%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW322+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n012.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 18:07:25 EDT 2024 % Result : Theorem 177.41s 177.17s % Output : CNFRefutation 177.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWW322+1 : TPTP v8.2.0. Released v5.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n012.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Wed Jun 19 08:07:39 EDT 2024 % 0.12/0.32 % CPUTime : % 0.18/0.55 start to proof:theBenchmark % 176.93/177.01 %------------------------------------------- % 176.93/177.01 % File :CSE---1.7 % 176.97/177.01 % Problem :theBenchmark % 176.97/177.01 % Transform :cnf % 176.97/177.01 % Format :tptp:raw % 176.97/177.01 % Command :java -jar mcs_scs.jar %d %s % 176.97/177.01 % 176.97/177.01 % Result :Theorem 162.200000s % 176.97/177.01 % Output :CNFRefutation 162.200000s % 176.97/177.01 %------------------------------------------- % 176.97/177.02 %------------------------------------------------------------------------------ % 176.97/177.02 % File : SWW322+1 : TPTP v8.2.0. Released v5.2.0. % 176.97/177.02 % Domain : Software Verification % 176.97/177.02 % Problem : Hoare's Logic with Procedures 435056, 5000 axioms selected % 176.97/177.02 % Version : Especial. % 176.97/177.02 % English : % 176.97/177.02 % 176.97/177.02 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 176.97/177.02 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 176.97/177.02 % Source : [Bla11] % 176.97/177.02 % Names : hoare_435056.5000.p [Bla11] % 176.97/177.02 % 176.97/177.02 % Status : ContradictoryAxioms % 176.97/177.02 % Rating : 0.56 v8.2.0, 0.53 v8.1.0, 0.61 v7.5.0, 0.62 v7.4.0, 0.73 v7.3.0, 0.69 v7.1.0, 0.70 v7.0.0, 0.77 v6.4.0, 0.73 v6.3.0, 0.67 v6.2.0, 0.76 v6.1.0, 0.80 v6.0.0, 0.70 v5.5.0, 0.74 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0 % 176.97/177.02 % Syntax : Number of formulae : 5233 (1678 unt; 0 def) % 176.97/177.02 % Number of atoms : 12735 (4453 equ) % 176.97/177.02 % Maximal formula atoms : 13 ( 2 avg) % 176.97/177.02 % Number of connectives : 8493 ( 991 ~; 148 |; 715 &) % 176.97/177.02 % ( 900 <=>;5739 =>; 0 <=; 0 <~>) % 176.97/177.02 % Maximal formula depth : 22 ( 6 avg) % 176.97/177.02 % Maximal term depth : 19 ( 2 avg) % 176.97/177.02 % Number of predicates : 148 ( 147 usr; 0 prp; 1-6 aty) % 176.97/177.02 % Number of functors : 392 ( 392 usr; 56 con; 0-7 aty) % 176.97/177.02 % Number of variables : 16645 (16492 !; 153 ?) % 176.97/177.02 % SPC : FOF_CAX_RFO_SEQ % 176.97/177.02 % 176.97/177.02 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 176.97/177.02 % 2011-03-01 11:50:13 % 176.97/177.02 %------------------------------------------------------------------------------ % 176.97/177.02 %----Relevant facts (4985) % 176.97/177.02 fof(fact_ext,axiom, % 176.97/177.02 ! [V_g_2,V_f_2] : % 176.97/177.02 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 176.97/177.02 => V_f_2 = V_g_2 ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_empty,axiom, % 176.97/177.02 ! [V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))) ). % 176.97/177.02 % 176.97/177.02 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 176.97/177.02 ! [V_a_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))) ). % 176.97/177.02 % 176.97/177.02 fof(fact_triple_Oinject,axiom, % 176.97/177.02 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_c] : % 176.97/177.02 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 176.97/177.02 <=> ( V_fun1_2 = V_fun1_H_2 % 176.97/177.02 & V_com_2 = V_com_H_2 % 176.97/177.02 & V_fun2_2 = V_fun2_H_2 ) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_cut,axiom, % 176.97/177.02 ! [V_Ga_2,V_ts_2,V_G_H_2,T_c] : % 176.97/177.02 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_G_H_2,V_ts_2) % 176.97/177.02 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_G_H_2) % 176.97/177.02 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_hoare__derivs_Oinsert,axiom, % 176.97/177.02 ! [V_ts_2,V_t_2,V_Ga_2,T_c] : % 176.97/177.02 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 176.97/177.02 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) % 176.97/177.02 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),V_ts_2)) ) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_derivs__insertD,axiom, % 176.97/177.02 ! [V_ts_2,V_t_2,V_Ga_2,T_c] : % 176.97/177.02 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),V_ts_2)) % 176.97/177.02 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 176.97/177.02 & c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_finite__imageI,axiom, % 176.97/177.02 ! [V_h_2,T_d,V_F_2,T_c] : % 176.97/177.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 176.97/177.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_h_2),V_F_2))) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_finite_OinsertI,axiom, % 176.97/177.02 ! [V_a_2,V_A_2,T_c] : % 176.97/177.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 176.97/177.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2))) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_finite_OemptyI,axiom, % 176.97/177.02 ! [T_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ). % 176.97/177.02 % 176.97/177.02 fof(fact_image__eqI,axiom, % 176.97/177.02 ! [T_c,V_A_2,T_d,V_x_2,V_f_2,V_b_2] : % 176.97/177.02 ( V_b_2 = hAPP(V_f_2,V_x_2) % 176.97/177.02 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2)) % 176.97/177.02 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) ) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_insertE,axiom, % 176.97/177.02 ! [V_A_2,V_b_2,V_a_2,T_c] : % 176.97/177.02 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2))) % 176.97/177.02 => ( V_a_2 != V_b_2 % 176.97/177.02 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_insertCI,axiom, % 176.97/177.02 ! [V_b_2,V_B_2,V_a_2,T_c] : % 176.97/177.02 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2)) % 176.97/177.02 => V_a_2 = V_b_2 ) % 176.97/177.02 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_emptyE,axiom, % 176.97/177.02 ! [V_a_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ). % 176.97/177.02 % 176.97/177.02 fof(fact_image__constant,axiom, % 176.97/177.02 ! [V_c_2,T_d,V_A_2,V_x_2,T_c] : % 176.97/177.02 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.02 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_image__constant__conv,axiom, % 176.97/177.02 ! [V_c_2,T_d,T_c,V_A_2] : % 176.97/177.02 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.02 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 176.97/177.02 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.02 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) ) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_insert__image,axiom, % 176.97/177.02 ! [V_f_2,T_d,V_A_2,V_x_2,T_c] : % 176.97/177.02 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.02 => hAPP(hAPP(c_Set_Oinsert(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) ) ). % 176.97/177.02 % 176.97/177.02 fof(fact_singleton__iff,axiom, % 176.97/177.03 ! [V_a_2,V_b_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),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))))) % 176.97/177.03 <=> V_b_2 = V_a_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_singletonE,axiom, % 176.97/177.03 ! [V_a_2,V_b_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),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))))) % 176.97/177.03 => V_b_2 = V_a_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_equalityCE,axiom, % 176.97/177.03 ! [V_c_2,T_c,V_B_2,V_A_2] : % 176.97/177.03 ( V_A_2 = V_B_2 % 176.97/177.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 176.97/177.03 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) % 176.97/177.03 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 176.97/177.03 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_eq__mem__trans,axiom, % 176.97/177.03 ! [V_A_2,T_c,V_b_2,V_a_2] : % 176.97/177.03 ( V_a_2 = V_b_2 % 176.97/177.03 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2)) % 176.97/177.03 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_eqelem__imp__iff,axiom, % 176.97/177.03 ! [V_A_2,T_c,V_y_2,V_x_2] : % 176.97/177.03 ( V_x_2 = V_y_2 % 176.97/177.03 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_eqset__imp__iff,axiom, % 176.97/177.03 ! [V_x_2,T_c,V_B_2,V_A_2] : % 176.97/177.03 ( V_A_2 = V_B_2 % 176.97/177.03 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_mem__def,axiom, % 176.97/177.03 ! [V_A_2,V_x_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_finite__code,axiom, % 176.97/177.03 ! [V_A_2,T_c] : % 176.97/177.03 ( class_Finite__Set_Ofinite(T_c) % 176.97/177.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_finite,axiom, % 176.97/177.03 ! [V_A_2,T_c] : % 176.97/177.03 ( class_Finite__Set_Ofinite(T_c) % 176.97/177.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insert__code,axiom, % 176.97/177.03 ! [V_x_2,V_A_2,V_y_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),V_A_2),V_x_2)) % 176.97/177.03 <=> ( V_y_2 = V_x_2 % 176.97/177.03 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insert__commute,axiom, % 176.97/177.03 ! [V_A_2,V_y_2,V_x_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insert__absorb2,axiom, % 176.97/177.03 ! [V_A_2,V_x_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2) ). % 176.97/177.03 % 176.97/177.03 fof(fact_image__image,axiom, % 176.97/177.03 ! [V_A_2,V_g_2,T_e,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_e,T_c,hAPP(hAPP(c_COMBB(T_d,T_c,T_e),V_f_2),V_g_2)),V_A_2) ). % 176.97/177.03 % 176.97/177.03 fof(fact_equals0D,axiom, % 176.97/177.03 ! [V_a_2,T_c,V_A_2] : % 176.97/177.03 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.03 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_empty__iff,axiom, % 176.97/177.03 ! [V_c_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ). % 176.97/177.03 % 176.97/177.03 fof(fact_ex__in__conv,axiom, % 176.97/177.03 ! [V_A_2,T_c] : % 176.97/177.03 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 176.97/177.03 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_all__not__in__conv,axiom, % 176.97/177.03 ! [V_A_2,T_c] : % 176.97/177.03 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 176.97/177.03 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insert__absorb,axiom, % 176.97/177.03 ! [V_A_2,V_a_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 176.97/177.03 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) = V_A_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insertI2,axiom, % 176.97/177.03 ! [V_b_2,V_B_2,V_a_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2)) % 176.97/177.03 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insert__ident,axiom, % 176.97/177.03 ! [V_B_2,V_A_2,V_x_2,T_c] : % 176.97/177.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) % 176.97/177.03 => ( hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2) % 176.97/177.03 <=> V_A_2 = V_B_2 ) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insert__iff,axiom, % 176.97/177.03 ! [V_A_2,V_b_2,V_a_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2))) % 176.97/177.03 <=> ( V_a_2 = V_b_2 % 176.97/177.03 | hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insertI1,axiom, % 176.97/177.03 ! [V_B_2,V_a_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2))) ). % 176.97/177.03 % 176.97/177.03 fof(fact_rev__image__eqI,axiom, % 176.97/177.03 ! [T_d,V_f_2,V_b_2,V_A_2,V_x_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 176.97/177.03 => hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_imageI,axiom, % 176.97/177.03 ! [V_f_2,T_d,V_A_2,V_x_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_image__iff,axiom, % 176.97/177.03 ! [V_A_2,V_f_2,T_d,V_z_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) % 176.97/177.03 <=> ? [B_x] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 176.97/177.03 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_finite_Oequations_I1_J,axiom, % 176.97/177.03 ! [T_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ). % 176.97/177.03 % 176.97/177.03 fof(fact_singleton__inject,axiom, % 176.97/177.03 ! [V_b_2,V_a_2,T_c] : % 176.97/177.03 ( 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_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) % 176.97/177.03 => V_a_2 = V_b_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_doubleton__eq__iff,axiom, % 176.97/177.03 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 176.97/177.03 ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 176.97/177.03 <=> ( ( V_a_2 = V_c_2 % 176.97/177.03 & V_b_2 = V_d_2 ) % 176.97/177.03 | ( V_a_2 = V_d_2 % 176.97/177.03 & V_b_2 = V_c_2 ) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_insert__not__empty,axiom, % 176.97/177.03 ! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 176.97/177.03 % 176.97/177.03 fof(fact_empty__not__insert,axiom, % 176.97/177.03 ! [V_A_2,V_a_2,T_c] : c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) ). % 176.97/177.03 % 176.97/177.03 fof(fact_finite__insert,axiom, % 176.97/177.03 ! [V_A_2,V_a_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2))) % 176.97/177.03 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_image__is__empty,axiom, % 176.97/177.03 ! [V_A_2,V_f_2,T_c,T_d] : % 176.97/177.03 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.03 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_image__empty,axiom, % 176.97/177.03 ! [V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 176.97/177.03 % 176.97/177.03 fof(fact_empty__is__image,axiom, % 176.97/177.03 ! [V_A_2,V_f_2,T_d,T_c] : % 176.97/177.03 ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) % 176.97/177.03 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_image__insert,axiom, % 176.97/177.03 ! [V_B_2,V_a_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)) ). % 176.97/177.03 % 176.97/177.03 fof(fact_the__elem__eq,axiom, % 176.97/177.03 ! [V_x_2,T_c] : c_Set_Othe__elem(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ). % 176.97/177.03 % 176.97/177.03 fof(fact_bot__fun__def,axiom, % 176.97/177.03 ! [V_x_2,T_d,T_c] : % 176.97/177.03 ( class_Orderings_Obot(T_c) % 176.97/177.03 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Obot__class_Obot(T_c) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_bot__empty__eq,axiom, % 176.97/177.03 ! [V_x_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_x_2)) % 176.97/177.03 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_triple_Osimps_I2_J,axiom, % 176.97/177.03 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_c,T_d] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_d,T_c,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_d),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 176.97/177.03 % 176.97/177.03 fof(fact_triple_Orecs,axiom, % 176.97/177.03 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_c,T_d] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_d,T_c,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_d),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 176.97/177.03 % 176.97/177.03 fof(fact_folding__one_Oinsert,axiom, % 176.97/177.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] : % 176.97/177.03 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 176.97/177.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 176.97/177.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.03 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_bot__apply,axiom, % 176.97/177.03 ! [V_x_2,T_d,T_c] : % 176.97/177.03 ( class_Orderings_Obot(T_c) % 176.97/177.03 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Obot__class_Obot(T_c) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_escape,axiom, % 176.97/177.03 ! [V_Qa_2,V_c_2,V_Ga_2,T_c,V_Pa_2] : % 176.97/177.03 ( ! [B_Z,B_s] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 176.97/177.03 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_c),hAPP(V_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) % 176.97/177.03 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 176.97/177.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] : % 176.97/177.03 ( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) % 176.97/177.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 176.97/177.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.03 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 176.97/177.03 ! [V_a2_2,V_a1_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ). % 176.97/177.03 % 176.97/177.03 fof(fact_hoare__derivs_OSkip,axiom, % 176.97/177.03 ! [V_Pa_2,V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ). % 176.97/177.03 % 176.97/177.03 fof(fact_conseq1,axiom, % 176.97/177.03 ! [V_Pa_2,V_Qa_2,V_c_2,V_P_Ha_2,V_Ga_2,T_c] : % 176.97/177.03 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_P_Ha_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 176.97/177.03 => ( ! [B_Z,B_s] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 176.97/177.03 => hBOOL(hAPP(hAPP(V_P_Ha_2,B_Z),B_s)) ) % 176.97/177.03 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_folding__one__idem_Oidem,axiom, % 176.97/177.03 ! [V_x_2,V_F_2,V_f_2,T_c] : % 176.97/177.03 ( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) % 176.97/177.03 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_eq__mem,axiom, % 176.97/177.03 ! [V_y_2,V_x_2,T_c] : % 176.97/177.03 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_fequal,V_y_2))) % 176.97/177.03 <=> V_x_2 = V_y_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_folding__one_Osingleton,axiom, % 176.97/177.03 ! [V_x_2,V_F_2,V_f_2,T_c] : % 176.97/177.03 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 176.97/177.03 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_folding__one__idem_Oin__idem,axiom, % 176.97/177.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] : % 176.97/177.03 ( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) % 176.97/177.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 176.97/177.03 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.03 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_pred__equals__eq,axiom, % 176.97/177.03 ! [V_S_2,V_R_2,T_c] : % 176.97/177.03 ( hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2) = hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2) % 176.97/177.03 <=> V_R_2 = V_S_2 ) ). % 176.97/177.03 % 176.97/177.03 fof(fact_folding__one_Oclosed,axiom, % 176.97/177.03 ! [V_A_2,V_F_2,V_f_2,T_c] : % 176.97/177.03 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 176.97/177.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 176.97/177.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.04 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 176.97/177.04 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 176.97/177.04 % 176.97/177.04 fof(fact_conseq2,axiom, % 176.97/177.04 ! [V_Qa_2,V_Q_Ha_2,V_c_2,V_Pa_2,V_Ga_2,T_c] : % 176.97/177.04 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Q_Ha_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 176.97/177.04 => ( ! [B_Z,B_s] : % 176.97/177.04 ( hBOOL(hAPP(hAPP(V_Q_Ha_2,B_Z),B_s)) % 176.97/177.04 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) ) % 176.97/177.04 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ) ). % 176.97/177.04 % 176.97/177.04 fof(fact_Comp,axiom, % 176.97/177.04 ! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_2,V_Ga_2,T_c] : % 176.97/177.04 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 176.97/177.04 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 176.97/177.04 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ) ). % 176.97/177.04 % 176.97/177.04 fof(fact_the__elem__def,axiom, % 176.97/177.04 ! [V_X_2,T_c] : c_Set_Othe__elem(T_c,V_X_2) = c_HOL_OThe(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),hAPP(c_fequal,V_X_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))))) ). % 176.97/177.04 % 176.97/177.04 fof(fact_LoopF,axiom, % 176.97/177.04 ! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(hAPP(c_COMBC(T_c,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_c),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_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ). % 176.97/177.04 % 176.97/177.04 fof(fact_folding__one__idem_Ohom__commute,axiom, % 176.97/177.04 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_c] : % 176.97/177.04 ( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) % 176.97/177.04 => ( ! [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)) % 176.97/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 176.97/177.04 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.04 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 176.97/177.04 % 176.97/177.04 fof(fact_folding__image__simple_Oinsert,axiom, % 176.97/177.04 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 176.97/177.04 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 176.97/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 176.97/177.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2)) % 176.97/177.04 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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)) ) ) ) ). % 176.97/177.04 % 176.97/177.04 fof(fact_folding__one_Oremove,axiom, % 176.97/177.04 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] : % 176.97/177.04 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 176.97/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 176.97/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 176.97/177.04 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 176.97/177.04 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 177.02/177.04 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.04 => 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_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)))))) ) ) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 177.02/177.04 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.04 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_finite__induct,axiom, % 177.02/177.04 ! [V_Pa_2,V_F_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.04 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.04 => ( ! [B_x,B_F] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_F)) % 177.02/177.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_F)) % 177.02/177.04 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 177.02/177.04 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_c),B_x),B_F))) ) ) ) % 177.02/177.04 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 177.02/177.04 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2)) % 177.02/177.04 => 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) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_image__ident,axiom, % 177.02/177.04 ! [V_Y_2,T_c] : hAPP(c_Set_Oimage(T_c,T_c,c_COMBI(T_c)),V_Y_2) = V_Y_2 ). % 177.02/177.04 % 177.02/177.04 fof(fact_DiffE,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.04 => ~ ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_DiffI,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_finite__Diff,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff__idemp,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__image__simple__idem_Oidem,axiom, % 177.02/177.04 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.04 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_DiffD2,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.04 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_DiffD1,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff__iff,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.04 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.04 & ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff__cancel,axiom, % 177.02/177.04 ! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff__empty,axiom, % 177.02/177.04 ! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_A_2 ). % 177.02/177.04 % 177.02/177.04 fof(fact_empty__Diff,axiom, % 177.02/177.04 ! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.04 % 177.02/177.04 fof(fact_finite__Diff2,axiom, % 177.02/177.04 ! [V_A_2,V_B_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.04 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 177.02/177.04 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.04 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_insert__Diff1,axiom, % 177.02/177.04 ! [V_A_2,V_B_2,V_x_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) % 177.02/177.04 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_insert__Diff__if,axiom, % 177.02/177.04 ! [V_A_2,V_B_2,V_x_2,T_c] : % 177.02/177.04 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) % 177.02/177.04 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ) % 177.02/177.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) % 177.02/177.04 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_insert__Diff__single,axiom, % 177.02/177.04 ! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff__insert2,axiom, % 177.02/177.04 ! [V_B_2,V_a_2,V_A_2,T_c] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),V_B_2) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff__insert,axiom, % 177.02/177.04 ! [V_B_2,V_a_2,V_A_2,T_c] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_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)))) ). % 177.02/177.04 % 177.02/177.04 fof(fact_finite__Diff__insert,axiom, % 177.02/177.04 ! [V_B_2,V_a_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_a_2),V_B_2)))) % 177.02/177.04 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__image__simple_Oempty,axiom, % 177.02/177.04 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.04 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2 ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__image__simple_Oremove,axiom, % 177.02/177.04 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2)) % 177.02/177.04 => 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_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_insert__Diff,axiom, % 177.02/177.04 ! [V_A_2,V_a_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.04 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = V_A_2 ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff__insert__absorb,axiom, % 177.02/177.04 ! [V_A_2,V_x_2,T_c] : % 177.02/177.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),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)))) = V_A_2 ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__one_Oinsert__remove,axiom, % 177.02/177.04 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.04 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.04 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) % 177.02/177.04 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.04 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_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)))))) ) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__diff__def,axiom, % 177.02/177.04 ! [V_x_2,V_B_2,V_A_2,T_d,T_c] : % 177.02/177.04 ( class_Groups_Ominus(T_c) % 177.02/177.04 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,T_c)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I12_J,axiom, % 177.02/177.04 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I13_J,axiom, % 177.02/177.04 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I16_J,axiom, % 177.02/177.04 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I17_J,axiom, % 177.02/177.04 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I46_J,axiom, % 177.02/177.04 ! [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) ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I47_J,axiom, % 177.02/177.04 ! [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) ). % 177.02/177.04 % 177.02/177.04 fof(fact_minus__apply,axiom, % 177.02/177.04 ! [V_x_2,V_B_2,V_A_2,T_d,T_c] : % 177.02/177.04 ( class_Groups_Ominus(T_c) % 177.02/177.04 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,T_c)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__image,axiom, % 177.02/177.04 ! [V_y_2,V_f_2,T_d,V_A_2,V_x_2,T_c] : % 177.02/177.04 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hAPP(c_Set_Oimage(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,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)))))) ) % 177.02/177.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hAPP(c_Set_Oimage(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_finite__empty__induct,axiom, % 177.02/177.04 ! [V_Pa_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.04 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 177.02/177.04 => ( ! [B_a,B_A] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_A)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A)) % 177.02/177.04 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 177.02/177.04 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_c),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) % 177.02/177.04 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__left__comm__idem__remove,axiom, % 177.02/177.04 ! [T_c] : c_Finite__Set_Ofun__left__comm__idem(T_c,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_c),hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)))),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))))) ). % 177.02/177.04 % 177.02/177.04 fof(fact_the__sym__eq__trivial,axiom, % 177.02/177.04 ! [V_x_2,T_c] : c_HOL_OThe(T_c,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__triv,axiom, % 177.02/177.04 ! [V_x_2,V_f_2,T_d,T_c] : c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__idem__iff,axiom, % 177.02/177.04 ! [V_y_2,V_x_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2) = V_f_2 % 177.02/177.04 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__upd,axiom, % 177.02/177.04 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_d,T_c] : c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_z_2) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__same,axiom, % 177.02/177.04 ! [V_y_2,V_x_2,V_f_2,T_c,T_d] : hAPP(c_Fun_Ofun__upd(T_d,T_c,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__apply,axiom, % 177.02/177.04 ! [V_y_2,V_f_2,T_d,T_c,V_x_2,V_z_2] : % 177.02/177.04 ( ( V_z_2 = V_x_2 % 177.02/177.04 => hAPP(c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) % 177.02/177.04 & ( V_z_2 != V_x_2 % 177.02/177.04 => hAPP(c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__twist,axiom, % 177.02/177.04 ! [V_d_2,V_b_2,V_m_2,T_d,T_c,V_c_2,V_a_2] : % 177.02/177.04 ( V_a_2 != V_c_2 % 177.02/177.04 => c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__other,axiom, % 177.02/177.04 ! [V_y_2,V_f_2,T_d,T_c,V_x_2,V_z_2] : % 177.02/177.04 ( V_z_2 != V_x_2 % 177.02/177.04 => hAPP(c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__idem,axiom, % 177.02/177.04 ! [T_c,T_d,V_y_2,V_x_2,V_f_2] : % 177.02/177.04 ( hAPP(V_f_2,V_x_2) = V_y_2 % 177.02/177.04 => c_Fun_Ofun__upd(T_d,T_c,V_f_2,V_x_2,V_y_2) = V_f_2 ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 177.02/177.04 ! [V_z_2,V_x_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) % 177.02/177.04 => 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) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__upd__def,axiom, % 177.02/177.04 ! [V_b_2,V_f_2,T_d,T_c,V_a_2,V_x_2] : % 177.02/177.04 ( ( V_x_2 = V_a_2 % 177.02/177.04 => hAPP(c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) % 177.02/177.04 & ( V_x_2 != V_a_2 % 177.02/177.04 => hAPP(c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 177.02/177.04 ! [V_g_2,T_e,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) % 177.02/177.04 => c_Finite__Set_Ofun__left__comm__idem(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_d),T_e),V_f_2),V_g_2)) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_fun__left__comm__idem__insert,axiom, % 177.02/177.04 ! [T_c] : c_Finite__Set_Ofun__left__comm__idem(T_c,tc_fun(T_c,tc_HOL_Obool),c_Set_Oinsert(T_c)) ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I5_J,axiom, % 177.02/177.04 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 177.02/177.04 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 177.02/177.04 <=> ( V_fun_2 = V_fun_H_2 % 177.02/177.04 & V_com_2 = V_com_H_2 ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_com_Osimps_I3_J,axiom, % 177.02/177.04 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 177.02/177.04 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 177.02/177.04 <=> ( V_com1_2 = V_com1_H_2 % 177.02/177.04 & V_com2_2 = V_com2_H_2 ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_the__eq__trivial,axiom, % 177.02/177.04 ! [V_a_2,T_c] : c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 177.02/177.04 % 177.02/177.04 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 177.02/177.04 ! [V_y_2,V_z_2,V_f_2,T_d,V_A_2,V_x_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => ( c_Nitpick_Ofold__graph_H(T_c,T_d,V_f_2,V_z_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)))),V_y_2) % 177.02/177.04 => c_Nitpick_Ofold__graph_H(T_c,T_d,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_Diff1__fold__graph,axiom, % 177.02/177.04 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_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))))),V_y_2)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_inj__on__insert,axiom, % 177.02/177.04 ! [V_A_2,V_a_2,V_f_2,T_d,T_c] : % 177.02/177.04 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) % 177.02/177.04 <=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.04 & ~ hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_folding__one_Oeq__fold_H,axiom, % 177.02/177.04 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.04 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,V_f_2),V_x_2),V_A_2) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_minus__fold__remove,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.04 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,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_c),hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)))),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))))),V_B_2),V_A_2) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_the__inv__into__def,axiom, % 177.02/177.04 ! [V_x_2,V_f_2,V_A_2,T_d,T_c] : hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_c,hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_x_2))) ). % 177.02/177.04 % 177.02/177.04 fof(fact_subset__insert__iff,axiom, % 177.02/177.04 ! [V_B_2,V_x_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) % 177.02/177.04 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2)) ) % 177.02/177.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_diff__single__insert,axiom, % 177.02/177.04 ! [V_B_2,V_x_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_setsum__diff1,axiom, % 177.02/177.04 ! [V_f_2,V_a_2,V_A_2,T_c,T_d] : % 177.02/177.04 ( class_Groups_Oab__group__add(T_d) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.04 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.04 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 177.02/177.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.04 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) ) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_setsum__diff1__ring,axiom, % 177.02/177.04 ! [V_f_2,V_a_2,V_A_2,T_c,T_d] : % 177.02/177.04 ( class_Rings_Oring(T_d) % 177.02/177.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.04 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_override__on__def,axiom, % 177.02/177.04 ! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] : % 177.02/177.04 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.04 => hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 177.02/177.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.04 => hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_order__refl,axiom, % 177.02/177.04 ! [V_x,T_a] : % 177.02/177.04 ( class_Orderings_Opreorder(T_a) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_equalityI,axiom, % 177.02/177.04 ! [V_B_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.04 => V_A_2 = V_B_2 ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_subsetD,axiom, % 177.02/177.04 ! [V_c_2,V_B_2,V_A_2,T_c] : % 177.02/177.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_empty__subsetI,axiom, % 177.02/177.04 ! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2)) ). % 177.02/177.04 % 177.02/177.04 fof(fact_inj__on__empty,axiom, % 177.02/177.04 ! [V_f_2,T_d,T_c] : c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ). % 177.02/177.04 % 177.02/177.04 fof(fact_linorder__le__cases,axiom, % 177.02/177.04 ! [V_y,V_x,T_a] : % 177.02/177.04 ( class_Orderings_Olinorder(T_a) % 177.02/177.04 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 177.02/177.04 % 177.02/177.04 fof(fact_le__funE,axiom, % 177.02/177.04 ! [V_x_2,V_g_2,V_f_2,T_c,T_d] : % 177.02/177.04 ( class_Orderings_Oord(T_d) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_xt1_I6_J,axiom, % 177.02/177.05 ! [V_z,V_x,V_y,T_a] : % 177.02/177.05 ( class_Orderings_Oorder(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_xt1_I5_J,axiom, % 177.02/177.05 ! [V_x,V_y,T_a] : % 177.02/177.05 ( class_Orderings_Oorder(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.05 => V_x = V_y ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_order__trans,axiom, % 177.02/177.05 ! [V_z,V_y,V_x,T_a] : % 177.02/177.05 ( class_Orderings_Opreorder(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_order__antisym,axiom, % 177.02/177.05 ! [V_y,V_x,T_a] : % 177.02/177.05 ( class_Orderings_Oorder(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.05 => V_x = V_y ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_xt1_I4_J,axiom, % 177.02/177.05 ! [V_c,V_a,V_b,T_a] : % 177.02/177.05 ( class_Orderings_Oorder(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.02/177.05 => ( V_b = V_c % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_ord__le__eq__trans,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Orderings_Oord(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.05 => ( V_b = V_c % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_xt1_I3_J,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Orderings_Oorder(T_a) % 177.02/177.05 => ( V_a = V_b % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_ord__eq__le__trans,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Orderings_Oord(T_a) % 177.02/177.05 => ( V_a = V_b % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_predicate1D,axiom, % 177.02/177.05 ! [V_x_2,V_Qa_2,V_Pa_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 177.02/177.05 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.02/177.05 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_order__antisym__conv,axiom, % 177.02/177.05 ! [V_x_2,V_y_2,T_c] : % 177.02/177.05 ( class_Orderings_Oorder(T_c) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.05 <=> V_x_2 = V_y_2 ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_le__funD,axiom, % 177.02/177.05 ! [V_x_2,V_g_2,V_f_2,T_c,T_d] : % 177.02/177.05 ( class_Orderings_Oord(T_d) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_order__eq__refl,axiom, % 177.02/177.05 ! [V_y,V_x,T_a] : % 177.02/177.05 ( class_Orderings_Opreorder(T_a) % 177.02/177.05 => ( V_x = V_y % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_rev__predicate1D,axiom, % 177.02/177.05 ! [V_Qa_2,T_c,V_x_2,V_Pa_2] : % 177.02/177.05 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) % 177.02/177.05 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_order__eq__iff,axiom, % 177.02/177.05 ! [V_y_2,V_x_2,T_c] : % 177.02/177.05 ( class_Orderings_Oorder(T_c) % 177.02/177.05 => ( V_x_2 = V_y_2 % 177.02/177.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_linorder__linear,axiom, % 177.02/177.05 ! [V_y,V_x,T_a] : % 177.02/177.05 ( class_Orderings_Olinorder(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.05 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_le__fun__def,axiom, % 177.02/177.05 ! [V_g_2,V_f_2,T_c,T_d] : % 177.02/177.05 ( class_Orderings_Oord(T_d) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.02/177.05 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__commute,axiom, % 177.02/177.05 ! [V_A_2,V_B_2,V_f_2,T_e,T_d,T_c] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_c),T_e),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2))),V_A_2)),V_B_2) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_equalityE,axiom, % 177.02/177.05 ! [T_c,V_B_2,V_A_2] : % 177.02/177.05 ( V_A_2 = V_B_2 % 177.02/177.05 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__trans,axiom, % 177.02/177.05 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_equalityD2,axiom, % 177.02/177.05 ! [T_c,V_B_2,V_A_2] : % 177.02/177.05 ( V_A_2 = V_B_2 % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_equalityD1,axiom, % 177.02/177.05 ! [T_c,V_B_2,V_A_2] : % 177.02/177.05 ( V_A_2 = V_B_2 % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_set__eq__subset,axiom, % 177.02/177.05 ! [T_c,V_B_2,V_A_2] : % 177.02/177.05 ( V_A_2 = V_B_2 % 177.02/177.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__refl,axiom, % 177.02/177.05 ! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__inj__on,axiom, % 177.02/177.05 ! [V_A_2,V_B_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__def,axiom, % 177.02/177.05 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 <=> ! [B_x] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.05 => ! [B_xa] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_A_2)) % 177.02/177.05 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 177.02/177.05 => B_x = B_xa ) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__id2,axiom, % 177.02/177.05 ! [V_A_2,T_c] : c_Fun_Oinj__on(T_c,T_c,c_COMBI(T_c),V_A_2) ). % 177.02/177.05 % 177.02/177.05 fof(fact_the__inv__into__f__eq,axiom, % 177.02/177.05 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_the__inv__into__f__f,axiom, % 177.02/177.05 ! [V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_the__inv__into__onto,axiom, % 177.02/177.05 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => hAPP(c_Set_Oimage(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = V_A_2 ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__the__inv__into,axiom, % 177.02/177.05 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => c_Fun_Oinj__on(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_the__inv__into__into,axiom, % 177.02/177.05 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__diff__nat,axiom, % 177.02/177.05 ! [V_f_2,V_A_2,V_B_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_Nat_Onat),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,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__subtractf,axiom, % 177.02/177.05 ! [V_A_2,V_g_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( class_Groups_Oab__group__add(T_c) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),V_A_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__def,axiom, % 177.02/177.05 ! [V_A_2,V_z_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_Finite__Set_Ofold(T_d,T_c,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_c,c_Finite__Set_Ofold__graph(T_d,T_c,V_f_2,V_z_2,V_A_2)) ). % 177.02/177.05 % 177.02/177.05 fof(fact_endo__inj__surj,axiom, % 177.02/177.05 ! [V_f_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_c,V_f_2),V_A_2)),V_A_2)) % 177.02/177.05 => ( c_Fun_Oinj__on(T_c,T_c,V_f_2,V_A_2) % 177.02/177.05 => hAPP(c_Set_Oimage(T_c,T_c,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_finite__surj__inj,axiom, % 177.02/177.05 ! [V_f_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_c,V_f_2),V_A_2))) % 177.02/177.05 => c_Fun_Oinj__on(T_c,T_c,V_f_2,V_A_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__image__set__diff,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.05 => hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__onD,axiom, % 177.02/177.05 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 177.02/177.05 => V_x_2 = V_y_2 ) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__iff,axiom, % 177.02/177.05 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 177.02/177.05 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.02/177.05 <=> V_x_2 = V_y_2 ) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__contraD,axiom, % 177.02/177.05 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( V_x_2 != V_y_2 % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 177.02/177.05 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__diff,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__diff,axiom, % 177.02/177.05 ! [V_f_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.05 ( class_Groups_Oab__group__add(T_d) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 177.02/177.05 ! [V_z_2,V_f_2,T_d,T_c] : c_Nitpick_Ofold__graph_H(T_c,T_d,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_z_2) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 177.02/177.05 ! [V_a2_2,V_a1_2,T_d,T_c] : c_Nitpick_Ofold__graph_H(T_c,T_d,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_a2_2) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__empty,axiom, % 177.02/177.05 ! [V_z_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_Finite__Set_Ofold(T_d,T_c,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2 ). % 177.02/177.05 % 177.02/177.05 fof(fact_f__the__inv__into__f,axiom, % 177.02/177.05 ! [V_y_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.05 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_set__mp,axiom, % 177.02/177.05 ! [V_x_2,V_B_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_set__rev__mp,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_x_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_in__mono,axiom, % 177.02/177.05 ! [V_x_2,V_B_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_bot__least,axiom, % 177.02/177.05 ! [V_x,T_a] : % 177.02/177.05 ( class_Orderings_Obot(T_a) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__empty,axiom, % 177.02/177.05 ! [V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.05 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_finite__subset,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_rev__finite__subset,axiom, % 177.02/177.05 ! [V_A_2,V_B_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_insert__mono,axiom, % 177.02/177.05 ! [V_a_2,V_D_2,V_C_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_D_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_D_2))) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__insertI2,axiom, % 177.02/177.05 ! [V_b_2,V_B_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__insertI,axiom, % 177.02/177.05 ! [V_a_2,V_B_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2))) ). % 177.02/177.05 % 177.02/177.05 fof(fact_image__mono,axiom, % 177.02/177.05 ! [V_f_2,T_d,V_B_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__image__iff,axiom, % 177.02/177.05 ! [V_A_2,V_f_2,T_d,V_B_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) % 177.02/177.05 <=> ? [B_AA] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),B_AA),V_A_2)) % 177.02/177.05 & V_B_2 = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),B_AA) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_double__diff,axiom, % 177.02/177.05 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.05 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_Diff__mono,axiom, % 177.02/177.05 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_D_2),V_B_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_Diff__subset,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 177.02/177.05 % 177.02/177.05 fof(fact_thin,axiom, % 177.02/177.05 ! [V_Ga_2,V_ts_2,V_G_H_2,T_c] : % 177.02/177.05 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_G_H_2,V_ts_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) % 177.02/177.05 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_weaken,axiom, % 177.02/177.05 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_c] : % 177.02/177.05 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_H_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 177.02/177.05 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_asm,axiom, % 177.02/177.05 ! [V_Ga_2,V_ts_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_ts_2),V_Ga_2)) % 177.02/177.05 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_empty__fold__graphE,axiom, % 177.02/177.05 ! [V_x_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2)) % 177.02/177.05 => V_x_2 = V_z_2 ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__graph_OemptyI,axiom, % 177.02/177.05 ! [V_z_2,V_f_2,T_d,T_c] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_z_2)) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__graph_Oequations_I1_J,axiom, % 177.02/177.05 ! [V_z_2,V_f_2,T_d,T_c] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_z_2)) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__graph__imp__finite,axiom, % 177.02/177.05 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_x_2)) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_pred__subset__eq,axiom, % 177.02/177.05 ! [V_S_2,V_R_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2))) % 177.02/177.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_finite__imageD,axiom, % 177.02/177.05 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) % 177.02/177.05 => ( c_Fun_Oinj__on(T_d,T_c,V_f_2,V_A_2) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__insert,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_x_2,T_c] : % 177.02/177.05 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) % 177.02/177.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_insert__subset,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_x_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2)) % 177.02/177.05 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) % 177.02/177.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_subset__singletonD,axiom, % 177.02/177.05 ! [V_x_2,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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))))) % 177.02/177.05 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.05 | 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))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_finite__surj,axiom, % 177.02/177.05 ! [V_f_2,V_B_2,T_d,V_A_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_image__diff__subset,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__graph_OinsertI,axiom, % 177.02/177.05 ! [V_y_2,V_z_2,V_f_2,T_d,V_A_2,V_x_2,T_c] : % 177.02/177.05 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__diff1__nat,axiom, % 177.02/177.05 ! [V_f_2,V_A_2,V_a_2,T_c] : % 177.02/177.05 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 177.02/177.05 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.05 => 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) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__fun__updI,axiom, % 177.02/177.05 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.05 => c_Fun_Oinj__on(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_override__on__apply__in,axiom, % 177.02/177.05 ! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.05 => hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_override__on__apply__notin,axiom, % 177.02/177.05 ! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] : % 177.02/177.05 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.05 => hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_override__on__emptyset,axiom, % 177.02/177.05 ! [V_g_2,V_f_2,T_d,T_c] : c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_f_2 ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 177.02/177.05 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 177.02/177.05 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 177.02/177.05 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,V_f_2),V_a_2),V_A_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_folding__one__idem_Osubset__idem,axiom, % 177.02/177.05 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.05 => 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) ) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_inj__on__iff__surj,axiom, % 177.02/177.05 ! [V_A_H_2,T_d,T_c,V_A_2] : % 177.02/177.05 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.05 => ( ? [B_f] : % 177.02/177.05 ( c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) % 177.02/177.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_A_H_2)) ) % 177.02/177.05 <=> ? [B_g] : hAPP(c_Set_Oimage(T_d,T_c,B_g),V_A_H_2) = V_A_2 ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__rec,axiom, % 177.02/177.05 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_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)))))) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold1Set_Ointros,axiom, % 177.02/177.05 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,V_a_2,V_A_2),V_x_2)) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_x_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_flat__lub__def,axiom, % 177.02/177.05 ! [V_b_2,V_A_2,T_c] : % 177.02/177.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) % 177.02/177.05 => c_Partial__Function_Oflat__lub(T_c,V_b_2,V_A_2) = V_b_2 ) % 177.02/177.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) % 177.02/177.05 => c_Partial__Function_Oflat__lub(T_c,V_b_2,V_A_2) = c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 177.02/177.05 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_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)))))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 177.02/177.05 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_d,T_c] : % 177.02/177.05 ( c_Nitpick_Ofold__graph_H(T_c,T_d,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 177.02/177.05 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.05 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 177.02/177.05 | ? [B_x,B_y] : % 177.02/177.05 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 177.02/177.05 & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_a2_2)) % 177.02/177.05 & c_Nitpick_Ofold__graph_H(T_c,T_d,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),B_y) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_diff__eq__diff__less__eq,axiom, % 177.02/177.05 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.05 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.05 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) % 177.02/177.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 177.02/177.05 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__insert,axiom, % 177.02/177.05 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_finite__subset__induct,axiom, % 177.02/177.05 ! [V_Pa_2,V_A_2,V_F_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.05 => ( ! [B_a,B_F] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_F)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2)) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_F)) % 177.02/177.05 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 177.02/177.05 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_F))) ) ) ) ) % 177.02/177.05 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum_Oremove,axiom, % 177.02/177.05 ! [V_g_2,V_x_2,V_A_2,T_c,T_d] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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)))))) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 177.02/177.05 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => 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)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__right__imp__eq,axiom, % 177.02/177.05 ! [V_c,V_a,V_b,T_a] : % 177.02/177.05 ( class_Groups_Ocancel__semigroup__add(T_a) % 177.02/177.05 => ( 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) % 177.02/177.05 => V_b = V_c ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__imp__eq,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 177.02/177.05 => ( 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) % 177.02/177.05 => V_b = V_c ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__left__imp__eq,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Ocancel__semigroup__add(T_a) % 177.02/177.05 => ( 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) % 177.02/177.05 => V_b = V_c ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__right__cancel,axiom, % 177.02/177.05 ! [V_c_2,V_a_2,V_b_2,T_c] : % 177.02/177.05 ( class_Groups_Ocancel__semigroup__add(T_c) % 177.02/177.05 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2) % 177.02/177.05 <=> V_b_2 = V_c_2 ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__left__cancel,axiom, % 177.02/177.05 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.05 ( class_Groups_Ocancel__semigroup__add(T_c) % 177.02/177.05 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2) % 177.02/177.05 <=> V_b_2 = V_c_2 ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Oab__semigroup__add(T_a) % 177.02/177.05 => 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)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__le__imp__le__left,axiom, % 177.02/177.05 ! [V_b,V_a,V_c,T_a] : % 177.02/177.05 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.02/177.05 => ( 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))) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__le__imp__le__right,axiom, % 177.02/177.05 ! [V_b,V_c,V_a,T_a] : % 177.02/177.05 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.02/177.05 => ( 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))) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__mono,axiom, % 177.02/177.05 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.02/177.05 => 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))) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__left__mono,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.05 => 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))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__right__mono,axiom, % 177.02/177.05 ! [V_c,V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.05 => 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))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__le__cancel__left,axiom, % 177.02/177.05 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.05 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2))) % 177.02/177.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__le__cancel__right,axiom, % 177.02/177.05 ! [V_b_2,V_c_2,V_a_2,T_c] : % 177.02/177.05 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2))) % 177.02/177.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_add__diff__cancel,axiom, % 177.02/177.05 ! [V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Ogroup__add(T_a) % 177.02/177.05 => 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 ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_diff__add__cancel,axiom, % 177.02/177.05 ! [V_b,V_a,T_a] : % 177.02/177.05 ( class_Groups_Ogroup__add(T_a) % 177.02/177.05 => 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 ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 177.02/177.05 ! [V_g_2,T_e,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => c_Finite__Set_Ofun__left__comm(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_d),T_e),V_f_2),V_g_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__addf,axiom, % 177.02/177.05 ! [V_A_2,V_g_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Oplus__class_Oplus(T_c)),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_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),V_A_2)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 177.02/177.05 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_x_2)) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.02/177.05 => V_y_2 = V_x_2 ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_empty__fold1SetE,axiom, % 177.02/177.05 ! [V_x_2,V_f_2,T_c] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2)) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold1Set__nonempty,axiom, % 177.02/177.05 ! [V_x_2,V_A_2,V_f_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2),V_x_2)) % 177.02/177.05 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum_Odistrib,axiom, % 177.02/177.05 ! [V_h_2,V_g_2,V_A_2,T_c,T_d] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Oplus__class_Oplus(T_d)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_A_2)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_diff__eq__diff__eq,axiom, % 177.02/177.05 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.05 ( class_Groups_Oab__group__add(T_c) % 177.02/177.05 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2) % 177.02/177.05 => ( V_a_2 = V_b_2 % 177.02/177.05 <=> V_c_2 = V_d_2 ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 177.02/177.05 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__equality,axiom, % 177.02/177.05 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.02/177.05 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold1Set__sing,axiom, % 177.02/177.05 ! [V_b_2,V_a_2,V_f_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(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)))),V_b_2)) % 177.02/177.05 <=> V_a_2 = V_b_2 ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum_Oinsert,axiom, % 177.02/177.05 ! [V_g_2,V_x_2,V_A_2,T_c,T_d] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__insert,axiom, % 177.02/177.05 ! [V_f_2,V_a_2,V_F_2,T_c,T_d] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_F_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_F_2)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum_Oinsert__remove,axiom, % 177.02/177.05 ! [V_x_2,V_g_2,V_A_2,T_c,T_d] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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)))))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 177.02/177.05 ! [V_z_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2))) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_setsum__diff1_H,axiom, % 177.02/177.05 ! [V_f_2,V_a_2,V_A_2,T_c,T_d] : % 177.02/177.05 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.05 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 177.02/177.05 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2)) % 177.02/177.05 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.05 => ? [B_y_H] : % 177.02/177.05 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 177.02/177.05 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fold1Set_Oequations,axiom, % 177.02/177.05 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2)),V_a3_2)) % 177.02/177.05 <=> ? [B_a,B_A] : % 177.02/177.05 ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_A) % 177.02/177.05 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,B_a,B_A),V_a3_2)) % 177.02/177.05 & ~ hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A)) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_insert__fold1SetE,axiom, % 177.02/177.05 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_c] : % 177.02/177.05 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_X_2)),V_x_2)) % 177.02/177.05 => ~ ! [B_a,B_A] : % 177.02/177.05 ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_A) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,B_a,B_A),V_x_2)) % 177.02/177.05 => hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A)) ) ) ) ). % 177.02/177.05 % 177.02/177.05 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 177.02/177.05 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.05 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.02/177.05 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_v_2)) % 177.02/177.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.05 => ~ ! [B_y] : % 177.02/177.05 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 177.02/177.05 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_fold__graph__permute__diff,axiom, % 177.02/177.06 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_c] : % 177.02/177.06 ( class_Groups_Oab__semigroup__mult(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_b_2,V_A_2),V_x_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_b_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_setsum__reindex__cong,axiom, % 177.02/177.06 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c,T_e] : % 177.02/177.06 ( class_Groups_Ocomm__monoid__add(T_e) % 177.02/177.06 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.06 => ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) % 177.02/177.06 => ( ! [B_a] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2)) % 177.02/177.06 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 177.02/177.06 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),V_g_2),V_A_2) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_psubset__insert__iff,axiom, % 177.02/177.06 ! [V_B_2,V_x_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) % 177.02/177.06 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 177.02/177.06 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) % 177.02/177.06 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2)) ) % 177.02/177.06 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__monoid__big_Oinfinite,axiom, % 177.02/177.06 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.06 ( c_Big__Operators_Ocomm__monoid__big(T_c,T_d,V_f_2,V_z_2,V_F_2) % 177.02/177.06 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.06 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Max__mono,axiom, % 177.02/177.06 ! [V_N_2,V_M_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_M_2),V_N_2)) % 177.02/177.06 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2))) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Min__antimono,axiom, % 177.02/177.06 ! [V_N_2,V_M_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_M_2),V_N_2)) % 177.02/177.06 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_M_2))) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_finite__nonempty__imp__fold1Set,axiom, % 177.02/177.06 ! [V_f_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2),B_x1)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oab__semigroup__mult(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_mult__left__idem,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_mult__idem,axiom, % 177.02/177.06 ! [V_x,T_a] : % 177.02/177.06 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.02/177.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_times_Oidem,axiom, % 177.02/177.06 ! [V_a,T_a] : % 177.02/177.06 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 177.02/177.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__cases,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => ( V_x != V_y % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__asym,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I10_J,axiom, % 177.02/177.06 ! [V_z,V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__trans,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I2_J,axiom, % 177.02/177.06 ! [V_c,V_a,V_b,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.02/177.06 => ( V_b = V_c % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_ord__less__eq__trans,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Oord(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.06 => ( V_b = V_c % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I1_J,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( V_a = V_b % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_ord__eq__less__trans,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Oord(T_a) % 177.02/177.06 => ( V_a = V_b % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I9_J,axiom, % 177.02/177.06 ! [V_a,V_b,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__asym_H,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__imp__not__eq2,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => V_y != V_x ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__imp__not__eq,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => V_x != V_y ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__imp__not__less,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__not__sym,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_less__imp__neq,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => V_x != V_y ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__neqE,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( V_x != V_y % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__antisym__conv3,axiom, % 177.02/177.06 ! [V_x_2,V_y_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2)) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> V_x_2 = V_y_2 ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__less__linear,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 | V_x = V_y % 177.02/177.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_not__less__iff__gr__or__eq,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2)) % 177.02/177.06 | V_x_2 = V_y_2 ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__neq__iff,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( V_x_2 != V_y_2 % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__irrefl,axiom, % 177.02/177.06 ! [V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_psubset__trans,axiom, % 177.02/177.06 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_less__fun__def,axiom, % 177.02/177.06 ! [V_g_2,V_f_2,T_c,T_d] : % 177.02/177.06 ( class_Orderings_Oord(T_d) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.02/177.06 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_g_2),V_f_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I8_J,axiom, % 177.02/177.06 ! [V_z,V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__le__less__trans,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I7_J,axiom, % 177.02/177.06 ! [V_z,V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__le__trans,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I11_J,axiom, % 177.02/177.06 ! [V_a,V_b,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.02/177.06 => ( V_a != V_b % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__le__neq__trans,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.06 => ( V_a != V_b % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__le__imp__less__or__eq,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 | V_x = V_y ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__antisym__conv2,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> V_x_2 = V_y_2 ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__imp__le,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Opreorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_leD,axiom, % 177.02/177.06 ! [V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_xt1_I12_J,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( V_a != V_b % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__neq__le__trans,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Oorder(T_a) % 177.02/177.06 => ( V_a != V_b % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__antisym__conv1,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> V_x_2 = V_y_2 ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_not__leE,axiom, % 177.02/177.06 ! [V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_leI,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__le__less,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Oorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 | V_x_2 = V_y_2 ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_less__le__not__le,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Opreorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_order__less__le,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Oorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 & V_x_2 != V_y_2 ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__le__less__linear,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__not__le,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__not__less,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_psubsetD,axiom, % 177.02/177.06 ! [V_c_2,V_B_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__less__cancel__right,axiom, % 177.02/177.06 ! [V_b_2,V_c_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__less__cancel__left,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__strict__right__mono,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__strict__left__mono,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__strict__mono,axiom, % 177.02/177.06 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.02/177.06 => 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))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__less__imp__less__right,axiom, % 177.02/177.06 ! [V_b,V_c,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.02/177.06 => ( 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))) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__less__imp__less__left,axiom, % 177.02/177.06 ! [V_b,V_a,V_c,T_a] : % 177.02/177.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.02/177.06 => ( 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))) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_not__psubset__empty,axiom, % 177.02/177.06 ! [V_A_2,T_c] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ). % 177.02/177.06 % 177.02/177.06 fof(fact_diff__eq__diff__less,axiom, % 177.02/177.06 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_subset__psubset__trans,axiom, % 177.02/177.06 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_psubset__subset__trans,axiom, % 177.02/177.06 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_psubset__imp__subset,axiom, % 177.02/177.06 ! [V_B_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_subset__iff__psubset__eq,axiom, % 177.02/177.06 ! [V_B_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 | V_A_2 = V_B_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_psubset__eq,axiom, % 177.02/177.06 ! [V_B_2,V_A_2,T_c] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 & V_A_2 != V_B_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_fun__left__comm,axiom, % 177.02/177.06 ! [T_c] : % 177.02/177.06 ( class_Groups_Oab__semigroup__mult(T_c) % 177.02/177.06 => c_Finite__Set_Ofun__left__comm(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_fun__left__comm__idem,axiom, % 177.02/177.06 ! [T_c] : % 177.02/177.06 ( class_Lattices_Oab__semigroup__idem__mult(T_c) % 177.02/177.06 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_setsum__right__distrib,axiom, % 177.02/177.06 ! [V_A_2,V_f_2,T_d,V_r_2,T_c] : % 177.02/177.06 ( class_Rings_Osemiring__0(T_c) % 177.02/177.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_r_2)),V_f_2)),V_A_2) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_setsum__left__distrib,axiom, % 177.02/177.06 ! [V_r_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.06 ( class_Rings_Osemiring__0(T_c) % 177.02/177.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_r_2)),V_A_2) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_setsum__product,axiom, % 177.02/177.06 ! [V_B_2,V_g_2,T_e,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.06 ( class_Rings_Osemiring__0(T_c) % 177.02/177.06 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,T_c)),T_d),c_COMBB(T_c,T_c,T_e)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__le__less__mono,axiom, % 177.02/177.06 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.02/177.06 => 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))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__less__le__mono,axiom, % 177.02/177.06 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.02/177.06 => 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))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_inj__on__strict__subset,axiom, % 177.02/177.06 ! [V_A_2,V_B_2,V_f_2,T_d,T_c] : % 177.02/177.06 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Min_Osingleton,axiom, % 177.02/177.06 ! [V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Max_Osingleton,axiom, % 177.02/177.06 ! [V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_fold__graph__insert__swap,axiom, % 177.02/177.06 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_c] : % 177.02/177.06 ( class_Groups_Oab__semigroup__mult(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_b_2,V_A_2),V_y_2)) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_z_2),V_y_2))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Min__le,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_x_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Max__ge,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Min__in,axiom, % 177.02/177.06 ! [V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_A_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Max__in,axiom, % 177.02/177.06 ! [V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),V_A_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_less__add__iff2,axiom, % 177.02/177.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] : % 177.02/177.06 ( class_Rings_Oordered__ring(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_less__add__iff1,axiom, % 177.02/177.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] : % 177.02/177.06 ( class_Rings_Oordered__ring(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_le__add__iff2,axiom, % 177.02/177.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] : % 177.02/177.06 ( class_Rings_Oordered__ring(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_le__add__iff1,axiom, % 177.02/177.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] : % 177.02/177.06 ( class_Rings_Oordered__ring(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_eq__add__iff2,axiom, % 177.02/177.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] : % 177.02/177.06 ( class_Rings_Oring(T_c) % 177.02/177.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2) % 177.02/177.06 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_eq__add__iff1,axiom, % 177.02/177.06 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] : % 177.02/177.06 ( class_Rings_Oring(T_c) % 177.02/177.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2) % 177.02/177.06 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_crossproduct__noteq,axiom, % 177.02/177.06 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c) % 177.02/177.06 => ( ( V_a_2 != V_b_2 % 177.02/177.06 & V_c_2 != V_d_2 ) % 177.02/177.06 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__class_Odistrib,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_linorder__neqE__linordered__idom,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.06 => ( V_x != V_y % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 177.02/177.06 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 177.02/177.06 ! [V_d,V_c,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 177.02/177.06 ! [V_d,V_c,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 177.02/177.06 ! [V_c,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 177.02/177.06 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 177.02/177.06 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 177.02/177.06 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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))) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 177.02/177.06 ! [V_rx,V_ly,V_lx,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 177.02/177.06 ! [V_rx,V_ly,V_lx,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 177.02/177.06 ! [V_ry,V_rx,V_lx,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 177.02/177.06 ! [V_ry,V_rx,V_lx,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_crossproduct__eq,axiom, % 177.02/177.06 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_c] : % 177.02/177.06 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c) % 177.02/177.06 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> ( V_w_2 = V_x_2 % 177.02/177.06 | V_y_2 = V_z_2 ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_combine__common__factor,axiom, % 177.02/177.06 ! [V_c,V_b,V_e,V_a,T_a] : % 177.02/177.06 ( class_Rings_Osemiring(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 177.02/177.06 ! [V_b,V_m,V_a,T_a] : % 177.02/177.06 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_setsum__strict__mono,axiom, % 177.02/177.06 ! [V_g_2,V_f_2,V_A_2,T_c,T_d] : % 177.02/177.06 ( ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.06 & class_Groups_Oordered__cancel__ab__semigroup__add(T_d) ) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => ( ! [B_x] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_A_2))) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Min_Oremove,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = V_x_2 ) % 177.02/177.06 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,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)))))) ) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Max_Oremove,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = V_x_2 ) % 177.02/177.06 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,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)))))) ) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_fold1__eq__fold,axiom, % 177.02/177.06 ! [V_a_2,V_A_2,T_c] : % 177.02/177.06 ( class_Groups_Oab__semigroup__mult(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.06 => hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)),V_a_2),V_A_2) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_fold1__insert,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_c] : % 177.02/177.06 ( class_Groups_Oab__semigroup__mult(T_c) % 177.02/177.06 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)) ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_setprod_Oremove,axiom, % 177.02/177.06 ! [V_g_2,V_x_2,V_A_2,T_c,T_d] : % 177.02/177.06 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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)))))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Min__eqI,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( ! [B_y] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_y)) ) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = V_x_2 ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Max__eqI,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.06 => ( ! [B_y] : % 177.02/177.06 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_y),V_x_2)) ) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.06 => c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = V_x_2 ) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__Max__eq__Min,axiom, % 177.02/177.06 ! [V_S_2,T_c] : % 177.02/177.06 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.06 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),V_S_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__Min__eq__Max,axiom, % 177.02/177.06 ! [V_S_2,T_c] : % 177.02/177.06 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.06 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.06 => hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),V_S_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_ComplI,axiom, % 177.02/177.06 ! [V_A_2,V_c_2,T_c] : % 177.02/177.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.06 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_inj__uminus,axiom, % 177.02/177.06 ! [V_A_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => c_Fun_Oinj__on(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c),V_A_2) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_neg__equal__iff__equal,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Ogroup__add(T_c) % 177.02/177.06 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) % 177.02/177.06 <=> V_a_2 = V_b_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__equation__iff,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Ogroup__add(T_c) % 177.02/177.06 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = V_b_2 % 177.02/177.06 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) = V_a_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_equation__minus__iff,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Ogroup__add(T_c) % 177.02/177.06 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) % 177.02/177.06 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__min__eq__max,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__max__eq__min,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Groups_Olinordered__ab__group__add(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__minus,axiom, % 177.02/177.06 ! [V_a,T_a] : % 177.02/177.06 ( class_Groups_Ogroup__add(T_a) % 177.02/177.06 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Odistrib__sup__le,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)))) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Odistrib__inf__le,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)))) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 177.02/177.06 ! [V_x,V_z,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__inf__distrib2,axiom, % 177.02/177.06 ! [V_x,V_z,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__assoc,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf_Oassoc,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__assoc,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup_Oassoc,axiom, % 177.02/177.06 ! [V_c,V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_compl__eq__compl__iff,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Lattices_Oboolean__algebra(T_c) % 177.02/177.06 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2) % 177.02/177.06 <=> V_x_2 = V_y_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__inf__distrib1,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__left__commute,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 177.02/177.06 ! [V_c,V_a,V_b,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__left__commute,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup_Oleft__commute,axiom, % 177.02/177.06 ! [V_c,V_a,V_b,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__left__idem,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__left__idem,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup_Oleft__idem,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__sup__absorb,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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 ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__inf__absorb,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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 ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__commute,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf_Ocommute,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__commute,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup_Ocommute,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_uminus__apply,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_d,T_c] : % 177.02/177.06 ( class_Groups_Ouminus(T_c) % 177.02/177.06 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,T_c)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(V_A_2,V_x_2)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf_Oidem,axiom, % 177.02/177.06 ! [V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup_Oidem,axiom, % 177.02/177.06 ! [V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_double__compl,axiom, % 177.02/177.06 ! [V_x,T_a] : % 177.02/177.06 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.06 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_fun__Compl__def,axiom, % 177.02/177.06 ! [V_x_2,V_A_2,T_d,T_c] : % 177.02/177.06 ( class_Groups_Ouminus(T_c) % 177.02/177.06 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,T_c)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(V_A_2,V_x_2)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Min_Oidem,axiom, % 177.02/177.06 ! [V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_Max_Oidem,axiom, % 177.02/177.06 ! [V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__supE,axiom, % 177.02/177.06 ! [V_x,V_b,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( 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)) % 177.02/177.06 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__mono,axiom, % 177.02/177.06 ! [V_d,V_b,V_c,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.02/177.06 => 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))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__least,axiom, % 177.02/177.06 ! [V_z,V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 177.02/177.06 => 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)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__supI,axiom, % 177.02/177.06 ! [V_b,V_x,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.02/177.06 => 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)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__absorb1,axiom, % 177.02/177.06 ! [V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Osup__absorb2,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__supI2,axiom, % 177.02/177.06 ! [V_a,V_b,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__supI1,axiom, % 177.02/177.06 ! [V_b,V_a,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__sup__iff,axiom, % 177.02/177.06 ! [V_z_2,V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) % 177.02/177.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__iff__sup,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2) = V_y_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_le__maxI2,axiom, % 177.02/177.06 ! [V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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))) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_le__maxI1,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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))) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_le__max__iff__disj,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,V_z_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2))) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_x_2)) % 177.02/177.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_y_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_compl__mono,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_compl__le__compl__iff,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Lattices_Oboolean__algebra(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_le__minus__iff,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__le__iff,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2)) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),V_a_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_neg__le__iff__le,axiom, % 177.02/177.06 ! [V_a_2,V_b_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_le__imp__neg__le,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__infE,axiom, % 177.02/177.06 ! [V_b,V_a,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( 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))) % 177.02/177.06 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.02/177.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__mono,axiom, % 177.02/177.06 ! [V_d,V_b,V_c,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.02/177.06 => 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))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__greatest,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 177.02/177.06 => 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))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__infI,axiom, % 177.02/177.06 ! [V_b,V_a,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.02/177.06 => 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))) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__absorb2,axiom, % 177.02/177.06 ! [V_x,V_y,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__absorb1,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.06 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__infI2,axiom, % 177.02/177.06 ! [V_a,V_x,V_b,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.02/177.06 => 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)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__infI1,axiom, % 177.02/177.06 ! [V_b,V_x,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.02/177.06 => 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)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__inf__iff,axiom, % 177.02/177.06 ! [V_z_2,V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_y_2),V_z_2))) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Ole__iff__inf,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.06 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2) = V_x_2 ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__le2,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oinf__le1,axiom, % 177.02/177.06 ! [V_y,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__le__iff__disj,axiom, % 177.02/177.06 ! [V_z_2,V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) % 177.02/177.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oless__supI2,axiom, % 177.02/177.06 ! [V_a,V_b,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oless__supI1,axiom, % 177.02/177.06 ! [V_b,V_a,V_x,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 177.02/177.06 => 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))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_max__less__iff__conj,axiom, % 177.02/177.06 ! [V_z_2,V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_z_2)) % 177.02/177.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_less__max__iff__disj,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,V_z_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2))) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2)) % 177.02/177.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_neg__less__iff__less,axiom, % 177.02/177.06 ! [V_a_2,V_b_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__less__iff,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2)) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),V_a_2)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_less__minus__iff,axiom, % 177.02/177.06 ! [V_b_2,V_a_2,T_c] : % 177.02/177.06 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2))) % 177.02/177.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oless__infI2,axiom, % 177.02/177.06 ! [V_a,V_x,V_b,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 177.02/177.06 => 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)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__max_Oless__infI1,axiom, % 177.02/177.06 ! [V_b,V_x,V_a,T_a] : % 177.02/177.06 ( class_Orderings_Olinorder(T_a) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 177.02/177.06 => 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)) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__less__iff__disj,axiom, % 177.02/177.06 ! [V_z_2,V_y_2,V_x_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2)) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_z_2)) % 177.02/177.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_min__less__iff__conj,axiom, % 177.02/177.06 ! [V_y_2,V_x_2,V_z_2,T_c] : % 177.02/177.06 ( class_Orderings_Olinorder(T_c) % 177.02/177.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2))) % 177.02/177.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2)) % 177.02/177.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2)) ) ) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_max__add__distrib__left,axiom, % 177.02/177.06 ! [V_z,V_y,V_x,T_a] : % 177.02/177.06 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__add__distrib,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Oab__group__add(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__add,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Ogroup__add(T_a) % 177.02/177.06 => 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)) ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_add__minus__cancel,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Ogroup__add(T_a) % 177.02/177.06 => 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 ) ). % 177.02/177.06 % 177.02/177.06 fof(fact_minus__add__cancel,axiom, % 177.02/177.06 ! [V_b,V_a,T_a] : % 177.02/177.06 ( class_Groups_Ogroup__add(T_a) % 177.02/177.07 => 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 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_minus__mult__right,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Rings_Oring(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_minus__mult__left,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Rings_Oring(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_minus__mult__commute,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Rings_Oring(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_minus__mult__minus,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Rings_Oring(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_square__eq__iff,axiom, % 177.02/177.07 ! [V_b_2,V_a_2,T_c] : % 177.02/177.07 ( class_Rings_Oidom(T_c) % 177.02/177.07 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_b_2) % 177.02/177.07 <=> ( V_a_2 = V_b_2 % 177.02/177.07 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__add__distrib__left,axiom, % 177.02/177.07 ! [V_z,V_y,V_x,T_a] : % 177.02/177.07 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_ComplE,axiom, % 177.02/177.07 ! [V_A_2,V_c_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) % 177.02/177.07 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_ComplD,axiom, % 177.02/177.07 ! [V_A_2,V_c_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) % 177.02/177.07 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Compl__iff,axiom, % 177.02/177.07 ! [V_A_2,V_c_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) % 177.02/177.07 <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_OF__eq,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omax(T_c)),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_OF__eq,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_max__diff__distrib__left,axiom, % 177.02/177.07 ! [V_z,V_y,V_x,T_a] : % 177.02/177.07 ( class_Groups_Oordered__ab__group__add(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_minus__diff__eq,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Groups_Oab__group__add(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__diff__distrib__left,axiom, % 177.02/177.07 ! [V_z,V_y,V_x,T_a] : % 177.02/177.07 ( class_Groups_Oordered__ab__group__add(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Compl__anti__mono,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Compl__subset__Compl__iff,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2))) % 177.02/177.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_setprod__timesf,axiom, % 177.02/177.07 ! [V_A_2,V_g_2,V_f_2,T_d,T_c] : % 177.02/177.07 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.02/177.07 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_g_2),V_A_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Ofold1__belowI,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_a_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__below__iff,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2)) % 177.02/177.07 <=> ? [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_x_2)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Obelow__fold1__iff,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2))) % 177.02/177.07 <=> ! [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_x)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_setsum__negf,axiom, % 177.02/177.07 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.07 ( class_Groups_Oab__group__add(T_c) % 177.02/177.07 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Ouminus__class_Ouminus(T_c)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__strict__below__iff,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2)) % 177.02/177.07 <=> ? [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_x_2)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_strict__below__fold1__iff,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2))) % 177.02/177.07 <=> ! [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),B_x)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__antimono,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2))) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_diff__def,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Groups_Ogroup__add(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_ab__diff__minus,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Groups_Oab__group__add(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_diff__minus__eq__add,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Groups_Ogroup__add(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Rings_Ocomm__ring__1(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_subset__Compl__self__eq,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( 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)),V_A_2))) % 177.02/177.07 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_setprod_Odistrib,axiom, % 177.02/177.07 ! [V_h_2,V_g_2,V_A_2,T_c,T_d] : % 177.02/177.07 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Otimes__class_Otimes(T_d)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_A_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__singleton__def,axiom, % 177.02/177.07 ! [V_a_2,V_f_2,T_c,V_g_2] : % 177.02/177.07 ( V_g_2 = c_Finite__Set_Ofold1(T_c,V_f_2) % 177.02/177.07 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__singleton,axiom, % 177.02/177.07 ! [V_a_2,V_f_2,T_c] : hAPP(c_Finite__Set_Ofold1(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)))) = V_a_2 ). % 177.02/177.07 % 177.02/177.07 fof(fact_folding__one_Oeq__fold,axiom, % 177.02/177.07 ! [V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.07 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Ofold__sup__insert,axiom, % 177.02/177.07 ! [V_a_2,V_b_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),V_A_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Oin__idem,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Ofold__inf__insert,axiom, % 177.02/177.07 ! [V_a_2,V_b_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),V_A_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Oin__idem,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__def,axiom, % 177.02/177.07 ! [V_A_2,V_f_2,T_c] : hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2) = c_HOL_OThe(T_c,c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_setprod_Oinsert,axiom, % 177.02/177.07 ! [V_g_2,V_x_2,V_A_2,T_c,T_d] : % 177.02/177.07 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_setprod__insert,axiom, % 177.02/177.07 ! [V_f_2,V_a_2,V_A_2,T_c,T_d] : % 177.02/177.07 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Osup__le__fold__sup,axiom, % 177.02/177.07 ! [V_b_2,V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),V_A_2))) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 177.02/177.07 ! [V_b_2,V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),V_b_2))) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max__insert,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min__insert,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Osubset__idem,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Osubset__idem,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Oeq__fold__idem_H,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_a_2),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Oeq__fold__idem_H,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_a_2),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_setprod_Oinsert__remove,axiom, % 177.02/177.07 ! [V_x_2,V_g_2,V_A_2,T_c,T_d] : % 177.02/177.07 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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)))))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__insert__idem,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Lattices_Oab__semigroup__idem__mult(T_c) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__eq__fold__idem,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Lattices_Oab__semigroup__idem__mult(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)),V_a_2),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Oinsert,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Oinsert,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Oinsert__remove,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) % 177.02/177.07 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,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)))))) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Oinsert__remove,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) % 177.02/177.07 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,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)))))) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Oeq__fold_H,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_x_2),V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Oeq__fold_H,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_x_2),V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_semilattice__big_OF__eq,axiom, % 177.02/177.07 ! [V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.07 ( c_Big__Operators_Osemilattice__big(T_c,V_f_2,V_F_2) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_dual__min,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => c_Orderings_Oord_Omin(T_c,hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c))) = c_Orderings_Oord__class_Omax(T_c) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_dual__max,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => c_Orderings_Oord_Omax(T_c,hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c))) = c_Orderings_Oord__class_Omin(T_c) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_max__ord__max,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Orderings_Oord(T_c) % 177.02/177.07 => c_Orderings_Oord__class_Omax(T_c) = c_Orderings_Oord_Omax(T_c,c_Orderings_Oord__class_Oless__eq(T_c)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__ord__min,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Orderings_Oord(T_c) % 177.02/177.07 => c_Orderings_Oord__class_Omin(T_c) = c_Orderings_Oord_Omin(T_c,c_Orderings_Oord__class_Oless__eq(T_c)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Oclosed,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Oclosed,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold1__in,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Groups_Oab__semigroup__mult(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oremove,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = V_x_2 ) % 177.02/177.07 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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)))))) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oremove,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = V_x_2 ) % 177.02/177.07 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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)))))) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Compl__eq__Compl__iff,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( 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_c,tc_HOL_Obool)),V_B_2) % 177.02/177.07 <=> V_A_2 = V_B_2 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_double__complement,axiom, % 177.02/177.07 ! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__le__Sup,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2))) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 177.02/177.07 ! [V_x_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 177.02/177.07 ! [V_x_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omax(T_c)),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = V_a_2 ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Osup__Inf__absorb,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = V_a_2 ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_a_2),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 177.02/177.07 ! [V_a_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_a_2),V_A_2) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) % 177.02/177.07 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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)))))) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) % 177.02/177.07 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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)))))) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_x_2),V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_x_2),V_A_2) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),V_A_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 177.02/177.07 ! [V_N_2,V_h_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.07 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 177.02/177.07 ! [V_N_2,V_h_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.07 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max_Ohom__commute,axiom, % 177.02/177.07 ! [V_N_2,V_h_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.07 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min_Ohom__commute,axiom, % 177.02/177.07 ! [V_N_2,V_h_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.07 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_hom__fold1__commute,axiom, % 177.02/177.07 ! [V_N_2,V_h_2,T_c] : % 177.02/177.07 ( class_Lattices_Oab__semigroup__idem__mult(T_c) % 177.02/177.07 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.07 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 177.02/177.07 ! [V_c_2,V_b_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ! [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_2)) ) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_b_2),V_c_2))) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 177.02/177.07 ! [V_c_2,V_b_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ! [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),B_x)) ) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_c_2),V_A_2))) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_card__Diff2__less,axiom, % 177.02/177.07 ! [V_y_2,V_x_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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))))),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_card__Diff1__less,axiom, % 177.02/177.07 ! [V_x_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),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)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inj__image__Compl__subset,axiom, % 177.02/177.07 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.07 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold__image__insert,axiom, % 177.02/177.07 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_c,T_d] : % 177.02/177.07 ( class_Groups_Oab__semigroup__mult(T_d) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.07 => 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(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_a_2)),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),V_A_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_setsum__mono,axiom, % 177.02/177.07 ! [V_g_2,V_f_2,V_K_2,T_c,T_d] : % 177.02/177.07 ( ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.07 & class_Groups_Oordered__ab__semigroup__add(T_d) ) % 177.02/177.07 => ( ! [B_i] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_K_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_i)),hAPP(V_g_2,B_i))) ) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_K_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_K_2))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Max__Un,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Min__Un,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( class_Orderings_Olinorder(T_c) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)) ) ) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_top1I,axiom, % 177.02/177.07 ! [V_x_2,T_c] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_x_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup1E,axiom, % 177.02/177.07 ! [V_x_2,V_B_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 177.02/177.07 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 177.02/177.07 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup1CI,axiom, % 177.02/177.07 ! [T_c,V_A_2,V_x_2,V_B_2] : % 177.02/177.07 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 177.02/177.07 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 177.02/177.07 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_UNIV__I,axiom, % 177.02/177.07 ! [V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 177.02/177.07 % 177.02/177.07 fof(fact_UnE,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_UnCI,axiom, % 177.02/177.07 ! [V_A_2,V_B_2,V_c_2,T_c] : % 177.02/177.07 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_finite__option__UNIV,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool)))) % 177.02/177.07 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_finite__Plus__UNIV__iff,axiom, % 177.02/177.07 ! [T_d,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool)))) % 177.02/177.07 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.07 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_finite__Prod__UNIV,axiom, % 177.02/177.07 ! [T_d,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) % 177.02/177.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Sup__fin_Oidem,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Olattice(T_a) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__UNIV__left,axiom, % 177.02/177.07 ! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__UNIV__right,axiom, % 177.02/177.07 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__absorb,axiom, % 177.02/177.07 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__commute,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : 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_c,tc_HOL_Obool)),V_B_2),V_A_2) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__left__absorb,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_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_c,tc_HOL_Obool)),V_A_2),V_B_2) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__left__commute,axiom, % 177.02/177.07 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__assoc,axiom, % 177.02/177.07 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_bex__Un,axiom, % 177.02/177.07 ! [V_Pa_2,V_B_2,V_A_2,T_c] : % 177.02/177.07 ( ? [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.02/177.07 <=> ( ? [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.02/177.07 | ? [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_B_2)) % 177.02/177.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_ball__Un,axiom, % 177.02/177.07 ! [V_Pa_2,V_B_2,V_A_2,T_c] : % 177.02/177.07 ( ! [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.02/177.07 <=> ( ! [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.02/177.07 & ! [B_x] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_B_2)) % 177.02/177.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_top__apply,axiom, % 177.02/177.07 ! [V_x_2,T_d,T_c] : % 177.02/177.07 ( class_Orderings_Otop(T_c) % 177.02/177.07 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Otop__class_Otop(T_c) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup1I1,axiom, % 177.02/177.07 ! [V_B_2,T_c,V_x_2,V_A_2] : % 177.02/177.07 ( hBOOL(hAPP(V_A_2,V_x_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup1I2,axiom, % 177.02/177.07 ! [V_A_2,T_c,V_x_2,V_B_2] : % 177.02/177.07 ( hBOOL(hAPP(V_B_2,V_x_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__top__left,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Obounded__lattice__top(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__top__right,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Obounded__lattice__top(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup_Oidem,axiom, % 177.02/177.07 ! [V_a,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__idem,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__fun__def,axiom, % 177.02/177.07 ! [V_x_2,V_g_2,V_f_2,T_d,T_c] : % 177.02/177.07 ( class_Lattices_Olattice(T_c) % 177.02/177.07 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup_Ocommute,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inf__sup__aci_I5_J,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Olattice(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__commute,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup_Oleft__idem,axiom, % 177.02/177.07 ! [V_b,V_a,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inf__sup__aci_I8_J,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Olattice(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__left__idem,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup_Oleft__commute,axiom, % 177.02/177.07 ! [V_c,V_a,V_b,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inf__sup__aci_I7_J,axiom, % 177.02/177.07 ! [V_z,V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Olattice(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__left__commute,axiom, % 177.02/177.07 ! [V_z,V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup_Oassoc,axiom, % 177.02/177.07 ! [V_c,V_b,V_a,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inf__sup__aci_I6_J,axiom, % 177.02/177.07 ! [V_z,V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Olattice(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__assoc,axiom, % 177.02/177.07 ! [V_z,V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__apply,axiom, % 177.02/177.07 ! [V_x_2,V_g_2,V_f_2,T_d,T_c] : % 177.02/177.07 ( class_Lattices_Olattice(T_c) % 177.02/177.07 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_finite__fun__UNIVD2,axiom, % 177.02/177.07 ! [T_d,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool)))) % 177.02/177.