11829,4797,10845,10848,4806,11321,11324,11516,11627,11647,11687,4150,11684,12030,12034,12701,12709,3992,11247,11253,11273,12277,12406,12485,3849,11391,11519,12511,12620,12630,12706,12761,12769,4320,3994,10982,11354,11525,11559,11570,12705,3815,10898,10901,10994,11163,3817,4800,11969,4796,13067,4801,10738,10851,11636,12573,12582,12626,12823,12826,4414,11120,12591,12606,4327,4030,3971,3972,4798,10574,10577,10940,10943,11843,12035,4799,11949,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541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% 188.31/188.32 cnf(13119,plain, % 188.31/188.32 (P107(f334(f334(f242(a1),x131191),x131191))), % 188.31/188.32 inference(rename_variables,[],[3555])). % 188.31/188.32 cnf(13122,plain, % 188.31/188.32 (P107(f334(f66(a927),f312(a927,x131221,x131222)))), % 188.31/188.32 inference(rename_variables,[],[3758])). % 188.31/188.32 cnf(13125,plain, % 188.31/188.32 (P107(f334(f66(a927),f312(a927,x131251,x131252)))), % 188.31/188.32 inference(rename_variables,[],[3758])). % 188.31/188.32 cnf(13128,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x131281),x131281))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(13129,plain, % 188.31/188.32 (~E(f334(a119,x131291),f2(a927))), % 188.31/188.32 inference(rename_variables,[],[4729])). % 188.31/188.32 cnf(13146,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f50(a927,x131461,x131462)),x131461))), % 188.31/188.32 inference(rename_variables,[],[4006])). % 188.31/188.32 cnf(13151,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x131511),f334(a119,x131511)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(13154,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x131541),f334(a119,x131541)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(13155,plain, % 188.31/188.32 (~P107(f334(f334(f243(a927),x131551),f2(a927)))), % 188.31/188.32 inference(rename_variables,[],[4780])). % 188.31/188.32 cnf(13164,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x131641)),f2(a1)))), % 188.31/188.32 inference(rename_variables,[],[4791])). % 188.31/188.32 cnf(13165,plain, % 188.31/188.32 (P107(f334(f250(f935(x131651,a922)),x131652))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(13168,plain, % 188.31/188.32 (~P107(f334(f334(f243(a1),f334(f107(a1),x131681)),f2(a1)))), % 188.31/188.32 inference(rename_variables,[],[4791])). % 188.31/188.32 cnf(13169,plain, % 188.31/188.32 (P107(f334(f250(f935(x131691,a922)),x131692))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(13172,plain, % 188.31/188.32 (P107(f334(f250(f935(x131721,a922)),x131722))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(13175,plain, % 188.31/188.32 (P107(f334(f250(f935(x131751,a922)),x131752))), % 188.31/188.32 inference(rename_variables,[],[3614])). % 188.31/188.32 cnf(13183,plain, % 188.31/188.32 (~P107(f334(f334(f336(x131831),x131832),f195(f935(x131831,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(13184,plain, % 188.31/188.32 (P107(f334(f66(x131841),f195(f935(x131841,a922))))), % 188.31/188.32 inference(rename_variables,[],[3629])). % 188.31/188.32 cnf(13187,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x131871),x131871))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(13196,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),f2(a927)),x131961))), % 188.31/188.32 inference(rename_variables,[],[3574])). % 188.31/188.32 cnf(13199,plain, % 188.31/188.32 (~P107(f334(f334(f336(x131991),x131992),f195(f935(x131991,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(13202,plain, % 188.31/188.32 (~P107(f334(f334(f336(x132021),x132022),f195(f935(x132021,a922))))), % 188.31/188.32 inference(rename_variables,[],[4789])). % 188.31/188.32 cnf(13205,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x132051),x132051))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(13213,plain, % 188.31/188.32 (P107(f334(f334(f243(a927),x132131),f334(a119,x132131)))), % 188.31/188.32 inference(rename_variables,[],[3621])). % 188.31/188.32 cnf(13216,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x132161),x132161))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(13221,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x132211),x132211))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.32 cnf(13224,plain, % 188.31/188.32 (P107(f334(f334(f242(a927),x132241),x132241))), % 188.31/188.32 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13227,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x132271),x132271))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13230,plain, % 188.31/188.33 (E(f334(f334(f23(f935(x132301,a922)),f195(f935(x132301,a922))),x132302),f195(f935(x132301,a922)))), % 188.31/188.33 inference(rename_variables,[],[3819])). % 188.31/188.33 cnf(13231,plain, % 188.31/188.33 (P107(f334(f66(x132311),f195(f935(x132311,a922))))), % 188.31/188.33 inference(rename_variables,[],[3629])). % 188.31/188.33 cnf(13234,plain, % 188.31/188.33 (E(f334(f334(f23(f935(x132341,a922)),f195(f935(x132341,a922))),x132342),f195(f935(x132341,a922)))), % 188.31/188.33 inference(rename_variables,[],[3819])). % 188.31/188.33 cnf(13235,plain, % 188.31/188.33 (P107(f334(f66(x132351),f195(f935(x132351,a922))))), % 188.31/188.33 inference(rename_variables,[],[3629])). % 188.31/188.33 cnf(13238,plain, % 188.31/188.33 (E(f334(f334(f23(f935(x132381,a922)),f195(f935(x132381,a922))),x132382),f195(f935(x132381,a922)))), % 188.31/188.33 inference(rename_variables,[],[3819])). % 188.31/188.33 cnf(13239,plain, % 188.31/188.33 (P107(f334(f66(x132391),f195(f935(x132391,a922))))), % 188.31/188.33 inference(rename_variables,[],[3629])). % 188.31/188.33 cnf(13242,plain, % 188.31/188.33 (E(f334(f334(f23(f935(x132421,a922)),f195(f935(x132421,a922))),x132422),f195(f935(x132421,a922)))), % 188.31/188.33 inference(rename_variables,[],[3819])). % 188.31/188.33 cnf(13243,plain, % 188.31/188.33 (P107(f334(f66(x132431),f195(f935(x132431,a922))))), % 188.31/188.33 inference(rename_variables,[],[3629])). % 188.31/188.33 cnf(13247,plain, % 188.31/188.33 (E(f334(f291(x132471,x132471),f271(x132471,x132472)),x132472)), % 188.31/188.33 inference(rename_variables,[],[3514])). % 188.31/188.33 cnf(13252,plain, % 188.31/188.33 (E(f334(f334(f23(f935(x132521,a922)),f195(f935(x132521,a922))),x132522),f195(f935(x132521,a922)))), % 188.31/188.33 inference(rename_variables,[],[3819])). % 188.31/188.33 cnf(13253,plain, % 188.31/188.33 (P107(f334(f66(x132531),f195(f935(x132531,a922))))), % 188.31/188.33 inference(rename_variables,[],[3629])). % 188.31/188.33 cnf(13257,plain, % 188.31/188.33 (P107(f334(f66(x132571),f195(f935(x132571,a922))))), % 188.31/188.33 inference(rename_variables,[],[3629])). % 188.31/188.33 