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 177.02/177.07 ! [V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.07 => ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.07 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Compl__partition,axiom, % 177.02/177.07 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Compl__partition2,axiom, % 177.02/177.07 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__compl__top,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_compl__sup__top,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.07 => 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) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inf__sup__ord_I3_J,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Olattice(T_a) % 177.02/177.07 => 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))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__ge1,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inf__sup__ord_I4_J,axiom, % 177.02/177.07 ! [V_x,V_y,T_a] : % 177.02/177.07 ( class_Lattices_Olattice(T_a) % 177.02/177.07 => 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))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__ge2,axiom, % 177.02/177.07 ! [V_x,V_y,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => 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))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_le__iff__sup,axiom, % 177.02/177.07 ! [V_y_2,V_x_2,T_c] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_c) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.07 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) = V_y_2 ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_le__sup__iff,axiom, % 177.02/177.07 ! [V_z_2,V_y_2,V_x_2,T_c] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_c) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2)),V_z_2)) % 177.02/177.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) % 177.02/177.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_le__supI1,axiom, % 177.02/177.07 ! [V_b,V_a,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.02/177.07 => 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))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_le__supI2,axiom, % 177.02/177.07 ! [V_a,V_b,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.02/177.07 => 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))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__absorb2,axiom, % 177.02/177.07 ! [V_y,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__absorb1,axiom, % 177.02/177.07 ! [V_x,V_y,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_le__supI,axiom, % 177.02/177.07 ! [V_b,V_x,V_a,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.02/177.07 => 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)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__least,axiom, % 177.02/177.07 ! [V_z,V_x,V_y,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 177.02/177.07 => 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)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__mono,axiom, % 177.02/177.07 ! [V_d,V_b,V_c,V_a,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.02/177.07 => 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))) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_le__supE,axiom, % 177.02/177.07 ! [V_x,V_b,V_a,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( 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)) % 177.02/177.07 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.02/177.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_less__supI1,axiom, % 177.02/177.07 ! [V_b,V_a,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 177.02/177.07 => 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))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_less__supI2,axiom, % 177.02/177.07 ! [V_a,V_b,V_x,T_a] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_a) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 177.02/177.07 => 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))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__bot__left,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__bot__right,axiom, % 177.02/177.07 ! [V_x,T_a] : % 177.02/177.07 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__eq__bot__iff,axiom, % 177.02/177.07 ! [V_y_2,V_x_2,T_c] : % 177.02/177.07 ( class_Lattices_Obounded__lattice__bot(T_c) % 177.02/177.07 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_c) % 177.02/177.07 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_c) % 177.02/177.07 & V_y_2 = c_Orderings_Obot__class_Obot(T_c) ) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__iff,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.07 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.07 | hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_UnI1,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_UnI2,axiom, % 177.02/177.07 ! [V_A_2,V_B_2,V_c_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__max,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( ( class_Lattices_Osemilattice__sup(T_c) % 177.02/177.07 & class_Orderings_Olinorder(T_c) ) % 177.02/177.07 => c_Lattices_Osemilattice__sup__class_Osup(T_c) = c_Orderings_Oord__class_Omax(T_c) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__empty__left,axiom, % 177.02/177.07 ! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__empty__right,axiom, % 177.02/177.07 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_A_2 ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__empty,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( hAPP(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)) % 177.02/177.07 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.07 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_finite__Un,axiom, % 177.02/177.07 ! [V_Ga_2,V_F_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2))) % 177.02/177.07 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.07 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_finite__UnI,axiom, % 177.02/177.07 ! [V_Ga_2,V_F_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2)) % 177.02/177.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__insert__right,axiom, % 177.02/177.07 ! [V_B_2,V_a_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__insert__left,axiom, % 177.02/177.07 ! [V_C_2,V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__upper1,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__upper2,axiom, % 177.02/177.07 ! [V_A_2,V_B_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 177.02/177.07 % 177.02/177.07 fof(fact_subset__Un__eq,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.07 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__absorb1,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__absorb2,axiom, % 177.02/177.07 ! [V_A_2,V_B_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__least,axiom, % 177.02/177.07 ! [V_B_2,V_C_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_C_2)) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__mono,axiom, % 177.02/177.07 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.02/177.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) % 177.02/177.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_image__Un,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__Diff__cancel,axiom, % 177.02/177.07 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__Diff__cancel2,axiom, % 177.02/177.07 ! [V_A_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2) ). % 177.02/177.07 % 177.02/177.07 fof(fact_Un__Diff,axiom, % 177.02/177.07 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_UNIV__not__empty,axiom, % 177.02/177.07 ! [T_c] : c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.07 % 177.02/177.07 fof(fact_finite__UNIV,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Finite__Set_Ofinite(T_c) % 177.02/177.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_subset__UNIV,axiom, % 177.02/177.07 ! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inj__eq,axiom, % 177.02/177.07 ! [V_y_2,V_x_2,V_f_2,T_d,T_c] : % 177.02/177.07 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.07 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.02/177.07 <=> V_x_2 = V_y_2 ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_injD,axiom, % 177.02/177.07 ! [V_y_2,V_x_2,V_f_2,T_d,T_c] : % 177.02/177.07 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.07 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.02/177.07 => V_x_2 = V_y_2 ) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_fold__image__empty,axiom, % 177.02/177.07 ! [V_z_2,V_g_2,V_f_2,T_d,T_c] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2 ). % 177.02/177.07 % 177.02/177.07 fof(fact_fun__left__comm__idem__sup,axiom, % 177.02/177.07 ! [T_c] : % 177.02/177.07 ( class_Lattices_Osemilattice__sup(T_c) % 177.02/177.07 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_sup__Un__eq,axiom, % 177.02/177.07 ! [V_x_2,V_S_2,V_R_2,T_c] : % 177.02/177.07 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2)) % 177.02/177.07 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_range__composition,axiom, % 177.02/177.07 ! [V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(hAPP(c_COMBB(T_e,T_c,T_d),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_e,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_e,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) ). % 177.02/177.07 % 177.02/177.07 fof(fact_inj__fun,axiom, % 177.02/177.07 ! [T_e,V_f_2,T_d,T_c] : % 177.02/177.07 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.07 => c_Fun_Oinj__on(T_c,tc_fun(T_e,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,T_d),T_c),c_COMBK(T_d,T_e)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.02/177.07 % 177.02/177.07 fof(fact_top__greatest,axiom, % 177.02/177.08 ! [V_x,T_a] : % 177.02/177.08 ( class_Orderings_Otop(T_a) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_fold__image__def,axiom, % 177.02/177.08 ! [V_g_2,V_f_2,T_d,T_c] : hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_d,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__insert__le,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__mono,axiom, % 177.02/177.08 ! [V_A_2,V_B_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__seteq,axiom, % 177.02/177.08 ! [V_A_2,V_B_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) % 177.02/177.08 => V_A_2 = V_B_2 ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__image__le,axiom, % 177.02/177.08 ! [V_f_2,T_d,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_pigeonhole,axiom, % 177.02/177.08 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_d),V_A_2))) % 177.02/177.08 => ~ c_Fun_Oinj__on(T_d,T_c,V_f_2,V_A_2) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__image,axiom, % 177.02/177.08 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_insert__is__Un,axiom, % 177.02/177.08 ! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_A_2) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Diff__subset__conv,axiom, % 177.02/177.08 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Diff__partition,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.08 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_psubset__card__mono,axiom, % 177.02/177.08 ! [V_A_2,V_B_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__on__Un__image__eq__iff,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.08 => ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2) % 177.02/177.08 <=> V_A_2 = V_B_2 ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_rangeI,axiom, % 177.02/177.08 ! [T_d,V_x_2,V_f_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_range__eqI,axiom, % 177.02/177.08 ! [T_d,T_c,V_x_2,V_f_2,V_b_2] : % 177.02/177.08 ( V_b_2 = hAPP(V_f_2,V_x_2) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_image__eq__fold__image,axiom, % 177.02/177.08 ! [V_f_2,T_d,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_d,tc_HOL_Obool),T_c,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_d,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_d)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))),V_A_2) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Diff__UNIV,axiom, % 177.02/177.08 ! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Compl__Diff__eq,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__image__eq__iff,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2) % 177.02/177.08 <=> V_A_2 = V_B_2 ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Compl__empty__eq,axiom, % 177.02/177.08 ! [T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Compl__UNIV__eq,axiom, % 177.02/177.08 ! [T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_finite__compl,axiom, % 177.02/177.08 ! [V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) % 177.02/177.08 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Compl__eq__Diff__UNIV,axiom, % 177.02/177.08 ! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_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_A_2) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__singleton,axiom, % 177.02/177.08 ! [T_c] : c_Fun_Oinj__on(T_c,tc_fun(T_c,tc_HOL_Obool),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))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_finite__range__imageI,axiom, % 177.02/177.08 ! [V_f_2,T_e,V_g_2,T_d,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) % 177.02/177.08 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_e),hAPP(c_Set_Oimage(T_d,T_e,hAPP(hAPP(c_COMBB(T_c,T_e,T_d),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_the__inv__f__f,axiom, % 177.02/177.08 ! [V_x_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => hAPP(c_Fun_Othe__inv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.08 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 177.02/177.08 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.08 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__on__iff__eq__card,axiom, % 177.02/177.08 ! [V_f_2,T_d,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.08 <=> hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_eq__card__imp__inj__on,axiom, % 177.02/177.08 ! [V_f_2,T_d,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) % 177.02/177.08 => c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__card__le__card__Diff,axiom, % 177.02/177.08 ! [V_A_2,V_B_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => 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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_fold__sup__insert,axiom, % 177.02/177.08 ! [V_a_2,V_b_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Osemilattice__sup(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),V_A_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__psubset,axiom, % 177.02/177.08 ! [V_A_2,V_B_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_compl__top__eq,axiom, % 177.02/177.08 ! [T_a] : % 177.02/177.08 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.08 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_compl__bot__eq,axiom, % 177.02/177.08 ! [T_a] : % 177.02/177.08 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.08 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_range__ex1__eq,axiom, % 177.02/177.08 ! [V_b_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 177.02/177.08 <=> ? [B_x] : % 177.02/177.08 ( V_b_2 = hAPP(V_f_2,B_x) % 177.02/177.08 & ! [B_y] : % 177.02/177.08 ( V_b_2 = hAPP(V_f_2,B_y) % 177.02/177.08 => B_y = B_x ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__image__mem__iff,axiom, % 177.02/177.08 ! [V_A_2,V_a_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_finite__UNIV__inj__surj,axiom, % 177.02/177.08 ! [V_f_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.08 => ( c_Fun_Oinj__on(T_c,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => hAPP(c_Set_Oimage(T_c,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_c,tc_HOL_Obool)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_finite__UNIV__surj__inj,axiom, % 177.02/177.08 ! [V_f_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.08 => ( hAPP(c_Set_Oimage(T_c,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_c,tc_HOL_Obool)) % 177.02/177.08 => c_Fun_Oinj__on(T_c,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__image__subset__iff,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_image__set__diff,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_surj__Compl__image__subset,axiom, % 177.02/177.08 ! [V_A_2,V_f_2,T_c,T_d] : % 177.02/177.08 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_folding__one__idem_Ounion__idem,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.08 ( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => 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)) ) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__monoid__big_OF__eq,axiom, % 177.02/177.08 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Big__Operators_Ocomm__monoid__big(T_c,T_d,V_f_2,V_z_2,V_F_2) % 177.02/177.08 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.08 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),V_A_2) ) % 177.02/177.08 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.08 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__Diff1__le,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),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)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_sup__le__fold__sup,axiom, % 177.02/177.08 ! [V_b_2,V_a_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Osemilattice__sup(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),V_A_2))) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__inj__on__le,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2))) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__bij__eq,axiom, % 177.02/177.08 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2)) % 177.02/177.08 => ( c_Fun_Oinj__on(T_d,T_c,V_g_2,V_B_2) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2)),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_d),V_B_2) ) ) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__Diff__subset,axiom, % 177.02/177.08 ! [V_A_2,V_B_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_union__fold__insert,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,tc_fun(T_c,tc_HOL_Obool),c_Set_Oinsert(T_c)),V_B_2),V_A_2) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_fold1__Un2,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Oab__semigroup__idem__mult(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_B_2)) ) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__on__iff__card__le,axiom, % 177.02/177.08 ! [V_B_2,T_d,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.08 => ( ? [B_f] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) % 177.02/177.08 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_B_2)) ) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2))) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__Diff__singleton__if,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 177.02/177.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),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))))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__Diff__singleton,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__less__mono,axiom, % 177.02/177.08 ! [V_c,V_b,V_a] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 177.02/177.08 => 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__diff__iff,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 177.02/177.08 => ( 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))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__less__mono2,axiom, % 177.02/177.08 ! [V_l,V_n,V_m] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 177.02/177.08 => 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__imp__diff__less,axiom, % 177.02/177.08 ! [V_n,V_k,V_j] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__diff__inverse,axiom, % 177.02/177.08 ! [V_n,V_m] : % 177.02/177.08 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => 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 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__diff__conv,axiom, % 177.02/177.08 ! [V_k_2,V_j_2,V_i_2] : % 177.02/177.08 ( 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))) % 177.02/177.08 <=> 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__UNIV__unit,axiom, % 177.02/177.08 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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__refl,axiom, % 177.02/177.08 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__add2,axiom, % 177.02/177.08 ! [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))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__add1,axiom, % 177.02/177.08 ! [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))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__on__add__nat,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__iff__add,axiom, % 177.02/177.08 ! [V_n_2,V_m_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.08 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__le__linear,axiom, % 177.02/177.08 ! [V_n,V_m] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__add__left__cancel__le,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.08 ( 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))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_eq__imp__le,axiom, % 177.02/177.08 ! [V_n,V_m] : % 177.02/177.08 ( V_m = V_n % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_trans__le__add1,axiom, % 177.02/177.08 ! [V_m,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_trans__le__add2,axiom, % 177.02/177.08 ! [V_m,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__le__mono1,axiom, % 177.02/177.08 ! [V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__trans,axiom, % 177.02/177.08 ! [V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__antisym,axiom, % 177.02/177.08 ! [V_n,V_m] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.08 => V_m = V_n ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__le__mono,axiom, % 177.02/177.08 ! [V_l,V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 177.02/177.08 => 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__leD2,axiom, % 177.02/177.08 ! [V_n,V_k,V_m] : % 177.02/177.08 ( 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)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__leD1,axiom, % 177.02/177.08 ! [V_n,V_k,V_m] : % 177.02/177.08 ( 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)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__leE,axiom, % 177.02/177.08 ! [V_n,V_k,V_m] : % 177.02/177.08 ( 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)) % 177.02/177.08 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 177.02/177.08 ! [V_N_2] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 177.02/177.08 <=> ? [B_m] : % 177.02/177.08 ! [B_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__add__right__cancel,axiom, % 177.02/177.08 ! [V_n_2,V_k_2,V_m_2] : % 177.02/177.08 ( 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) % 177.02/177.08 <=> V_m_2 = V_n_2 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__add__left__cancel,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.08 ( 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) % 177.02/177.08 <=> V_m_2 = V_n_2 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__add__assoc,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__add__left__commute,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__add__commute,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_one__reorient,axiom, % 177.02/177.08 ! [V_x_2,T_c] : % 177.02/177.08 ( class_Groups_Oone(T_c) % 177.02/177.08 => ( c_Groups_Oone__class_Oone(T_c) = V_x_2 % 177.02/177.08 <=> V_x_2 = c_Groups_Oone__class_Oone(T_c) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__mult__eq__1__iff,axiom, % 177.02/177.08 ! [V_n_2,V_m_2] : % 177.02/177.08 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.02/177.08 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.02/177.08 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__mult__1__right,axiom, % 177.02/177.08 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__1__eq__mult__iff,axiom, % 177.02/177.08 ! [V_n_2,V_m_2] : % 177.02/177.08 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 177.02/177.08 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.02/177.08 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__mult__1,axiom, % 177.02/177.08 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__mult__distrib2,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__mult__distrib,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_mult__le__mono,axiom, % 177.02/177.08 ! [V_l,V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 177.02/177.08 => 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_mult__le__mono2,axiom, % 177.02/177.08 ! [V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_mult__le__mono1,axiom, % 177.02/177.08 ! [V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__cube,axiom, % 177.02/177.08 ! [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)))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__square,axiom, % 177.02/177.08 ! [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))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_mult_Ocomm__neutral,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.02/177.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_mult__1__right,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_mult__1,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.02/177.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_mult__1__left,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__eq__1__iff,axiom, % 177.02/177.08 ! [V_f_2,V_F_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.08 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.02/177.08 <=> ! [B_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_F_2)) % 177.02/177.08 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__1,axiom, % 177.02/177.08 ! [V_A_2,T_d,T_c] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Oone__class_Oone(T_c))),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__add__one,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => 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)))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__1__mult,axiom, % 177.02/177.08 ! [V_n,V_m,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 177.02/177.08 => 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))) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 177.02/177.08 ! [V_m,V_a,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 177.02/177.08 ! [V_a,V_m,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 177.02/177.08 ! [V_m,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 177.02/177.08 ! [V_x,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__ring__1(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_square__eq__1__iff,axiom, % 177.02/177.08 ! [V_x_2,T_c] : % 177.02/177.08 ( class_Rings_Oring__1__no__zero__divisors(T_c) % 177.02/177.08 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_c) % 177.02/177.08 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_c) % 177.02/177.08 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod_Oempty,axiom, % 177.02/177.08 ! [V_g_2,T_d,T_c] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_c) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__empty,axiom, % 177.02/177.08 ! [V_f_2,T_d,T_c] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_c) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__infinite,axiom, % 177.02/177.08 ! [V_f_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_d) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod_Oinfinite,axiom, % 177.02/177.08 ! [V_g_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_d) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__eq__setsum,axiom, % 177.02/177.08 ! [V_A_2,T_c] : hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_c),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__less__le,axiom, % 177.02/177.08 ! [V_n_2,V_m_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.08 & V_m_2 != V_n_2 ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__eq__less__or__eq,axiom, % 177.02/177.08 ! [V_n_2,V_m_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.08 | V_m_2 = V_n_2 ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__imp__le__nat,axiom, % 177.02/177.08 ! [V_n,V_m] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__neq__implies__less,axiom, % 177.02/177.08 ! [V_n,V_m] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => ( V_m != V_n % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__or__eq__imp__le,axiom, % 177.02/177.08 ! [V_n,V_m] : % 177.02/177.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 | V_m = V_n ) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__lessD1,axiom, % 177.02/177.08 ! [V_k,V_j,V_i] : % 177.02/177.08 ( 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)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__add__eq__less,axiom, % 177.02/177.08 ! [V_n,V_m,V_l,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 177.02/177.08 => ( 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) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__less__mono,axiom, % 177.02/177.08 ! [V_l,V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 177.02/177.08 => 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__less__mono1,axiom, % 177.02/177.08 ! [V_k,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_trans__less__add2,axiom, % 177.02/177.08 ! [V_m,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_trans__less__add1,axiom, % 177.02/177.08 ! [V_m,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__add__left__cancel__less,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.08 ( 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))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_not__add__less2,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_not__add__less1,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__not__refl,axiom, % 177.02/177.08 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__neq__iff,axiom, % 177.02/177.08 ! [V_n_2,V_m_2] : % 177.02/177.08 ( V_m_2 != V_n_2 % 177.02/177.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.08 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_linorder__neqE__nat,axiom, % 177.02/177.08 ! [V_y,V_x] : % 177.02/177.08 ( V_x != V_y % 177.02/177.08 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__irrefl__nat,axiom, % 177.02/177.08 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__not__refl2,axiom, % 177.02/177.08 ! [V_m,V_n] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 177.02/177.08 => V_m != V_n ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_less__not__refl3,axiom, % 177.02/177.08 ! [V_t,V_s] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 177.02/177.08 => V_s != V_t ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__less__cases,axiom, % 177.02/177.08 ! [V_Pa_2,V_n_2,V_m_2] : % 177.02/177.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 177.02/177.08 => ( ( V_m_2 = V_n_2 % 177.02/177.08 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 177.02/177.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 177.02/177.08 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_finite__nat__set__iff__bounded,axiom, % 177.02/177.08 ! [V_N_2] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 177.02/177.08 <=> ? [B_m] : % 177.02/177.08 ! [B_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__delta,axiom, % 177.02/177.08 ! [V_b_2,V_a_2,V_S_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.08 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 177.02/177.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = c_Groups_Oone__class_Oone(T_d) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__delta_H,axiom, % 177.02/177.08 ! [V_b_2,V_a_2,V_S_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.08 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 177.02/177.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = c_Groups_Oone__class_Oone(T_d) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__minus__add__max,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_min__diff,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__mult__distrib2,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__mult__distrib,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__add__inverse2,axiom, % 177.02/177.08 ! [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 ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__add__inverse,axiom, % 177.02/177.08 ! [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 ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__diff__left,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__commute,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__cancel,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__cancel2,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__diff__iff,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 177.02/177.08 => ( 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))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Nat_Odiff__diff__eq,axiom, % 177.02/177.08 ! [V_n,V_m,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 177.02/177.08 => 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) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_eq__diff__iff,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 177.02/177.08 => ( 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) % 177.02/177.08 <=> V_m_2 = V_n_2 ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__add__assoc2,axiom, % 177.02/177.08 ! [V_i,V_j,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__diff__assoc2,axiom, % 177.02/177.08 ! [V_i,V_j,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__add__assoc,axiom, % 177.02/177.08 ! [V_i,V_j,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__imp__diff__is__add,axiom, % 177.02/177.08 ! [V_k_2,V_j_2,V_i_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.02/177.08 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 177.02/177.08 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__add__diff__inverse2,axiom, % 177.02/177.08 ! [V_m,V_n] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.08 => 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 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__diff__conv2,axiom, % 177.02/177.08 ! [V_i_2,V_j_2,V_k_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 177.02/177.08 => ( 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))) % 177.02/177.08 <=> 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)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_add__diff__assoc,axiom, % 177.02/177.08 ! [V_i,V_j,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__add__diff__inverse,axiom, % 177.02/177.08 ! [V_m,V_n] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.08 => 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 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__diff__cancel,axiom, % 177.02/177.08 ! [V_n,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 177.02/177.08 => 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 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__le__mono,axiom, % 177.02/177.08 ! [V_l,V_n,V_m] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__le__mono2,axiom, % 177.02/177.08 ! [V_l,V_n,V_m] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__add__diff,axiom, % 177.02/177.08 ! [V_m,V_n,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_le__diff__conv,axiom, % 177.02/177.08 ! [V_i_2,V_k_2,V_j_2] : % 177.02/177.08 ( 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)) % 177.02/177.08 <=> 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__diff__right,axiom, % 177.02/177.08 ! [V_i,V_j,V_k] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_diff__le__self,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_fold__image__distrib,axiom, % 177.02/177.08 ! [V_h_2,V_g_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Otimes__class_Otimes(T_d)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_h_2),c_Groups_Oone__class_Oone(T_d)),V_A_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card_Oinsert,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),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_c),V_A_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod_OF__eq,axiom, % 177.02/177.08 ! [V_g_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = 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)),V_A_2) ) % 177.02/177.08 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_d) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod_Oeq__fold,axiom, % 177.02/177.08 ! [V_g_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = 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)),V_A_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card_Oinsert__remove,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),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_c),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)))))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card_Oremove,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),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_c),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)))))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_card__Diff__insert,axiom, % 177.02/177.08 ! [V_B_2,V_a_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2)) % 177.02/177.08 => hAPP(c_Finite__Set_Ocard(T_c),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_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__less__add__iff2,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.02/177.08 => ( 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))) % 177.02/177.08 <=> 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__less__add__iff1,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 177.02/177.08 => ( 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))) % 177.02/177.08 <=> 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)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__le__add__iff1,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 177.02/177.08 => ( 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))) % 177.02/177.08 <=> 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)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__diff__add__eq1,axiom, % 177.02/177.08 ! [V_n,V_m,V_u,V_i,V_j] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__eq__add__iff1,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 177.02/177.08 => ( 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) % 177.02/177.08 <=> 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 ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__le__add__iff2,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.02/177.08 => ( 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))) % 177.02/177.08 <=> 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__diff__add__eq2,axiom, % 177.02/177.08 ! [V_n,V_m,V_u,V_j,V_i] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__eq__add__iff2,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.02/177.08 => ( 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) % 177.02/177.08 <=> 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) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_sup__nat__def,axiom, % 177.02/177.08 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 177.02/177.08 % 177.02/177.08 fof(fact_infinite__UNIV__nat,axiom, % 177.02/177.08 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__mult__assoc,axiom, % 177.02/177.08 ! [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)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_nat__mult__commute,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_left__add__mult__distrib,axiom, % 177.02/177.08 ! [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) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OatMost__iff,axiom, % 177.02/177.08 ! [V_k_2,V_less__eq_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatMost(T_c,V_less__eq_2,V_k_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OatLeast__iff,axiom, % 177.02/177.08 ! [V_k_2,V_less__eq_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeast(T_c,V_less__eq_2,V_k_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OlessThan__iff,axiom, % 177.02/177.08 ! [V_k_2,V_less_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OlessThan(T_c,V_less_2,V_k_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OgreaterThan__iff,axiom, % 177.02/177.08 ! [V_k_2,V_less_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThan(T_c,V_less_2,V_k_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OatLeastAtMost__iff,axiom, % 177.02/177.08 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_c,V_less__eq_2,V_l_2,V_u_2))) % 177.02/177.08 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 177.02/177.08 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 177.02/177.08 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_c,V_less_2,V_l_2,V_u_2))) % 177.02/177.08 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 177.02/177.08 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OatLeastLessThan__iff,axiom, % 177.02/177.08 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_c,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 177.02/177.08 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 177.02/177.08 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 177.02/177.08 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_c,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 177.02/177.08 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 177.02/177.08 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__gen__delta,axiom, % 177.02/177.08 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.08 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 177.02/177.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_c_2),hAPP(c_Finite__Set_Ocard(T_c),V_S_2)) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_termination__basic__simps_I3_J,axiom, % 177.02/177.08 ! [V_z,V_y,V_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_termination__basic__simps_I4_J,axiom, % 177.02/177.08 ! [V_y,V_z,V_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_termination__basic__simps_I5_J,axiom, % 177.02/177.08 ! [V_y,V_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_termination__basic__simps_I2_J,axiom, % 177.02/177.08 ! [V_y,V_z,V_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_termination__basic__simps_I1_J,axiom, % 177.02/177.08 ! [V_z,V_y,V_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 177.02/177.08 => 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))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oremove,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = V_x_2 ) % 177.02/177.08 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,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)))))) ) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_iso__tuple__UNIV__I,axiom, % 177.02/177.08 ! [V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 177.02/177.08 ! [V_q,V_y,V_x,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 177.02/177.08 ! [V_q,V_p,V_x,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 177.02/177.08 ! [V_x,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 177.02/177.08 ! [V_q,V_p,V_x,T_a] : % 177.02/177.08 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Osingleton,axiom, % 177.02/177.08 ! [V_x_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__constant,axiom, % 177.02/177.08 ! [V_y_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(c_COMBK(T_d,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_y_2),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oin__idem,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_OF__eq,axiom, % 177.02/177.08 ! [V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_A_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oinsert__idem,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Osubset__idem,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Ounion__idem,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) ) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 177.02/177.08 ! [V_a_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_a_2),V_A_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oinsert,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oinsert__remove,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) % 177.02/177.08 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,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)))))) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.08 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_x_2),V_A_2) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__le__imp__le__exp,axiom, % 177.02/177.08 ! [V_n,V_m,V_a,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.08 => ( 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))) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__increasing__iff,axiom, % 177.02/177.08 ! [V_y_2,V_x_2,V_b_2,T_c] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_c) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_b_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_y_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__minus,axiom, % 177.02/177.08 ! [V_n,V_a,T_a] : % 177.02/177.08 ( class_Rings_Oring__1(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__increasing,axiom, % 177.02/177.08 ! [V_a,V_N,V_n,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.08 => 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))) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__strict__increasing,axiom, % 177.02/177.08 ! [V_a,V_N,V_n,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.08 => 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))) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__less__imp__less__exp,axiom, % 177.02/177.08 ! [V_n,V_m,V_a,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.08 => ( 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))) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__strict__increasing__iff,axiom, % 177.02/177.08 ! [V_y_2,V_x_2,V_b_2,T_c] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_c) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_b_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_y_2))) % 177.02/177.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__less__power__Suc,axiom, % 177.02/177.08 ! [V_n,V_a,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.08 => 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)))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__commutes,axiom, % 177.02/177.08 ! [V_n,V_a,T_a] : % 177.02/177.08 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__mult__distrib,axiom, % 177.02/177.08 ! [V_n,V_b,V_a,T_a] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__one,axiom, % 177.02/177.08 ! [V_n,T_a] : % 177.02/177.08 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__mult,axiom, % 177.02/177.08 ! [V_n,V_m,V_a,T_a] : % 177.02/177.08 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__one__right,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.08 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_one__le__power,axiom, % 177.02/177.08 ! [V_n,V_a,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.08 => 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))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__inject__exp,axiom, % 177.02/177.08 ! [V_n_2,V_m_2,V_a_2,T_c] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_c) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)) % 177.02/177.08 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2) % 177.02/177.08 <=> V_m_2 = V_n_2 ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__add,axiom, % 177.02/177.08 ! [V_n,V_m,V_a,T_a] : % 177.02/177.08 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__gt1__lemma,axiom, % 177.02/177.08 ! [V_n,V_a,T_a] : % 177.02/177.08 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.08 => 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)))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_power__power__power,axiom, % 177.02/177.08 ! [T_c] : % 177.02/177.08 ( class_Power_Opower(T_c) % 177.02/177.08 => c_Power_Opower__class_Opower(T_c) = c_Power_Opower_Opower(T_c,c_Groups_Oone__class_Oone(T_c),c_Groups_Otimes__class_Otimes(T_c)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Oclosed,axiom, % 177.02/177.08 ! [V_A_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),V_A_2)) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inj__vimage__singleton,axiom, % 177.02/177.08 ! [V_a_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_c),c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Sup__fin_Ohom__commute,axiom, % 177.02/177.08 ! [V_N_2,V_h_2,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.08 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.08 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_c,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_SUPR__fold__sup,axiom, % 177.02/177.08 ! [V_f_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_d)),V_f_2)),c_Orderings_Obot__class_Obot(T_d)),V_A_2) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__mono__one__right,axiom, % 177.02/177.08 ! [V_f_2,V_S_2,V_T_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.02/177.08 => ( ! [B_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) % 177.02/177.08 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) ) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_setprod__mono__one__left,axiom, % 177.02/177.08 ! [V_f_2,V_S_2,V_T_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.02/177.08 => ( ! [B_x] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) % 177.02/177.08 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) ) % 177.02/177.08 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_fold__Un__disjoint,axiom, % 177.02/177.08 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.08 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.08 => ( 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)) % 177.02/177.08 => 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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),V_A_2)),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)),V_B_2)) ) ) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf1I,axiom, % 177.02/177.08 ! [T_c,V_B_2,V_x_2,V_A_2] : % 177.02/177.08 ( hBOOL(hAPP(V_A_2,V_x_2)) % 177.02/177.08 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf1E,axiom, % 177.02/177.08 ! [V_x_2,V_B_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 177.02/177.08 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 177.02/177.08 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_SUP1__I,axiom, % 177.02/177.08 ! [T_d,V_b_2,V_B_2,V_A_2,V_a_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 177.02/177.08 => hBOOL(hAPP(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_b_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_SUP2__I,axiom, % 177.02/177.08 ! [T_e,T_d,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_IntI,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_IntE,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.08 => ~ ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.08 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_finite__Int,axiom, % 177.02/177.08 ! [V_Ga_2,V_F_2,T_c] : % 177.02/177.08 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.08 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2)) ) % 177.02/177.08 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_vimageI,axiom, % 177.02/177.08 ! [T_d,V_B_2,T_c,V_b_2,V_a_2,V_f_2] : % 177.02/177.08 ( hAPP(V_f_2,V_a_2) = V_b_2 % 177.02/177.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_B_2)) % 177.02/177.08 => hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2))) ) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Inf__fin_Oidem,axiom, % 177.02/177.08 ! [V_x,T_a] : % 177.02/177.08 ( class_Lattices_Olattice(T_a) % 177.02/177.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Int__absorb,axiom, % 177.02/177.08 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 177.02/177.08 % 177.02/177.08 fof(fact_Int__commute,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : 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_c,tc_HOL_Obool)),V_B_2),V_A_2) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Int__left__absorb,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_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_c,tc_HOL_Obool)),V_A_2),V_B_2) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Int__left__commute,axiom, % 177.02/177.08 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_vimage__Int,axiom, % 177.02/177.08 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_Int__assoc,axiom, % 177.02/177.08 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 177.02/177.08 % 177.02/177.08 fof(fact_vimage__code,axiom, % 177.02/177.08 ! [V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2),V_x_2)) % 177.02/177.08 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf1D1,axiom, % 177.02/177.08 ! [V_x_2,V_B_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 177.02/177.08 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf1D2,axiom, % 177.02/177.08 ! [V_x_2,V_B_2,V_A_2,T_c] : % 177.02/177.08 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 177.02/177.08 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf_Oidem,axiom, % 177.02/177.08 ! [V_a,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__idem,axiom, % 177.02/177.08 ! [V_x,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__fun__def,axiom, % 177.02/177.08 ! [V_x_2,V_g_2,V_f_2,T_d,T_c] : % 177.02/177.08 ( class_Lattices_Olattice(T_c) % 177.02/177.08 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf_Ocommute,axiom, % 177.02/177.08 ! [V_b,V_a,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__sup__aci_I1_J,axiom, % 177.02/177.08 ! [V_y,V_x,T_a] : % 177.02/177.08 ( class_Lattices_Olattice(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__commute,axiom, % 177.02/177.08 ! [V_y,V_x,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf_Oleft__idem,axiom, % 177.02/177.08 ! [V_b,V_a,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__sup__aci_I4_J,axiom, % 177.02/177.08 ! [V_y,V_x,T_a] : % 177.02/177.08 ( class_Lattices_Olattice(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__left__idem,axiom, % 177.02/177.08 ! [V_y,V_x,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => 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) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf_Oleft__commute,axiom, % 177.02/177.08 ! [V_c,V_a,V_b,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__sup__aci_I3_J,axiom, % 177.02/177.08 ! [V_z,V_y,V_x,T_a] : % 177.02/177.08 ( class_Lattices_Olattice(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__left__commute,axiom, % 177.02/177.08 ! [V_z,V_y,V_x,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf_Oassoc,axiom, % 177.02/177.08 ! [V_c,V_b,V_a,T_a] : % 177.02/177.08 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__sup__aci_I2_J,axiom, % 177.02/177.08 ! [V_z,V_y,V_x,T_a] : % 177.02/177.08 ( class_Lattices_Olattice(T_a) % 177.02/177.08 => 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)) ) ). % 177.02/177.08 % 177.02/177.08 fof(fact_inf__assoc,axiom, % 177.02/177.09 ! [V_z,V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__apply,axiom, % 177.02/177.09 ! [V_x_2,V_g_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( class_Lattices_Olattice(T_c) % 177.02/177.09 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__ident,axiom, % 177.02/177.09 ! [V_Y_2,T_c] : hAPP(c_Set_Ovimage(T_c,T_c,c_COMBI(T_c)),V_Y_2) = V_Y_2 ). % 177.02/177.09 % 177.02/177.09 fof(fact_image__vimage__eq,axiom, % 177.02/177.09 ! [V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_finite__UN,axiom, % 177.02/177.09 ! [V_B_2,T_d,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__sup__ord_I1_J,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Olattice(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__le1,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__sup__ord_I2_J,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Olattice(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__le2,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__iff__inf,axiom, % 177.02/177.09 ! [V_y_2,V_x_2,T_c] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.09 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) = V_x_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__inf__iff,axiom, % 177.02/177.09 ! [V_z_2,V_y_2,V_x_2,T_c] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_y_2),V_z_2))) % 177.02/177.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__infI1,axiom, % 177.02/177.09 ! [V_b,V_x,V_a,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 177.02/177.09 => 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)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__infI2,axiom, % 177.02/177.09 ! [V_a,V_x,V_b,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 177.02/177.09 => 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)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__absorb1,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__absorb2,axiom, % 177.02/177.09 ! [V_x,V_y,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__infI,axiom, % 177.02/177.09 ! [V_b,V_a,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 177.02/177.09 => 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))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__greatest,axiom, % 177.02/177.09 ! [V_z,V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 177.02/177.09 => 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))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__mono,axiom, % 177.02/177.09 ! [V_d,V_b,V_c,V_a,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 177.02/177.09 => 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))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__infE,axiom, % 177.02/177.09 ! [V_b,V_a,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( 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))) % 177.02/177.09 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.02/177.09 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__infI1,axiom, % 177.02/177.09 ! [V_b,V_x,V_a,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 177.02/177.09 => 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)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__infI2,axiom, % 177.02/177.09 ! [V_a,V_x,V_b,T_a] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_a) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 177.02/177.09 => 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)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__bot__left,axiom, % 177.02/177.09 ! [V_x,T_a] : % 177.02/177.09 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.02/177.09 => 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) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__bot__right,axiom, % 177.02/177.09 ! [V_x,T_a] : % 177.02/177.09 ( class_Lattices_Obounded__lattice__bot(T_a) % 177.02/177.09 => 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) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__sup__absorb,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Olattice(T_a) % 177.02/177.09 => 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 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_sup__inf__absorb,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Olattice(T_a) % 177.02/177.09 => 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 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__sup__distrib1,axiom, % 177.02/177.09 ! [V_z,V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Odistrib__lattice(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_sup__inf__distrib1,axiom, % 177.02/177.09 ! [V_z,V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Odistrib__lattice(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__sup__distrib2,axiom, % 177.02/177.09 ! [V_x,V_z,V_y,T_a] : % 177.02/177.09 ( class_Lattices_Odistrib__lattice(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_sup__inf__distrib2,axiom, % 177.02/177.09 ! [V_x,V_z,V_y,T_a] : % 177.02/177.09 ( class_Lattices_Odistrib__lattice(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__top__left,axiom, % 177.02/177.09 ! [V_x,T_a] : % 177.02/177.09 ( class_Lattices_Obounded__lattice__top(T_a) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__top__right,axiom, % 177.02/177.09 ! [V_x,T_a] : % 177.02/177.09 ( class_Lattices_Obounded__lattice__top(T_a) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__eq__top__iff,axiom, % 177.02/177.09 ! [V_y_2,V_x_2,T_c] : % 177.02/177.09 ( class_Lattices_Obounded__lattice__top(T_c) % 177.02/177.09 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_c) % 177.02/177.09 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_c) % 177.02/177.09 & V_y_2 = c_Orderings_Otop__class_Otop(T_c) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__eq,axiom, % 177.02/177.09 ! [V_B_2,V_f_2,T_d,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2))) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimageD,axiom, % 177.02/177.09 ! [V_A_2,V_f_2,T_d,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimageI2,axiom, % 177.02/177.09 ! [T_d,V_A_2,V_a_2,V_f_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__iff,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.09 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_IntD1,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_IntD2,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_c_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__min,axiom, % 177.02/177.09 ! [T_c] : % 177.02/177.09 ( ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 & class_Orderings_Olinorder(T_c) ) % 177.02/177.09 => c_Lattices_Osemilattice__inf__class_Oinf(T_c) = c_Orderings_Oord__class_Omin(T_c) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__empty,axiom, % 177.02/177.09 ! [V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__empty__left,axiom, % 177.02/177.09 ! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__empty__right,axiom, % 177.02/177.09 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_disjoint__iff__not__equal,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( 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)) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.09 => ! [B_xa] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_B_2)) % 177.02/177.09 => B_x != B_xa ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__mono,axiom, % 177.02/177.09 ! [V_f_2,T_d,V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__UNIV,axiom, % 177.02/177.09 ! [V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_insert__inter__insert,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__Un,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__lower1,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__lower2,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__absorb2,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__absorb1,axiom, % 177.02/177.09 ! [V_A_2,V_B_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__greatest,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__mono,axiom, % 177.02/177.09 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__UNIV__left,axiom, % 177.02/177.09 ! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__UNIV__right,axiom, % 177.02/177.09 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = V_A_2 ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__Un__distrib,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__Int__distrib,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__Un__distrib2,axiom, % 177.02/177.09 ! [V_A_2,V_C_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__Int__distrib2,axiom, % 177.02/177.09 ! [V_A_2,V_C_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__Int__crazy,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__Diff,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,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_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__Int__distrib,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_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_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__Diff,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__Int__distrib2,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__Int2,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inj__on__Int,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.09 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.02/177.09 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__Compl,axiom, % 177.02/177.09 ! [V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_fun__left__comm__idem__inf,axiom, % 177.02/177.09 ! [T_c] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__Int__eq,axiom, % 177.02/177.09 ! [V_x_2,V_S_2,V_R_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_distrib__inf__le,axiom, % 177.02/177.09 ! [V_z,V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Olattice(T_a) % 177.02/177.09 => 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)))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_distrib__sup__le,axiom, % 177.02/177.09 ! [V_z,V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Olattice(T_a) % 177.02/177.09 => 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)))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__compl__bot,axiom, % 177.02/177.09 ! [V_x,T_a] : % 177.02/177.09 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.09 => 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) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_compl__inf__bot,axiom, % 177.02/177.09 ! [V_x,T_a] : % 177.02/177.09 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.09 => 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) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_diff__eq,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_compl__inf,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_compl__sup,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__insert__right,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_a_2,T_c] : % 177.02/177.09 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 177.02/177.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__insert__left,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,V_a_2,T_c] : % 177.02/177.09 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 177.02/177.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__insert__right__if0,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_a_2,T_c] : % 177.02/177.09 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__insert__left__if0,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,V_a_2,T_c] : % 177.02/177.09 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__insert__right__if1,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__insert__left__if1,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_image__vimage__subset,axiom, % 177.02/177.09 ! [V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2))),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_surj__image__vimage__eq,axiom, % 177.02/177.09 ! [V_A_2,V_f_2,T_c,T_d] : % 177.02/177.09 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_image__Int__subset,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__triv,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__Int__assoc__eq,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__Diff__Int,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),V_B_2)) = V_A_2 ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__Un,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__Int,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUP__UN__eq,axiom, % 177.02/177.09 ! [V_x_2,V_r_2,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Compl__disjoint,axiom, % 177.02/177.09 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Compl__disjoint2,axiom, % 177.02/177.09 ! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Compl__Int,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Compl__Un,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__Compl,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Diff__eq,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__singleton__eq,axiom, % 177.02/177.09 ! [V_b_2,V_f_2,T_d,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) % 177.02/177.09 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_fold__inf__insert,axiom, % 177.02/177.09 ! [V_a_2,V_b_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),V_A_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__Sup__absorb,axiom, % 177.02/177.09 ! [V_a_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Olattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = V_a_2 ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__insert,axiom, % 177.02/177.09 ! [V_B_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_finite__vimageD,axiom, % 177.02/177.09 ! [V_F_2,V_h_2,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_d,V_h_2),V_F_2))) % 177.02/177.09 => ( hAPP(c_Set_Oimage(T_c,T_d,V_h_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)) % 177.02/177.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_F_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__subsetD,axiom, % 177.02/177.09 ! [V_A_2,V_B_2,V_f_2,T_c,T_d] : % 177.02/177.09 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2)),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_finite__vimageI,axiom, % 177.02/177.09 ! [V_h_2,T_d,V_F_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.09 => ( c_Fun_Oinj__on(T_d,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 177.02/177.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Ovimage(T_d,T_c,V_h_2),V_F_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inj__vimage__image__eq,axiom, % 177.02/177.09 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.09 => hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = V_A_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inj__on__image__Int,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) % 177.02/177.09 => hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_image__Int,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.09 => hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_disjoint__eq__subset__Compl,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( 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)) % 177.02/177.09 <=> 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)),V_B_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__const,axiom, % 177.02/177.09 ! [T_d,V_A_2,V_c_2,T_c] : % 177.02/177.09 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.09 => hAPP(c_Set_Ovimage(T_d,T_c,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.09 => hAPP(c_Set_Ovimage(T_d,T_c,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_folding__image__simple_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.09 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_compl__unique,axiom, % 177.02/177.09 ! [V_y,V_x,T_a] : % 177.02/177.09 ( class_Lattices_Oboolean__algebra(T_a) % 177.02/177.09 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 177.02/177.09 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 177.02/177.09 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_fold__inf__le__inf,axiom, % 177.02/177.09 ! [V_b_2,V_a_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),V_b_2))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_fold1__belowI,axiom, % 177.02/177.09 ! [V_a_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2)),V_a_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_below__fold1__iff,axiom, % 177.02/177.09 ! [V_x_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2))) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_x)) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setsum__Un__Int,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__subsetI,axiom, % 177.02/177.09 ! [V_A_2,V_B_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),V_A_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setprod_Ounion__inter,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setprod__Un__Int,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_card_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_card__Un__Int,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_card__Diff__subset__Int,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.09 => hAPP(c_Finite__Set_Ocard(T_c),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__if,axiom, % 177.02/177.09 ! [V_B_2,T_d,V_d_2,V_A_2,V_c_2,T_c] : % 177.02/177.09 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.09 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) % 177.02/177.09 => hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) % 177.02/177.09 => hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 177.02/177.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) % 177.02/177.09 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) % 177.02/177.09 => hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_B_2) ) % 177.02/177.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) % 177.02/177.09 => hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_folding__one_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.09 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => 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)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_folding__one_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] : % 177.02/177.09 ( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => 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)) ) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.09 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 177.02/177.09 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setsum__Un__disjoint,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setsum__Un,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Oab__group__add(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setprod__Un__disjoint,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setprod_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_sup__SUPR__fold__sup,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_d),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_d)),V_f_2)),V_B_2),V_A_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_card__Un__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inj__on__Un,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.09 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.09 <=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.02/177.09 & c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.02/177.09 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_fold__image__Un__Int,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),V_A_2)),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)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_fold1__Un,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Groups_Oab__semigroup__mult(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_B_2)) ) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Sup__fin_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Olattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_c,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__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Olattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => c_Big__Operators_Olattice__class_OSup__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) ) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Min_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Min_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)) ) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Max_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Max_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)) ) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) ) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : % 177.02/177.09 ( class_Orderings_Olinorder(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => ( 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)) % 177.02/177.09 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) ) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setsum__Un__nat,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_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_c,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__eq__UN,axiom, % 177.02/177.09 ! [V_B_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Ovimage(T_c,T_d,V_f_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),c_Set_Oinsert(T_d)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_image__eq__UN,axiom, % 177.02/177.09 ! [V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__I,axiom, % 177.02/177.09 ! [V_B_2,V_b_2,T_d,V_A_2,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2))) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__SUPI,axiom, % 177.02/177.09 ! [V_M_2,V_A_2,V_i_2,T_c,T_d] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_M_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUP__subset,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_B_2),V_f_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUP__const,axiom, % 177.02/177.09 ! [V_M_2,T_c,V_A_2,T_d] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),hAPP(c_COMBK(T_d,T_c),V_M_2)) = V_M_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__insert,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_a_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I3_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__UN__flatten,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I9_J,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_ball__UN,axiom, % 177.02/177.09 ! [V_Pa_2,V_B_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.09 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => ! [B_xa] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),hAPP(V_B_2,B_x))) % 177.02/177.09 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I9_J,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUP1__iff,axiom, % 177.02/177.09 ! [V_b_2,V_B_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(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_b_2)) % 177.02/177.09 <=> ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUP2__iff,axiom, % 177.02/177.09 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 177.02/177.09 <=> ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inf__nat__def,axiom, % 177.02/177.09 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__iff,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,V_b_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) % 177.02/177.09 <=> ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UNION__empty__conv_I2_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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)) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__constant,axiom, % 177.02/177.09 ! [V_c_2,T_d,T_c,V_A_2] : % 177.02/177.09 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.09 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = V_c_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__empty2,axiom, % 177.02/177.09 ! [V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UNION__empty__conv_I1_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( c_Orderings_Obot__class_Obot(tc_fun(T_c,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) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__subset__iff,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_I_2,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I10_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_d,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),V_B_2),V_f_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_image__UN,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_e,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Oimage(T_d,T_c,V_f_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I10_J,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_B_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__Un__distrib,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_I_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__Un,axiom, % 177.02/177.09 ! [V_M_2,V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I5_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I4_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I5_J,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__UN__distrib,axiom, % 177.02/177.09 ! [V_A_2,V_I_2,T_d,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I4_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__UN__distrib2,axiom, % 177.02/177.09 ! [V_B_2,V_J_2,T_e,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e)),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_d),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUP__commute,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,T_e,V_A_2,T_d,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),T_c,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,T_c),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,T_c),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),T_c,T_e),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUPR__apply,axiom, % 177.02/177.09 ! [V_x_2,V_f_2,V_A_2,T_e,T_d,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,T_c)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBC(T_d,T_e,T_c),V_f_2),V_x_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I6_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I6_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__UN,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_e,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Ovimage(T_c,T_d,V_f_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__insert__distrib,axiom, % 177.02/177.09 ! [V_B_2,V_a_2,T_d,V_A_2,V_u_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_u_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__upper,axiom, % 177.02/177.09 ! [V_B_2,T_d,V_A_2,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__absorb,axiom, % 177.02/177.09 ! [V_A_2,T_d,V_I_2,V_k_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_k_2),V_I_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I1_J,axiom, % 177.02/177.09 ! [V_B_2,V_a_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__singleton,axiom, % 177.02/177.09 ! [V_A_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_c,tc_HOL_Obool)),V_A_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)))) = V_A_2 ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I1_J,axiom, % 177.02/177.09 ! [V_B_2,V_a_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_SUP__le__iff,axiom, % 177.02/177.09 ! [V_u_2,V_M_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_M_2)),V_u_2)) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__SUP__iff,axiom, % 177.02/177.09 ! [V_f_2,V_A_2,T_d,V_a_2,T_c] : % 177.02/177.09 ( ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 & class_Orderings_Olinorder(T_c) ) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_f_2))) % 177.02/177.09 <=> ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I2_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I3_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I2_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_fold__image__Un__one,axiom, % 177.02/177.09 ! [V_f_2,V_T_2,V_S_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 177.02/177.09 => ( ! [B_x] : % 177.02/177.09 ( 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_S_2),V_T_2))) % 177.02/177.09 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) ) % 177.02/177.09 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_T_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setprod__Un__one,axiom, % 177.02/177.09 ! [V_f_2,V_T_2,V_S_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 177.02/177.09 => ( ! [B_x] : % 177.02/177.09 ( 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_S_2),V_T_2))) % 177.02/177.09 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) ) % 177.02/177.09 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_setprod_Ounion__inter__neutral,axiom, % 177.02/177.09 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.09 => ( ! [B_x] : % 177.02/177.09 ( 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))) % 177.02/177.09 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_d) ) % 177.02/177.09 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inf__fin_Oremove,axiom, % 177.02/177.09 ! [V_x_2,V_A_2,T_c] : % 177.02/177.09 ( class_Lattices_Olattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.09 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = V_x_2 ) % 177.02/177.09 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,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)))))) ) ) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INFI__fold__inf,axiom, % 177.02/177.09 ! [V_f_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_d)),V_f_2)),c_Orderings_Otop__class_Otop(T_d)),V_A_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_card__Suc__Diff1,axiom, % 177.02/177.09 ! [V_x_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.09 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),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)))))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inf__fold__inf,axiom, % 177.02/177.09 ! [V_A_2,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_InterE,axiom, % 177.02/177.09 ! [V_X_2,V_C_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2))) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_InterD,axiom, % 177.02/177.09 ! [V_X_2,V_C_2,V_A_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2))) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_finite__Inter,axiom, % 177.02/177.09 ! [V_M_2,T_c] : % 177.02/177.09 ( ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_M_2)) % 177.02/177.09 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_x)) ) % 177.02/177.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_M_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF1__D,axiom, % 177.02/177.09 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF1__E,axiom, % 177.02/177.09 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 177.02/177.09 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 177.02/177.09 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__D,axiom, % 177.02/177.09 ! [V_a_2,V_B_2,V_A_2,T_d,V_b_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__E,axiom, % 177.02/177.09 ! [V_a_2,V_B_2,V_A_2,T_d,V_b_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) % 177.02/177.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 177.02/177.09 => ~ hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),V_A_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF2__D,axiom, % 177.02/177.09 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF2__E,axiom, % 177.02/177.09 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 177.02/177.09 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 177.02/177.09 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_finite__INT,axiom, % 177.02/177.09 ! [V_A_2,T_d,V_I_2,T_c] : % 177.02/177.09 ( ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 177.02/177.09 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_A_2,B_x))) ) % 177.02/177.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__mono,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_lessI,axiom, % 177.02/177.09 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__Inter__image,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_d,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_d),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)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_C_2))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INFI__apply,axiom, % 177.02/177.09 ! [V_x_2,V_f_2,V_A_2,T_e,T_d,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_e,T_c)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBC(T_d,T_e,T_c),V_f_2),V_x_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__Inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_n__not__Suc__n,axiom, % 177.02/177.09 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__n__not__n,axiom, % 177.02/177.09 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 177.02/177.09 % 177.02/177.09 fof(fact_nat_Oinject,axiom, % 177.02/177.09 ! [V_nat_H_2,V_nat_2] : % 177.02/177.09 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 177.02/177.09 <=> V_nat_2 = V_nat_H_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__inject,axiom, % 177.02/177.09 ! [V_y,V_x] : % 177.02/177.09 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 177.02/177.09 => V_x = V_y ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF__commute,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,T_e,V_A_2,T_d,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),T_c,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,T_c),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,T_c),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),T_c,T_e),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__less__SucD,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__lessD,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__SucE,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 177.02/177.09 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => V_m = V_n ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__trans__Suc,axiom, % 177.02/177.09 ! [V_k,V_j,V_i] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__lessI,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__SucI,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__antisym,axiom, % 177.02/177.09 ! [V_m,V_n] : % 177.02/177.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 177.02/177.09 => V_m = V_n ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_not__less__less__Suc__eq,axiom, % 177.02/177.09 ! [V_m_2,V_n_2] : % 177.02/177.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 177.02/177.09 <=> V_n_2 = V_m_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__less__eq,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( 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))) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__Suc__eq,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.02/177.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.09 | V_m_2 = V_n_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_not__less__eq,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_add__Suc__right,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_add__Suc,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_add__Suc__shift,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__leD,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__SucE,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 177.02/177.09 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__SucI,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__le__mono,axiom, % 177.02/177.09 ! [V_m_2,V_n_2] : % 177.02/177.09 ( 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))) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__Suc__eq,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.02/177.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.09 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_not__less__eq__eq,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__n__not__le__n,axiom, % 177.02/177.09 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__diff__diff,axiom, % 177.02/177.09 ! [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) ). % 177.02/177.09 % 177.02/177.09 fof(fact_diff__Suc__Suc,axiom, % 177.02/177.09 ! [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) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__mult__cancel1,axiom, % 177.02/177.09 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.09 ( 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) % 177.02/177.09 <=> V_m_2 = V_n_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inter__UNIV,axiom, % 177.02/177.09 ! [T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inf__fin__Inf,axiom, % 177.02/177.09 ! [V_A_2,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inter__anti__mono,axiom, % 177.02/177.09 ! [V_A_2,V_B_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inter__lower,axiom, % 177.02/177.09 ! [V_A_2,V_B_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inter__empty,axiom, % 177.02/177.09 ! [T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Int__eq__Inter,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inter__insert,axiom, % 177.02/177.09 ! [V_B_2,V_a_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inter__Un__distrib,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__iff,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,V_b_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__simps_I5_J,axiom, % 177.02/177.09 ! [V_B_2,V_a_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__extend__simps_I5_J,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,T_d,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__subset__iff,axiom, % 177.02/177.09 ! [V_A_2,V_I_2,T_d,V_B_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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)) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__extend__simps_I10_J,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,T_e,V_A_2,T_c,T_d] : 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(T_e,tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_B_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__simps_I10_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_d,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),V_B_2),V_f_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__INT__distrib2,axiom, % 177.02/177.09 ! [V_B_2,V_J_2,T_e,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e)),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_d),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__extend__simps_I6_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Un__INT__distrib,axiom, % 177.02/177.09 ! [V_A_2,V_I_2,T_d,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__extend__simps_I7_J,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__simps_I6_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__simps_I7_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__Int__distrib,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_I_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__extend__simps_I9_J,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__simps_I9_J,axiom, % 177.02/177.09 ! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_min__Suc__Suc,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_max__Suc__Suc,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_vimage__INT,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_e,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Ovimage(T_c,T_d,V_f_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__Inf__iff,axiom, % 177.02/177.09 ! [V_A_2,V_b_2,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2))) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),B_x)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inf__less__iff,axiom, % 177.02/177.09 ! [V_a_2,V_S_2,T_c] : % 177.02/177.09 ( ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 & class_Orderings_Olinorder(T_c) ) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Complete__Lattice_OInf__class_OInf(T_c,V_S_2)),V_a_2)) % 177.02/177.09 <=> ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_a_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_power_Opower_Opower__Suc,axiom, % 177.02/177.09 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_c] : hAPP(hAPP(c_Power_Opower_Opower(T_c,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_c,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_inj__Suc,axiom, % 177.02/177.09 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 177.02/177.09 % 177.02/177.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 177.02/177.09 ! [V_q,V_x,T_a] : % 177.02/177.09 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 177.02/177.09 ! [V_q,V_x,T_a] : % 177.02/177.09 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 177.02/177.09 ! [V_q,V_x,T_a] : % 177.02/177.09 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_power__Suc2,axiom, % 177.02/177.09 ! [V_n,V_a,T_a] : % 177.02/177.09 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.09 => 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) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_power__Suc,axiom, % 177.02/177.09 ! [V_n,V_a,T_a] : % 177.02/177.09 ( class_Power_Opower(T_a) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__add__Suc1,axiom, % 177.02/177.09 ! [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)))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__add__Suc2,axiom, % 177.02/177.09 ! [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)))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__iff__Suc__add,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.09 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__INF__iff,axiom, % 177.02/177.09 ! [V_M_2,V_A_2,T_d,V_u_2,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_M_2))) % 177.02/177.09 <=> ! [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__le__lessD,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__less__Suc__eq,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 177.02/177.09 <=> V_n_2 = V_m_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__leI,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_le__imp__less__Suc,axiom, % 177.02/177.09 ! [V_n,V_m] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__le__eq,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__Suc__eq__le,axiom, % 177.02/177.09 ! [V_n_2,V_m_2] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__eq__Suc__le,axiom, % 177.02/177.09 ! [V_m_2,V_n_2] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF__less__iff,axiom, % 177.02/177.09 ! [V_a_2,V_f_2,V_A_2,T_d,T_c] : % 177.02/177.09 ( ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 & class_Orderings_Olinorder(T_c) ) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_f_2)),V_a_2)) % 177.02/177.09 <=> ? [B_x] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.02/177.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__insert__distrib,axiom, % 177.02/177.09 ! [V_B_2,V_a_2,T_d,V_A_2,V_u_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_u_2),V_A_2)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_diff__less__Suc,axiom, % 177.02/177.09 ! [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))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__mult__less__cancel1,axiom, % 177.02/177.09 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.09 ( 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))) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__lower,axiom, % 177.02/177.09 ! [V_B_2,T_d,V_A_2,V_a_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF__INT__eq,axiom, % 177.02/177.09 ! [V_x_2,V_r_2,T_d,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2)) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_mult__Suc,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_mult__Suc__right,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__absorb,axiom, % 177.02/177.09 ! [V_A_2,T_d,V_I_2,V_k_2,T_c] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_member(T_c),V_k_2),V_I_2)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF__const,axiom, % 177.02/177.09 ! [V_M_2,T_c,V_A_2,T_d] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),hAPP(c_COMBK(T_d,T_c),V_M_2)) = V_M_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__diff__le,axiom, % 177.02/177.09 ! [V_m,V_n] : % 177.02/177.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.09 => 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)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Suc__mult__le__cancel1,axiom, % 177.02/177.09 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.09 ( 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))) % 177.02/177.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__constant,axiom, % 177.02/177.09 ! [V_c_2,T_d,T_c,V_A_2] : % 177.02/177.09 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.09 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = V_c_2 ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__empty,axiom, % 177.02/177.09 ! [V_B_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__extend__simps_I1_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__extend__simps_I2_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.09 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 177.02/177.09 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.09 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__insert,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_a_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INT__Un,axiom, % 177.02/177.09 ! [V_M_2,V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_diff__Suc__1,axiom, % 177.02/177.09 ! [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 ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__simps_I7_J,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_UN__extend__simps_I7_J,axiom, % 177.02/177.09 ! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inter__Un__subset,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Compl__UN,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,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)) = 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_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool))),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Compl__INT,axiom, % 177.02/177.09 ! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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_OSUPR(T_d,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_d),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool))),V_B_2)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inf__fin_Osingleton,axiom, % 177.02/177.09 ! [V_x_2,T_c] : % 177.02/177.09 ( class_Lattices_Olattice(T_c) % 177.02/177.09 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_less__eq__Suc__le__raw,axiom, % 177.02/177.09 ! [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)) ). % 177.02/177.09 % 177.02/177.09 fof(fact_Inf__lower,axiom, % 177.02/177.09 ! [V_A_2,V_x_2,T_c] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)),V_x_2)) ) ) ). % 177.02/177.09 % 177.02/177.09 fof(fact_INF__subset,axiom, % 177.02/177.09 ! [V_f_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.09 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__singleton,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.10 => c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2 ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__empty,axiom, % 177.02/177.10 ! [T_c] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.10 => c_Complete__Lattice_OInf__class_OInf(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_c) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__UNIV,axiom, % 177.02/177.10 ! [T_c] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.10 => c_Complete__Lattice_OInf__class_OInf(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_c) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__insert,axiom, % 177.02/177.10 ! [V_A_2,V_a_2,T_c] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.10 => c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INT__simps_I1_J,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.10 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.10 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INT__simps_I2_J,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.10 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.10 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__gt1,axiom, % 177.02/177.10 ! [V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.10 => 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)))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INT__extend__simps_I3_J,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.10 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))),V_B_2) ) % 177.02/177.10 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INT__simps_I3_J,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.10 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.10 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INT__extend__simps_I4_J,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.10 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 177.02/177.10 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__Suc__diff__eq1,axiom, % 177.02/177.10 ! [V_m,V_j,V_k] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.02/177.10 => 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)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__Suc__diff__eq2,axiom, % 177.02/177.10 ! [V_m,V_j,V_k] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 177.02/177.10 => 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)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INF__leI,axiom, % 177.02/177.10 ! [V_M_2,V_A_2,V_i_2,T_c,T_d] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_A_2)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_sup__Inf__absorb,axiom, % 177.02/177.10 ! [V_a_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = V_a_2 ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Oin__idem,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_OF__eq,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INT__simps_I4_J,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_d,T_c,V_C_2] : % 177.02/177.10 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) % 177.02/177.10 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__insert__if,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) % 177.02/177.10 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),V_A_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__insert__disjoint,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),V_A_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__binary,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.10 => c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),V_b_2) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_inf__Inf__fold__inf,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_c] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_B_2),V_A_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Oinsert__idem,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Osubset__idem,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Ounion__idem,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.10 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,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__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__le__Sup,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 177.02/177.10 ! [V_a_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_a_2),V_A_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_inf__INFI__fold__inf,axiom, % 177.02/177.10 ! [V_f_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Complete__Lattice_Ocomplete__lattice(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_d),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_d)),V_f_2)),V_B_2),V_A_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__insert,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),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)))))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Oinsert,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.10 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Oinsert__remove,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) % 177.02/177.10 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,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)))))) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Ounion__inter,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.10 => ( 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)) % 177.02/177.10 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.10 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => ( 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)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,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__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) ) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 177.02/177.10 ! [V_x_2,V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.10 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_x_2),V_A_2) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__Suc__eq__diff__pred,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Suc__eq__plus1__left,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Suc__eq__plus1,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Oclosed,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),V_A_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_finite__fun__UNIVD1,axiom, % 177.02/177.10 ! [T_d,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool)))) % 177.02/177.10 => ( hAPP(c_Finite__Set_Ocard(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.02/177.10 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inf__fin_Ohom__commute,axiom, % 177.02/177.10 ! [V_N_2,V_h_2,T_c] : % 177.02/177.10 ( class_Lattices_Olattice(T_c) % 177.02/177.10 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.10 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_c,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_less__zeroE,axiom, % 177.02/177.10 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_le0,axiom, % 177.02/177.10 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__Suc,axiom, % 177.02/177.10 ! [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))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inter__def,axiom, % 177.02/177.10 ! [V_S_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_c,tc_HOL_Obool))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INTER__eq__Inter__image,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_2)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Inter__image__eq,axiom, % 177.02/177.10 ! [V_A_2,V_B_2,T_d,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INF2__iff,axiom, % 177.02/177.10 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 177.02/177.10 <=> ! [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.10 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_INF1__iff,axiom, % 177.02/177.10 ! [V_b_2,V_B_2,V_A_2,T_d,T_c] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 177.02/177.10 <=> ! [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.10 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__reorient,axiom, % 177.02/177.10 ! [V_x_2,T_c] : % 177.02/177.10 ( class_Groups_Ozero(T_c) % 177.02/177.10 => ( c_Groups_Ozero__class_Ozero(T_c) = V_x_2 % 177.02/177.10 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_bot__nat__def,axiom, % 177.02/177.10 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__eq__0__iff,axiom, % 177.02/177.10 ! [V_n_2,V_a_2,T_c] : % 177.02/177.10 ( ( class_Power_Opower(T_c) % 177.02/177.10 & class_Rings_Omult__zero(T_c) % 177.02/177.10 & class_Rings_Ono__zero__divisors(T_c) % 177.02/177.10 & class_Rings_Ozero__neq__one(T_c) ) % 177.02/177.10 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__0__left,axiom, % 177.02/177.10 ! [V_n,T_a] : % 177.02/177.10 ( ( class_Power_Opower(T_a) % 177.02/177.10 & class_Rings_Osemiring__0(T_a) ) % 177.02/177.10 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => 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) ) % 177.02/177.10 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => 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) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__0__left,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Omonoid__add(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__0,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_double__zero__sym,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) % 177.02/177.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__0__right,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Omonoid__add(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add_Ocomm__neutral,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__0__iff,axiom, % 177.02/177.10 ! [V_a_2,V_b_2,T_c] : % 177.02/177.10 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c) % 177.02/177.10 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2) % 177.02/177.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__zero__left,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Omult__zero(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__zero__right,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Omult__zero(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__eq__0__iff,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Oring__no__zero__divisors(T_c) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 | V_b_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_no__zero__divisors,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Ono__zero__divisors(T_a) % 177.02/177.10 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.10 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_divisors__zero,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Ono__zero__divisors(T_a) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.10 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.10 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__0__right,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__self,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_a) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_eq__iff__diff__eq__0,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Oab__group__add(T_c) % 177.02/177.10 => ( V_a_2 = V_b_2 % 177.02/177.10 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_right__minus__eq,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_c) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 <=> V_a_2 = V_b_2 ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__neq__one,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Rings_Ozero__neq__one(T_a) % 177.02/177.10 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_one__neq__zero,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Rings_Ozero__neq__one(T_a) % 177.02/177.10 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__equal__zero,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = V_a_2 % 177.02/177.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__equal__0__iff__equal,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_c) % 177.02/177.10 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_equal__neg__zero,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) % 177.02/177.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__0__equal__iff__equal,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_c) % 177.02/177.10 => ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) % 177.02/177.10 <=> c_Groups_Ozero__class_Ozero(T_c) = V_a_2 ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_minus__zero,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_a) % 177.02/177.10 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Suc__neq__Zero,axiom, % 177.02/177.10 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Zero__neq__Suc,axiom, % 177.02/177.10 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat_Osimps_I3_J,axiom, % 177.02/177.10 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Suc__not__Zero,axiom, % 177.02/177.10 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat_Osimps_I2_J,axiom, % 177.02/177.10 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Zero__not__Suc,axiom, % 177.02/177.10 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__Suc__0,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 177.02/177.10 ! [V_m_2,V_x_2] : % 177.02/177.10 ( 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)) % 177.02/177.10 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_field__power__not__zero,axiom, % 177.02/177.10 ! [V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 177.02/177.10 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.10 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__zero__less__power__iff,axiom, % 177.02/177.10 ! [V_n_2,V_x_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 177.02/177.10 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__power__less__imp__less,axiom, % 177.02/177.10 ! [V_n,V_m,V_i] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 177.02/177.10 => ( 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))) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_not__less0,axiom, % 177.02/177.10 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neq0__conv,axiom, % 177.02/177.10 ! [V_n_2] : % 177.02/177.10 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_less__nat__zero__code,axiom, % 177.02/177.10 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_gr__implies__not0,axiom, % 177.02/177.10 ! [V_n,V_m] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.10 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_gr0I,axiom, % 177.02/177.10 ! [V_n] : % 177.02/177.10 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__eq__self__zero,axiom, % 177.02/177.10 ! [V_n,V_m] : % 177.02/177.10 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 177.02/177.10 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__is__0,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Nat_Oadd__0__right,axiom, % 177.02/177.10 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 177.02/177.10 % 177.02/177.10 fof(fact_plus__nat_Oadd__0,axiom, % 177.02/177.10 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 177.02/177.10 % 177.02/177.10 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 177.02/177.10 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_le__0__eq,axiom, % 177.02/177.10 ! [V_n_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 177.02/177.10 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__0__eq__0,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_minus__nat_Odiff__0,axiom, % 177.02/177.10 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__self__eq__0,axiom, % 177.02/177.10 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diffs0__imp__equal,axiom, % 177.02/177.10 ! [V_n,V_m] : % 177.02/177.10 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => V_m = V_n ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__mult__eq__cancel__disj,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.10 ( 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) % 177.02/177.10 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 | V_m_2 = V_n_2 ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__0,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__0__right,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__is__0,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__cancel1,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.10 ( 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) % 177.02/177.10 <=> ( V_m_2 = V_n_2 % 177.02/177.10 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__cancel2,axiom, % 177.02/177.10 ! [V_n_2,V_k_2,V_m_2] : % 177.02/177.10 ( 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) % 177.02/177.10 <=> ( V_m_2 = V_n_2 % 177.02/177.10 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_sum__squares__eq__zero__iff,axiom, % 177.02/177.10 ! [V_y_2,V_x_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 & V_y_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_min__0L,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_min__0R,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_max__0L,axiom, % 177.02/177.10 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 177.02/177.10 % 177.02/177.10 fof(fact_max__0R,axiom, % 177.02/177.10 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__eq__imp__eq__base,axiom, % 177.02/177.10 ! [V_b,V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( 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) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => V_a = V_b ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__0,axiom, % 177.02/177.10 ! [V_A_2,T_d,T_c] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power_Opower_Opower__0,axiom, % 177.02/177.10 ! [V_a_2,V_times_2,V_one_2,T_c] : hAPP(hAPP(c_Power_Opower_Opower(T_c,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__strict__mono,axiom, % 177.02/177.10 ! [V_n,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => 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))) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_sum__squares__le__zero__iff,axiom, % 177.02/177.10 ! [V_y_2,V_x_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 & V_y_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_sum__squares__ge__zero,axiom, % 177.02/177.10 ! [V_y,V_x,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__ring(T_a) % 177.02/177.10 => 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)))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_sum__squares__gt__zero__iff,axiom, % 177.02/177.10 ! [V_y_2,V_x_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2)))) % 177.02/177.10 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 | V_y_2 != c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_not__sum__squares__lt__zero,axiom, % 177.02/177.10 ! [V_y,V_x,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__ring(T_a) % 177.02/177.10 => ~ 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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__nonpos__nonpos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__increasing2,axiom, % 177.02/177.10 ! [V_a,V_b,V_c,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__increasing,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__nonneg__eq__0__iff,axiom, % 177.02/177.10 ! [V_y_2,V_x_2,T_c] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_x_2)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_y_2)) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 & V_y_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__nonneg__nonneg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__le__square,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__ring(T_a) % 177.02/177.10 => 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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__le__mult__iff,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2))) % 177.02/177.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2)) ) % 177.02/177.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__le__0__iff,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c))) ) % 177.02/177.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__nonneg__nonneg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__nonneg__nonpos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__nonneg__nonpos2,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__nonpos__nonneg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__nonpos__nonpos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__ring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__right__mono,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__left__mono,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_comm__mult__left__mono,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__comm__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__right__mono__neg,axiom, % 177.02/177.10 ! [V_c,V_a,V_b,T_a] : % 177.02/177.10 ( class_Rings_Oordered__ring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__left__mono__neg,axiom, % 177.02/177.10 ! [V_c,V_a,V_b,T_a] : % 177.02/177.10 ( class_Rings_Oordered__ring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__mono_H,axiom, % 177.02/177.10 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__mono,axiom, % 177.02/177.10 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__semiring(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_split__mult__pos__le,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__ring(T_a) % 177.02/177.10 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 177.02/177.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_split__mult__neg__le,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Oordered__cancel__semiring(T_a) % 177.02/177.10 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 177.02/177.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__pos__pos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__neg__neg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_pos__add__strict,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_not__square__less__zero,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__ring(T_a) % 177.02/177.10 => ~ 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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__cancel__right__disj,axiom, % 177.02/177.10 ! [V_b_2,V_c_2,V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2))) % 177.02/177.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) % 177.02/177.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__cancel__left__disj,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) % 177.02/177.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) % 177.02/177.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__cancel__left__pos,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__pos__pos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__pos__neg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__pos__neg2,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__mult__pos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__mult__pos2,axiom, % 177.02/177.10 ! [V_a,V_b,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__cancel__left__neg,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__neg__pos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__neg__neg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__strict__right__mono,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__strict__left__mono,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_comm__mult__strict__left__mono,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__strict__right__mono__neg,axiom, % 177.02/177.10 ! [V_c,V_a,V_b,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__strict__left__mono__neg,axiom, % 177.02/177.10 ! [V_c,V_a,V_b,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_le__iff__diff__le__0,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_less__iff__diff__less__0,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__scale__eq__noteq,axiom, % 177.02/177.10 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 177.02/177.10 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 177.02/177.10 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.10 => ( ( V_a = V_b % 177.02/177.10 & V_c != V_d ) % 177.02/177.10 => 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)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__le__one,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => 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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_not__one__le__zero,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ~ 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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__one,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_not__one__less__zero,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__0__le__iff__le,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_le__minus__self__iff,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__le__0__iff__le,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_minus__le__self__iff,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2)) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_less__minus__self__iff,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__0__less__iff__less,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__less__0__iff__less,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_neg__less__nonneg,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2)) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_minus__unique,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_a) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.10 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_ab__left__minus,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Oab__group__add(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_left__minus,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_eq__neg__iff__add__eq__0,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_c) % 177.02/177.10 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) % 177.02/177.10 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_right__minus,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__mono,axiom, % 177.02/177.10 ! [V_n,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__le__power,axiom, % 177.02/177.10 ! [V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__power,axiom, % 177.02/177.10 ! [V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__0,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Groups_Ogroup__add(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__empty,axiom, % 177.02/177.10 ! [V_f_2,T_d,T_c] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_c) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum_Oempty,axiom, % 177.02/177.10 ! [V_g_2,T_d,T_c] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_c) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum_Oinfinite,axiom, % 177.02/177.10 ! [V_g_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__infinite,axiom, % 177.02/177.10 ! [V_f_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__0__Suc,axiom, % 177.02/177.10 ! [V_n,T_a] : % 177.02/177.10 ( ( class_Power_Opower(T_a) % 177.02/177.10 & class_Rings_Osemiring__0(T_a) ) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setprod__zero__iff,axiom, % 177.02/177.10 ! [V_f_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( ( class_Rings_Ocomm__semiring__1(T_d) % 177.02/177.10 & class_Rings_Ono__zero__divisors(T_d) ) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) % 177.02/177.10 <=> ? [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.10 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setprod__zero,axiom, % 177.02/177.10 ! [V_f_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Rings_Ocomm__semiring__1(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( ? [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.10 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_gr0__conv__Suc,axiom, % 177.02/177.10 ! [V_n_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.02/177.10 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_less__Suc0,axiom, % 177.02/177.10 ! [V_n_2] : % 177.02/177.10 ( 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)))) % 177.02/177.10 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_less__Suc__eq__0__disj,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.02/177.10 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 | ? [B_j] : % 177.02/177.10 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_one__is__add,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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) % 177.02/177.10 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.02/177.10 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.10 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__is__1,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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)) % 177.02/177.10 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.02/177.10 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.10 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__gr__0,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 177.02/177.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__one__le__power,axiom, % 177.02/177.10 ! [V_n,V_i] : % 177.02/177.10 ( 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)) % 177.02/177.10 => 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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__0,axiom, % 177.02/177.10 ! [V_a,T_a] : % 177.02/177.10 ( class_Power_Opower(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 177.02/177.10 ! [V_x,T_a] : % 177.02/177.10 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.10 => 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) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card_Oempty,axiom, % 177.02/177.10 ! [T_c] : hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__infinite,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__eq__1__iff,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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)) % 177.02/177.10 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.02/177.10 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__diff,axiom, % 177.02/177.10 ! [V_m_2,V_n_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__less,axiom, % 177.02/177.10 ! [V_m,V_n] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.02/177.10 => 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)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__0__less__mult__iff,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__cancel1,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__cancel2,axiom, % 177.02/177.10 ! [V_n_2,V_k_2,V_m_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.02/177.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__mono1,axiom, % 177.02/177.10 ! [V_k,V_j,V_i] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__mono2,axiom, % 177.02/177.10 ! [V_k,V_j,V_i] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__mult__less__cancel1,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.02/177.10 => ( 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))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__mult__eq__cancel1,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.02/177.10 => ( 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) % 177.02/177.10 <=> V_m_2 = V_n_2 ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__add__0,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__eq__if,axiom, % 177.02/177.10 ! [V_p,V_m] : % 177.02/177.10 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 177.02/177.10 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => 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)))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__is__0__eq_H,axiom, % 177.02/177.10 ! [V_n,V_m] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__is__0__eq,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_One__nat__def,axiom, % 177.02/177.10 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__eq__self__implies__10,axiom, % 177.02/177.10 ! [V_n,V_m] : % 177.02/177.10 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 177.02/177.10 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.02/177.10 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__eq__0__iff,axiom, % 177.02/177.10 ! [V_f_2,V_F_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) % 177.02/177.10 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 <=> ! [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_F_2)) % 177.02/177.10 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Suc__pred_H,axiom, % 177.02/177.10 ! [V_n] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => 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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__eq__if,axiom, % 177.02/177.10 ! [V_n,V_m] : % 177.02/177.10 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 177.02/177.10 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => 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)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__nonpos__neg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__neg__nonpos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__strict__increasing2,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__strict__increasing,axiom, % 177.02/177.10 ! [V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__nonneg__pos,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_add__pos__nonneg,axiom, % 177.02/177.10 ! [V_b,V_a,T_a] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__le__cancel__left__pos,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__le__cancel__left__neg,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__ring__strict(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__strict__mono,axiom, % 177.02/177.10 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__strict__mono_H,axiom, % 177.02/177.10 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__le__imp__less,axiom, % 177.02/177.10 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__le__less__imp__less,axiom, % 177.02/177.10 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => 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))) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__right__less__imp__less,axiom, % 177.02/177.10 ! [V_b,V_c,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__imp__less__right,axiom, % 177.02/177.10 ! [V_b,V_c,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__left__less__imp__less,axiom, % 177.02/177.10 ! [V_b,V_a,V_c,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__less__imp__less__left,axiom, % 177.02/177.10 ! [V_b,V_a,V_c,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__right__le__imp__le,axiom, % 177.02/177.10 ! [V_b,V_c,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__left__le__imp__le,axiom, % 177.02/177.10 ! [V_b,V_a,V_c,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__strict(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__eq__if,axiom, % 177.02/177.10 ! [V_n,V_m] : % 177.02/177.10 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.10 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => 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)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__right__le__one__le,axiom, % 177.02/177.10 ! [V_y,V_x,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 177.02/177.10 => 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)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__left__le__one__le,axiom, % 177.02/177.10 ! [V_y,V_x,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 177.02/177.10 => 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)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zero__less__two,axiom, % 177.02/177.10 ! [T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => 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)))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__less__imp__less__base,axiom, % 177.02/177.10 ! [V_b,V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( 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))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__le__imp__le__base,axiom, % 177.02/177.10 ! [V_b,V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( 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)))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__inject__base,axiom, % 177.02/177.10 ! [V_b,V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( 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)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.10 => V_a = V_b ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__eq__0__iff,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__ge__0__finite,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( 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_c),V_A_2))) % 177.02/177.10 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_diff__Suc__less,axiom, % 177.02/177.10 ! [V_i,V_n] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => 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)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Suc__pred,axiom, % 177.02/177.10 ! [V_n] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => 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 ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_n__less__m__mult__n,axiom, % 177.02/177.10 ! [V_m,V_n] : % 177.02/177.10 ( 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)) % 177.02/177.10 => ( 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)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_n__less__n__mult__m,axiom, % 177.02/177.10 ! [V_m,V_n] : % 177.02/177.10 ( 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)) % 177.02/177.10 => ( 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)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_one__less__mult,axiom, % 177.02/177.10 ! [V_m,V_n] : % 177.02/177.10 ( 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)) % 177.02/177.10 => ( 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)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__diff__split__asm,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_Pa_2] : % 177.02/177.10 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 177.02/177.10 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.02/177.10 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.02/177.10 | ? [B_d] : % 177.02/177.10 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 177.02/177.10 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__diff__split,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_Pa_2] : % 177.02/177.10 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 177.02/177.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.02/177.10 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.02/177.10 & ! [B_d] : % 177.02/177.10 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 177.02/177.10 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_one__le__mult__iff,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( 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)) % 177.02/177.10 & 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)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__le__cancel1,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_mult__le__cancel2,axiom, % 177.02/177.10 ! [V_n_2,V_k_2,V_m_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_nat__mult__le__cancel1,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,V_k_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.02/177.10 => ( 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))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__eq__Suc0__iff,axiom, % 177.02/177.10 ! [V_f_2,V_A_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.02/177.10 <=> ? [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.10 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.02/177.10 & ! [B_xa] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_A_2)) % 177.02/177.10 => ( B_x != B_xa % 177.02/177.10 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__eq__1__iff,axiom, % 177.02/177.10 ! [V_f_2,V_A_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.02/177.10 <=> ? [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.10 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 177.02/177.10 & ! [B_xa] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_A_2)) % 177.02/177.10 => ( B_x != B_xa % 177.02/177.10 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__delta,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_S_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.10 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 177.02/177.10 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__delta_H,axiom, % 177.02/177.10 ! [V_b_2,V_a_2,V_S_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.10 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 177.02/177.10 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setprod__pos__nat__iff,axiom, % 177.02/177.10 ! [V_f_2,V_S_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.10 => ( 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_c,tc_Nat_Onat),V_f_2),V_S_2))) % 177.02/177.10 <=> ! [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_convex__bound__le,axiom, % 177.02/177.10 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__1(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 177.02/177.10 => 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)) ) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__Suc__less,axiom, % 177.02/177.10 ! [V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__Suc__less__one,axiom, % 177.02/177.10 ! [V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__strict__decreasing,axiom, % 177.02/177.10 ! [V_a,V_N,V_n,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.02/177.10 => 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))) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_power__decreasing,axiom, % 177.02/177.10 ! [V_a,V_N,V_n,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 177.02/177.10 => 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))) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_one__less__power,axiom, % 177.02/177.10 ! [V_n,V_a,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => 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))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__gt__0__iff,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( 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_c),V_A_2))) % 177.02/177.10 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.10 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_finite__UNIV__card__ge__0,axiom, % 177.02/177.10 ! [T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.10 => 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_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum_Oeq__fold,axiom, % 177.02/177.10 ! [V_g_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Oplus__class_Oplus(T_d)),V_g_2),c_Groups_Ozero__class_Ozero(T_d)),V_A_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum_OF__eq,axiom, % 177.02/177.10 ! [V_g_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Oplus__class_Oplus(T_d)),V_g_2),c_Groups_Ozero__class_Ozero(T_d)),V_A_2) ) % 177.02/177.10 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Suc__diff__1,axiom, % 177.02/177.10 ! [V_n] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.10 => 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 ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__restrict__set,axiom, % 177.02/177.10 ! [V_B_2,V_f_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_d))),V_A_2) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__def,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_c,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_c),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 177.02/177.10 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card_Oeq__fold__g,axiom, % 177.02/177.10 ! [V_A_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_c,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_c),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_convex__bound__lt,axiom, % 177.02/177.10 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 177.02/177.10 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 177.02/177.10 => 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)) ) ) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_triple_Osize_I1_J,axiom, % 177.02/177.10 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_c,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_even__less__0__iff,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_triple_Osize_I2_J,axiom, % 177.02/177.10 ! [V_fun2_2,V_com_2,V_fun1_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card_Ounion__inter__neutral,axiom, % 177.02/177.10 ! [V_B_2,V_A_2,T_c] : % 177.02/177.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.10 => ( ( ? [B_x] : 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))) % 177.02/177.10 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.10 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__mono2,axiom, % 177.02/177.10 ! [V_f_2,V_A_2,V_B_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Oordered__comm__monoid__add(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.10 => ( ! [B_b] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_b))) ) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2))) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_arith__series__nat,axiom, % 177.02/177.10 ! [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)))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_finite__lessThan,axiom, % 177.02/177.10 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_lessThan__eq__iff,axiom, % 177.02/177.10 ! [V_y_2,V_x_2,T_c] : % 177.02/177.10 ( class_Orderings_Olinorder(T_c) % 177.02/177.10 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2) % 177.02/177.10 <=> V_x_2 = V_y_2 ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__lessThan,axiom, % 177.02/177.10 ! [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 ). % 177.02/177.10 % 177.02/177.10 fof(fact_lessThan__0,axiom, % 177.02/177.10 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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_lessThan__Suc,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_UN__lessThan__UNIV,axiom, % 177.02/177.10 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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 177.02/177.10 ! [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))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__lessThan__Suc,axiom, % 177.02/177.10 ! [V_n_2,V_f_2,T_c] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_lessThan__iff,axiom, % 177.02/177.10 ! [V_k_2,V_i_2,T_c] : % 177.02/177.10 ( class_Orderings_Oord(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_i_2),V_k_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_lessThan__subset__iff,axiom, % 177.02/177.10 ! [V_y_2,V_x_2,T_c] : % 177.02/177.10 ( class_Orderings_Olinorder(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_lessThan__strict__subset__iff,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,T_c] : % 177.02/177.10 ( class_Orderings_Olinorder(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_n_2))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_n_2)) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zpower__zadd__distrib,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zpower__zpower,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_single__Diff__lessThan,axiom, % 177.02/177.10 ! [V_k_2,T_c] : % 177.02/177.10 ( class_Orderings_Oorder(T_c) % 177.02/177.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_double__eq__0__iff,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Groups_Olinordered__ab__group__add(T_c) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_arith__series__general,axiom, % 177.02/177.10 ! [V_n_2,V_d_2,V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Ocomm__semiring__1(T_c) % 177.02/177.10 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_c)),c_Nat_Osemiring__1__class_Oof__nat(T_c))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__Un__zero,axiom, % 177.02/177.10 ! [V_f_2,V_T_2,V_S_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 177.02/177.10 => ( ! [B_x] : % 177.02/177.10 ( 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_S_2),V_T_2))) % 177.02/177.10 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum_Ounion__inter__neutral,axiom, % 177.02/177.10 ! [V_g_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.10 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.10 => ( ! [B_x] : % 177.02/177.10 ( 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))) % 177.02/177.10 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) % 177.02/177.10 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_card__Suc__eq,axiom, % 177.02/177.10 ! [V_k_2,V_A_2,T_c] : % 177.02/177.10 ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 177.02/177.10 <=> ? [B_b,B_B] : % 177.02/177.10 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_c),B_b),B_B) % 177.02/177.10 & ~ hBOOL(hAPP(hAPP(c_member(T_c),B_b),B_B)) % 177.02/177.10 & hAPP(c_Finite__Set_Ocard(T_c),B_B) = V_k_2 % 177.02/177.10 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_setsum__mono3,axiom, % 177.02/177.10 ! [V_f_2,V_A_2,V_B_2,T_c,T_d] : % 177.02/177.10 ( ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.10 & class_Groups_Oordered__ab__semigroup__add(T_d) ) % 177.02/177.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.10 => ( ! [B_x] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_x))) ) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2))) ) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Ints__odd__less__0,axiom, % 177.02/177.10 ! [V_a_2,T_c] : % 177.02/177.10 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_negative__zless,axiom, % 177.02/177.10 ! [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))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_pos__zmult__eq__1__iff,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 177.02/177.10 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.02/177.10 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.02/177.10 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__zless__mono2,axiom, % 177.02/177.10 ! [V_k,V_j,V_i] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_Ints__of__nat,axiom, % 177.02/177.10 ! [V_n_2,T_c] : % 177.02/177.10 ( class_Rings_Oring__1(T_c) % 177.02/177.10 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Int_Oring__1__class_OInts(T_c))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__zminus,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__assoc,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__commute,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zdiff__zmult__distrib2,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zdiff__zmult__distrib,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zadd__zmult__distrib,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zadd__zmult__distrib2,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__1,axiom, % 177.02/177.10 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__1__right,axiom, % 177.02/177.10 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 177.02/177.10 % 177.02/177.10 fof(fact_of__nat__eq__iff,axiom, % 177.02/177.10 ! [V_n_2,V_m_2,T_c] : % 177.02/177.10 ( class_Nat_Osemiring__char__0(T_c) % 177.02/177.10 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2) % 177.02/177.10 <=> V_m_2 = V_n_2 ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__zle__neg,axiom, % 177.02/177.10 ! [V_m_2,V_n_2] : % 177.02/177.10 ( 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)))) % 177.02/177.10 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__le__0__conv,axiom, % 177.02/177.10 ! [V_n_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__eq__0__conv,axiom, % 177.02/177.10 ! [V_n_2] : % 177.02/177.10 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.10 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__0,axiom, % 177.02/177.10 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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_negative__eq__positive,axiom, % 177.02/177.10 ! [V_m_2,V_n_2] : % 177.02/177.10 ( 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) % 177.02/177.10 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.10 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zless__iff__Suc__zadd,axiom, % 177.02/177.10 ! [V_z_2,V_w_2] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 177.02/177.10 <=> ? [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))) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__Suc,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_negative__zless__0,axiom, % 177.02/177.10 ! [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))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_not__zle__0__negative,axiom, % 177.02/177.10 ! [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))))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zless__int,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zadd__int,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zadd__int__left,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zle__int,axiom, % 177.02/177.10 ! [V_n_2,V_m_2] : % 177.02/177.10 ( 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))) % 177.02/177.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__mult,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__int,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__1,axiom, % 177.02/177.10 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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_inj__int,axiom, % 177.02/177.10 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))) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zpower__int,axiom, % 177.02/177.10 ! [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)) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__power,axiom, % 177.02/177.10 ! [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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__setsum,axiom, % 177.02/177.10 ! [V_A_2,V_f_2,T_c] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__setprod,axiom, % 177.02/177.10 ! [V_A_2,V_f_2,T_c] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 177.02/177.10 % 177.02/177.10 fof(fact_int__Suc0__eq__1,axiom, % 177.02/177.10 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) ). % 177.02/177.10 % 177.02/177.10 fof(fact_zmult__zless__mono2__lemma,axiom, % 177.02/177.10 ! [V_k,V_j,V_i] : % 177.02/177.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 177.02/177.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.02/177.10 => 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))) ) ) ). % 177.02/177.10 % 177.02/177.11 fof(fact_zero__less__int__conv,axiom, % 177.02/177.11 ! [V_n_2] : % 177.02/177.11 ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__0__le__iff,axiom, % 177.02/177.11 ! [V_n,T_a] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zero__le__imp__of__nat,axiom, % 177.02/177.11 ! [V_m,T_a] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiff__int,axiom, % 177.02/177.11 ! [V_m,V_n] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__less__0__iff,axiom, % 177.02/177.11 ! [V_m,T_a] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.11 => ~ 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__0,axiom, % 177.02/177.11 ! [T_a] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__less__imp__less,axiom, % 177.02/177.11 ! [V_n,V_m,T_a] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.11 => ( 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))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_less__imp__of__nat__less,axiom, % 177.02/177.11 ! [V_n,V_m,T_a] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__less__iff,axiom, % 177.02/177.11 ! [V_n_2,V_m_2,T_c] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__le__iff,axiom, % 177.02/177.11 ! [V_n_2,V_m_2,T_c] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__add,axiom, % 177.02/177.11 ! [V_n,V_m,T_a] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__mult,axiom, % 177.02/177.11 ! [V_n,V_m,T_a] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__1,axiom, % 177.02/177.11 ! [T_a] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__power,axiom, % 177.02/177.11 ! [V_n,V_m,T_a] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__setsum,axiom, % 177.02/177.11 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_c) % 177.02/177.11 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,T_d),c_Nat_Osemiring__1__class_Oof__nat(T_c)),V_f_2)),V_A_2) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_inj__of__nat,axiom, % 177.02/177.11 ! [T_c] : % 177.02/177.11 ( class_Nat_Osemiring__char__0(T_c) % 177.02/177.11 => c_Fun_Oinj__on(tc_Nat_Onat,T_c,c_Nat_Osemiring__1__class_Oof__nat(T_c),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__0,axiom, % 177.02/177.11 ! [T_c] : % 177.02/177.11 ( class_Rings_Oring__1(T_c) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Int_Oring__1__class_OInts(T_c))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__add,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Rings_Oring__1(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__mult,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Rings_Oring__1(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__diff,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Rings_Oring__1(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__1,axiom, % 177.02/177.11 ! [T_c] : % 177.02/177.11 ( class_Rings_Oring__1(T_c) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Oone__class_Oone(T_c)),c_Int_Oring__1__class_OInts(T_c))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__minus,axiom, % 177.02/177.11 ! [V_a_2,T_c] : % 177.02/177.11 ( class_Rings_Oring__1(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__power,axiom, % 177.02/177.11 ! [V_n_2,V_a_2,T_c] : % 177.02/177.11 ( class_Rings_Oring__1(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__setprod,axiom, % 177.02/177.11 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.11 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 177.02/177.11 & class_Rings_Osemiring__1(T_c) ) % 177.02/177.11 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,T_d),c_Nat_Osemiring__1__class_Oof__nat(T_c)),V_f_2)),V_A_2) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__Suc,axiom, % 177.02/177.11 ! [V_m,T_a] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__diff,axiom, % 177.02/177.11 ! [V_m,V_n,T_a] : % 177.02/177.11 ( class_Rings_Oring__1(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__constant,axiom, % 177.02/177.11 ! [V_A_2,V_y_2,T_d,T_c] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_c) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(c_COMBK(T_c,T_d),V_y_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_d),V_A_2))),V_y_2) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__0__less__iff,axiom, % 177.02/177.11 ! [V_n_2,T_c] : % 177.02/177.11 ( class_Rings_Olinordered__semidom(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__double__eq__0__iff,axiom, % 177.02/177.11 ! [V_a_2,T_c] : % 177.02/177.11 ( class_Int_Oring__char__0(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.11 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Ints__odd__nonzero,axiom, % 177.02/177.11 ! [V_a_2,T_c] : % 177.02/177.11 ( class_Int_Oring__char__0(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c))) % 177.02/177.11 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 177.02/177.11 ! [V_n_2,T_c] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_c) % 177.02/177.11 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_Groups_Oone__class_Oone(T_c)),V_n_2,c_Groups_Ozero__class_Ozero(T_c)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiff__int__split,axiom, % 177.02/177.11 ! [V_y_2,V_x_2,V_Pa_2] : % 177.02/177.11 ( 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)))) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 177.02/177.11 => 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)))) ) % 177.02/177.11 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__bounded,axiom, % 177.02/177.11 ! [V_K_2,V_f_2,V_A_2,T_c,T_d] : % 177.02/177.11 ( ( class_Groups_Oordered__ab__semigroup__add(T_d) % 177.02/177.11 & class_Rings_Osemiring__1(T_d) ) % 177.02/177.11 => ( ! [B_i] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_A_2)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_i)),V_K_2)) ) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_d),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_K_2))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 177.02/177.11 ! [V_x_2,V_y_2,V_c_2] : % 177.02/177.11 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 177.02/177.11 => 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_c_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_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 177.02/177.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 177.02/177.11 => 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_c_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))) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 177.02/177.11 => 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_c_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)) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__atLeastLessThan,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_negative__zle,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__less__0__conv,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zle__iff__zadd,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 177.02/177.11 <=> ? [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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 177.02/177.11 ! [V_Pa_2] : % 177.02/177.11 ( ! [B_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.02/177.11 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 177.02/177.11 ! [V_Pa_2] : % 177.02/177.11 ( ? [B_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.02/177.11 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.02/177.11 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zero__zle__int,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_negative__zle__0,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__int__eq,axiom, % 177.02/177.11 ! [V_n_2,V_m_2] : % 177.02/177.11 ( 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) % 177.02/177.11 <=> V_m_2 = V_n_2 ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_not__int__zless__negative,axiom, % 177.02/177.11 ! [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)))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 177.02/177.11 ! [V_y_2,V_x_2] : % 177.02/177.11 ( 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) % 177.02/177.11 <=> V_x_2 = V_y_2 ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 177.02/177.11 ! [V_B_2,V_A_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.11 <=> 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 177.02/177.11 ! [V_A_2,V_x_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 177.02/177.11 <=> 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 177.02/177.11 ! [V_B_2,V_A_2] : % 177.02/177.11 ( V_A_2 = V_B_2 % 177.02/177.11 <=> 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 177.02/177.11 ! [V_B_2,V_A_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.11 <=> 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zless__add1__eq,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( 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)))) % 177.02/177.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 177.02/177.11 | V_w_2 = V_z_2 ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zless__linear,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 177.02/177.11 | V_x = V_y % 177.02/177.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zminus__zminus,axiom, % 177.02/177.11 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__commute,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__left__commute,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__assoc,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_diff__int__def,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_diff__int__def__symmetric,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zminus__zadd__distrib,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__strict__right__mono,axiom, % 177.02/177.11 ! [V_k,V_j,V_i] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__zless__mono,axiom, % 177.02/177.11 ! [V_z,V_z_H,V_w,V_w_H] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zless__le,axiom, % 177.02/177.11 ! [V_w_2,V_z_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 177.02/177.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 177.02/177.11 & V_z_2 != V_w_2 ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__zminus__inverse2,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 177.02/177.11 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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zle__refl,axiom, % 177.02/177.11 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zle__linear,axiom, % 177.02/177.11 ! [V_w,V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 177.02/177.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__left__mono,axiom, % 177.02/177.11 ! [V_k,V_j,V_i] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zle__trans,axiom, % 177.02/177.11 ! [V_k,V_j,V_i] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zle__antisym,axiom, % 177.02/177.11 ! [V_w,V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 177.02/177.11 => V_z = V_w ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__0__right,axiom, % 177.02/177.11 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 177.02/177.11 % 177.02/177.11 fof(fact_zadd__0,axiom, % 177.02/177.11 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 177.02/177.11 % 177.02/177.11 fof(fact_zminus__0,axiom, % 177.02/177.11 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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_less__bin__lemma,axiom, % 177.02/177.11 ! [V_l_2,V_k_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 177.02/177.11 <=> 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__0__neq__1,axiom, % 177.02/177.11 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 177.02/177.11 % 177.02/177.11 fof(fact_odd__nonzero,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 177.02/177.11 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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zle__diff1__eq,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( 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)))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__one__le__iff__zero__less,axiom, % 177.02/177.11 ! [V_z_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zle__add1__eq__le,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( 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)))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_add1__zle__eq,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( 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)) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_le__imp__0__less,axiom, % 177.02/177.11 ! [V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zless__imp__add1__zle,axiom, % 177.02/177.11 ! [V_z,V_w] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_odd__less__0,axiom, % 177.02/177.11 ! [V_z_2] : % 177.02/177.11 ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__0__less__1,axiom, % 177.02/177.11 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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 177.02/177.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2)) % 177.02/177.11 => V_b_2 = V_d_2 ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 177.02/177.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2)) % 177.02/177.11 => V_a_2 = V_c_2 ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__eq__iff,axiom, % 177.02/177.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2)) % 177.02/177.11 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2) % 177.02/177.11 <=> ( V_a_2 = V_c_2 % 177.02/177.11 & V_b_2 = V_d_2 ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__add__Un,axiom, % 177.02/177.11 ! [V_k_2,V_j_2,V_i_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan0,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeast0LessThan,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_subset__card__intvl__is__intvl,axiom, % 177.02/177.11 ! [V_k_2,V_A_2] : % 177.02/177.11 ( 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))))) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__atLeastLessThan,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__Suc__atLeastLessThan,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__empty,axiom, % 177.02/177.11 ! [V_a_2,V_b_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2)) % 177.02/177.11 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__empty__iff,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.11 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__empty__iff2,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) % 177.02/177.11 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__subset__iff,axiom, % 177.02/177.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2)) % 177.02/177.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2)) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 177.02/177.11 ! [V_n_2,V_m_2,V_f_2,T_c] : % 177.02/177.11 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__un_I17_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2)) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 177.02/177.11 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_c] : % 177.02/177.11 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__diff,axiom, % 177.02/177.11 ! [V_m_2,V_n_2,V_i_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_i_2),V_n_2)) % 177.02/177.11 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_n_2),V_m_2) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__int_I11_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__add__atLeastLessThan,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__add__nat__ivl,axiom, % 177.02/177.11 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_c] : % 177.02/177.11 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 177.02/177.11 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__diff__nat__ivl,axiom, % 177.02/177.11 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_c] : % 177.02/177.11 ( class_Groups_Oab__group__add(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 177.02/177.11 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 177.02/177.11 ! [V_i_2,V_inc_2,T_c] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_c) % 177.02/177.11 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 177.02/177.11 ! [V_i_2,V_n_2,V_inc_2,T_c] : % 177.02/177.11 ( class_Rings_Osemiring__1(T_c) % 177.02/177.11 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 177.02/177.11 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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThan__singleton,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 177.02/177.11 ! [V_y_2,V_x_2] : % 177.02/177.11 ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 177.02/177.11 ! [V_y_2,V_x_2] : % 177.02/177.11 ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_UN__UN__finite__eq,axiom, % 177.02/177.11 ! [V_A_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),tc_fun(T_c,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_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 177.02/177.11 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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Int__atLeastLessThan,axiom, % 177.02/177.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__un_I8_J,axiom, % 177.02/177.11 ! [V_u_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__int_I2_J,axiom, % 177.02/177.11 ! [V_u_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 177.02/177.11 ! [V_k_2,V_f_2,T_c] : % 177.02/177.11 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__head__upt__Suc,axiom, % 177.02/177.11 ! [V_f_2,V_n_2,V_m_2,T_c] : % 177.02/177.11 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 177.02/177.11 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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 177.02/177.11 ! [V_n,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastLessThanSuc,axiom, % 177.02/177.11 ! [V_n_2,V_m_2] : % 177.02/177.11 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.11 => 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)) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 177.02/177.11 ! [V_A_2] : % 177.02/177.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 177.02/177.11 <=> 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__op__ivl__Suc,axiom, % 177.02/177.11 ! [V_f_2,V_m_2,V_n_2,T_c] : % 177.02/177.11 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_self__quotient__aux2,axiom, % 177.02/177.11 ! [V_q,V_r,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.11 => ( 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)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_self__quotient__aux1,axiom, % 177.02/177.11 ! [V_q,V_r,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.11 => ( 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)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_q__pos__lemma,axiom, % 177.02/177.11 ! [V_r_H,V_q_H,V_b_H] : % 177.02/177.11 ( 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))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_q__neg__lemma,axiom, % 177.02/177.11 ! [V_r_H,V_q_H,V_b_H] : % 177.02/177.11 ( 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))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_unique__quotient__lemma,axiom, % 177.02/177.11 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 177.02/177.11 ( 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))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__mono2__lemma,axiom, % 177.02/177.11 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 177.02/177.11 ( 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) % 177.02/177.11 => ( 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))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__atLeastLessThan__int,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_infinite__UNIV__int,axiom, % 177.02/177.11 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__add__int__atLeastLessThan,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__mono2__neg__lemma,axiom, % 177.02/177.11 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 177.02/177.11 ( 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) % 177.02/177.11 => ( 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))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_unique__quotient__lemma__neg,axiom, % 177.02/177.11 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 177.02/177.11 ( 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))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_all__nat__less__eq,axiom, % 177.02/177.11 ! [V_Pa_2,V_n_2] : % 177.02/177.11 ( ! [B_m] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 177.02/177.11 <=> ! [B_x] : % 177.02/177.11 ( 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))) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ex__nat__less__eq,axiom, % 177.02/177.11 ! [V_Pa_2,V_n_2] : % 177.02/177.11 ( ? [B_m] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 177.02/177.11 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 177.02/177.11 <=> ? [B_x] : % 177.02/177.11 ( 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))) % 177.02/177.11 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_UN__finite2__subset,axiom, % 177.02/177.11 ! [V_B_2,V_k_2,V_A_2,T_c] : % 177.02/177.11 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_UN__finite2__eq,axiom, % 177.02/177.11 ! [V_B_2,V_k_2,V_A_2,T_c] : % 177.02/177.11 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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) % 177.02/177.11 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_UN__finite__subset,axiom, % 177.02/177.11 ! [V_C_2,V_A_2,T_c] : % 177.02/177.11 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_tsub__def,axiom, % 177.02/177.11 ! [V_x,V_y] : % 177.02/177.11 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 177.02/177.11 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 177.02/177.11 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__un_I3_J,axiom, % 177.02/177.11 ! [V_u_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2)) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__power__div__base,axiom, % 177.02/177.11 ! [V_k,V_m] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.02/177.11 => 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)))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__INT,axiom, % 177.02/177.11 ! [V_j_2,V_B_2,V_A_2,T_e,V_C_2,V_f_2,T_d,T_c] : % 177.02/177.11 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2) % 177.02/177.11 => ( ! [B_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_member(T_e),B_x),V_A_2)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_e),V_j_2),V_A_2)) % 177.02/177.11 => hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_e),c_Set_Oimage(T_c,T_d,V_f_2)),V_B_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_com_Osize_I4_J,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__greaterThanLessThan,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__greaterThanLessThan__int,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__zero,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__zminus__zminus,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__zminus2,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__by__0,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__0,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__by__1,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__neg__pos__less0,axiom, % 177.02/177.11 ! [V_b,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 177.02/177.11 ! [V_a_2,V_b_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 177.02/177.11 ! [V_a_2,V_b_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__self,axiom, % 177.02/177.11 ! [V_a] : % 177.02/177.11 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__mult1__if,axiom, % 177.02/177.11 ! [V_b,V_a,V_c,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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) ) % 177.02/177.11 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__self2__is__id,axiom, % 177.02/177.11 ! [V_a,V_b,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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 ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__self1__is__id,axiom, % 177.02/177.11 ! [V_a,V_b,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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 ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__mult2,axiom, % 177.02/177.11 ! [V_b,V_a,V_c,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__mult1,axiom, % 177.02/177.11 ! [V_b,V_a,V_c,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__self,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_greaterThanLessThan__empty,axiom, % 177.02/177.11 ! [V_k_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_k_2)) % 177.02/177.11 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__eq__0__iff,axiom, % 177.02/177.11 ! [V_k_2,V_i_2] : % 177.02/177.11 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.11 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 177.02/177.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 177.02/177.11 ! [V_a_2,V_b_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 177.02/177.11 ! [V_i_2,V_k_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.02/177.11 => ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 177.02/177.11 ! [V_b_2,V_a_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 177.02/177.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__mono2,axiom, % 177.02/177.11 ! [V_b,V_b_H,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__nonneg__neg__le0,axiom, % 177.02/177.11 ! [V_b,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__pos__pos__trivial,axiom, % 177.02/177.11 ! [V_b,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 177.02/177.11 ! [V_a_2,V_b_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__nonpos__pos__le0,axiom, % 177.02/177.11 ! [V_b,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__mono2__neg,axiom, % 177.02/177.11 ! [V_b,V_b_H,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__neg__neg__trivial,axiom, % 177.02/177.11 ! [V_b,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__mono1,axiom, % 177.02/177.11 ! [V_b,V_a_H,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__mono1__neg,axiom, % 177.02/177.11 ! [V_b,V_a_H,V_a] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__uminus__greaterThanLessThan,axiom, % 177.02/177.11 ! [V_y_2,V_x_2,T_c] : % 177.02/177.11 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.11 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__div__less__self,axiom, % 177.02/177.11 ! [V_k,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__zmult2__eq,axiom, % 177.02/177.11 ! [V_b,V_a,V_c] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__self2,axiom, % 177.02/177.11 ! [V_c,V_a,V_b,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__self1,axiom, % 177.02/177.11 ! [V_c,V_a,V_b,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__add__self2,axiom, % 177.02/177.11 ! [V_a,V_b,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__add__self1,axiom, % 177.02/177.11 ! [V_a,V_b,T_a] : % 177.02/177.11 ( class_Divides_Osemiring__div(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_com_Osize_I1_J,axiom, % 177.02/177.11 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__int_I9_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Int__greaterThanLessThan,axiom, % 177.02/177.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__greaterThanLessThan,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_split__zdiv,axiom, % 177.02/177.11 ! [V_k_2,V_n_2,V_Pa_2] : % 177.02/177.11 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 177.02/177.11 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.02/177.11 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.02/177.11 => ! [B_i] : % 177.02/177.11 ( ? [B_j] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 177.02/177.11 & 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) ) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 177.02/177.11 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => ! [B_i] : % 177.02/177.11 ( ? [B_j] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 & 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) ) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divmod__int__rel__div__eq,axiom, % 177.02/177.11 ! [V_r_1,V_y,V_b_1,V_a_1] : % 177.02/177.11 ( 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) % 177.02/177.11 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 177.02/177.11 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_tsub__eq,axiom, % 177.02/177.11 ! [V_x,V_y] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 177.02/177.11 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__un_I15_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_m_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2)) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_com_Osize_I6_J,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_z3div__def,axiom, % 177.02/177.11 ! [V_k,V_l] : % 177.02/177.11 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.02/177.11 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__un_I4_J,axiom, % 177.02/177.11 ! [V_u_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2)) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Powp__mono,axiom, % 177.02/177.11 ! [V_B_2,V_A_2,T_c] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_c,V_A_2)),c_Predicate_OPowp(T_c,V_B_2))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__Plus__conv__if,axiom, % 177.02/177.11 ! [V_B_2,T_d,V_A_2,T_c] : % 177.02/177.11 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.11 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) % 177.02/177.11 => hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2)) ) % 177.02/177.11 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.11 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) % 177.02/177.11 => hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_com_Osize_I12_J,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__greaterThanAtMost,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__greaterThanAtMost__int,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult2__eq,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__le__dividend,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__le__mono,axiom, % 177.02/177.11 ! [V_k,V_n,V_m] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__1,axiom, % 177.02/177.11 ! [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 ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__less,axiom, % 177.02/177.11 ! [V_n,V_m] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__mult__div__cancel__disj,axiom, % 177.02/177.11 ! [V_n,V_m,V_k] : % 177.02/177.11 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.11 => 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) ) % 177.02/177.11 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.11 => 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) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zdiv__int,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_greaterThanAtMost__empty,axiom, % 177.02/177.11 ! [V_k_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_k_2)) % 177.02/177.11 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_greaterThanAtMost__empty__iff,axiom, % 177.02/177.11 ! [V_l_2,V_k_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.11 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_l_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 177.02/177.11 ! [V_l_2,V_k_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) % 177.02/177.11 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_l_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__un_I20_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2)) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__int_I14_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__le__mono2,axiom, % 177.02/177.11 ! [V_k,V_n,V_m] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 177.02/177.11 => 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__mult__div__cancel1,axiom, % 177.02/177.11 ! [V_n,V_m,V_k] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__self1__is__m,axiom, % 177.02/177.11 ! [V_m,V_n] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.11 => 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 ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__mult__self__is__m,axiom, % 177.02/177.11 ! [V_m,V_n] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.11 => 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 ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__less__dividend,axiom, % 177.02/177.11 ! [V_m,V_n] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__greaterThanAtMost,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_com_Osize_I9_J,axiom, % 177.02/177.11 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__geq,axiom, % 177.02/177.11 ! [V_m,V_n] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.11 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_div__if,axiom, % 177.02/177.11 ! [V_m,V_n] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.11 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.11 => 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)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_split__div,axiom, % 177.02/177.11 ! [V_k_2,V_n_2,V_Pa_2] : % 177.02/177.11 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 177.02/177.11 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.02/177.11 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.11 => ! [B_i,B_j] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 177.02/177.11 => ( 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) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Int__greaterThanAtMost,axiom, % 177.02/177.11 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__uminus__atLeastLessThan,axiom, % 177.02/177.11 ! [V_y_2,V_x_2,T_c] : % 177.02/177.11 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.11 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__uminus__greaterThanAtMost,axiom, % 177.02/177.11 ! [V_y_2,V_x_2,T_c] : % 177.02/177.11 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.11 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__int_I10_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Oorder(T_c) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__Plus__iff,axiom, % 177.02/177.11 ! [V_B_2,V_A_2,T_d,T_c] : % 177.02/177.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2))) % 177.02/177.11 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.11 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__Plus,axiom, % 177.02/177.11 ! [V_B_2,T_d,V_A_2,T_c] : % 177.02/177.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.11 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__PlusD_I1_J,axiom, % 177.02/177.11 ! [V_B_2,V_A_2,T_d,T_c] : % 177.02/177.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2))) % 177.02/177.11 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_finite__PlusD_I2_J,axiom, % 177.02/177.11 ! [V_B_2,V_A_2,T_d,T_c] : % 177.02/177.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2))) % 177.02/177.11 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_le__div__geq,axiom, % 177.02/177.11 ! [V_m,V_n] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_split__div_H,axiom, % 177.02/177.11 ! [V_n_2,V_m_2,V_Pa_2] : % 177.02/177.11 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 177.02/177.11 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.11 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 177.02/177.11 | ? [B_q] : % 177.02/177.11 ( 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)) % 177.02/177.11 & 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)))) % 177.02/177.11 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_split__div__lemma,axiom, % 177.02/177.11 ! [V_m_2,V_q_2,V_n_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.02/177.11 => ( ( 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)) % 177.02/177.11 & 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)))) ) % 177.02/177.11 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__Plus,axiom, % 177.02/177.11 ! [V_B_2,T_d,V_A_2,T_c] : % 177.02/177.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.11 => hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ivl__disj__un_I16_J,axiom, % 177.02/177.11 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.11 ( class_Orderings_Olinorder(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_u_2)) % 177.02/177.11 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_com_Osize_I14_J,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_UNIV__Plus__UNIV,axiom, % 177.02/177.11 ! [T_d,T_c] : c_Sum__Type_OPlus(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Plus__eq__empty__conv,axiom, % 177.02/177.11 ! [V_B_2,V_A_2,T_d,T_c] : % 177.02/177.11 ( c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool)) % 177.02/177.11 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.11 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setprod__diff1,axiom, % 177.02/177.11 ! [V_a_2,V_f_2,V_A_2,T_c,T_d] : % 177.02/177.11 ( class_Fields_Ofield(T_d) % 177.02/177.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.11 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_d) % 177.02/177.11 => ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_image__atLeastZeroLessThan__int,axiom, % 177.02/177.11 ! [V_u_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__nonneg__0,axiom, % 177.02/177.11 ! [V_i_2,V_f_2,V_s_2,T_c,T_d] : % 177.02/177.11 ( class_Groups_Oordered__ab__group__add(T_d) % 177.02/177.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2)) % 177.02/177.11 => ( ! [B_i] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_s_2)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_i))) ) % 177.02/177.11 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_d) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_s_2)) % 177.02/177.11 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_power__divide,axiom, % 177.02/177.11 ! [V_n,V_b,V_a,T_a] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__int,axiom, % 177.02/177.11 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__zero__left,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__zero,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_minus__divide__left,axiom, % 177.02/177.11 ! [V_b,V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__1,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_diff__divide__distrib,axiom, % 177.02/177.11 ! [V_c,V_b,V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_times__divide__eq__right,axiom, % 177.02/177.11 ! [V_c,V_b,V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_add__divide__distrib,axiom, % 177.02/177.11 ! [V_c,V_b,V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_setsum__divide__distrib,axiom, % 177.02/177.11 ! [V_r_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.11 ( class_Fields_Ofield(T_c) % 177.02/177.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_r_2)),V_A_2) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_eq__divide__imp,axiom, % 177.02/177.11 ! [V_b,V_a,V_c,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 177.02/177.11 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__eq__imp,axiom, % 177.02/177.11 ! [V_a,V_b,V_c,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 177.02/177.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nonzero__divide__eq__eq,axiom, % 177.02/177.11 ! [V_a_2,V_b_2,V_c_2,T_c] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_c) % 177.02/177.11 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.11 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = V_a_2 % 177.02/177.11 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nonzero__eq__divide__eq,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_c) % 177.02/177.11 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.11 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) % 177.02/177.11 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_right__inverse__eq,axiom, % 177.02/177.11 ! [V_a_2,V_b_2,T_c] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_c) % 177.02/177.11 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.11 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_c) % 177.02/177.11 <=> V_a_2 = V_b_2 ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__self,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__self__if,axiom, % 177.02/177.11 ! [V_a,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 177.02/177.11 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 177.02/177.11 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nonzero__minus__divide__divide,axiom, % 177.02/177.11 ! [V_a,V_b,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nonzero__minus__divide__right,axiom, % 177.02/177.11 ! [V_a,V_b,T_a] : % 177.02/177.11 ( class_Rings_Odivision__ring(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nonzero__power__divide,axiom, % 177.02/177.11 ! [V_n,V_a,V_b,T_a] : % 177.02/177.11 ( class_Fields_Ofield(T_a) % 177.02/177.11 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__0,axiom, % 177.02/177.11 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 177.02/177.11 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_eq__nat__nat__iff,axiom, % 177.02/177.11 ! [V_z_H_2,V_z_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 177.02/177.11 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 177.02/177.11 <=> V_z_2 = V_z_H_2 ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 177.02/177.11 ! [V_y_2,V_x_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 177.02/177.11 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 177.02/177.11 <=> V_x_2 = V_y_2 ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_all__nat,axiom, % 177.02/177.11 ! [V_Pa_2] : % 177.02/177.11 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.02/177.11 <=> ! [B_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_ex__nat,axiom, % 177.02/177.11 ! [V_Pa_2] : % 177.02/177.11 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.02/177.11 <=> ? [B_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.02/177.11 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_power__one__over,axiom, % 177.02/177.11 ! [V_n,V_a,T_a] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 177.02/177.11 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__int__nat__set__return__embed,axiom, % 177.02/177.11 ! [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 ). % 177.02/177.11 % 177.02/177.11 fof(fact_setprod__dividef,axiom, % 177.02/177.11 ! [V_g_2,V_f_2,V_A_2,T_c,T_d] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_d) % 177.02/177.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Rings_Oinverse__class_Odivide(T_d)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__greaterThanAtMost__int,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 177.02/177.11 ! [V_A_2,V_f_2,T_c] : % 177.02/177.11 ( ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 & class_Groups_Ocomm__monoid__mult(T_c) ) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 177.02/177.11 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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__0__iff,axiom, % 177.02/177.11 ! [V_i_2] : % 177.02/177.11 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__le__0,axiom, % 177.02/177.11 ! [V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zless__nat__conj,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( 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))) % 177.02/177.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__mono__iff,axiom, % 177.02/177.11 ! [V_w_2,V_z_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 177.02/177.11 => ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 177.02/177.11 ! [V_y_2,V_x_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 177.02/177.11 => ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__1,axiom, % 177.02/177.11 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__nat__eq,axiom, % 177.02/177.11 ! [V_z] : % 177.02/177.11 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => 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) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_int__eq__iff,axiom, % 177.02/177.11 ! [V_z_2,V_m_2] : % 177.02/177.11 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 177.02/177.11 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__0__le,axiom, % 177.02/177.11 ! [V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zless__nat__eq__int__zless,axiom, % 177.02/177.11 ! [V_z_2,V_m_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 177.02/177.11 <=> 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__div__distrib,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__zminus__int,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 177.02/177.11 ! [V_A_2,V_f_2,T_c] : % 177.02/177.11 ( ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.11 & class_Groups_Ocomm__monoid__mult(T_c) ) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__atLeastZeroLessThan__int,axiom, % 177.02/177.11 ! [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) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__atLeastLessThan__int,axiom, % 177.02/177.11 ! [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)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zero__less__nat__eq,axiom, % 177.02/177.11 ! [V_z_2] : % 177.02/177.11 ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_power__diff,axiom, % 177.02/177.11 ! [V_m,V_n,V_a,T_a] : % 177.02/177.11 ( class_Fields_Ofield(T_a) % 177.02/177.11 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.11 => 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)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__less__eq__zless,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.02/177.11 => ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 177.02/177.11 ! [V_y_2,V_x_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 177.02/177.11 => ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__eq__iff,axiom, % 177.02/177.11 ! [V_m_2,V_w_2] : % 177.02/177.11 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.02/177.11 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.02/177.11 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__eq__iff2,axiom, % 177.02/177.11 ! [V_w_2,V_m_2] : % 177.02/177.11 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.02/177.11 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.02/177.11 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__le__eq__zle,axiom, % 177.02/177.11 ! [V_z_2,V_w_2] : % 177.02/177.11 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.02/177.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 177.02/177.11 => ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_split__nat,axiom, % 177.02/177.11 ! [V_i_2,V_Pa_2] : % 177.02/177.11 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 177.02/177.11 <=> ( ! [B_n] : % 177.02/177.11 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 177.02/177.11 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__add__distrib,axiom, % 177.02/177.11 ! [V_z_H,V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__mult__distrib,axiom, % 177.02/177.11 ! [V_z_H,V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 177.02/177.11 ! [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))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__diff__distrib,axiom, % 177.02/177.11 ! [V_z,V_z_H] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 177.02/177.11 ! [V_A_2,V_f_2,T_c] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 177.02/177.11 ! [V_n,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__power__eq,axiom, % 177.02/177.11 ! [V_n,V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 177.02/177.11 ! [V_A_2,V_f_2,T_c] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 177.02/177.11 ! [V_y,V_x] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.11 => 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)) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_one__less__nat__eq,axiom, % 177.02/177.11 ! [V_z_2] : % 177.02/177.11 ( 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))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__less__iff,axiom, % 177.02/177.11 ! [V_m_2,V_w_2] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 177.02/177.11 <=> 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))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 177.02/177.11 ! [V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_nat__mult__distrib__neg,axiom, % 177.02/177.11 ! [V_z_H,V_z] : % 177.02/177.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.11 => 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))) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_card__greaterThanLessThan__int,axiom, % 177.02/177.11 ! [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)))) ). % 177.02/177.11 % 177.02/177.11 fof(fact_geometric__sum,axiom, % 177.02/177.11 ! [V_n_2,V_x_2,T_c] : % 177.02/177.11 ( class_Fields_Ofield(T_c) % 177.02/177.11 => ( V_x_2 != c_Groups_Oone__class_Oone(T_c) % 177.02/177.11 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(c_Power_Opower__class_Opower(T_c),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_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_x_2),c_Groups_Oone__class_Oone(T_c))) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_le__divide__eq,axiom, % 177.02/177.11 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__le__eq,axiom, % 177.02/177.11 ! [V_a_2,V_c_2,V_b_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) % 177.02/177.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_pos__le__divide__eq,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_pos__divide__le__eq,axiom, % 177.02/177.11 ! [V_a_2,V_b_2,V_c_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) % 177.02/177.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_mult__imp__div__pos__le,axiom, % 177.02/177.11 ! [V_z,V_x,V_y,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.11 => ( 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))) % 177.02/177.11 => 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)) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_times__divide__times__eq,axiom, % 177.02/177.11 ! [V_w,V_z,V_y,V_x,T_a] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_minus__divide__divide,axiom, % 177.02/177.11 ! [V_b,V_a,T_a] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.11 => 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) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_minus__divide__right,axiom, % 177.02/177.11 ! [V_b,V_a,T_a] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.11 => 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)) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zero__le__divide__iff,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2))) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2)) ) % 177.02/177.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__le__0__iff,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c))) ) % 177.02/177.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2)) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__right__mono,axiom, % 177.02/177.11 ! [V_c,V_b,V_a,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__right__mono__neg,axiom, % 177.02/177.11 ! [V_c,V_b,V_a,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_zero__less__divide__iff,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2))) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2)) ) % 177.02/177.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__less__0__iff,axiom, % 177.02/177.11 ! [V_b_2,V_a_2,T_c] : % 177.02/177.11 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c))) ) % 177.02/177.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2)) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__pos__pos,axiom, % 177.02/177.11 ! [V_y,V_x,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__pos__neg,axiom, % 177.02/177.11 ! [V_y,V_x,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__neg__pos,axiom, % 177.02/177.11 ! [V_y,V_x,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__neg__neg,axiom, % 177.02/177.11 ! [V_y,V_x,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__strict__right__mono,axiom, % 177.02/177.11 ! [V_c,V_b,V_a,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_divide__strict__right__mono__neg,axiom, % 177.02/177.11 ! [V_c,V_a,V_b,T_a] : % 177.02/177.11 ( class_Fields_Olinordered__field(T_a) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.02/177.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.11 => 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))) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_frac__eq__eq,axiom, % 177.02/177.11 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_c] : % 177.02/177.11 ( class_Fields_Ofield(T_c) % 177.02/177.11 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.11 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.11 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_w_2),V_z_2) % 177.02/177.11 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2) ) ) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_mult__divide__mult__cancel__left,axiom, % 177.02/177.11 ! [V_b,V_a,V_c,T_a] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.11 => 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) ) ) ). % 177.02/177.11 % 177.02/177.11 fof(fact_mult__divide__mult__cancel__right,axiom, % 177.02/177.11 ! [V_b,V_a,V_c,T_a] : % 177.02/177.11 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.12 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__eq__eq,axiom, % 177.02/177.12 ! [V_a_2,V_c_2,V_b_2,T_c] : % 177.02/177.12 ( class_Fields_Ofield__inverse__zero(T_c) % 177.02/177.12 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = V_a_2 % 177.02/177.12 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.12 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) ) % 177.02/177.12 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.12 => V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_eq__divide__eq,axiom, % 177.02/177.12 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Fields_Ofield__inverse__zero(T_c) % 177.02/177.12 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) % 177.02/177.12 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) = V_b_2 ) % 177.02/177.12 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.12 => V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__nonneg__pos,axiom, % 177.02/177.12 ! [V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__nonneg__neg,axiom, % 177.02/177.12 ! [V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_frac__less2,axiom, % 177.02/177.12 ! [V_z,V_w,V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 177.02/177.12 => 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))) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_frac__less,axiom, % 177.02/177.12 ! [V_z,V_w,V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 177.02/177.12 => 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))) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_frac__le,axiom, % 177.02/177.12 ! [V_z,V_w,V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 177.02/177.12 => 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))) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__nonpos__pos,axiom, % 177.02/177.12 ! [V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__nonpos__neg,axiom, % 177.02/177.12 ! [V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_less__divide__eq,axiom, % 177.02/177.12 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.12 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__less__eq,axiom, % 177.02/177.12 ! [V_a_2,V_c_2,V_b_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) % 177.02/177.12 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_pos__less__divide__eq,axiom, % 177.02/177.12 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_pos__divide__less__eq,axiom, % 177.02/177.12 ! [V_a_2,V_b_2,V_c_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mult__imp__div__pos__less,axiom, % 177.02/177.12 ! [V_z,V_x,V_y,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.12 => ( 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))) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mult__imp__less__div__pos,axiom, % 177.02/177.12 ! [V_x,V_z,V_y,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.12 => ( 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)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_neg__less__divide__eq,axiom, % 177.02/177.12 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_neg__divide__less__eq,axiom, % 177.02/177.12 ! [V_a_2,V_b_2,V_c_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__strict__left__mono,axiom, % 177.02/177.12 ! [V_c,V_a,V_b,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.12 => ( 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))) % 177.02/177.12 => 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))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__strict__left__mono__neg,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.12 => ( 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))) % 177.02/177.12 => 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))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_add__frac__eq,axiom, % 177.02/177.12 ! [V_w,V_x,V_z,V_y,T_a] : % 177.02/177.12 ( class_Fields_Ofield(T_a) % 177.02/177.12 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__add__eq__iff,axiom, % 177.02/177.12 ! [V_y,V_x,V_z,T_a] : % 177.02/177.12 ( class_Fields_Ofield(T_a) % 177.02/177.12 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_add__frac__num,axiom, % 177.02/177.12 ! [V_z,V_x,V_y,T_a] : % 177.02/177.12 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.12 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_add__divide__eq__iff,axiom, % 177.02/177.12 ! [V_y,V_x,V_z,T_a] : % 177.02/177.12 ( class_Fields_Ofield(T_a) % 177.02/177.12 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_add__num__frac,axiom, % 177.02/177.12 ! [V_x,V_z,V_y,T_a] : % 177.02/177.12 ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.12 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_diff__frac__eq,axiom, % 177.02/177.12 ! [V_w,V_x,V_z,V_y,T_a] : % 177.02/177.12 ( class_Fields_Ofield(T_a) % 177.02/177.12 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__diff__eq__iff,axiom, % 177.02/177.12 ! [V_y,V_x,V_z,T_a] : % 177.02/177.12 ( class_Fields_Ofield(T_a) % 177.02/177.12 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_diff__divide__eq__iff,axiom, % 177.02/177.12 ! [V_y,V_x,V_z,T_a] : % 177.02/177.12 ( class_Fields_Ofield(T_a) % 177.02/177.12 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_less__half__sum,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.12 => 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))))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_gt__half__sum,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__left__mono__neg,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.12 => ( 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))) % 177.02/177.12 => 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))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divide__left__mono,axiom, % 177.02/177.12 ! [V_c,V_a,V_b,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 177.02/177.12 => ( 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))) % 177.02/177.12 => 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))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_neg__divide__le__eq,axiom, % 177.02/177.12 ! [V_a_2,V_b_2,V_c_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_neg__le__divide__eq,axiom, % 177.02/177.12 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mult__imp__le__div__pos,axiom, % 177.02/177.12 ! [V_x,V_z,V_y,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.12 => ( 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)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_nat__aux__def,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 177.02/177.12 ! [V_B_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => 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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 177.02/177.12 ! [V_B_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => 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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__morphism__nat__int,axiom, % 177.02/177.12 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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 177.02/177.12 ! [V_f_2,V_A_2,T_c] : % 177.02/177.12 ( ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 & class_Groups_Ocomm__monoid__mult(T_c) ) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 177.02/177.12 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 177.02/177.12 ! [V_B_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 177.02/177.12 ! [V_B_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_nat__set__def,axiom, % 177.02/177.12 ! [V_S_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_S_2) % 177.02/177.12 <=> ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 177.02/177.12 ! [V_B_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => ( V_A_2 = V_B_2 % 177.02/177.12 <=> 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) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 177.02/177.12 ! [V_x_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__nat__int__set__return__embed,axiom, % 177.02/177.12 ! [V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => 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 ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 177.02/177.12 ! [V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 177.02/177.12 <=> 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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 177.02/177.12 ! [V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 177.02/177.12 ! [V_B_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.12 <=> 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 177.02/177.12 ! [V_B_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.12 <=> 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 177.02/177.12 ! [V_f_2,V_A_2,T_c] : % 177.02/177.12 ( ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 & class_Groups_Ocomm__monoid__mult(T_c) ) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setprod__Un,axiom, % 177.02/177.12 ! [V_f_2,V_B_2,V_A_2,T_c,T_d] : % 177.02/177.12 ( class_Fields_Ofield(T_d) % 177.02/177.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( 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))) % 177.02/177.12 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_d) ) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 177.02/177.12 ! [V_A_2,V_x_2] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x_2) % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 177.02/177.12 <=> 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__of__nat,axiom, % 177.02/177.12 ! [V_k,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => 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)))) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__nonneg__leq__bound,axiom, % 177.02/177.12 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_c,T_d] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add(T_d) % 177.02/177.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2)) % 177.02/177.12 => ( ! [B_i] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_s_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_i))) ) % 177.02/177.12 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_s_2) = V_B_2 % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_s_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_greaterThan__0,axiom, % 177.02/177.12 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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_greaterThan__eq__iff,axiom, % 177.02/177.12 ! [V_y_2,V_x_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2) % 177.02/177.12 <=> V_x_2 = V_y_2 ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__eq__iff,axiom, % 177.02/177.12 ! [V_z_2,V_w_2,T_c] : % 177.02/177.12 ( class_Int_Oring__char__0(T_c) % 177.02/177.12 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2) % 177.02/177.12 <=> V_w_2 = V_z_2 ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__int__eq,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 177.02/177.12 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x) % 177.02/177.12 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 177.02/177.12 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 177.02/177.12 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x) % 177.02/177.12 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x) % 177.02/177.12 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 177.02/177.12 ! [V_n,V_x] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x) % 177.02/177.12 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__0,axiom, % 177.02/177.12 ! [T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__0__eq__iff,axiom, % 177.02/177.12 ! [V_z_2,T_c] : % 177.02/177.12 ( class_Int_Oring__char__0(T_c) % 177.02/177.12 => ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2) % 177.02/177.12 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__eq__0__iff,axiom, % 177.02/177.12 ! [V_z_2,T_c] : % 177.02/177.12 ( class_Int_Oring__char__0(T_c) % 177.02/177.12 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.12 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__le__iff,axiom, % 177.02/177.12 ! [V_z_2,V_w_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__less__iff,axiom, % 177.02/177.12 ! [V_z_2,V_w_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__add,axiom, % 177.02/177.12 ! [V_z,V_w,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__mult,axiom, % 177.02/177.12 ! [V_z,V_w,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__1,axiom, % 177.02/177.12 ! [T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__diff,axiom, % 177.02/177.12 ! [V_z,V_w,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__of__nat__eq,axiom, % 177.02/177.12 ! [V_n,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__minus,axiom, % 177.02/177.12 ! [V_z,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Ints__of__int,axiom, % 177.02/177.12 ! [V_z_2,T_c] : % 177.02/177.12 ( class_Rings_Oring__1(T_c) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Int_Oring__1__class_OInts(T_c))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__power,axiom, % 177.02/177.12 ! [V_n,V_z,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_is__nat__def,axiom, % 177.02/177.12 ! [V_x_2] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x_2) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_greaterThan__iff,axiom, % 177.02/177.12 ! [V_k_2,V_i_2,T_c] : % 177.02/177.12 ( class_Orderings_Oord(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_i_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_greaterThan__subset__iff,axiom, % 177.02/177.12 ! [V_y_2,V_x_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__setsum,axiom, % 177.02/177.12 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.12 ( class_Rings_Oring__1(T_c) % 177.02/177.12 => hAPP(c_Int_Oring__1__class_Oof__int(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,T_d),c_Int_Oring__1__class_Oof__int(T_c)),V_f_2)),V_A_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 177.02/177.12 ! [V_x_2,V_A_2] : % 177.02/177.12 ( c_Nat__Transfer_Onat__set(V_A_2) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__setprod,axiom, % 177.02/177.12 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.12 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 177.02/177.12 & class_Rings_Oring__1(T_c) ) % 177.02/177.12 => hAPP(c_Int_Oring__1__class_Oof__int(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,T_d),c_Int_Oring__1__class_Oof__int(T_c)),V_f_2)),V_A_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_INT__greaterThan__UNIV,axiom, % 177.02/177.12 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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__0__le__iff,axiom, % 177.02/177.12 ! [V_z_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__le__0__iff,axiom, % 177.02/177.12 ! [V_z_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__0__less__iff,axiom, % 177.02/177.12 ! [V_z_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__int__less__0__iff,axiom, % 177.02/177.12 ! [V_z_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_of__nat__nat,axiom, % 177.02/177.12 ! [V_z,T_a] : % 177.02/177.12 ( class_Rings_Oring__1(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I11_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__uminus__lessThan,axiom, % 177.02/177.12 ! [V_x_2,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.12 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__uminus__greaterThan,axiom, % 177.02/177.12 ! [V_x_2,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.12 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I5_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_greaterThan__Suc,axiom, % 177.02/177.12 ! [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)))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 177.02/177.12 ! [V_f_2,V_A_2,T_c] : % 177.02/177.12 ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,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_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_c),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 177.02/177.12 ! [V_f_2,V_A_2,T_c] : % 177.02/177.12 ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_c),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sum__diff__distrib,axiom, % 177.02/177.12 ! [V_n_2,V_Pa_2,V_Qa_2] : % 177.02/177.12 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x))) % 177.02/177.12 => 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_Qa_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_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__natinterval__difff,axiom, % 177.02/177.12 ! [V_f_2,V_n_2,V_m_2,T_c] : % 177.02/177.12 ( class_Groups_Oab__group__add(T_c) % 177.02/177.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c),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)))) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_gauss__sum,axiom, % 177.02/177.12 ! [V_n_2,T_c] : % 177.02/177.12 ( class_Rings_Ocomm__semiring__1(T_c) % 177.02/177.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_c)),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_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Groups_Oone__class_Oone(T_c))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_finite__atLeastAtMost,axiom, % 177.02/177.12 ! [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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_all__nat__less,axiom, % 177.02/177.12 ! [V_Pa_2,V_n_2] : % 177.02/177.12 ( ! [B_m] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 177.02/177.12 <=> ! [B_x] : % 177.02/177.12 ( 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))) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ex__nat__less,axiom, % 177.02/177.12 ! [V_Pa_2,V_n_2] : % 177.02/177.12 ( ? [B_m] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 177.02/177.12 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 177.02/177.12 <=> ? [B_x] : % 177.02/177.12 ( 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))) % 177.02/177.12 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastatMost__empty__iff2,axiom, % 177.02/177.12 ! [V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) % 177.02/177.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastatMost__empty__iff,axiom, % 177.02/177.12 ! [V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.12 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastatMost__empty,axiom, % 177.02/177.12 ! [V_a_2,V_b_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2)) % 177.02/177.12 => c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastatMost__subset__iff,axiom, % 177.02/177.12 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2))) % 177.02/177.12 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) % 177.02/177.12 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2)) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastAtMost__singleton_H,axiom, % 177.02/177.12 ! [V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( V_a_2 = V_b_2 % 177.02/177.12 => c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastAtMost__singleton__iff,axiom, % 177.02/177.12 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) % 177.02/177.12 <=> ( V_a_2 = V_b_2 % 177.02/177.12 & V_b_2 = V_c_2 ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastAtMost__singleton,axiom, % 177.02/177.12 ! [V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__uminus__atLeastAtMost,axiom, % 177.02/177.12 ! [V_y_2,V_x_2,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.12 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__Suc__atLeastAtMost,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 177.02/177.12 ! [V_n_2,V_m_2,V_f_2,T_c] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 177.02/177.12 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_c] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__add__atLeastAtMost,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_card__atLeastAtMost,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastAtMostSuc__conv,axiom, % 177.02/177.12 ! [V_n_2,V_m_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 177.02/177.12 ! [V_k_2,V_f_2] : % 177.02/177.12 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I21_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I15_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Int__atLeastAtMost,axiom, % 177.02/177.12 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastatMost__psubset__iff,axiom, % 177.02/177.12 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2))) % 177.02/177.12 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) % 177.02/177.12 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2)) % 177.02/177.12 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_a_2)) % 177.02/177.12 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_d_2)) ) ) ) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I22_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I4_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I16_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I13_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I12_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I7_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__head__Suc,axiom, % 177.02/177.12 ! [V_f_2,V_n_2,V_m_2,T_c] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__cl__ivl__Suc,axiom, % 177.02/177.12 ! [V_f_2,V_m_2,V_n_2,T_c] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__head,axiom, % 177.02/177.12 ! [V_Pa_2,V_n_2,V_m_2,T_c] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__ub__add__nat,axiom, % 177.02/177.12 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_c] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 => ( 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)))) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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)))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I6_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I5_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I18_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I19_J,axiom, % 177.02/177.12 ! [V_u_2,V_m_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_m_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeast__Suc,axiom, % 177.02/177.12 ! [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)))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_UN__le__eq__Un0,axiom, % 177.02/177.12 ! [V_M_2,V_n_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I12_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_decr__mult__lemma,axiom, % 177.02/177.12 ! [V_k_2,V_Pa_2,V_d_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.02/177.12 => 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)))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_negD,axiom, % 177.02/177.12 ! [V_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => ? [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))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_finite__atLeastAtMost__int,axiom, % 177.02/177.12 ! [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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_finite__atMost,axiom, % 177.02/177.12 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atMost__eq__iff,axiom, % 177.02/177.12 ! [V_y_2,V_x_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2) % 177.02/177.12 <=> V_x_2 = V_y_2 ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeast__eq__iff,axiom, % 177.02/177.12 ! [V_y_2,V_x_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2) % 177.02/177.12 <=> V_x_2 = V_y_2 ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__uminus__atMost,axiom, % 177.02/177.12 ! [V_x_2,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.12 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__uminus__atLeast,axiom, % 177.02/177.12 ! [V_x_2,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add(T_c) % 177.02/177.12 => hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atMost__Int__atLeast,axiom, % 177.02/177.12 ! [V_n_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 177.02/177.12 ! [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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 177.02/177.12 ! [V_y_2,V_x_2] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x_2) % 177.02/177.12 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeast0AtMost,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_lessThan__Suc__atMost,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_card__atMost,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atMost__Suc,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atMost__iff,axiom, % 177.02/177.12 ! [V_k_2,V_i_2,T_c] : % 177.02/177.12 ( class_Orderings_Oord(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_i_2),V_k_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeast__iff,axiom, % 177.02/177.12 ! [V_k_2,V_i_2,T_c] : % 177.02/177.12 ( class_Orderings_Oord(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_k_2),V_i_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeast__subset__iff,axiom, % 177.02/177.12 ! [V_y_2,V_x_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atMost__subset__iff,axiom, % 177.02/177.12 ! [V_y_2,V_x_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeast__0,axiom, % 177.02/177.12 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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 177.02/177.12 ! [V_y_2,V_x_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 177.02/177.12 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Compl__atLeast,axiom, % 177.02/177.12 ! [V_k_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Compl__lessThan,axiom, % 177.02/177.12 ! [V_k_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Compl__greaterThan,axiom, % 177.02/177.12 ! [V_k_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Compl__atMost,axiom, % 177.02/177.12 ! [V_k_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atLeast__Suc__greaterThan,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_UN__atMost__UNIV,axiom, % 177.02/177.12 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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 177.02/177.12 ! [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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__atMost__Suc,axiom, % 177.02/177.12 ! [V_n_2,V_f_2,T_c] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_atMost__0,axiom, % 177.02/177.12 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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I14_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_simp__from__to,axiom, % 177.02/177.12 ! [V_i_2,V_j_2] : % 177.02/177.