cnf(13260,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x132601),x132601))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13264,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),x132641),x132641))), % 188.31/188.33 inference(rename_variables,[],[3555])). % 188.31/188.33 cnf(13271,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x132711),x132711))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13284,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x132841),x132841))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13287,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),x132871),x132871))), % 188.31/188.33 inference(rename_variables,[],[3555])). % 188.31/188.33 cnf(13297,plain, % 188.31/188.33 (~P107(f334(f334(f336(x132971),x132972),f195(f935(x132971,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13308,plain, % 188.31/188.33 (P107(f334(f334(f336(x133081),x133082),f250(f935(x133081,a922))))), % 188.31/188.33 inference(rename_variables,[],[3705])). % 188.31/188.33 cnf(13309,plain, % 188.31/188.33 (E(f334(f199(x133091,x133092),x133093),f128(x133091,x133092))), % 188.31/188.33 inference(rename_variables,[],[3468])). % 188.31/188.33 cnf(13312,plain, % 188.31/188.33 (P107(f334(f334(f336(x133121),f334(x133122,x133123)),f334(f317(x133124,x133121,x133122),f250(f935(x133124,a922)))))), % 188.31/188.33 inference(rename_variables,[],[4150])). % 188.31/188.33 cnf(13316,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x133161,a922)),x133162),f250(f935(x133161,a922))))), % 188.31/188.33 inference(rename_variables,[],[3934])). % 188.31/188.33 cnf(13319,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x133191,a922)),x133192),x133192))), % 188.31/188.33 inference(rename_variables,[],[3849])). % 188.31/188.33 cnf(13325,plain, % 188.31/188.33 (~P107(f334(f334(f243(a927),x133251),f2(a927)))), % 188.31/188.33 inference(rename_variables,[],[4780])). % 188.31/188.33 cnf(13326,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),x133261),x133261))), % 188.31/188.33 inference(rename_variables,[],[3555])). % 188.31/188.33 cnf(13330,plain, % 188.31/188.33 (~P107(f334(f334(f243(a927),x133301),f2(a927)))), % 188.31/188.33 inference(rename_variables,[],[4780])). % 188.31/188.33 cnf(13331,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),x133311),x133311))), % 188.31/188.33 inference(rename_variables,[],[3555])). % 188.31/188.33 cnf(13336,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x133361),x133361))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13343,plain, % 188.31/188.33 (E(f334(f334(f16(x133431,x133432),x133433),x133434),x133433)), % 188.31/188.33 inference(rename_variables,[],[3545])). % 188.31/188.33 cnf(13346,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x133461,a922)),f334(f179(x133461),f183(x133461,x133462,x133463))),f334(f179(x133461),x133462)))), % 188.31/188.33 inference(rename_variables,[],[4241])). % 188.31/188.33 cnf(13350,plain, % 188.31/188.33 (~P107(f334(f334(f243(a927),x133501),f2(a927)))), % 188.31/188.33 inference(rename_variables,[],[4780])). % 188.31/188.33 cnf(13351,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),x133511),x133511))), % 188.31/188.33 inference(rename_variables,[],[3555])). % 188.31/188.33 cnf(13355,plain, % 188.31/188.33 (~P107(f334(f334(f243(a927),x133551),f2(a927)))), % 188.31/188.33 inference(rename_variables,[],[4780])). % 188.31/188.33 cnf(13356,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),x133561),x133561))), % 188.31/188.33 inference(rename_variables,[],[3555])). % 188.31/188.33 cnf(13361,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x133611),x133611))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13363,plain, % 188.31/188.33 (~P107(f334(f334(f243(f935(a927,a922)),f311(a927,f334(a119,x133631),f334(a119,x133631))),f311(a927,x133632,x133631)))), % 188.31/188.33 inference(scs_inference,[],[4812,4209,12788,12810,12943,12945,3786,11406,12467,12564,12567,12659,12698,12702,12710,12782,12918,3796,12531,13031,13033,3804,3459,12021,3523,12978,12980,12982,3524,12937,3490,12864,4750,4751,12052,4481,12995,3528,13006,3360,3422,12957,3423,12961,3424,3425,3426,12738,12911,4749,3851,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,12527,12691,12752,3609,3572,13002,3755,12225,3474,4729,10719,10819,11286,11386,13042,13046,3158,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3180,3187,3194,3197,3202,3205,3214,3215,3216,3222,3236,3242,3253,3257,3258,3259,3271,3277,3279,3280,3283,3284,3285,3293,3304,3305,3306,3307,3314,3316,3317,3318,3319,3320,3325,3338,4712,3342,3421,4713,3889,4113,11986,3396,11695,3536,3511,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,12441,12635,12842,12899,12907,12916,12927,12929,12933,12935,12965,12971,12973,13041,13045,3485,12723,12727,12731,3491,3500,4008,4308,3468,13309,3620,12785,12867,3385,3749,4100,11741,3608,12985,3450,3382,3412,3870,3407,4219,4108,3932,4677,3394,3395,3366,3372,4022,3431,3610,11132,11256,12528,12742,3484,4183,4740,10552,10716,11597,12683,12724,12728,4747,12695,3545,12076,12079,4140,4787,11312,11411,11650,11653,3951,3657,3876,4765,3624,12903,12905,12969,3447,3448,10619,10949,3709,3488,12949,3439,3363,3470,11731,4322,12713,12854,4186,11332,11467,11528,12670,12676,12799,12802,12832,4807,11234,11480,11591,11617,11658,11664,12614,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,12570,12611,12694,3916,3698,4600,4601,3768,3893,3853,3895,4065,3819,13230,13234,13238,13242,13252,4110,12561,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,12508,12836,13112,13151,13154,13213,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,12617,12717,13058,13077,13080,13104,13155,13325,13330,13350,4791,11846,11877,11912,11919,11952,13164,13168,3984,3757,3758,12270,13083,13086,13089,13092,13122,4132,3580,3582,3556,4777,3446,4737,3942,4247,3740,4794,4315,11614,3875,3593,12097,12100,12535,12639,12813,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,12161,4286,4246,12242,12585,4194,11129,12426,12595,4241,11335,12464,12534,12594,12638,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,12486,12747,12809,12829,12839,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,12578,12642,12758,12805,13105,13128,13187,13205,13216,13221,13224,13227,13260,13271,13284,13336,13361,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,12351,13119,13264,13287,13326,13331,13351,3629,12456,13184,13231,13235,13239,13243,13253,13257,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,12549,12645,12648,12751,12791,12876,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,12690,12879,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,12482,12623,12667,12673,12770,12773,12795,12853,12859,12870,12891,13183,13199,13202,3614,10946,10976,10985,10988,10991,11583,12792,12806,13165,13169,13172,13175,3653,3646,4