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 177.02/177.12 => 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)) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I8_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Int__atLeastAtMostR1,axiom, % 177.02/177.12 ! [V_d_2,V_c_2,V_b_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Int__atLeastAtMostL1,axiom, % 177.02/177.12 ! [V_d_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Int__atLeastAtMostR2,axiom, % 177.02/177.12 ! [V_d_2,V_c_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),V_d_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Int__atLeastAtMostL2,axiom, % 177.02/177.12 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),V_b_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_UN__atLeast__UNIV,axiom, % 177.02/177.12 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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I9_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_UN__le__add__shift,axiom, % 177.02/177.12 ! [V_k_2,V_M_2,V_n_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_c,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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I3_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I1_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__int_I6_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Oorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_card__atLeastAtMost__int,axiom, % 177.02/177.12 ! [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))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 177.02/177.12 ! [V_n_2,V_m_2] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_m_2) % 177.02/177.12 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 177.02/177.12 => 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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I2_J,axiom, % 177.02/177.12 ! [V_u_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I10_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I1_J,axiom, % 177.02/177.12 ! [V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I13_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ivl__disj__un_I7_J,axiom, % 177.02/177.12 ! [V_u_2,V_l_2,T_c] : % 177.02/177.12 ( class_Orderings_Olinorder(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2)) % 177.02/177.12 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_aset_I6_J,axiom, % 177.02/177.12 ! [V_A_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( 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)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 177.02/177.12 => 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)) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_bset_I8_J,axiom, % 177.02/177.12 ! [V_B_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( 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)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 177.02/177.12 => 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))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_aset_I4_J,axiom, % 177.02/177.12 ! [V_A_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( B_x != V_t_2 % 177.02/177.12 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_bset_I4_J,axiom, % 177.02/177.12 ! [V_B_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( B_x != V_t_2 % 177.02/177.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_bset_I7_J,axiom, % 177.02/177.12 ! [V_B_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 177.02/177.12 => 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))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_bset_I3_J,axiom, % 177.02/177.12 ! [V_B_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( 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)) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xa] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 177.02/177.12 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 177.02/177.12 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_aset_I3_J,axiom, % 177.02/177.12 ! [V_A_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( 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)) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xa] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 177.02/177.12 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 177.02/177.12 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_aset_I5_J,axiom, % 177.02/177.12 ! [V_A_2,V_t_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 177.02/177.12 => 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)) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_bset_I6_J,axiom, % 177.02/177.12 ! [V_t_2,V_B_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_aset_I8_J,axiom, % 177.02/177.12 ! [V_t_2,V_A_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_periodic__finite__ex,axiom, % 177.02/177.12 ! [V_Pa_2,V_d_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 177.02/177.12 => ( ! [B_x,B_k] : % 177.02/177.12 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.02/177.12 <=> 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)))) ) % 177.02/177.12 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.02/177.12 <=> ? [B_x] : % 177.02/177.12 ( 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))) % 177.02/177.12 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_bset_I5_J,axiom, % 177.02/177.12 ! [V_t_2,V_B_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_aset_I7_J,axiom, % 177.02/177.12 ! [V_t_2,V_A_2,V_D_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( ! [B_xa] : % 177.02/177.12 ( 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))) % 177.02/177.12 => ! [B_xb] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 177.02/177.12 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_incr__mult__lemma,axiom, % 177.02/177.12 ! [V_k_2,V_Pa_2,V_d_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.02/177.12 => ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.02/177.12 => 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)))) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_ex__least__nat__less,axiom, % 177.02/177.12 ! [V_n_2,V_Pa_2] : % 177.02/177.12 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 177.02/177.12 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 177.02/177.12 => ? [B_k] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 177.02/177.12 & ! [B_i] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 177.02/177.12 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 177.02/177.12 & 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)))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zero__less__imp__eq__int,axiom, % 177.02/177.12 ! [V_k] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.02/177.12 => ? [B_n] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 177.02/177.12 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__mono__zero__right,axiom, % 177.02/177.12 ! [V_f_2,V_S_2,V_T_2,T_c,T_d] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) % 177.02/177.12 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_S_2) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__mono__zero__left,axiom, % 177.02/177.12 ! [V_f_2,V_S_2,V_T_2,T_c,T_d] : % 177.02/177.12 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) % 177.02/177.12 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_card__Pow,axiom, % 177.02/177.12 ! [V_A_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.12 => hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),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_c),V_A_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_min__Suc2,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_min__Suc1,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_PowI,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_finite__Pow__iff,axiom, % 177.02/177.12 ! [V_A_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2))) % 177.02/177.12 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__Pow__surj,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,V_f_2,T_c,T_d] : % 177.02/177.12 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = V_B_2 % 177.02/177.12 => hAPP(c_Set_Oimage(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Set_Oimage(T_d,T_c,V_f_2)),hAPP(c_Set_OPow(T_d),V_A_2)) = hAPP(c_Set_OPow(T_c),V_B_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__top,axiom, % 177.02/177.12 ! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_A_2))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Cantors__paradox,axiom, % 177.02/177.12 ! [V_A_2,T_c] : % 177.02/177.12 ~ ? [B_f] : hAPP(c_Set_Oimage(T_c,tc_fun(T_c,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_c),V_A_2) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__not__empty,axiom, % 177.02/177.12 ! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__INT__eq,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Set_OPow(T_c),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(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_d),c_Set_OPow(T_c)),V_B_2)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__bottom,axiom, % 177.02/177.12 ! [V_B_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_Set_OPow(T_c),V_B_2))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_PowD,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2))) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__iff,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_nat__case__0,axiom, % 177.02/177.12 ! [V_f2_2,V_f1_2,T_c] : c_Nat_Onat_Onat__case(T_c,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 177.02/177.12 % 177.02/177.12 fof(fact_nat__case__Suc,axiom, % 177.02/177.12 ! [V_nat_2,V_f2_2,V_f1_2,T_c] : c_Nat_Onat_Onat__case(T_c,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__mono,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__insert,axiom, % 177.02/177.12 ! [V_A_2,V_a_2,T_c] : hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_c),V_a_2)),hAPP(c_Set_OPow(T_c),V_A_2))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__UNIV,axiom, % 177.02/177.12 ! [T_c] : hAPP(c_Set_OPow(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_UN__Pow__subset,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_d),c_Set_OPow(T_c)),V_B_2))),hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__Int__eq,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_c] : hAPP(c_Set_OPow(T_c),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(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__Pow__mono,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Set_Oimage(T_d,T_c,V_f_2)),hAPP(c_Set_OPow(T_d),V_A_2))),hAPP(c_Set_OPow(T_c),V_B_2))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Pow__empty,axiom, % 177.02/177.12 ! [T_c] : hAPP(c_Set_OPow(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_max__Suc2,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_max__Suc1,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Un__Pow__subset,axiom, % 177.02/177.12 ! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2))),hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Powp__Pow__eq,axiom, % 177.02/177.12 ! [V_x_2,V_A_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(c_Predicate_OPowp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)),V_x_2)) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_c),V_A_2))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_diff__Suc,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_field__le__mult__one__interval,axiom, % 177.02/177.12 ! [V_y,V_x,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.02/177.12 => ( ! [B_z] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 177.02/177.12 => 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)) ) ) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 177.02/177.12 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_c] : % 177.02/177.12 ( ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 & class_Groups_Ocomm__monoid__mult(T_c) ) % 177.02/177.12 => ( V_A_2 = V_B_2 % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.02/177.12 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),V_g_2),V_B_2) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_split__pos__lemma,axiom, % 177.02/177.12 ! [V_n_2,V_Pa_2,V_k_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.02/177.12 => ( 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))) % 177.02/177.12 <=> ! [B_i,B_j] : % 177.02/177.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 177.02/177.12 & 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) ) % 177.02/177.12 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_split__neg__lemma,axiom, % 177.02/177.12 ! [V_n_2,V_Pa_2,V_k_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => ( 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))) % 177.02/177.12 <=> ! [B_i,B_j] : % 177.02/177.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 & 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) ) % 177.02/177.12 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zpower__zmod,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiff__zmod__left,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiff__zmod__right,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__diff__cong,axiom, % 177.02/177.12 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 177.02/177.12 ( class_Divides_Oring__div(T_a) % 177.02/177.12 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 177.02/177.12 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 177.02/177.12 => 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) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__diff__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Oring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__diff__left__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Oring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__diff__right__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Oring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__simps_I3_J,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zmult1__eq,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__self,axiom, % 177.02/177.12 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zero,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__add__cong,axiom, % 177.02/177.12 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 177.02/177.12 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 177.02/177.12 => 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) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__simps_I1_J,axiom, % 177.02/177.12 ! [V_b,V_c,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__simps_I2_J,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__add__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__add__left__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__add__right__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__add__self1,axiom, % 177.02/177.12 ! [V_a,V_b,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__add__self2,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__minus__eq,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Oring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__minus__cong,axiom, % 177.02/177.12 ! [V_a_H,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Oring__div(T_a) % 177.02/177.12 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__self,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__by__0,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__0,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mod__trivial,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__cong,axiom, % 177.02/177.12 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 177.02/177.12 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 177.02/177.12 => 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) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__simps_I4_J,axiom, % 177.02/177.12 ! [V_b,V_c,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__mult2,axiom, % 177.02/177.12 ! [V_b,V_c,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__mult1,axiom, % 177.02/177.12 ! [V_b,V_a,V_c,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__left__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__right__eq,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zminus__zmod,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zminus__zminus,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zminus2,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( c_Nat__Transfer_Ois__nat(V_x) % 177.02/177.12 => ( c_Nat__Transfer_Ois__nat(V_y) % 177.02/177.12 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__self1__is__0,axiom, % 177.02/177.12 ! [V_a,V_b,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__self2__is__0,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__self2,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__self1,axiom, % 177.02/177.12 ! [V_b,V_c,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__by__1,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__div__trivial,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__le__nonneg__dividend,axiom, % 177.02/177.12 ! [V_k,V_m] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.12 => 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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_pos__mod__bound,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_neg__mod__bound,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => 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))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__eq__0__iff,axiom, % 177.02/177.12 ! [V_d_2,V_m_2] : % 177.02/177.12 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zminus1__not__zero,axiom, % 177.02/177.12 ! [V_l,V_k] : % 177.02/177.12 ( 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) % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zminus2__not__zero,axiom, % 177.02/177.12 ! [V_l,V_k] : % 177.02/177.12 ( 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) % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zdiv__trivial,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_DIVISION__BY__ZERO,axiom, % 177.02/177.12 ! [V_a] : % 177.02/177.12 ( 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) % 177.02/177.12 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiv__zadd1__eq,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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 ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__div__equality2,axiom, % 177.02/177.12 ! [V_a,V_b,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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 ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__div__equality,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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 ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_div__mod__equality2,axiom, % 177.02/177.12 ! [V_c,V_a,V_b,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_div__mod__equality,axiom, % 177.02/177.12 ! [V_c,V_b,V_a,T_a] : % 177.02/177.12 ( class_Divides_Osemiring__div(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__neg__neg__trivial,axiom, % 177.02/177.12 ! [V_b,V_a] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_neg__mod__conj,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => ( 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))) % 177.02/177.12 & 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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_neg__mod__sign,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => 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))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__pos__pos__trivial,axiom, % 177.02/177.12 ! [V_b,V_a] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_pos__mod__conj,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.02/177.12 => ( 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))) % 177.02/177.12 & 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_pos__mod__sign,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.02/177.12 => 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))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zminus2__eq__if,axiom, % 177.02/177.12 ! [V_b,V_a] : % 177.02/177.12 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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) ) % 177.02/177.12 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zminus1__eq__if,axiom, % 177.02/177.12 ! [V_b,V_a] : % 177.02/177.12 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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) ) % 177.02/177.12 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zdiv__equality,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiv__zmult1__eq,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiv__zmod__equality,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiv__zmod__equality2,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmult__div__cancel,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zdiv__equality_H,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__pos__neg__trivial,axiom, % 177.02/177.12 ! [V_b,V_a] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.12 => ( 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))) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_divmod__int__rel__mod__eq,axiom, % 177.02/177.12 ! [V_y,V_q_1,V_b_1,V_a_1] : % 177.02/177.12 ( 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) % 177.02/177.12 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 177.02/177.12 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmult2__lemma__aux2,axiom, % 177.02/177.12 ! [V_q,V_r,V_b,V_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmult2__lemma__aux1,axiom, % 177.02/177.12 ! [V_q,V_r,V_b,V_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmult2__lemma__aux4,axiom, % 177.02/177.12 ! [V_q,V_b,V_r,V_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmult2__lemma__aux3,axiom, % 177.02/177.12 ! [V_q,V_b,V_r,V_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 177.02/177.12 => 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))) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_split__zmod,axiom, % 177.02/177.12 ! [V_k_2,V_n_2,V_Pa_2] : % 177.02/177.12 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 177.02/177.12 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 177.02/177.12 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 177.02/177.12 => ! [B_i,B_j] : % 177.02/177.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 177.02/177.12 & 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) ) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 177.02/177.12 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 => ! [B_i,B_j] : % 177.02/177.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 177.02/177.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.12 & 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) ) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__zmult2__eq,axiom, % 177.02/177.12 ! [V_b,V_a,V_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiv__zminus2__eq__if,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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)) ) % 177.02/177.12 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zdiv__zminus1__eq__if,axiom, % 177.02/177.12 ! [V_a,V_b] : % 177.02/177.12 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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)) ) % 177.02/177.12 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => 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)) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 177.02/177.12 ! [V_n_2,V_m_2] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 177.02/177.12 <=> 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_z3mod__def,axiom, % 177.02/177.12 ! [V_k,V_l] : % 177.02/177.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.02/177.12 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__neg,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__1__neg,axiom, % 177.02/177.12 ! [V_a_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c)) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__if,axiom, % 177.02/177.12 ! [V_x,T_a] : % 177.02/177.12 ( class_Groups_Osgn__if(T_a) % 177.02/177.12 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 177.02/177.12 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__less,axiom, % 177.02/177.12 ! [V_n,V_m] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__distrib,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__distrib2,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__less__eq__dividend,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__sgn,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__0__0,axiom, % 177.02/177.12 ! [V_a_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.12 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn0,axiom, % 177.02/177.12 ! [T_a] : % 177.02/177.12 ( class_Groups_Osgn__if(T_a) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__times,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__Suc,axiom, % 177.02/177.12 ! [V_n,V_m] : % 177.02/177.12 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.12 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__1,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__less__divisor,axiom, % 177.02/177.12 ! [V_m,V_n] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__eq__0__iff,axiom, % 177.02/177.12 ! [V_d_2,V_m_2] : % 177.02/177.12 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.12 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__if,axiom, % 177.02/177.12 ! [V_n,V_m] : % 177.02/177.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.12 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.12 => 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) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__geq,axiom, % 177.02/177.12 ! [V_n,V_m] : % 177.02/177.12 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__self3,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_le__mod__geq,axiom, % 177.02/177.12 ! [V_m,V_n] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zmod__int,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_div__add1__eq,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__le__divisor,axiom, % 177.02/177.12 ! [V_m,V_n] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult__self4,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__greater,axiom, % 177.02/177.12 ! [V_a_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Osgn__class_Osgn(T_c,V_a_2))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__less,axiom, % 177.02/177.12 ! [V_a_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Osgn__class_Osgn(T_c,V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__mult2__eq,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_div__mult1__eq,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_div__mod__equality_H,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mult__div__cancel,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Divides_Omod__div__equality_H,axiom, % 177.02/177.12 ! [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)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_split__mod,axiom, % 177.02/177.12 ! [V_k_2,V_n_2,V_Pa_2] : % 177.02/177.12 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 177.02/177.12 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 177.02/177.12 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.12 => ! [B_i,B_j] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 177.02/177.12 => ( 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) % 177.02/177.12 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_mod__lemma,axiom, % 177.02/177.12 ! [V_q,V_b,V_r,V_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 177.02/177.12 => 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))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Suc__times__mod__eq,axiom, % 177.02/177.12 ! [V_m,V_k] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_nat__mod__distrib,axiom, % 177.02/177.12 ! [V_y,V_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 177.02/177.12 => 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)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__pos,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_sgn__1__pos,axiom, % 177.02/177.12 ! [V_a_2,T_c] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.12 => ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = c_Groups_Oone__class_Oone(T_c) % 177.02/177.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_zsgn__def,axiom, % 177.02/177.12 ! [V_i] : % 177.02/177.12 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.02/177.12 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 177.02/177.12 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 177.02/177.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 177.02/177.12 => 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)) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_decr__lemma,axiom, % 177.02/177.12 ! [V_z,V_x,V_d] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_incr__lemma,axiom, % 177.02/177.12 ! [V_x,V_z,V_d] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 177.02/177.12 => 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)))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 177.02/177.12 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_c] : % 177.02/177.12 ( ( class_Groups_Ocomm__monoid__add(T_c) % 177.02/177.12 & class_Groups_Ocomm__monoid__mult(T_c) ) % 177.02/177.12 => ( V_A_2 = V_B_2 % 177.02/177.12 => ( c_Nat__Transfer_Onat__set(V_B_2) % 177.02/177.12 => ( ! [B_x] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.02/177.12 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 177.02/177.12 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),V_g_2),V_B_2) ) ) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Sup__fold__sup,axiom, % 177.02/177.12 ! [V_A_2,T_c] : % 177.02/177.12 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.12 => c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_UnionI,axiom, % 177.02/177.12 ! [V_A_2,V_C_2,V_X_2,T_c] : % 177.02/177.12 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2)) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2))) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__abs,axiom, % 177.02/177.12 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_setsum__abs__ge__zero,axiom, % 177.02/177.12 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.02/177.12 => 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__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Union__Pow__eq,axiom, % 177.02/177.12 ! [V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_OPow(T_c),V_A_2)) = V_A_2 ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__minus__commute,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__le__D1,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__ge__self,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__one,axiom, % 177.02/177.12 ! [T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__minus__cancel,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__of__nat,axiom, % 177.02/177.12 ! [V_n,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_power__abs,axiom, % 177.02/177.12 ! [V_n,V_a,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__idempotent,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__mult,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__mult__self,axiom, % 177.02/177.12 ! [V_a,T_a] : % 177.02/177.12 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.12 => 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) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__add__abs,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__eq__0,axiom, % 177.02/177.12 ! [V_a_2,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.02/177.12 => ( hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.12 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__zero,axiom, % 177.02/177.12 ! [T_a] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.12 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__int__eq,axiom, % 177.02/177.12 ! [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) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__divide,axiom, % 177.02/177.12 ! [V_b,V_a,T_a] : % 177.02/177.12 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.02/177.12 => 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)) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__setsum__abs,axiom, % 177.02/177.12 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.12 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.02/177.12 => hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_abs__setprod,axiom, % 177.02/177.12 ! [V_A_2,V_f_2,T_d,T_c] : % 177.02/177.12 ( class_Fields_Olinordered__field(T_c) % 177.02/177.12 => hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2) ) ). % 177.02/177.12 % 177.02/177.12 fof(fact_image__Union,axiom, % 177.02/177.12 ! [V_S_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_d,T_c,V_f_2)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Int__Union2,axiom, % 177.02/177.12 ! [V_A_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)) ). % 177.02/177.12 % 177.02/177.12 fof(fact_Int__Union,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_UN__extend__simps_I8_J,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) ). % 177.02/177.13 % 177.02/177.13 fof(fact_UN__simps_I8_J,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__le__iff,axiom, % 177.02/177.13 ! [V_b_2,V_A_2,T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)),V_b_2)) % 177.02/177.13 <=> ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_2)) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__Sup__iff,axiom, % 177.02/177.13 ! [V_S_2,V_a_2,T_c] : % 177.02/177.13 ( ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 & class_Orderings_Olinorder(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_S_2))) % 177.02/177.13 <=> ? [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.02/177.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),B_x)) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_vimage__Union,axiom, % 177.02/177.13 ! [V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_c,T_d,V_f_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__ge__zero,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__le__zero__iff,axiom, % 177.02/177.13 ! [V_a_2,T_c] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__of__nonneg,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__of__pos,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zero__less__abs__iff,axiom, % 177.02/177.13 ! [V_a_2,T_c] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2))) % 177.02/177.13 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__not__less__zero,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => ~ 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__triangle__ineq,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__mult__less,axiom, % 177.02/177.13 ! [V_d,V_b,V_c,V_a,T_a] : % 177.02/177.13 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 177.02/177.13 => 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))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__triangle__ineq2__sym,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__triangle__ineq2,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__triangle__ineq3,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__le__D2,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__leI,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__le__iff,axiom, % 177.02/177.13 ! [V_b_2,V_a_2,T_c] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2)) % 177.02/177.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) % 177.02/177.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2)) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__ge__minus__self,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__less__iff,axiom, % 177.02/177.13 ! [V_b_2,V_a_2,T_c] : % 177.02/177.13 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2)) % 177.02/177.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) % 177.02/177.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2)) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nonzero__abs__divide,axiom, % 177.02/177.13 ! [V_a,V_b,T_a] : % 177.02/177.13 ( class_Fields_Olinordered__field(T_a) % 177.02/177.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__power__minus,axiom, % 177.02/177.13 ! [V_n,V_a,T_a] : % 177.02/177.13 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__zmult__eq__1,axiom, % 177.02/177.13 ! [V_n,V_m] : % 177.02/177.13 ( 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) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__disjoint,axiom, % 177.02/177.13 ! [V_A_2,V_C_2,T_c] : % 177.02/177.13 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 <=> ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_C_2)) % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__upper,axiom, % 177.02/177.13 ! [V_A_2,V_B_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mult__sgn__abs,axiom, % 177.02/177.13 ! [V_x,T_a] : % 177.02/177.13 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.13 => 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 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__sgn,axiom, % 177.02/177.13 ! [V_k,T_a] : % 177.02/177.13 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__empty,axiom, % 177.02/177.13 ! [T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__mono,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__insert,axiom, % 177.02/177.13 ! [V_B_2,V_a_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__UnionD,axiom, % 177.02/177.13 ! [V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2))) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_subset__Pow__Union,axiom, % 177.02/177.13 ! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__UNIV,axiom, % 177.02/177.13 ! [T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__Un__distrib,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__eq__mult,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Rings_Oordered__ring__abs(T_a) % 177.02/177.13 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.02/177.13 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 177.02/177.13 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 177.02/177.13 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__mult__pos,axiom, % 177.02/177.13 ! [V_y,V_x,T_a] : % 177.02/177.13 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_UNION__eq__Union__image,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__image__eq,axiom, % 177.02/177.13 ! [V_A_2,V_B_2,T_d,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__diff__triangle__ineq,axiom, % 177.02/177.13 ! [V_d,V_c,V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__triangle__ineq4,axiom, % 177.02/177.13 ! [V_b,V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__of__nonpos,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__minus__le__zero,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__if,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oabs__if(T_a) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__of__neg,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zero__le__power__abs,axiom, % 177.02/177.13 ! [V_n,V_a,T_a] : % 177.02/177.13 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__div__pos,axiom, % 177.02/177.13 ! [V_x,V_y,T_a] : % 177.02/177.13 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__upper,axiom, % 177.02/177.13 ! [V_A_2,V_x_2,T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__empty,axiom, % 177.02/177.13 ! [T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => c_Complete__Lattice_OSup__class_OSup(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_c) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__singleton,axiom, % 177.02/177.13 ! [V_a_2,T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zabs__less__one__iff,axiom, % 177.02/177.13 ! [V_z_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__insert,axiom, % 177.02/177.13 ! [V_A_2,V_a_2,T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zabs__def,axiom, % 177.02/177.13 ! [V_i] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.13 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__UNIV,axiom, % 177.02/177.13 ! [T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => c_Complete__Lattice_OSup__class_OSup(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_c) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__abs__mult__distrib,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zero__le__zpower__abs,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_INT__simps_I8_J,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_INT__extend__simps_I8_J,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Un__eq__Union,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Un__Union__image,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_d,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_d),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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_C_2))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__Int__subset,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zero__less__zpower__abs__iff,axiom, % 177.02/177.13 ! [V_n_2,V_x_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.13 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__binary,axiom, % 177.02/177.13 ! [V_b_2,V_a_2,T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),V_b_2) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_sup__Sup__fold__sup,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_B_2),V_A_2) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Sup__fin__Sup,axiom, % 177.02/177.13 ! [V_A_2,T_c] : % 177.02/177.13 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nitpick_Oint__lcm__def,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_inj__on__Inter,axiom, % 177.02/177.13 ! [V_f_2,T_d,T_c,V_S_2] : % 177.02/177.13 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) % 177.02/177.13 => ( ! [B_A] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_A),V_S_2)) % 177.02/177.13 => c_Fun_Oinj__on(T_c,T_d,V_f_2,B_A) ) % 177.02/177.13 => c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_S_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Inter__subset,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : % 177.02/177.13 ( ! [B_X] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_X),V_B_2)) ) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_int__val__lemma,axiom, % 177.02/177.13 ! [V_k_2,V_f_2,V_n_2] : % 177.02/177.13 ( ! [B_i] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 177.02/177.13 => 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))) ) % 177.02/177.13 => ( 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)) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 177.02/177.13 => ? [B_i] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 177.02/177.13 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__def,axiom, % 177.02/177.13 ! [V_S_2,T_c] : 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_c,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_c,tc_HOL_Obool))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nitpick_Onat__lcm__def,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Union,axiom, % 177.02/177.13 ! [V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) % 177.02/177.13 => ( ! [B_M] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_M),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_M)) ) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_insert__partition,axiom, % 177.02/177.13 ! [V_F_2,V_x_2,T_c] : % 177.02/177.13 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2))) % 177.02/177.13 => ! [B_xa] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2))) % 177.02/177.13 => ( B_x != B_xa % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_card__partition,axiom, % 177.02/177.13 ! [V_k_2,V_C_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_C_2)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2))) % 177.02/177.13 => ( ! [B_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c),V_C_2)) % 177.02/177.13 => hAPP(c_Finite__Set_Ocard(T_c),B_c) = V_k_2 ) % 177.02/177.13 => ( ! [B_c1] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c1),V_C_2)) % 177.02/177.13 => ! [B_c2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c2),V_C_2)) % 177.02/177.13 => ( B_c1 != B_c2 % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) % 177.02/177.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__gcd_Osimps,axiom, % 177.02/177.13 ! [V_x,V_y] : % 177.02/177.13 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.13 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 177.02/177.13 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nitpick_Oint__gcd__def,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat0__intermed__int__val,axiom, % 177.02/177.13 ! [V_k_2,V_f_2,V_n_2] : % 177.02/177.13 ( ! [B_i] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 177.02/177.13 => 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))) ) % 177.02/177.13 => ( 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)) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 177.02/177.13 => ? [B_i] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 177.02/177.13 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setprod__pos__nat,axiom, % 177.02/177.13 ! [V_f_2,V_S_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.02/177.13 => 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))) ) % 177.02/177.13 => 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_c,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_inj__on__INTER,axiom, % 177.02/177.13 ! [V_A_2,V_f_2,T_e,T_d,T_c,V_I_2] : % 177.02/177.13 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => ( ! [B_i] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_I_2)) % 177.02/177.13 => c_Fun_Oinj__on(T_d,T_e,V_f_2,hAPP(V_A_2,B_i)) ) % 177.02/177.13 => c_Fun_Oinj__on(T_d,T_e,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] : % 177.02/177.13 ( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) % 177.02/177.13 => hAPP(V_g_2,B_x) = V_z_2 ) % 177.02/177.13 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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)) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_card__less__Suc2,axiom, % 177.02/177.13 ! [V_i_2,V_M_2] : % 177.02/177.13 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 177.02/177.13 => 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))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_card__less,axiom, % 177.02/177.13 ! [V_i_2,V_M_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_card__less__Suc,axiom, % 177.02/177.13 ! [V_i_2,V_M_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 177.02/177.13 => 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))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_CollectI,axiom, % 177.02/177.13 ! [T_c,V_a_2,V_Pa_2] : % 177.02/177.13 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Collect__conjI,axiom, % 177.02/177.13 ! [V_Qa_2,V_Pa_2,T_c] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Collect__less__nat,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Collect__le__nat,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__disj__eq,axiom, % 177.02/177.13 ! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_Set_OCollect(T_c),V_Qa_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__conj__eq,axiom, % 177.02/177.13 ! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_Set_OCollect(T_c),V_Qa_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_CollectE,axiom, % 177.02/177.13 ! [V_Pa_2,V_a_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_CollectD,axiom, % 177.02/177.13 ! [V_Pa_2,V_a_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mem__Collect__eq,axiom, % 177.02/177.13 ! [V_Pa_2,V_a_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__mem__eq,axiom, % 177.02/177.13 ! [V_A_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)) = V_A_2 ). % 177.02/177.13 % 177.02/177.13 fof(fact_empty__def,axiom, % 177.02/177.13 ! [T_c] : c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fFalse)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_empty__Collect__eq,axiom, % 177.02/177.13 ! [V_Pa_2,T_c] : % 177.02/177.13 ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),V_Pa_2) % 177.02/177.13 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__empty__eq,axiom, % 177.02/177.13 ! [V_Pa_2,T_c] : % 177.02/177.13 ( hAPP(c_Set_OCollect(T_c),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__def,axiom, % 177.02/177.13 ! [V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),V_Pa_2) = V_Pa_2 ). % 177.02/177.13 % 177.02/177.13 fof(fact_UNIV__def,axiom, % 177.02/177.13 ! [T_c] : c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fTrue)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_insert__Collect,axiom, % 177.02/177.13 ! [V_Pa_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Collect__disjI,axiom, % 177.02/177.13 ! [V_Qa_2,V_Pa_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),V_Pa_2)),V_Qa_2)))) % 177.02/177.13 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__neg__eq,axiom, % 177.02/177.13 ! [V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_vimage__Collect__eq,axiom, % 177.02/177.13 ! [V_Pa_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Set_OCollect(T_d),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_d,tc_HOL_Obool,T_c),V_Pa_2),V_f_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_insert__compr,axiom, % 177.02/177.13 ! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_insert__compr__raw,axiom, % 177.02/177.13 ! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Un__def,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),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_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Int__def,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Int__Collect,axiom, % 177.02/177.13 ! [V_Pa_2,V_A_2,V_x_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))) % 177.02/177.13 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.13 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_singleton__conv2,axiom, % 177.02/177.13 ! [V_a_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_singleton__conv,axiom, % 177.02/177.13 ! [V_a_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__conv__if2,axiom, % 177.02/177.13 ! [T_c,V_a_2,V_Pa_2] : % 177.02/177.13 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 177.02/177.13 => hAPP(c_Set_OCollect(T_c),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 177.02/177.13 => hAPP(c_Set_OCollect(T_c),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__conv__if,axiom, % 177.02/177.13 ! [T_c,V_a_2,V_Pa_2] : % 177.02/177.13 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 177.02/177.13 => hAPP(c_Set_OCollect(T_c),hAPP(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,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 177.02/177.13 => hAPP(c_Set_OCollect(T_c),hAPP(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,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_set__diff__eq,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Collect__not,axiom, % 177.02/177.13 ! [V_Pa_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)))) % 177.02/177.13 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_insert__def,axiom, % 177.02/177.13 ! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Compl__eq,axiom, % 177.02/177.13 ! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_vimage__def,axiom, % 177.02/177.13 ! [V_B_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(T_d)),V_f_2)),V_B_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Collect__imp__eq,axiom, % 177.02/177.13 ! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2))),hAPP(c_Set_OCollect(T_c),V_Qa_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__M__bounded__by__nat,axiom, % 177.02/177.13 ! [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))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setsum__setsum__restrict,axiom, % 177.02/177.13 ! [V_R_2,V_f_2,V_T_2,T_d,V_S_2,T_c,T_e] : % 177.02/177.13 ( class_Groups_Ocomm__monoid__add(T_e) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_T_2)) % 177.02/177.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),hAPP(hAPP(c_COMBS(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_e),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_e),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e)),hAPP(c_COMBC(T_c,T_d,T_e),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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_S_2)))),hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_if__image__distrib,axiom, % 177.02/177.13 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBS(T_d,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_d),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_d),V_Pa_2)))),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d),c_fNot),V_Pa_2))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__seg__image__imp__finite,axiom, % 177.02/177.13 ! [V_n_2,V_f_2,T_c,V_A_2] : % 177.02/177.13 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_c,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))) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setsum__restrict__set_H,axiom, % 177.02/177.13 ! [V_B_2,V_f_2,V_A_2,T_c,T_d] : % 177.02/177.13 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_d))),V_A_2) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setsum__image__gen,axiom, % 177.02/177.13 ! [V_f_2,T_e,V_g_2,V_S_2,T_c,T_d] : % 177.02/177.13 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_e),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),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_S_2)))),hAPP(c_COMBC(T_c,T_e,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_e,tc_HOL_Obool),T_c),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_c,T_e,V_f_2),V_S_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setsum__cases,axiom, % 177.02/177.13 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_c,T_d] : % 177.02/177.13 ( class_Groups_Ocomm__monoid__add(T_d) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_Set_OCollect(T_c),V_Pa_2))))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setsum__multicount,axiom, % 177.02/177.13 ! [V_k_2,V_R_2,V_T_2,T_d,V_S_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_T_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_T_2)) % 177.02/177.13 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_S_2))),hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 177.02/177.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),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_d),V_T_2)) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 177.02/177.13 ! [V_x_2,V_A_2,T_c] : % 177.02/177.13 ( class_Orderings_Olinorder(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 177.02/177.13 ! [V_x_2,V_A_2,T_c] : % 177.02/177.13 ( class_Orderings_Olinorder(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : % 177.02/177.13 ( class_Orderings_Olinorder(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Orderings_Oord__class_Omax(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Collect__subsets,axiom, % 177.02/177.13 ! [V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),V_A_2)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Pow__Compl,axiom, % 177.02/177.13 ! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBS(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_c))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Pow__def,axiom, % 177.02/177.13 ! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),V_A_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__image__set,axiom, % 177.02/177.13 ! [V_f_2,T_d,V_Pa_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_d),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_c,T_d),tc_fun(T_c,tc_HOL_Obool)),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)),V_f_2)))),V_Pa_2))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__Collect__bounded__ex,axiom, % 177.02/177.13 ! [V_Qa_2,T_d,V_Pa_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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),V_Pa_2))),V_Qa_2))))) % 177.02/177.13 <=> ! [B_y] : % 177.02/177.13 ( hBOOL(hAPP(V_Pa_2,B_y)) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Qa_2),B_y)))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__Min__commute,axiom, % 177.02/177.13 ! [V_k_2,V_N_2,T_c] : % 177.02/177.13 ( class_Groups_Olinordered__ab__semigroup__add(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_N_2))))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__Max__commute,axiom, % 177.02/177.13 ! [V_k_2,V_N_2,T_c] : % 177.02/177.13 ( class_Groups_Olinordered__ab__semigroup__add(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2)) % 177.02/177.13 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_N_2))))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_sup__Inf2__distrib,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : % 177.02/177.13 ( class_Lattices_Odistrib__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_sup__Inf1__distrib,axiom, % 177.02/177.13 ! [V_x_2,V_A_2,T_c] : % 177.02/177.13 ( class_Lattices_Odistrib__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_inf__Sup2__distrib,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : % 177.02/177.13 ( class_Lattices_Odistrib__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_inf__Sup1__distrib,axiom, % 177.02/177.13 ! [V_x_2,V_A_2,T_c] : % 177.02/177.13 ( class_Lattices_Odistrib__lattice(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_c] : % 177.02/177.13 ( class_Orderings_Olinorder(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.02/177.13 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.02/177.13 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Orderings_Oord__class_Omin(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setsum__multicount__gen,axiom, % 177.02/177.13 ! [V_k_2,V_R_2,V_t_2,T_d,V_s_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_t_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_t_2)) % 177.02/177.13 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_s_2))),hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 177.02/177.13 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__conv__nat__seg__image,axiom, % 177.02/177.13 ! [V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_c,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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_pigeonhole__infinite,axiom, % 177.02/177.13 ! [V_f_2,T_d,V_A_2,T_c] : % 177.02/177.13 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.02/177.13 => ? [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_card__quotient__disjoint,axiom, % 177.02/177.13 ! [V_r_2,V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( c_Fun_Oinj__on(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Equiv__Relations_Oquotient(T_c)),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))))),V_r_2),V_A_2) % 177.02/177.13 => hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotient__is__empty,axiom, % 177.02/177.13 ! [V_r_2,V_A_2,T_c] : % 177.02/177.13 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) % 177.02/177.13 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotient__is__empty2,axiom, % 177.02/177.13 ! [V_r_2,V_A_2,T_c] : % 177.02/177.13 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) % 177.02/177.13 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotient__empty,axiom, % 177.02/177.13 ! [V_r_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotient__diff1,axiom, % 177.02/177.13 ! [V_a_2,V_A_2,V_r_2,T_c] : % 177.02/177.13 ( c_Fun_Oinj__on(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Equiv__Relations_Oquotient(T_c)),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))))),V_r_2),V_A_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.13 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotient__def,axiom, % 177.02/177.13 ! [V_r_2,V_A_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_c,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)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_singleton__quotient,axiom, % 177.02/177.13 ! [V_r_2,V_x_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_finite__UN__I,axiom, % 177.02/177.13 ! [V_B_2,T_d,V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( ! [B_a] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_a))) ) % 177.02/177.13 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_inj__on__diff__nat,axiom, % 177.02/177.13 ! [V_k_2,V_N_2] : % 177.02/177.13 ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotientI,axiom, % 177.02/177.13 ! [V_r_2,V_A_2,V_x_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Image__eq__UN,axiom, % 177.02/177.13 ! [V_B_2,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Relation_OImage(T_d,T_c,V_r_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),c_Set_Oinsert(T_d)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Image__INT__subset,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_e,V_r_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Image__Int__subset,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,V_R_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Image__UN,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,T_e,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Image__empty,axiom, % 177.02/177.13 ! [V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Image__mono,axiom, % 177.02/177.13 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_d,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_d,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_c,T_d,V_r_2),V_A_2))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Image__Un,axiom, % 177.02/177.13 ! [V_B_2,V_A_2,V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Un__Image,axiom, % 177.02/177.13 ! [V_A_2,V_S_2,V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_S_2),V_A_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotientE,axiom, % 177.02/177.13 ! [V_r_2,V_A_2,V_X_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.02/177.13 => ~ ! [B_x] : % 177.02/177.13 ( V_X_2 = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.02/177.13 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_diff__nat__eq__if,axiom, % 177.02/177.13 ! [V_z_2,V_z_H_2] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_setsum__SucD,axiom, % 177.02/177.13 ! [V_n_2,V_A_2,V_f_2,T_c] : % 177.02/177.13 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 177.02/177.13 => ? [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 & 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))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__mod__eq__lemma,axiom, % 177.02/177.13 ! [V_y,V_n,V_x] : % 177.02/177.13 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 177.02/177.13 => ? [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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__neg__int,axiom, % 177.02/177.13 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__neg__1,axiom, % 177.02/177.13 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__by__empty,axiom, % 177.02/177.13 ! [V_B_2,T_c,V_A_2] : % 177.02/177.13 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__neg__0,axiom, % 177.02/177.13 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__neg__eq__ge__0,axiom, % 177.02/177.13 ! [V_x_2] : % 177.02/177.13 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_neg__def,axiom, % 177.02/177.13 ! [V_Z_2] : % 177.02/177.13 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_neg__nat,axiom, % 177.02/177.13 ! [V_z] : % 177.02/177.13 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 177.02/177.13 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__neg__nat,axiom, % 177.02/177.13 ! [V_z] : % 177.02/177.13 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 177.02/177.13 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_neg__zminus__int,axiom, % 177.02/177.13 ! [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))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osize_I5_J,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osize_I13_J,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_fold__image__1,axiom, % 177.02/177.13 ! [V_f_2,V_S_2,T_c,T_d] : % 177.02/177.13 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.02/177.13 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) ) % 177.02/177.13 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_S_2) = c_Groups_Oone__class_Oone(T_d) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_card_Oneutral,axiom, % 177.02/177.13 ! [V_A_2,T_c] : % 177.02/177.13 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.13 => hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I4_J,axiom, % 177.02/177.13 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 177.02/177.13 ( 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) % 177.02/177.13 <=> ( V_fun_2 = V_fun_H_2 % 177.02/177.13 & V_com1_2 = V_com1_H_2 % 177.02/177.13 & V_com2_2 = V_com2_H_2 ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I52_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I53_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I45_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I44_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I15_J,axiom, % 177.02/177.13 ! [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 ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I14_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mod__induct__0,axiom, % 177.02/177.13 ! [V_i_2,V_Pa_2,V_p_2] : % 177.02/177.13 ( ! [B_i] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 177.02/177.13 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 177.02/177.13 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 177.02/177.13 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 177.02/177.13 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_InterI,axiom, % 177.02/177.13 ! [V_A_2,V_C_2,T_c] : % 177.02/177.13 ( ! [B_X] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_C_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),B_X)) ) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_fold__image__cong,axiom, % 177.02/177.13 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_c,T_d] : % 177.02/177.13 ( class_Groups_Oab__semigroup__mult(T_d) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 177.02/177.13 => 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),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_inf__le__fold__inf,axiom, % 177.02/177.13 ! [V_c_2,V_b_2,V_A_2,T_c] : % 177.02/177.13 ( class_Lattices_Osemilattice__inf(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),B_x)) ) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_c_2),V_A_2))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_fold__sup__le__sup,axiom, % 177.02/177.13 ! [V_c_2,V_b_2,V_A_2,T_c] : % 177.02/177.13 ( class_Lattices_Osemilattice__sup(T_c) % 177.02/177.13 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_2)) ) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_b_2),V_c_2))) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_expand__Suc,axiom, % 177.02/177.13 ! [V_v] : % 177.02/177.13 ( 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))) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_quotient__disj,axiom, % 177.02/177.13 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.02/177.13 => ( V_X_2 = V_Y_2 % 177.02/177.13 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osize_I3_J,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_of__nat__number__of__eq,axiom, % 177.02/177.13 ! [V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_of__nat__number__of__lemma,axiom, % 177.02/177.13 ! [V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => ( ( 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))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => 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) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__eq,axiom, % 177.02/177.13 ! [V_k,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_of__int__number__of__eq,axiom, % 177.02/177.13 ! [V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I2_J,axiom, % 177.02/177.13 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 177.02/177.13 ( 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) % 177.02/177.13 <=> ( V_loc_2 = V_loc_H_2 % 177.02/177.13 & V_fun_2 = V_fun_H_2 % 177.02/177.13 & V_com_2 = V_com_H_2 ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__reorient,axiom, % 177.02/177.13 ! [V_x_2,V_w_2,T_c] : % 177.02/177.13 ( class_Int_Onumber(T_c) % 177.02/177.13 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = V_x_2 % 177.02/177.13 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__number__of,axiom, % 177.02/177.13 ! [V_y_2,V_x_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Int_Oring__char__0(T_c) ) % 177.02/177.13 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) % 177.02/177.13 <=> V_x_2 = V_y_2 ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I39_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I38_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I37_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I36_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I34_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I35_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I11_J,axiom, % 177.02/177.13 ! [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 ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osimps_I10_J,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__number__of__eq__not__less,axiom, % 177.02/177.13 ! [V_w_2,V_v_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber(T_c) % 177.02/177.13 & class_Orderings_Olinorder(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_right__distrib__number__of,axiom, % 177.02/177.13 ! [V_c,V_b,V_v,T_b] : % 177.02/177.13 ( ( class_Int_Onumber(T_b) % 177.02/177.13 & class_Rings_Osemiring(T_b) ) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_left__distrib__number__of,axiom, % 177.02/177.13 ! [V_v,V_b,V_a,T_b] : % 177.02/177.13 ( ( class_Int_Onumber(T_b) % 177.02/177.13 & class_Rings_Osemiring(T_b) ) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_right__diff__distrib__number__of,axiom, % 177.02/177.13 ! [V_c,V_b,V_v,T_b] : % 177.02/177.13 ( ( class_Int_Onumber(T_b) % 177.02/177.13 & class_Rings_Oring(T_b) ) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_left__diff__distrib__number__of,axiom, % 177.02/177.13 ! [V_v,V_b,V_a,T_b] : % 177.02/177.13 ( ( class_Int_Onumber(T_b) % 177.02/177.13 & class_Rings_Oring(T_b) ) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__number__of,axiom, % 177.02/177.13 ! [V_y_2,V_x_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__number__of,axiom, % 177.02/177.13 ! [V_y_2,V_x_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_min__number__of,axiom, % 177.02/177.13 ! [V_v,V_u,T_b] : % 177.02/177.13 ( ( class_Int_Onumber(T_b) % 177.02/177.13 & class_Orderings_Oord(T_b) ) % 177.02/177.13 => ( ( 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))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => 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) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_max__number__of,axiom, % 177.02/177.13 ! [V_v,V_u,T_b] : % 177.02/177.13 ( ( class_Int_Onumber(T_b) % 177.02/177.13 & class_Orderings_Oord(T_b) ) % 177.02/177.13 => ( ( 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))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => 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) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__number__of__left,axiom, % 177.02/177.13 ! [V_z,V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__number__of__eq,axiom, % 177.02/177.13 ! [V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__add,axiom, % 177.02/177.13 ! [V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mult__number__of__left,axiom, % 177.02/177.13 ! [V_z,V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_arith__simps_I32_J,axiom, % 177.02/177.13 ! [V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__mult,axiom, % 177.02/177.13 ! [V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__diff,axiom, % 177.02/177.13 ! [V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_arith__simps_I30_J,axiom, % 177.02/177.13 ! [V_w,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__minus,axiom, % 177.02/177.13 ! [V_w,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Ints__number__of,axiom, % 177.02/177.13 ! [V_w_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Int_Oring__1__class_OInts(T_c))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Union__quotient,axiom, % 177.02/177.13 ! [V_r_2,V_A_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.02/177.13 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)) = V_A_2 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__eq__eq__number__of1,axiom, % 177.02/177.13 ! [V_a_2,V_w_2,V_b_2,T_c] : % 177.02/177.13 ( ( class_Fields_Ofield__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) = V_a_2 % 177.02/177.13 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) ) % 177.02/177.13 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__eq__eq__number__of,axiom, % 177.02/177.13 ! [V_w_2,V_c_2,V_b_2,T_c] : % 177.02/177.13 ( ( class_Fields_Ofield__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) % 177.02/177.13 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2) ) % 177.02/177.13 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__divide__eq__number__of,axiom, % 177.02/177.13 ! [V_c_2,V_b_2,V_w_2,T_c] : % 177.02/177.13 ( ( class_Fields_Ofield__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) % 177.02/177.13 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2) = V_b_2 ) % 177.02/177.13 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__divide__eq__number__of1,axiom, % 177.02/177.13 ! [V_w_2,V_b_2,V_a_2,T_c] : % 177.02/177.13 ( ( class_Fields_Ofield__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) % 177.02/177.13 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) = V_b_2 ) % 177.02/177.13 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 => V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__number__of__diff1,axiom, % 177.02/177.13 ! [V_c,V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_minus__number__of__mult,axiom, % 177.02/177.13 ! [V_z,V_w,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_diff__number__of__eq,axiom, % 177.02/177.13 ! [V_w,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__less__eq__number__of1,axiom, % 177.02/177.13 ! [V_a_2,V_w_2,V_b_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2)) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__less__eq__number__of,axiom, % 177.02/177.13 ! [V_w_2,V_c_2,V_b_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__divide__eq__number__of,axiom, % 177.02/177.13 ! [V_c_2,V_b_2,V_w_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__divide__eq__number__of1,axiom, % 177.02/177.13 ! [V_w_2,V_b_2,V_a_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_abs__number__of,axiom, % 177.02/177.13 ! [V_x,T_a] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_a) % 177.02/177.13 & class_Rings_Olinordered__idom(T_a) ) % 177.02/177.13 => ( ( 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))) % 177.02/177.13 => 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)) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => 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) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__number__of__diff2,axiom, % 177.02/177.13 ! [V_w,V_c,V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__divide__eq__number__of1,axiom, % 177.02/177.13 ! [V_w_2,V_b_2,V_a_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__divide__eq__number__of,axiom, % 177.02/177.13 ! [V_c_2,V_b_2,V_w_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__le__eq__number__of,axiom, % 177.02/177.13 ! [V_w_2,V_c_2,V_b_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__le__eq__number__of1,axiom, % 177.02/177.13 ! [V_a_2,V_w_2,V_b_2,T_c] : % 177.02/177.13 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.13 & class_Int_Onumber(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2)) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_equiv__class__self,axiom, % 177.02/177.13 ! [V_a_2,V_r_2,V_A_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_OImage(T_c,T_c,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)))))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_com_Osize_I11_J,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_UN__equiv__class,axiom, % 177.02/177.13 ! [V_a_2,V_f_2,T_d,V_r_2,V_A_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.02/177.13 => ( c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.13 => hAPP(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_r_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) = hAPP(V_f_2,V_a_2) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_UN__equiv__class2,axiom, % 177.02/177.13 ! [V_a2_2,V_a1_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2) % 177.02/177.13 => ( c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2) % 177.02/177.13 => ( c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a1_2),V_A1_2)) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_a2_2),V_A2_2)) % 177.02/177.13 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_d,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_one__mod__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.02/177.13 => 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)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.02/177.13 => 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))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_one__div__nat__number__of,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__eq__number__of__int__code,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_minus__numeral__code_I5_J,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__is__id,axiom, % 177.02/177.13 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 177.02/177.13 % 177.02/177.13 fof(fact_times__numeral__code_I5_J,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_plus__numeral__code_I9_J,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__number__of__int__code,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_int__number__of__def,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of__def,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_congruent2__implies__congruent,axiom, % 177.02/177.13 ! [V_a_2,V_f_2,V_r2_2,T_e,T_d,V_r1_2,V_A_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r1_2) % 177.02/177.13 => ( c_Equiv__Relations_Ocongruent2(T_c,T_d,T_e,V_r1_2,V_r2_2,V_f_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.02/177.13 => c_Equiv__Relations_Ocongruent(T_d,T_e,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_minus__numeral__code_I6_J,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_neg__imp__number__of__eq__0,axiom, % 177.02/177.13 ! [V_v] : % 177.02/177.13 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_int__eq__iff__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_m_2] : % 177.02/177.13 ( 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) % 177.02/177.13 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 177.02/177.13 & 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))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H_2,V_v_2] : % 177.02/177.13 ( 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) % 177.02/177.13 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 177.02/177.13 => 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))) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 177.02/177.13 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 177.02/177.13 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of__add__left,axiom, % 177.02/177.13 ! [V_k,V_v_H,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.02/177.13 => 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) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_int__nat__number__of,axiom, % 177.02/177.13 ! [V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mod__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 177.02/177.13 => 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))) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_congruent2__implies__congruent__UN,axiom, % 177.02/177.13 ! [V_a_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2) % 177.02/177.13 => ( c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2) % 177.02/177.13 => ( c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),V_A2_2)) % 177.02/177.13 => c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_e,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_d,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_div__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_power__nat__number__of,axiom, % 177.02/177.13 ! [V_n,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_power__nat__number__of__number__of,axiom, % 177.02/177.13 ! [V_w,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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)) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__nat__number__of__add,axiom, % 177.02/177.13 ! [V_n,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_diff__nat__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_v_H_2] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_min__Suc__number__of,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_min__number__of__Suc,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I19_J,axiom, % 177.02/177.13 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_diff__bin__simps_I1_J,axiom, % 177.02/177.13 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 177.02/177.13 % 177.02/177.13 fof(fact_minus__Pls,axiom, % 177.02/177.13 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__Pls__right,axiom, % 177.02/177.13 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__Pls,axiom, % 177.02/177.13 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 177.02/177.13 % 177.02/177.13 fof(fact_mult__Pls,axiom, % 177.02/177.13 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 177.02/177.13 % 177.02/177.13 fof(fact_succ__pred,axiom, % 177.02/177.13 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I2_J,axiom, % 177.02/177.13 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Pls__def,axiom, % 177.02/177.13 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 177.02/177.13 % 177.02/177.13 fof(fact_semiring__norm_I112_J,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__Pls,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__numeral__0,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__numeral__0__right,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_bin__less__0__simps_I1_J,axiom, % 177.02/177.13 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_semiring__norm_I113_J,axiom, % 177.02/177.13 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of__Pls,axiom, % 177.02/177.13 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zero__is__num__zero,axiom, % 177.02/177.13 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__diff__number__of,axiom, % 177.02/177.13 ! [V_m,V_v] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__neg__number__of__Pls,axiom, % 177.02/177.13 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of__add__1,axiom, % 177.02/177.13 ! [V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__1__add__number__of,axiom, % 177.02/177.13 ! [V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__iff__pred__less,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_pred__def,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of__diff__1,axiom, % 177.02/177.13 ! [V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__Numeral0,axiom, % 177.02/177.13 ! [V_x,T_a] : % 177.02/177.13 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.13 & class_Int_Onumber__ring(T_a) ) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__number__of__0,axiom, % 177.02/177.13 ! [V_v_2] : % 177.02/177.13 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__0__number__of,axiom, % 177.02/177.13 ! [V_v_2] : % 177.02/177.13 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of2,axiom, % 177.02/177.13 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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H_2,V_v_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 177.02/177.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H_2,V_v_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_succ__def,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__special_I1_J,axiom, % 177.02/177.13 ! [V_y_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__special_I3_J,axiom, % 177.02/177.13 ! [V_x_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__special_I3_J,axiom, % 177.02/177.13 ! [V_x_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__special_I1_J,axiom, % 177.02/177.13 ! [V_y_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__0__number__of,axiom, % 177.02/177.13 ! [V_v_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 177.02/177.13 => 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)) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__succ,axiom, % 177.02/177.13 ! [V_k,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__pred,axiom, % 177.02/177.13 ! [V_w,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mult__nat__number__of,axiom, % 177.02/177.13 ! [V_v_H,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of__mult__left,axiom, % 177.02/177.13 ! [V_k,V_v_H,V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 177.02/177.13 => 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) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_neg__number__of__pred__iff__0,axiom, % 177.02/177.13 ! [V_v_2] : % 177.02/177.13 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 177.02/177.13 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__number__of__Suc,axiom, % 177.02/177.13 ! [V_n_2,V_v_2] : % 177.02/177.13 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 177.02/177.13 <=> 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))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__eq__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_n_2] : % 177.02/177.13 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 177.02/177.13 <=> 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))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__case__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_f_2,V_a_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__Suc__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_n_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> 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))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__number__of__Suc,axiom, % 177.02/177.13 ! [V_n_2,V_v_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__Suc__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_n_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> 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))))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__number__of__Suc,axiom, % 177.02/177.13 ! [V_n_2,V_v_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__nat__number__of,axiom, % 177.02/177.13 ! [V_v] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_max__number__of__Suc,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_max__Suc__number__of,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__case__add__eq__if,axiom, % 177.02/177.13 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_c,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__rec__add__eq__if,axiom, % 177.02/177.13 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_c,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,T_c),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_c,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_c,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))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__rec__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_f_2,V_a_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,T_c),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_c,V_a_2,V_f_2)),c_Int_Onat)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_UN__equiv__class__type2,axiom, % 177.02/177.13 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2) % 177.02/177.13 => ( c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2) % 177.02/177.13 => ( c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A1_2),V_r1_2))) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_d),V_A2_2),V_r2_2))) % 177.02/177.13 => ( ! [B_x1] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x1),V_A1_2)) % 177.02/177.13 => ! [B_x2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x2),V_A2_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_e,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_UN__equiv__class__type,axiom, % 177.02/177.13 ! [V_B_2,V_X_2,V_f_2,T_d,V_r_2,V_A_2,T_c] : % 177.02/177.13 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.02/177.13 => ( c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.02/177.13 => ( ! [B_x] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 177.02/177.13 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__rec__0,axiom, % 177.02/177.13 ! [V_f2_2,V_f1_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__rec__Suc,axiom, % 177.02/177.13 ! [V_nat_2,V_f2_2,V_f1_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c,V_f1_2,V_f2_2),V_nat_2)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__special_I3_J,axiom, % 177.02/177.13 ! [V_x_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.13 <=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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)))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__special_I1_J,axiom, % 177.02/177.13 ! [V_y_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) % 177.02/177.13 <=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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)))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_power__number__of__odd__number__of,axiom, % 177.02/177.13 ! [V_v_2,V_w_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => ( ( 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))) % 177.02/177.13 => hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)))),c_COMBI(T_c))) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zpower__number__of__odd,axiom, % 177.02/177.13 ! [V_z_2,V_w_2] : % 177.02/177.13 ( ( 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))) % 177.02/177.13 => 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))) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => 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) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_iszero__number__of__Bit1,axiom, % 177.02/177.13 ! [V_w,T_a] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_a) % 177.02/177.13 & class_Int_Oring__char__0(T_a) ) % 177.02/177.13 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I34_J,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__eq__int__code_I16_J,axiom, % 177.02/177.13 ! [V_k2_2,V_k1_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I51_J,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 177.02/177.13 <=> V_k_2 = V_l_2 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I17_J,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__int__code_I16_J,axiom, % 177.02/177.13 ! [V_k2_2,V_k1_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I46_J,axiom, % 177.02/177.13 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I39_J,axiom, % 177.02/177.13 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__iszero__Numeral1,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_iszero__0,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Rings_Osemiring__1(T_a) % 177.02/177.13 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_iszero__def,axiom, % 177.02/177.13 ! [V_z_2,T_c] : % 177.02/177.13 ( class_Rings_Osemiring__1(T_c) % 177.02/177.13 => ( c_Int_Oiszero(T_c,V_z_2) % 177.02/177.13 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_not__iszero__1,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Rings_Osemiring__1(T_a) % 177.02/177.13 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_bin__less__0__simps_I4_J,axiom, % 177.02/177.13 ! [V_w_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I22_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I12_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Bit1__def,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_neg__number__of__Bit1,axiom, % 177.02/177.13 ! [V_w_2] : % 177.02/177.13 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 177.02/177.13 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_minus__Bit1,axiom, % 177.02/177.13 ! [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))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_succ__Pls,axiom, % 177.02/177.13 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 177.02/177.13 % 177.02/177.13 fof(fact_number__of__Bit1,axiom, % 177.02/177.13 ! [V_w,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mult__numeral__1,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mult__numeral__1__right,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_numeral__1__eq__1,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_semiring__norm_I110_J,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I5_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I29_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__Numeral1,axiom, % 177.02/177.13 ! [V_x,T_a] : % 177.02/177.13 ( ( class_Fields_Ofield(T_a) % 177.02/177.13 & class_Int_Onumber__ring(T_a) ) % 177.02/177.13 => 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 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_divide__numeral__1,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( ( class_Fields_Ofield(T_a) % 177.02/177.13 & class_Int_Onumber__ring(T_a) ) % 177.02/177.13 => 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 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__special_I2_J,axiom, % 177.02/177.13 ! [V_y_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => ( c_Groups_Oone__class_Oone(T_c) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) % 177.02/177.13 <=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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)))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__special_I4_J,axiom, % 177.02/177.13 ! [V_x_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = c_Groups_Oone__class_Oone(T_c) % 177.02/177.13 <=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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))))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_one__is__num__one,axiom, % 177.02/177.13 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__numeral__1__eq__1,axiom, % 177.02/177.13 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Numeral1__eq1__nat,axiom, % 177.02/177.13 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 177.02/177.13 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_iszero__Numeral0,axiom, % 177.02/177.13 ! [T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_numeral__3__eq__3,axiom, % 177.02/177.13 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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_numeral__1__eq__Suc__0,axiom, % 177.02/177.13 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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_power3__eq__cube,axiom, % 177.02/177.13 ! [V_a,T_a] : % 177.02/177.13 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 177.02/177.13 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))))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc3__eq__add__3,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 177.02/177.13 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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 177.02/177.13 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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__special_I2_J,axiom, % 177.02/177.13 ! [V_y_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_le__special_I4_J,axiom, % 177.02/177.13 ! [V_x_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__special_I4_J,axiom, % 177.02/177.13 ! [V_x_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__special_I2_J,axiom, % 177.02/177.13 ! [V_y_2,T_c] : % 177.02/177.13 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.13 & class_Rings_Olinordered__idom(T_c) ) % 177.02/177.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__special_I2_J,axiom, % 177.02/177.13 ! [V_w,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__special_I3_J,axiom, % 177.02/177.13 ! [V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__diff__eq__diff__pred,axiom, % 177.02/177.13 ! [V_m,V_n] : % 177.02/177.13 ( 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)) % 177.02/177.13 => 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__mod__eq__add3__mod,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mod__Suc__eq__mod__add3,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Suc__div__eq__add3__div,axiom, % 177.02/177.13 ! [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) ). % 177.02/177.13 % 177.02/177.13 fof(fact_div__Suc__eq__div__add3,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_eq__number__of__eq,axiom, % 177.02/177.13 ! [V_y_2,V_x_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) % 177.02/177.13 <=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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)))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_diff__special_I1_J,axiom, % 177.02/177.13 ! [V_w,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_diff__special_I2_J,axiom, % 177.02/177.13 ! [V_v,T_a] : % 177.02/177.13 ( class_Int_Onumber__ring(T_a) % 177.02/177.13 => 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)))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_nat__number__of__Bit1,axiom, % 177.02/177.13 ! [V_w_2] : % 177.02/177.13 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.02/177.13 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.02/177.13 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 177.02/177.13 => 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)))) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_power__number__of__odd,axiom, % 177.02/177.13 ! [V_z_2,V_w_2,T_c] : % 177.02/177.13 ( class_Int_Onumber__ring(T_c) % 177.02/177.13 => ( ( 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))) % 177.02/177.13 => hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_z_2))),c_COMBI(T_c))) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) ) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_zmod__number__of__Bit1,axiom, % 177.02/177.13 ! [V_v,V_w] : % 177.02/177.13 ( ( 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))) % 177.02/177.13 => 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)) ) % 177.02/177.13 & ( ~ 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))) % 177.02/177.13 => 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)) ) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_neg__zmod__mult__2,axiom, % 177.02/177.13 ! [V_b,V_a] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.13 => 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)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_arith__series__int,axiom, % 177.02/177.13 ! [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)))) ). % 177.02/177.13 % 177.02/177.13 fof(fact_pos__zdiv__mult__2,axiom, % 177.02/177.13 ! [V_b,V_a] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.13 => 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) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I49_J,axiom, % 177.02/177.13 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I50_J,axiom, % 177.02/177.13 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Bit0__Pls,axiom, % 177.02/177.13 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I38_J,axiom, % 177.02/177.13 ! [V_l_2] : % 177.02/177.13 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 177.02/177.13 <=> c_Int_OPls = V_l_2 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I44_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.13 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 177.02/177.13 <=> V_k_2 = c_Int_OPls ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_minus__Bit0,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__int__code_I13_J,axiom, % 177.02/177.13 ! [V_k2_2,V_k1_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I14_J,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_Bit0__def,axiom, % 177.02/177.13 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 177.02/177.13 % 177.02/177.13 fof(fact_add__Bit0__Bit0,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I48_J,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 177.02/177.13 <=> V_k_2 = V_l_2 ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_mult__Bit0,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_diff__bin__simps_I7_J,axiom, % 177.02/177.13 ! [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)) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__eq__int__code_I13_J,axiom, % 177.02/177.13 ! [V_k2_2,V_k1_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I31_J,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_bin__less__0__simps_I3_J,axiom, % 177.02/177.13 ! [V_w_2] : % 177.02/177.13 ( 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))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I21_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I27_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I32_J,axiom, % 177.02/177.13 ! [V_l_2,V_k_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_less__eq__int__code_I14_J,axiom, % 177.02/177.13 ! [V_k2_2,V_k1_2] : % 177.02/177.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.02/177.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.13 % 177.02/177.13 fof(fact_rel__simps_I4_J,axiom, % 177.02/177.13 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I10_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I16_J,axiom, % 177.02/177.14 ! [V_l_2,V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_less__int__code_I15_J,axiom, % 177.02/177.14 ! [V_k2_2,V_k1_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__Bit0__Bit1,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__Bit1__Bit0,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I3_J,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I10_J,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I9_J,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zdiv__number__of__Bit0,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_neg__number__of__Bit0,axiom, % 177.02/177.14 ! [V_w_2] : % 177.02/177.14 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 177.02/177.14 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_pred__Bit1,axiom, % 177.02/177.14 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 177.02/177.14 % 177.02/177.14 fof(fact_pred__Bit0,axiom, % 177.02/177.14 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_iszero__number__of__Bit0,axiom, % 177.02/177.14 ! [V_w_2,T_c] : % 177.02/177.14 ( ( class_Int_Onumber__ring(T_c) % 177.02/177.14 & class_Int_Oring__char__0(T_c) ) % 177.02/177.14 => ( c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(V_w_2))) % 177.02/177.14 <=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_succ__Bit0,axiom, % 177.02/177.14 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 177.02/177.14 % 177.02/177.14 fof(fact_succ__Bit1,axiom, % 177.02/177.14 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_nat__number__of__Bit0,axiom, % 177.02/177.14 ! [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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_number__of__Bit0,axiom, % 177.02/177.14 ! [V_w,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_less__eq__int__code_I15_J,axiom, % 177.02/177.14 ! [V_k2_2,V_k1_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I33_J,axiom, % 177.02/177.14 ! [V_l_2,V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_less__int__code_I14_J,axiom, % 177.02/177.14 ! [V_k2_2,V_k1_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I15_J,axiom, % 177.02/177.14 ! [V_l_2,V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_card__UNIV__bool,axiom, % 177.02/177.14 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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mult__Bit1,axiom, % 177.02/177.14 ! [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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I8_J,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__Bit1__Bit1,axiom, % 177.02/177.14 ! [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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__number__of__even,axiom, % 177.02/177.14 ! [V_w_2,V_z_2,T_c] : % 177.02/177.14 ( class_Int_Onumber__ring(T_c) % 177.02/177.14 => hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Otimes__class_Otimes(T_c)),c_COMBI(T_c))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zpower__number__of__even,axiom, % 177.02/177.14 ! [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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_double__number__of__Bit0,axiom, % 177.02/177.14 ! [V_w,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_number__of1,axiom, % 177.02/177.14 ! [V_n] : % 177.02/177.14 ( 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))) % 177.02/177.14 => ( 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)))) % 177.02/177.14 & 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)))) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 177.02/177.14 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__number__of__even__number__of,axiom, % 177.02/177.14 ! [V_w_2,V_v_2,T_c] : % 177.02/177.14 ( class_Int_Onumber__ring(T_c) % 177.02/177.14 => hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Otimes__class_Otimes(T_c)),c_COMBI(T_c))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mult__2,axiom, % 177.02/177.14 ! [V_z,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mult__2__right,axiom, % 177.02/177.14 ! [V_z,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_one__add__one__is__two,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zero__eq__power2,axiom, % 177.02/177.14 ! [V_a_2,T_c] : % 177.02/177.14 ( class_Rings_Oring__1__no__zero__divisors(T_c) % 177.02/177.14 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) % 177.02/177.14 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zero__power2,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( class_Rings_Osemiring__1(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_semiring__norm_I115_J,axiom, % 177.02/177.14 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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_numeral__2__eq__2,axiom, % 177.02/177.14 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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 177.02/177.14 ! [V_x,T_a] : % 177.02/177.14 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.14 => 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)))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__eq__square,axiom, % 177.02/177.14 ! [V_a,T_a] : % 177.02/177.14 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 177.02/177.14 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))))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__2__eq__Suc,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__2__eq__Suc_H,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_one__power2,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( class_Rings_Osemiring__1(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__minus,axiom, % 177.02/177.14 ! [V_a,T_a] : % 177.02/177.14 ( class_Rings_Oring__1(T_a) % 177.02/177.14 => 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)))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_nat__mult__2,axiom, % 177.02/177.14 ! [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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_nat__mult__2__right,axiom, % 177.02/177.14 ! [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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__even__eq,axiom, % 177.02/177.14 ! [V_n,V_a,T_a] : % 177.02/177.14 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.14 => 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)))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 177.02/177.14 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)))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 177.02/177.14 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)))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_abs__power2,axiom, % 177.02/177.14 ! [V_a,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => 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)))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__abs,axiom, % 177.02/177.14 ! [V_a,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => 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)))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_nat__1__add__1,axiom, % 177.02/177.14 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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mod2__Suc__Suc,axiom, % 177.02/177.14 ! [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)))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_div2__Suc__Suc,axiom, % 177.02/177.14 ! [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))))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zmod__number__of__Bit0,axiom, % 177.02/177.14 ! [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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__self__div__2,axiom, % 177.02/177.14 ! [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 ). % 177.02/177.14 % 177.02/177.14 fof(fact_half__gt__zero__iff,axiom, % 177.02/177.14 ! [V_r_2,T_c] : % 177.02/177.14 ( ( class_Fields_Olinordered__field__inverse__zero(T_c) % 177.02/177.14 & class_Int_Onumber__ring(T_c) ) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_r_2)) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_half__gt__zero,axiom, % 177.02/177.14 ! [V_r,T_a] : % 177.02/177.14 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 177.02/177.14 & class_Int_Onumber__ring(T_a) ) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 177.02/177.14 => 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)))))) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zero__le__power2,axiom, % 177.02/177.14 ! [V_a,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => 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)))))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__le__imp__le,axiom, % 177.02/177.14 ! [V_y,V_x,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.14 => ( 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)))))) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__eq__imp__eq,axiom, % 177.02/177.14 ! [V_y,V_x,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.14 => ( 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)))) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.14 => V_x = V_y ) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zero__less__power2,axiom, % 177.02/177.14 ! [V_a_2,T_c] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 177.02/177.14 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__less__0,axiom, % 177.02/177.14 ! [V_a,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => ~ 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))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_sum__power2__eq__zero__iff,axiom, % 177.02/177.14 ! [V_y_2,V_x_2,T_c] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.14 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c) % 177.02/177.14 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.14 & V_y_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__eq__square__number__of,axiom, % 177.02/177.14 ! [V_w,T_b] : % 177.02/177.14 ( ( class_Groups_Omonoid__mult(T_b) % 177.02/177.14 & class_Int_Onumber(T_b) ) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_less__2__cases,axiom, % 177.02/177.14 ! [V_n] : % 177.02/177.14 ( 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))))) % 177.02/177.14 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.02/177.14 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_nat__2,axiom, % 177.02/177.14 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))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__eq__1__iff,axiom, % 177.02/177.14 ! [V_a_2,T_c] : % 177.02/177.14 ( class_Rings_Oring__1__no__zero__divisors(T_c) % 177.02/177.14 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) % 177.02/177.14 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_c) % 177.02/177.14 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c)) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 177.02/177.14 ! [V_n,V_x,T_a] : % 177.02/177.14 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__minus__even,axiom, % 177.02/177.14 ! [V_n,V_a,T_a] : % 177.02/177.14 ( class_Rings_Oring__1(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__less__imp__less,axiom, % 177.02/177.14 ! [V_y,V_x,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__semidom(T_a) % 177.02/177.14 => ( 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)))))) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 177.02/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_sum__power2__ge__zero,axiom, % 177.02/177.14 ! [V_y,V_x,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => 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))))))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_sum__power2__le__zero__iff,axiom, % 177.02/177.14 ! [V_y_2,V_x_2,T_c] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c))) % 177.02/177.14 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.14 & V_y_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_sum__power2__gt__zero__iff,axiom, % 177.02/177.14 ! [V_y_2,V_x_2,T_c] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_c) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 177.02/177.14 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.02/177.14 | V_y_2 != c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_not__sum__power2__lt__zero,axiom, % 177.02/177.14 ! [V_y,V_x,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => ~ 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))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__sum,axiom, % 177.02/177.14 ! [V_y,V_x,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zero__le__even__power_H,axiom, % 177.02/177.14 ! [V_n,V_a,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => 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)))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__odd__eq,axiom, % 177.02/177.14 ! [V_n,V_a,T_a] : % 177.02/177.14 ( class_Groups_Omonoid__mult(T_a) % 177.02/177.14 => 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))))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 177.02/177.14 ! [V_n,V_x,T_a] : % 177.02/177.14 ( class_Rings_Ocomm__semiring__1(T_a) % 177.02/177.14 => 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))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__minus1__even,axiom, % 177.02/177.14 ! [V_n,T_a] : % 177.02/177.14 ( class_Rings_Oring__1(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zdiv__number__of__Bit1,axiom, % 177.02/177.14 ! [V_v,V_w] : % 177.02/177.14 ( ( 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))) % 177.02/177.14 => 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)) ) % 177.02/177.14 & ( ~ 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))) % 177.02/177.14 => 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)) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mod2__gr__0,axiom, % 177.02/177.14 ! [V_m_2] : % 177.02/177.14 ( 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)))))) % 177.02/177.14 <=> 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_div__2__gt__zero,axiom, % 177.02/177.14 ! [V_n] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 177.02/177.14 => 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)))))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power2__diff,axiom, % 177.02/177.14 ! [V_y,V_x,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_odd__0__le__power__imp__0__le,axiom, % 177.02/177.14 ! [V_n,V_a,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => ( 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))))) % 177.02/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_odd__power__less__zero,axiom, % 177.02/177.14 ! [V_n,V_a,T_a] : % 177.02/177.14 ( class_Rings_Olinordered__idom(T_a) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 177.02/177.14 => 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))) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__minus1__odd,axiom, % 177.02/177.14 ! [V_n,T_a] : % 177.02/177.14 ( class_Rings_Oring__1(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_Suc__n__div__2__gt__zero,axiom, % 177.02/177.14 ! [V_n] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.02/177.14 => 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)))))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_of__nat__double,axiom, % 177.02/177.14 ! [V_x,T_a] : % 177.02/177.14 ( class_Rings_Osemiring__1(T_a) % 177.02/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 177.02/177.14 => 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))) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_pos__zmod__mult__2,axiom, % 177.02/177.14 ! [V_b,V_a] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.02/177.14 => 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))) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_neg__zdiv__mult__2,axiom, % 177.02/177.14 ! [V_b,V_a] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_int__of__code,axiom, % 177.02/177.14 ! [V_k] : % 177.02/177.14 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.02/177.14 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.02/177.14 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.02/177.14 => ( ( 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) % 177.02/177.14 => 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)))))) ) % 177.02/177.14 & ( 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) % 177.02/177.14 => 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)) ) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_of__int__num,axiom, % 177.02/177.14 ! [V_k_2,T_c] : % 177.02/177.14 ( class_Rings_Oring__1(T_c) % 177.02/177.14 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.14 => hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_k_2) = c_Groups_Ozero__class_Ozero(T_c) ) % 177.02/177.14 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.02/177.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.14 => hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 177.02/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.02/177.14 => hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_c,T_c)),tc_fun(tc_Int_Oint,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),T_c),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_c,T_c)),tc_fun(tc_Int_Oint,T_c)),tc_Int_Oint),c_COMBB(tc_fun(T_c,T_c),T_c,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,T_c),T_c),tc_Int_Oint),c_HOL_OLet(T_c,T_c)),c_Int_Oring__1__class_Oof__int(T_c)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_c,T_c),tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,T_c)),tc_Int_Oint),c_COMBS(T_c,T_c,T_c)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_c,T_c),tc_fun(T_c,tc_fun(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_fun(T_c,T_c))),tc_Int_Oint),c_COMBB(T_c,tc_fun(T_c,T_c),T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),tc_Int_Oint),c_If(T_c)),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_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_COMBI(T_c))))),hAPP(hAPP(c_COMBC(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Oplus__class_Oplus(T_c)),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_COMBI(T_c)))),c_Groups_Oone__class_Oone(T_c))))),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))))) ) ) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_power__m1__odd,axiom, % 177.02/177.14 ! [V_n,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I45_J,axiom, % 177.02/177.14 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I42_J,axiom, % 177.02/177.14 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I24_J,axiom, % 177.02/177.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_code__numeral__zero__minus__one,axiom, % 177.02/177.14 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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I7_J,axiom, % 177.02/177.14 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I37_J,axiom, % 177.02/177.14 c_Int_OPls != c_Int_OMin ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I40_J,axiom, % 177.02/177.14 c_Int_OMin != c_Int_OPls ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I47_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 177.02/177.14 <=> V_k_2 = c_Int_OMin ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I43_J,axiom, % 177.02/177.14 ! [V_l_2] : % 177.02/177.14 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 177.02/177.14 <=> c_Int_OMin = V_l_2 ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_Bit1__Min,axiom, % 177.02/177.14 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 177.02/177.14 % 177.02/177.14 fof(fact_bin__less__0__simps_I2_J,axiom, % 177.02/177.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I20_J,axiom, % 177.02/177.14 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I23_J,axiom, % 177.02/177.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I30_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I26_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I3_J,axiom, % 177.02/177.14 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I6_J,axiom, % 177.02/177.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I13_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I9_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I28_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I8_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_eq__number__of__Pls__Min,axiom, % 177.02/177.14 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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_Int_OMin__def,axiom, % 177.02/177.14 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mult__Min,axiom, % 177.02/177.14 ! [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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_neg__number__of__Min,axiom, % 177.02/177.14 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 177.02/177.14 % 177.02/177.14 fof(fact_pred__Pls,axiom, % 177.02/177.14 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__Min__right,axiom, % 177.02/177.14 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 177.02/177.14 % 177.02/177.14 fof(fact_add__Min,axiom, % 177.02/177.14 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 177.02/177.14 % 177.02/177.14 fof(fact_pred__Min,axiom, % 177.02/177.14 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 177.02/177.14 % 177.02/177.14 fof(fact_nonzero__number__of__Min,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_succ__Min,axiom, % 177.02/177.14 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I2_J,axiom, % 177.02/177.14 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mult__minus1__right,axiom, % 177.02/177.14 ! [V_z,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_mult__minus1,axiom, % 177.02/177.14 ! [V_z,T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_arith__simps_I31_J,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_number__of__Min,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_abs__minus__one,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( ( class_Int_Onumber__ring(T_a) % 177.02/177.14 & class_Rings_Olinordered__idom(T_a) ) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_divide__minus1,axiom, % 177.02/177.14 ! [V_x,T_a] : % 177.02/177.14 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.14 & class_Int_Onumber__ring(T_a) ) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I25_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_rel__simps_I11_J,axiom, % 177.02/177.14 ! [V_k_2] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 177.02/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zmod__minus1__right,axiom, % 177.02/177.14 ! [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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I4_J,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_minus__Min,axiom, % 177.02/177.14 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zmult__eq__1__iff,axiom, % 177.02/177.14 ! [V_n_2,V_m_2] : % 177.02/177.14 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.02/177.14 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.02/177.14 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 177.02/177.14 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 177.02/177.14 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 177.02/177.14 ! [V_n,V_m] : % 177.02/177.14 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.02/177.14 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 177.02/177.14 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I6_J,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_diff__bin__simps_I5_J,axiom, % 177.02/177.14 ! [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)) ). % 177.02/177.14 % 177.02/177.14 fof(fact_of__int__m1,axiom, % 177.02/177.14 ! [T_a] : % 177.02/177.14 ( class_Int_Onumber__ring(T_a) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zdiv__minus1__right,axiom, % 177.02/177.14 ! [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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_zero__code__numeral__code,axiom, % 177.02/177.14 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) ). % 177.02/177.14 % 177.02/177.14 fof(fact_minus1__divide,axiom, % 177.02/177.14 ! [V_x,T_a] : % 177.02/177.14 ( ( class_Fields_Ofield__inverse__zero(T_a) % 177.02/177.14 & class_Int_Onumber__ring(T_a) ) % 177.02/177.14 => 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)) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_abs__power__minus__one,axiom, % 177.02/177.14 ! [V_n,T_a] : % 177.02/177.14 ( ( class_Int_Onumber__ring(T_a) % 177.02/177.14 & class_Rings_Olinordered__idom(T_a) ) % 177.02/177.14 => 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) ) ). % 177.02/177.14 % 177.02/177.14 fof(fact_div__eq__minus1,axiom, % 177.02/177.14 ! [V_b] : % 177.02/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.02/177.14 => 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) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__pos__neg__trivial,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( 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))) % 177.41/177.14 => 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) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_zmod__minus1,axiom, % 177.41/177.14 ! [V_b] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => 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)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_one__code__numeral__code,axiom, % 177.41/177.14 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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_power__m1__even,axiom, % 177.41/177.14 ! [V_n,T_a] : % 177.41/177.14 ( class_Int_Onumber__ring(T_a) % 177.41/177.14 => 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) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nitpick_OFrac__def,axiom, % 177.41/177.14 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)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_int__ge__less__than__def,axiom, % 177.41/177.14 ! [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)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_int__ge__less__than2__def,axiom, % 177.41/177.14 ! [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)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_inj__graph,axiom, % 177.41/177.14 ! [T_d,T_c] : c_Fun_Oinj__on(tc_fun(T_c,T_d),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,T_d)),c_Set_OCollect(tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,T_d)),c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool)),hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,T_d,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nitpick_Oprod__def,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : c_Nitpick_Oprod(T_c,T_d,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),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(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat__of__aux__code,axiom, % 177.41/177.14 ! [V_n,V_i] : % 177.41/177.14 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.14 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 177.41/177.14 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__rel__def,axiom, % 177.41/177.14 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__correct,axiom, % 177.41/177.14 ! [V_a,V_b] : % 177.41/177.14 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_zmult2__lemma,axiom, % 177.41/177.14 ! [V_c,V_r,V_q,V_b,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osize_I1_J,axiom, % 177.41/177.14 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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nats__number__of,axiom, % 177.41/177.14 ! [V_w_2,T_c] : % 177.41/177.14 ( class_Int_Onumber__ring(T_c) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_sup__Un__eq2,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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)) % 177.41/177.14 <=> 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_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pred__subset__eq2,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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))) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_bot__empty__eq2,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_x_2),V_y_2)) % 177.41/177.14 <=> 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pred__equals__eq2,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,T_d,T_c] : % 177.41/177.14 ( 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_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) % 177.41/177.14 <=> V_R_2 = V_S_2 ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_inf__Int__eq2,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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)) % 177.41/177.14 <=> 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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_congruentD,axiom, % 177.41/177.14 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_d,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Ocongruent(T_c,T_d,V_r_2,V_f_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_z_2)),V_r_2)) % 177.41/177.14 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_congruent2D,axiom, % 177.41/177.14 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_e,T_d,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Ocongruent2(T_c,T_d,T_e,V_r1_2,V_r2_2,V_f_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y1_2),V_z1_2)),V_r1_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),V_y2_2),V_z2_2)),V_r2_2)) % 177.41/177.14 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Image__iff,axiom, % 177.41/177.14 ! [V_A_2,V_r_2,T_d,V_b_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2))) % 177.41/177.14 <=> ? [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.41/177.14 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rev__ImageI,axiom, % 177.41/177.14 ! [V_r_2,V_b_2,T_d,V_A_2,V_a_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Relation_OImage(T_c,T_d,V_r_2),V_A_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_unique__remainder,axiom, % 177.41/177.14 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( 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))) % 177.41/177.14 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => V_r = V_r_H ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_unique__quotient,axiom, % 177.41/177.14 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( 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))) % 177.41/177.14 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => V_q = V_q_H ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_self__remainder,axiom, % 177.41/177.14 ! [V_r,V_q,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__rel__0,axiom, % 177.41/177.14 ! [V_b] : % 177.41/177.14 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_INF__INT__eq2,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_r_2,T_e,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2)) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_SUP__UN__eq2,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_r_2,T_e,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2)) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_self__quotient,axiom, % 177.41/177.14 ! [V_r,V_q,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__rel__mod,axiom, % 177.41/177.14 ! [V_r,V_q,V_b,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__rel__div,axiom, % 177.41/177.14 ! [V_r,V_q,V_b,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nats__0,axiom, % 177.41/177.14 ! [T_c] : % 177.41/177.14 ( class_Rings_Osemiring__1(T_c) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__mod__div,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nats__add,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,T_c] : % 177.41/177.14 ( class_Rings_Osemiring__1(T_c) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Nat_Osemiring__1__class_ONats(T_c))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Nat_Osemiring__1__class_ONats(T_c))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nats__mult,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,T_c] : % 177.41/177.14 ( class_Rings_Osemiring__1(T_c) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Nat_Osemiring__1__class_ONats(T_c))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Nat_Osemiring__1__class_ONats(T_c))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nats__1,axiom, % 177.41/177.14 ! [T_c] : % 177.41/177.14 ( class_Rings_Osemiring__1(T_c) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Oone__class_Oone(T_c)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_of__nat__in__Nats,axiom, % 177.41/177.14 ! [V_n_2,T_c] : % 177.41/177.14 ( class_Rings_Osemiring__1(T_c) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Image__singleton__iff,axiom, % 177.41/177.14 ! [V_a_2,V_r_2,T_d,V_b_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2),V_b_2)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equiv__class__eq,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.14 => hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_quotient__eqI,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_X_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_Y_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.14 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_quotient__eq__iff,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_X_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_Y_2)) % 177.41/177.14 => ( V_X_2 = V_Y_2 % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__rel__div__mod,axiom, % 177.41/177.14 ! [V_a,V_b] : % 177.41/177.14 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Image__singleton,axiom, % 177.41/177.14 ! [V_a_2,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_c),c_member(tc_prod(T_d,T_c))),hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2))),V_r_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_eq__equiv__class,axiom, % 177.41/177.14 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_c] : % 177.41/177.14 ( hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.41/177.14 => ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_eq__equiv__class__iff,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 177.41/177.14 => ( hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equiv__class__eq__iff,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.14 <=> ( hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.41/177.14 & hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.14 & hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equiv__class__subset,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_eq__equiv__class__iff2,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 177.41/177.14 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_zadd1__lemma,axiom, % 177.41/177.14 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( 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))) % 177.41/177.14 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_zminus1__lemma,axiom, % 177.41/177.14 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) % 177.41/177.14 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_subset__equiv__class,axiom, % 177.41/177.14 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_c,T_c,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)))))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equiv__class__nondisjoint,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__relI,axiom, % 177.41/177.14 ! [V_r,V_q,V_b,V_a] : % 177.41/177.14 ( 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) % 177.41/177.14 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 177.41/177.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 177.41/177.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 177.41/177.14 => 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))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_zmult1__lemma,axiom, % 177.41/177.14 ! [V_a,V_r,V_q,V_c,V_b] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pair__imageI,axiom, % 177.41/177.14 ! [V_f_2,T_e,V_A_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_A_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_e),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_e,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)),V_A_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_norm__frac_Osimps,axiom, % 177.41/177.14 ! [V_a_2,V_b_2] : % 177.41/177.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.41/177.14 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 177.41/177.14 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.41/177.14 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_adjust__eq,axiom, % 177.41/177.14 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_sup2CI,axiom, % 177.41/177.14 ! [T_d,T_c,V_A_2,V_y_2,V_x_2,V_B_2] : % 177.41/177.14 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_sup2E,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 177.41/177.14 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_inf2E,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 177.41/177.14 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.41/177.14 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_inf2I,axiom, % 177.41/177.14 ! [T_d,T_c,V_B_2,V_y_2,V_x_2,V_A_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mem__splitI,axiom, % 177.41/177.14 ! [T_e,T_d,V_b_2,V_a_2,V_c_2,V_z_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(T_c,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_splitI,axiom, % 177.41/177.14 ! [T_d,T_c,V_b_2,V_a_2,V_f_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_prod__caseI,axiom, % 177.41/177.14 ! [T_d,T_c,V_b_2,V_a_2,V_f1_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_bot2E,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,T_d,T_c] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_splitD_H,axiom, % 177.41/177.14 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_e,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_e,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_c_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_swap__inj__on,axiom, % 177.41/177.14 ! [V_A_2,T_d,T_c] : c_Fun_Oinj__on(tc_prod(T_c,T_d),tc_prod(T_d,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,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_A_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_sup2I2,axiom, % 177.41/177.14 ! [V_A_2,T_d,T_c,V_y_2,V_x_2,V_B_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_sup2I1,axiom, % 177.41/177.14 ! [V_B_2,T_d,T_c,V_y_2,V_x_2,V_A_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rev__predicate2D,axiom, % 177.41/177.14 ! [V_Qa_2,T_d,T_c,V_y_2,V_x_2,V_Pa_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_Pa_2),V_Qa_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_predicate2D,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_Pa_2),V_Qa_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_inf2D2,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_inf2D1,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Pair__inject,axiom, % 177.41/177.14 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 177.41/177.14 ( 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) % 177.41/177.14 => ~ ( V_a = V_a_H % 177.41/177.14 => V_b != V_b_H ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Pair__eq,axiom, % 177.41/177.14 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.14 ( hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_H_2),V_b_H_2) % 177.41/177.14 <=> ( V_a_2 = V_a_H_2 % 177.41/177.14 & V_b_2 = V_b_H_2 ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__paired__All,axiom, % 177.41/177.14 ! [T_d,T_c,V_Pa_2] : % 177.41/177.14 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.41/177.14 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__weak__cong,axiom, % 177.41/177.14 ! [V_c_2,T_e,T_d,T_c,V_q_2,V_p_2] : % 177.41/177.14 ( V_p_2 = V_q_2 % 177.41/177.14 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_c_2),V_q_2) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__twice,axiom, % 177.41/177.14 ! [V_p_2,V_g_2,T_g,T_f,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_g,tc_prod(T_d,T_e)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_g,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(T_g,T_c),T_f),hAPP(c_COMBB(tc_prod(T_d,T_e),T_c,T_g),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2))),V_g_2)),V_p_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__conv,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_prod_Osimps_I2_J,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_splitD,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,V_f_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__eta,axiom, % 177.41/177.14 ! [V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_e),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_e,T_d),V_f_2)),c_Product__Type_OPair(T_c,T_d))) = V_f_2 ). % 177.41/177.14 % 177.41/177.14 fof(fact_The__split__eq,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__paired__The,axiom, % 177.41/177.14 ! [V_Pa_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),V_Pa_2) = c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_adjust__def,axiom, % 177.41/177.14 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_in__rel__def,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_R_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_c,T_d,V_R_2),V_x_2),V_y_2)) % 177.41/177.14 <=> 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)),V_R_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__mod__code__numeral__def,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 177.41/177.14 ! [V_w] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( 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)))) % 177.41/177.14 => 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))) ) % 177.41/177.14 & ( ~ 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)))) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg__correct,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg__div__mod,axiom, % 177.41/177.14 ! [V_l,V_k] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg__minus1,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg_Osimps,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( ( ( 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))) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( ~ ( 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))) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => 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))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg__eqn,axiom, % 177.41/177.14 ! [V_a,V_b] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => ( ( 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))) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( ~ 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))) % 177.41/177.14 => 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))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg__eqn__number__of,axiom, % 177.41/177.14 ! [V_w,V_v] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( 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)))) % 177.41/177.14 => 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))) ) % 177.41/177.14 & ( ~ 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)))) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nitpick_Orefl_H__def,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Nitpick_Orefl_H(T_c,V_r_2) % 177.41/177.14 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 177.41/177.14 ! [V_w] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( 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))) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( ~ 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))) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg_Osimps,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => 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) ) % 177.41/177.14 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => 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))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg__0,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg__correct,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg__div__mod,axiom, % 177.41/177.14 ! [V_l,V_k] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg__eqn__number__of,axiom, % 177.41/177.14 ! [V_w,V_v] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( 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))) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( ~ 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))) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg__eqn,axiom, % 177.41/177.14 ! [V_a,V_b] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.41/177.14 => 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) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 177.41/177.14 => 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))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__def,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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))) ) ) ) ) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => 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))) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__step,axiom, % 177.41/177.14 ! [V_m,V_n] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__pdivmod,axiom, % 177.41/177.14 ! [V_l_2,V_k_2] : % 177.41/177.14 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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) ) % 177.41/177.14 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)))) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negateSnd__def,axiom, % 177.41/177.14 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_apsnd__conv,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),hAPP(V_f_2,V_y_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__zero,axiom, % 177.41/177.14 ! [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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__base,axiom, % 177.41/177.14 ! [V_n,V_m] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 177.41/177.14 => 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) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negateSnd__eq,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__div__mod,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__rel__neg,axiom, % 177.41/177.14 ! [V_qr,V_b,V_a] : % 177.41/177.14 ( 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)) % 177.41/177.14 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__if,axiom, % 177.41/177.14 ! [V_m_2,V_n_2] : % 177.41/177.14 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 177.41/177.14 => 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) ) % 177.41/177.14 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pdivmod__def,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pdivmod__posDivAlg,axiom, % 177.41/177.14 ! [V_k,V_l] : % 177.41/177.14 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__int__code,axiom, % 177.41/177.14 ! [V_l_2,V_k_2] : % 177.41/177.14 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)) ) % 177.41/177.14 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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) ) % 177.41/177.14 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 => 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)))) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_UN__equiv__class__inject,axiom, % 177.41/177.14 ! [V_Y_2,V_X_2,V_f_2,T_d,V_r_2,V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.14 => ( c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2) % 177.41/177.14 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_Y_2),V_f_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.41/177.14 => ( ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.14 => ! [B_y] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) % 177.41/177.14 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2)) ) ) ) % 177.41/177.14 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 177.41/177.14 ! [V_a,V_r,V_q,V_c,V_b] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.41/177.14 => 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)))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 177.41/177.14 ! [V_c,V_r,V_q,V_b,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__rel__unique,axiom, % 177.41/177.14 ! [V_qr_H,V_qr,V_n,V_m] : % 177.41/177.14 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 177.41/177.14 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 177.41/177.14 => V_qr = V_qr_H ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 177.41/177.14 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__eq,axiom, % 177.41/177.14 ! [V_qr,V_n,V_m] : % 177.41/177.14 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 177.41/177.14 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__def,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__eq,axiom, % 177.41/177.14 ! [V_r,V_q,V_n,V_m] : % 177.41/177.14 ( 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))) % 177.41/177.14 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__eq,axiom, % 177.41/177.14 ! [V_r,V_q,V_n,V_m] : % 177.41/177.14 ( 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))) % 177.41/177.14 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__rel,axiom, % 177.41/177.14 ! [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)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__rel__add1__eq,axiom, % 177.41/177.14 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( 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))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 177.41/177.14 => 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)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg_Opsimps,axiom, % 177.41/177.14 ! [V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 177.41/177.14 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) % 177.41/177.14 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg_Opsimps,axiom, % 177.41/177.14 ! [V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 177.41/177.14 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) % 177.41/177.14 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__pos__neg__1__number__of,axiom, % 177.41/177.14 ! [V_w] : % 177.41/177.14 ( 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))) % 177.41/177.14 => 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))))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_apsnd__eq__conv,axiom, % 177.41/177.14 ! [V_g_2,V_x_2,V_f_2,T_c,T_d,T_e] : % 177.41/177.14 ( hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_g_2),V_x_2) % 177.41/177.14 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_snd__apsnd,axiom, % 177.41/177.14 ! [V_x_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_snd__def,axiom, % 177.41/177.14 ! [V_p_2,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_c),hAPP(c_COMBK(tc_fun(T_c,T_c),T_d),c_COMBI(T_c))),V_p_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_snd__conv,axiom, % 177.41/177.14 ! [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 ). % 177.41/177.14 % 177.41/177.14 fof(fact_snd__eqD,axiom, % 177.41/177.14 ! [V_a,V_y,V_x,T_a,T_b] : % 177.41/177.14 ( 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 % 177.41/177.14 => V_y = V_a ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__int__def,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__neg__pos,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__pos__pos,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__pos__pos__1__number__of,axiom, % 177.41/177.14 ! [V_w] : % 177.41/177.14 ( 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))) % 177.41/177.14 => 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))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__pos__neg,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => 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)))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__neg__neg,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => 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)))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_norm__frac_Opsimps,axiom, % 177.41/177.14 ! [V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 177.41/177.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.41/177.14 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 177.41/177.14 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 177.41/177.14 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 177.41/177.14 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_negDivAlg_Opinduct,axiom, % 177.41/177.14 ! [V_Pa_2,V_a1_2,V_a0_2] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ! [B_a,B_b] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( ~ ( 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))) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => 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))) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_posDivAlg_Opinduct,axiom, % 177.41/177.14 ! [V_Pa_2,V_a1_2,V_a0_2] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ! [B_a,B_b] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 177.41/177.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 177.41/177.14 => 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))) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mod__nat__def,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_accp__subset,axiom, % 177.41/177.14 ! [V_R2_2,V_R1_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_c,V_R2_2)),c_Wellfounded_Oaccp(T_c,V_R1_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_irrefl__def,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Relation_Oirrefl(T_c,V_r_2) % 177.41/177.14 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_norm__frac_Opinduct,axiom, % 177.41/177.14 ! [V_Pa_2,V_a1_2,V_a0_2] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ! [B_a,B_b] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => 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))) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_accp_Osimps,axiom, % 177.41/177.14 ! [V_a_2,V_r_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_a_2)) % 177.41/177.14 <=> ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 177.41/177.14 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),B_x)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_accp_Oequations,axiom, % 177.41/177.14 ! [V_a_2,V_r_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_a_2)) % 177.41/177.14 <=> ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 177.41/177.14 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),B_x)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_accp__downward,axiom, % 177.41/177.14 ! [V_a_2,V_b_2,V_r_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_b_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.41/177.14 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_a_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat__gcd_Opsimps,axiom, % 177.41/177.14 ! [V_y_2,V_x_2] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.14 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 177.41/177.14 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.14 => 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)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat_Osize_I2_J,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_in__measure,axiom, % 177.41/177.14 ! [V_f_2,V_y_2,V_x_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_c),V_f_2))) % 177.41/177.14 <=> 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))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat_Osize_I1_J,axiom, % 177.41/177.14 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__pos__neg__1__number__of,axiom, % 177.41/177.14 ! [V_w] : % 177.41/177.14 ( 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))) % 177.41/177.14 => 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))))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat__def,axiom, % 177.41/177.14 ! [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)))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat__gcd_Opinduct,axiom, % 177.41/177.14 ! [V_Pa_2,V_a1_2,V_a0_2] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ! [B_x,B_y] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_fst__apsnd,axiom, % 177.41/177.14 ! [V_x_2,V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_c,T_e),V_x_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_fst__def,axiom, % 177.41/177.14 ! [V_p_2,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_c),c_COMBK(T_c,T_d)),V_p_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Rep__Integ__inject,axiom, % 177.41/177.14 ! [V_y_2,V_x_2] : % 177.41/177.14 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 177.41/177.14 <=> V_x_2 = V_y_2 ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_fst__conv,axiom, % 177.41/177.14 ! [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 ). % 177.41/177.14 % 177.41/177.14 fof(fact_fst__eqD,axiom, % 177.41/177.14 ! [V_a,V_y,V_x,T_b,T_a] : % 177.41/177.14 ( 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 % 177.41/177.14 => V_x = V_a ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Pair__fst__snd__eq,axiom, % 177.41/177.14 ! [T_d,T_c,V_t_2,V_s_2] : % 177.41/177.14 ( V_s_2 = V_t_2 % 177.41/177.14 <=> ( hAPP(c_Product__Type_Ofst(T_c,T_d),V_s_2) = hAPP(c_Product__Type_Ofst(T_c,T_d),V_t_2) % 177.41/177.14 & hAPP(c_Product__Type_Osnd(T_c,T_d),V_s_2) = hAPP(c_Product__Type_Osnd(T_c,T_d),V_t_2) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_prod__eqI,axiom, % 177.41/177.14 ! [V_q,V_p,T_b,T_a] : % 177.41/177.14 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 177.41/177.14 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 177.41/177.14 => V_p = V_q ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_surjective__pairing,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pair__collapse,axiom, % 177.41/177.14 ! [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 ). % 177.41/177.14 % 177.41/177.14 fof(fact_prod__case__beta,axiom, % 177.41/177.14 ! [V_p_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_p_2)),hAPP(c_Product__Type_Osnd(T_d,T_e),V_p_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__int__def,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__comp__eq,axiom, % 177.41/177.14 ! [V_g_2,V_f_2,T_f,T_e,T_d,T_c] : hAPP(hAPP(c_COMBS(tc_prod(T_c,T_d),T_d,T_e),hAPP(hAPP(c_COMBB(T_f,tc_fun(T_d,T_e),tc_prod(T_c,T_d)),V_f_2),hAPP(hAPP(c_COMBB(T_c,T_f,tc_prod(T_c,T_d)),V_g_2),c_Product__Type_Ofst(T_c,T_d)))),c_Product__Type_Osnd(T_c,T_d)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),hAPP(hAPP(c_COMBB(T_f,tc_fun(T_d,T_e),T_c),V_f_2),V_g_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__beta,axiom, % 177.41/177.14 ! [V_z_2,V_Pa_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_z_2)),hAPP(c_Product__Type_Osnd(T_d,T_e),V_z_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_split__def,axiom, % 177.41/177.14 ! [V_p_2,V_c_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_p_2)),hAPP(c_Product__Type_Osnd(T_d,T_e),V_p_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_The__split,axiom, % 177.41/177.14 ! [V_Pa_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_c,T_d),hAPP(hAPP(c_COMBS(tc_prod(T_c,T_d),T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_HOL_Obool),tc_prod(T_c,T_d)),V_Pa_2),c_Product__Type_Ofst(T_c,T_d))),c_Product__Type_Osnd(T_c,T_d))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__neg__pos,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__pos__pos,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__pos__pos__1__number__of,axiom, % 177.41/177.14 ! [V_w] : % 177.41/177.14 ( 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))) % 177.41/177.14 => 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))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__pos__neg,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => 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)))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__neg__neg,axiom, % 177.41/177.14 ! [V_b,V_a] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 177.41/177.14 => 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)))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_prod__size__simp,axiom, % 177.41/177.14 ! [V_p_2,V_g_2,V_f_2,T_d,T_c] : c_Product__Type_Oprod_Oprod__size(T_c,T_d,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_c,T_d),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_exI__realizer,axiom, % 177.41/177.14 ! [T_c,T_d,V_x_2,V_y_2,V_Pa_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_d,T_c),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_conjI__realizer,axiom, % 177.41/177.14 ! [T_d,T_c,V_q_2,V_Qa_2,V_p_2,V_Pa_2] : % 177.41/177.14 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 177.41/177.14 => ( hBOOL(hAPP(V_Qa_2,V_q_2)) % 177.41/177.14 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_p_2),V_q_2)))) % 177.41/177.14 & hBOOL(hAPP(V_Qa_2,hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_p_2),V_q_2)))) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_div__nat__def,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_divmod__nat__rel__def,axiom, % 177.41/177.14 ! [V_qr_2,V_n_2,V_m_2] : % 177.41/177.14 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 177.41/177.14 <=> ( 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)) % 177.41/177.14 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.14 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.41/177.14 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.41/177.14 => ( 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))) % 177.41/177.14 & 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)) ) ) % 177.41/177.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 177.41/177.14 => ( 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))) % 177.41/177.14 & 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))) ) ) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_inv__image__def,axiom, % 177.41/177.14 ! [V_f_2,V_r_2,T_c,T_d] : hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_d),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_d,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_d,T_d)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_d),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_d,T_d)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_d),tc_fun(T_c,tc_prod(T_d,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_d)),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_prod(T_d,T_d))),T_c),c_COMBB(T_d,tc_prod(T_d,T_d),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_prod(T_d,T_d)),T_c),c_Product__Type_OPair(T_d,T_d)),V_f_2))),V_f_2)))),V_r_2))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mlex__leq,axiom, % 177.41/177.14 ! [V_R_2,T_c,V_y_2,V_x_2,V_f_2] : % 177.41/177.14 ( 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))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_R_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_c,V_f_2,V_R_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osize_I2_J,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Oinject,axiom, % 177.41/177.14 ! [V_code__numeral_H_2,V_code__numeral_2] : % 177.41/177.14 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 177.41/177.14 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osimps_I3_J,axiom, % 177.41/177.14 ! [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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osimps_I2_J,axiom, % 177.41/177.14 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 177.41/177.14 % 177.41/177.14 fof(fact_in__inv__image,axiom, % 177.41/177.14 ! [V_f_2,V_r_2,T_d,V_y_2,V_x_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),V_r_2),V_f_2))) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Suc__code__numeral__minus__one,axiom, % 177.41/177.14 ! [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 ). % 177.41/177.14 % 177.41/177.14 fof(fact_mlex__less,axiom, % 177.41/177.14 ! [V_R_2,T_c,V_y_2,V_x_2,V_f_2] : % 177.41/177.14 ( 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))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_c,V_f_2,V_R_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osize_I4_J,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rp__inv__image__def,axiom, % 177.41/177.14 ! [T_d,T_c] : c_FunDef_Orp__inv__image(T_c,T_d) = hAPP(c_Product__Type_Oprod_Oprod__case(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(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(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_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_COMBS(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(T_d,T_c)),c_Product__Type_OPair(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),c_Relation_Oinv__image(T_c,T_d))))),c_Relation_Oinv__image(T_c,T_d))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_finite__psubset__def,axiom, % 177.41/177.14 ! [T_c] : c_Wellfounded_Ofinite__psubset(T_c) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBS(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_c)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osize_I3_J,axiom, % 177.41/177.14 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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_in__finite__psubset,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_c))) % 177.41/177.14 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.41/177.14 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat_Osize_I4_J,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_prod_Orecs,axiom, % 177.41/177.14 ! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : c_Product__Type_Oprod_Oprod__rec(T_d,T_e,T_c,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_in__lex__prod,axiom, % 177.41/177.14 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_c,T_d,V_r_2,V_s_2))) % 177.41/177.14 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_H_2)),V_r_2)) % 177.41/177.14 | ( V_a_2 = V_a_H_2 % 177.41/177.14 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat__size,axiom, % 177.41/177.14 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat_Osize_I3_J,axiom, % 177.41/177.14 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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_same__fstI,axiom, % 177.41/177.14 ! [T_c,V_R_2,V_y_2,V_y_H_2,T_d,V_x_2,V_Pa_2] : % 177.41/177.14 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_c,T_d,V_Pa_2,V_R_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equivp__equiv,axiom, % 177.41/177.14 ! [V_A_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequiv(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_A_2) % 177.41/177.14 <=> c_Equiv__Relations_Oequivp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_A_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_apsnd__apfst,axiom, % 177.41/177.14 ! [V_x_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_f,T_c,T_e,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_f,T_e),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_f,T_e),V_x_2))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_apfst__conv,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_f_2,T_d,T_c,T_e] : hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_e,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_x_2)),V_y_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_apfst__eq__conv,axiom, % 177.41/177.14 ! [V_g_2,V_x_2,V_f_2,T_d,T_c,T_e] : % 177.41/177.14 ( hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_g_2),V_x_2) % 177.41/177.14 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_fst__apfst,axiom, % 177.41/177.14 ! [V_x_2,V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_snd__apfst,axiom, % 177.41/177.14 ! [V_x_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_e,T_c),V_x_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_identity__equivp,axiom, % 177.41/177.14 ! [T_c] : c_Equiv__Relations_Oequivp(T_c,c_fequal) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equivp__def,axiom, % 177.41/177.14 ! [V_R_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.14 <=> ! [B_x,B_y] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 177.41/177.14 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equivp__reflp,axiom, % 177.41/177.14 ! [V_x_2,V_R_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equivp__symp,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_R_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equivp__transp,axiom, % 177.41/177.14 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_c] : % 177.41/177.14 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_apsnd__apfst__commute,axiom, % 177.41/177.14 ! [V_p_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_f,T_c,T_e,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_f,T_c,T_d,V_g_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_f,V_f_2),V_p_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_apfst__apsnd,axiom, % 177.41/177.14 ! [V_x_2,V_g_2,T_f,V_f_2,T_d,T_c,T_e] : hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),hAPP(c_Product__Type_Oapsnd(T_f,T_d,T_e,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_f),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_e,T_f),V_x_2))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pair__lessI2,axiom, % 177.41/177.14 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_ImageE,axiom, % 177.41/177.14 ! [V_A_2,V_r_2,T_d,V_b_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2))) % 177.41/177.14 => ~ ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2)) % 177.41/177.14 => ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mlex__prod__def,axiom, % 177.41/177.14 ! [V_R_2,V_f_2,T_c] : c_Wellfounded_Omlex__prod(T_c,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_c),T_c),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_c,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(tc_Nat_Onat,T_c)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,tc_prod(tc_Nat_Onat,T_c)),T_c),c_Product__Type_OPair(tc_Nat_Onat,T_c)),V_f_2)),c_COMBI(T_c))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pair__less__def,axiom, % 177.41/177.14 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 177.41/177.14 % 177.41/177.14 fof(fact_measure__def,axiom, % 177.41/177.14 ! [T_c] : c_Wellfounded_Omeasure(T_c) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_c),c_Wellfounded_Oless__than) ). % 177.41/177.14 % 177.41/177.14 fof(fact_less__than__iff,axiom, % 177.41/177.14 ! [V_y_2,V_x_2] : % 177.41/177.14 ( 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)) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pair__lessI1,axiom, % 177.41/177.14 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pair__leqI2,axiom, % 177.41/177.14 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_smin__insertI,axiom, % 177.41/177.14 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => 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)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_smax__insertI,axiom, % 177.41/177.14 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => 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)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_smin__emptyI,axiom, % 177.41/177.14 ! [V_X_2] : % 177.41/177.14 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 177.41/177.14 => 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)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_smax__emptyI,axiom, % 177.41/177.14 ! [V_Y_2] : % 177.41/177.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 177.41/177.14 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 177.41/177.14 => 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)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pair__leqI1,axiom, % 177.41/177.14 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wmax__insertI,axiom, % 177.41/177.14 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => 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)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wmin__insertI,axiom, % 177.41/177.14 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => ( 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)) % 177.41/177.14 => 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)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Field__insert,axiom, % 177.41/177.14 ! [V_r_2,V_b_2,V_a_2,T_c] : hAPP(c_Relation_OField(T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_c),V_r_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Field__Union,axiom, % 177.41/177.14 ! [V_R_2,T_c] : hAPP(c_Relation_OField(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Relation_OField(T_c)),V_R_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Field__empty,axiom, % 177.41/177.14 ! [T_c] : hAPP(c_Relation_OField(T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mono__Field,axiom, % 177.41/177.14 ! [V_s_2,V_r_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OField(T_c),V_r_2)),hAPP(c_Relation_OField(T_c),V_s_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Field__Un,axiom, % 177.41/177.14 ! [V_s_2,V_r_2,T_c] : hAPP(c_Relation_OField(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OField(T_c),V_r_2)),hAPP(c_Relation_OField(T_c),V_s_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_finite__Field,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_OField(T_c),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wmax__emptyI,axiom, % 177.41/177.14 ! [V_X_2] : % 177.41/177.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 177.41/177.14 => 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)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wmin__emptyI,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_min__weak__def,axiom, % 177.41/177.14 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)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__weak__def,axiom, % 177.41/177.14 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)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Id__on__def,axiom, % 177.41/177.14 ! [V_A_2,T_c] : c_Relation_OId__on(T_c,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,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_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),c_COMBI(T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Id__on__def_H,axiom, % 177.41/177.14 ! [V_A_2,T_c] : c_Relation_OId__on(T_c,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),c_fequal))),V_A_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Id__on__empty,axiom, % 177.41/177.14 ! [T_c] : c_Relation_OId__on(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Image__Id__on,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_c] : hAPP(c_Relation_OImage(T_c,T_c,c_Relation_OId__on(T_c,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Id__on__eqI,axiom, % 177.41/177.14 ! [V_A_2,T_c,V_b_2,V_a_2] : % 177.41/177.14 ( V_a_2 = V_b_2 % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Relation_OId__on(T_c,V_A_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Id__on__iff,axiom, % 177.41/177.14 ! [V_A_2,V_y_2,V_x_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Relation_OId__on(T_c,V_A_2))) % 177.41/177.14 <=> ( V_x_2 = V_y_2 % 177.41/177.14 & hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__strict__def,axiom, % 177.41/177.14 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__ext__additive,axiom, % 177.41/177.14 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_c,V_R_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_c,V_R_2))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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))),c_Wellfounded_Omax__ext(T_c,V_R_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_min__strict__def,axiom, % 177.41/177.14 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__extp__max__ext__eq,axiom, % 177.41/177.14 ! [V_xa_2,V_x_2,V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Omax__extp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_R_2),V_x_2,V_xa_2) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_c,V_R_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_min__rpair__set,axiom, % 177.41/177.14 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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__rpair__set,axiom, % 177.41/177.14 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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rp__inv__image__rp,axiom, % 177.41/177.14 ! [V_f_2,T_d,V_Pa_2,T_c] : % 177.41/177.14 ( c_FunDef_Oreduction__pair(T_c,V_Pa_2) % 177.41/177.14 => c_FunDef_Oreduction__pair(T_d,hAPP(hAPP(c_FunDef_Orp__inv__image(T_c,T_d),V_Pa_2),V_f_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equiv__intrel__iff,axiom, % 177.41/177.14 ! [V_y_2,V_x_2] : % 177.41/177.14 ( 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)))) % 177.41/177.14 <=> 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)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_intrel__iff,axiom, % 177.41/177.14 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 177.41/177.14 ( 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)) % 177.41/177.14 <=> 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) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Id__onE,axiom, % 177.41/177.14 ! [V_A_2,V_c_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_c_2),c_Relation_OId__on(T_c,V_A_2))) % 177.41/177.14 => ~ ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.14 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_equiv__intrel,axiom, % 177.41/177.14 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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_of__int,axiom, % 177.41/177.14 ! [V_j_2,V_i_2,T_c] : % 177.41/177.14 ( class_Rings_Oring__1(T_c) % 177.41/177.14 => hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_j_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_One__int__def,axiom, % 177.41/177.14 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))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_mult,axiom, % 177.41/177.14 ! [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))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Rep__Integ__inverse,axiom, % 177.41/177.14 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 177.41/177.14 % 177.41/177.14 fof(fact_minus,axiom, % 177.41/177.14 ! [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))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Zero__int__def,axiom, % 177.41/177.14 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))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_int__def,axiom, % 177.41/177.14 ! [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))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_add,axiom, % 177.41/177.14 ! [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))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_nat,axiom, % 177.41/177.14 ! [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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_minus__int__def,axiom, % 177.41/177.14 ! [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))))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_less,axiom, % 177.41/177.14 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 177.41/177.14 ( 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))))))) % 177.41/177.14 <=> 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))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_le,axiom, % 177.41/177.14 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 177.41/177.14 ( 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))))))) % 177.41/177.14 <=> 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))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_eq__Abs__Integ,axiom, % 177.41/177.14 ! [V_z_2] : % 177.41/177.14 ~ ! [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))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Integ__def,axiom, % 177.41/177.14 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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osimps_I5_J,axiom, % 177.41/177.14 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_c,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Rep__Integ,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_code__numeral_Osimps_I4_J,axiom, % 177.41/177.14 ! [V_f2_2,V_f1_2,T_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_c,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition__Integ,axiom, % 177.41/177.14 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) ). % 177.41/177.14 % 177.41/177.14 fof(fact_accp__acc__eq,axiom, % 177.41/177.14 ! [V_x_2,V_r_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2)),V_x_2)) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__def,axiom, % 177.41/177.14 ! [V_s_2,V_r_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_e))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_c),c_COMBS(T_e,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,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_e),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_c),c_COMBC(T_e,tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_e),tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_c,T_e)))),c_Product__Type_OPair(T_c,T_e)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_e,T_d)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_e,T_d),tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_e,T_d)))),hAPP(c_COMBC(T_e,T_d,tc_prod(T_e,T_d)),c_Product__Type_OPair(T_e,T_d))))),V_s_2))))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__compI,axiom, % 177.41/177.14 ! [V_s_2,V_c_2,T_e,V_r_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_b_2),V_c_2)),V_s_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__UNION__distrib,axiom, % 177.41/177.14 ! [V_r_2,V_I_2,T_f,V_s_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_f),hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_s_2)),V_r_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__UNION__distrib2,axiom, % 177.41/177.14 ! [V_s_2,V_r_2,V_I_2,T_f,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_f),c_Relation_Orel__comp(T_c,T_e,T_d)),V_r_2)),V_s_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__empty1,axiom, % 177.41/177.14 ! [V_R_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__empty2,axiom, % 177.41/177.14 ! [V_R_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__distrib,axiom, % 177.41/177.14 ! [V_T_2,V_S_2,V_R_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_R_2),V_T_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__distrib2,axiom, % 177.41/177.14 ! [V_R_2,V_T_2,V_S_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_e),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_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_T_2),V_R_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_rel__comp__mono,axiom, % 177.41/177.14 ! [V_s_2,V_s_H_2,T_e,V_r_2,V_r_H_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_O__assoc,axiom, % 177.41/177.14 ! [V_T_2,V_S_2,V_R_2,T_f,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_f,T_e),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_f,T_d),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_f,T_e,T_d),V_S_2),V_T_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_union__comp__emptyL,axiom, % 177.41/177.14 ! [V_B_2,V_C_2,V_A_2,T_c] : % 177.41/177.14 ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) % 177.41/177.14 => ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) % 177.41/177.14 => hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_union__comp__emptyR,axiom, % 177.41/177.14 ! [V_C_2,V_B_2,V_A_2,T_c] : % 177.41/177.14 ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) % 177.41/177.14 => ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) % 177.41/177.14 => hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_acc__subset,axiom, % 177.41/177.14 ! [V_R2_2,V_R1_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Oacc(T_c,V_R2_2)),c_Wellfounded_Oacc(T_c,V_R1_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_acc_Osimps,axiom, % 177.41/177.14 ! [V_r_2,V_a_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,V_r_2))) % 177.41/177.14 <=> ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),V_a_2)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Wellfounded_Oacc(T_c,V_r_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_acc__downward,axiom, % 177.41/177.14 ! [V_a_2,V_r_2,V_b_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Wellfounded_Oacc(T_c,V_r_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__ext__compat,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_S_2)),V_R_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_c,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_c,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_c,V_R_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_min__ext__compat,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_S_2)),V_R_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_c,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_c,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_c,V_R_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition_OAbs__image,axiom, % 177.41/177.14 ! [V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] : % 177.41/177.14 ( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2) % 177.41/177.14 => hAPP(c_Set_Oimage(T_d,T_c,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition_ORep__range,axiom, % 177.41/177.14 ! [V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] : % 177.41/177.14 ( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2) % 177.41/177.14 => hAPP(c_Set_Oimage(T_c,T_d,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = V_A_2 ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition_OAbs__inject,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] : % 177.41/177.14 ( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),V_A_2)) % 177.41/177.14 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 177.41/177.14 <=> V_x_2 = V_y_2 ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition_ORep__inject,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] : % 177.41/177.14 ( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2) % 177.41/177.14 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 177.41/177.14 <=> V_x_2 = V_y_2 ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition_ORep__inverse,axiom, % 177.41/177.14 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] : % 177.41/177.14 ( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2) % 177.41/177.14 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition_ORep,axiom, % 177.41/177.14 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] : % 177.41/177.14 ( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_type__definition_OAbs__inverse,axiom, % 177.41/177.14 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] : % 177.41/177.14 ( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),V_A_2)) % 177.41/177.14 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pred__comp__rel__comp__eq,axiom, % 177.41/177.14 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_e,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_c,T_d,T_e,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_r_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e)))),V_s_2)),V_x_2),V_y_2)) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_reduction__pairI,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_R_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_S_2)),V_R_2)) % 177.41/177.14 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(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)),V_R_2),V_S_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__extp_Oequations,axiom, % 177.41/177.14 ! [V_a2_2,V_a1_2,V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Omax__extp(T_c,V_R_2,V_a1_2,V_a2_2) % 177.41/177.14 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a1_2)) % 177.41/177.14 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a2_2)) % 177.41/177.14 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.14 & ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_a1_2)) % 177.41/177.14 => ? [B_xa] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_a2_2)) % 177.41/177.14 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__less__than,axiom, % 177.41/177.14 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pred__comp_Ointros,axiom, % 177.41/177.14 ! [T_e,T_d,T_c,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_c,T_d,T_e,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__empty,axiom, % 177.41/177.14 ! [T_c] : c_Wellfounded_Owf(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__inv__image,axiom, % 177.41/177.14 ! [V_f_2,T_d,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(T_d,hAPP(hAPP(c_Relation_Oinv__image(T_c,T_d),V_r_2),V_f_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__lex__prod,axiom, % 177.41/177.14 ! [V_rb_2,T_d,V_ra_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_ra_2) % 177.41/177.14 => ( c_Wellfounded_Owf(T_d,V_rb_2) % 177.41/177.14 => c_Wellfounded_Owf(tc_prod(T_c,T_d),c_Wellfounded_Olex__prod(T_c,T_d,V_ra_2,V_rb_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__measure,axiom, % 177.41/177.14 ! [V_f_2,T_c] : c_Wellfounded_Owf(T_c,hAPP(c_Wellfounded_Omeasure(T_c),V_f_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__comp__self,axiom, % 177.41/177.14 ! [V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_R_2) % 177.41/177.14 <=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_R_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__subset,axiom, % 177.41/177.14 ! [V_p_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_p_2),V_r_2)) % 177.41/177.14 => c_Wellfounded_Owf(T_c,V_p_2) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_min__ext__wf,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_c,V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__less,axiom, % 177.41/177.14 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)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__finite__psubset,axiom, % 177.41/177.14 ! [T_c] : c_Wellfounded_Owf(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_c)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pred__comp_Oequations,axiom, % 177.41/177.14 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_e,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_c,T_d,T_e,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 177.41/177.14 <=> ? [B_b] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 177.41/177.14 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__Int2,axiom, % 177.41/177.14 ! [V_r_H_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__Int1,axiom, % 177.41/177.14 ! [V_r_H_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__mlex,axiom, % 177.41/177.14 ! [V_f_2,V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_R_2) % 177.41/177.14 => c_Wellfounded_Owf(T_c,c_Wellfounded_Omlex__prod(T_c,V_f_2,V_R_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__pair__less,axiom, % 177.41/177.14 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__ext__wf,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_c,V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__irrefl,axiom, % 177.41/177.14 ! [V_a_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__asym,axiom, % 177.41/177.14 ! [V_x_2,V_a_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_x_2)),V_r_2)) % 177.41/177.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_a_2)),V_r_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__not__sym,axiom, % 177.41/177.14 ! [V_x_2,V_a_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_x_2)),V_r_2)) % 177.41/177.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_a_2)),V_r_2)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__not__refl,axiom, % 177.41/177.14 ! [V_a_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__int__ge__less__than2,axiom, % 177.41/177.14 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__int__ge__less__than,axiom, % 177.41/177.14 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__acc__iff,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Wellfounded_Oacc(T_c,V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_acc__wfD,axiom, % 177.41/177.14 ! [V_x_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__no__loop,axiom, % 177.41/177.14 ! [V_R_2,T_c] : % 177.41/177.14 ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) % 177.41/177.14 => c_Wellfounded_Owf(T_c,V_R_2) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__union__merge,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) % 177.41/177.14 <=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_S_2),V_R_2))),V_S_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 <=> ~ ? [B_f] : % 177.41/177.14 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wfE__pf,axiom, % 177.41/177.14 ! [V_A_2,V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_R_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_c,T_c,V_R_2),V_A_2))) % 177.41/177.14 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__union__compatible,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_R_2) % 177.41/177.14 => ( c_Wellfounded_Owf(T_c,V_S_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_S_2)),V_R_2)) % 177.41/177.14 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf,axiom, % 177.41/177.14 ! [T_c] : % 177.41/177.14 ( class_Orderings_Owellorder(T_c) % 177.41/177.14 => c_Wellfounded_Owf(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_c)))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_reduction__pair__def,axiom, % 177.41/177.14 ! [V_Pa_2,T_c] : % 177.41/177.14 ( c_FunDef_Oreduction__pair(T_c,V_Pa_2) % 177.41/177.14 <=> ( c_Wellfounded_Owf(T_c,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2)) % 177.41/177.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_reduction__pair__lemma,axiom, % 177.41/177.14 ! [V_S_2,V_R_2,V_Pa_2,T_c] : % 177.41/177.14 ( c_FunDef_Oreduction__pair(T_c,V_Pa_2) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2))) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2))) % 177.41/177.14 => ( c_Wellfounded_Owf(T_c,V_S_2) % 177.41/177.14 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__lenlex,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(tc_List_Olist(T_c),c_List_Olenlex(T_c,V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__if__measure,axiom, % 177.41/177.14 ! [T_c,V_g_2,V_f_2,V_Pa_2] : % 177.41/177.14 ( ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.14 => 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))) ) % 177.41/177.14 => c_Wellfounded_Owf(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),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),V_Pa_2))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),V_g_2))))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_max__ext_Ointros,axiom, % 177.41/177.14 ! [V_R_2,V_Y_2,V_X_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_X_2)) % 177.41/177.14 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Y_2)) % 177.41/177.14 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.14 => ( ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_X_2)) % 177.41/177.14 => ? [B_xa] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_Y_2)) % 177.41/177.14 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_xa)),V_R_2)) ) ) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_c,V_R_2))) ) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_pred__nat__def,axiom, % 177.41/177.14 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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__lex,axiom, % 177.41/177.14 ! [V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(tc_List_Olist(T_c),c_List_Olex(T_c,V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__lexn,axiom, % 177.41/177.14 ! [V_n_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => c_Wellfounded_Owf(tc_List_Olist(T_c),hAPP(c_List_Olexn(T_c,V_r_2),V_n_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_lex__def,axiom, % 177.41/177.14 ! [V_r_2,T_c] : c_List_Olex(T_c,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_c,V_r_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_lexn_Osimps_I1_J,axiom, % 177.41/177.14 ! [V_r_2,T_c] : hAPP(c_List_Olexn(T_c,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__pred__nat,axiom, % 177.41/177.14 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__same__fst,axiom, % 177.41/177.14 ! [T_c,V_R_2,T_d,V_Pa_2] : % 177.41/177.14 ( ! [B_x] : % 177.41/177.14 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.14 => c_Wellfounded_Owf(T_d,hAPP(V_R_2,B_x)) ) % 177.41/177.14 => c_Wellfounded_Owf(tc_prod(T_c,T_d),c_Recdef_Osame__fst(T_c,T_d,V_Pa_2,V_R_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nitpick_Ozero__frac__def,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__Collect__split,axiom, % 177.41/177.14 ! [V_Pa_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(c_Set_OCollect(tc_prod(T_d,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d)),hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Pa_2))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_RangeI,axiom, % 177.41/177.14 ! [V_r_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Relation_ORange(T_c,T_d),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__Id__on,axiom, % 177.41/177.14 ! [V_A_2,T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Relation_OId__on(T_c,V_A_2)) = V_A_2 ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__Diff__subset,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_d,T_c),V_A_2)),hAPP(c_Relation_ORange(T_d,T_c),V_B_2))),hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__Union,axiom, % 177.41/177.14 ! [V_S_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_d,T_c)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__empty__iff,axiom, % 177.41/177.14 ! [V_r_2,T_c,T_d] : % 177.41/177.14 ( hAPP(c_Relation_ORange(T_d,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.14 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__empty,axiom, % 177.41/177.14 ! [T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__Un__eq,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,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(c_Relation_ORange(T_d,T_c),V_A_2)),hAPP(c_Relation_ORange(T_d,T_c),V_B_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_finite__Range,axiom, % 177.41/177.14 ! [V_r_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Relation_ORange(T_c,T_d),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_snd__eq__Range,axiom, % 177.41/177.14 ! [V_R_2,T_c,T_d] : hAPP(c_Set_Oimage(tc_prod(T_d,T_c),T_c,c_Product__Type_Osnd(T_d,T_c)),V_R_2) = hAPP(c_Relation_ORange(T_d,T_c),V_R_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__iff,axiom, % 177.41/177.14 ! [V_r_2,T_d,V_a_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ORange(T_d,T_c),V_r_2))) % 177.41/177.14 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),V_a_2)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__insert,axiom, % 177.41/177.14 ! [V_r_2,V_b_2,V_a_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),hAPP(c_Relation_ORange(T_d,T_c),V_r_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Range__Int__subset,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_d,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(c_Relation_ORange(T_d,T_c),V_A_2)),hAPP(c_Relation_ORange(T_d,T_c),V_B_2)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nitpick_Oone__frac__def,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 177.41/177.14 ! [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))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_RangeP__Range__eq,axiom, % 177.41/177.14 ! [V_x_2,V_r_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Predicate_ORangeP(T_c,T_d,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_r_2)),V_x_2)) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Relation_ORange(T_c,T_d),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_RangeP_Ointros,axiom, % 177.41/177.14 ! [T_d,T_c,V_b_2,V_a_2,V_r_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.41/177.14 => hBOOL(hAPP(c_Predicate_ORangeP(T_c,T_d,V_r_2),V_b_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_RangeP_Oequations,axiom, % 177.41/177.14 ! [V_a2_2,V_r_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Predicate_ORangeP(T_c,T_d,V_r_2),V_a2_2)) % 177.41/177.14 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Nitpick_Ofrac__def,axiom, % 177.41/177.14 ! [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)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_RangeE,axiom, % 177.41/177.14 ! [V_r_2,T_d,V_b_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_d,T_c),V_r_2))) % 177.41/177.14 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_wf__Un,axiom, % 177.41/177.14 ! [V_s_2,V_r_2,T_c] : % 177.41/177.14 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.14 => ( c_Wellfounded_Owf(T_c,V_s_2) % 177.41/177.14 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_c),V_r_2)),hAPP(c_Relation_ORange(T_c,T_c),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.14 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_DomainI,axiom, % 177.41/177.14 ! [V_r_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__Id__on,axiom, % 177.41/177.14 ! [V_A_2,T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Relation_OId__on(T_c,V_A_2)) = V_A_2 ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__empty__iff,axiom, % 177.41/177.14 ! [V_r_2,T_d,T_c] : % 177.41/177.14 ( hAPP(c_Relation_ODomain(T_c,T_d),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.14 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__empty,axiom, % 177.41/177.14 ! [T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__mono,axiom, % 177.41/177.14 ! [V_s_2,V_r_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_s_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__Un__eq,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),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(c_Relation_ODomain(T_c,T_d),V_A_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_B_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_finite__Domain,axiom, % 177.41/177.14 ! [V_r_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),V_r_2)) % 177.41/177.14 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_fst__eq__Domain,axiom, % 177.41/177.14 ! [V_R_2,T_d,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_c,c_Product__Type_Ofst(T_c,T_d)),V_R_2) = hAPP(c_Relation_ODomain(T_c,T_d),V_R_2) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__iff,axiom, % 177.41/177.14 ! [V_r_2,T_d,V_a_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) % 177.41/177.14 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),B_y)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__insert,axiom, % 177.41/177.14 ! [V_r_2,V_b_2,V_a_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__Int__subset,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),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_Relation_ODomain(T_c,T_d),V_A_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_B_2)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__Diff__subset,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_d),V_A_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_B_2))),hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Field__def,axiom, % 177.41/177.14 ! [V_r_2,T_c] : hAPP(c_Relation_OField(T_c),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_c),V_r_2)),hAPP(c_Relation_ORange(T_c,T_c),V_r_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__Union,axiom, % 177.41/177.14 ! [V_S_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_c,T_d)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Domain__Collect__split,axiom, % 177.41/177.14 ! [V_Pa_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d)),V_Pa_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_DomainP__Domain__eq,axiom, % 177.41/177.14 ! [V_x_2,V_r_2,T_d,T_c] : % 177.41/177.14 ( hBOOL(hAPP(c_Predicate_ODomainP(T_c,T_d,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_r_2)),V_x_2)) % 177.41/177.14 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_DomainE,axiom, % 177.41/177.14 ! [V_r_2,T_d,V_a_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) % 177.41/177.14 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),B_y)),V_r_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_image__split__eq__Sigma,axiom, % 177.41/177.14 ! [V_A_2,V_g_2,V_f_2,T_d,T_c,T_e] : hAPP(c_Set_Oimage(T_e,tc_prod(T_c,T_d),hAPP(hAPP(c_COMBS(T_e,T_d,tc_prod(T_c,T_d)),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_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Set_Oimage(T_e,T_c,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_Oimage(T_e,T_d,V_g_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_e,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool),T_c),c_Set_Ovimage(T_e,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)))))),V_A_2))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_DomainP_Ointros,axiom, % 177.41/177.14 ! [T_d,T_c,V_b_2,V_a_2,V_r_2] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.41/177.14 => hBOOL(hAPP(c_Predicate_ODomainP(T_c,T_d,V_r_2),V_a_2)) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_SigmaI,axiom, % 177.41/177.14 ! [V_B_2,V_b_2,T_d,V_A_2,V_a_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.41/177.14 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2))) % 177.41/177.14 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Sigma__empty1,axiom, % 177.41/177.14 ! [V_B_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Times__eq__cancel2,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,V_C_2,V_x_2,T_c] : % 177.41/177.14 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_C_2)) % 177.41/177.14 => ( hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2)) % 177.41/177.14 <=> V_A_2 = V_B_2 ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Sigma__Union,axiom, % 177.41/177.14 ! [V_B_2,V_X_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Product__Type_OSigma(T_c,T_d)),V_B_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_card__cartesian__product,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Finite__Set_Ocard(tc_prod(T_c,T_d)),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_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_setsum__cartesian__product,axiom, % 177.41/177.14 ! [V_A_2,V_B_2,V_f_2,T_e,T_d,T_c] : % 177.41/177.14 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_d,T_e),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2)),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))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Times__empty,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,T_d,T_c] : % 177.41/177.14 ( 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)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) % 177.41/177.14 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.14 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Sigma__empty2,axiom, % 177.41/177.14 ! [V_A_2,T_d,T_c] : 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),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Compl__Times__UNIV2,axiom, % 177.41/177.14 ! [V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Compl__Times__UNIV1,axiom, % 177.41/177.14 ! [V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_A_2))) ). % 177.41/177.14 % 177.41/177.14 fof(fact_setprod__cartesian__product,axiom, % 177.41/177.14 ! [V_A_2,V_B_2,V_f_2,T_e,T_d,T_c] : % 177.41/177.14 ( class_Groups_Ocomm__monoid__mult(T_c) % 177.41/177.14 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_e,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_d,T_e),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2)),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))) ) ). % 177.41/177.14 % 177.41/177.14 fof(fact_Sigma__Un__distrib2,axiom, % 177.41/177.14 ! [V_B_2,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_B_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Times__Un__distrib1,axiom, % 177.41/177.15 ! [V_C_2,V_B_2,V_A_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sigma__Un__distrib1,axiom, % 177.41/177.15 ! [V_C_2,V_J_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_J_2),V_C_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__comp__subset__Sigma,axiom, % 177.41/177.15 ! [V_C_2,V_s_2,T_e,V_B_2,V_A_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_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)))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_B_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_C_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_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_C_2)))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_swap__product,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(c_Set_Oimage(tc_prod(T_d,T_c),tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_c,T_d)),hAPP(c_COMBC(T_c,T_d,tc_prod(T_c,T_d)),c_Product__Type_OPair(T_c,T_d)))),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_B_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_A_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__cartesian__product,axiom, % 177.41/177.15 ! [V_B_2,T_d,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),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)))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_equiv__type,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sigma__Int__distrib1,axiom, % 177.41/177.15 ! [V_C_2,V_J_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_J_2),V_C_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Times__Int__distrib1,axiom, % 177.41/177.15 ! [V_C_2,V_B_2,V_A_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sigma__Int__distrib2,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_B_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Id__on__subset__Times,axiom, % 177.41/177.15 ! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Relation_OId__on(T_c,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sigma__Diff__distrib1,axiom, % 177.41/177.15 ! [V_C_2,V_J_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_J_2),V_C_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Times__Diff__distrib1,axiom, % 177.41/177.15 ! [V_C_2,V_B_2,V_A_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sigma__Diff__distrib2,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_B_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_DomainP_Oequations,axiom, % 177.41/177.15 ! [V_a1_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Predicate_ODomainP(T_c,T_d,V_r_2),V_a1_2)) % 177.41/177.15 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_UNIV__Times__UNIV,axiom, % 177.41/177.15 ! [T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_mem__Sigma__iff,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_SigmaD1,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_SigmaD2,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_SigmaE2,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) % 177.41/177.15 => ~ ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_card__cartesian__product__singleton,axiom, % 177.41/177.15 ! [V_A_2,V_x_2,T_d,T_c] : hAPP(c_Finite__Set_Ocard(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_d),V_A_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Times__subset__cancel2,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_d,V_C_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_C_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2)))) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Image__subset,axiom, % 177.41/177.15 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_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)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_d,V_r_2),V_C_2)),V_B_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__cartesian__productD1,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),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)))) % 177.41/177.15 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__cartesian__productD2,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),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)))) % 177.41/177.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Collect__split,axiom, % 177.41/177.15 ! [V_Qa_2,V_Pa_2,T_d,T_c] : hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_OCollect(T_d),V_Qa_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_SetCompr__Sigma__eq,axiom, % 177.41/177.15 ! [V_Qa_2,V_Pa_2,T_d,T_c] : hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),V_Qa_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fst__image__times,axiom, % 177.41/177.15 ! [V_A_2,T_d,T_c,V_B_2] : % 177.41/177.15 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 => hAPP(c_Set_Oimage(tc_prod(T_d,T_c),T_d,c_Product__Type_Ofst(T_d,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 177.41/177.15 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 => hAPP(c_Set_Oimage(tc_prod(T_d,T_c),T_d,c_Product__Type_Ofst(T_d,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2))) = V_A_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_snd__image__times,axiom, % 177.41/177.15 ! [V_B_2,T_d,T_c,V_A_2] : % 177.41/177.15 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 => hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_d,c_Product__Type_Osnd(T_c,T_d)),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))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 177.41/177.15 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 => hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_d,c_Product__Type_Osnd(T_c,T_d)),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))) = V_B_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_insert__times__insert,axiom, % 177.41/177.15 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__equiv__class,axiom, % 177.41/177.15 ! [V_X_2,V_r_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_X_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_UN__Times__distrib,axiom, % 177.41/177.15 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_d,T_c,T_f,T_e] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_e,T_f),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_e,T_f),V_A_2),hAPP(c_COMBK(tc_fun(T_f,tc_HOL_Obool),T_e),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_f,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),tc_fun(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_f,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),tc_fun(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),T_e),c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_f)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_e),c_Product__Type_OSigma(T_c,T_d)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_f),c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(T_d,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sigma__def,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_prod(T_c,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_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),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_fun(tc_prod(T_c,T_d),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_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_d),c_Set_Oinsert(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__quotient,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setsum__mult__setsum__if__inj,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_d,T_c,T_e] : % 177.41/177.15 ( class_Rings_Osemiring__0(T_e) % 177.41/177.15 => ( c_Fun_Oinj__on(tc_prod(T_c,T_d),T_e,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_e),tc_fun(T_d,T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_e),tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,T_e)),T_c),c_COMBB(T_e,T_e,T_d)),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_e,T_e),T_c),c_Groups_Otimes__class_Otimes(T_e)),V_f_2))),V_g_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))) % 177.41/177.15 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_e),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_e),c_Fun_Oid(T_e)),hAPP(c_Set_OCollect(T_e),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_e),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_e),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_e,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(T_c,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_e),c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool))),T_e),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_c),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_e),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,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_d),c_fconj))),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_e)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_e)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_e),c_COMBB(tc_fun(T_d,T_e),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,tc_HOL_Obool)),T_e),c_COMBB(T_e,tc_HOL_Obool,T_d)),c_fequal))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_e),tc_fun(T_d,T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_e),tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,T_e)),T_c),c_COMBB(T_e,T_e,T_d)),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_e,T_e),T_c),c_Groups_Otimes__class_Otimes(T_e)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),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(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))))))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 177.41/177.15 ! [V_A_2,V_I_2,T_d,T_c] : % 177.41/177.15 ? [B_f] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,tc_prod(T_d,T_c),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,tc_prod(T_d,T_c),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_I_2),V_A_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fold__image__Sigma,axiom, % 177.41/177.15 ! [V_g_2,V_B_2,T_d,V_A_2,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__mult(T_e) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) ) % 177.41/177.15 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_c,c_Groups_Otimes__class_Otimes(T_e)),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBC(T_c,T_e,tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(T_e,tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e)),T_c),c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e))),V_g_2)),c_Groups_Oone__class_Oone(T_e))),V_B_2)),c_Groups_Oone__class_Oone(T_e)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,tc_prod(T_c,T_d),c_Groups_Otimes__class_Otimes(T_e)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_g_2)),c_Groups_Oone__class_Oone(T_e)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_image__id,axiom, % 177.41/177.15 ! [V_Y_2,T_c] : hAPP(c_Set_Oimage(T_c,T_c,c_Fun_Oid(T_c)),V_Y_2) = V_Y_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_inj__on__id,axiom, % 177.41/177.15 ! [V_A_2,T_c] : c_Fun_Oinj__on(T_c,T_c,c_Fun_Oid(T_c),V_A_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_vimage__id,axiom, % 177.41/177.15 ! [V_A_2,T_c] : hAPP(c_Set_Ovimage(T_c,T_c,c_Fun_Oid(T_c)),V_A_2) = V_A_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_id__apply,axiom, % 177.41/177.15 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 177.41/177.15 % 177.41/177.15 fof(fact_id__def,axiom, % 177.41/177.15 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 177.41/177.15 % 177.41/177.15 fof(fact_apsnd__id,axiom, % 177.41/177.15 ! [T_c,T_d] : c_Product__Type_Oapsnd(T_d,T_d,T_c,c_Fun_Oid(T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_apfst__id,axiom, % 177.41/177.15 ! [T_d,T_c] : c_Product__Type_Oapfst(T_c,T_c,T_d,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_c,T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_of__int__eq__id,axiom, % 177.41/177.15 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 177.41/177.15 % 177.41/177.15 fof(fact_surj__id,axiom, % 177.41/177.15 ! [T_c] : hAPP(c_Set_Oimage(T_c,T_c,c_Fun_Oid(T_c)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_split__Pair,axiom, % 177.41/177.15 ! [T_d,T_c] : hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_c,T_d)),c_Product__Type_OPair(T_c,T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setsum__reindex__id,axiom, % 177.41/177.15 ! [V_B_2,V_f_2,T_c,T_d] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__add(T_d) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_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_Oimage(T_c,T_d,V_f_2),V_B_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setprod__reindex__id,axiom, % 177.41/177.15 ! [V_B_2,V_f_2,T_c,T_d] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setprod__Sigma,axiom, % 177.41/177.15 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__mult(T_e) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) ) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e)),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_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setsum__Sigma,axiom, % 177.41/177.15 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__add(T_e) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) ) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e)),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_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_card__SigmaI,axiom, % 177.41/177.15 ! [V_B_2,T_d,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) ) % 177.41/177.15 => hAPP(c_Finite__Set_Ocard(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),V_B_2)),V_A_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__SigmaI,axiom, % 177.41/177.15 ! [V_B_2,T_d,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( ! [B_a] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_a))) ) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_SigmaE,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_c_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) % 177.41/177.15 => ~ ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_d),B_y),hAPP(V_B_2,B_x))) % 177.41/177.15 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__surj,axiom, % 177.41/177.15 ! [V_g_2,T_e,T_f,V_f_2,T_c,T_d] : % 177.41/177.15 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 => ( hAPP(c_Set_Oimage(T_f,T_e,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_f,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)) % 177.41/177.15 => hAPP(c_Set_Oimage(tc_prod(T_d,T_f),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_d,T_c,T_f,T_e,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_d,T_f),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__imageI,axiom, % 177.41/177.15 ! [V_g_2,V_f_2,T_f,T_e,V_R_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_R_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_e,T_f)),hAPP(hAPP(c_Product__Type_OPair(T_e,T_f),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_e,T_f),c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,V_f_2,V_g_2)),V_R_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__simp,axiom, % 177.41/177.15 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_d,T_f,T_c,T_e] : hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_e,T_f),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__ident,axiom, % 177.41/177.15 ! [V_z_2,T_d,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_c,T_d,T_d,c_COMBI(T_c),c_COMBI(T_d)),V_z_2) = V_z_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_snd__prod__fun,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_f,T_e,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(c_Product__Type_Omap__pair(T_e,T_d,T_f,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_e,T_f),V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fst__map__pair,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_f,T_e,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_f),V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair_Oidentity,axiom, % 177.41/177.15 ! [T_d,T_c] : c_Product__Type_Omap__pair(T_c,T_c,T_d,T_d,c_COMBI(T_c),c_COMBI(T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_apsnd__def,axiom, % 177.41/177.15 ! [V_f_2,T_c,T_e,T_d] : c_Product__Type_Oapsnd(T_d,T_e,T_c,V_f_2) = c_Product__Type_Omap__pair(T_c,T_c,T_d,T_e,c_Fun_Oid(T_c),V_f_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_apfst__def,axiom, % 177.41/177.15 ! [V_f_2,T_d,T_e,T_c] : c_Product__Type_Oapfst(T_c,T_e,T_d,V_f_2) = c_Product__Type_Omap__pair(T_c,T_e,T_d,T_d,V_f_2,c_Fun_Oid(T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair_Oid,axiom, % 177.41/177.15 ! [T_d,T_c] : c_Product__Type_Omap__pair(T_c,T_c,T_d,T_d,c_Fun_Oid(T_c),c_Fun_Oid(T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__def,axiom, % 177.41/177.15 ! [V_g_2,V_f_2,T_f,T_d,T_e,T_c] : c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_e,T_f)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_f),tc_fun(T_d,tc_prod(T_e,T_f))),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_e,T_f)),tc_fun(tc_fun(T_d,T_f),tc_fun(T_d,tc_prod(T_e,T_f))),T_c),c_COMBB(T_f,tc_prod(T_e,T_f),T_d)),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_f,tc_prod(T_e,T_f)),T_c),c_Product__Type_OPair(T_e,T_f)),V_f_2))),V_g_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__surj__on,axiom, % 177.41/177.15 ! [V_B_H_2,V_B_2,V_g_2,T_e,T_f,V_A_H_2,V_A_2,V_f_2,T_c,T_d] : % 177.41/177.15 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = V_A_H_2 % 177.41/177.15 => ( hAPP(c_Set_Oimage(T_f,T_e,V_g_2),V_B_2) = V_B_H_2 % 177.41/177.15 => hAPP(c_Set_Oimage(tc_prod(T_d,T_f),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_d,T_c,T_f,T_e,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_f),V_A_2),hAPP(c_COMBK(tc_fun(T_f,tc_HOL_Obool),T_d),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_H_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_H_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__map__pair__image,axiom, % 177.41/177.15 ! [V_f_2,T_d,V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.15 => c_Wellfounded_Owf(T_d,hAPP(c_Set_Oimage(tc_prod(T_c,T_c),tc_prod(T_d,T_d),c_Product__Type_Omap__pair(T_c,T_d,T_c,T_d,V_f_2,V_f_2)),V_r_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__inj__on,axiom, % 177.41/177.15 ! [V_B_2,V_g_2,T_f,T_e,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.15 => ( c_Fun_Oinj__on(T_e,T_f,V_g_2,V_B_2) % 177.41/177.15 => c_Fun_Oinj__on(tc_prod(T_c,T_e),tc_prod(T_d,T_f),c_Product__Type_Omap__pair(T_c,T_d,T_e,T_f,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))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_prod__fun__imageE,axiom, % 177.41/177.15 ! [V_R_2,V_g_2,V_f_2,T_f,T_e,V_c_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_e,T_f),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),V_R_2))) % 177.41/177.15 => ~ ! [B_x,B_y] : % 177.41/177.15 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_e,T_f)),hAPP(hAPP(c_Product__Type_OPair(T_e,T_f),B_x),B_y)),V_R_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__def,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) % 177.41/177.15 & ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfP__def,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_OwfP(T_c,V_r_2) % 177.41/177.15 <=> c_Wellfounded_Owf(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfP__empty,axiom, % 177.41/177.15 ! [T_c] : c_Wellfounded_OwfP(T_c,hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fFalse))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__Id__on,axiom, % 177.41/177.15 ! [V_A_2,T_c] : c_Relation_Orefl__on(T_c,V_A_2,c_Relation_OId__on(T_c,V_A_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfP__accp__iff,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_OwfP(T_c,V_r_2) % 177.41/177.15 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),B_x1)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_accp__wfPD,axiom, % 177.41/177.15 ! [V_x_2,V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_OwfP(T_c,V_r_2) % 177.41/177.15 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_x_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfP__subset,axiom, % 177.41/177.15 ! [V_p_2,V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_OwfP(T_c,V_r_2) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),V_p_2),V_r_2)) % 177.41/177.15 => c_Wellfounded_OwfP(T_c,V_p_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__empty,axiom, % 177.41/177.15 ! [T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__Un,axiom, % 177.41/177.15 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 => ( c_Relation_Orefl__on(T_c,V_B_2,V_s_2) % 177.41/177.15 => c_Relation_Orefl__on(T_c,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(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__Int,axiom, % 177.41/177.15 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 => ( c_Relation_Orefl__on(T_c,V_B_2,V_s_2) % 177.41/177.15 => c_Relation_Orefl__on(T_c,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(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__onD,axiom, % 177.41/177.15 ! [V_a_2,V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),V_r_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__onD1,axiom, % 177.41/177.15 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__onD2,axiom, % 177.41/177.15 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__in__rel,axiom, % 177.41/177.15 ! [V_R_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,V_R_2) % 177.41/177.15 => c_Wellfounded_OwfP(T_c,c_FunDef_Oin__rel(T_c,T_c,V_R_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfP__wf__eq,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2)) % 177.41/177.15 <=> c_Wellfounded_Owf(T_c,V_r_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_reflp__def,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Predicate_Oreflp(T_c,V_r_2) % 177.41/177.15 <=> c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__onI,axiom, % 177.41/177.15 ! [V_A_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) ) % 177.41/177.15 => c_Relation_Orefl__on(T_c,V_A_2,V_r_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfP__acyclicP,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_OwfP(T_c,V_r_2) % 177.41/177.15 => c_Wellfounded_Oacyclic(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acyclic__subset,axiom, % 177.41/177.15 ! [V_r_2,V_s_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Oacyclic(T_c,V_s_2) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.15 => c_Wellfounded_Oacyclic(T_c,V_r_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_reflpE,axiom, % 177.41/177.15 ! [V_x_2,V_r_2,T_c] : % 177.41/177.15 ( c_Predicate_Oreflp(T_c,V_r_2) % 177.41/177.15 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__acyclic,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.15 => c_Wellfounded_Oacyclic(T_c,V_r_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__iff__acyclic__if__finite,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) % 177.41/177.15 => ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.15 <=> c_Wellfounded_Oacyclic(T_c,V_r_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__acyclic__wf,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) % 177.41/177.15 => ( c_Wellfounded_Oacyclic(T_c,V_r_2) % 177.41/177.15 => c_Wellfounded_Owf(T_c,V_r_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Owf_H__def,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Nitpick_Owf_H(T_c,V_r_2) % 177.41/177.15 <=> ( c_Wellfounded_Oacyclic(T_c,V_r_2) % 177.41/177.15 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) % 177.41/177.15 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Rep__Integ__induct,axiom, % 177.41/177.15 ! [V_Pa_2,V_y_2] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 177.41/177.15 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Rep__Integ__cases,axiom, % 177.41/177.15 ! [V_y_2] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 177.41/177.15 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__def_H,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 <=> ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))),B_x)) ) % 177.41/177.15 & ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Abs__Integ__induct,axiom, % 177.41/177.15 ! [V_x_2,V_Pa_2] : % 177.41/177.15 ( ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Abs__Integ__cases,axiom, % 177.41/177.15 ! [V_x_2] : % 177.41/177.15 ~ ! [B_y] : % 177.41/177.15 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_INFI__bool__eq,axiom, % 177.41/177.15 ! [T_c] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_HOL_Obool) = c_Set_OBall(T_c) ). % 177.41/177.15 % 177.41/177.15 fof(fact_ball__empty,axiom, % 177.41/177.15 ! [V_Pa_2,T_c,B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Powp__def,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Predicate_OPowp(T_c,V_A_2),V_B_2)) % 177.41/177.15 <=> ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_B_2)) % 177.41/177.15 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Collect__ball__eq,axiom, % 177.41/177.15 ! [V_Pa_2,V_A_2,T_d,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fimplies),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),V_Pa_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_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_OCollect(T_c)),hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_Pa_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_congruent__def,axiom, % 177.41/177.15 ! [V_f_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( c_Equiv__Relations_Ocongruent(T_c,T_d,V_r_2,V_f_2) % 177.41/177.15 <=> ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),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_c),c_COMBB(T_d,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_INTER__def,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_c,T_d] : 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(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fimplies),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d)),c_member(T_c))),V_B_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sup__Inf,axiom, % 177.41/177.15 ! [V_A_2,T_c] : % 177.41/177.