069,4006,10598,11975,12003,13146,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,3574,10979,11137,11207,12004,12154,12356,12554,12579,4031,12103,13099,3763,4784,4043,4077,4768,4771,4772,3531,3535,4770,4769,4805,3865,4461,11829,4797,10845,10848,4806,11321,11324,11516,11627,11647,11687,4150,11684,12030,12034,12701,12709,12798,3992,11247,11253,11273,12277,12406,12485,3849,11391,11519,12511,12620,12630,12706,12761,12769,12888,4320,3994,10982,11354,11525,11559,11570,12705,3815,10898,10901,10994,11163,3817,4800,11969,4796,13067,4801,10738,10851,11636,12573,12582,12626,12823,12826,4414,11120,12591,12606,4327,4030,12894,3971,3972,4798,10574,10577,10940,10943,11843,12035,12835,4799,11949,12040,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405,6431,6448,6500,6537,6538,6559,6560,6567,6572,6573,6576,6588,6603,6624,6625,6630,6633,6642,6657,6680,6686,6688,6703,6704,6708,6710,6711,6712,6714,6716,6717,6718,6720,6726,6727,6729,6730,6736,6738,6779,6784,6800,6802,6803,6804,6837,6842,6844,6849,6850,6858,6862,6874,6897,6898,6900,6901,6912,6916,6919,6937,6940,6958,6989,6990,6991,6997,7006,7025,7027,7029,7031,7036,7042,7045,7057,7062,7063,7097,7098,7099,7114,7115,7117,7118,7119,7137,7139,7154,7180,7203,7214,7216,7218,7220,7221,7252,7253,7257,7258,7266,7268,7269,7270,7292,7301,7302,7312,7322,7362,7372,7376,7383,7394,7399,7401,7408,7416,7429,7446,7467,7469,7488,7539,7540,7541,7543,7546,7550,7555,7609,7638,7653,7669,7700,7703,7725,7748,7766,7769,7770,7780,7799,7801,7803,7805,7806,7807,7830,7856,7857,7888,7890,7891,7892,7897,7917,7935,7940,7947,7949,7957,7969,7970,7972,7994,8000,8023,8091,8092,8093,8136,8142,8143,8163,8164,8181,8182,8183,8238,8239,8269,8300,8309,8321,8333,8363,8367,8373,8385,8403,8409,8429,8474,8504,8518,8537,8540,8563,8589,8644,8645,8648,8649,8717,8755,8756,8757,8758,8815,8845,8853,8854,8889,8909,8955,8964,9015,9018,9035,9042,9087,9132,9133,9150,9151,9165,9275,9281,9285,9299,9310,9338,9340,9343,9349,9351,9352,9363,9364,9386,9392,9402,9409,9449,9467,9529,9530,9532,9571,9597,9603,9635,9645,9646,9647,9649,9650,9664,9685,9700,9713,9714,9715,9717,9756,9890,9891,9939,9940,9983,10027,10130,10175,10236,10237,10322,10341,10454,3,2878,2879,2880,2882,2883,2889,2894,2899,2900,2901,2908,2909,2910,2911,2912,2916,2920,2921,2925,2927,2929,2930,2931,2937,2938,2939,2940,2941,2949,2951,2952,2953,2954,2955,2963,2964,2966,2977,2978,2979,2987,2989,2992,2993,2994,3000,3001,3002,3007,3008,3009,3010,3011,3012,3014,3015,3016,3019,3020,3021,3036,3037,3046,3048,3050,3051,3052,3053,3054,3056,3057,3058,3068,3069,3088,3090,3092,3094,3102,3104,3105,3124,3125,3141,3142,5394,5397,5527,5566,5712,5713,5714,5795,5899,5931,5965,5981,5983,5989,6051,6052,6053,6054,6062,6099,6230,6268,6278,6300,6334,6371,6516,6521,6557,6558,6579,6581,6583,6590,6591,6592,6593,6594,6595,6596,6597,6681,6750,6751,6836,6869,6870,6909,6910,7044,7056,7109,7127,7128,7134,7155,7186,7188,7235,7255,7256,7274,7275,7311,7356,7357,7453,7520,7521,7522,7523,7538,7565,7614,7615,7624,7629,7630,7641,7672,7673,7674,7675,7811,7812,7814,7816,7822,7823,7930,8031,8037,8038,8050,8088,8089,8158,8197,8251,8274,8275,8349,8442,8514,8515,8519,8549,8610,8611,8677,8694,8695])). % 188.31/188.33 cnf(13364,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x133641),x133641))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13367,plain, % 188.31/188.33 (~P107(f334(f334(f242(a927),f334(a119,x133671)),x133671))), % 188.31/188.33 inference(rename_variables,[],[4786])). % 188.31/188.33 cnf(13372,plain, % 188.31/188.33 (E(x133721,f461(f334(f5(x133722),f334(f5(x133722),x133721)),f5(x133722),x133722,x133722))), % 188.31/188.33 inference(scs_inference,[],[4812,4209,12788,12810,12943,12945,3786,11406,12467,12564,12567,12659,12698,12702,12710,12782,12918,12920,3796,12531,13031,13033,3804,3459,12021,3523,12978,12980,12982,3524,12937,3490,12864,4750,4751,12052,4481,12995,3528,13006,3360,3422,12957,3423,12961,3424,3425,3426,12738,12911,4749,3851,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,12527,12691,12752,3609,3572,13002,3755,12225,3474,4729,10719,10819,11286,11386,13042,13046,3158,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3180,3187,3194,3197,3202,3205,3214,3215,3216,3222,3236,3242,3253,3257,3258,3259,3271,3277,3279,3280,3283,3284,3285,3293,3304,3305,3306,3307,3314,3316,3317,3318,3319,3320,3325,3338,4712,3342,3421,4713,3889,4113,11986,3396,11695,3536,3511,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,12441,12635,12842,12899,12907,12916,12927,12929,12933,12935,12965,12971,12973,13041,13045,3485,12723,12727,12731,3491,3500,4008,4308,3468,13309,3620,12785,12867,3385,3386,3749,4100,11741,3608,12985,3450,3382,3412,3870,3407,4219,4108,3932,4677,3394,3395,3366,3372,4022,3431,3610,11132,11256,12528,12742,3484,4183,4740,10552,10716,11597,12683,12724,12728,4747,12695,3545,12076,12079,4140,4787,11312,11411,11650,11653,3951,3657,3876,4765,3624,12903,12905,12969,3447,3448,10619,10949,3709,3488,12949,3439,3363,3470,11731,4322,12713,12854,4186,11332,11467,11528,12670,12676,12799,12802,12832,4807,11234,11480,11591,11617,11658,11664,12614,4808,11365,11483,11594,4809,11486,4810,11546,4811,3469,3747,12570,12611,12694,3916,3698,4600,4601,3768,3893,3853,3895,4065,3819,13230,13234,13238,13242,13252,4110,12561,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,12508,12836,13112,13151,13154,13213,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,12617,12717,13058,13077,13080,13104,13155,13325,13330,13350,4791,11846,11877,11912,11919,11952,13164,13168,3984,3757,3758,12270,13083,13086,13089,13092,13122,4132,3580,3582,3556,4777,3446,4737,3942,4247,3740,4794,4315,11614,3875,3593,12097,12100,12535,12639,12813,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,12161,4286,4246,12242,12585,4194,11129,12426,12595,4241,11335,12464,12534,12594,12638,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,12486,12747,12809,12829,12839,4795,11080,11491,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,12578,12642,12758,12805,13105,13128,13187,13205,13216,13221,13224,13227,13260,13271,13284,13336,13361,13364,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,12351,13119,13264,13287,13326,13331,13351,3629,12456,13184,13231,13235,13239,13243,13253,13257,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,12549,12645,12648,12751,12791,12876,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,12690,12879,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,12482,12623,12667,12673,12770,12773,12795,12853,12859,12870,12891,13183,13199,13202,3614,10946,10976,10985,10988,10991,11583,12792,12806,13165,13169,13172,13175,3653,3646,4069,4006,10598,11975,12003,13146,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,13367,3574,10979,11137,11207,12004,12154,12356,12554,12579,4031,12103,13099,3763,4784,4043,4077,4768,4771,4772,3531,3535,4770,4769,4805,3865,4461,11829,4797,10845,10848,4806,11321,11324,11516,11627,11647,11687,4150,11684,12030,12034,12701,12709,12798,13312,3992,11247,11253,11273,12277,12406,12485,3849,11391,11519,12511,12620,12630,12706,12761,12769,12888,4320,3994,10982,11354,11525,11559,11570,12705,3815,10898,10901,10994,11163,3817,4800,11969,4796,13067,4801,10738,10851,11636,12573,12582,12626,12823,12826,4414,11120,12591,12606,4327,4030,12894,3971,3972,4798,10574,10577,10940,10943,11843,12035,12835,4799,11949,12040,3995,10904,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405,6431,6448,6500,6537,6538,6559,6560,6567,6572,6573,6576,6588,6603,6624,6625,6630,6633,6642,6657,6680,6686,6688,6703,6704,6708,6710,6711,6712,6714,6716,6717,6718,6720,6726,6727,6729,6730,6736,6738,6779,6784,6800,6802,6803,6804,6837,6842,6844,6849,6850,6858,6862,6874,6897,6898,6900,6901,6912,6916,6919,6937,6940,6958,6989,6990,6991,6997,7006,7025,7027,7029,7031,7036,7042,7045,7057,7062,7063,7097,7098,7099,7114,7115,7117,7118,7119,7137,7139,7154,7180,7203,7214,7216,7218,7220,7221,7252,7253,7257,7258,7266,7268,7269,7270,7292,7301,7302,7312,7322,7362,7372,7376,7383,7394,7399,7401,7408,7416,7429,7446,7467,7469,7488,7539,7540,7541,7543,7546,7550,7555,7609,7638,7653,7669,7700,7703,7725,7748,7766,7769,7770,7780,7799,7801,7803,7805,7806,7807,7830,7856,7857,7888,7890,7891,7892,7897,7917,7935,7940,7947,7949,7957,7969,7970,7972,7994,8000,8023,8091,8092,8093,8136,8142,8143,8163,8164,8181,8182,8183,8238,8239,8269,8300,8309,8321,8333,8363,8367,8373,8385,8403,8409,8429,8474,8504,8518,8537,8540,8563,8589,8644,8645,8648,8649,8717,8755,8756,8757,8758,8815,8845,8853,8854,8889,8909,8955,8964,9015,9018,9035,9042,9087,9132,9133,9150,9151,9165,9275,9281,9285,9299,9310,9338,9340,9343,9349,9351,9352,9363,9364,9386,9392,9402,9409,9449,9467,9529,9530,9532,9571,9597,9603,9635,9645,9646,9647,9649,9650,9664,9685,9700,9713,9714,9715,9717,9756,9890,9891,9939,9940,9983,10027,10130,10175,10236,10237,10322,10341,10454,3,2878,2879,2880,2882,2883,2889,2894,2899,2900,2901,2908,2909,2910,2911,2912,2916,2920,2921,2925,2927,2929,2930,2931,2937,2938,2939,2940,2941,2949,2951,2952,2953,2954,2955,2963,2964,2966,2977,2978,2979,2987,2989,2992,2993,2994,3000,3001,3002,3007,3008,3009,3010,3011,3012,3014,3015,3016,3019,3020,3021,3036,3037,3046,3048,3050,3051,3052,3053,3054,3056,3057,3058,3068,3069,3088,3090,3092,3094,3102,3104,3105,3124,3125,3141,3142,5394,5397,5527,5566,5712,5713,5714,5795,5899,5931,5965,5981,5983,5989,6051,6052,6053,6054,6062,6099,6230,6268,6278,6300,6334,6371,6516,6521,6557,6558,6579,6581,6583,6590,6591,6592,6593,6594,6595,6596,6597,6681,6750,6751,6836,6869,6870,6909,6910,7044,7056,7109,7127,7128,7134,7155,7186,7188,7235,7255,7256,7274,7275,7311,7356,7357,7453,7520,7521,7522,7523,7538,7565,7614,7615,7624,7629,7630,7641,7672,7673,7674,7675,7811,7812,7814,7816,7822,7823,7930,8031,8037,8038,8050,8088,8089,8158,8197,8251,8274,8275,8349,8442,8514,8515,8519,8549,8610,8611,8677,8694,8695,8696,8697,8849])). % 188.31/188.33 cnf(13373,plain, % 188.31/188.33 (P107(f334(f334(f336(x133731),f334(x133732,x133733)),f334(f317(x133734,x133731,x133732),f250(f935(x133734,a922)))))), % 188.31/188.33 inference(rename_variables,[],[4150])). % 188.31/188.33 cnf(13374,plain, % 188.31/188.33 (P27(x133741,x133741,f5(x133741),x133742)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13379,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x133791,a922)),x133792),f250(f935(x133791,a922))))), % 188.31/188.33 inference(rename_variables,[],[3934])). % 188.31/188.33 cnf(13380,plain, % 188.31/188.33 (P27(x133801,x133801,f5(x133801),x133802)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13384,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x133841,a922)),x133842),f250(f935(x133841,a922))))), % 188.31/188.33 inference(rename_variables,[],[3934])). % 188.31/188.33 cnf(13385,plain, % 188.31/188.33 (P27(x133851,x133851,f5(x133851),x133852)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13389,plain, % 188.31/188.33 (P27(x133891,x133891,f5(x133891),x133892)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13392,plain, % 188.31/188.33 (~P107(f334(f334(f243(f935(x133921,a922)),x133922),f195(f935(x133921,a922))))), % 188.31/188.33 inference(rename_variables,[],[4795])). % 188.31/188.33 cnf(13395,plain, % 188.31/188.33 (P27(x133951,x133951,f5(x133951),x133952)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13398,plain, % 188.31/188.33 (P27(x133981,x133981,f5(x133981),x133982)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13404,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x134041,a922)),x134042),f250(f935(x134041,a922))))), % 188.31/188.33 inference(rename_variables,[],[3934])). % 188.31/188.33 cnf(13409,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x134091,a922)),f195(f935(x134091,a922))),x134092))), % 188.31/188.33 inference(rename_variables,[],[3994])). % 188.31/188.33 cnf(13413,plain, % 188.31/188.33 (E(f334(f291(x134131,x134131),f271(x134131,x134132)),x134132)), % 188.31/188.33 inference(rename_variables,[],[3514])). % 188.31/188.33 cnf(13417,plain, % 188.31/188.33 (~P107(f334(f334(f336(x134171),x134172),f195(f935(x134171,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13422,plain, % 188.31/188.33 (P27(x134221,x134221,f5(x134221),x134222)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13425,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x134251,a922)),x134252),f250(f935(x134251,a922))))), % 188.31/188.33 inference(rename_variables,[],[3934])). % 188.31/188.33 cnf(13429,plain, % 188.31/188.33 (P107(f334(f334(f336(x134291),x134292),f250(f935(x134291,a922))))), % 188.31/188.33 inference(rename_variables,[],[3705])). % 188.31/188.33 cnf(13433,plain, % 188.31/188.33 (E(f334(f334(f16(x134331,x134332),x134333),x134334),x134333)), % 188.31/188.33 inference(rename_variables,[],[3545])). % 188.31/188.33 cnf(13436,plain, % 188.31/188.33 (~P107(f334(f334(f336(x134361),x134362),f195(f935(x134361,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13439,plain, % 188.31/188.33 (~P107(f334(f334(f336(x134391),x134392),f195(f935(x134391,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13443,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x134431),x134431))), % 188.31/188.33 inference(rename_variables,[],[3554])). % 188.31/188.33 cnf(13446,plain, % 188.31/188.33 (P107(f334(f334(f243(a927),x134461),f334(a119,x134461)))), % 188.31/188.33 inference(rename_variables,[],[3621])). % 188.31/188.33 cnf(13447,plain, % 188.31/188.33 (~E(f334(a119,x134471),x134471)), % 188.31/188.33 inference(rename_variables,[],[4717])). % 188.31/188.33 cnf(13450,plain, % 188.31/188.33 (P107(f334(f334(f243(a927),x134501),f334(a119,f334(f334(f86(a927),x134502),x134501))))), % 188.31/188.33 inference(rename_variables,[],[3995])). % 188.31/188.33 cnf(13451,plain, % 188.31/188.33 (P107(f334(f334(f243(a927),x134511),f334(a119,x134511)))), % 188.31/188.33 inference(rename_variables,[],[3621])). % 188.31/188.33 cnf(13453,plain, % 188.31/188.33 (~E(f334(f334(f87(a927),f334(a119,f2(a927))),f126(x134531)),f334(f334(f87(a927),f334(a119,f2(a927))),f133(x134531,x134532,x134533)))), % 188.31/188.33 inference(scs_inference,[],[4812,4209,12788,12810,12943,12945,12947,3786,11406,12467,12564,12567,12659,12698,12702,12710,12782,12918,12920,13374,13380,13385,13389,13395,13398,3796,12531,13031,13033,3804,3459,12021,3523,12978,12980,12982,3524,12937,3490,12864,4750,4751,12052,4481,12995,3528,13006,3360,3422,12957,3423,12961,3424,3425,3426,12738,12911,4749,3851,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,12527,12691,12752,12897,13447,3609,3572,13002,3755,12225,3474,4729,10719,10819,11286,11386,13042,13046,3158,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3180,3187,3194,3197,3202,3205,3214,3215,3216,3222,3236,3242,3253,3257,3258,3259,3271,3277,3279,3280,3283,3284,3285,3293,3304,3305,3306,3307,3314,3316,3317,3318,3319,3320,3325,3338,4712,3342,3421,4713,3889,4113,11986,3396,11695,3536,3511,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,12441,12635,12842,12899,12907,12916,12927,12929,12933,12935,12965,12971,12973,13041,13045,13247,3485,12723,12727,12731,3491,3500,4008,4308,3468,13309,3620,12785,12867,3385,3386,3749,4100,11741,3608,12985,3450,3382,3412,3870,3407,4219,4108,3932,4677,3394,3395,3366,3372,4022,3431,3610,11132,11256,12528,12742,3484,4183,4740,10552,10716,11597,12683,12724,12728,4747,12695,3545,12076,12079,13343,4140,4787,11312,11411,11650,11653,3951,3542,3657,3876,4765,3624,12903,12905,12969,3447,3448,10619,10949,4774,3709,3488,12949,3439,3363,3470,11731,4322,12713,12854,4186,11332,11467,11528,12670,12676,12799,12802,12832,4807,11234,11480,11591,11617,11658,11664,12614,4808,11365,11483,11594,4809,11486,11539,4810,11546,4811,3469,3747,12570,12611,12694,3916,3698,4600,4601,3768,3893,3853,3895,4065,3819,13230,13234,13238,13242,13252,4110,12561,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,12508,12836,13112,13151,13154,13213,13446,3997,11972,3538,3633,11803,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,12617,12717,13058,13077,13080,13104,13155,13325,13330,13350,4791,11846,11877,11912,11919,11952,13164,13168,3984,3757,3758,12270,13083,13086,13089,13092,13122,3760,4132,3580,3582,3556,4777,3446,4737,3942,4247,3740,4794,4315,11614,3875,3593,12097,12100,12535,12639,12813,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,12161,4286,4246,12242,12585,4194,11129,12426,12595,4241,11335,12464,12534,12594,12638,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,12486,12747,12809,12829,12839,13316,13379,13384,13404,4795,11080,11491,12598,13392,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,12578,12642,12758,12805,13105,13128,13187,13205,13216,13221,13224,13227,13260,13271,13284,13336,13361,13364,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,12351,13119,13264,13287,13326,13331,13351,3629,12456,13184,13231,13235,13239,13243,13253,13257,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,12549,12645,12648,12751,12791,12876,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,12690,12879,13308,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,12482,12623,12667,12673,12770,12773,12795,12853,12859,12870,12891,13183,13199,13202,13297,13417,13436,3614,10946,10976,10985,10988,10991,11583,12792,12806,13165,13169,13172,13175,3653,3646,4069,4006,10598,11975,12003,13146,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,13367,3574,10979,11137,11207,12004,12154,12356,12554,12579,4031,12103,13099,3763,4784,4043,4077,4768,4771,4772,3531,3535,4770,4769,4805,3865,11968,4461,11829,4797,10845,10848,4806,11321,11324,11516,11627,11647,11687,4150,11684,12030,12034,12701,12709,12798,13312,13373,3992,11247,11253,11273,12277,12406,12485,12766,3849,11391,11519,12511,12620,12630,12706,12761,12769,12888,4320,3994,10982,11354,11525,11559,11570,12705,12755,3815,10898,10901,10994,11163,3817,4800,11969,4796,13067,4801,10738,10851,11636,12573,12582,12626,12823,12826,12883,4414,11120,12591,12606,12629,4327,4030,12894,3971,3972,4798,10574,10577,10940,10943,11843,12035,12835,4799,11949,12040,3995,10904,11169,4261,4821,4847,4902,4906,4934,4949,4956,4958,4994,4999,5029,5035,5119,5145,5146,5161,5211,5212,5234,5235,5249,5252,5277,5283,5299,5302,5303,5304,5309,5310,5333,5357,5359,5360,5371,5381,5417,5418,5426,5434,5438,5440,5454,5456,5462,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5690,5704,5705,5720,5730,5752,5758,5780,5781,5784,5806,5814,5815,5820,5821,5831,5834,5850,5854,5863,5864,5866,5867,5883,5888,5897,5898,5909,5916,5932,5936,5939,5945,5946,5947,5950,5955,5991,5992,5995,5997,5999,6001,6002,6003,6005,6007,6009,6014,6021,6036,6050,6056,6057,6060,6071,6072,6079,6083,6085,6090,6100,6137,6150,6159,6162,6171,6174,6175,6176,6177,6178,6182,6187,6197,6203,6221,6224,6234,6263,6277,6301,6318,6319,6322,6336,6338,6340,6342,6357,6358,6361,6363,6366,6367,6381,6389,6390,6391,6395,6397,6428,6429,6434,6437,6443,6447,6481,6483,6485,6487,6497,6499,6501,6507,6509,6514,6517,6525,6533,6535,6536,6541,6562,6563,6564,6565,6566,6569,6575,6578,6611,6612,6615,6616,6617,6619,6620,6621,6622,6632,6664,6665,6666,6675,6698,6699,6719,6721,6733,6734,6740,6767,6769,6785,6789,6824,6826,6827,6879,6902,6945,6964,6973,6974,6975,6976,6995,6996,7003,7010,7013,7015,7017,7018,7019,7021,7035,7047,7048,7049,7060,7112,7124,7126,7147,7148,7182,7189,7195,7225,7254,7310,7338,7393,7414,7422,7425,7485,7498,7554,7556,7564,7573,7574,7575,7591,7595,7597,7642,7652,7655,7670,7717,7719,7722,7764,7765,7783,7848,7866,7889,7912,7923,7938,7950,7961,7962,7989,7991,7993,8004,8040,8053,8078,8133,8161,8193,8231,8247,8249,8265,8266,8330,8342,8407,8430,8435,8449,8476,8477,8516,8517,8534,8570,8572,8574,8581,8595,8599,8614,8633,8641,8643,8654,8659,8663,8664,8665,8666,8667,8668,8687,8701,8702,8719,8720,8729,8730,8731,8732,8733,8751,8752,8753,8763,8776,8778,8789,8794,8796,8798,8799,8800,8807,8812,8820,8823,8841,8842,8851,8852,8860,8874,8887,8890,8910,8932,8935,8936,8943,8952,8953,8954,8974,8986,8996,8997,8998,9001,9024,9025,9038,9090,9096,9103,9105,9121,9124,9136,9137,9138,9148,9211,9242,9243,9244,9259,9272,9278,9279,9301,9302,9377,9410,9416,9426,9427,9428,9435,9463,9479,9483,9487,9512,9513,9540,9606,9611,9614,9639,9640,9641,9665,9666,9680,9701,9707,9727,9757,9778,9787,9788,9789,9790,9803,9805,9810,9847,9848,9854,9855,9905,9906,9917,9918,9944,9962,9964,9965,9973,9982,9995,10023,10044,10055,10057,10061,10107,10142,10143,10144,10153,10154,10159,10173,10257,