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.15 => c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),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(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c)))))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Inf__Sup,axiom, % 177.41/177.15 ! [V_A_2,T_c] : % 177.41/177.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.15 => c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),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)))),c_Orderings_Oord__class_Oless__eq(T_c))))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfP__SUP,axiom, % 177.41/177.15 ! [T_c,V_r_2,T_d] : % 177.41/177.15 ( ! [B_i] : c_Wellfounded_OwfP(T_d,hAPP(V_r_2,B_i)) % 177.41/177.15 => ( ! [B_i,B_j] : % 177.41/177.15 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 177.41/177.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),c_Predicate_ODomainP(T_d,T_d,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_d,T_d,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) % 177.41/177.15 => c_Wellfounded_OwfP(T_d,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_mem__splitI2,axiom, % 177.41/177.15 ! [V_c_2,V_z_2,T_e,T_d,T_c,V_p_2] : % 177.41/177.15 ( ! [B_a,B_b] : % 177.41/177.15 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_e),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_e),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_e,tc_HOL_Obool)),V_c_2),V_p_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_mem__splitE,axiom, % 177.41/177.15 ! [V_p_2,V_c_2,T_e,T_d,V_z_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2))) % 177.41/177.15 => ~ ! [B_x,B_y] : % 177.41/177.15 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Inter__eq,axiom, % 177.41/177.15 ! [V_A_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_c,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_c,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,tc_HOL_Obool))),V_A_2)))),c_member(T_c)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_vimage__Times,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_f_2,T_e,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,tc_prod(T_d,T_e),V_f_2),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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,T_c,c_Product__Type_Ofst(T_d,T_e)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_e,hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_e,T_c,c_Product__Type_Osnd(T_d,T_e)),V_f_2)),V_B_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Eps__split,axiom, % 177.41/177.15 ! [V_Pa_2,T_d,T_c] : c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(hAPP(c_COMBS(tc_prod(T_c,T_d),T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_HOL_Obool),tc_prod(T_c,T_d)),V_Pa_2),c_Product__Type_Ofst(T_c,T_d))),c_Product__Type_Osnd(T_c,T_d))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wfI__pf,axiom, % 177.41/177.15 ! [V_R_2,T_c] : % 177.41/177.15 ( ! [B_A] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_c,T_c,V_R_2),B_A))) % 177.41/177.15 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 177.41/177.15 => c_Wellfounded_Owf(T_c,V_R_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_id__o,axiom, % 177.41/177.15 ! [V_g_2,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_d,T_c,c_Fun_Oid(T_d)),V_g_2) = V_g_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__id,axiom, % 177.41/177.15 ! [V_f_2,T_d,T_c] : hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_f_2),c_Fun_Oid(T_c)) = V_f_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__eq__id__dest,axiom, % 177.41/177.15 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_c,T_d,T_e] : % 177.41/177.15 ( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_d,T_c,c_Fun_Oid(T_d)),V_c_2) % 177.41/177.15 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 177.41/177.15 ! [V_x_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fun__upd__comp,axiom, % 177.41/177.15 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),c_Fun_Ofun__upd(T_c,T_e,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_vimage__compose,axiom, % 177.41/177.15 ! [V_x_2,V_f_2,V_g_2,T_e,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_c,T_e,V_f_2),hAPP(c_Set_Ovimage(T_e,T_d,V_g_2),V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__assoc,axiom, % 177.41/177.15 ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__apply,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__eq__dest,axiom, % 177.41/177.15 ! [V_v_2,V_d_2,V_c_2,T_f,V_b_2,V_a_2,T_c,T_d,T_e] : % 177.41/177.15 ( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,V_c_2),V_d_2) % 177.41/177.15 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__eq__elim,axiom, % 177.41/177.15 ! [V_d_2,V_c_2,T_f,V_b_2,V_a_2,T_c,T_d,T_e] : % 177.41/177.15 ( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,V_c_2),V_d_2) % 177.41/177.15 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_tfl__some,axiom, % 177.41/177.15 ! [T_c,B_P] : % 177.41/177.15 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 177.41/177.15 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_c,B_P))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_someI,axiom, % 177.41/177.15 ! [T_c,V_x_2,V_Pa_2] : % 177.41/177.15 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_c,V_Pa_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_comp__cong,axiom, % 177.41/177.15 ! [T_g,T_f,T_e,T_c,T_d,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 177.41/177.15 ( 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)) % 177.41/177.15 => hAPP(hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_f,T_c,T_g,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__eq__dest__lhs,axiom, % 177.41/177.15 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_c,T_d,T_e] : % 177.41/177.15 ( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = V_c_2 % 177.41/177.15 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 177.41/177.15 ! [V_y_2,V_x_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_someI__ex,axiom, % 177.41/177.15 ! [T_c,V_Pa_2] : % 177.41/177.15 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_c,V_Pa_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_some__eq__ex,axiom, % 177.41/177.15 ! [T_c,V_Pa_2] : % 177.41/177.15 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_c,V_Pa_2))) % 177.41/177.15 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_some__eq__trivial,axiom, % 177.41/177.15 ! [V_x_2,T_c] : c_Hilbert__Choice_OEps(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_some__sym__eq__trivial,axiom, % 177.41/177.15 ! [V_x_2,T_c] : c_Hilbert__Choice_OEps(T_c,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_K__record__comp,axiom, % 177.41/177.15 ! [V_x_2,V_f_2,V_c_2,T_e,T_c,T_d] : hAPP(hAPP(c_Fun_Ocomp(T_d,T_c,T_e,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_f_2),V_x_2) = V_c_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_o__def,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_exE__some,axiom, % 177.41/177.15 ! [T_c,V_c_2,V_Pa_2] : % 177.41/177.15 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.41/177.15 => ( V_c_2 = c_Hilbert__Choice_OEps(T_c,V_Pa_2) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_apsnd__compose,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_f,T_e,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_x_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_apfst__compose,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,T_f,V_f_2,T_d,T_c,T_e] : hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),hAPP(c_Product__Type_Oapfst(T_f,T_e,T_d,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_f,T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_f,V_f_2),V_g_2)),V_x_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_inj__on__imageI2,axiom, % 177.41/177.15 ! [V_A_2,V_f_2,V_f_H_2,T_e,T_d,T_c] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_H_2),V_f_2),V_A_2) % 177.41/177.15 => c_Fun_Oinj__on(T_c,T_e,V_f_2,V_A_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_inj__comp,axiom, % 177.41/177.15 ! [V_g_2,T_e,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.15 => ( c_Fun_Oinj__on(T_e,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) % 177.41/177.15 => c_Fun_Oinj__on(T_e,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_comp__surj,axiom, % 177.41/177.15 ! [V_g_2,T_e,V_f_2,T_c,T_d] : % 177.41/177.15 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 => ( hAPP(c_Set_Oimage(T_c,T_e,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)) % 177.41/177.15 => hAPP(c_Set_Oimage(T_d,T_e,hAPP(c_Fun_Ocomp(T_c,T_e,T_d,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_comp__inj__on__iff,axiom, % 177.41/177.15 ! [V_f_H_2,T_e,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.15 => ( c_Fun_Oinj__on(T_d,T_e,V_f_H_2,hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) % 177.41/177.15 <=> c_Fun_Oinj__on(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_f_H_2),V_f_2),V_A_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_comp__inj__on,axiom, % 177.41/177.15 ! [V_g_2,T_e,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.15 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) % 177.41/177.15 => c_Fun_Oinj__on(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_g_2),V_f_2),V_A_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_inj__on__imageI,axiom, % 177.41/177.15 ! [V_A_2,V_f_2,V_g_2,T_e,T_d,T_c] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_g_2),V_f_2),V_A_2) % 177.41/177.15 => c_Fun_Oinj__on(T_e,T_d,V_g_2,hAPP(c_Set_Oimage(T_c,T_e,V_f_2),V_A_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_image__compose,axiom, % 177.41/177.15 ! [V_r_2,V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_c,T_d,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_e,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_e,V_g_2),V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair_Ocompositionality,axiom, % 177.41/177.15 ! [V_prod_2,V_i_2,V_h_2,T_h,T_g,V_g_2,V_f_2,T_d,T_f,T_c,T_e] : hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_g,T_e,T_h,T_f,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_g,T_c,T_h,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_h,V_g_2),V_i_2)),V_prod_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair__compose,axiom, % 177.41/177.15 ! [V_g2_2,V_g1_2,T_h,V_f2_2,V_f1_2,T_g,T_f,T_d,T_e,T_c] : c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_h,T_f,T_d,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_g,T_h),tc_prod(T_e,T_f),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_g,T_e,T_h,T_f,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_c,T_g,T_d,T_h,V_f2_2,V_g2_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_map__pair_Ocomp,axiom, % 177.41/177.15 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_d,T_c,T_f,T_e,T_h,T_g] : hAPP(c_Fun_Ocomp(tc_prod(T_g,T_h),tc_prod(T_e,T_f),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_g,T_e,T_h,T_f,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_c,T_g,T_d,T_h,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_h,T_f,T_d,V_g_2),V_i_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setsum__reindex,axiom, % 177.41/177.15 ! [V_h_2,V_B_2,V_f_2,T_d,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__add(T_e) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_h_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2)),V_B_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setprod__reindex,axiom, % 177.41/177.15 ! [V_h_2,V_B_2,V_f_2,T_d,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__mult(T_e) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e),V_h_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2)),V_B_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setprod__reindex__cong,axiom, % 177.41/177.15 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__mult(T_e) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.15 => ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) % 177.41/177.15 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),V_g_2),V_A_2) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Eps__split__eq,axiom, % 177.41/177.15 ! [V_y_2,V_x_2,T_d,T_c] : c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_split__paired__Eps,axiom, % 177.41/177.15 ! [V_Pa_2,T_d,T_c] : c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setsum_Oreindex,axiom, % 177.41/177.15 ! [V_g_2,V_h_2,V_A_2,T_c,T_d] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__add(T_d) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setprod_Oreindex,axiom, % 177.41/177.15 ! [V_g_2,V_h_2,V_A_2,T_c,T_d] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__mult(T_d) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_the__inv__into__comp,axiom, % 177.41/177.15 ! [V_x_2,V_A_2,V_g_2,T_e,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2)) % 177.41/177.15 => ( c_Fun_Oinj__on(T_e,T_c,V_g_2,V_A_2) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2)))) % 177.41/177.15 => hAPP(c_Fun_Othe__inv__into(T_e,T_d,V_A_2,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_e,T_d,c_Fun_Othe__inv__into(T_e,T_c,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_c,T_d,hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fold__image__reindex,axiom, % 177.41/177.15 ! [V_z_2,V_g_2,V_h_2,T_d,V_A_2,T_c,T_e] : % 177.41/177.15 ( class_Groups_Oab__semigroup__mult(T_e) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_h_2,V_A_2) % 177.41/177.15 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_c,T_d,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_c,c_Groups_Otimes__class_Otimes(T_e)),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Oremove,axiom, % 177.41/177.15 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.15 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__image_Oreindex,axiom, % 177.41/177.15 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.41/177.15 => ( c_Fun_Oinj__on(T_d,T_d,V_h_2,V_A_2) % 177.41/177.15 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_d,T_d,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_d,T_c,T_d,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ounion,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.41/177.15 => ( 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)) % 177.41/177.15 => 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(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 177.41/177.15 ! [V_h_2,V_g_2,T_h,V_f_2,T_e,T_f,T_g,V_F_2,V_fa_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_fa_2,V_F_2) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_g,T_f,T_e,V_f_2),hAPP(c_Fun_Ocomp(T_h,T_g,T_e,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_h,T_f,T_e,hAPP(c_Fun_Ocomp(T_g,T_f,T_h,V_f_2),V_g_2)),V_h_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ocommute__comp,axiom, % 177.41/177.15 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ocommute__left__comp,axiom, % 177.41/177.15 ! [V_g_2,V_x_2,V_y_2,T_e,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_UN__o,axiom, % 177.41/177.15 ! [V_f_2,V_g_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_c,tc_HOL_Obool),T_d,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_g_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_fst__comp__map__pair,axiom, % 177.41/177.15 ! [V_g_2,V_f_2,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),T_e,tc_prod(T_c,T_d),c_Product__Type_Ofst(T_e,T_f)),c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_e,tc_prod(T_c,T_d),V_f_2),c_Product__Type_Ofst(T_c,T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_snd__comp__map__pair,axiom, % 177.41/177.15 ! [V_g_2,V_f_2,T_d,T_c,T_e,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_e),T_e,tc_prod(T_c,T_d),c_Product__Type_Osnd(T_f,T_e)),c_Product__Type_Omap__pair(T_c,T_f,T_d,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_e,tc_prod(T_c,T_d),V_g_2),c_Product__Type_Osnd(T_c,T_d)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__image_Odistrib,axiom, % 177.41/177.15 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.41/177.15 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),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)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_split__comp,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_f,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),hAPP(c_Fun_Ocomp(T_f,tc_fun(T_e,T_c),T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ocommute__comp_H,axiom, % 177.41/177.15 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ocommute__left__comp_H,axiom, % 177.41/177.15 ! [V_g_2,V_x_2,T_e,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ocommute__comp_H_H,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 177.41/177.15 ! [V_g_2,T_e,V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Oempty,axiom, % 177.41/177.15 ! [V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Fun_Oid(T_d) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Oeq__fold,axiom, % 177.41/177.15 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_s_2),V_A_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__image_Oeq__fold,axiom, % 177.41/177.15 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.41/177.15 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Oinsert,axiom, % 177.41/177.15 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.15 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Ounion__inter,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding_Oinsert__remove,axiom, % 177.41/177.15 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_hoare__derivs_OIf,axiom, % 177.41/177.15 ! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_c] : % 177.41/177.15 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,V_b_2)),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 177.41/177.15 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 177.41/177.15 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Loop,axiom, % 177.41/177.15 ! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_c] : % 177.41/177.15 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,V_b_2)),V_c_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 177.41/177.15 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setsum__reindex__nonzero,axiom, % 177.41/177.15 ! [T_d,V_h_2,V_f_2,V_S_2,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__add(T_e) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.41/177.15 => ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_S_2)) % 177.41/177.15 => ( B_x != B_y % 177.41/177.15 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 177.41/177.15 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_e) ) ) ) ) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_h_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_peek__and__def,axiom, % 177.41/177.15 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,V_p_2),V_Z_2),V_s_2)) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) % 177.41/177.15 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__idem_Ounion__idem,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.41/177.15 => 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(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__idem_Oinsert__idem,axiom, % 177.41/177.15 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__idem_Oidem__left__comp,axiom, % 177.41/177.15 ! [V_g_2,V_x_2,T_e,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__idem_Oidem__comp,axiom, % 177.41/177.15 ! [V_x_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_folding__idem_Oin__comp__idem,axiom, % 177.41/177.15 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] : % 177.41/177.15 ( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2) % 177.41/177.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.15 => hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_strong__setprod__reindex__cong,axiom, % 177.41/177.15 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c,T_e] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__mult(T_e) % 177.41/177.15 => ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.15 => ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2),B_x) ) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),V_g_2),V_A_2) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Sigma__mono,axiom, % 177.41/177.15 ! [V_D_2,V_B_2,T_d,V_C_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_C_2),V_D_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_not__acc__down,axiom, % 177.41/177.15 ! [V_R_2,V_x_2,T_c] : % 177.41/177.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_R_2))) % 177.41/177.15 => ~ ! [B_z] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_z),V_x_2)),V_R_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),B_z),c_Wellfounded_Oacc(T_c,V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acc_OaccI,axiom, % 177.41/177.15 ! [V_r_2,V_x_2,T_c] : % 177.41/177.15 ( ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_x_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),B_y),c_Wellfounded_Oacc(T_c,V_r_2))) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_max__ext_Osimps,axiom, % 177.41/177.15 ! [V_R_2,V_a2_2,V_a1_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_c,V_R_2))) % 177.41/177.15 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a1_2)) % 177.41/177.15 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a2_2)) % 177.41/177.15 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 & ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_a1_2)) % 177.41/177.15 => ? [B_xa] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_a2_2)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__no__infinite__down__chainE,axiom, % 177.41/177.15 ! [V_f_2,V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.15 => ~ ! [B_k] : 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,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_scomp__unfold,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_c,T_f,T_e,T_d] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_d,T_e,T_f,T_c),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_f),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_e,T_f),hAPP(V_f_2,V_x_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setsum__ivl__cong,axiom, % 177.41/177.15 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_c,T_d] : % 177.41/177.15 ( ( class_Groups_Ocomm__monoid__add(T_d) % 177.41/177.15 & class_Orderings_Oord(T_c) ) % 177.41/177.15 => ( V_a_2 = V_c_2 % 177.41/177.15 => ( V_b_2 = V_d_2 % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),B_x)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_d_2)) % 177.41/177.15 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 177.41/177.15 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_less__eq,axiom, % 177.41/177.15 ! [V_n_2,V_m_2] : % 177.41/177.15 ( 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))) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Pair__scomp,axiom, % 177.41/177.15 ! [V_f_2,V_x_2,T_d,T_e,T_c] : hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_e,T_c,T_d),hAPP(c_Product__Type_OPair(T_e,T_c),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_scomp__Pair,axiom, % 177.41/177.15 ! [V_x_2,T_e,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,tc_prod(T_d,T_e)),V_x_2),c_Product__Type_OPair(T_d,T_e)) = V_x_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_scomp__scomp,axiom, % 177.41/177.15 ! [V_h_2,V_g_2,V_f_2,T_h,T_g,T_d,T_f,T_e,T_c] : hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_e,T_f,T_d),hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_g,T_h,tc_prod(T_e,T_f)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_g,T_h,T_d),V_f_2),hAPP(hAPP(c_COMBC(T_g,tc_fun(T_e,tc_fun(T_f,T_d)),tc_fun(T_h,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_h,tc_prod(T_e,T_f)),tc_fun(tc_fun(T_e,tc_fun(T_f,T_d)),tc_fun(T_h,T_d)),T_g),c_Product__Type_Oscomp(T_h,T_e,T_f,T_d)),V_g_2)),V_h_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__trancl,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.15 => c_Wellfounded_Owf(T_c,c_Transitive__Closure_Otrancl(T_c,V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_scomp__apply,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_c,T_f,T_e,T_d] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_d,T_e,T_f,T_c),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_c),V_g_2),hAPP(V_f_2,V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_scomp__def,axiom, % 177.41/177.15 ! [V_x_2,V_g_2,V_f_2,T_c,T_f,T_e,T_d] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_d,T_e,T_f,T_c),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_c),V_g_2),hAPP(V_f_2,V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_less__than__def,axiom, % 177.41/177.15 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acyclic__def,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Oacyclic(T_c,V_r_2) % 177.41/177.15 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl_Or__into__trancl,axiom, % 177.41/177.15 ! [V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__subset__Field2,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),hAPP(c_Relation_OField(T_c),V_r_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_Relation_OField(T_c),V_r_2))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__Int__subset,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),V_s_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_r__into__trancl_H,axiom, % 177.41/177.15 ! [V_r_2,V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__empty,axiom, % 177.41/177.15 ! [T_c] : c_Transitive__Closure_Otrancl(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__domain,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)) = hAPP(c_Relation_ODomain(T_c,T_c),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__range,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)) = hAPP(c_Relation_ORange(T_c,T_c),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__trancl,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__trans,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__into__trancl2,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_r__r__into__trancl,axiom, % 177.41/177.15 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_R_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),V_R_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__mono,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_s_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__unfold,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)),V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__subset__Sigma,axiom, % 177.41/177.15 ! [V_A_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_iterate_Osimps,axiom, % 177.41/177.15 ! [V_x_2,V_f_2,T_c,T_d,V_k_2] : % 177.41/177.15 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.15 => hAPP(c_Random_Oiterate(T_d,T_c,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2) ) % 177.41/177.15 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.15 => hAPP(c_Random_Oiterate(T_d,T_c,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_c,tc_prod(T_d,T_c)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_d,T_c,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)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__insert,axiom, % 177.41/177.15 ! [V_r_2,V_x_2,V_y_2,T_c] : c_Transitive__Closure_Otrancl(T_c,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,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_c),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_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_c),c_member(tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBC(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),V_y_2))),c_Transitive__Closure_Ortrancl(T_c,V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_c),c_member(tc_prod(T_c,T_c))),hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2))),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_r__into__rtrancl,axiom, % 177.41/177.15 ! [V_r_2,V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl_Ortrancl__refl,axiom, % 177.41/177.15 ! [V_r_2,V_a_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__into__rtrancl,axiom, % 177.41/177.15 ! [V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__rtrancl__absorb,axiom, % 177.41/177.15 ! [V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,c_Transitive__Closure_Otrancl(T_c,V_R_2)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__trancl__absorb,axiom, % 177.41/177.15 ! [V_R_2,T_c] : c_Transitive__Closure_Otrancl(T_c,c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__unfold__right,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__unfold__left,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_r_2),c_Transitive__Closure_Ortrancl(T_c,V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Domain__rtrancl,axiom, % 177.41/177.15 ! [V_R_2,T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Range__rtrancl,axiom, % 177.41/177.15 ! [V_R_2,T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__rtrancl__UnI,axiom, % 177.41/177.15 ! [V_S_2,V_R_2,V_x_2,T_c] : % 177.41/177.15 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_x_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_x_2),c_Transitive__Closure_Ortrancl(T_c,V_S_2))) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_x_2),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_r__comp__rtrancl__eq,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_r_2),c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__idemp__self__comp,axiom, % 177.41/177.15 ! [V_R_2,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__subset__rtrancl,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_c,V_s_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),c_Transitive__Closure_Ortrancl(T_c,V_s_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__subset,axiom, % 177.41/177.15 ! [V_S_2,V_R_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 => c_Transitive__Closure_Ortrancl(T_c,V_S_2) = c_Transitive__Closure_Ortrancl(T_c,V_R_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__mono,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),c_Transitive__Closure_Ortrancl(T_c,V_s_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__Un__subset,axiom, % 177.41/177.15 ! [V_S_2,V_R_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Transitive__Closure_Ortrancl(T_c,V_S_2))),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__Un__rtrancl,axiom, % 177.41/177.15 ! [V_S_2,V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Transitive__Closure_Ortrancl(T_c,V_S_2))) = c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Image__closed__trancl,axiom, % 177.41/177.15 ! [V_X_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),V_X_2)),V_X_2)) % 177.41/177.15 => hAPP(c_Relation_OImage(T_c,T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_X_2) = V_X_2 ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__idemp,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = c_Transitive__Closure_Ortrancl(T_c,V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__trans,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__rtrancl,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__trancl__trancl,axiom, % 177.41/177.15 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__rtrancl__trancl,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__into__trancl1,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtranclD,axiom, % 177.41/177.15 ! [V_R_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 => ( V_a_2 = V_b_2 % 177.41/177.15 | ( V_a_2 != V_b_2 % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2))) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__into__trancl2,axiom, % 177.41/177.15 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__eq__or__trancl,axiom, % 177.41/177.15 ! [V_R_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 <=> ( V_x_2 = V_y_2 % 177.41/177.15 | ( V_x_2 != V_y_2 % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2))) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Not__Domain__rtrancl,axiom, % 177.41/177.15 ! [V_y_2,V_R_2,V_x_2,T_c] : % 177.41/177.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ODomain(T_c,T_c),V_R_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 <=> V_x_2 = V_y_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acc__downwards,axiom, % 177.41/177.15 ! [V_b_2,V_r_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acc__downwards__aux,axiom, % 177.41/177.15 ! [V_r_2,V_a_2,V_b_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__insert,axiom, % 177.41/177.15 ! [V_r_2,V_x_2,V_y_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_2)),V_r_2)) % 177.41/177.15 <=> ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.15 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acyclic__insert,axiom, % 177.41/177.15 ! [V_r_2,V_x_2,V_y_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Oacyclic(T_c,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_2)),V_r_2)) % 177.41/177.15 <=> ( c_Wellfounded_Oacyclic(T_c,V_r_2) % 177.41/177.15 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_pred__nat__trancl__eq__le,axiom, % 177.41/177.15 ! [V_n_2,V_m_2] : % 177.41/177.15 ( 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))) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__subset__Sigma__aux,axiom, % 177.41/177.15 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) % 177.41/177.15 => ( V_a_2 = V_b_2 % 177.41/177.15 | hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_log_Osimps,axiom, % 177.41/177.15 ! [V_i,V_b] : % 177.41/177.15 ( ( ( 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))) % 177.41/177.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 177.41/177.15 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 177.41/177.15 & ( ~ ( 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))) % 177.41/177.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 177.41/177.15 => 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))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_minus__shift__def,axiom, % 177.41/177.15 ! [V_r,V_l,V_k] : % 177.41/177.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 177.41/177.15 => 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) ) % 177.41/177.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 177.41/177.15 => 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) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_inc__shift__def,axiom, % 177.41/177.15 ! [V_k,V_v] : % 177.41/177.15 ( ( V_v = V_k % 177.41/177.15 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 177.41/177.15 & ( V_v != V_k % 177.41/177.15 => 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)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_range,axiom, % 177.41/177.15 ! [V_s,V_k] : % 177.41/177.15 ( 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)) % 177.41/177.15 => 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)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_irrefl__tranclI,axiom, % 177.41/177.15 ! [V_x_2,V_r_2,T_c] : % 177.41/177.15 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_sequence__trans,axiom, % 177.41/177.15 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_c] : % 177.41/177.15 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => 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,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_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acyclic__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Oacyclic(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) % 177.41/177.15 <=> c_Wellfounded_Oacyclic(T_c,V_r_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__UNION,axiom, % 177.41/177.15 ! [V_r_2,V_S_2,T_e,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_e),c_Relation_Oconverse(T_d,T_c)),V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__rel__comp,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_e,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_e,T_c),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(c_Relation_Oconverse(T_e,T_c),V_s_2)),hAPP(c_Relation_Oconverse(T_d,T_e),V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__Un,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_s_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__Id__on,axiom, % 177.41/177.15 ! [V_A_2,T_c] : hAPP(c_Relation_Oconverse(T_c,T_c),c_Relation_OId__on(T_c,V_A_2)) = c_Relation_OId__on(T_c,V_A_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__inv__image,axiom, % 177.41/177.15 ! [V_f_2,V_R_2,T_d,T_c] : hAPP(c_Relation_Oconverse(T_c,T_c),hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_d),V_R_2)),V_f_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__Int,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_s_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) = V_r_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__converse,axiom, % 177.41/177.15 ! [V_r_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2))) % 177.41/177.15 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_d,T_c)),V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Field__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hAPP(c_Relation_OField(T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_OField(T_c),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__iff,axiom, % 177.41/177.15 ! [V_r_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2))) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_b_2),V_a_2)),V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converseI,axiom, % 177.41/177.15 ! [V_r_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converseD,axiom, % 177.41/177.15 ! [V_r_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_b_2),V_a_2)),V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__converse,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) % 177.41/177.15 <=> c_Relation_Orefl__on(T_c,V_A_2,V_r_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__INTER,axiom, % 177.41/177.15 ! [V_r_2,V_S_2,T_e,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_e),c_Relation_Oconverse(T_d,T_c)),V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__converse__trancl,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) % 177.41/177.15 => c_Wellfounded_Owf(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_equiv__comp__eq,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.15 => hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),V_r_2) = V_r_2 ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Range__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) = hAPP(c_Relation_ODomain(T_c,T_d),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Domain__converse,axiom, % 177.41/177.15 ! [V_r_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)) = hAPP(c_Relation_ORange(T_d,T_c),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Range__def,axiom, % 177.41/177.15 ! [V_r_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),V_r_2) = hAPP(c_Relation_ODomain(T_c,T_d),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__converseI,axiom, % 177.41/177.15 ! [V_r_2,V_x_2,V_y_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__converseD,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__converseI,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__converseD,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Image__subset__eq,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2)),V_B_2)) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_d,hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2))))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__on__comp__subset,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_comp__equivI,axiom, % 177.41/177.15 ! [V_A_2,V_r_2,T_c] : % 177.41/177.15 ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),V_r_2) = V_r_2 % 177.41/177.15 => ( hAPP(c_Relation_ODomain(T_c,T_c),V_r_2) = V_A_2 % 177.41/177.15 => c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__acyclic__wf__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) % 177.41/177.15 => ( c_Wellfounded_Oacyclic(T_c,V_r_2) % 177.41/177.15 => c_Wellfounded_Owf(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__def,axiom, % 177.41/177.15 ! [V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),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_r_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Image__INT__eq,axiom, % 177.41/177.15 ! [V_B_2,T_e,V_A_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( c_Relation_Osingle__valued(T_c,T_d,hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)) % 177.41/177.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_e,tc_HOL_Obool)) % 177.41/177.15 => hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_reflcl__set__eq,axiom, % 177.41/177.15 ! [V_y_2,V_x_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2)),c_fequal),V_x_2),V_y_2)) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_IdI,axiom, % 177.41/177.15 ! [V_a_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),c_Relation_OId(T_c))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converse__Id,axiom, % 177.41/177.15 ! [T_c] : hAPP(c_Relation_Oconverse(T_c,T_c),c_Relation_OId(T_c)) = c_Relation_OId(T_c) ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valued__subset,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.15 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 177.41/177.15 => c_Relation_Osingle__valued(T_c,T_d,V_r_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valued__rel__comp,axiom, % 177.41/177.15 ! [V_s_2,T_e,V_r_2,T_d,T_c] : % 177.41/177.15 ( c_Relation_Osingle__valued(T_c,T_d,V_r_2) % 177.41/177.15 => ( c_Relation_Osingle__valued(T_d,T_e,V_s_2) % 177.41/177.15 => c_Relation_Osingle__valued(T_c,T_e,hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valued__Id,axiom, % 177.41/177.15 ! [T_c] : c_Relation_Osingle__valued(T_c,T_c,c_Relation_OId(T_c)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Image__Id,axiom, % 177.41/177.15 ! [V_A_2,T_c] : hAPP(c_Relation_OImage(T_c,T_c,c_Relation_OId(T_c)),V_A_2) = V_A_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_Id__O__R,axiom, % 177.41/177.15 ! [V_R_2,T_d,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_d),c_Relation_OId(T_c)),V_R_2) = V_R_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_R__O__Id,axiom, % 177.41/177.15 ! [V_R_2,T_d,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_d),V_R_2),c_Relation_OId(T_d)) = V_R_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valued__Id__on,axiom, % 177.41/177.15 ! [V_A_2,T_c] : c_Relation_Osingle__valued(T_c,T_c,c_Relation_OId__on(T_c,V_A_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_pair__in__Id__conv,axiom, % 177.41/177.15 ! [V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Relation_OId(T_c))) % 177.41/177.15 <=> V_a_2 = V_b_2 ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Domain__Id,axiom, % 177.41/177.15 ! [T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Relation_OId(T_c)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__empty,axiom, % 177.41/177.15 ! [T_c] : c_Transitive__Closure_Ortrancl(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) = c_Relation_OId(T_c) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Range__Id,axiom, % 177.41/177.15 ! [T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Relation_OId(T_c)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__reflcl,axiom, % 177.41/177.15 ! [V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_c))) = c_Transitive__Closure_Ortrancl(T_c,V_R_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__reflcl__absorb,axiom, % 177.41/177.15 ! [V_R_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Relation_OId(T_c)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__Id,axiom, % 177.41/177.15 ! [T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Relation_OId(T_c)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__r__diff__Id,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) = c_Transitive__Closure_Ortrancl(T_c,V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valuedD,axiom, % 177.41/177.15 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_d,T_c] : % 177.41/177.15 ( c_Relation_Osingle__valued(T_c,T_d,V_r_2) % 177.41/177.15 => ( 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)),V_r_2)) % 177.41/177.15 => ( 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_z_2)),V_r_2)) % 177.41/177.15 => V_y_2 = V_z_2 ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valued__def,axiom, % 177.41/177.15 ! [V_r_2,T_d,T_c] : % 177.41/177.15 ( c_Relation_Osingle__valued(T_c,T_d,V_r_2) % 177.41/177.15 <=> ! [B_x,B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_r_2)) % 177.41/177.15 => ! [B_z] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_z)),V_r_2)) % 177.41/177.15 => B_y = B_z ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_pair__leq__def,axiom, % 177.41/177.15 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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_reflcl__trancl,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),c_Relation_OId(T_c)) = c_Transitive__Closure_Ortrancl(T_c,V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__reflcl,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) = c_Transitive__Closure_Ortrancl(T_c,V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__unfold,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Relation_OId(T_c)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_refl__reflcl,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Id__def,axiom, % 177.41/177.15 ! [T_c] : c_Relation_OId(T_c) = hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_c,T_c)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(tc_prod(T_c,T_c),tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_HOL_Obool)),tc_prod(T_c,T_c)),c_COMBB(tc_prod(T_c,T_c),tc_HOL_Obool,T_c)),c_fequal)),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),c_COMBI(T_c))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_irrefl__diff__Id,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Relation_Oirrefl(T_c,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valued__confluent,axiom, % 177.41/177.15 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c] : % 177.41/177.15 ( c_Relation_Osingle__valued(T_c,T_c,V_r_2) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Image__Int__eq,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,V_R_2,T_d,T_c] : % 177.41/177.15 ( c_Relation_Osingle__valued(T_c,T_d,hAPP(c_Relation_Oconverse(T_d,T_c),V_R_2)) % 177.41/177.15 => hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__Int__subset,axiom, % 177.41/177.15 ! [V_r_2,V_s_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Relation_OId(T_c)),V_s_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_s_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_total__on__diff__Id,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Ototal__on(T_c,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) % 177.41/177.15 <=> c_Relation_Ototal__on(T_c,V_A_2,V_r_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 177.41/177.15 ! [V_R_2,V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_c,T_c),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_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_single__valued__rel__pow,axiom, % 177.41/177.15 ! [V_n_2,V_R_2,T_c] : % 177.41/177.15 ( c_Relation_Osingle__valued(T_c,T_c,V_R_2) % 177.41/177.15 => c_Relation_Osingle__valued(T_c,T_c,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_comp__funpow,axiom, % 177.41/177.15 ! [V_f_2,V_n_2,T_d,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),V_n_2),c_Fun_Ocomp(T_d,T_d,T_c,V_f_2)) = c_Fun_Ocomp(T_d,T_d,T_c,hAPP(hAPP(c_Nat_Ocompow(T_d,T_d),V_n_2),V_f_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__exp,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)) % 177.41/177.15 => c_Wellfounded_Owf(T_c,V_R_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_funpow__mult,axiom, % 177.41/177.15 ! [V_f_2,V_m_2,V_n_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_funpow__swap1,axiom, % 177.41/177.15 ! [V_x_2,V_n_2,T_c,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__1,axiom, % 177.41/177.15 ! [V_R_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__commute,axiom, % 177.41/177.15 ! [V_n_2,V_R_2,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__imp__rtrancl,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__power,axiom, % 177.41/177.15 ! [V_R_2,V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),B_n),V_R_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_relpow_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__add,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,V_m_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c,T_c,T_c),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_relpow_Osimps_I1_J,axiom, % 177.41/177.15 ! [V_R_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_c) ). % 177.41/177.15 % 177.41/177.15 fof(fact_total__on__empty,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_Relation_Ototal__on(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_r_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_total__on__converse,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Ototal__on(T_c,V_A_2,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) % 177.41/177.15 <=> c_Relation_Ototal__on(T_c,V_A_2,V_r_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__0__I,axiom, % 177.41/177.15 ! [V_R_2,V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__0__E,axiom, % 177.41/177.15 ! [V_R_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 177.41/177.15 => V_x_2 = V_y_2 ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__Suc__I2,axiom, % 177.41/177.15 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_R_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__Suc__I,axiom, % 177.41/177.15 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_z_2)),V_R_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_funpow_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_f_2,V_n_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_funpow__add,axiom, % 177.41/177.15 ! [V_f_2,V_n_2,V_m_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_funpow_Osimps_I1_J,axiom, % 177.41/177.15 ! [V_f_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_c) ). % 177.41/177.15 % 177.41/177.15 fof(fact_trancl__power,axiom, % 177.41/177.15 ! [V_R_2,V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_R_2))) % 177.41/177.15 <=> ? [B_n] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_total__on__def,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Ototal__on(T_c,V_A_2,V_r_2) % 177.41/177.15 <=> ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => ! [B_xa] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_A_2)) % 177.41/177.15 => ( B_x != B_xa % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_xa)),V_r_2)) % 177.41/177.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 177.41/177.15 ! [V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_c,T_c),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_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_funpow__code__def,axiom, % 177.41/177.15 ! [T_c] : c_Nat_Ofunpow(T_c) = c_Nat_Ocompow(T_c,T_c) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__E2,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) % 177.41/177.15 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => V_x_2 != V_z_2 ) % 177.41/177.15 => ~ ! [B_y,B_m] : % 177.41/177.15 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),V_R_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__E,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) % 177.41/177.15 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => V_x_2 != V_z_2 ) % 177.41/177.15 => ~ ! [B_y,B_m] : % 177.41/177.15 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),B_m),V_R_2))) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_acyclicI,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) % 177.41/177.15 => c_Wellfounded_Oacyclic(T_c,V_r_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__Un__separator__converseE,axiom, % 177.41/177.15 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2),V_Qa_2)))) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2))) % 177.41/177.15 => ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_Qa_2)) % 177.41/177.15 => B_y = B_x ) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__Un__separatorE,axiom, % 177.41/177.15 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2),V_Qa_2)))) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2))) % 177.41/177.15 => ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_Qa_2)) % 177.41/177.15 => B_x = B_y ) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__Suc__D2,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 177.41/177.15 => ? [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),V_R_2)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__Suc__E2,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 177.41/177.15 => ~ ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),V_R_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__pow__Suc__E,axiom, % 177.41/177.15 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 177.41/177.15 => ~ ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),V_R_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_tranclD2,axiom, % 177.41/177.15 ! [V_R_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2))) % 177.41/177.15 => ? [B_z] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_z),V_y_2)),V_R_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_tranclD,axiom, % 177.41/177.15 ! [V_R_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2))) % 177.41/177.15 => ? [B_z] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_z)),V_R_2)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_IdE,axiom, % 177.41/177.15 ! [V_p_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Relation_OId(T_c))) % 177.41/177.15 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nat__intermed__int__val,axiom, % 177.41/177.15 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 177.41/177.15 ( ! [B_i] : % 177.41/177.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 177.41/177.15 => 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))) ) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 177.41/177.15 => ? [B_i] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 177.41/177.15 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_mod__div__decomp,axiom, % 177.41/177.15 ! [V_b,V_a,T_a] : % 177.41/177.15 ( class_Divides_Osemiring__div(T_a) % 177.41/177.15 => 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)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_wf__eq__minimal,axiom, % 177.41/177.15 ! [V_r_2,T_c] : % 177.41/177.15 ( c_Wellfounded_Owf(T_c,V_r_2) % 177.41/177.15 <=> ! [B_Q] : % 177.41/177.15 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_Q)) % 177.41/177.15 => ? [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_Q)) % 177.41/177.15 & ! [B_y] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_r_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_y),B_Q)) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_transfer__nat__int__set__cong,axiom, % 177.41/177.15 ! [V_P_Ha_2,V_Pa_2] : % 177.41/177.15 ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 177.41/177.15 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.15 <=> hBOOL(hAPP(V_P_Ha_2,B_x)) ) ) % 177.41/177.15 => 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_Ha_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Int__Collect__mono,axiom, % 177.41/177.15 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.15 => hBOOL(hAPP(V_Qa_2,B_x)) ) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_c),V_Qa_2)))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_UnionE,axiom, % 177.41/177.15 ! [V_C_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2))) % 177.41/177.15 => ~ ! [B_X] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),B_X)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rel__compE,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_e,V_xz_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_r_2),V_s_2))) % 177.41/177.15 => ~ ! [B_x,B_y,B_z] : % 177.41/177.15 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_z) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),B_x),B_y)),V_r_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_e,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_e,T_d),B_y),B_z)),V_s_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_converseE,axiom, % 177.41/177.15 ! [V_r_2,V_yx_2,T_d,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_yx_2),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2))) % 177.41/177.15 => ~ ! [B_x,B_y] : % 177.41/177.15 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_y),B_x) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),B_y)),V_r_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Oplus__frac__def,axiom, % 177.41/177.15 ! [V_r_2,V_q_2,T_c] : c_Nitpick_Oplus__frac(T_c,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_c),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_c),V_q_2),hAPP(c_Nitpick_Odenom(T_c),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_c),tc_Int_Oint),c_Nitpick_Ofrac(T_c)),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_c),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_c),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_c),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_c),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setprod__pos,axiom, % 177.41/177.15 ! [V_f_2,V_A_2,T_c,T_d] : % 177.41/177.15 ( class_Rings_Olinordered__semidom(T_d) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_x))) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Otimes__frac__def,axiom, % 177.41/177.15 ! [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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Oof__frac__def,axiom, % 177.41/177.15 ! [V_q,T_a,T_b] : % 177.41/177.15 ( ( class_Rings_Oinverse(T_b) % 177.41/177.15 & class_Rings_Oring__1(T_b) ) % 177.41/177.15 => 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))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 177.41/177.15 ! [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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Oless__frac__def,axiom, % 177.41/177.15 ! [V_r_2,V_q_2,T_c] : % 177.41/177.15 ( c_Nitpick_Oless__frac(T_c,V_q_2,V_r_2) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_c),c_Nitpick_Oplus__frac(T_c,V_q_2,c_Nitpick_Ouminus__frac(T_c,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 177.41/177.15 ! [V_r_2,V_q_2,T_c] : % 177.41/177.15 ( c_Nitpick_Oless__eq__frac(T_c,V_q_2,V_r_2) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_c),c_Nitpick_Oplus__frac(T_c,V_q_2,c_Nitpick_Ouminus__frac(T_c,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Onum__def,axiom, % 177.41/177.15 ! [T_c] : c_Nitpick_Onum(T_c) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_c,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_c)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Odenom__def,axiom, % 177.41/177.15 ! [T_c] : c_Nitpick_Odenom(T_c) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_c,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_c)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_internal__split__def,axiom, % 177.41/177.15 ! [T_e,T_d,T_c] : c_Product__Type_Ointernal__split(T_c,T_d,T_e) = c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e) ). % 177.41/177.15 % 177.41/177.15 fof(fact_setprod__nonneg,axiom, % 177.41/177.15 ! [V_f_2,V_A_2,T_c,T_d] : % 177.41/177.15 ( class_Rings_Olinordered__semidom(T_d) % 177.41/177.15 => ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_x))) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_internal__split__conv,axiom, % 177.41/177.15 ! [V_b_2,V_a_2,V_c_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_d,T_e,T_c),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_bool_Osize_I1_J,axiom, % 177.41/177.15 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.41/177.15 % 177.41/177.15 fof(fact_bool_Osize_I2_J,axiom, % 177.41/177.15 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__less__ub,axiom, % 177.41/177.15 ! [V_u_2,V_f_2] : % 177.41/177.15 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 177.41/177.15 => 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)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lenlex__def,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_List_Olenlex(T_c,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_c)),tc_List_Olist(T_c)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_c),c_Wellfounded_Oless__than,c_List_Olex(T_c,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_prod(tc_Nat_Onat,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_c),tc_prod(tc_Nat_Onat,tc_List_Olist(T_c))),tc_List_Olist(T_c)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_c))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),c_COMBI(tc_List_Olist(T_c)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_neq__if__length__neq,axiom, % 177.41/177.15 ! [V_ys,V_xs,T_a] : % 177.41/177.15 ( 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) % 177.41/177.15 => V_xs != V_ys ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lexn__length,axiom, % 177.41/177.15 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_c,V_r_2),V_n_2))) % 177.41/177.15 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = V_n_2 % 177.41/177.15 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) = V_n_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lenlex__conv,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_List_Olenlex(T_c,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBS(tc_List_Olist(T_c),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBS(tc_List_Olist(T_c),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBC(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))))),c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c))))),c_List_Olex(T_c,V_r_2)))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_length__sublist,axiom, % 177.41/177.15 ! [V_I_2,V_xs_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Osublist(T_c,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_c)),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)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lexn_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_n_2,V_r_2,T_c] : hAPP(c_List_Olexn(T_c,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_c),tc_List_Olist(T_c)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_c,tc_List_Olist(T_c)),tc_prod(T_c,tc_List_Olist(T_c))),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_Product__Type_Omap__pair(tc_prod(T_c,tc_List_Olist(T_c)),tc_List_Olist(T_c),tc_prod(T_c,tc_List_Olist(T_c)),tc_List_Olist(T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)))),c_Wellfounded_Olex__prod(T_c,tc_List_Olist(T_c),V_r_2,hAPP(c_List_Olexn(T_c,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_impossible__Cons,axiom, % 177.41/177.15 ! [V_x,V_ys,V_xs,T_a] : % 177.41/177.15 ( 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))) % 177.41/177.15 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_not__Cons__self,axiom, % 177.41/177.15 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 177.41/177.15 % 177.41/177.15 fof(fact_not__Cons__self2,axiom, % 177.41/177.15 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 177.41/177.15 % 177.41/177.15 fof(fact_list_Oinject,axiom, % 177.41/177.15 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_c] : % 177.41/177.15 ( hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_H_2),V_list_H_2) % 177.41/177.15 <=> ( V_a_2 = V_a_H_2 % 177.41/177.15 & V_list_2 = V_list_H_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list_Osize_I4_J,axiom, % 177.41/177.15 ! [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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Cons__in__lex,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olex(T_c,V_r_2))) % 177.41/177.15 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.15 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) % 177.41/177.15 | ( V_x_2 = V_y_2 % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olex(T_c,V_r_2))) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__Cons__def,axiom, % 177.41/177.15 ! [V_XS_2,V_A_2,T_c] : c_List_Oset__Cons(T_c,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_c)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_List_Olist(T_c)),c_COMBS(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),T_c),c_COMBS(tc_List_Olist(T_c),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_List_Olist(T_c)),c_COMBB(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_List_Olist(T_c),tc_HOL_Obool,tc_List_Olist(T_c))),c_fequal))),c_List_Olist_OCons(T_c)))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),T_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c))),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_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_c))),V_XS_2)))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_pick_Osimps,axiom, % 177.41/177.15 ! [V_xs,V_x,T_a,V_i] : % 177.41/177.15 ( ( 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))) % 177.41/177.15 => 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) ) % 177.41/177.15 & ( ~ 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))) % 177.41/177.15 => 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))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_select__weight__cons__zero,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,T_c] : c_Random_Oselect__weight(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_c),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_c,V_xs_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lexord__cons__cons,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_y_2))),c_List_Olexord(T_c,V_r_2))) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.15 | ( V_a_2 = V_b_2 % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lexord__lex,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olex(T_c,V_r_2))) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) % 177.41/177.15 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_y_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 177.41/177.15 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list_Osize_I2_J,axiom, % 177.41/177.15 ! [V_list_2,V_a_2,V_fa_2,T_c] : c_List_Olist_Olist__size(T_c,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),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_c,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Cons__acc__listrel1I,axiom, % 177.41/177.15 ! [V_xs_2,V_r_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_r_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1__mono,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel1(T_c,V_r_2)),c_List_Olistrel1(T_c,V_s_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel1(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1__converse,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_List_Olistrel1(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olistrel1(T_c,V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 177.41/177.15 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1I2,axiom, % 177.41/177.15 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_ys_2))),c_List_Olistrel1(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__listrel1__eq__len,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) % 177.41/177.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_y_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1__eq__len,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__listrel1__converse,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olistrel1(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)))) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olistrel1(T_c,V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1I1,axiom, % 177.41/177.15 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_xs_2))),c_List_Olistrel1(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Cons__listrel1__Cons,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.15 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.15 & V_xs_2 = V_ys_2 ) % 177.41/177.15 | ( V_x_2 = V_y_2 % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__Cons,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,V_r_2,T_c] : hAPP(c_Relation_OImage(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))) = c_List_Oset__Cons(T_c,hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lexord__irreflexive,axiom, % 177.41/177.15 ! [V_y_2,V_r_2,T_c] : % 177.41/177.15 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_y_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__rtrancl__refl,axiom, % 177.41/177.15 ! [V_r_2,V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_xs_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__mono,axiom, % 177.41/177.15 ! [V_s_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel(T_c,V_r_2)),c_List_Olistrel(T_c,V_s_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 177.41/177.15 ! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel(T_c,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__eq__len,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__rtrancl__trans,axiom, % 177.41/177.15 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_ys_2),V_zs_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_zs_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__reflcl__if__listrel1,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1__subset__listrel,axiom, % 177.41/177.15 ! [V_r_H_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 177.41/177.15 => ( c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_r_H_2) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel1(T_c,V_r_2)),c_List_Olistrel(T_c,V_r_H_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel_OCons,axiom, % 177.41/177.15 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olistrel(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrelp__listrel__eq,axiom, % 177.41/177.15 ! [V_xa_2,V_x_2,V_r_2,T_c] : % 177.41/177.15 ( c_List_Olistrelp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2),V_x_2,V_xa_2) % 177.41/177.15 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_xa_2)),c_List_Olistrel(T_c,V_r_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__Cons2,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 => ~ ! [B_x,B_xs] : % 177.41/177.15 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_x),B_xs) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),V_y_2)),V_r_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),B_xs),V_ys_2)),c_List_Olistrel(T_c,V_r_2))) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrelp_OCons,axiom, % 177.41/177.15 ! [V_ys_2,V_xs_2,T_c,V_y_2,V_x_2,V_r_2] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 177.41/177.15 => ( c_List_Olistrelp(T_c,V_r_2,V_xs_2,V_ys_2) % 177.41/177.15 => c_List_Olistrelp(T_c,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrelp_Oequations_I2_J,axiom, % 177.41/177.15 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_c] : % 177.41/177.15 ( c_List_Olistrelp(T_c,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a2_2),V_a4_2)) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 177.41/177.15 & c_List_Olistrelp(T_c,V_r_2,V_a3_2,V_a4_2) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__Cons1,axiom, % 177.41/177.15 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 => ~ ! [B_y,B_ys] : % 177.41/177.15 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_y),B_ys) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),B_y)),V_r_2)) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_ys_2),B_ys)),c_List_Olistrel(T_c,V_r_2))) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__subset,axiom, % 177.41/177.15 ! [V_A_2,V_r_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olists(T_c,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_List_Olist(T_c)),c_List_Olists(T_c,V_A_2))))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lists__UNIV,axiom, % 177.41/177.15 ! [T_c] : c_List_Olists(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lists__mono,axiom, % 177.41/177.15 ! [V_B_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),c_List_Olists(T_c,V_A_2)),c_List_Olists(T_c,V_B_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_equiv__listrel,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.15 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_c),c_List_Olists(T_c,V_A_2),c_List_Olistrel(T_c,V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__refl__on,axiom, % 177.41/177.15 ! [V_r_2,V_A_2,T_c] : % 177.41/177.15 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.15 => c_Relation_Orefl__on(tc_List_Olist(T_c),c_List_Olists(T_c,V_A_2),c_List_Olistrel(T_c,V_r_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Cons__in__lists__iff,axiom, % 177.41/177.15 ! [V_A_2,V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),c_List_Olists(T_c,V_A_2))) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,V_A_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lists__accD,axiom, % 177.41/177.15 ! [V_r_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,c_Wellfounded_Oacc(T_c,V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lists__accI,axiom, % 177.41/177.15 ! [V_r_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,c_Wellfounded_Oacc(T_c,V_r_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__iff__nth,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) % 177.41/177.15 & ! [B_n] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lexord__linear,axiom, % 177.41/177.15 ! [V_y_2,V_x_2,V_r_2,T_c] : % 177.41/177.15 ( ! [B_a,B_b] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_a),B_b)),V_r_2)) % 177.41/177.15 | B_a = B_b % 177.41/177.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_b),B_a)),V_r_2)) ) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) % 177.41/177.15 | V_x_2 = V_y_2 % 177.41/177.15 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_y_2),V_x_2)),c_List_Olexord(T_c,V_r_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_infinite__UNIV__listI,axiom, % 177.41/177.15 ! [T_c] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__eq__iff__nth__eq,axiom, % 177.41/177.15 ! [T_c,V_ys_2,V_xs_2] : % 177.41/177.15 ( V_xs_2 = V_ys_2 % 177.41/177.15 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) % 177.41/177.15 & ! [B_i] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__Cons__0,axiom, % 177.41/177.15 ! [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 ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__Cons__Suc,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth_Osimps,axiom, % 177.41/177.15 ! [V_n_2,V_xs_2,V_x_2,T_c] : hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_c,V_x_2,hAPP(c_List_Onth(T_c),V_xs_2),V_n_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__Cons_H,axiom, % 177.41/177.15 ! [V_xs,V_x,T_a,V_n] : % 177.41/177.15 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 177.41/177.15 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => 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))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__Cons__number__of,axiom, % 177.41/177.15 ! [V_xs,V_x,T_a,V_v] : % 177.41/177.15 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => 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 ) % 177.41/177.15 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => 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))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lexord__take__index__conv,axiom, % 177.41/177.15 ! [V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) % 177.41/177.15 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_y_2))) % 177.41/177.15 & hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_x_2)),V_y_2) = V_x_2 ) % 177.41/177.15 | ? [B_i] : % 177.41/177.15 ( 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_c)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_y_2)))) % 177.41/177.15 & hAPP(hAPP(c_List_Otake(T_c),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_c),B_i),V_y_2) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(hAPP(c_List_Onth(T_c),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_y_2),B_i))),V_r_2)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__sublist,axiom, % 177.41/177.15 ! [V_I_2,V_xs_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_c,tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_c),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_c)),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))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__set,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_List_Oset(T_c),V_xs_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__subset__Cons,axiom, % 177.41/177.15 ! [V_x_2,V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__all,axiom, % 177.41/177.15 ! [V_n,V_xs,T_a] : % 177.41/177.15 ( 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)) % 177.41/177.15 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__take__subset,axiom, % 177.41/177.15 ! [V_xs_2,V_n_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_c),V_xs_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__take__subset__set__take,axiom, % 177.41/177.15 ! [V_xs_2,T_c,V_n_2,V_m_2] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__sublist__subset,axiom, % 177.41/177.15 ! [V_I_2,V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_c),V_xs_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__take,axiom, % 177.41/177.15 ! [V_xs,T_a,V_n,V_i] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 177.41/177.15 => 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) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_notin__set__sublistI,axiom, % 177.41/177.15 ! [V_I_2,V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__set__takeD,axiom, % 177.41/177.15 ! [V_xs_2,V_n_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__set__sublistD,axiom, % 177.41/177.15 ! [V_I_2,V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__ConsD,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,V_y_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)))) % 177.41/177.15 => ( V_y_2 = V_x_2 % 177.41/177.15 | hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__Suc__Cons,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_length__take,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__take,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_List_Oset_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_sublist__upt__eq__take,axiom, % 177.41/177.15 ! [V_n_2,V_l_2,T_c] : c_List_Osublist(T_c,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_l_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_card__length,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_all__set__conv__all__nth,axiom, % 177.41/177.15 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.15 ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.15 <=> ! [B_i] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__size__estimation,axiom, % 177.41/177.15 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_c,V_f_2,V_xs_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__size__estimation_H,axiom, % 177.41/177.15 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_c,V_f_2,V_xs_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__lists__conv__set,axiom, % 177.41/177.15 ! [V_A_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,V_A_2))) % 177.41/177.15 <=> ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_length__pos__if__in__set,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => 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_c)),V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__mem,axiom, % 177.41/177.15 ! [V_xs_2,T_c,V_n_2] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__set__conv__nth,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 <=> ? [B_i] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 & hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i) = V_x_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lists__eq__set,axiom, % 177.41/177.15 ! [V_A_2,T_c] : c_List_Olists(T_c,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),V_A_2)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__conv__nth,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),V_xs_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_c,tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_c),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_c)),V_xs_2))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__lists__length__eq,axiom, % 177.41/177.15 ! [V_n_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_n_2))))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_finite__lists__length__le,axiom, % 177.41/177.15 ! [V_n_2,V_A_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_n_2))))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__iff__zip,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) % 177.41/177.15 & ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_c)),hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_ys_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2)),B_x)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__zip,axiom, % 177.41/177.15 ! [V_ys_2,V_xs_2,T_d,T_c] : hAPP(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_c,T_d)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_c,T_d),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_c,T_d)),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_c,T_d)),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_c,T_d),tc_fun(tc_Nat_Onat,tc_prod(T_c,T_d)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_c,T_d)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_c,T_d)),c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),tc_Nat_Onat),c_Product__Type_OPair(T_c,T_d)),hAPP(c_List_Onth(T_c),V_xs_2))),hAPP(c_List_Onth(T_d),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_c)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2)))))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__zip,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_length__zip,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_zip__Cons__Cons,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__eq__iff__zip__eq,axiom, % 177.41/177.15 ! [T_c,V_ys_2,V_xs_2] : % 177.41/177.15 ( V_xs_2 = V_ys_2 % 177.41/177.15 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) % 177.41/177.15 & ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_c)),hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_ys_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_zip__same,axiom, % 177.41/177.15 ! [V_xs_2,V_b_2,V_a_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_c,T_c)),hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_xs_2)))) % 177.41/177.15 <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 & V_a_2 = V_b_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__zip__leftD,axiom, % 177.41/177.15 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_d,T_c] : % 177.41/177.15 ( 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(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__zip__rightD,axiom, % 177.41/177.15 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_d,T_c] : % 177.41/177.15 ( 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(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_List_Oset(T_d),V_ys_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__set__zipE,axiom, % 177.41/177.15 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_d,T_c] : % 177.41/177.15 ( 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(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)))) % 177.41/177.15 => ~ ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => ~ hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_List_Oset(T_d),V_ys_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__zip,axiom, % 177.41/177.15 ! [V_ys,T_b,V_xs,T_a,V_i] : % 177.41/177.15 ( 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))) % 177.41/177.15 => ( 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))) % 177.41/177.15 => 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)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_greaterThanLessThan__upto,axiom, % 177.41/177.15 ! [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)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listsum__setsum__nth,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(c_List_Onth(T_c),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_c)),V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_atLeastAtMost__upto,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__upto,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 177.41/177.15 ! [V_ns_2] : % 177.41/177.15 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 <=> ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 177.41/177.15 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_elem__le__listsum__nat,axiom, % 177.41/177.15 ! [V_ns,V_k] : % 177.41/177.15 ( 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))) % 177.41/177.15 => 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))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listsum__simps_I2_J,axiom, % 177.41/177.15 ! [V_xs,V_x,T_a] : % 177.41/177.15 ( class_Groups_Omonoid__add(T_a) % 177.41/177.15 => 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)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_atLeastLessThan__upto,axiom, % 177.41/177.15 ! [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)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_greaterThanAtMost__upto,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nat__list__def,axiom, % 177.41/177.15 ! [V_l_2] : % 177.41/177.15 ( c_List_Onat__list(V_l_2) % 177.41/177.15 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__size__pointwise,axiom, % 177.41/177.15 ! [V_g_2,V_f_2,V_xs_2,T_c] : % 177.41/177.15 ( ! [B_x] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_c,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_c,V_g_2,V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listsum__update__nat,axiom, % 177.41/177.15 ! [V_n,V_ns,V_k] : % 177.41/177.15 ( 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))) % 177.41/177.15 => 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)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_butlast__take,axiom, % 177.41/177.15 ! [V_xs,T_a,V_n] : % 177.41/177.15 ( 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))) % 177.41/177.15 => 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) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__beyond,axiom, % 177.41/177.15 ! [V_x,V_i,V_xs,T_a] : % 177.41/177.15 ( 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)) % 177.41/177.15 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__list__update__neq,axiom, % 177.41/177.15 ! [V_x,V_xs,T_a,V_j,V_i] : % 177.41/177.15 ( V_i != V_j % 177.41/177.15 => 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) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__id,axiom, % 177.41/177.15 ! [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 ). % 177.41/177.15 % 177.41/177.15 fof(fact_length__list__update,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_butlast__list__update,axiom, % 177.41/177.15 ! [V_x,V_xs,T_a,V_k] : % 177.41/177.15 ( ( 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)) % 177.41/177.15 => 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) ) % 177.41/177.15 & ( 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)) % 177.41/177.15 => 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) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_zip__update,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_update__zip,axiom, % 177.41/177.15 ! [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))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__overwrite,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__swap,axiom, % 177.41/177.15 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 177.41/177.15 ( V_i != V_i_H % 177.41/177.15 => 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) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_c] : hAPP(hAPP(c_List_Olist__update(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_c),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_c,tc_List_Olist(T_c)),c_List_Olist__update(T_c,V_xs_2)),V_v_2)),V_i_2) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__code_I2_J,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__code_I3_J,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_in__set__butlastD,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,V_xs_2)))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__update__subsetI,axiom, % 177.41/177.15 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),V_A_2)) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__update__subset__insert,axiom, % 177.41/177.15 ! [V_x_2,V_i_2,V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__list__update,axiom, % 177.41/177.15 ! [V_x,V_j,V_xs,T_a,V_i] : % 177.41/177.15 ( 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))) % 177.41/177.15 => ( ( V_i = V_j % 177.41/177.15 => 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 ) % 177.41/177.15 & ( V_i != V_j % 177.41/177.15 => 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) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__same__conv,axiom, % 177.41/177.15 ! [V_x_2,V_xs_2,T_c,V_i_2] : % 177.41/177.15 ( 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_xs_2))) % 177.41/177.15 => ( hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 177.41/177.15 <=> hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_i_2) = V_x_2 ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__list__update__eq,axiom, % 177.41/177.15 ! [V_x,V_xs,T_a,V_i] : % 177.41/177.15 ( 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))) % 177.41/177.15 => 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 ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__butlast,axiom, % 177.41/177.15 ! [V_xs,T_a,V_n] : % 177.41/177.15 ( 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))) % 177.41/177.15 => 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) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_length__butlast,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__update__memI,axiom, % 177.41/177.15 ! [V_x_2,V_xs_2,T_c,V_n_2] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_n_2),V_x_2)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_butlast__conv__take,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel1__iff__update,axiom, % 177.41/177.15 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.15 <=> ? [B_y,B_n] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_n)),B_y)),V_r_2)) % 177.41/177.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),B_n),B_y) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__list__update,axiom, % 177.41/177.15 ! [V_i_2,V_a_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_a_2))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__upto,axiom, % 177.41/177.15 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__take,axiom, % 177.41/177.15 ! [V_i,V_xs,T_a] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__sublistI,axiom, % 177.41/177.15 ! [V_I_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__zipI1,axiom, % 177.41/177.15 ! [V_ys,T_b,V_xs,T_a] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__zipI2,axiom, % 177.41/177.15 ! [V_xs,T_b,V_ys,T_a] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) % 177.41/177.15 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.15 & hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_card__distinct,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__card,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.15 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__conv__nth,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.15 <=> ! [B_i] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => ! [B_j] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => ( B_i != B_j % 177.41/177.15 => hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_j) ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__eq__iff__index__eq,axiom, % 177.41/177.15 ! [V_j_2,V_i_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.15 => ( 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_xs_2))) % 177.41/177.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.15 => ( hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_j_2) % 177.41/177.15 <=> V_i_2 = V_j_2 ) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__listsum__conv__Setsum,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.15 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_COMBI(T_c)),hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_Nitpick_Ocard_H__def,axiom, % 177.41/177.15 ! [V_A_2,T_c] : % 177.41/177.15 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => c_Nitpick_Ocard_H(T_c,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_Hilbert__Choice_OEps(tc_List_Olist(T_c),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_List_Oset(T_c))),V_A_2))),c_List_Odistinct(T_c)))) ) % 177.41/177.15 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.15 => c_Nitpick_Ocard_H(T_c,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_nth__take__lemma,axiom, % 177.41/177.15 ! [V_ys,V_xs,T_a,V_k] : % 177.41/177.15 ( 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))) % 177.41/177.15 => ( 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))) % 177.41/177.15 => ( ! [B_i] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 177.41/177.15 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 177.41/177.15 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__remove1__eq,axiom, % 177.41/177.15 ! [V_x_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.15 => hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__Cons__number__of,axiom, % 177.41/177.15 ! [V_xs,V_x,T_a,V_v] : % 177.41/177.15 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => 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) ) % 177.41/177.15 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 => 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)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_lists_ONil,axiom, % 177.41/177.15 ! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_List_Olists(T_c,V_A_2))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__Nil1,axiom, % 177.41/177.15 ! [V_r_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xs_2)),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 => V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrel__Nil2,axiom, % 177.41/177.15 ! [V_r_2,V_xs_2,T_c] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),c_List_Olist_ONil(T_c))),c_List_Olistrel(T_c,V_r_2))) % 177.41/177.15 => V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__butlast,axiom, % 177.41/177.15 ! [T_a,V_xs] : % 177.41/177.15 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.15 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct__remove1,axiom, % 177.41/177.15 ! [V_x,V_xs,T_a] : % 177.41/177.15 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.15 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_distinct_Osimps_I1_J,axiom, % 177.41/177.15 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 177.41/177.15 % 177.41/177.15 fof(fact_butlast_Osimps_I1_J,axiom, % 177.41/177.15 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.41/177.15 % 177.41/177.15 fof(fact_butlast_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_x,T_a,V_xs] : % 177.41/177.15 ( ( V_xs = c_List_Olist_ONil(T_a) % 177.41/177.15 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 177.41/177.15 & ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.15 => 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)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list_Osimps_I2_J,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list_Osimps_I3_J,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_remove1_Osimps_I2_J,axiom, % 177.41/177.15 ! [V_xs,T_a,V_y,V_x] : % 177.41/177.15 ( ( V_x = V_y % 177.41/177.15 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 177.41/177.15 & ( V_x != V_y % 177.41/177.15 => 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)) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_upto__empty,axiom, % 177.41/177.15 ! [V_i,V_j] : % 177.41/177.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 177.41/177.15 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__eq__Nil,axiom, % 177.41/177.15 ! [V_xs_2,V_n_2,T_c] : % 177.41/177.15 ( hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.15 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 | V_xs_2 = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__0,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_take__Nil,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_sublist__nil,axiom, % 177.41/177.15 ! [V_A_2,T_c] : c_List_Osublist(T_c,c_List_Olist_ONil(T_c),V_A_2) = c_List_Olist_ONil(T_c) ). % 177.41/177.15 % 177.41/177.15 fof(fact_remove1__commute,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_remove1_Osimps_I1_J,axiom, % 177.41/177.15 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrelp_Oequations_I1_J,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_List_Olistrelp(T_c,V_r_2,c_List_Olist_ONil(T_c),c_List_Olist_ONil(T_c)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listrelp_ONil,axiom, % 177.41/177.15 ! [V_r_2,T_c] : c_List_Olistrelp(T_c,V_r_2,c_List_Olist_ONil(T_c),c_List_Olist_ONil(T_c)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_zip__Nil,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_zip_Osimps_I1_J,axiom, % 177.41/177.15 ! [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)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_listsum__simps_I1_J,axiom, % 177.41/177.15 ! [T_a] : % 177.41/177.15 ( class_Groups_Omonoid__add(T_a) % 177.41/177.15 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_length__0__conv,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.15 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list_Osize_I3_J,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__empty,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( hAPP(c_List_Oset(T_c),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.15 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_set__empty2,axiom, % 177.41/177.15 ! [V_xs_2,T_c] : % 177.41/177.15 ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_List_Oset(T_c),V_xs_2) % 177.41/177.15 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_List_Oset_Osimps_I1_J,axiom, % 177.41/177.15 ! [T_c] : hAPP(c_List_Oset(T_c),c_List_Olist_ONil(T_c)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list_Osize_I1_J,axiom, % 177.41/177.15 ! [V_fa_2,T_c] : c_List_Olist_Olist__size(T_c,V_fa_2,c_List_Olist_ONil(T_c)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__code_I1_J,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update_Osimps_I1_J,axiom, % 177.41/177.15 ! [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) ). % 177.41/177.15 % 177.41/177.15 fof(fact_list__update__nonempty,axiom, % 177.41/177.15 ! [V_x_2,V_k_2,V_xs_2,T_c] : % 177.41/177.15 ( hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_c) % 177.41/177.15 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.15 % 177.41/177.15 fof(fact_remove1__idem,axiom, % 177.41/177.15 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oremove1(T_c,V_x_2,V_xs_2) = V_xs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_notin__set__remove1,axiom, % 177.41/177.16 ! [V_y_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_y_2,V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_in__set__remove1,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_b_2,V_a_2] : % 177.41/177.16 ( V_a_2 != V_b_2 % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_b_2,V_xs_2)))) % 177.41/177.16 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublist__empty,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : c_List_Osublist(T_c,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_c) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__remove1__subset,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_c),V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__greater__0__conv,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( 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_c)),V_xs_2))) % 177.41/177.16 <=> V_xs_2 != c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__1__Cons,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_not__Nil__listrel1,axiom, % 177.41/177.16 ! [V_r_2,V_xs_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xs_2)),c_List_Olistrel1(T_c,V_r_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_not__listrel1__Nil,axiom, % 177.41/177.16 ! [V_r_2,V_xs_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),c_List_Olist_ONil(T_c))),c_List_Olistrel1(T_c,V_r_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listrel_ONil,axiom, % 177.41/177.16 ! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_List_Olist_ONil(T_c))),c_List_Olistrel(T_c,V_r_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lexord__Nil__right,axiom, % 177.41/177.16 ! [V_r_2,V_x_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),c_List_Olist_ONil(T_c))),c_List_Olexord(T_c,V_r_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Nil__notin__lex,axiom, % 177.41/177.16 ! [V_r_2,V_ys_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_ys_2)),c_List_Olex(T_c,V_r_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Nil2__notin__lex,axiom, % 177.41/177.16 ! [V_r_2,V_xs_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),c_List_Olist_ONil(T_c))),c_List_Olex(T_c,V_r_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__Cons,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_n_2,T_c] : hAPP(hAPP(c_List_Otake(T_c),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_c),c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_c),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Otake(T_c)),V_xs_2)),V_n_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upto_Osimps,axiom, % 177.41/177.16 ! [V_j,V_i] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.41/177.16 => 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)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 177.41/177.16 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublist__singleton,axiom, % 177.41/177.16 ! [V_x_2,T_c,V_A_2] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 177.41/177.16 => c_List_Osublist(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 177.41/177.16 => c_List_Osublist(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)),V_A_2) = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lists__empty,axiom, % 177.41/177.16 ! [T_c] : c_List_Olists(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__Cons_H,axiom, % 177.41/177.16 ! [V_xs,V_x,T_a,V_n] : % 177.41/177.16 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => 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) ) % 177.41/177.16 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => 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)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upto__rec__number__of,axiom, % 177.41/177.16 ! [V_n,V_m] : % 177.41/177.16 ( ( 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))) % 177.41/177.16 => 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))) ) % 177.41/177.16 & ( ~ 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))) % 177.41/177.16 => 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) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listrel__Nil,axiom, % 177.41/177.16 ! [V_r_2,T_c] : hAPP(c_Relation_OImage(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__Cons__sing__Nil,axiom, % 177.41/177.16 ! [V_A_2,T_c] : c_List_Oset__Cons(T_c,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_c,tc_List_Olist(T_c),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))),V_A_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__remove1,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremove1(T_c,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_c)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremove1(T_c,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upto_Opsimps,axiom, % 177.41/177.16 ! [V_j_2,V_i_2] : % 177.41/177.16 ( 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))) % 177.41/177.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 177.41/177.16 => 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)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 177.41/177.16 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_select,axiom, % 177.41/177.16 ! [V_s_2,T_c,V_xs_2] : % 177.41/177.16 ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Product__Type_Ofst(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_c,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listset_Osimps_I1_J,axiom, % 177.41/177.16 ! [T_c] : c_List_Olistset(T_c,c_List_Olist_ONil(tc_fun(T_c,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__Cons,axiom, % 177.41/177.16 ! [V_ys_2,V_y_2,V_xs_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_c,T_d)),T_c,c_List_Olist_ONil(tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),T_c),c_List_Olist_OCons(tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBC(T_c,T_d,tc_prod(T_c,T_d)),c_Product__Type_OPair(T_c,T_d)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d))),c_List_Ozip(T_c,T_d)),V_ys_2))),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list_Osimps_I5_J,axiom, % 177.41/177.16 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_d,T_c] : hAPP(c_List_Olist_Olist__case(T_c,T_d,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list_Osimps_I4_J,axiom, % 177.41/177.16 ! [V_f2_2,V_f1_2,T_d,T_c] : hAPP(c_List_Olist_Olist__case(T_c,T_d,V_f1_2,V_f2_2),c_List_Olist_ONil(T_d)) = V_f1_2 ). % 177.41/177.16 % 177.41/177.16 fof(fact_listset_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_As_2,V_A_2,T_c] : c_List_Olistset(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_c,V_A_2,c_List_Olistset(T_c,V_As_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__Cons1,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_x_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_c,T_d)),T_d,c_List_Olist_ONil(tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d)))),T_d),c_COMBB(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(T_d))),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),T_d),c_List_Olist_OCons(tc_prod(T_c,T_d))),hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2)))),hAPP(c_List_Ozip(T_c,T_d),V_xs_2))),V_ys_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__list__of__set__remove,axiom, % 177.41/177.16 ! [V_x_2,V_A_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.16 => c_List_Olinorder__class_Osorted__list__of__set(T_c,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))))) = c_List_Oremove1(T_c,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_c,V_A_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upto_Opinduct,axiom, % 177.41/177.16 ! [V_Pa_2,V_a1_2,V_a0_2] : % 177.41/177.16 ( 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))) % 177.41/177.16 => ( ! [B_i,B_j] : % 177.41/177.16 ( 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))) % 177.41/177.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 177.41/177.16 => 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)) ) % 177.41/177.16 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 177.41/177.16 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__list__of__set__empty,axiom, % 177.41/177.16 ! [T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Olinorder__class_Osorted__list__of__set(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_anamorph_Osimps,axiom, % 177.41/177.16 ! [V_x_2,V_f_2,T_c,T_d,V_k_2] : % 177.41/177.16 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.16 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_d,T_c,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),T_d),c_List_Olist_ONil(T_c)),V_x_2) ) % 177.41/177.16 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.16 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_d,T_c,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(T_c,T_d),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),T_d),c_List_Olist_ONil(T_c)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(tc_List_Olist(T_c),T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d)),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(tc_List_Olist(T_c),T_d)),tc_fun(tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d)),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),T_c),c_COMBB(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(tc_List_Olist(T_c),T_d),T_d)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),tc_fun(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(tc_List_Olist(T_c),T_d)),T_c),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),T_d,tc_prod(tc_List_Olist(T_c),T_d))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),T_c),hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d)),tc_List_Olist(T_c)),c_Product__Type_OPair(tc_List_Olist(T_c),T_d))),c_List_Olist_OCons(T_c))))),hAPP(c_Lazy__Sequence_Oanamorph(T_d,T_c,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)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublist__Cons,axiom, % 177.41/177.16 ! [V_A_2,V_l_2,V_x_2,T_c] : c_List_Osublist(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_c)),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_c),V_x_2),c_List_Olist_ONil(T_c))),c_List_Olist_ONil(T_c))),c_List_Osublist(T_c,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)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__eq__Cons__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) % 177.41/177.16 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_c) % 177.41/177.16 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) ) % 177.41/177.16 | ? [B_ys_H] : % 177.41/177.16 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_ys_H) % 177.41/177.16 & hAPP(hAPP(c_List_Oappend(T_c),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Cons__eq__append__conv,axiom, % 177.41/177.16 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2) % 177.41/177.16 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_c) % 177.41/177.16 & hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) = V_zs_2 ) % 177.41/177.16 | ? [B_ys_H] : % 177.41/177.16 ( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_ys_H) = V_ys_2 % 177.41/177.16 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys_H),V_zs_2) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append1__eq__conv,axiom, % 177.41/177.16 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c))) = hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),c_List_Olist_ONil(T_c))) % 177.41/177.16 <=> ( V_xs_2 = V_ys_2 % 177.41/177.16 & V_x_2 = V_y_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__Cons,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Cons__eq__appendI,axiom, % 177.41/177.16 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 177.41/177.16 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 177.41/177.16 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 177.41/177.16 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__in__lists__conv,axiom, % 177.41/177.16 ! [V_A_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)),c_List_Olists(T_c,V_A_2))) % 177.41/177.16 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,V_A_2))) % 177.41/177.16 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_ys_2),c_List_Olists(T_c,V_A_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__eq__appendI,axiom, % 177.41/177.16 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 177.41/177.16 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 177.41/177.16 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__same__eq,axiom, % 177.41/177.16 ! [V_zs_2,V_xs_2,V_ys_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_c),V_zs_2),V_xs_2) % 177.41/177.16 <=> V_ys_2 = V_zs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_same__append__eq,axiom, % 177.41/177.16 ! [V_zs_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_zs_2) % 177.41/177.16 <=> V_ys_2 = V_zs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__eq__append__conv2,axiom, % 177.41/177.16 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_c),V_zs_2),V_ts_2) % 177.41/177.16 <=> ? [B_us] : % 177.41/177.16 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),V_zs_2),B_us) % 177.41/177.16 & hAPP(hAPP(c_List_Oappend(T_c),B_us),V_ys_2) = V_ts_2 ) % 177.41/177.16 | ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),B_us) = V_zs_2 % 177.41/177.16 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),V_ts_2) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__assoc,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__append,axiom, % 177.41/177.16 ! [V_ys,V_xs,T_a] : % 177.41/177.16 ( class_Groups_Omonoid__add(T_a) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__append,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__append,axiom, % 177.41/177.16 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 177.41/177.16 ( 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) % 177.41/177.16 => ( 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) % 177.41/177.16 => 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)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__Nil,axiom, % 177.41/177.16 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 177.41/177.16 % 177.41/177.16 fof(fact_Nil__is__append__conv,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( c_List_Olist_ONil(T_c) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) % 177.41/177.16 <=> ( V_xs_2 = c_List_Olist_ONil(T_c) % 177.41/177.16 & V_ys_2 = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__Nil2,axiom, % 177.41/177.16 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 177.41/177.16 % 177.41/177.16 fof(fact_self__append__conv,axiom, % 177.41/177.16 ! [V_ys_2,T_c,V_xs_2] : % 177.41/177.16 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) % 177.41/177.16 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_self__append__conv2,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_ys_2] : % 177.41/177.16 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__is__Nil__conv,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> ( V_xs_2 = c_List_Olist_ONil(T_c) % 177.41/177.16 & V_ys_2 = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__self__conv,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = V_xs_2 % 177.41/177.16 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__self__conv2,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = V_ys_2 % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_eq__Nil__appendI,axiom, % 177.41/177.16 ! [T_a,V_ys,V_xs] : % 177.41/177.16 ( V_xs = V_ys % 177.41/177.16 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_butlast__append,axiom, % 177.41/177.16 ! [V_xs,T_a,V_ys] : % 177.41/177.16 ( ( V_ys = c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 177.41/177.16 & ( V_ys != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__append__length,axiom, % 177.41/177.16 ! [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 ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__append__length__plus,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__append,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__update__append1,axiom, % 177.41/177.16 ! [V_x,V_ys,V_xs,T_a,V_i] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__update__length,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remove1__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oremove1(T_c,V_x_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),c_List_Oremove1(T_c,V_x_2,V_xs_2)),V_ys_2) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oremove1(T_c,V_x_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),c_List_Oremove1(T_c,V_x_2,V_ys_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_in__set__butlast__appendI,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,V_xs_2)))) % 177.41/177.16 | hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,V_ys_2)))) ) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2))))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_butlast__snoc,axiom, % 177.41/177.16 ! [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 ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__listrel1I,axiom, % 177.41/177.16 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.16 & V_us_2 = V_vs_2 ) % 177.41/177.16 | ( V_xs_2 = V_ys_2 % 177.41/177.16 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_us_2),V_vs_2)),c_List_Olistrel1(T_c,V_r_2))) ) ) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))),c_List_Olistrel1(T_c,V_r_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lexord__append__leftI,axiom, % 177.41/177.16 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_u_2),V_v_2)),c_List_Olexord(T_c,V_r_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_v_2))),c_List_Olexord(T_c,V_r_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2))) % 177.41/177.16 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 & hBOOL(hAPP(c_List_Odistinct(T_c),V_ys_2)) % 177.41/177.16 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__append,axiom, % 177.41/177.16 ! [V_ys,V_xs,T_a,V_n] : % 177.41/177.16 ( ( 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))) % 177.41/177.16 => 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) ) % 177.41/177.16 & ( ~ 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))) % 177.41/177.16 => 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))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__update__append,axiom, % 177.41/177.16 ! [V_x,V_ys,V_xs,T_a,V_n] : % 177.41/177.16 ( ( 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))) % 177.41/177.16 => 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) ) % 177.41/177.16 & ( ~ 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))) % 177.41/177.16 => 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)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublist__append,axiom, % 177.41/177.16 ! [V_A_2,V_l_H_2,V_l_2,T_c] : c_List_Osublist(T_c,hAPP(hAPP(c_List_Oappend(T_c),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_c),c_List_Osublist(T_c,V_l_2,V_A_2)),c_List_Osublist(T_c,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_c)),V_l_2)))),V_A_2)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listrel1I,axiom, % 177.41/177.16 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) % 177.41/177.16 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_vs_2)) % 177.41/177.16 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_vs_2)) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lexord__append__left__rightI,axiom, % 177.41/177.16 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_c),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_y_2)))),c_List_Olexord(T_c,V_r_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__Suc__conv__app__nth,axiom, % 177.41/177.16 ! [V_xs,T_a,V_i] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_snoc__listrel1__snoc__iff,axiom, % 177.41/177.16 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)))),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),c_List_Olist_ONil(T_c))))),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.16 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.16 & V_x_2 = V_y_2 ) % 177.41/177.16 | ( V_xs_2 = V_ys_2 % 177.41/177.16 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listrel1E,axiom, % 177.41/177.16 ! [V_r_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) % 177.41/177.16 => ~ ! [B_x,B_y] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2)) % 177.41/177.16 => ! [B_us,B_vs] : % 177.41/177.16 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),B_x),B_vs)) % 177.41/177.16 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),B_y),B_vs)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lexord__append__leftD,axiom, % 177.41/177.16 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_v_2))),c_List_Olexord(T_c,V_r_2))) % 177.41/177.16 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_a),B_a)),V_r_2)) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_u_2),V_v_2)),c_List_Olexord(T_c,V_r_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate1__def,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_List_Orotate1(T_c),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Oappend(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c)))),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upd__conv__take__nth__drop,axiom, % 177.41/177.16 ! [V_a,V_xs,T_a,V_i] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__take__drop__id,axiom, % 177.41/177.16 ! [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 ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__1__Cons,axiom, % 177.41/177.16 ! [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 ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__Suc__Cons,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__via__drop,axiom, % 177.41/177.16 ! [V_ys,V_y,V_xs,V_n,T_a] : % 177.41/177.16 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 177.41/177.16 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__drop,axiom, % 177.41/177.16 ! [V_i,V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct1__rotate,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Orotate1(T_c),V_xs_2))) % 177.41/177.16 <=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_butlast__drop,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__butlast,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__take,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__drop,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__0,axiom, % 177.41/177.16 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__drop,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__zip,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__drop,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__rotate1,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__rotate1,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Orotate1(T_c),V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_in__set__dropD,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__drop__subset,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_c),V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__Nil,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate1__is__Nil__conv,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Orotate1(T_c),V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__drop__subset__set__drop,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_m_2,V_n_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__eq__Nil,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)),V_n_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__all,axiom, % 177.41/177.16 ! [V_n,V_xs,T_a] : % 177.41/177.16 ( 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)) % 177.41/177.16 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__append,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__eq__conv__conj,axiom, % 177.41/177.16 ! [V_zs_2,V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = V_zs_2 % 177.41/177.16 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)),V_zs_2) % 177.41/177.16 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)),V_zs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__Cons,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_n_2,T_c] : hAPP(hAPP(c_List_Odrop(T_c),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Odrop(T_c)),V_xs_2),V_n_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__Cons_H,axiom, % 177.41/177.16 ! [V_xs,V_x,T_a,V_n] : % 177.41/177.16 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => 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) ) % 177.41/177.16 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => 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) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__drop,axiom, % 177.41/177.16 ! [V_xs,T_a,V_i,V_n] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__eq__append__conv__if,axiom, % 177.41/177.16 ! [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_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_c),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 177.41/177.16 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_092_060_094isub_0621_2))) % 177.41/177.16 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 177.41/177.16 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_092_060_094isub_0621_2))) % 177.41/177.16 => ( hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 177.41/177.16 & hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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 ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__drop_H,axiom, % 177.41/177.16 ! [V_xs,T_a,V_i] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__simps,axiom, % 177.41/177.16 ! [V_xs,V_x,T_b,T_a] : % 177.41/177.16 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 177.41/177.16 & 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__Cons__number__of,axiom, % 177.41/177.16 ! [V_xs,V_x,T_a,V_v] : % 177.41/177.16 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => 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) ) % 177.41/177.16 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => 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) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__add,axiom, % 177.41/177.16 ! [V_xs,T_a,V_j,V_i] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate1__length01,axiom, % 177.41/177.16 ! [V_xs,T_a] : % 177.41/177.16 ( 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))) % 177.41/177.16 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__append2,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__append1,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_id__take__nth__drop,axiom, % 177.41/177.16 ! [V_xs,T_a,V_i] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__hd__drop,axiom, % 177.41/177.16 ! [V_xs,T_a,V_n] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__drop__conv__nth,axiom, % 177.41/177.16 ! [V_n,T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => ( 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))) % 177.41/177.16 => 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) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd_Osimps,axiom, % 177.41/177.16 ! [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 ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__append2,axiom, % 177.41/177.16 ! [V_ys,T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__append,axiom, % 177.41/177.16 ! [V_ys,T_a,V_xs] : % 177.41/177.16 ( ( V_xs = c_List_Olist_ONil(T_a) % 177.41/177.16 => 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) ) % 177.41/177.16 & ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__in__set,axiom, % 177.41/177.16 ! [T_c,V_xs_2] : % 177.41/177.16 ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_List_Ohd(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__conv__nth,axiom, % 177.41/177.16 ! [T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate1__hd__tl,axiom, % 177.41/177.16 ! [T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__rotate__conv__nth,axiom, % 177.41/177.16 ! [V_n,T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__tl,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_tl__drop,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_tl_Osimps_I2_J,axiom, % 177.41/177.16 ! [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 ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__tl,axiom, % 177.41/177.16 ! [V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__rotate,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2))) % 177.41/177.16 <=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__add,axiom, % 177.41/177.16 ! [V_n_2,V_m_2,T_c] : c_List_Orotate(T_c,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Orotate(T_c,V_m_2)),c_List_Orotate(T_c,V_n_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate0,axiom, % 177.41/177.16 ! [T_c] : c_List_Orotate(T_c,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_c)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__rotate,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__rotate,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__rotate,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_tl_Osimps_I1_J,axiom, % 177.41/177.16 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__is__Nil__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate1__rotate__swap,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__def,axiom, % 177.41/177.16 ! [V_n_2,T_c] : c_List_Orotate(T_c,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_n_2),c_List_Orotate1(T_c)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_tl__append2,axiom, % 177.41/177.16 ! [V_ys,T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__tl,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__conv__mod,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__Suc,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__Suc,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_tl__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : hAPP(c_List_Otl(T_c),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,hAPP(c_List_Otl(T_c),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Oappend(T_c)),V_ys_2))),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__id,axiom, % 177.41/177.16 ! [V_xs,T_a,V_n] : % 177.41/177.16 ( 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) % 177.41/177.16 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__length01,axiom, % 177.41/177.16 ! [V_n,V_xs,T_a] : % 177.41/177.16 ( 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))) % 177.41/177.16 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__tl,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_tl__take,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__Suc,axiom, % 177.41/177.16 ! [V_n,T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__drop__take,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_fold1__set,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Lattices_Oab__semigroup__idem__mult(T_c) % 177.41/177.16 => ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),hAPP(c_List_Ohd(T_c),V_xs_2)),hAPP(c_List_Otl(T_c),V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lexord__append__rightI,axiom, % 177.41/177.16 ! [V_r_2,V_x_2,T_c,V_y_2] : % 177.41/177.16 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_b),B_z) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_y_2))),c_List_Olexord(T_c,V_r_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__Nil,axiom, % 177.41/177.16 ! [V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),c_List_Olist_ONil(T_d)) = V_a_2 ). % 177.41/177.16 % 177.41/177.16 fof(fact_start__le__sum,axiom, % 177.41/177.16 ! [V_ns_2,V_n_2,V_m_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__assoc,axiom, % 177.41/177.16 ! [V_zs_2,V_y_2,V_x_2,T_c] : % 177.41/177.16 ( class_Groups_Osemigroup__add(T_c) % 177.41/177.16 => hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_y_2),V_zs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__absorb0,axiom, % 177.41/177.16 ! [V_zs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Groups_Omonoid__add(T_c) % 177.41/177.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_zs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_zs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__Cons,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_d),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__foldl,axiom, % 177.41/177.16 ! [T_c] : % 177.41/177.16 ( class_Groups_Omonoid__add(T_c) % 177.41/177.16 => c_List_Omonoid__add__class_Olistsum(T_c) = c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),c_Groups_Ozero__class_Ozero(T_c)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sum__eq__0__conv,axiom, % 177.41/177.16 ! [V_ns_2,V_m_2] : % 177.41/177.16 ( 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) % 177.41/177.16 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 & ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 177.41/177.16 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 177.41/177.16 ! [V_xs_2,V_y_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) % 177.41/177.16 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_d),V_f_2),V_y_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Sup__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.16 => c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Orderings_Obot__class_Obot(T_c)),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Inf__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.16 => c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Orderings_Otop__class_Otop(T_c)),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Sup__fin__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Lattices_Olattice(T_c) % 177.41/177.16 => c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Inf__fin__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Lattices_Olattice(T_c) % 177.41/177.16 => c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Min__fin__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omin(T_c),V_x_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Max__fin__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),V_x_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_min__max_OInf__fin__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omin(T_c),V_x_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_min__max_OSup__fin__set__fold,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),V_x_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_SUPR__set__fold,axiom, % 177.41/177.16 ! [V_f_2,V_xs_2,T_d,T_c] : % 177.41/177.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.16 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),hAPP(c_List_Oset(T_d),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_c,T_d,hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_INFI__set__fold,axiom, % 177.41/177.16 ! [V_f_2,V_xs_2,T_d,T_c] : % 177.41/177.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.16 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),hAPP(c_List_Oset(T_d),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_c,T_d,hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_elem__le__sum,axiom, % 177.41/177.16 ! [V_ns_2,V_n_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__list__of__set__insert,axiom, % 177.41/177.16 ! [V_x_2,V_A_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.16 => c_List_Olinorder__class_Osorted__list__of__set(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_c,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)))))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lexord__Nil__left,axiom, % 177.41/177.16 ! [V_r_2,V_y_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_y_2)),c_List_Olexord(T_c,V_r_2))) % 177.41/177.16 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_a),B_x) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__key_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_x_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),c_List_Olist_ONil(T_c)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__key_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_ys_2,T_d,V_y_2,V_x_2,V_f_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__insort,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__insort,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_fun__left__comm__insort,axiom, % 177.41/177.16 ! [T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_Finite__Set_Ofun__left__comm(T_c,tc_List_Olist(T_c),c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__left__comm,axiom, % 177.41/177.16 ! [V_xs_2,V_y_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__key__left__comm,axiom, % 177.41/177.16 ! [V_xs_2,T_d,V_y_2,V_x_2,V_f_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_y_2),V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remove1__insort,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Oremove1(T_c,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__not__Nil,axiom, % 177.41/177.16 ! [V_xs_2,V_a_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__insort,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),V_xs_2))) % 177.41/177.16 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 & hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__insert__insort__key,axiom, % 177.41/177.16 ! [V_xs_2,T_d,V_x_2,V_f_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_List_Oset(T_d),V_xs_2)))) % 177.41/177.16 => c_List_Olinorder__class_Oinsort__insert__key(T_d,T_c,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__insert__insort,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__insort__insert,axiom, % 177.41/177.16 ! [V_x_2,V_f_2,V_xs_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_d,V_f_2,V_x_2,V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__insert__triv,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__insort__insert,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => hAPP(c_List_Oset(T_c),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__insert__key__triv,axiom, % 177.41/177.16 ! [V_xs_2,T_d,V_x_2,V_f_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_List_Oset(T_d),V_xs_2)))) % 177.41/177.16 => c_List_Olinorder__class_Oinsort__insert__key(T_d,T_c,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__list__update,axiom, % 177.41/177.16 ! [V_x,V_k,T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => ( ( 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)) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 177.41/177.16 & ( 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)) % 177.41/177.16 => 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) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__conv__nth,axiom, % 177.41/177.16 ! [T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last_Osimps,axiom, % 177.41/177.16 ! [V_x,T_a,V_xs] : % 177.41/177.16 ( ( V_xs = c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 177.41/177.16 & ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__ConsR,axiom, % 177.41/177.16 ! [V_x,T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__ConsL,axiom, % 177.41/177.16 ! [V_x,T_a,V_xs] : % 177.41/177.16 ( V_xs = c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__append,axiom, % 177.41/177.16 ! [V_xs,T_a,V_ys] : % 177.41/177.16 ( ( V_ys = c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 177.41/177.16 & ( V_ys != c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__appendR,axiom, % 177.41/177.16 ! [V_xs,T_a,V_ys] : % 177.41/177.16 ( V_ys != c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__appendL,axiom, % 177.41/177.16 ! [V_xs,T_a,V_ys] : % 177.41/177.16 ( V_ys = c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__in__set,axiom, % 177.41/177.16 ! [T_c,V_as_2] : % 177.41/177.16 ( V_as_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(T_c),c_List_Olast(T_c,V_as_2)),hAPP(c_List_Oset(T_c),V_as_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__snoc,axiom, % 177.41/177.16 ! [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 ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__drop,axiom, % 177.41/177.16 ! [V_xs,T_a,V_n] : % 177.41/177.16 ( 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))) % 177.41/177.16 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__butlast__last__id,axiom, % 177.41/177.16 ! [T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => 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 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_snoc__eq__iff__butlast,axiom, % 177.41/177.16 ! [V_ys_2,V_x_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c))) = V_ys_2 % 177.41/177.16 <=> ( V_ys_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 & c_List_Obutlast(T_c,V_ys_2) = V_xs_2 % 177.41/177.16 & c_List_Olast(T_c,V_ys_2) = V_x_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lists_Osimps,axiom, % 177.41/177.16 ! [V_A_2,V_a_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_a_2),c_List_Olists(T_c,V_A_2))) % 177.41/177.16 <=> ( V_a_2 = c_List_Olist_ONil(T_c) % 177.41/177.16 | ? [B_a,B_l] : % 177.41/177.16 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_a),B_l) % 177.41/177.16 & hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2)) % 177.41/177.16 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_l),c_List_Olists(T_c,V_A_2))) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_select__weigth__select,axiom, % 177.41/177.16 ! [T_c,V_xs_2] : % 177.41/177.16 ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => c_Random_Oselect__weight(T_c,hAPP(hAPP(c_List_Omap(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,T_c)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_c),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_c,V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_inj__mapI,axiom, % 177.41/177.16 ! [V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.16 => c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__map,axiom, % 177.41/177.16 ! [V_f_2,T_d,T_c,V_xs_2] : % 177.41/177.16 ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => c_List_Olast(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_c,V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_e,V_a_2,V_g_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_e,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,T_c)),T_c),c_COMBB(T_d,T_c,T_e)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,V_n_2,T_c] : hAPP(c_List_Orotate(T_c,V_n_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Orotate(T_d,V_n_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__tl,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Otl(T_d),V_xs_2)) = hAPP(c_List_Otl(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__map2,axiom, % 177.41/177.16 ! [V_ys_2,V_f_2,T_e,V_xs_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,tc_prod(T_c,T_d)),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_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__zip__map2,axiom, % 177.41/177.16 ! [V_ys_2,V_g_2,T_f,V_xs_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),T_c),V_f_2),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),hAPP(hAPP(c_List_Omap(T_f,T_e),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_f),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_f,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_d,T_e)),tc_fun(T_f,T_c),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),T_c,T_f),V_f_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_f,T_e),tc_fun(T_f,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_f,T_e),tc_fun(T_f,tc_prod(T_d,T_e))),T_d),c_COMBB(T_e,tc_prod(T_d,T_e),T_f)),c_Product__Type_OPair(T_d,T_e))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_f),V_xs_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__zip__map,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_g_2,T_f,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),T_c),V_f_2),hAPP(hAPP(c_List_Ozip(T_d,T_e),hAPP(hAPP(c_List_Omap(T_f,T_d),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_f,T_e),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_e,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,T_c),T_f),hAPP(c_COMBB(tc_prod(T_d,T_e),T_c,T_e),V_f_2)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_f),c_Product__Type_OPair(T_d,T_e)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_f,T_e),V_xs_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__map1,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_f_2,T_e,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,tc_prod(T_c,T_d)),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_f_2))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__map__map,axiom, % 177.41/177.16 ! [V_ys_2,V_g_2,T_f,V_xs_2,V_f_2,T_e,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_f,T_d),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_f),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_f,T_d),tc_fun(T_f,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_f,T_d),tc_fun(T_f,tc_prod(T_c,T_d))),T_e),c_COMBB(T_d,tc_prod(T_c,T_d),T_f)),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_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_e,T_f),V_xs_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__same__conv__map,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_c,T_c)),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),c_COMBI(T_c))),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__is__Nil__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_d) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Olist_ONil(T_d)) = c_List_Olist_ONil(T_c) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Nil__is__map__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist_ONil(T_c) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_d) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__update,axiom, % 177.41/177.16 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Olist__update(T_d,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__eq__conv,axiom, % 177.41/177.16 ! [V_g_2,V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2) % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),hAPP(c_List_Oset(T_d),V_xs_2))) % 177.41/177.16 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__eq__imp__length__eq,axiom, % 177.41/177.16 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_e)),V_ys_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__addf,axiom, % 177.41/177.16 ! [V_xs_2,V_g_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Oplus__class_Oplus(T_c)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__subtractf,axiom, % 177.41/177.16 ! [V_xs_2,V_g_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Groups_Oab__group__add(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__0,axiom, % 177.41/177.16 ! [V_xs_2,T_d,T_c] : % 177.41/177.16 ( class_Groups_Omonoid__add(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Ozero__class_Ozero(T_c))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__const__mult,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,V_c_2,T_d,T_c] : % 177.41/177.16 ( class_Rings_Osemiring__0(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__mult__const,axiom, % 177.41/177.16 ! [V_xs_2,V_c_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Rings_Osemiring__0(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))),V_c_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_inj__map__eq__map,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.16 => ( hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_ys_2) % 177.41/177.16 <=> V_xs_2 = V_ys_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__injective,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2) % 177.41/177.16 => ( c_Fun_Oinj__on(T_d,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 177.41/177.16 => V_xs_2 = V_ys_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__ident,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_c),c_COMBI(T_c)),V_xs_2) = V_xs_2 ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,V_n_2,T_c] : hAPP(hAPP(c_List_Otake(T_c),V_n_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Otake(T_d),V_n_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__butlast,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Obutlast(T_d,V_xs_2)) = c_List_Obutlast(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_List_Oset(T_d),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Oappend(T_d),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__map,axiom, % 177.41/177.16 ! [V_f_2,T_d,T_c,V_xs_2] : % 177.41/177.16 ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => hAPP(c_List_Ohd(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,V_n_2,T_c] : hAPP(hAPP(c_List_Odrop(T_c),V_n_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Odrop(T_d),V_n_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_List_Omap_Ocomp,axiom, % 177.41/177.16 ! [V_g_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_e),tc_List_Olist(T_d),tc_List_Olist(T_c),hAPP(c_List_Omap(T_e,T_d),V_f_2)),hAPP(c_List_Omap(T_c,T_e),V_g_2)) = hAPP(c_List_Omap(T_c,T_d),hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),V_g_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__comp__map,axiom, % 177.41/177.16 ! [V_g_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_e),tc_List_Olist(T_d),tc_List_Olist(T_c),hAPP(c_List_Omap(T_e,T_d),V_f_2)),hAPP(c_List_Omap(T_c,T_e),V_g_2)) = hAPP(c_List_Omap(T_c,T_d),hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),V_g_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_List_Omap_Ocompositionality,axiom, % 177.41/177.16 ! [V_list_2,V_g_2,T_e,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_e,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_list_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__map,axiom, % 177.41/177.16 ! [V_xs_2,V_g_2,T_e,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_e,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_List_Omap_Oidentity,axiom, % 177.41/177.16 ! [T_c] : hAPP(c_List_Omap(T_c,T_c),c_COMBI(T_c)) = c_Fun_Oid(tc_List_Olist(T_c)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_List_Omap_Oid,axiom, % 177.41/177.16 ! [T_c] : hAPP(c_List_Omap(T_c,T_c),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_List_Olist(T_c)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__size__map,axiom, % 177.41/177.16 ! [V_xs_2,V_g_2,T_d,V_f_2,T_c] : c_List_Olist_Olist__size(T_c,V_f_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_d,hAPP(c_Fun_Ocomp(T_c,tc_Nat_Onat,T_d,V_f_2),V_g_2),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_inj__on__map__eq__map,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(T_c,T_d,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))) % 177.41/177.16 => ( hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_ys_2) % 177.41/177.16 <=> V_xs_2 = V_ys_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__inj__on,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2) % 177.41/177.16 => ( c_Fun_Oinj__on(T_d,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_List_Oset(T_d),V_xs_2)),hAPP(c_List_Oset(T_d),V_ys_2))) % 177.41/177.16 => V_xs_2 = V_ys_2 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__map,axiom, % 177.41/177.16 ! [V_f_2,T_d,V_xs_2,T_c,V_n_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => hAPP(hAPP(c_List_Onth(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_n_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__fun__upd,axiom, % 177.41/177.16 ! [V_v_2,V_f_2,T_d,V_xs_2,V_y_2,T_c] : % 177.41/177.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hAPP(hAPP(c_List_Omap(T_c,T_d),c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) % 177.41/177.16 <=> ( hBOOL(hAPP(c_List_Odistinct(T_d),V_xs_2)) % 177.41/177.16 & c_Fun_Oinj__on(T_d,T_c,V_f_2,hAPP(c_List_Oset(T_d),V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__abs,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Groups_Oordered__ab__group__add__abs(T_c) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_c,T_c),c_Groups_Oabs__class_Oabs(T_c)),V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_uminus__listsum__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Groups_Oab__group__add(T_c) % 177.41/177.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,c_Groups_Ouminus__class_Ouminus(T_c)),V_f_2)),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_inj__on__mapI,axiom, % 177.41/177.16 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),c_List_Oset(T_c)),V_A_2))) % 177.41/177.16 => c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),V_A_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_inj__mapD,axiom, % 177.41/177.16 ! [V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))) % 177.41/177.16 => c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_inj__map,axiom, % 177.41/177.16 ! [V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))) % 177.41/177.16 <=> c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 177.41/177.16 ! [V_f_2,V_xs_2,T_c,T_d] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_d) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__triv,axiom, % 177.41/177.16 ! [V_xs_2,V_r_2,T_d,T_c] : % 177.41/177.16 ( class_Rings_Osemiring__1(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_COMBK(T_c,T_d),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_xs_2))),V_r_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__map__remove1,axiom, % 177.41/177.16 ! [V_f_2,V_xs_2,V_x_2,T_c,T_d] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_d) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2)))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Nitpick_Osetsum_H__def,axiom, % 177.41/177.16 ! [V_f_2,V_A_2,T_c,T_d] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_d) % 177.41/177.16 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.16 => c_Nitpick_Osetsum_H(T_c,T_d,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_c),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_List_Oset(T_c))),V_A_2))),c_List_Odistinct(T_c))))) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.16 => c_Nitpick_Osetsum_H(T_c,T_d,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_pick__same,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_l_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => hAPP(c_Random_Opick(T_c,hAPP(hAPP(c_List_Omap(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,T_c)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_c),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_c),V_xs_2),V_l_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zero__code__numeral__def,axiom, % 177.41/177.16 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_times__code__numeral__code,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 177.41/177.16 ! [V_m_2,V_n_2] : % 177.41/177.16 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 177.41/177.16 <=> V_n_2 = V_m_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 177.41/177.16 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.16 % 177.41/177.16 fof(fact_one__code__numeral__def,axiom, % 177.41/177.16 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_less__code__numeral__code,axiom, % 177.41/177.16 ! [V_m_2,V_n_2] : % 177.41/177.16 ( 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))) % 177.41/177.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_code__numeral_Oof__nat__inject,axiom, % 177.41/177.16 ! [V_y_2,V_x_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.41/177.16 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 177.41/177.16 <=> V_x_2 = V_y_2 ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__fst__zip,axiom, % 177.41/177.16 ! [V_ys_2,T_d,V_xs_2,T_c] : % 177.41/177.16 ( 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) % 177.41/177.16 => hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_c),c_Product__Type_Ofst(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__snd__zip,axiom, % 177.41/177.16 ! [V_ys_2,T_d,V_xs_2,T_c] : % 177.41/177.16 ( 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) % 177.41/177.16 => hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_d),c_Product__Type_Osnd(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_number__of__code__numeral__def,axiom, % 177.41/177.16 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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__map__fst__snd,axiom, % 177.41/177.16 ! [V_zs_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_c),c_Product__Type_Ofst(T_c,T_d)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_d),c_Product__Type_Osnd(T_c,T_d)),V_zs_2)) = V_zs_2 ). % 177.41/177.16 % 177.41/177.16 fof(fact_plus__code__numeral__code,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_less__eq__code__numeral__code,axiom, % 177.41/177.16 ! [V_m_2,V_n_2] : % 177.41/177.16 ( 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))) % 177.41/177.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_pick__member,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_i_2] : % 177.41/177.16 ( 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_c),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Random_Opick(T_c,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),T_c),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__eq__conv,axiom, % 177.41/177.16 ! [V_zs_2,V_ys_2,T_d,V_xs_2,T_c] : % 177.41/177.16 ( 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) % 177.41/177.16 => ( hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2) = V_zs_2 % 177.41/177.16 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_c),c_Product__Type_Ofst(T_c,T_d)),V_zs_2) = V_xs_2 % 177.41/177.16 & hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_d),c_Product__Type_Osnd(T_c,T_d)),V_zs_2) = V_ys_2 ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__size__conv__listsum,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c] : c_List_Olist_Olist__size(T_c,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_c,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_code__numeral__not__eq__zero,axiom, % 177.41/177.16 ! [V_i_2] : % 177.41/177.16 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.41/177.16 <=> 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 177.41/177.16 ! [V_j_2,V_i_2,V_f_2,T_c] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.16 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),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_c),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_c),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 177.41/177.16 ! [V_l_2,V_k_2,V_f_2,T_c] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_c),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_c),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_select__weight__member,axiom, % 177.41/177.16 ! [V_s_2,V_xs_2,T_c] : % 177.41/177.16 ( 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_c),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Product__Type_Ofst(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_c,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),T_c),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_select__weight__def,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : c_Random_Oselect__weight(T_c,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_c,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_c),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_c,V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_select__def,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : c_Random_Oselect(T_c,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_c,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_c)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_c),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_subtract__code__numeral__code,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_times__code__numeral__def,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nat__of__inverse,axiom, % 177.41/177.16 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 177.41/177.16 % 177.41/177.16 fof(fact_of__nat__nat__of,axiom, % 177.41/177.16 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 177.41/177.16 % 177.41/177.16 fof(fact_nat__of__of__nat,axiom, % 177.41/177.16 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 177.41/177.16 % 177.41/177.16 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 177.41/177.16 ! [V_l_2,V_k_2] : % 177.41/177.16 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 177.41/177.16 <=> V_k_2 = V_l_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_code__numeral_Onat__of__inject,axiom, % 177.41/177.16 ! [V_y_2,V_x_2] : % 177.41/177.16 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 177.41/177.16 <=> V_x_2 = V_y_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_type__definition__code__numeral,axiom, % 177.41/177.16 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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_less__code__numeral__def,axiom, % 177.41/177.16 ! [V_m_2,V_n_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 177.41/177.16 <=> 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nat__of,axiom, % 177.41/177.16 ! [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)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nat__of__number,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_int__of__def,axiom, % 177.41/177.16 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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_less__eq__code__numeral__def,axiom, % 177.41/177.16 ! [V_m_2,V_n_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 177.41/177.16 <=> 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nat__of__code,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nat__of__aux__def,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Suc__code__numeral__def,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_minus__code__numeral__def,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_of__nat__inverse,axiom, % 177.41/177.16 ! [V_y_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.41/177.16 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_plus__code__numeral__def,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_div__code__numeral__def,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_subtract__code__numeral__def,axiom, % 177.41/177.16 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.16 % 177.41/177.16 fof(fact_minus__code__numeral__code,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_mod__code__numeral__def,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_code__numeral__decr,axiom, % 177.41/177.16 ! [V_k] : % 177.41/177.16 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__mono,axiom, % 177.41/177.16 ! [V_g_2,V_f_2,V_xs_2,T_c,T_d] : % 177.41/177.16 ( ( class_Groups_Omonoid__add(T_d) % 177.41/177.16 & class_Groups_Oordered__ab__semigroup__add(T_d) ) % 177.41/177.16 => ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_g_2),V_xs_2)))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_partition__set,axiom, % 177.41/177.16 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( c_List_Opartition(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_yes_2),V_no_2) % 177.41/177.16 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_yes_2)),hAPP(c_List_Oset(T_c),V_no_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lists__IntI,axiom, % 177.41/177.16 ! [V_B_2,V_A_2,V_l_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_l_2),c_List_Olists(T_c,V_A_2))) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_l_2),c_List_Olists(T_c,V_B_2))) % 177.41/177.16 => hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_l_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp_ONil,axiom, % 177.41/177.16 ! [V_A_2,T_c] : hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),c_List_Olist_ONil(T_c))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp_Oequations_I1_J,axiom, % 177.41/177.16 ! [V_A_2,T_c] : hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),c_List_Olist_ONil(T_c))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_in__listsp__conv__set,axiom, % 177.41/177.16 ! [V_xs_2,V_A_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_xs_2)) % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp__conj__eq,axiom, % 177.41/177.16 ! [V_x_2,V_B_2,V_A_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(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),V_A_2)),V_B_2)),V_x_2)) % 177.41/177.16 <=> ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_x_2)) % 177.41/177.16 & hBOOL(hAPP(c_List_Olistsp(T_c,V_B_2),V_x_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp__infI,axiom, % 177.41/177.16 ! [V_B_2,V_l_2,V_A_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_l_2)) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Olistsp(T_c,V_B_2),V_l_2)) % 177.41/177.16 => hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp__inf__eq,axiom, % 177.41/177.16 ! [V_B_2,V_A_2,T_c] : c_List_Olistsp(T_c,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(tc_List_Olist(T_c),tc_HOL_Obool)),c_List_Olistsp(T_c,V_A_2)),c_List_Olistsp(T_c,V_B_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp_Oequations_I2_J,axiom, % 177.41/177.16 ! [V_a2_2,V_a1_2,V_A_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a1_2),V_a2_2))) % 177.41/177.16 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 177.41/177.16 & hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_a2_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_append__in__listsp__conv,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_A_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2))) % 177.41/177.16 <=> ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_xs_2)) % 177.41/177.16 & hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_ys_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp__mono,axiom, % 177.41/177.16 ! [V_B_2,V_A_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),c_List_Olistsp(T_c,V_A_2)),c_List_Olistsp(T_c,V_B_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_partition__P,axiom, % 177.41/177.16 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( c_List_Opartition(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_yes_2),V_no_2) % 177.41/177.16 => ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_yes_2))) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.16 & ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_no_2))) % 177.41/177.16 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_partition_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_Pa_2,T_c] : c_List_Opartition(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_List_Olist_ONil(T_c)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsp__lists__eq,axiom, % 177.41/177.16 ! [V_x_2,V_A_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)),V_x_2)) % 177.41/177.16 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_x_2),c_List_Olists(T_c,V_A_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_partition_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_Pa_2,T_c] : c_List_Opartition(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_List_Olist(T_c)),c_COMBS(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_List_Olist(T_c)),hAPP(c_If(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_List_Olist(T_c)),c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(c_List_Olist_OCons(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_List_Olist(T_c)),c_COMBB(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_List_Olist(T_c))),c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(c_List_Olist_OCons(T_c),V_x_2)))),c_List_Opartition(T_c,V_Pa_2,V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_lists__Int__eq,axiom, % 177.41/177.16 ! [V_B_2,V_A_2,T_c] : c_List_Olistsp(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_c))),c_List_Olists(T_c,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_c))),c_List_Olists(T_c,V_B_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_product_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_x_2,T_d,T_c] : c_Enum_Oproduct(T_c,T_d,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Omap(T_d,tc_prod(T_c,T_d)),hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_c,T_d,V_xs_2,V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__def,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 <=> ( 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) % 177.41/177.16 & ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__map1,axiom, % 177.41/177.16 ! [V_bs_2,V_as_2,V_f_2,T_e,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Omap(T_e,T_c),V_f_2),V_as_2),V_bs_2) % 177.41/177.16 <=> c_List_Olist__all2(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__map2,axiom, % 177.41/177.16 ! [V_bs_2,V_f_2,T_e,V_as_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_bs_2)) % 177.41/177.16 <=> c_List_Olist__all2(T_c,T_e,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_HOL_Obool)),T_c),c_COMBB(T_d,tc_HOL_Obool,T_e)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__dropI,axiom, % 177.41/177.16 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_as_2,V_bs_2) % 177.41/177.16 => c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_d),V_n_2),V_bs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__appendI,axiom, % 177.41/177.16 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_a_2,V_b_2) % 177.41/177.16 => ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_c_2,V_d_2) % 177.41/177.16 => c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_d),V_b_2),V_d_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__append,axiom, % 177.41/177.16 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_d,V_xs_2,T_c] : % 177.41/177.16 ( 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) % 177.41/177.16 => ( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_d),V_ys_2),V_vs_2)) % 177.41/177.16 <=> ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 & c_List_Olist__all2(T_c,T_d,V_Pa_2,V_us_2,V_vs_2) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__Cons,axiom, % 177.41/177.16 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) % 177.41/177.16 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 177.41/177.16 & c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__takeI,axiom, % 177.41/177.16 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 => c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_d),V_n_2),V_ys_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__eq,axiom, % 177.41/177.16 ! [T_c,V_ys_2,V_xs_2] : % 177.41/177.16 ( V_xs_2 = V_ys_2 % 177.41/177.16 <=> c_List_Olist__all2(T_c,T_c,c_fequal,V_xs_2,V_ys_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__lengthD,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__Nil,axiom, % 177.41/177.16 ! [V_ys_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,c_List_Olist_ONil(T_c),V_ys_2) % 177.41/177.16 <=> V_ys_2 = c_List_Olist_ONil(T_d) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__Nil2,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_d)) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_product_Osimps_I1_J,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__conv__all__nth,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 <=> ( 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) % 177.41/177.16 & ! [B_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_d),V_ys_2),B_i))) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__nthD,axiom, % 177.41/177.16 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 => ( 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_xs_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_d),V_ys_2),V_p_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__nthD2,axiom, % 177.41/177.16 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_d),V_ys_2),V_p_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__update__cong,axiom, % 177.41/177.16 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_d,V_xs_2,T_c,V_i_2] : % 177.41/177.16 ( 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_xs_2))) % 177.41/177.16 => ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 177.41/177.16 => c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_d,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__update__cong2,axiom, % 177.41/177.16 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2))) % 177.41/177.16 => c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_d,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__product,axiom, % 177.41/177.16 ! [V_ys,T_b,V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_product__list__set,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_d,T_c] : hAPP(c_List_Oset(tc_prod(T_c,T_d)),c_Enum_Oproduct(T_c,T_d,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_List_Oset(T_d),V_ys_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublists__powset,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_Set_Oimage(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),c_List_Oset(T_c)),hAPP(c_List_Oset(tc_List_Olist(T_c)),c_Enum_Osublists(T_c,V_xs_2))) = hAPP(c_Set_OPow(T_c),hAPP(c_List_Oset(T_c),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__sublists,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublists_Osimps_I1_J,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublists_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : c_Enum_Osublists(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_Enum_Osublists(T_c,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_c)),tc_fun(tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),tc_List_Olist(tc_List_Olist(T_c))),c_List_Oappend(tc_List_Olist(T_c))),hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(c_List_Olist_OCons(T_c),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_c))))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__set__sublists,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool)),c_List_Oset(T_c)),c_Enum_Osublists(T_c,V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__n__lists,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,T_c] : hAPP(c_List_Oset(tc_List_Olist(T_c)),c_Enum_On__lists(T_c,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),hAPP(c_List_Oset(T_c),V_xs_2)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_enum__the__def,axiom, % 177.41/177.16 ! [V_Pa_2,T_c] : c_Enum_Oenum__the(T_c,V_Pa_2) = c_HOL_OThe(T_c,V_Pa_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__n__lists,axiom, % 177.41/177.16 ! [V_n,V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_n__lists__Nil,axiom, % 177.41/177.16 ! [T_a,V_n] : % 177.41/177.16 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => 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))) ) % 177.41/177.16 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_n__lists_Osimps_I1_J,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__n__lists,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__n__lists__elem,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,V_ys_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_c)),c_Enum_On__lists(T_c,V_n_2,V_xs_2)))) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) = V_n_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2I,axiom, % 177.41/177.16 ! [V_Pa_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.16 ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_a_2),V_b_2)))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2),B_x)) ) % 177.41/177.16 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_b_2) % 177.41/177.16 => c_List_Olist__all2(T_c,T_d,V_Pa_2,V_a_2,V_b_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_all__nth__imp__all__set,axiom, % 177.41/177.16 ! [V_x_2,V_Pa_2,V_xs_2,T_c] : % 177.41/177.16 ( ! [B_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i))) ) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 177.41/177.16 ! [V_xs_2,V_y_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) % 177.41/177.16 => hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_d),V_f_2),V_y_2),c_List_Oremdups(T_c,V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__removeAll__inj__on,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),hAPP(c_List_OremoveAll(T_c,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_d,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__remdups,axiom, % 177.41/177.16 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__remdups__leq,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__remdups__id,axiom, % 177.41/177.16 ! [V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__removeAll,axiom, % 177.41/177.16 ! [V_x,V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups__id__iff__distinct,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( c_List_Oremdups(T_c,V_xs_2) = V_xs_2 % 177.41/177.16 <=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__remdups,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Oremdups(T_c,V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__remdups__eq,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremdups(T_c,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) % 177.41/177.16 <=> c_List_Oremdups(T_c,V_xs_2) = V_xs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups__remdups,axiom, % 177.41/177.16 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups__eq__nil__iff,axiom, % 177.41/177.16 ! [V_x_2,T_c] : % 177.41/177.16 ( c_List_Oremdups(T_c,V_x_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> V_x_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_removeAll_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups__eq__nil__right__iff,axiom, % 177.41/177.16 ! [V_x_2,T_c] : % 177.41/177.16 ( c_List_Olist_ONil(T_c) = c_List_Oremdups(T_c,V_x_2) % 177.41/177.16 <=> V_x_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups_Osimps_I1_J,axiom, % 177.41/177.16 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.41/177.16 % 177.41/177.16 fof(fact_removeAll_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs,T_a,V_y,V_x] : % 177.41/177.16 ( ( V_x = V_y % 177.41/177.16 => 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) ) % 177.41/177.16 & ( V_x != V_y % 177.41/177.16 => 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)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_removeAll__append,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups__map__remdups,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : c_List_Oremdups(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oremdups(T_d,V_xs_2))) = c_List_Oremdups(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remove1__remdups,axiom, % 177.41/177.16 ! [V_x,V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_removeAll__id,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hAPP(c_List_OremoveAll(T_c,V_x_2),V_xs_2) = V_xs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__remove1__removeAll,axiom, % 177.41/177.16 ! [V_x,V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oremdups(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_List_Oremdups(T_c,V_xs_2) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oremdups(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Oremdups(T_c,V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__remdups__card__conv,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremdups(T_c,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__removeAll__inj,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.16 => hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),hAPP(c_List_OremoveAll(T_c,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_d,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__removeAll,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_OremoveAll(T_c,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__remdups__concat,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremdups(T_c,c_List_Oconcat(T_c,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xss_2)),c_List_Oset(T_c))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Olinorder__class_Osorted__list__of__set(T_c,hAPP(c_List_Oset(T_c),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_c,T_c,c_COMBI(T_c),c_List_Oremdups(T_c,V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sort__key__simps_I1_J,axiom, % 177.41/177.16 ! [V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__conv__concat,axiom, % 177.41/177.16 ! [V_xss_2,V_xs_2,T_c] : hAPP(c_List_Ofoldl(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Oappend(T_c),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),c_List_Oconcat(T_c,V_xss_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat__conv__foldl,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : c_List_Oconcat(T_c,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Oappend(T_c),c_List_Olist_ONil(T_c)),V_xss_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__sort,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__sort,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => hAPP(c_List_Oset(T_c),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__sort,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2))) % 177.41/177.16 <=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat_Osimps_I1_J,axiom, % 177.41/177.16 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat_Osimps_I2_J,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat__eq__Nil__conv,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : % 177.41/177.16 ( c_List_Oconcat(T_c,V_xss_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xss_2))) % 177.41/177.16 => B_x = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Nil__eq__concat__conv,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : % 177.41/177.16 ( c_List_Olist_ONil(T_c) = c_List_Oconcat(T_c,V_xss_2) % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xss_2))) % 177.41/177.16 => B_x = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__concat,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oconcat(T_d,V_xs_2)) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_d),tc_List_Olist(T_c)),hAPP(c_List_Omap(T_d,T_c),V_f_2)),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__concat,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oconcat(T_c,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__concat,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Oconcat(T_c,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2)),c_List_Oset(T_c)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sort__key__simps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat__append,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sort__foldl__insort,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Olinorder__class_Osort__key(T_c,T_c,c_COMBI(T_c),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_c),T_c,hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c))),c_List_Olist_ONil(T_c)),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat__injective,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( c_List_Oconcat(T_c,V_xs_2) = c_List_Oconcat(T_c,V_ys_2) % 177.41/177.16 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_ys_2) % 177.41/177.16 => ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),B_x)) ) % 177.41/177.16 => V_xs_2 = V_ys_2 ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat__eq__concat__iff,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),B_x)) ) % 177.41/177.16 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_ys_2) % 177.41/177.16 => ( c_List_Oconcat(T_c,V_xs_2) = c_List_Oconcat(T_c,V_ys_2) % 177.41/177.16 <=> V_xs_2 = V_ys_2 ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_concat__map__singleton,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(T_d,tc_List_Olist(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_d),c_List_Olist_OCons(T_c)),V_f_2)),c_List_Olist_ONil(T_c))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_n__lists_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,V_n_2,T_c] : c_Enum_On__lists(T_c,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),tc_List_Olist(T_c)),c_List_Omap(T_c,tc_List_Olist(T_c))),hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)))),V_xs_2)),c_Enum_On__lists(T_c,V_n_2,V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose_Osimps_I3_J,axiom, % 177.41/177.16 ! [V_xss_2,V_xs_2,V_x_2,T_c] : c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),c_COMBK(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))))),V_xss_2)))),c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_c)),T_c,c_List_Olist_ONil(tc_List_Olist(T_c)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_OCons(tc_List_Olist(T_c))),c_List_Olist_ONil(tc_List_Olist(T_c)))))),V_xss_2))))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__aux__filter__head,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),c_COMBK(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),T_c),c_List_Ohd(T_c)),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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__concat,axiom, % 177.41/177.16 ! [V_xs_2,V_p_2,T_c] : hAPP(c_List_Ofilter(T_c,V_p_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Ofilter(T_c,V_p_2)),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__sort,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,V_Pa_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__filter,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__is__subset,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_c),V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__id__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) = V_xs_2 % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sum__length__filter__compl,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__filter__le,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_partition__filter1,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Opartition(T_c,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__filter,axiom, % 177.41/177.16 ! [V_xs_2,V_Qa_2,V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(c_List_Ofilter(T_c,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,hAPP(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),V_Qa_2)),V_Pa_2)),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__remove1,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_Qa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Qa_2),c_List_Oremove1(T_c,V_x_2,V_xs_2)) = c_List_Oremove1(T_c,V_x_2,hAPP(c_List_Ofilter(T_c,V_Qa_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remove1__filter__not,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_x_2,V_Pa_2] : % 177.41/177.16 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_Oremove1(T_c,V_x_2,hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__insort__triv,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c,V_x_2,V_Pa_2,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Ofilter(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,V_Pa_2),V_f_2)),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose_Osimps_I1_J,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_x_2,V_Pa_2] : % 177.41/177.16 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__empty__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_remdups__filter,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : c_List_Oremdups(T_c,hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Oremdups(T_c,V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_removeAll__filter__not,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_x_2,V_Pa_2] : % 177.41/177.16 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => hAPP(c_List_OremoveAll(T_c,V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_removeAll__filter__not__eq,axiom, % 177.41/177.16 ! [V_x_2,T_c] : c_List_OremoveAll(T_c,V_x_2) = c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(c_fequal,V_x_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_partition__filter2,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Opartition(T_c,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_c,c_fNot),V_Pa_2)),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose_Osimps_I2_J,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__transpose,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_i_2] : % 177.41/177.16 ( 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_c))),c_List_Otranspose(T_c,V_xs_2)))) % 177.41/177.16 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),c_List_Otranspose(T_c,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,T_c),c_List_Onth(T_c)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__map__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : c_List_Otranspose(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_d),tc_List_Olist(T_c)),hAPP(c_List_Omap(T_d,T_c),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_d),tc_List_Olist(T_c)),hAPP(c_List_Omap(T_d,T_c),V_f_2)),c_List_Otranspose(T_d,V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__filter,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_c),hAPP(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)),hAPP(c_List_Oset(T_c),V_xs_2)))),V_Pa_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__filter__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),hAPP(c_List_Ofilter(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,V_Pa_2),V_f_2)),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__filter__less,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_partition__filter__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_c] : c_List_Opartition(T_c,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_c,c_fNot),V_f_2)),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__minus__filter__out,axiom, % 177.41/177.16 ! [V_y_2,V_xs_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_c),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__in__sublist,axiom, % 177.41/177.16 ! [V_s_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_c,V_xs_2,V_s_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__empty,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( c_List_Otranspose(T_c,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_c)) % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => B_x = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__filter__conv__card,axiom, % 177.41/177.16 ! [V_xs_2,V_p_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,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_c)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_c),V_xs_2))))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__aux__filter__tail,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_c)),T_c,c_List_Olist_ONil(tc_List_Olist(T_c)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_OCons(tc_List_Olist(T_c))),c_List_Olist_ONil(tc_List_Olist(T_c)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Otl(T_c)),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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose_Opsimps_I3_J,axiom, % 177.41/177.16 ! [V_xss_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_c)),c_List_Otranspose__rel(T_c)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_xss_2))) % 177.41/177.16 => c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),c_COMBK(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))))),V_xss_2)))),c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_c)),T_c,c_List_Olist_ONil(tc_List_Olist(T_c)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_OCons(tc_List_Olist(T_c))),c_List_Olist_ONil(tc_List_Olist(T_c)))))),V_xss_2))))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose_Opsimps_I2_J,axiom, % 177.41/177.16 ! [V_xss_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_c)),c_List_Otranspose__rel(T_c)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xss_2))) % 177.41/177.16 => c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xss_2)) = c_List_Otranspose(T_c,V_xss_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublist__shift__lemma__Suc,axiom, % 177.41/177.16 ! [V_is_2,V_xs_2,V_Pa_2,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_c,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_c,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_c,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_c,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_c,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_c,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_select__weigth__drop__zero,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : c_Random_Oselect__weight(T_c,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_c)),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_c,V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_pick__drop__zero,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : c_Random_Opick(T_c,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_c)),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_c,V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose_Opsimps_I1_J,axiom, % 177.41/177.16 ! [T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_c)),c_List_Otranspose__rel(T_c)),c_List_Olist_ONil(tc_List_Olist(T_c)))) % 177.41/177.16 => c_List_Otranspose(T_c,c_List_Olist_ONil(tc_List_Olist(T_c))) = c_List_Olist_ONil(tc_List_Olist(T_c)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__max__length,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : 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))),c_List_Otranspose(T_c,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),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_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__aux__max,axiom, % 177.41/177.16 ! [V_xss_2,T_d,V_xs_2,T_c] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_d),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_d)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_d))),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_c)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_d),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_d)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_d),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_d)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_d)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_d),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_d)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_d),tc_List_Olist(T_d),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_d)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldr_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_a_2,V_f_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,c_List_Olist_ONil(T_d),V_a_2) = V_a_2 ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldr_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_d,T_c,V_f_2,V_xs_2,V_a_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldr__append,axiom, % 177.41/177.16 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,hAPP(hAPP(c_List_Oappend(T_d),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_d,T_c,V_f_2,V_xs_2,c_List_Ofoldr(T_d,T_c,V_f_2,V_ys_2,V_a_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldr__conv__foldl,axiom, % 177.41/177.16 ! [V_a_2,V_xs_2,T_c] : % 177.41/177.16 ( class_Groups_Oab__semigroup__add(T_c) % 177.41/177.16 => c_List_Ofoldr(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldr__map,axiom, % 177.41/177.16 ! [V_a_2,V_xs_2,V_f_2,T_e,V_g_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_g_2,hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_e,T_c,hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_c),T_e,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__foldr1,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Groups_Omonoid__add(T_c) % 177.41/177.16 => hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_xs_2) = c_List_Ofoldr(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_xs_2,c_Groups_Ozero__class_Ozero(T_c)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__foldr1__lemma,axiom, % 177.41/177.16 ! [V_xs_2,V_a_2,T_c] : % 177.41/177.16 ( class_Groups_Omonoid__add(T_c) % 177.41/177.16 => hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),c_List_Ofoldr(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_xs_2,c_Groups_Ozero__class_Ozero(T_c))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__transpose,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),c_List_Otranspose(T_c,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_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublist__def,axiom, % 177.41/177.16 ! [V_A_2,V_xs_2,T_c] : c_List_Osublist(T_c,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_c,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_c)),V_xs_2))))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sublist__shift__lemma,axiom, % 177.41/177.16 ! [V_i_2,V_xs_2,V_A_2,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_c,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_c)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_c,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_c)),V_xs_2))))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__upt,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_atLeastLessThan__upt,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__Suc__append,axiom, % 177.41/177.16 ! [V_j,V_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__Suc,axiom, % 177.41/177.16 ! [V_j,V_i] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => 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))) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__add__eq__append,axiom, % 177.41/177.16 ! [V_k,V_j,V_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__rec,axiom, % 177.41/177.16 ! [V_j,V_i] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => 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)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__conv__Cons,axiom, % 177.41/177.16 ! [V_j,V_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__eq__Nil__conv,axiom, % 177.41/177.16 ! [V_j_2,V_i_2] : % 177.41/177.16 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 177.41/177.16 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__conv__Nil,axiom, % 177.41/177.16 ! [V_i,V_j] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 177.41/177.16 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__0,axiom, % 177.41/177.16 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 177.41/177.16 % 177.41/177.16 fof(fact_take__upt,axiom, % 177.41/177.16 ! [V_n,V_m,V_i] : % 177.41/177.16 ( 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)) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__list__of__set__range,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__upt,axiom, % 177.41/177.16 ! [V_j,V_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_drop__upt,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__upt,axiom, % 177.41/177.16 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__upt,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__rec__number__of,axiom, % 177.41/177.16 ! [V_n,V_m] : % 177.41/177.16 ( ( 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))) % 177.41/177.16 => 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))) ) % 177.41/177.16 & ( ~ 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))) % 177.41/177.16 => 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) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_upt__eq__Cons__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 177.41/177.16 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 177.41/177.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 177.41/177.16 & V_i_2 = V_x_2 % 177.41/177.16 & 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 ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__upt,axiom, % 177.41/177.16 ! [V_j,V_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__Suc__upt,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_atLeastAtMost__upt,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_atLeast__upt,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__upt,axiom, % 177.41/177.16 ! [V_j,V_k,V_i] : % 177.41/177.16 ( 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)) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_greaterThanAtMost__upt,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_greaterThanLessThan__upt,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_atMost__upto,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__nth,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),hAPP(c_List_Onth(T_c),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) = V_xs_2 ). % 177.41/177.16 % 177.41/177.16 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 177.41/177.16 ! [V_n_2,V_m_2,V_f_2,T_c] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.16 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 177.41/177.16 ! [V_n_2,V_m_2,V_f_2,T_c] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_c) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),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_c),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__map__upt,axiom, % 177.41/177.16 ! [V_f_2,T_c,V_m_2,V_n_2,V_i_2] : % 177.41/177.16 ( 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))) % 177.41/177.16 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__rectangle,axiom, % 177.41/177.16 ! [V_n_2,T_c,V_xs_2] : % 177.41/177.16 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_c)) % 177.41/177.16 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.41/177.16 => ( ! [B_i] : % 177.41/177.16 ( 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_c))),V_xs_2))) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),B_i)) = V_n_2 ) % 177.41/177.16 => c_List_Otranspose(T_c,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_c)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_c)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_c)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_Nat_Onat,T_c),tc_Nat_Onat),c_List_Onth(T_c)),hAPP(c_List_Onth(tc_List_Olist(T_c)),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_c))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__key__remove1,axiom, % 177.41/177.16 ! [V_f_2,V_xs_2,V_a_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) % 177.41/177.16 => ( hAPP(c_List_Ohd(T_c),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_d,tc_HOL_Obool,T_c),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_a_2),c_List_Oremove1(T_c,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted_ONil,axiom, % 177.41/177.16 ! [T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__single,axiom, % 177.41/177.16 ! [V_x,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__upt,axiom, % 177.41/177.16 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__sort,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,c_List_Olinorder__class_Osort__key(T_c,T_c,c_COMBI(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__insort__insert,axiom, % 177.41/177.16 ! [V_x_2,V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),V_x_2,V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__drop,axiom, % 177.41/177.16 ! [V_n,V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__upto,axiom, % 177.41/177.16 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__take,axiom, % 177.41/177.16 ! [V_n,V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__remove1,axiom, % 177.41/177.16 ! [V_a,V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__tl,axiom, % 177.41/177.16 ! [V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__insort,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2)) % 177.41/177.16 <=> c_List_Olinorder__class_Osorted(T_c,V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__butlast,axiom, % 177.41/177.16 ! [V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted_Oequations_I1_J,axiom, % 177.41/177.16 ! [T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__many,axiom, % 177.41/177.16 ! [V_zs,V_y,V_x,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 177.41/177.16 => 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))) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__many__eq,axiom, % 177.41/177.16 ! [V_zs_2,V_y_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_zs_2))) % 177.41/177.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) % 177.41/177.16 & c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_zs_2)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__remdups,axiom, % 177.41/177.16 ! [V_l,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__distinct__set__unique,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_ys_2) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_ys_2)) % 177.41/177.16 => ( hAPP(c_List_Oset(T_c),V_xs_2) = hAPP(c_List_Oset(T_c),V_ys_2) % 177.41/177.16 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__sort__key,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Olinorder__class_Osort__key(T_d,T_c,V_f_2,V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__insort__insert__key,axiom, % 177.41/177.16 ! [V_x_2,V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_d,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__map__remove1,axiom, % 177.41/177.16 ! [V_x_2,V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oremove1(T_d,V_x_2,V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__insort__key,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2))) % 177.41/177.16 <=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__filter,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Ofilter(T_d,V_Pa_2),V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__map__same,axiom, % 177.41/177.16 ! [V_xs_2,V_g_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Ofilter(T_d,hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_d),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__same,axiom, % 177.41/177.16 ! [V_xs_2,V_g_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__Cons,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) % 177.41/177.16 <=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 & ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_x)) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__append,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) % 177.41/177.16 <=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 & c_List_Olinorder__class_Osorted(T_c,V_ys_2) % 177.41/177.16 & ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ! [B_xa] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),hAPP(c_List_Oset(T_c),V_ys_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),B_xa)) ) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__insort,axiom, % 177.41/177.16 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) % 177.41/177.16 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => hAPP(c_List_Ofilter(T_d,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_d,V_Pa_2),V_xs_2)) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted_Oequations_I2_J,axiom, % 177.41/177.16 ! [V_a1_2,V_a2_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_a2_2),V_a1_2)) % 177.41/177.16 <=> ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_a1_2))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a2_2),B_x)) ) % 177.41/177.16 & c_List_Olinorder__class_Osorted(T_c,V_a1_2) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__list__of__set,axiom, % 177.41/177.16 ! [V_A_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.16 => ( hAPP(c_List_Oset(T_c),c_List_Olinorder__class_Osorted__list__of__set(T_c,V_A_2)) = V_A_2 % 177.41/177.16 & c_List_Olinorder__class_Osorted(T_c,c_List_Olinorder__class_Osorted__list__of__set(T_c,V_A_2)) % 177.41/177.16 & hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Olinorder__class_Osorted__list__of__set(T_c,V_A_2))) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insort__remove1,axiom, % 177.41/177.16 ! [V_xs_2,V_a_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_a_2),c_List_Oremove1(T_c,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__equals__nth__mono,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 <=> ! [B_j] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => ! [B_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_j))) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__nth__mono,axiom, % 177.41/177.16 ! [V_j,V_i,V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => ( 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))) % 177.41/177.16 => 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))) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_map__sorted__distinct__set__unique,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_d] : % 177.41/177.16 ( class_Orderings_Olinorder(T_d) % 177.41/177.16 => ( c_Fun_Oinj__on(T_c,T_d,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))) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2))) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_ys_2)) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_ys_2))) % 177.41/177.16 => ( hAPP(c_List_Oset(T_c),V_xs_2) = hAPP(c_List_Oset(T_c),V_ys_2) % 177.41/177.16 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__column,axiom, % 177.41/177.16 ! [V_i_2,V_xs_2,T_c] : % 177.41/177.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xs_2))) % 177.41/177.16 => ( 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_c))),V_xs_2))) % 177.41/177.16 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,T_c),c_List_Onth(T_c)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),c_List_Otranspose(T_c,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),V_i_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__nth__transpose__sorted,axiom, % 177.41/177.16 ! [V_j_2,V_i_2,V_xs_2,T_c] : % 177.41/177.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xs_2))) % 177.41/177.16 => ( 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_c))),c_List_Otranspose(T_c,V_xs_2)))) % 177.41/177.16 => ( 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_c))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_xs_2)))) % 177.41/177.16 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),c_List_Otranspose(T_c,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_inj__on__rev,axiom, % 177.41/177.16 ! [V_A_2,T_c] : c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Orev(T_c),V_A_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__rev,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Orev(T_c),V_xs_2))) % 177.41/177.16 <=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__is__Nil__conv,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Orev(T_c),V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_Nil__is__rev__conv,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( c_List_Olist_ONil(T_c) = hAPP(c_List_Orev(T_c),V_xs_2) % 177.41/177.16 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev_Osimps_I1_J,axiom, % 177.41/177.16 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 177.41/177.16 % 177.41/177.16 fof(fact_singleton__rev__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) = hAPP(c_List_Orev(T_c),V_xs_2) % 177.41/177.16 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__singleton__conv,axiom, % 177.41/177.16 ! [V_x_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) % 177.41/177.16 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__append,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__concat,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_List_Orev(T_c),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Orev(T_c)),hAPP(c_List_Orev(tc_List_Olist(T_c)),V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,T_c] : hAPP(c_List_Orev(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Orev(T_d),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__filter,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hAPP(c_List_Orev(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(c_List_Orev(T_c),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__rev,axiom, % 177.41/177.16 ! [V_ys,T_b,V_xs,T_a] : % 177.41/177.16 ( 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) % 177.41/177.16 => 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)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__rev,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Orev(T_c),V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__rev,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2),hAPP(c_List_Orev(T_d),V_ys_2)) % 177.41/177.16 <=> c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_list__all2__rev1,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : % 177.41/177.16 ( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2),V_ys_2) % 177.41/177.16 <=> c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_d),V_ys_2)) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__rev__ident,axiom, % 177.41/177.16 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__swap,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Orev(T_c),V_xs_2) = V_ys_2 % 177.41/177.16 <=> V_xs_2 = hAPP(c_List_Orev(T_c),V_ys_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__is__rev__conv,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(c_List_Orev(T_c),V_ys_2) % 177.41/177.16 <=> V_xs_2 = V_ys_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__rev,axiom, % 177.41/177.16 ! [V_xs,T_a] : % 177.41/177.16 ( class_Groups_Ocomm__monoid__add(T_a) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__rev,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldr__foldl,axiom, % 177.41/177.16 ! [V_a_2,V_xs_2,V_f_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_c,T_d,hAPP(c_COMBC(T_d,T_c,T_c),V_f_2),V_a_2),hAPP(c_List_Orev(T_d),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldl__foldr,axiom, % 177.41/177.16 ! [V_xs_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_c),V_f_2),hAPP(c_List_Orev(T_d),V_xs_2),V_a_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__eq__Cons__iff,axiom, % 177.41/177.16 ! [V_ys_2,V_y_2,V_xs_2,T_c] : % 177.41/177.16 ( hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2) % 177.41/177.16 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),hAPP(c_List_Orev(T_c),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),c_List_Olist_ONil(T_c))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev_Osimps_I2_J,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__rev,axiom, % 177.41/177.16 ! [T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_last__rev,axiom, % 177.41/177.16 ! [T_a,V_xs] : % 177.41/177.16 ( V_xs != c_List_Olist_ONil(T_a) % 177.41/177.16 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__transpose,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),c_List_Otranspose(T_c,V_xs_2)))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__foldl__cons,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_c),T_c,hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c)),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__drop,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__take,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rotate__rev,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__nth,axiom, % 177.41/177.16 ! [V_xs,T_a,V_n] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_rev__update,axiom, % 177.41/177.16 ! [V_y,V_xs,T_a,V_k] : % 177.41/177.16 ( 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))) % 177.41/177.16 => 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) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__rev__nth__mono,axiom, % 177.41/177.16 ! [V_j,V_i,V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 177.41/177.16 => ( 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))) % 177.41/177.16 => 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))) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_foldr__max__sorted,axiom, % 177.41/177.16 ! [V_y_2,V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(c_List_Orev(T_c),V_xs_2)) % 177.41/177.16 => ( ( V_xs_2 = c_List_Olist_ONil(T_c) % 177.41/177.16 => c_List_Ofoldr(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),V_xs_2,V_y_2) = V_y_2 ) % 177.41/177.16 & ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => c_List_Ofoldr(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__transpose__sorted,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xs_2))) % 177.41/177.16 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_c)) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),c_List_Otranspose(T_c,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 177.41/177.16 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_c)) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),c_List_Otranspose(T_c,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__column__length,axiom, % 177.41/177.16 ! [V_i_2,V_xs_2,T_c] : % 177.41/177.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xs_2))) % 177.41/177.16 => ( 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_c))),V_xs_2))) % 177.41/177.16 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),c_List_Otranspose(T_c,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),V_i_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transpose__transpose,axiom, % 177.41/177.16 ! [V_xs_2,T_c] : % 177.41/177.16 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xs_2))) % 177.41/177.16 => c_List_Otranspose(T_c,c_List_Otranspose(T_c,V_xs_2)) = c_List_OtakeWhile(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_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 177.41/177.16 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__takeWhile,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__takeWhile__le,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_set__takeWhileD,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)))) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__eq__all__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = V_xs_2 % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__takeWhile__snd,axiom, % 177.41/177.16 ! [V_ys_2,V_Pa_2,V_xs_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),c_List_OtakeWhile(T_d,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_c,T_d),hAPP(c_Fun_Ocomp(T_d,tc_HOL_Obool,tc_prod(T_c,T_d),V_Pa_2),c_Product__Type_Osnd(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_zip__takeWhile__fst,axiom, % 177.41/177.16 ! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_c,T_d),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_c,T_d),V_Pa_2),c_Product__Type_Ofst(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_OtakeWhile(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,V_Pa_2),V_f_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__tail,axiom, % 177.41/177.16 ! [V_l_2,V_xs_2,T_c,V_x_2,V_Pa_2] : % 177.41/177.16 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_l_2))) = c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_x_2,V_Pa_2] : % 177.41/177.16 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_Pa_2,T_c] : c_List_OtakeWhile(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__eq__take,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__takeWhile,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_return__list__def,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__append1,axiom, % 177.41/177.16 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__nth,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c,V_j_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)))) % 177.41/177.16 => hAPP(hAPP(c_List_Onth(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_j_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_nth__length__takeWhile,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__not__last,axiom, % 177.41/177.16 ! [T_c,V_xs_2] : % 177.41/177.16 ( V_xs_2 != c_List_Olist_ONil(T_c) % 177.41/177.16 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),c_List_Olast(T_c,V_xs_2))),V_xs_2) = c_List_Obutlast(T_c,V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 177.41/177.16 ! [V_t_2,V_xs_2,V_f_2,T_d,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(c_List_Orev(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) % 177.41/177.16 => hAPP(c_List_Ofilter(T_d,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_d),hAPP(c_Orderings_Oord__class_Oless(T_c),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_d,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_d),hAPP(c_Orderings_Oord__class_Oless(T_c),V_t_2)),V_f_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transfer__nat__int__list__return__embed,axiom, % 177.41/177.16 ! [V_l] : % 177.41/177.16 ( c_List_Onat__list(V_l) % 177.41/177.16 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 177.41/177.16 ! [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))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_embed__list__def,axiom, % 177.41/177.16 ! [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) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__neq__rev,axiom, % 177.41/177.16 ! [V_x_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_c),V_xs_2)) = hAPP(c_List_Orev(T_c),hAPP(c_List_Otl(T_c),c_List_OdropWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile__neq__rev,axiom, % 177.41/177.16 ! [V_x_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_OdropWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_c),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(c_List_Orev(T_c),c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__dropWhile__id,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hAPP(hAPP(c_List_Oappend(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)) = V_xs_2 ). % 177.41/177.16 % 177.41/177.16 fof(fact_hd__dropWhile,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_c) % 177.41/177.16 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__dropWhile,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_c,c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__dropWhile__le,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile__eq__Nil__conv,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_c) % 177.41/177.16 <=> ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile_Osimps_I2_J,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_x_2,V_Pa_2] : % 177.41/177.16 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) ) % 177.41/177.16 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile_Osimps_I1_J,axiom, % 177.41/177.16 ! [V_Pa_2,T_c] : c_List_OdropWhile(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__dropWhile,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile__map,axiom, % 177.41/177.16 ! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_OdropWhile(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,V_Pa_2),V_f_2),V_xs_2)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile__append1,axiom, % 177.41/177.16 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.16 => c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)),V_ys_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile__eq__Cons__conv,axiom, % 177.41/177.16 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2) % 177.41/177.16 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) % 177.41/177.16 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile__eq__drop,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))),V_xs_2) ). % 177.41/177.16 % 177.41/177.16 fof(fact_dropWhile__nth,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c,V_j_2] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)))) % 177.41/177.16 => hAPP(hAPP(c_List_Onth(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_c),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_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_listsum__map__filter,axiom, % 177.41/177.16 ! [V_f_2,V_Pa_2,V_xs_2,T_c,T_d] : % 177.41/177.16 ( class_Groups_Omonoid__add(T_d) % 177.41/177.16 => ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => ( ~ hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.16 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) ) % 177.41/177.16 => hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted__nth__monoI,axiom, % 177.41/177.16 ! [V_xs,T_a] : % 177.41/177.16 ( class_Orderings_Olinorder(T_a) % 177.41/177.16 => ( ! [B_i,B_j] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 177.41/177.16 => ( 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))) % 177.41/177.16 => 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))) ) ) % 177.41/177.16 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__eq__filter,axiom, % 177.41/177.16 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.16 ( ! [B_x] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)))) % 177.41/177.16 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.16 => c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_takeWhile__eq__take__P__nth,axiom, % 177.41/177.16 ! [V_Pa_2,V_xs_2,T_c,V_n_2] : % 177.41/177.16 ( ! [B_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 177.41/177.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i))) ) ) % 177.41/177.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.16 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_n_2))) ) % 177.41/177.16 => c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_length__takeWhile__less__P__nth,axiom, % 177.41/177.16 ! [V_xs_2,T_c,V_Pa_2,V_j_2] : % 177.41/177.16 ( ! [B_i] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 177.41/177.16 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i))) ) % 177.41/177.16 => ( 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_c)),V_xs_2))) % 177.41/177.16 => 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_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)))) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_sorted_Osimps,axiom, % 177.41/177.16 ! [V_a_2,T_c] : % 177.41/177.16 ( class_Orderings_Olinorder(T_c) % 177.41/177.16 => ( c_List_Olinorder__class_Osorted(T_c,V_a_2) % 177.41/177.16 <=> ( V_a_2 = c_List_Olist_ONil(T_c) % 177.41/177.16 | ? [B_xs,B_x] : % 177.41/177.16 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_x),B_xs) % 177.41/177.16 & ! [B_xa] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),hAPP(c_List_Oset(T_c),B_xs))) % 177.41/177.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),B_xa)) ) % 177.41/177.16 & c_List_Olinorder__class_Osorted(T_c,B_xs) ) ) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_List_Oinsert__def,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oinsert(T_c,V_x_2,V_xs_2) = V_xs_2 ) % 177.41/177.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oinsert(T_c,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) ) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_not__in__set__insert,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oinsert(T_c,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_insert__remdups,axiom, % 177.41/177.16 ! [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)) ). % 177.41/177.16 % 177.41/177.16 fof(fact_distinct__insert,axiom, % 177.41/177.16 ! [V_x,V_xs,T_a] : % 177.41/177.16 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 177.41/177.16 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_in__set__insert,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.16 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.16 => c_List_Oinsert(T_c,V_x_2,V_xs_2) = V_xs_2 ) ). % 177.41/177.16 % 177.41/177.16 fof(fact_List_Oset__insert,axiom, % 177.41/177.16 ! [V_xs_2,V_x_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Oinsert(T_c,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_insert__Nil,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_maps__def,axiom, % 177.41/177.17 ! [V_xs_2,V_f_2,T_c,T_d] : c_List_Omaps(T_d,T_c,V_f_2,V_xs_2) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(T_d,tc_List_Olist(T_c)),V_f_2),V_xs_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_concat__map__maps,axiom, % 177.41/177.17 ! [V_xs_2,V_f_2,T_d,T_c] : c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(T_d,tc_List_Olist(T_c)),V_f_2),V_xs_2)) = c_List_Omaps(T_d,T_c,V_f_2,V_xs_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_maps__simps_I2_J,axiom, % 177.41/177.17 ! [V_f_2,T_c,T_d] : c_List_Omaps(T_d,T_c,V_f_2,c_List_Olist_ONil(T_d)) = c_List_Olist_ONil(T_c) ). % 177.41/177.17 % 177.41/177.17 fof(fact_maps__simps_I1_J,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,V_f_2,T_c,T_d] : c_List_Omaps(T_d,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_d,T_c,V_f_2,V_xs_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_distinct__concat,axiom, % 177.41/177.17 ! [V_xs_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_c)),V_xs_2)) % 177.41/177.17 => ( ! [B_ys] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(c_List_Odistinct(T_c),B_ys)) ) % 177.41/177.17 => ( ! [B_ys] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.17 => ! [B_zs] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.17 => ( B_ys != B_zs % 177.41/177.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),B_ys)),hAPP(c_List_Oset(T_c),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) % 177.41/177.17 => hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Oconcat(T_c,V_xs_2))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_measures__lesseq,axiom, % 177.41/177.17 ! [V_fs_2,T_c,V_y_2,V_x_2,V_f_2] : % 177.41/177.17 ( 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))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,V_fs_2))) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_wf__measures,axiom, % 177.41/177.17 ! [V_fs_2,T_c] : c_Wellfounded_Owf(T_c,c_List_Omeasures(T_c,V_fs_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__measures_I1_J,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,c_List_Olist_ONil(tc_fun(T_c,tc_Nat_Onat))))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_measures__def,axiom, % 177.41/177.17 ! [V_fs_2,T_c] : c_List_Omeasures(T_c,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_c),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(tc_fun(T_c,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_c,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_c),c_List_Omap(tc_fun(T_c,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_c,tc_Nat_Onat),T_c,tc_Nat_Onat),c_COMBI(tc_fun(T_c,tc_Nat_Onat))))),V_fs_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__measures_I2_J,axiom, % 177.41/177.17 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 177.41/177.17 <=> ( 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))) % 177.41/177.17 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 177.41/177.17 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,V_fs_2))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_measures__less,axiom, % 177.41/177.17 ! [V_fs_2,T_c,V_y_2,V_x_2,V_f_2] : % 177.41/177.17 ( 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))) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_foldl__apply,axiom, % 177.41/177.17 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_d,T_e,V_xs_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hAPP(c_Fun_Ocomp(T_e,T_e,T_d,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_d,T_e,T_d,V_h_2),hAPP(V_g_2,B_x)) ) % 177.41/177.17 => hAPP(c_List_Ofoldl(T_e,T_c,hAPP(c_COMBC(T_c,T_e,T_e),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_d),V_g_2),V_s_2),V_xs_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_order__fun_I2_J,axiom, % 177.41/177.17 ! [V_g_2,V_f_2,T_c,T_d] : % 177.41/177.17 ( ( class_Orderings_Oorder(T_d) % 177.41/177.17 & class_Enum_Oenum(T_c) ) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.41/177.