10351,10352,10353,10354,10452,10476,2,8,9,4834,4835,4853,4895,4896,4898,4921,4929,4930,4938,4983,4985,5034,5162,5163,5176,5200,5255,5256,5262,5263,5265,5267,5276,5279,5280,5288,5300,5301,5307,5328,5329,5346,5351,5352,5353,5354,5358,5366,5369,5370,5376,5431,5436,5437,5442,5448,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5696,5701,5703,5737,5739,5740,5742,5743,5745,5746,5748,5757,5762,5763,5764,5766,5768,5769,5770,5771,5772,5773,5782,5794,5797,5809,5825,5826,5829,5844,5846,5847,5848,5875,5885,5900,5901,5910,5911,5913,5915,5920,5957,5962,5964,6023,6058,6059,6064,6070,6073,6074,6075,6076,6091,6092,6097,6101,6102,6111,6134,6163,6181,6185,6186,6188,6211,6215,6218,6219,6220,6232,6236,6246,6247,6279,6280,6284,6303,6306,6309,6330,6331,6359,6362,6370,6380,6388,6394,6402,6403,6404,6405,6431,6448,6500,6537,6538,6559,6560,6567,6572,6573,6576,6588,6603,6624,6625,6630,6633,6642,6657,6680,6686,6688,6703,6704,6708,6710,6711,6712,6714,6716,6717,6718,6720,6726,6727,6729,6730,6736,6738,6779,6784,6800,6802,6803,6804,6837,6842,6844,6849,6850,6858,6862,6874,6897,6898,6900,6901,6912,6916,6919,6937,6940,6958,6989,6990,6991,6997,7006,7025,7027,7029,7031,7036,7042,7045,7057,7062,7063,7097,7098,7099,7114,7115,7117,7118,7119,7137,7139,7154,7180,7203,7214,7216,7218,7220,7221,7252,7253,7257,7258,7266,7268,7269,7270,7292,7301,7302,7312,7322,7362,7372,7376,7383,7394,7399,7401,7408,7416,7429,7446,7467,7469,7488,7539,7540,7541,7543,7546,7550,7555,7609,7638,7653,7669,7700,7703,7725,7748,7766,7769,7770,7780,7799,7801,7803,7805,7806,7807,7830,7856,7857,7888,7890,7891,7892,7897,7917,7935,7940,7947,7949,7957,7969,7970,7972,7994,8000,8023,8091,8092,8093,8136,8142,8143,8163,8164,8181,8182,8183,8238,8239,8269,8300,8309,8321,8333,8363,8367,8373,8385,8403,8409,8429,8474,8504,8518,8537,8540,8563,8589,8644,8645,8648,8649,8717,8755,8756,8757,8758,8815,8845,8853,8854,8889,8909,8955,8964,9015,9018,9035,9042,9087,9132,9133,9150,9151,9165,9275,9281,9285,9299,9310,9338,9340,9343,9349,9351,9352,9363,9364,9386,9392,9402,9409,9449,9467,9529,9530,9532,9571,9597,9603,9635,9645,9646,9647,9649,9650,9664,9685,9700,9713,9714,9715,9717,9756,9890,9891,9939,9940,9983,10027,10130,10175,10236,10237,10322,10341,10454,3,2878,2879,2880,2882,2883,2889,2894,2899,2900,2901,2908,2909,2910,2911,2912,2916,2920,2921,2925,2927,2929,2930,2931,2937,2938,2939,2940,2941,2949,2951,2952,2953,2954,2955,2963,2964,2966,2977,2978,2979,2987,2989,2992,2993,2994,3000,3001,3002,3007,3008,3009,3010,3011,3012,3014,3015,3016,3019,3020,3021,3036,3037,3046,3048,3050,3051,3052,3053,3054,3056,3057,3058,3068,3069,3088,3090,3092,3094,3102,3104,3105,3124,3125,3141,3142,5394,5397,5527,5566,5712,5713,5714,5795,5899,5931,5965,5981,5983,5989,6051,6052,6053,6054,6062,6099,6230,6268,6278,6300,6334,6371,6516,6521,6557,6558,6579,6581,6583,6590,6591,6592,6593,6594,6595,6596,6597,6681,6750,6751,6836,6869,6870,6909,6910,7044,7056,7109,7127,7128,7134,7155,7186,7188,7235,7255,7256,7274,7275,7311,7356,7357,7453,7520,7521,7522,7523,7538,7565,7614,7615,7624,7629,7630,7641,7672,7673,7674,7675,7811,7812,7814,7816,7822,7823,7930,8031,8037,8038,8050,8088,8089,8158,8197,8251,8274,8275,8349,8442,8514,8515,8519,8549,8610,8611,8677,8694,8695,8696,8697,8849,9107,9108,9179,9193,9245,9246,9355,9395,9421,9451,9492,9683,9817,9974,10152,10196,10198,10360,6662,6663,6753])). % 188.31/188.33 cnf(13455,plain, % 188.31/188.33 (~E(f334(a119,x134551),x134551)), % 188.31/188.33 inference(rename_variables,[],[4717])). % 188.31/188.33 cnf(13460,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),f2(a1)),f334(f107(a1),x134601)))), % 188.31/188.33 inference(rename_variables,[],[3653])). % 188.31/188.33 cnf(13463,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),f2(a927)),x134631))), % 188.31/188.33 inference(rename_variables,[],[3574])). % 188.31/188.33 cnf(13467,plain, % 188.31/188.33 (~E(f334(a119,x134671),f2(a927))), % 188.31/188.33 inference(rename_variables,[],[4729])). % 188.31/188.33 cnf(13476,plain, % 188.31/188.33 (~P107(f334(f334(f336(x134761),x134762),f195(f935(x134761,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13479,plain, % 188.31/188.33 (P107(f334(f66(a927),f312(a927,x134791,x134792)))), % 188.31/188.33 inference(rename_variables,[],[3758])). % 188.31/188.33 cnf(13480,plain, % 188.31/188.33 (E(f334(f334(f246(a927),f334(a119,x134801)),f334(a119,x134802)),f334(a119,f334(f334(f246(a927),x134801),x134802)))), % 188.31/188.33 inference(rename_variables,[],[3722])). % 188.31/188.33 cnf(13483,plain, % 188.31/188.33 (P107(f334(f66(a927),f312(a927,x134831,x134832)))), % 188.31/188.33 inference(rename_variables,[],[3758])). % 188.31/188.33 cnf(13484,plain, % 188.31/188.33 (E(f334(f334(f241(a927),f334(a119,x134841)),f334(a119,x134842)),f334(a119,f334(f334(f241(a927),x134841),x134842)))), % 188.31/188.33 inference(rename_variables,[],[3723])). % 188.31/188.33 cnf(13487,plain, % 188.31/188.33 (P107(f334(f66(a927),f312(a927,x134871,x134872)))), % 188.31/188.33 inference(rename_variables,[],[3758])). % 188.31/188.33 cnf(13496,plain, % 188.31/188.33 (~P107(f334(f334(f336(x134961),x134962),f195(f935(x134961,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13497,plain, % 188.31/188.33 (E(f334(f334(f16(x134971,x134972),x134973),x134974),x134973)), % 188.31/188.33 inference(rename_variables,[],[3545])). % 188.31/188.33 cnf(13500,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x135001,a922)),f334(f179(x135001),f334(f143(x135001,x135002),x135003))),f334(f179(x135001),x135003)))), % 188.31/188.33 inference(rename_variables,[],[4194])). % 188.31/188.33 cnf(13501,plain, % 188.31/188.33 (E(f334(f334(f16(x135011,x135012),x135013),x135014),x135013)), % 188.31/188.33 inference(rename_variables,[],[3545])). % 188.31/188.33 cnf(13504,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x135041,a922)),f334(f179(x135041),f334(f334(f182(x135041),x135042),x135043))),f334(f179(x135041),x135043)))), % 188.31/188.33 inference(rename_variables,[],[4237])). % 188.31/188.33 cnf(13505,plain, % 188.31/188.33 (E(f334(f334(f16(x135051,x135052),x135053),x135054),x135053)), % 188.31/188.33 inference(rename_variables,[],[3545])). % 188.31/188.33 cnf(13509,plain, % 188.31/188.33 (E(f334(f334(f16(x135091,x135092),x135093),x135094),x135093)), % 188.31/188.33 inference(rename_variables,[],[3545])). % 188.31/188.33 cnf(13522,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),f2(a1)),f334(f107(a1),x135221)))), % 188.31/188.33 inference(rename_variables,[],[3653])). % 188.31/188.33 cnf(13527,plain, % 188.31/188.33 (P27(x135271,x135271,f5(x135271),x135272)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13530,plain, % 188.31/188.33 (~P107(f334(f334(f336(x135301),x135302),f195(f935(x135301,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13531,plain, % 188.31/188.33 (E(f334(f291(x135311,x135311),f271(x135311,x135312)),x135312)), % 188.31/188.33 inference(rename_variables,[],[3514])). % 188.31/188.33 cnf(13532,plain, % 188.31/188.33 (P27(x135321,x135321,f5(x135321),x135322)), % 188.31/188.33 inference(rename_variables,[],[3786])). % 188.31/188.33 cnf(13536,plain, % 188.31/188.33 (E(f334(f291(x135361,x135361),f271(x135361,x135362)),x135362)), % 188.31/188.33 inference(rename_variables,[],[3514])). % 188.31/188.33 cnf(13550,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),f2(a927)),x135501))), % 188.31/188.33 inference(rename_variables,[],[3574])). % 188.31/188.33 cnf(13551,plain, % 188.31/188.33 (P107(f334(f334(f243(a927),f2(a927)),f334(a119,x135511)))), % 188.31/188.33 inference(rename_variables,[],[3633])). % 188.31/188.33 cnf(13552,plain, % 188.31/188.33 (E(f334(f291(x135521,x135521),f271(x135521,x135522)),x135522)), % 188.31/188.33 inference(rename_variables,[],[3514])). % 188.31/188.33 cnf(13634,plain, % 188.31/188.33 (~P107(f334(f334(f243(a1),f2(a1)),f2(a1)))), % 188.31/188.33 inference(scs_inference,[],[4812,4209,12788,12810,12943,12945,12947,3786,11406,12467,12564,12567,12659,12698,12702,12710,12782,12918,12920,13374,13380,13385,13389,13395,13398,13422,13527,13532,3796,12531,13031,13033,3804,3459,12021,12024,3523,12978,12980,12982,3524,12937,3490,12864,4750,4751,12052,4481,12995,3528,13006,3360,3422,12957,3423,12961,3424,3425,3426,12738,12911,4749,3851,4717,10492,10502,10515,10526,10627,10630,10633,10735,10870,11182,11376,11379,11398,11401,11600,11698,11705,11719,11765,11768,11804,11819,11882,11939,11955,12253,12281,12293,12322,12328,12423,12527,12691,12752,12897,13447,13455,3609,3572,13002,3755,12225,3474,4729,10719,10819,11286,11386,13042,13046,13129,13467,3158,3160,3161,3163,3164,3166,3167,3170,3171,3172,3175,3178,3180,3187,3194,3197,3202,3205,3214,3215,3216,3220,3222,3236,3237,3242,3247,3253,3254,3257,3258,3259,3271,3277,3279,3280,3283,3284,3285,3293,3296,3304,3305,3306,3307,3314,3316,3317,3318,3319,3320,3325,3338,4712,3342,3421,4713,3889,4113,11986,3396,11695,3536,3511,3514,10561,10564,10654,10657,10973,11710,11713,11788,11830,11869,11874,11981,12441,12635,12842,12899,12907,12916,12927,12929,12933,12935,12965,12971,12973,13041,13045,13247,13413,13531,13536,13552,3485,12723,12727,12731,3491,3500,4008,4308,3468,13309,3620,12785,12867,3385,3386,3525,3749,4100,11741,3608,12985,3450,3382,3412,3870,3407,4219,4108,3932,4677,3394,3395,3366,3372,4022,3431,3610,11132,11256,12528,12742,3484,4183,4740,10552,10716,11597,12683,12724,12728,4747,12695,3545,12076,12079,13343,13433,13497,13501,13505,13509,4140,4787,11312,11411,11650,11653,3519,3951,3463,3542,3657,3876,3649,4765,3624,12903,12905,12969,3447,3448,10619,10949,4774,3709,3488,12949,3439,3363,3470,11731,4322,12713,12854,4186,11332,11467,11528,12670,12676,12799,12802,12832,4807,11234,11480,11591,11617,11658,11664,12614,4808,11365,11483,11594,4809,11486,11539,4810,11546,4811,3469,3747,12570,12611,12694,3916,3698,4600,4601,3731,3768,3893,3853,3895,4065,3819,13230,13234,13238,13242,13252,4110,12561,3733,3987,3621,10638,10758,10836,10909,10912,10952,11056,11302,11916,12070,12165,12249,12315,12344,12394,12432,12505,12508,12836,13112,13151,13154,13213,13446,13451,3997,11972,3538,3633,11803,12091,13551,3814,4780,10529,10532,10558,10679,10854,11064,11077,11192,11642,11734,11915,12140,12145,12164,12370,12373,12453,12617,12717,13058,13077,13080,13104,13155,13325,13330,13350,13355,4791,11846,11877,11912,11919,11952,13164,13168,3984,3757,3758,12270,13083,13086,13089,13092,13122,13125,13479,13483,13487,3760,4132,3722,13480,3723,13484,3580,3582,3556,4777,3446,4737,3942,4247,3740,4794,4315,11614,3875,3593,12097,12100,12535,12639,12813,4785,10520,10523,10687,10782,10801,10808,10831,10839,10842,10859,11047,11289,11508,11797,11891,12043,12158,12161,4286,4246,12242,12585,4194,11129,12426,12595,12741,13500,4237,13504,4241,11335,12464,12534,12594,12638,13346,4242,3917,11923,12252,12401,12472,12518,4274,3934,10682,10779,11338,11416,11501,11565,12422,12486,12747,12809,12829,12839,13316,13379,13384,13404,13425,4795,11080,11491,12598,13392,3554,10647,10745,10895,10959,11036,11083,11086,11117,11140,11176,11214,11250,12046,12094,12222,12280,12296,12299,12302,12305,12479,12493,12496,12499,12502,12578,12642,12758,12805,13105,13128,13187,13205,13216,13221,13224,13227,13260,13271,13284,13336,13361,13364,13443,3555,10674,10730,10964,11059,11179,11822,12125,12128,12137,12228,12239,12258,12263,12308,12331,12351,13119,13264,13287,13326,13331,13351,13356,3629,12456,13184,13231,13235,13239,13243,13253,13257,4776,10569,10595,11101,11143,11152,12000,12027,12196,12199,12202,12205,12292,12311,12314,12327,12382,12385,12388,12391,12546,12549,12645,12648,12751,12791,12876,3705,10824,10915,11187,11231,11470,11473,11554,11639,11807,12055,12690,12879,13308,13429,4789,11110,11223,11241,11244,11315,11318,11329,11432,11440,11454,11494,11513,11522,11562,11603,11608,11611,11630,11633,11667,11672,11675,11678,11681,11922,12073,12106,12376,12379,12413,12457,12482,12623,12667,12673,12770,12773,12795,12853,12859,12870,12891,13183,13199,13202,13297,13417,13436,13439,13476,13496,13530,3614,10946,10976,10985,10988,10991,11583,12792,12806,13165,13169,13172,13175,3653,13460,13522,3646,4069,4006,10598,11975,12003,13146,4786,10549,10934,10937,11435,11451,11938,11991,12031,12056,12069,12155,12184,12187,12190,12193,12452,13367,3574,10979,11137,11207,12004,12154,12356,12554,12579,13196,13463,13550,4031,12103,13099,3763,4784,4043,4077,4768,4771,4772,3531,3535,4770,4769,4805,4534,3865,11968,4461,11829,4797,10845,10848,4806,11321,11324,11516,11627,11647,11687,4150,11684,12030,12034,12701,12709,12798,13312,13373,3992,11247,11253,11273,12277,12406,12485,12766,3849,11391,11519,12511,12620,12630,12706,12761,12769,12888,13319,4320,3994,10982,11354,11525,11559,11570,12705,12755,13409,3815,10898,10901,10994,11163,3817,4800,11969,4796,13067,4801,10738,10851,11636,12573,12582,12626,12823,12826,12883,4414,11120,12591,12606,12629,4327,4030,12894,3971,3972,4798,10574,10577,10940,10943,11843,12035,12835,4799,1194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% 188.31/188.33 cnf(13791,plain, % 188.31/188.33 (P107(f334(f334(f242(a1),x137911),x137911))), % 188.31/188.33 inference(rename_variables,[],[3555])). % 188.31/188.33 cnf(13794,plain, % 188.31/188.33 (~P107(f334(f334(f336(f934(x137941,x137941)),x137942),f271(x137941,f195(f935(x137941,a922)))))), % 188.31/188.33 inference(rename_variables,[],[11240])). % 188.31/188.33 cnf(13797,plain, % 188.31/188.33 (E(f334(f334(f141(x137971),x137972),f120(x137971)),x137972)), % 188.31/188.33 inference(rename_variables,[],[3485])). % 188.31/188.33 cnf(13811,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x138111),f334(f334(f87(a927),x138111),x138111)))), % 188.31/188.33 inference(rename_variables,[],[3815])). % 188.31/188.33 cnf(13819,plain, % 188.31/188.33 (~P107(f334(f334(f336(a927),x138191),f334(f307(a927),f2(a927))))), % 188.31/188.33 inference(rename_variables,[],[12122])). % 188.31/188.33 cnf(13822,plain, % 188.31/188.33 (~E(f334(f334(f158(x138221),x138222),x138223),x138223)), % 188.31/188.33 inference(rename_variables,[],[4740])). % 188.31/188.33 cnf(13825,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x138251),f334(f334(f86(a927),x138251),x138252)))), % 188.31/188.33 inference(rename_variables,[],[3817])). % 188.31/188.33 cnf(13832,plain, % 188.31/188.33 (~E(x138321,f334(a119,x138321))), % 188.31/188.33 inference(rename_variables,[],[10581])). % 188.31/188.33 cnf(13835,plain, % 188.31/188.33 (~E(x138351,f334(a119,x138351))), % 188.31/188.33 inference(rename_variables,[],[10581])). % 188.31/188.33 cnf(13838,plain, % 188.31/188.33 (~P36(x138381,x138382,x138383,f334(f334(f161(x138384,x138381),x138385),f334(a119,f120(x138384))),f120(x138382))), % 188.31/188.33 inference(rename_variables,[],[11530])). % 188.31/188.33 cnf(13841,plain, % 188.31/188.33 (E(f334(x138411,f540(x138411,x138412,f334(x138411,x138413))),f334(x138411,x138413))), % 188.31/188.33 inference(rename_variables,[],[11270])). % 188.31/188.33 cnf(13851,plain, % 188.31/188.33 (~P107(f334(f334(f336(f934(x138511,x138511)),x138512),f271(x138511,f195(f935(x138511,a922)))))), % 188.31/188.33 inference(rename_variables,[],[11240])). % 188.31/188.33 cnf(13857,plain, % 188.31/188.33 (P107(f334(f334(f242(f935(x138571,a922)),f334(f179(x138571),f183(x138571,x138572,x138573))),f334(f179(x138571),x138572)))), % 188.31/188.33 inference(rename_variables,[],[4241])). % 188.31/188.33 cnf(13873,plain, % 188.31/188.33 (~E(f334(f334(f246(a927),f334(a119,x138731)),x138731),f334(a119,x138731))), % 188.31/188.33 inference(rename_variables,[],[11860])). % 188.31/188.33 cnf(13885,plain, % 188.31/188.33 (~E(f334(f334(f158(x138851),x138852),x138853),f120(x138851))), % 188.31/188.33 inference(rename_variables,[],[4747])). % 188.31/188.33 cnf(13890,plain, % 188.31/188.33 (~P107(f334(f334(f336(x138901),x138902),f195(f935(x138901,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(13912,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x139121),f334(f334(f86(a927),x139121),x139122)))), % 188.31/188.33 inference(rename_variables,[],[3817])). % 188.31/188.33 cnf(13923,plain, % 188.31/188.33 (~P107(f334(f334(f243(a927),x139231),x139231))), % 188.31/188.33 inference(rename_variables,[],[4776])). % 188.31/188.33 cnf(13928,plain, % 188.31/188.33 (~P107(f334(f334(f336(a927),x139281),f334(f307(a927),f2(a927))))), % 188.31/188.33 inference(rename_variables,[],[12122])). % 188.31/188.33 cnf(13931,plain, % 188.31/188.33 (~P107(f334(f334(f336(f934(f928(x139311),f928(x139311))),f334(f334(f260(f928(x139311),f928(x139311)),x139312),f120(x139311))),f152(x139311,x139313)))), % 188.31/188.33 inference(rename_variables,[],[4807])). % 188.31/188.33 cnf(13934,plain, % 188.31/188.33 (~E(f334(f334(f158(x139341),x139342),x139343),x139343)), % 188.31/188.33 inference(rename_variables,[],[4740])). % 188.31/188.33 cnf(13958,plain, % 188.31/188.33 (E(f334(f334(f141(x139581),f120(x139581)),x139582),x139582)), % 188.31/188.33 inference(rename_variables,[],[3509])). % 188.31/188.33 cnf(13963,plain, % 188.31/188.33 (~P107(f334(f334(f336(f934(x139631,x139631)),x139632),f271(x139631,f195(f935(x139631,a922)))))), % 188.31/188.33 inference(rename_variables,[],[11240])). % 188.31/188.33 cnf(13976,plain, % 188.31/188.33 (E(f334(f291(x139761,x139761),f271(x139761,x139762)),x139762)), % 188.31/188.33 inference(rename_variables,[],[3514])). % 188.31/188.33 cnf(13979,plain, % 188.31/188.33 (~P107(f334(f334(f243(a927),x139791),x139791))), % 188.31/188.33 inference(rename_variables,[],[4776])). % 188.31/188.33 cnf(13984,plain, % 188.31/188.33 (~P107(f334(f334(f336(a927),x139841),f334(f307(a927),f2(a927))))), % 188.31/188.33 inference(rename_variables,[],[12122])). % 188.31/188.33 cnf(14000,plain, % 188.31/188.33 (~P107(f334(f334(f336(f934(x140001,x140001)),x140002),f271(x140001,f195(f935(x140001,a922)))))), % 188.31/188.33 inference(rename_variables,[],[11240])). % 188.31/188.33 cnf(14009,plain, % 188.31/188.33 (~P107(f334(f334(f336(x140091),x140092),f195(f935(x140091,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(14019,plain, % 188.31/188.33 (P107(f334(f334(f242(a927),x140191),f334(f334(f86(a927),x140191),x140192)))), % 188.31/188.33 inference(rename_variables,[],[3817])). % 188.31/188.33 cnf(14052,plain, % 188.31/188.33 (~P107(f334(f334(f336(x140521),x140522),f195(f935(x140521,a922))))), % 188.31/188.33 inference(rename_variables,[],[4789])). % 188.31/188.33 cnf(14064,plain, % 188.31/188.33 (P107(f334(f334(f336(x140641),f334(x140642,x140643)),f334(f317(x140644,x140641,x140642),f250(f935(x140644,a922)))))), % 188.31/188.33 inference(rename_variables,[],[4150])). % 188.31/188.33 cnf(14067,plain, % 188.31/188.33 (~P107(f334(f334(f195(f935(x140671,f935(x140672,a922))),x140673),x140674))), % 188.31/188.33 inference(rename_variables,[],[4801])). % 188.31/188.33 cnf(14117,plain, % 188.31/188.33 ($false), % 188.31/188.33 inference(scs_inference,[],[3984,3582,4322,3342,4800,3535,4777,4186,4807,13931,4770,3997,4150,14064,4789,13890,14009,14052,4241,13857,3653,4729,4740,13822,13934,4747,13885,4765,4805,3633,3554,3555,13791,4006,3992,3849,3815,13811,3817,13825,13912,14019,4414,3995,3514,13976,3485,13797,3509,13958,4808,4809,4811,4776,13923,13979,4797,4796,4801,14067,4799,11860,13873,10581,13832,13835,13453,10635,12181,12581,13101,10888,13114,11383,12856,11186,11270,13841,10560,13372,10998,13363,11003,13634,12006,12619,12122,13819,13928,13984,11240,13794,13851,13963,14000,11243,10993,12384,11530,13838,11534,11403,11145,3185,9,8,6301,5581,6514,10353,5309,5720,8731,7189,8952,5555,7010,7765,9479,9917,5556,7573,9540,6342,8860,8890,9487,6017,6338,6533,6734,10351,2,6976,8574,8789,7993,8330,5470,5561,10142,5958,6699,7783,8659,8570,6429,9848,9962,5728,5863,6319,9138,5175,6021,9847,6575,7961,9410,6487,6159,6390,8133,10173,8851,5854,6318,5605,6517,7989,9641,5000,5999,5295,5947,8753,10476,5489,5831,7148,7554,7556,8719,5664,8800,9279,4950,5573,9211,5212,5277,6616,8663,9038,9416,5211,8953,9105,5909,6366,8599,9278,9918,5654,6224,6611,8732,8778,5468,5946,6187,8996,9639,6975,6115,5464,9148,7991,6176,6621,4999,5310,6085,6197,9789,9854,6785,9302,9483,5483,6509,9606,6363,8852,9790,9973,10154,4934]), % 188.31/188.33 ['proof']). % 188.31/188.33 % SZS output end Proof % 188.31/188.33 % Total time :171.080000s %------------------------------------------------------------------------------