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.41/177.17 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBS(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_g_2)))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_enum__ex__prod__def,axiom, % 177.41/177.17 ! [V_Pa_2,T_c,T_d] : % 177.41/177.17 ( ( class_Enum_Oenum(T_d) % 177.41/177.17 & class_Enum_Oenum(T_c) ) % 177.41/177.17 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_c,T_d)),V_Pa_2)) % 177.41/177.17 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_Enum_Oenum__class_Oenum__ex(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d))))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_enum__ex,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : % 177.41/177.17 ( class_Enum_Oenum(T_c) % 177.41/177.17 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),V_Pa_2)) % 177.41/177.17 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_exists__code,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : % 177.41/177.17 ( class_Enum_Oenum(T_c) % 177.41/177.17 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.41/177.17 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),V_Pa_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_zip__obtain__same__length,axiom, % 177.41/177.17 ! [V_Pa_2,V_ys_2,T_d,V_xs_2,T_c] : % 177.41/177.17 ( ( 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_c)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),hAPP(hAPP(c_List_Otake(T_d),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_c,T_d),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_c)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_d),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)))) ) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pos__not__random__dseq__def,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dropWhile__append2,axiom, % 177.41/177.17 ! [V_ys_2,V_Pa_2,V_xs_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 => c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_c,V_Pa_2,V_ys_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all2__all__nthI,axiom, % 177.41/177.17 ! [V_Pa_2,V_b_2,T_d,V_a_2,T_c] : % 177.41/177.17 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_b_2) % 177.41/177.17 => ( ! [B_n] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_a_2))) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_d),V_b_2),B_n))) ) % 177.41/177.17 => c_List_Olist__all2(T_c,T_d,V_Pa_2,V_a_2,V_b_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_finite__sorted__distinct__unique,axiom, % 177.41/177.17 ! [V_A_2,T_c] : % 177.41/177.17 ( class_Orderings_Olinorder(T_c) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.17 => ? [B_x] : % 177.41/177.17 ( hAPP(c_List_Oset(T_c),B_x) = V_A_2 % 177.41/177.17 & c_List_Olinorder__class_Osorted(T_c,B_x) % 177.41/177.17 & hBOOL(hAPP(c_List_Odistinct(T_c),B_x)) % 177.41/177.17 & ! [B_y] : % 177.41/177.17 ( ( hAPP(c_List_Oset(T_c),B_y) = V_A_2 % 177.41/177.17 & c_List_Olinorder__class_Osorted(T_c,B_y) % 177.41/177.17 & hBOOL(hAPP(c_List_Odistinct(T_c),B_y)) ) % 177.41/177.17 => B_y = B_x ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_takeWhile__append2,axiom, % 177.41/177.17 ! [V_ys_2,V_Pa_2,V_xs_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 => c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_insort__is__Cons,axiom, % 177.41/177.17 ! [V_a_2,V_f_2,V_xs_2,T_c,T_d] : % 177.41/177.17 ( class_Orderings_Olinorder(T_d) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 177.41/177.17 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_xs_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Cons__eq__filter__iff,axiom, % 177.41/177.17 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_c] : % 177.41/177.17 ( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_ys_2) % 177.41/177.17 <=> ? [B_us,B_vs] : % 177.41/177.17 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_vs)) % 177.41/177.17 & ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),B_us))) % 177.41/177.17 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 & V_xs_2 = hAPP(c_List_Ofilter(T_c,V_Pa_2),B_vs) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_filter__eq__Cons__iff,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_c] : % 177.41/177.17 ( hAPP(c_List_Ofilter(T_c,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) % 177.41/177.17 <=> ? [B_us,B_vs] : % 177.41/177.17 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_vs)) % 177.41/177.17 & ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),B_us))) % 177.41/177.17 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 & V_xs_2 = hAPP(c_List_Ofilter(T_c,V_Pa_2),B_vs) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_order__fun_I1_J,axiom, % 177.41/177.17 ! [V_g_2,V_f_2,T_c,T_d] : % 177.41/177.17 ( ( class_Orderings_Oorder(T_d) % 177.41/177.17 & class_Enum_Oenum(T_c) ) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) % 177.41/177.17 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),hAPP(hAPP(c_COMBS(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_Orderings_Oord__class_Oless__eq(T_d)),V_f_2)),V_g_2))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_all__code,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : % 177.41/177.17 ( class_Enum_Oenum(T_c) % 177.41/177.17 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 177.41/177.17 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),V_Pa_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_enum__all,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : % 177.41/177.17 ( class_Enum_Oenum(T_c) % 177.41/177.17 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),V_Pa_2)) % 177.41/177.17 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_enum__all__prod__def,axiom, % 177.41/177.17 ! [V_Pa_2,T_c,T_d] : % 177.41/177.17 ( ( class_Enum_Oenum(T_d) % 177.41/177.17 & class_Enum_Oenum(T_c) ) % 177.41/177.17 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_c,T_d)),V_Pa_2)) % 177.41/177.17 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_Enum_Oenum__class_Oenum__all(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d))))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ball__nth,axiom, % 177.41/177.17 ! [V_Pa_2,V_xs_2,T_c,V_n_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_n_2))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sorted_OCons,axiom, % 177.41/177.17 ! [V_x_2,V_xs_2,T_c] : % 177.41/177.17 ( class_Orderings_Olinorder(T_c) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_x)) ) % 177.41/177.17 => ( c_List_Olinorder__class_Osorted(T_c,V_xs_2) % 177.41/177.17 => c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__length,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ? [B_n] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_n))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__set__conv__decomp,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_zs)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__simps_I2_J,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : ~ c_List_Olist__ex(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__append,axiom, % 177.41/177.17 ! [V_ys_2,V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) % 177.41/177.17 <=> ( c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 | c_List_Olist__ex(T_c,V_Pa_2,V_ys_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__iff,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__rev,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex(T_c,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2)) % 177.41/177.17 <=> c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__simps_I1_J,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) % 177.41/177.17 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 | c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__set__conv__decomp__first,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 <=> ? [B_ys] : % 177.41/177.17 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_zs)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),B_ys))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__set__conv__decomp__last,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 <=> ? [B_ys,B_zs] : % 177.41/177.17 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_zs)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),B_zs))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__length,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__all(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ! [B_n] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_n))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_measure__function__int,axiom, % 177.41/177.17 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))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__simps_I2_J,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : c_List_Olist__all(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__append,axiom, % 177.41/177.17 ! [V_ys_2,V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__all(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) % 177.41/177.17 <=> ( c_List_Olist__all(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 & c_List_Olist__all(T_c,V_Pa_2,V_ys_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_measure__size,axiom, % 177.41/177.17 ! [T_c] : % 177.41/177.17 ( class_Nat_Osize(T_c) % 177.41/177.17 => c_FunDef_Ois__measure(T_c,c_Nat_Osize__class_Osize(T_c)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_is__measure_Osimps,axiom, % 177.41/177.17 ! [V_a_2,T_c] : c_FunDef_Ois__measure(T_c,V_a_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_is__measure_Oequations,axiom, % 177.41/177.17 ! [V_a_2,T_c] : c_FunDef_Ois__measure(T_c,V_a_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_is__measure_Ointros,axiom, % 177.41/177.17 ! [V_f_2,T_c] : c_FunDef_Ois__measure(T_c,V_f_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__iff,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__all(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_measure__fst,axiom, % 177.41/177.17 ! [T_d,V_f_2,T_c] : % 177.41/177.17 ( c_FunDef_Ois__measure(T_c,V_f_2) % 177.41/177.17 => c_FunDef_Ois__measure(tc_prod(T_c,T_d),hAPP(hAPP(c_COMBB(T_c,tc_Nat_Onat,tc_prod(T_c,T_d)),V_f_2),c_Product__Type_Ofst(T_c,T_d))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_measure__snd,axiom, % 177.41/177.17 ! [T_d,V_f_2,T_c] : % 177.41/177.17 ( c_FunDef_Ois__measure(T_c,V_f_2) % 177.41/177.17 => c_FunDef_Ois__measure(tc_prod(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_Nat_Onat,tc_prod(T_d,T_c)),V_f_2),c_Product__Type_Osnd(T_d,T_c))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__rev,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__all(T_c,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2)) % 177.41/177.17 <=> c_List_Olist__all(T_c,V_Pa_2,V_xs_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__simps_I1_J,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__all(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) % 177.41/177.17 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 & c_List_Olist__all(T_c,V_Pa_2,V_xs_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Ball__set__list__all,axiom, % 177.41/177.17 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 <=> c_List_Olist__all(T_c,V_Pa_2,V_xs_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__iff__raw,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__all(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex1__simps_I2_J,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex1(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) % 177.41/177.17 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 => c_List_Olist__all(T_c,hAPP(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_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 177.41/177.17 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 => c_List_Olist__ex1(T_c,V_Pa_2,V_xs_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_transfer__morphism__int__nat,axiom, % 177.41/177.17 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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex1__simps_I1_J,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : ~ c_List_Olist__ex1(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bool_Osize_I4_J,axiom, % 177.41/177.17 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bool_Osize_I3_J,axiom, % 177.41/177.17 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex1__iff,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex1(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.17 & ! [B_y] : % 177.41/177.17 ( ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 177.41/177.17 => B_y = B_x ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 177.41/177.17 ! [V_f_2,V_x_2,T_c,T_d,V_i_2] : % 177.41/177.17 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.17 => hAPP(c_New__DSequence_Oneg__decr__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_c) ) % 177.41/177.17 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.17 => hAPP(c_New__DSequence_Oneg__decr__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_d,T_c,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_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_c))),V_f_2),V_i_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 177.41/177.17 ! [V_f_2,V_x_2,T_c,T_d,V_i_2] : % 177.41/177.17 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.17 => hAPP(c_New__DSequence_Opos__decr__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_c) ) % 177.41/177.17 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 177.41/177.17 => hAPP(c_New__DSequence_Opos__decr__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_d,T_c,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_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2),V_i_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_c,T_d] : c_New__Random__Sequence_Oneg__decr__bind(T_d,T_c,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),hAPP(hAPP(c_COMBC(T_d,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_c)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_c,T_d] : c_New__Random__Sequence_Opos__decr__bind(T_d,T_c,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c))),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 177.41/177.17 ! [V_i_2,V_f_2,V_x_2,T_c,T_d] : hAPP(c_New__DSequence_Oneg__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_d,T_c,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_c))),V_f_2),V_i_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Opos__empty__def,axiom, % 177.41/177.17 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pos__empty__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,T_c] : c_New__Random__Sequence_Opos__empty(T_c,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_c) ). % 177.41/177.17 % 177.41/177.17 fof(fact_neg__bind__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_c,T_d] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_d,T_c,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),hAPP(hAPP(c_COMBC(T_d,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_c)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Opos__bind__def,axiom, % 177.41/177.17 ! [V_i_2,V_f_2,V_x_2,T_c,T_d] : hAPP(c_New__DSequence_Opos__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_d,T_c,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2),V_i_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_neg__map__def,axiom, % 177.41/177.17 ! [V_Pa_2,V_f_2,T_c,T_d] : c_New__Random__Sequence_Oneg__map(T_d,T_c,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_d,T_c,V_Pa_2,hAPP(c_Fun_Ocomp(T_c,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_c)))))),T_d,c_New__Random__Sequence_Oneg__single(T_c)),V_f_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_neg__single__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_c] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_c),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_c,V_x_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pos__bind__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_c,T_d] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_d,T_c,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c))),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Oneg__single__def,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pos__map__def,axiom, % 177.41/177.17 ! [V_Pa_2,V_f_2,T_c,T_d] : c_New__Random__Sequence_Opos__map(T_d,T_c,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_d,T_c,V_Pa_2,hAPP(c_Fun_Ocomp(T_c,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_c))))),T_d,c_New__Random__Sequence_Opos__single(T_c)),V_f_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pos__single__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_c] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_c),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_c,V_x_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_length__splice,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_splice_Osimps_I3_J,axiom, % 177.41/177.17 ! [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))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_splice_Osimps_I1_J,axiom, % 177.41/177.17 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 177.41/177.17 % 177.41/177.17 fof(fact_splice__Nil2,axiom, % 177.41/177.17 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 177.41/177.17 % 177.41/177.17 fof(fact_splice_Osimps_I2_J,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Opos__single__def,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_acyclicP__converse,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Wellfounded_Oacyclic(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),c_Predicate_Oconversep(T_c,T_c,V_r_2)))) % 177.41/177.17 <=> c_Wellfounded_Oacyclic(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversep__noteq,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_c,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 177.41/177.17 <=> V_x_2 != V_y_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversepD,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_r_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,V_r_2),V_a_2),V_b_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversep_Ointros,axiom, % 177.41/177.17 ! [T_d,T_c,V_b_2,V_a_2,V_r_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,V_r_2),V_b_2),V_a_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversep_Oequations,axiom, % 177.41/177.17 ! [V_a1_2,V_a2_2,V_r_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,V_r_2),V_a2_2),V_a1_2)) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversep__iff,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_r_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,V_r_2),V_a_2),V_b_2)) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversep__conversep,axiom, % 177.41/177.17 ! [V_r_2,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,c_Predicate_Oconversep(T_c,T_d,V_r_2)) = V_r_2 ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversep__eq,axiom, % 177.41/177.17 ! [T_c] : c_Predicate_Oconversep(T_c,T_c,c_fequal) = c_fequal ). % 177.41/177.17 % 177.41/177.17 fof(fact_converse__pred__comp,axiom, % 177.41/177.17 ! [V_s_2,V_r_2,T_e,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,c_Predicate_Opred__comp(T_d,T_e,T_c,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_c,T_e,T_d,c_Predicate_Oconversep(T_e,T_c,V_s_2),c_Predicate_Oconversep(T_d,T_e,V_r_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_converse__join,axiom, % 177.41/177.17 ! [V_s_2,V_r_2,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Predicate_Oconversep(T_d,T_c,V_r_2)),c_Predicate_Oconversep(T_d,T_c,V_s_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_converse__meet,axiom, % 177.41/177.17 ! [V_s_2,V_r_2,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Predicate_Oconversep(T_d,T_c,V_r_2)),c_Predicate_Oconversep(T_d,T_c,V_s_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_conversep__converse__eq,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,V_r_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,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_r_2)),V_x_2),V_y_2)) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_,axiom, % 177.41/177.17 ! [V_s2_2,V_s1_2,T_d,T_c] : c_Lazy__Sequence_Oproduct(T_c,T_d,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_c,tc_prod(T_c,T_d),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d)),T_c),c_Lazy__Sequence_Obind(T_d,tc_prod(T_c,T_d),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d))),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d)),T_d),c_Lazy__Sequence_Osingle(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_tl__replicate,axiom, % 177.41/177.17 ! [V_x,T_a,V_n] : % 177.41/177.17 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 => 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) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__length__filter,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,T_c] : c_List_Oreplicate(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_c,hAPP(c_fequal,V_x_2)),V_xs_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_length__replicate,axiom, % 177.41/177.17 ! [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 ). % 177.41/177.17 % 177.41/177.17 fof(fact_map__replicate__const,axiom, % 177.41/177.17 ! [V_lst_2,V_k_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_COMBK(T_c,T_d),V_k_2)),V_lst_2) = c_List_Oreplicate(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_lst_2),V_k_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__app__Cons__same,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__Suc,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_rev__replicate,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_drop__replicate,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_hd__replicate,axiom, % 177.41/177.17 ! [V_x,T_a,V_n] : % 177.41/177.17 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_take__replicate,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_last__replicate,axiom, % 177.41/177.17 ! [V_x,T_a,V_n] : % 177.41/177.17 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_zip__replicate,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Bex__set__replicate,axiom, % 177.41/177.17 ! [V_Pa_2,V_a_2,V_n_2,T_c] : % 177.41/177.17 ( ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_a_2)))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 177.41/177.17 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Ball__set__replicate,axiom, % 177.41/177.17 ! [V_Pa_2,V_a_2,V_n_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_a_2)))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 177.41/177.17 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__eq__replicate,axiom, % 177.41/177.17 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_c] : % 177.41/177.17 ( c_List_Oreplicate(T_c,V_m_2,V_x_2) = c_List_Oreplicate(T_c,V_n_2,V_y_2) % 177.41/177.17 <=> ( V_m_2 = V_n_2 % 177.41/177.17 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 => V_x_2 = V_y_2 ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_nth__replicate,axiom, % 177.41/177.17 ! [V_x,T_a,V_n,V_i] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 177.41/177.17 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_append__replicate__commute,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__add,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_filter__replicate,axiom, % 177.41/177.17 ! [V_n_2,T_c,V_x_2,V_Pa_2] : % 177.41/177.17 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 => hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_c,V_n_2,V_x_2) ) % 177.41/177.17 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 177.41/177.17 => hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Olist_ONil(T_c) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_concat__replicate__trivial,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__0,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_empty__replicate,axiom, % 177.41/177.17 ! [V_x_2,V_n_2,T_c] : % 177.41/177.17 ( c_List_Olist_ONil(T_c) = c_List_Oreplicate(T_c,V_n_2,V_x_2) % 177.41/177.17 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__empty,axiom, % 177.41/177.17 ! [V_x_2,V_n_2,T_c] : % 177.41/177.17 ( c_List_Oreplicate(T_c,V_n_2,V_x_2) = c_List_Olist_ONil(T_c) % 177.41/177.17 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_map__replicate,axiom, % 177.41/177.17 ! [V_x_2,V_n_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oreplicate(T_d,V_n_2,V_x_2)) = c_List_Oreplicate(T_c,V_n_2,hAPP(V_f_2,V_x_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__set__replicate,axiom, % 177.41/177.17 ! [V_y_2,V_n_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_y_2)))) % 177.41/177.17 <=> ( V_x_2 = V_y_2 % 177.41/177.17 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_replicate__append__same,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_map__replicate__trivial,axiom, % 177.41/177.17 ! [V_i_2,V_x_2,T_c] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),hAPP(c_COMBK(T_c,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_c,V_i_2,V_x_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_set__replicate,axiom, % 177.41/177.17 ! [V_x_2,T_c,V_n_2] : % 177.41/177.17 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 => hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_set__replicate__conv__if,axiom, % 177.41/177.17 ! [V_x_2,T_c,V_n_2] : % 177.41/177.17 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 => hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 177.41/177.17 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 => hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_set__replicate__Suc,axiom, % 177.41/177.17 ! [V_x_2,V_n_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_small__lazy__list_Osimps,axiom, % 177.41/177.17 ! [V_d_2,T_c] : % 177.41/177.17 ( class_Lazy__Sequence_Osmall__lazy(T_c) % 177.41/177.17 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_c),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_c),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c))),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_c,tc_List_Olist(T_c)),tc_List_Olist(T_c),c_Lazy__Sequence_Oproduct(T_c,tc_List_Olist(T_c),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_c,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_c),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_c,tc_List_Olist(T_c),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c))),T_c),hAPP(c_COMBB(tc_List_Olist(T_c),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c)),tc_List_Olist(T_c)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_c)))),c_List_Olist_OCons(T_c))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_c)))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_eq__comp__r,axiom, % 177.41/177.17 ! [V_R_2,T_c] : c_Predicate_Opred__comp(T_c,T_c,T_c,c_fequal,c_Predicate_Opred__comp(T_c,T_c,T_c,V_R_2,c_fequal)) = V_R_2 ). % 177.41/177.17 % 177.41/177.17 fof(fact_small__lazy__prod__def,axiom, % 177.41/177.17 ! [V_d,T_b,T_a] : % 177.41/177.17 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 177.41/177.17 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 177.41/177.17 => 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)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Opos__union__def,axiom, % 177.41/177.17 ! [V_i_2,V_yq_2,V_xq_2,T_c] : hAPP(c_New__DSequence_Opos__union(T_c,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_c,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_field__le__epsilon,axiom, % 177.41/177.17 ! [V_y,V_x,T_a] : % 177.41/177.17 ( class_Fields_Olinordered__field(T_a) % 177.41/177.17 => ( ! [B_e] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 177.41/177.17 => 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))) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pos__union__def,axiom, % 177.41/177.17 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_c] : c_New__Random__Sequence_Opos__union(T_c,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_c,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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_small__lazy_H_Osimps,axiom, % 177.41/177.17 ! [V_i,V_d] : % 177.41/177.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 177.41/177.17 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 177.41/177.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 177.41/177.17 => 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)))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_small__lazy__int__def,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_small__lazy_H_Opsimps,axiom, % 177.41/177.17 ! [V_i_2,V_d_2] : % 177.41/177.17 ( 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))) % 177.41/177.17 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 177.41/177.17 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 177.41/177.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 177.41/177.17 => 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)))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 177.41/177.17 ! [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))) ). % 177.41/177.17 % 177.41/177.17 fof(fact__01,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Oinject,axiom, % 177.41/177.17 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_c] : % 177.41/177.17 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_H_2,V_lazy__sequence_H_2) % 177.41/177.17 <=> ( V_a_2 = V_a_H_2 % 177.41/177.17 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 177.41/177.17 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_c] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,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_c,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_small__lazy_H_Opinduct,axiom, % 177.41/177.17 ! [V_Pa_2,V_a1_2,V_a0_2] : % 177.41/177.17 ( 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))) % 177.41/177.17 => ( ! [B_d,B_i] : % 177.41/177.17 ( 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))) % 177.41/177.17 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 177.41/177.17 => 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)))) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_size__code,axiom, % 177.41/177.17 ! [V_xq_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_c)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),T_c),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_c),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_c)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_c)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence__size__code,axiom, % 177.41/177.17 ! [V_xq_2,V_s_2,T_c] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_c,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat)),T_c),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_c),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_c)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),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_c),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat)),T_c),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_c),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_seq__case,axiom, % 177.41/177.17 ! [V_xq_2,V_g_2,V_f_2,T_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_c,T_d,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_c,tc_prod(T_d,tc_Lazy__Sequence_Olazy__sequence(T_d)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_d,tc_Lazy__Sequence_Olazy__sequence(T_d),T_c),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_d),V_xq_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_yieldn__def,axiom, % 177.41/177.17 ! [T_c] : c_Lazy__Sequence_Oyieldn(T_c) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_c),T_c,c_Lazy__Sequence_Oyield(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 177.41/177.17 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_d,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_refl__on__INTER,axiom, % 177.41/177.17 ! [V_r_2,V_A_2,T_d,V_S_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.41/177.17 => c_Relation_Orefl__on(T_d,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 177.41/177.17 => c_Relation_Orefl__on(T_d,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__set__member,axiom, % 177.41/177.17 ! [V_xs_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_c),V_xs_2),V_x_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_member__rec_I1_J,axiom, % 177.41/177.17 ! [V_y_2,V_xs_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_List_Omember(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_y_2)) % 177.41/177.17 <=> ( V_x_2 = V_y_2 % 177.41/177.17 | hBOOL(hAPP(hAPP(c_List_Omember(T_c),V_xs_2),V_y_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_member__set,axiom, % 177.41/177.17 ! [T_c] : c_List_Omember(T_c) = c_List_Oset(T_c) ). % 177.41/177.17 % 177.41/177.17 fof(fact_member__rec_I2_J,axiom, % 177.41/177.17 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_List_Omember__def,axiom, % 177.41/177.17 ! [V_x_2,V_xs_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_List_Omember(T_c),V_xs_2),V_x_2)) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pair__box_Osize_I1_J,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__size(T_c,T_d,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex1__iff__raw,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex1(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.17 & ! [B_y] : % 177.41/177.17 ( ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 177.41/177.17 => B_y = B_x ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pair__box_Osize_I2_J,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pair__box_Oinject,axiom, % 177.41/177.17 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_d,T_c] : % 177.41/177.17 ( c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_H_2,V_b_H_2) % 177.41/177.17 <=> ( V_a_2 = V_a_H_2 % 177.41/177.17 & V_b_2 = V_b_H_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pair__box_Osimps_I2_J,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : c_Nitpick_Opair__box_Opair__box__case(T_d,T_e,T_c,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_d,T_e,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_pair__box_Orecs,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : c_Nitpick_Opair__box_Opair__box__rec(T_d,T_e,T_c,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_d,T_e,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_THE__default__def,axiom, % 177.41/177.17 ! [V_d_2,T_c,V_Pa_2] : % 177.41/177.17 ( ( ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.17 & ! [B_y] : % 177.41/177.17 ( hBOOL(hAPP(V_Pa_2,B_y)) % 177.41/177.17 => B_y = B_x ) ) % 177.41/177.17 => c_FunDef_OTHE__default(T_c,V_d_2,V_Pa_2) = c_HOL_OThe(T_c,V_Pa_2) ) % 177.41/177.17 & ( ~ ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(V_Pa_2,B_x)) % 177.41/177.17 & ! [B_y] : % 177.41/177.17 ( hBOOL(hAPP(V_Pa_2,B_y)) % 177.41/177.17 => B_y = B_x ) ) % 177.41/177.17 => c_FunDef_OTHE__default(T_c,V_d_2,V_Pa_2) = V_d_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_setsum__UNION__zero,axiom, % 177.41/177.17 ! [V_f_2,V_S_2,T_c,T_d] : % 177.41/177.17 ( class_Groups_Ocomm__monoid__add(T_d) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_S_2)) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_S_2)) % 177.41/177.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_x)) ) % 177.41/177.17 => ( ! [B_T1] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_T1),V_S_2)) % 177.41/177.17 => ! [B_T2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_T2),V_S_2)) % 177.41/177.17 => ( B_T1 != B_T2 % 177.41/177.17 => ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_T1)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_T2)) % 177.41/177.17 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) ) % 177.41/177.17 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2)),V_S_2) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_INF2__I,axiom, % 177.41/177.17 ! [T_e,T_d,V_c_2,V_b_2,V_B_2,V_A_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_SUP2__E,axiom, % 177.41/177.17 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 177.41/177.17 => ~ ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.17 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_finite__maxlen,axiom, % 177.41/177.17 ! [V_M_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),V_M_2)) % 177.41/177.17 => ? [B_n] : % 177.41/177.17 ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_x),V_M_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),B_x)),B_n)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osize_I3_J,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osimps_I2_J,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osimps_I3_J,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact__02,axiom, % 177.41/177.17 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osimps_I4_J,axiom, % 177.41/177.17 ! [V_f2_2,V_f1_2,T_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_d)) = V_f1_2 ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Osize_I1_J,axiom, % 177.41/177.17 ! [V_fa_2,T_c] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__iff__all__interval__int,axiom, % 177.41/177.17 ! [V_j_2,V_i_2,V_Pa_2] : % 177.41/177.17 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 177.41/177.17 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__iff__not__all__inverval__int,axiom, % 177.41/177.17 ! [V_j_2,V_i_2,V_Pa_2] : % 177.41/177.17 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 177.41/177.17 <=> ~ 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) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_all__interval__int__def,axiom, % 177.41/177.17 ! [V_j_2,V_i_2,V_Pa_2] : % 177.41/177.17 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) % 177.41/177.17 <=> ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_code__numeral_Orecs_I2_J,axiom, % 177.41/177.17 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_c,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_c,V_f1_2,V_f2_2,V_code__numeral_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Random_Osimps,axiom, % 177.41/177.17 ! [V_size_2,V_g_2,T_c,V_nrandom_2] : % 177.41/177.17 ( ( 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))) % 177.41/177.17 => c_Random__Sequence_ORandom(T_c,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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_c)) ) % 177.41/177.17 & ( ~ 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))) % 177.41/177.17 => c_Random__Sequence_ORandom(T_c,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_c,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_c)))),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_c)))),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_c)))),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_c,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_c)))),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_c,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_c)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c)))),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_c,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_c)))),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_c)))),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_c))))),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_c)))),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_c)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c))))),tc_prod(T_c,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_c)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c)))),tc_prod(T_c,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_c)),c_Product__Type_Ofst(T_c,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_code__numeral_Orecs_I1_J,axiom, % 177.41/177.17 ! [V_f2_2,V_f1_2,T_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_c,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 177.41/177.17 % 177.41/177.17 fof(fact_Random__Sequence_Oempty__def,axiom, % 177.41/177.17 ! [V_size_2,V_nrandom_2,T_c] : c_Random__Sequence_Oempty(T_c,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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Random__Sequence_Osingle__def,axiom, % 177.41/177.17 ! [V_size_2,V_nrandom_2,V_x_2,T_c] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_c),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_c),V_x_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Random__Sequence_Omap__def,axiom, % 177.41/177.17 ! [V_Pa_2,V_f_2,T_c,T_d] : c_Random__Sequence_Omap(T_d,T_c,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_d,T_c,V_Pa_2,hAPP(c_Fun_Ocomp(T_c,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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_d,c_Random__Sequence_Osingle(T_c)),V_f_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_exE__realizer,axiom, % 177.41/177.17 ! [T_e,V_f_2,V_Qa_2,V_p_2,T_c,T_d,V_Pa_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_p_2)),hAPP(c_Product__Type_Ofst(T_d,T_c),V_p_2))) % 177.41/177.17 => ( ! [B_x,B_y] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 177.41/177.17 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 177.41/177.17 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_e),V_f_2),V_p_2))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Image__Collect__split,axiom, % 177.41/177.17 ! [V_A_2,V_Pa_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,hAPP(c_Set_OCollect(tc_prod(T_d,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_HOL_Obool),V_Pa_2))),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Pa_2)))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lexord__trans,axiom, % 177.41/177.17 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_y_2),V_z_2)),c_List_Olexord(T_c,V_r_2))) % 177.41/177.17 => ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_z_2)),c_List_Olexord(T_c,V_r_2))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__less__than,axiom, % 177.41/177.17 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__lex__prod,axiom, % 177.41/177.17 ! [V_R2_2,T_d,V_R1_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_R1_2) % 177.41/177.17 => ( c_Relation_Otrans(T_d,V_R2_2) % 177.41/177.17 => c_Relation_Otrans(tc_prod(T_c,T_d),c_Wellfounded_Olex__prod(T_c,T_d,V_R1_2,V_R2_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_transD,axiom, % 177.41/177.17 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_c_2)),V_r_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_c_2)),V_r_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__def,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 <=> ! [B_x,B_y] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2)) % 177.41/177.17 => ! [B_z] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_z)),V_r_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_z)),V_r_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Union__eq,axiom, % 177.41/177.17 ! [V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_c,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_c,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,tc_HOL_Obool))),V_A_2)))),c_member(T_c)))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__O__subset,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_r_2),V_r_2)),V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__Int,axiom, % 177.41/177.17 ! [V_s_2,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => ( c_Relation_Otrans(T_c,V_s_2) % 177.41/177.17 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__rtrancl,axiom, % 177.41/177.17 ! [V_r_2,T_c] : c_Relation_Otrans(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__Id,axiom, % 177.41/177.17 ! [T_c] : c_Relation_Otrans(T_c,c_Relation_OId(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__finite__psubset,axiom, % 177.41/177.17 ! [T_c] : c_Relation_Otrans(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trancl__id,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => c_Transitive__Closure_Otrancl(T_c,V_r_2) = V_r_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__trancl,axiom, % 177.41/177.17 ! [V_r_2,T_c] : c_Relation_Otrans(T_c,c_Transitive__Closure_Otrancl(T_c,V_r_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__Id__on,axiom, % 177.41/177.17 ! [V_A_2,T_c] : c_Relation_Otrans(T_c,c_Relation_OId__on(T_c,V_A_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lexord__transI,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => c_Relation_Otrans(tc_List_Olist(T_c),c_List_Olexord(T_c,V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bex__empty,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : % 177.41/177.17 ~ ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_listrel__trans,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => c_Relation_Otrans(tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__converse,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) % 177.41/177.17 <=> c_Relation_Otrans(T_c,V_r_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_finite__Collect__bex,axiom, % 177.41/177.17 ! [V_Qa_2,T_d,V_A_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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)))),V_Qa_2))))) % 177.41/177.17 <=> ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Qa_2),B_x)))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bex__UNIV,axiom, % 177.41/177.17 ! [V_Pa_2,T_c] : % 177.41/177.17 ( ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_SUPR__bool__eq,axiom, % 177.41/177.17 ! [T_c] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_HOL_Obool) = c_Set_OBex(T_c) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__reflclI,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__inv__image,axiom, % 177.41/177.17 ! [V_f_2,T_d,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => c_Relation_Otrans(T_d,hAPP(hAPP(c_Relation_Oinv__image(T_c,T_d),V_r_2),V_f_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Bex__set__list__ex,axiom, % 177.41/177.17 ! [V_Pa_2,V_xs_2,T_c] : % 177.41/177.17 ( ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 <=> c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__iff__raw,axiom, % 177.41/177.17 ! [V_xs_2,V_Pa_2,T_c] : % 177.41/177.17 ( c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) % 177.41/177.17 <=> ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_UN__eq,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),c_HOL_OEx(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d)),c_fequal)),V_B_2))))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_INT__eq,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),c_HOL_OEx(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d)),c_fequal)),V_B_2))))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Sup__fun__def,axiom, % 177.41/177.17 ! [V_x_2,V_A_2,T_d,T_c] : % 177.41/177.17 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.17 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_c,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)))))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Sup__apply,axiom, % 177.41/177.17 ! [V_x_2,V_A_2,T_d,T_c] : % 177.41/177.17 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.17 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_c,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)))))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Inf__apply,axiom, % 177.41/177.17 ! [V_x_2,V_A_2,T_d,T_c] : % 177.41/177.17 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.17 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_c,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)))))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Inf__fun__def,axiom, % 177.41/177.17 ! [V_x_2,V_A_2,T_d,T_c] : % 177.41/177.17 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 177.41/177.17 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_c,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)))))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_max__extp_Ointros,axiom, % 177.41/177.17 ! [V_R_2,V_Y_2,V_X_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_X_2)) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Y_2)) % 177.41/177.17 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_X_2)) % 177.41/177.17 => ? [B_xa] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_Y_2)) % 177.41/177.17 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) % 177.41/177.17 => c_Wellfounded_Omax__extp(T_c,V_R_2,V_X_2,V_Y_2) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_transp__def,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Predicate_Otransp(T_c,V_r_2) % 177.41/177.17 <=> c_Relation_Otrans(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_transpE,axiom, % 177.41/177.17 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c] : % 177.41/177.17 ( c_Predicate_Otransp(T_c,V_r_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_equivpE,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.17 => ~ ( c_Predicate_Oreflp(T_c,V_R_2) % 177.41/177.17 => ( c_Predicate_Osymp(T_c,V_R_2) % 177.41/177.17 => ~ c_Predicate_Otransp(T_c,V_R_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_equivpI,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Predicate_Oreflp(T_c,V_R_2) % 177.41/177.17 => ( c_Predicate_Osymp(T_c,V_R_2) % 177.41/177.17 => ( c_Predicate_Otransp(T_c,V_R_2) % 177.41/177.17 => c_Equiv__Relations_Oequivp(T_c,V_R_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sympE,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,V_r_2,T_c] : % 177.41/177.17 ( c_Predicate_Osymp(T_c,V_r_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_equivp__reflp__symp__transp,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.17 <=> ( c_Predicate_Oreflp(T_c,V_R_2) % 177.41/177.17 & c_Predicate_Osymp(T_c,V_R_2) % 177.41/177.17 & c_Predicate_Otransp(T_c,V_R_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_max__extp_Osimps,axiom, % 177.41/177.17 ! [V_a2_2,V_a1_2,V_R_2,T_c] : % 177.41/177.17 ( c_Wellfounded_Omax__extp(T_c,V_R_2,V_a1_2,V_a2_2) % 177.41/177.17 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a1_2)) % 177.41/177.17 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a2_2)) % 177.41/177.17 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.17 & ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_a1_2)) % 177.41/177.17 => ? [B_xa] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_a2_2)) % 177.41/177.17 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_trans__diff__Id,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => ( c_Relation_Oantisym(T_c,V_r_2) % 177.41/177.17 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisym__converse,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Oantisym(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) % 177.41/177.17 <=> c_Relation_Oantisym(T_c,V_r_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisym__empty,axiom, % 177.41/177.17 ! [T_c] : c_Relation_Oantisym(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisym__Id,axiom, % 177.41/177.17 ! [T_c] : c_Relation_Oantisym(T_c,c_Relation_OId(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisym__Id__on,axiom, % 177.41/177.17 ! [V_A_2,T_c] : c_Relation_Oantisym(T_c,c_Relation_OId__on(T_c,V_A_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisym__subset,axiom, % 177.41/177.17 ! [V_s_2,V_r_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 177.41/177.17 => ( c_Relation_Oantisym(T_c,V_s_2) % 177.41/177.17 => c_Relation_Oantisym(T_c,V_r_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisym__def,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Oantisym(T_c,V_r_2) % 177.41/177.17 <=> ! [B_x,B_y] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_r_2)) % 177.41/177.17 => B_x = B_y ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisymD,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Oantisym(T_c,V_r_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_a_2)),V_r_2)) % 177.41/177.17 => V_a_2 = V_b_2 ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_antisym__reflcl,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Oantisym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) % 177.41/177.17 <=> c_Relation_Oantisym(T_c,V_r_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_acyclic__impl__antisym__rtrancl,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Wellfounded_Oacyclic(T_c,V_r_2) % 177.41/177.17 => c_Relation_Oantisym(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_fun__lub__def,axiom, % 177.41/177.17 ! [V_x_2,V_A_2,V_L_2,T_e,T_c,T_d] : c_Partial__Function_Ofun__lub(T_d,T_c,T_e,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(tc_fun(T_e,T_d))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),T_d),hAPP(c_COMBS(tc_fun(T_e,T_d),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_e,T_d)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_e,T_d),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_e,T_d))),V_A_2)))),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_fun(T_e,T_d),T_d),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_e,T_d),T_d),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,tc_fun(T_e,T_d))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_e,T_d),T_e,T_d),c_COMBI(tc_fun(T_e,T_d))),V_x_2)))))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__trans__comp__subset,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),V_r_2)),V_r_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_symD,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_a_2)),V_r_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__def,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 <=> ! [B_x,B_y] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_r_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__Int,axiom, % 177.41/177.17 ! [V_s_2,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => ( c_Relation_Osym(T_c,V_s_2) % 177.41/177.17 => c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__rtrancl,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => c_Relation_Osym(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__Id,axiom, % 177.41/177.17 ! [T_c] : c_Relation_Osym(T_c,c_Relation_OId(T_c)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__Un,axiom, % 177.41/177.17 ! [V_s_2,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => ( c_Relation_Osym(T_c,V_s_2) % 177.41/177.17 => c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__trancl,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => c_Relation_Osym(T_c,c_Transitive__Closure_Otrancl(T_c,V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__Id__on,axiom, % 177.41/177.17 ! [V_A_2,T_c] : c_Relation_Osym(T_c,c_Relation_OId__on(T_c,V_A_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_listrel__sym,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => c_Relation_Osym(tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__conv__converse__eq,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 <=> hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2) = V_r_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__converse,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) % 177.41/177.17 <=> c_Relation_Osym(T_c,V_r_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__Un__converse,axiom, % 177.41/177.17 ! [V_r_2,T_c] : c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__inv__image,axiom, % 177.41/177.17 ! [V_f_2,T_d,V_r_2,T_c] : % 177.41/177.17 ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => c_Relation_Osym(T_d,hAPP(hAPP(c_Relation_Oinv__image(T_c,T_d),V_r_2),V_f_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_sym__Int__converse,axiom, % 177.41/177.17 ! [V_r_2,T_c] : c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_equiv__def,axiom, % 177.41/177.17 ! [V_r_2,V_A_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.17 <=> ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.17 & c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 & c_Relation_Otrans(T_c,V_r_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_equivI,axiom, % 177.41/177.17 ! [V_r_2,V_A_2,T_c] : % 177.41/177.17 ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.17 => ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => ( c_Relation_Otrans(T_c,V_r_2) % 177.41/177.17 => c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_equivE,axiom, % 177.41/177.17 ! [V_r_2,V_A_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) % 177.41/177.17 => ~ ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2) % 177.41/177.17 => ( c_Relation_Osym(T_c,V_r_2) % 177.41/177.17 => ~ c_Relation_Otrans(T_c,V_r_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_symp__def,axiom, % 177.41/177.17 ! [V_r_2,T_c] : % 177.41/177.17 ( c_Predicate_Osymp(T_c,V_r_2) % 177.41/177.17 <=> c_Relation_Osym(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_part__equivpI,axiom, % 177.41/177.17 ! [T_c,V_R_2] : % 177.41/177.17 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 177.41/177.17 => ( c_Predicate_Osymp(T_c,V_R_2) % 177.41/177.17 => ( c_Predicate_Otransp(T_c,V_R_2) % 177.41/177.17 => c_Equiv__Relations_Opart__equivp(T_c,V_R_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_part__equivp__refl__symp__transp,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Opart__equivp(T_c,V_R_2) % 177.41/177.17 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 177.41/177.17 & c_Predicate_Osymp(T_c,V_R_2) % 177.41/177.17 & c_Predicate_Otransp(T_c,V_R_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_equivp__implies__part__equivp,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.17 => c_Equiv__Relations_Opart__equivp(T_c,V_R_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_part__equivp__transp,axiom, % 177.41/177.17 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Opart__equivp(T_c,V_R_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_part__equivp__symp,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Opart__equivp(T_c,V_R_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_part__equivp__def,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Opart__equivp(T_c,V_R_2) % 177.41/177.17 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 177.41/177.17 & ! [B_x,B_y] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 177.41/177.17 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 177.41/177.17 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y)) % 177.41/177.17 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_part__equivpE,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Opart__equivp(T_c,V_R_2) % 177.41/177.17 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 177.41/177.17 => ( c_Predicate_Osymp(T_c,V_R_2) % 177.41/177.17 => ~ c_Predicate_Otransp(T_c,V_R_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_part__equivp__typedef,axiom, % 177.41/177.17 ! [V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Opart__equivp(T_c,V_R_2) % 177.41/177.17 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,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_c,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_COMBS(T_c,T_c,tc_HOL_Obool),V_R_2),c_COMBI(T_c))))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_R_2))))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inj__iff,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 <=> hAPP(c_Fun_Ocomp(T_d,T_c,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_c) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__o__cancel,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => hAPP(c_Fun_Ocomp(T_d,T_c,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_c) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__def,axiom, % 177.41/177.17 ! [V_y_2,V_f_2,T_d,T_c] : hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_c,hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_y_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__id,axiom, % 177.41/177.17 ! [T_c] : c_Hilbert__Choice_Oinv__into(T_c,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Fun_Oid(T_c)) = c_Fun_Oid(T_c) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__f__eq,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 177.41/177.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__f__f,axiom, % 177.41/177.17 ! [V_x_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__f__eq,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.17 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 177.41/177.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__f__f,axiom, % 177.41/177.17 ! [V_x_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 177.41/177.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_f__inv__into__f,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,V_y_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) % 177.41/177.17 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__into,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__injective,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_d,T_c] : % 177.41/177.17 ( hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_y_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) % 177.41/177.17 => V_x_2 = V_y_2 ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_image__surj__f__inv__f,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_c,T_d] : % 177.41/177.17 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.17 => hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_surj__f__inv__f,axiom, % 177.41/177.17 ! [V_y_2,V_f_2,T_c,T_d] : % 177.41/177.17 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.17 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_surj__iff__all,axiom, % 177.41/177.17 ! [V_f_2,T_c,T_d] : % 177.41/177.17 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.17 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_image__inv__into__cancel,axiom, % 177.41/177.17 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_c,T_d] : % 177.41/177.17 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = V_A_H_2 % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) % 177.41/177.17 => hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__def,axiom, % 177.41/177.17 ! [V_x_2,V_f_2,V_A_2,T_d,T_c] : hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_c,hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_x_2))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_o__inv__o__cancel,axiom, % 177.41/177.17 ! [V_g_2,T_e,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => hAPP(c_Fun_Ocomp(T_d,T_e,T_c,hAPP(c_Fun_Ocomp(T_c,T_e,T_d,V_g_2),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inj__imp__surj__inv,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_image__inv__f__f,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = V_A_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__image__comp,axiom, % 177.41/177.17 ! [V_X_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_X_2)) = V_X_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_surj__imp__inj__inv,axiom, % 177.41/177.17 ! [V_f_2,T_c,T_d] : % 177.41/177.17 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.17 => c_Fun_Oinj__on(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__image__cancel,axiom, % 177.41/177.17 ! [V_S_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2)) % 177.41/177.17 => hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_S_2)) = V_S_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inj__on__inv__into,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,V_B_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) % 177.41/177.17 => c_Fun_Oinj__on(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2),V_B_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__comp,axiom, % 177.41/177.17 ! [V_x_2,V_A_2,V_g_2,T_e,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2)) % 177.41/177.17 => ( c_Fun_Oinj__on(T_e,T_c,V_g_2,V_A_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2)))) % 177.41/177.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_e,T_d,V_A_2,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_e,T_d,c_Hilbert__Choice_Oinv__into(T_e,T_c,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_c,T_d,hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_surj__iff,axiom, % 177.41/177.17 ! [V_f_2,T_c,T_d] : % 177.41/177.17 ( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 177.41/177.17 <=> hAPP(c_Fun_Ocomp(T_d,T_c,T_c,V_f_2),c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_c) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inj__transfer,axiom, % 177.41/177.17 ! [V_x_2,V_Pa_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => ( ! [B_y] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_d),B_y),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_y))) ) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_fold__image__UN__disjoint,axiom, % 177.41/177.17 ! [V_g_2,V_A_2,T_d,V_I_2,T_c,T_e] : % 177.41/177.17 ( class_Groups_Ocomm__monoid__mult(T_e) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_I_2)) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 177.41/177.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_A_2,B_x))) ) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 177.41/177.17 => ! [B_xa] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_I_2)) % 177.41/177.17 => ( B_x != B_xa % 177.41/177.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ) ) % 177.41/177.17 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e)),V_g_2),c_Groups_Oone__class_Oone(T_e)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_c,c_Groups_Otimes__class_Otimes(T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),T_e,T_c),hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e)),V_g_2),c_Groups_Oone__class_Oone(T_e))),V_A_2)),c_Groups_Oone__class_Oone(T_e)),V_I_2) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_nat__of__cases,axiom, % 177.41/177.17 ! [V_y_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.41/177.17 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_nat__of__induct,axiom, % 177.41/177.17 ! [V_Pa_2,V_y_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.41/177.17 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_of__nat__cases,axiom, % 177.41/177.17 ! [V_x_2] : % 177.41/177.17 ~ ! [B_y] : % 177.41/177.17 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y) % 177.41/177.17 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_of__nat__induct,axiom, % 177.41/177.17 ! [V_x_2,V_Pa_2] : % 177.41/177.17 ( ! [B_y] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) ) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Orecs_I1_J,axiom, % 177.41/177.17 ! [V_f2_2,V_f1_2,T_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_d)) = V_f1_2 ). % 177.41/177.17 % 177.41/177.17 fof(fact_beyond__def,axiom, % 177.41/177.17 ! [V_l,V_k] : % 177.41/177.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 177.41/177.17 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 177.41/177.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 177.41/177.17 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_beyond__zero,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_lazy__sequence_Orecs_I2_J,axiom, % 177.41/177.17 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_d,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_c,T_d,V_f1_2,V_f2_2,V_lazy__sequence_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__image__Collect__eq,axiom, % 177.41/177.17 ! [V_Pa_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_d),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_curry__def,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,V_c_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Ocurry(T_d,T_e,T_c,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_curryI,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,T_d,T_c,V_f_2] : % 177.41/177.17 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__id,axiom, % 177.41/177.17 ! [V_A_2,T_c] : c_Fun_Obij__betw(T_c,T_c,c_Fun_Oid(T_c),V_A_2,V_A_2) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__inv__into,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 => c_Fun_Obij__betw(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__into__inv__into__eq,axiom, % 177.41/177.17 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 177.41/177.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inv__inv__eq,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__imp__bij__inv,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => c_Fun_Obij__betw(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_o__inv__distrib,axiom, % 177.41/177.17 ! [V_g_2,T_e,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => ( c_Fun_Obij__betw(T_e,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => c_Hilbert__Choice_Oinv__into(T_e,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_e,T_d,c_Hilbert__Choice_Oinv__into(T_e,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__image__INT,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,T_e,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_e),c_Set_Oimage(T_c,T_d,V_f_2)),V_B_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__comp__iff2,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_e,V_A_H_H_2,V_A_H_2,V_f_H_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_c,V_f_2),V_A_2)),V_A_H_2)) % 177.41/177.17 => ( c_Fun_Obij__betw(T_e,T_c,V_f_2,V_A_2,V_A_H_2) % 177.41/177.17 <=> c_Fun_Obij__betw(T_e,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__trans,axiom, % 177.41/177.17 ! [V_C_2,V_g_2,T_e,V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 => ( c_Fun_Obij__betw(T_d,T_e,V_g_2,V_B_2,V_C_2) % 177.41/177.17 => c_Fun_Obij__betw(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__comp__iff,axiom, % 177.41/177.17 ! [V_A_H_H_2,V_f_H_2,T_e,V_A_H_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2) % 177.41/177.17 => ( c_Fun_Obij__betw(T_d,T_e,V_f_H_2,V_A_H_2,V_A_H_H_2) % 177.41/177.17 <=> c_Fun_Obij__betw(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__comp,axiom, % 177.41/177.17 ! [V_g_2,T_e,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => ( c_Fun_Obij__betw(T_d,T_e,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) % 177.41/177.17 => c_Fun_Obij__betw(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,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_e,tc_HOL_Obool))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_curryE,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 177.41/177.17 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_curryD,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 177.41/177.17 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_curry__conv,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Ocurry(T_d,T_e,T_c,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_split__curry,axiom, % 177.41/177.17 ! [V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),c_Product__Type_Ocurry(T_c,T_d,T_e,V_f_2)) = V_f_2 ). % 177.41/177.17 % 177.41/177.17 fof(fact_curry__split,axiom, % 177.41/177.17 ! [V_f_2,T_e,T_d,T_c] : c_Product__Type_Ocurry(T_c,T_d,T_e,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)) = V_f_2 ). % 177.41/177.17 % 177.41/177.17 fof(fact_finite__vimage__iff,axiom, % 177.41/177.17 ! [V_F_2,V_h_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_h_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))) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_d,V_h_2),V_F_2))) % 177.41/177.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_F_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__image__Compl__eq,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__subset,axiom, % 177.41/177.17 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.41/177.17 => ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2) = V_B_H_2 % 177.41/177.17 => c_Fun_Obij__betw(T_c,T_d,V_f_2,V_B_2,V_B_H_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__is__surj,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_c,T_d,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)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__imp__surj,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 177.41/177.17 => hAPP(c_Set_Oimage(T_c,T_d,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)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__def,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 <=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.17 & hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = V_B_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inj__on__imp__bij__betw,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.17 => c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__imp__inj__on,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 => c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__is__inj,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__the__inv__into,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 => c_Fun_Obij__betw(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__same__card,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 => hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_d),V_B_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__empty2,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) % 177.41/177.17 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__empty1,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_A_2) % 177.41/177.17 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_BIJ,axiom, % 177.41/177.17 ! [V_B_2,T_d,V_A_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) % 177.41/177.17 => ( ? [B_f] : c_Fun_Obij__betw(T_c,T_d,B_f,V_A_2,V_B_2) % 177.41/177.17 <=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_d),V_B_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__finite,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 177.41/177.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__id__iff,axiom, % 177.41/177.17 ! [V_B_2,V_A_2,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_c,c_Fun_Oid(T_c),V_A_2,V_B_2) % 177.41/177.17 <=> V_A_2 = V_B_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__id,axiom, % 177.41/177.17 ! [T_c] : c_Fun_Obij__betw(T_c,T_c,c_Fun_Oid(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__combine,axiom, % 177.41/177.17 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2) % 177.41/177.17 => ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_C_2,V_D_2) % 177.41/177.17 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 177.41/177.17 => c_Fun_Obij__betw(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__betw__Disj__Un,axiom, % 177.41/177.17 ! [V_f_2,V_B_H_2,V_A_H_2,T_d,V_B_2,V_A_2,T_c] : % 177.41/177.17 ( 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)) % 177.41/177.17 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 177.41/177.17 => ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2) % 177.41/177.17 => ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_B_2,V_B_H_2) % 177.41/177.17 => c_Fun_Obij__betw(T_c,T_d,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_d,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__def,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 <=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 & hAPP(c_Set_Oimage(T_c,T_d,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)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bijI,axiom, % 177.41/177.17 ! [V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 177.41/177.17 => ( hAPP(c_Set_Oimage(T_c,T_d,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)) % 177.41/177.17 => c_Fun_Obij__betw(T_c,T_d,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))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_vimage__subset__eq,axiom, % 177.41/177.17 ! [V_A_2,V_B_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),V_A_2)) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bij__vimage__eq__inv__image,axiom, % 177.41/177.17 ! [V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Obij__betw(T_c,T_d,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))) % 177.41/177.17 => hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_ex__bij__betw__nat__finite__1,axiom, % 177.41/177.17 ! [V_M_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_M_2)) % 177.41/177.17 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_c,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_M_2)),V_M_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Cantor__Bernstein,axiom, % 177.41/177.17 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2)) % 177.41/177.17 => ( c_Fun_Oinj__on(T_d,T_c,V_g_2,V_B_2) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2)),V_A_2)) % 177.41/177.17 => ? [B_h] : c_Fun_Obij__betw(T_c,T_d,B_h,V_A_2,V_B_2) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_ex__bij__betw__nat__finite,axiom, % 177.41/177.17 ! [V_M_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_M_2)) % 177.41/177.17 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_c,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_c),V_M_2)),V_M_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_ex__bij__betw__finite__nat,axiom, % 177.41/177.17 ! [V_M_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_M_2)) % 177.41/177.17 => ? [B_h] : c_Fun_Obij__betw(T_c,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_c),V_M_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_refl__on__UNION,axiom, % 177.41/177.17 ! [V_r_2,V_A_2,T_d,V_S_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) % 177.41/177.17 => c_Relation_Orefl__on(T_d,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 177.41/177.17 => c_Relation_Orefl__on(T_d,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bex__reg__eqv,axiom, % 177.41/177.17 ! [V_Pa_2,V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.17 => ( ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Quotient_ORespects(T_c,V_R_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_in__respects,axiom, % 177.41/177.17 ! [V_R_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Quotient_ORespects(T_c,V_R_2))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Respects__def,axiom, % 177.41/177.17 ! [V_x_2,V_R_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(c_Quotient_ORespects(T_c,V_R_2),V_x_2)) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_bex__reg__right,axiom, % 177.41/177.17 ! [V_Pa_2,V_Qa_2,V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(V_Qa_2,B_x)) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 177.41/177.17 => ( ? [B_x1] : hBOOL(hAPP(V_Qa_2,B_x1)) % 177.41/177.17 => ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Quotient_ORespects(T_c,V_R_2))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_babs__reg__eqv,axiom, % 177.41/177.17 ! [V_Pa_2,T_d,V_R_2,T_c] : % 177.41/177.17 ( c_Equiv__Relations_Oequivp(T_c,V_R_2) % 177.41/177.17 => c_Quotient_OBabs(T_c,T_d,c_Quotient_ORespects(T_c,V_R_2),V_Pa_2) = V_Pa_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_Babs__def,axiom, % 177.41/177.17 ! [V_m_2,T_d,V_p_2,V_x_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_p_2)) % 177.41/177.17 => hAPP(c_Quotient_OBabs(T_c,T_d,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_wf__weak__decr__stable,axiom, % 177.41/177.17 ! [V_r_2,V_f_2,T_c] : % 177.41/177.17 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) % 177.41/177.17 => ( c_Wellfounded_Owf(T_c,c_Transitive__Closure_Otrancl(T_c,V_r_2)) % 177.41/177.17 => ? [B_i] : % 177.41/177.17 ! [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) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_INT__greatest,axiom, % 177.41/177.17 ! [V_B_2,V_C_2,T_d,V_A_2,T_c] : % 177.41/177.17 ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_INT__anti__mono,axiom, % 177.41/177.17 ! [V_g_2,V_f_2,T_d,V_A_2,V_B_2,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_rtrancl__induct2,axiom, % 177.41/177.17 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) % 177.41/177.17 => ( ! [B_a,B_b] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2))) % 177.41/177.17 => ! [B_aa,B_ba] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_aa),B_ba))),V_r_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_converse__rtranclE2,axiom, % 177.41/177.17 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2))) % 177.41/177.17 => ( hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_za_2),V_zb_2) % 177.41/177.17 => ~ ! [B_a,B_b] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b))),V_r_2)) % 177.41/177.17 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_converse__rtrancl__induct2,axiom, % 177.41/177.17 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_d,T_c] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) % 177.41/177.17 => ( ! [B_a,B_b,B_aa,B_ba] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_aa),B_ba))),V_r_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) ) % 177.41/177.17 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_congruent2I_H,axiom, % 177.41/177.17 ! [T_e,V_f_2,V_r2_2,T_d,V_r1_2,T_c] : % 177.41/177.17 ( ! [B_y1,B_z1] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y1),B_z1)),V_r1_2)) % 177.41/177.17 => ! [B_y2,B_z2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),B_y2),B_z2)),V_r2_2)) % 177.41/177.17 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) ) % 177.41/177.17 => c_Equiv__Relations_Ocongruent2(T_c,T_d,T_e,V_r1_2,V_r2_2,V_f_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_congruentI,axiom, % 177.41/177.17 ! [T_d,V_f_2,V_r_2,T_c] : % 177.41/177.17 ( ! [B_y,B_z] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_z)),V_r_2)) % 177.41/177.17 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) ) % 177.41/177.17 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r_2,V_f_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact__03,axiom, % 177.41/177.17 ! [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)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_all__interval__nat__def,axiom, % 177.41/177.17 ! [V_j_2,V_i_2,V_Pa_2] : % 177.41/177.17 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) % 177.41/177.17 <=> ! [B_x] : % 177.41/177.17 ( 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))) % 177.41/177.17 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact__04,axiom, % 177.41/177.17 ! [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) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__all__iff__all__interval__nat,axiom, % 177.41/177.17 ! [V_j_2,V_i_2,V_Pa_2] : % 177.41/177.17 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 177.41/177.17 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_list__ex__iff__not__all__inverval__nat,axiom, % 177.41/177.17 ! [V_j_2,V_i_2,V_Pa_2] : % 177.41/177.17 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 177.41/177.17 <=> ~ 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) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact__05,axiom, % 177.41/177.17 ! [V_f_2,V_xq_2,T_c,T_d] : hAPP(c_Lazy__Sequence_Obind(T_d,T_c,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_c,c_Lazy__Sequence_Omap(T_d,tc_Lazy__Sequence_Olazy__sequence(T_c),V_f_2,V_xq_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_folding__image_Ocong,axiom, % 177.41/177.17 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] : % 177.41/177.17 ( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) % 177.41/177.17 => ( ! [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 177.41/177.17 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 177.41/177.17 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact__06,axiom, % 177.41/177.17 ! [V_xq_2,V_x_2,V_f_2,T_c,T_d] : c_Lazy__Sequence_Omap(T_d,T_c,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_d,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_d,T_c,V_f_2,V_xq_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact__07,axiom, % 177.41/177.17 ! [V_f_2,T_c,T_d] : c_Lazy__Sequence_Omap(T_d,T_c,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_d)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c) ). % 177.41/177.17 % 177.41/177.17 fof(fact_New__DSequence_Opos__map__def,axiom, % 177.41/177.17 ! [V_i_2,V_xq_2,V_f_2,T_c,T_d] : c_New__DSequence_Opos__map(T_d,T_c,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_d,T_c,V_f_2,hAPP(V_xq_2,V_i_2)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_power__dvd__imp__le,axiom, % 177.41/177.17 ! [V_n,V_m,V_i] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_Oorder__refl,axiom, % 177.41/177.17 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__0__right,axiom, % 177.41/177.17 ! [V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__1__left,axiom, % 177.41/177.17 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__imp__le,axiom, % 177.41/177.17 ! [V_n,V_k] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult__cancel,axiom, % 177.41/177.17 ! [V_n,V_m,V_k] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(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))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_nat__mult__dvd__cancel1,axiom, % 177.41/177.17 ! [V_n_2,V_m_2,V_k_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(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))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_setprod__dvd__setprod__subset,axiom, % 177.41/177.17 ! [V_f_2,V_A_2,V_B_2,T_c,T_d] : % 177.41/177.17 ( ( class_Groups_Ocomm__monoid__mult(T_d) % 177.41/177.17 & class_Rings_Odvd(T_d) ) % 177.41/177.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_B_2))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inf__period_I4_J,axiom, % 177.41/177.17 ! [V_t_2,V_D_2,V_d_2,T_c] : % 177.41/177.17 ( ( class_Rings_Ocomm__ring(T_c) % 177.41/177.17 & class_Rings_Odvd(T_c) ) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),V_D_2)) % 177.41/177.17 => ! [B_x,B_k] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),B_x),V_t_2))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_k),V_D_2))),V_t_2))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_inf__period_I3_J,axiom, % 177.41/177.17 ! [V_t_2,V_D_2,V_d_2,T_c] : % 177.41/177.17 ( ( class_Rings_Ocomm__ring(T_c) % 177.41/177.17 & class_Rings_Odvd(T_c) ) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),V_D_2)) % 177.41/177.17 => ! [B_x,B_k] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),B_x),V_t_2))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_k),V_D_2))),V_t_2))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__div__eq__mult,axiom, % 177.41/177.17 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_c) % 177.41/177.17 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2)) % 177.41/177.17 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_b_2),V_a_2) = V_c_2 % 177.41/177.17 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__div__div__eq__mult,axiom, % 177.41/177.17 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_c] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_c) % 177.41/177.17 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.41/177.17 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_c_2),V_d_2)) % 177.41/177.17 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_d_2),V_c_2) % 177.41/177.17 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_d_2) ) ) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult__div__cancel,axiom, % 177.41/177.17 ! [V_b,V_a,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 177.41/177.17 => 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 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_div__mult__swap,axiom, % 177.41/177.17 ! [V_a,V_b,V_c,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 177.41/177.17 => 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) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__div__mult__self,axiom, % 177.41/177.17 ! [V_b,V_a,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 177.41/177.17 => 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 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__div__mult,axiom, % 177.41/177.17 ! [V_c,V_b,V_a,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 177.41/177.17 => 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) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_div__mult__div__if__dvd,axiom, % 177.41/177.17 ! [V_w,V_z,V_x,V_y,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) % 177.41/177.17 => 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)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__triv__left,axiom, % 177.41/177.17 ! [V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__triv__right,axiom, % 177.41/177.17 ! [V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult2,axiom, % 177.41/177.17 ! [V_c,V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult,axiom, % 177.41/177.17 ! [V_b,V_c,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_mult__dvd__mono,axiom, % 177.41/177.17 ! [V_d,V_c,V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) % 177.41/177.17 => hBOOL(hAPP(hAPP(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))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvdI,axiom, % 177.41/177.17 ! [V_k,V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Odvd(T_a) % 177.41/177.17 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult__left,axiom, % 177.41/177.17 ! [V_c,V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult__right,axiom, % 177.41/177.17 ! [V_c,V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult__cancel__left,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,V_c_2,T_c] : % 177.41/177.17 ( class_Rings_Oidom(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) % 177.41/177.17 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mult__cancel__right,axiom, % 177.41/177.17 ! [V_b_2,V_c_2,V_a_2,T_c] : % 177.41/177.17 ( class_Rings_Oidom(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2))) % 177.41/177.17 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_nat__mult__dvd__cancel__disj,axiom, % 177.41/177.17 ! [V_n_2,V_m_2,V_k_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(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))) % 177.41/177.17 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_unity__coeff__ex,axiom, % 177.41/177.17 ! [V_l_2,V_Pa_2,T_c] : % 177.41/177.17 ( ( class_Rings_Odvd(T_c) % 177.41/177.17 & class_Rings_Osemiring__0(T_c) ) % 177.41/177.17 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_l_2),B_x))) % 177.41/177.17 <=> ? [B_x] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),B_x),c_Groups_Ozero__class_Ozero(T_c)))) % 177.41/177.17 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom, % 177.41/177.17 ! [V_b_2,V_a_2] : % 177.41/177.17 ( V_a_2 = V_b_2 % 177.41/177.17 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastAtMost__singleton,axiom, % 177.41/177.17 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom, % 177.41/177.17 ! [V_c_2,V_b_2,V_a_2] : % 177.41/177.17 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) % 177.41/177.17 <=> ( V_a_2 = V_b_2 % 177.41/177.17 & V_b_2 = V_c_2 ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom, % 177.41/177.17 ! [V_b_2,V_a_2] : % 177.41/177.17 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) % 177.41/177.17 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom, % 177.41/177.17 ! [V_l_2,V_k_2] : % 177.41/177.17 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) % 177.41/177.17 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom, % 177.41/177.17 ! [V_b_2,V_a_2] : % 177.41/177.17 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 177.41/177.17 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom, % 177.41/177.17 ! [V_l_2,V_k_2] : % 177.41/177.17 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 177.41/177.17 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OgreaterThanLessThan__empty,axiom, % 177.41/177.17 ! [V_k_2,V_l_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 177.41/177.17 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastLessThan__empty,axiom, % 177.41/177.17 ! [V_a_2,V_b_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) % 177.41/177.17 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OgreaterThanAtMost__empty,axiom, % 177.41/177.17 ! [V_k_2,V_l_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 177.41/177.17 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom, % 177.41/177.17 ! [V_b_2,V_a_2] : % 177.41/177.17 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) % 177.41/177.17 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastatMost__empty__iff,axiom, % 177.41/177.17 ! [V_b_2,V_a_2] : % 177.41/177.17 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 177.41/177.17 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_OatLeastatMost__empty,axiom, % 177.41/177.17 ! [V_a_2,V_b_2] : % 177.41/177.17 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) % 177.41/177.17 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__div__neg,axiom, % 177.41/177.17 ! [V_x,V_y,T_a] : % 177.41/177.17 ( class_Divides_Oring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 177.41/177.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__neg__div,axiom, % 177.41/177.17 ! [V_x,V_y,T_a] : % 177.41/177.17 ( class_Divides_Oring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 177.41/177.17 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_minus__dvd__iff,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,T_c] : % 177.41/177.17 ( class_Rings_Ocomm__ring__1(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)),V_y_2)) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_x_2),V_y_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__minus__iff,axiom, % 177.41/177.17 ! [V_y_2,V_x_2,T_c] : % 177.41/177.17 ( class_Rings_Ocomm__ring__1(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_x_2),V_y_2)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__1__iff__1,axiom, % 177.41/177.17 ! [V_m_2] : % 177.41/177.17 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 177.41/177.17 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__imp__mod__0,axiom, % 177.41/177.17 ! [V_b,V_a,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 177.41/177.17 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__eq__mod__eq__0,axiom, % 177.41/177.17 ! [V_b_2,V_a_2,T_c] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2)) % 177.41/177.17 <=> c_Divides_Odiv__class_Omod(T_c,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_div__dvd__div,axiom, % 177.41/177.17 ! [V_c_2,V_b_2,V_a_2,T_c] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_c_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_c_2),V_a_2))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_b_2),V_c_2)) ) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__0__left,axiom, % 177.41/177.17 ! [V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 177.41/177.17 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mod__imp__dvd,axiom, % 177.41/177.17 ! [V_n,V_m,V_k,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mod,axiom, % 177.41/177.17 ! [V_n,V_m,V_k,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_mod__mod__cancel,axiom, % 177.41/177.17 ! [V_a,V_b,V_c,T_a] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 177.41/177.17 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__mod__iff,axiom, % 177.41/177.17 ! [V_m_2,V_n_2,V_k_2,T_c] : % 177.41/177.17 ( class_Divides_Osemiring__div(T_c) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_k_2),V_n_2)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_k_2),c_Divides_Odiv__class_Omod(T_c,V_m_2,V_n_2))) % 177.41/177.17 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_k_2),V_m_2)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__trans,axiom, % 177.41/177.17 ! [V_c,V_b,V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd__refl,axiom, % 177.41/177.17 ! [V_a,T_a] : % 177.41/177.17 ( class_Rings_Ocomm__semiring__1(T_a) % 177.41/177.17 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_Oless__asym,axiom, % 177.41/177.17 ! [V_y,V_x] : % 177.41/177.17 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 177.41/177.17 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 177.41/177.17 % 177.41/177.17 fof(fact_dvd_Oless__trans,axiom, % 177.41/177.17 ! [V_z,V_y,V_x] : % 177.41/177.17 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 177.41/177.17 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 177.41/177.17 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 177.41/177.17 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 177.41/177.17 % 177.41/177.17 %----Arity declarations (222) % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 177.41/177.17 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Obounded__lattice(T_1) % 177.41/177.17 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 177.41/177.17 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Obounded__lattice(T_1) % 177.41/177.17 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Obounded__lattice(T_1) % 177.41/177.17 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Olattice(T_1) % 177.41/177.17 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Olattice(T_1) % 177.41/177.17 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Odistrib__lattice(T_1) % 177.41/177.17 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Oboolean__algebra(T_1) % 177.41/177.17 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Orderings_Opreorder,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Orderings_Opreorder(T_1) % 177.41/177.17 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Finite__Set_Ofinite,axiom, % 177.41/177.17 ! [T_1,T_2] : % 177.41/177.17 ( ( class_Finite__Set_Ofinite(T_2) % 177.41/177.17 & class_Finite__Set_Ofinite(T_1) ) % 177.41/177.17 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Lattices_Olattice,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Lattices_Olattice(T_1) % 177.41/177.17 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Orderings_Oorder,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Orderings_Oorder(T_1) % 177.41/177.17 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Orderings_Otop,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Orderings_Otop(T_1) % 177.41/177.17 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Orderings_Oord,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Orderings_Oord(T_1) % 177.41/177.17 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Orderings_Obot,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Orderings_Obot(T_1) % 177.41/177.17 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Groups_Ouminus,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Groups_Ouminus(T_1) % 177.41/177.17 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Groups_Ominus,axiom, % 177.41/177.17 ! [T_2,T_1] : % 177.41/177.17 ( class_Groups_Ominus(T_1) % 177.41/177.17 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_fun__Enum_Oenum,axiom, % 177.41/177.17 ! [T_1,T_2] : % 177.41/177.17 ( ( class_Enum_Oenum(T_2) % 177.41/177.17 & class_Enum_Oenum(T_1) ) % 177.41/177.17 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Com__Ocom__Nat_Osize,axiom, % 177.41/177.17 class_Nat_Osize(tc_Com_Ocom) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 177.41/177.17 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 177.41/177.17 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 177.41/177.17 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 177.41/177.17 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 177.41/177.17 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 177.41/177.17 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 177.41/177.17 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 177.41/177.17 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 177.41/177.17 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 177.41/177.17 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 177.41/177.17 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 177.41/177.17 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 177.41/177.17 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 177.41/177.17 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 177.41/177.17 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 177.41/177.17 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 177.41/177.17 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 177.41/177.17 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 177.41/177.17 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 177.41/177.17 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 177.41/177.17 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 177.41/177.17 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 177.41/177.17 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 177.41/177.17 class_Divides_Osemiring__div(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 177.41/177.17 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 177.41/177.17 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 177.41/177.17 class_Groups_Oab__group__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 177.41/177.17 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 177.41/177.17 class_Rings_Oordered__ring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 177.41/177.17 class_Orderings_Opreorder(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 177.41/177.17 class_Orderings_Olinorder(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 177.41/177.17 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 177.41/177.17 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 177.41/177.17 class_Groups_Omonoid__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 177.41/177.17 class_Rings_Osemiring__1(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 177.41/177.17 class_Rings_Osemiring__0(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 177.41/177.17 class_Lattices_Olattice(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 177.41/177.17 class_Groups_Ogroup__add(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 177.41/177.17 class_Divides_Oring__div(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 177.41/177.17 class_Rings_Omult__zero(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 177.41/177.17 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 177.41/177.17 class_Orderings_Oorder(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 177.41/177.17 class_Int_Oring__char__0(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 177.41/177.17 class_Int_Onumber__ring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 177.41/177.17 class_Rings_Osemiring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Orderings_Oord,axiom, % 177.41/177.17 class_Orderings_Oord(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 177.41/177.17 class_Groups_Ouminus(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 177.41/177.17 class_Groups_Osgn__if(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 177.41/177.17 class_Groups_Oabs__if(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 177.41/177.17 class_Rings_Oring__1(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ominus,axiom, % 177.41/177.17 class_Groups_Ominus(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Power_Opower,axiom, % 177.41/177.17 class_Power_Opower(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Ozero,axiom, % 177.41/177.17 class_Groups_Ozero(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oring,axiom, % 177.41/177.17 class_Rings_Oring(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Oidom,axiom, % 177.41/177.17 class_Rings_Oidom(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Int_Onumber,axiom, % 177.41/177.17 class_Int_Onumber(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Groups_Oone,axiom, % 177.41/177.17 class_Groups_Oone(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Int__Oint__Rings_Odvd,axiom, % 177.41/177.17 class_Rings_Odvd(tc_Int_Oint) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 177.41/177.17 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 177.41/177.17 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 177.41/177.17 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 177.41/177.17 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 177.41/177.17 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 177.41/177.17 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 177.41/177.17 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 177.41/177.17 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 177.41/177.17 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 177.41/177.17 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 177.41/177.17 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 177.41/177.17 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 177.41/177.17 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 177.41/177.17 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 177.41/177.17 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 177.41/177.17 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 177.41/177.17 class_Orderings_Owellorder(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 177.41/177.17 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 177.41/177.17 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 177.41/177.17 class_Orderings_Opreorder(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 177.41/177.17 class_Orderings_Olinorder(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 177.41/177.17 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 177.41/177.17 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 177.41/177.17 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 177.41/177.17 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 177.41/177.17 class_Lattices_Olattice(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 177.41/177.17 class_Rings_Omult__zero(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 177.41/177.17 class_Orderings_Oorder(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 177.41/177.17 class_Rings_Osemiring(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 177.41/177.17 class_Orderings_Oord(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 177.41/177.17 class_Orderings_Obot(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 177.41/177.17 class_Groups_Ominus(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Power_Opower,axiom, % 177.41/177.17 class_Power_Opower(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 177.41/177.17 class_Groups_Ozero(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Int_Onumber,axiom, % 177.41/177.17 class_Int_Onumber(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Groups_Oone,axiom, % 177.41/177.17 class_Groups_Oone(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 177.41/177.17 class_Rings_Odvd(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nat__Onat__Nat_Osize,axiom, % 177.41/177.17 class_Nat_Osize(tc_Nat_Onat) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 177.41/177.17 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 177.41/177.17 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 177.41/177.17 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 177.41/177.17 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 177.41/177.17 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 177.41/177.17 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 177.41/177.17 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 177.41/177.17 class_Orderings_Opreorder(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 177.41/177.17 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 177.41/177.17 class_Lattices_Olattice(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 177.41/177.17 class_Orderings_Oorder(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 177.41/177.17 class_Orderings_Otop(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 177.41/177.17 class_Orderings_Oord(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 177.41/177.17 class_Orderings_Obot(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 177.41/177.17 class_Groups_Ouminus(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 177.41/177.17 class_Groups_Ominus(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 177.41/177.17 class_Enum_Oenum(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_HOL__Obool__Nat_Osize,axiom, % 177.41/177.17 class_Nat_Osize(tc_HOL_Obool) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Com__Ostate__Nat_Osize,axiom, % 177.41/177.17 class_Nat_Osize(tc_Com_Ostate) ). % 177.41/177.17 % 177.41/177.17 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 177.41/177.17 ! [T_1] : % 177.41/177.17 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 177.41/177.17 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_List__Olist__Nat_Osize,axiom, % 177.41/177.17 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 177.41/177.17 % 177.41/177.17 fof(arity_sum__Finite__Set_Ofinite,axiom, % 177.41/177.17 ! [T_1,T_2] : % 177.41/177.17 ( ( class_Finite__Set_Ofinite(T_2) % 177.41/177.17 & class_Finite__Set_Ofinite(T_1) ) % 177.41/177.17 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_sum__Enum_Oenum,axiom, % 177.41/177.17 ! [T_1,T_2] : % 177.41/177.17 ( ( class_Enum_Oenum(T_2) % 177.41/177.17 & class_Enum_Oenum(T_1) ) % 177.41/177.17 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_sum__Nat_Osize,axiom, % 177.41/177.17 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 177.41/177.17 ! [T_1] : % 177.41/177.17 ( class_Finite__Set_Ofinite(T_1) % 177.41/177.17 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 177.41/177.17 ! [T_1] : % 177.41/177.17 ( class_Enum_Oenum(T_1) % 177.41/177.17 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Option__Ooption__Nat_Osize,axiom, % 177.41/177.17 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 177.41/177.17 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 177.41/177.17 % 177.41/177.17 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 177.41/177.17 ! [T_1,T_2] : % 177.41/177.17 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 177.41/177.17 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 177.41/177.17 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_prod__Finite__Set_Ofinite,axiom, % 177.41/177.17 ! [T_1,T_2] : % 177.41/177.17 ( ( class_Finite__Set_Ofinite(T_2) % 177.41/177.17 & class_Finite__Set_Ofinite(T_1) ) % 177.41/177.17 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_prod__Enum_Oenum,axiom, % 177.41/177.17 ! [T_1,T_2] : % 177.41/177.17 ( ( class_Enum_Oenum(T_2) % 177.41/177.17 & class_Enum_Oenum(T_1) ) % 177.41/177.17 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 177.41/177.17 % 177.41/177.17 fof(arity_prod__Nat_Osize,axiom, % 177.41/177.17 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 177.41/177.17 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 177.41/177.17 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 177.41/177.17 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 177.41/177.17 class_Nat_Osize(tc_Product__Type_Ounit) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 177.41/177.17 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 177.41/177.17 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 177.41/177.17 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 177.41/177.17 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 177.41/177.17 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 177.41/177.17 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 177.41/177.17 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 177.41/177.17 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 177.41/177.17 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 177.41/177.17 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 177.41/177.17 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 177.41/177.17 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 177.41/177.17 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 177.41/177.17 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 177.41/177.17 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 177.41/177.17 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 177.41/177.17 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 177.41/177.17 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 177.41/177.17 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 177.41/177.17 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 177.41/177.17 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 177.41/177.17 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 177.41/177.17 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 177.41/177.17 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 177.41/177.17 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 177.41/177.17 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 177.41/177.17 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 177.41/177.17 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 177.41/177.17 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 177.41/177.17 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 177.41/177.17 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 177.41/177.17 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 177.41/177.17 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 177.41/177.17 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 177.41/177.17 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 177.41/177.17 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 177.41/177.17 % 177.41/177.17 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 177.41/177.17 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 177.41/177.17 % 177.41/177.17 %----Helper facts (20) % 177.41/177.17 fof(help_c__COMBI__1,axiom, % 177.41/177.17 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 177.41/177.17 % 177.41/177.17 fof(help_c__COMBK__1,axiom, % 177.41/177.17 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 177.41/177.17 % 177.41/177.17 fof(help_c__COMBB__1,axiom, % 177.41/177.17 ! [V_R_2,V_Qa_2,V_Pa_2,T_e,T_c,T_d] : hAPP(hAPP(hAPP(c_COMBB(T_d,T_c,T_e),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__COMBC__1,axiom, % 177.41/177.17 ! [V_R_2,V_Qa_2,V_Pa_2,T_c,T_e,T_d] : hAPP(hAPP(hAPP(c_COMBC(T_d,T_e,T_c),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__COMBS__1,axiom, % 177.41/177.17 ! [V_R_2,V_Qa_2,V_Pa_2,T_c,T_e,T_d] : hAPP(hAPP(hAPP(c_COMBS(T_d,T_e,T_c),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fequal__1,axiom, % 177.41/177.17 ! [V_y_2,V_x_2] : % 177.41/177.17 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 177.41/177.17 | V_x_2 = V_y_2 ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fequal__2,axiom, % 177.41/177.17 ! [V_y_2,V_x_2] : % 177.41/177.17 ( V_x_2 != V_y_2 % 177.41/177.17 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fFalse__1,axiom, % 177.41/177.17 ~ hBOOL(c_fFalse) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fTrue__1,axiom, % 177.41/177.17 hBOOL(c_fTrue) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fNot__1,axiom, % 177.41/177.17 ! [V_Pa_2] : % 177.41/177.17 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 177.41/177.17 | ~ hBOOL(V_Pa_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fNot__2,axiom, % 177.41/177.17 ! [V_Pa_2] : % 177.41/177.17 ( ~ ~ hBOOL(V_Pa_2) % 177.41/177.17 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fconj__1,axiom, % 177.41/177.17 ! [V_Qa_2,V_Pa_2] : % 177.41/177.17 ( ~ hBOOL(V_Pa_2) % 177.41/177.17 | ~ hBOOL(V_Qa_2) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fconj__2,axiom, % 177.41/177.17 ! [V_Qa_2,V_Pa_2] : % 177.41/177.17 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 177.41/177.17 | hBOOL(V_Pa_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fconj__3,axiom, % 177.41/177.17 ! [V_Qa_2,V_Pa_2] : % 177.41/177.17 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) % 177.41/177.17 | hBOOL(V_Qa_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fdisj__1,axiom, % 177.41/177.17 ! [V_Qa_2,V_Pa_2] : % 177.41/177.17 ( ~ hBOOL(V_Pa_2) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fdisj__2,axiom, % 177.41/177.17 ! [V_Pa_2,V_Qa_2] : % 177.41/177.17 ( ~ hBOOL(V_Qa_2) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fdisj__3,axiom, % 177.41/177.17 ! [V_Qa_2,V_Pa_2] : % 177.41/177.17 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) % 177.41/177.17 | hBOOL(V_Pa_2) % 177.41/177.17 | hBOOL(V_Qa_2) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fimplies__1,axiom, % 177.41/177.17 ! [V_Qa_2,V_Pa_2] : % 177.41/177.17 ( hBOOL(V_Pa_2) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fimplies__2,axiom, % 177.41/177.17 ! [V_Pa_2,V_Qa_2] : % 177.41/177.17 ( ~ hBOOL(V_Qa_2) % 177.41/177.17 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ). % 177.41/177.17 % 177.41/177.17 fof(help_c__fimplies__3,axiom, % 177.41/177.17 ! [V_Qa_2,V_Pa_2] : % 177.41/177.17 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) % 177.41/177.17 | ~ hBOOL(V_Pa_2) % 177.41/177.17 | hBOOL(V_Qa_2) ) ). % 177.41/177.17 % 177.41/177.17 %----Conjectures (6) % 177.41/177.17 fof(conj_0,hypothesis, % 177.41/177.17 ! [B_p] : % 177.41/177.17 ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,B_p)),hAPP(v_c0,B_p)),hAPP(v_Q_H,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) % 177.41/177.17 => c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,B_p)),hAPP(v_c0,B_p)),hAPP(v_Q,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ) ). % 177.41/177.17 % 177.41/177.17 fof(conj_1,hypothesis, % 177.41/177.17 hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)) ). % 177.41/177.17 % 177.41/177.17 fof(conj_2,hypothesis, % 177.41/177.17 ~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)) ). % 177.41/177.17 % 177.41/177.17 fof(conj_3,hypothesis, % 177.41/177.17 ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) % 177.41/177.17 => c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ) ). % 177.41/177.17 % 177.41/177.17 fof(conj_4,hypothesis, % 177.41/177.17 ( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) % 177.41/177.17 & c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ) ). % 177.41/177.17 % 177.41/177.17 fof(conj_5,conjecture, % 177.41/177.17 c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))) ). % 177.41/177.17 % 177.41/177.17 %------------------------------------------------------------------------------ % 177.41/177.17 %------------------------------------------- % 177.41/177.17 % Proof found % 177.41/177.17 % SZS status Theorem for theBenchmark % 177.41/177.17 % SZS output start Proof % 177.41/177.18 %ClaNum:10450(EqnAxiom:3092) % 177.41/177.18 %VarNum:71002(SingletonVarNum:20547) % 177.41/177.18 %MaxLitNum:8 % 177.41/177.18 %MaxfuncDepth:13 % 177.41/177.18 %SharedTerms:1064 % 177.41/177.18 %goalClause: 4737 % 177.41/177.18 %singleGoalClaCount:1 % 177.41/177.18 [3096]P1(a188) % 177.41/177.18 [3097]P2(a910) % 177.41/177.18 [3098]P2(a914) % 177.41/177.18 [3099]P65(a910) % 177.41/177.18 [3100]P65(a915) % 177.41/177.18 [3101]P66(a910) % 177.41/177.18 [3102]P66(a915) % 177.41/177.18 [3103]P66(a1) % 177.41/177.18 [3104]P66(a100) % 177.41/177.18 [3105]P67(a1) % 177.41/177.18 [3106]P106(a1) % 177.41/177.18 [3107]P107(a910) % 177.41/177.18 [3108]P107(a915) % 177.41/177.18 [3109]P107(a1) % 177.41/177.18 [3110]P107(a100) % 177.41/177.18 [3111]P108(a915) % 177.41/177.18 [3112]P108(a1) % 177.41/177.18 [3113]P108(a100) % 177.41/177.18 [3114]P109(a910) % 177.41/177.18 [3115]P109(a915) % 177.41/177.18 [3116]P109(a1) % 177.41/177.18 [3117]P109(a100) % 177.41/177.18 [3118]P110(a910) % 177.41/177.18 [3119]P110(a915) % 177.41/177.18 [3120]P110(a1) % 177.41/177.18 [3121]P110(a100) % 177.41/177.18 [3122]P68(a915) % 177.41/177.18 [3123]P68(a1) % 177.41/177.18 [3124]P68(a100) % 177.41/177.18 [3125]P78(a1) % 177.41/177.18 [3126]P69(a915) % 177.41/177.18 [3127]P69(a1) % 177.41/177.18 [3128]P69(a100) % 177.41/177.18 [3129]P70(a915) % 177.41/177.18 [3130]P70(a1) % 177.41/177.18 [3131]P70(a100) % 177.41/177.18 [3132]P71(a915) % 177.41/177.18 [3133]P71(a1) % 177.41/177.18 [3134]P71(a100) % 177.41/177.18 [3135]P82(a915) % 177.41/177.18 [3136]P82(a1) % 177.41/177.18 [3137]P82(a100) % 177.41/177.18 [3138]P83(a915) % 177.41/177.18 [3139]P83(a1) % 177.41/177.18 [3140]P83(a100) % 177.41/177.18 [3141]P74(a1) % 177.41/177.18 [3142]P72(a915) % 177.41/177.18 [3143]P72(a1) % 177.41/177.18 [3144]P72(a100) % 177.41/177.18 [3145]P85(a915) % 177.41/177.18 [3146]P85(a1) % 177.41/177.18 [3147]P85(a100) % 177.41/177.18 [3148]P139(a915) % 177.41/177.18 [3149]P139(a1) % 177.41/177.18 [3150]P139(a100) % 177.41/177.18 [3151]P111(a1) % 177.41/177.18 [3152]P112(a915) % 177.41/177.18 [3153]P112(a1) % 177.41/177.18 [3154]P112(a100) % 177.41/177.18 [3155]P144(a915) % 177.41/177.18 [3156]P144(a1) % 177.41/177.18 [3157]P113(a915) % 177.41/177.18 [3158]P113(a1) % 177.41/177.18 [3159]P113(a100) % 177.41/177.18 [3160]P119(a1) % 177.41/177.18 [3161]P140(a915) % 177.41/177.18 [3162]P140(a1) % 177.41/177.18 [3163]P140(a100) % 177.41/177.18 [3164]P75(a915) % 177.41/177.18 [3165]P75(a1) % 177.41/177.18 [3166]P75(a100) % 177.41/177.18 [3167]P76(a1) % 177.41/177.18 [3168]P86(a910) % 177.41/177.18 [3169]P87(a910) % 177.41/177.18 [3170]P87(a1) % 177.41/177.18 [3171]P120(a1) % 177.41/177.18 [3172]P114(a1) % 177.41/177.18 [3173]P96(a910) % 177.41/177.18 [3174]P96(a915) % 177.41/177.18 [3175]P96(a1) % 177.41/177.18 [3176]P115(a910) % 177.41/177.18 [3177]P97(a910) % 177.41/177.18 [3178]P101(a910) % 177.41/177.18 [3179]P101(a915) % 177.41/177.18 [3180]P101(a1) % 177.41/177.18 [3181]P98(a910) % 177.41/177.18 [3182]P79(a915) % 177.41/177.18 [3183]P79(a1) % 177.41/177.18 [3184]P79(a100) % 177.41/177.18 [3185]P80(a915) % 177.41/177.18 [3186]P80(a1) % 177.41/177.18 [3187]P80(a100) % 177.41/177.18 [3188]P126(a915) % 177.41/177.18 [3189]P126(a1) % 177.41/177.18 [3190]P126(a100) % 177.41/177.18 [3191]P141(a1) % 177.41/177.18 [3192]P142(a1) % 177.41/177.18 [3193]P116(a915) % 177.41/177.18 [3194]P116(a1) % 177.41/177.18 [3195]P116(a100) % 177.41/177.18 [3196]P3(a910) % 177.41/177.18 [3197]P102(a910) % 177.41/177.18 [3198]P102(a915) % 177.41/177.18 [3199]P102(a1) % 177.41/177.18 [3200]P100(a910) % 177.41/177.18 [3201]P100(a915) % 177.41/177.18 [3202]P100(a1) % 177.41/177.18 [3203]P91(a915) % 177.41/177.18 [3204]P91(a1) % 177.41/177.18 [3205]P91(a100) % 177.41/177.18 [3206]P129(a915) % 177.41/177.18 [3207]P129(a1) % 177.41/177.18 [3208]P129(a100) % 177.41/177.18 [3209]P134(a915) % 177.41/177.18 [3210]P134(a1) % 177.41/177.18 [3211]P134(a100) % 177.41/177.18 [3212]P145(a915) % 177.41/177.18 [3213]P145(a1) % 177.41/177.18 [3214]P145(a100) % 177.41/177.18 [3215]P81(a915) % 177.41/177.18 [3216]P81(a1) % 177.41/177.18 [3217]P81(a100) % 177.41/177.18 [3218]P143(a1) % 177.41/177.18 [3219]P127(a1) % 177.41/177.18 [3220]P128(a1) % 177.41/177.18 [3221]P88(a915) % 177.41/177.18 [3222]P88(a1) % 177.41/177.18 [3223]P88(a100) % 177.41/177.18 [3224]P135(a915) % 177.41/177.18 [3225]P135(a1) % 177.41/177.18 [3226]P135(a100) % 177.41/177.18 [3227]P137(a915) % 177.41/177.18 [3228]P137(a1) % 177.41/177.18 [3229]P137(a100) % 177.41/177.18 [3230]P136(a915) % 177.41/177.18 [3231]P136(a1) % 177.41/177.18 [3232]P136(a100) % 177.41/177.18 [3233]P130(a915) % 177.41/177.18 [3234]P130(a1) % 177.41/177.18 [3235]P130(a100) % 177.41/177.18 [3236]P124(a915) % 177.41/177.18 [3237]P124(a1) % 177.41/177.18 [3238]P124(a100) % 177.41/177.18 [3239]P131(a915) % 177.41/177.18 [3240]P131(a1) % 177.41/177.18 [3241]P131(a100) % 177.41/177.18 [3242]P132(a1) % 177.41/177.18 [3243]P133(a1) % 177.41/177.18 [3244]P103(a915) % 177.41/177.18 [3245]P103(a1) % 177.41/177.18 [3246]P103(a100) % 177.41/177.18 [3247]P146(a915) % 177.41/177.18 [3248]P146(a1) % 177.41/177.18 [3249]P146(a100) % 177.41/177.18 [3250]P92(a1) % 177.41/177.18 [3251]P58(a915) % 177.41/177.18 [3252]P58(a1) % 177.41/177.18 [3253]P58(a100) % 177.41/177.18 [3254]P59(a1) % 177.41/177.18 [3255]P89(a1) % 177.41/177.18 [3256]P84(a1) % 177.41/177.18 [3257]P138(a1) % 177.41/177.18 [3258]P73(a1) % 177.41/177.18 [3259]P77(a915) % 177.41/177.18 [3260]P77(a1) % 177.41/177.18 [3261]P77(a100) % 177.41/177.18 [3262]P93(a1) % 177.41/177.18 [3263]P94(a915) % 177.41/177.18 [3264]P94(a1) % 177.41/177.18 [3265]P94(a100) % 177.41/177.18 [3266]P117(a915) % 177.41/177.18 [3267]P90(a915) % 177.41/177.18 [3268]P90(a1) % 177.41/177.18 [3269]P90(a100) % 177.41/177.18 [3270]P60(a910) % 177.41/177.18 [3271]P60(a914) % 177.41/177.18 [3272]P105(a910) % 177.41/177.18 [3273]P105(a911) % 177.41/177.18 [3274]P105(a915) % 177.41/177.18 [3275]P105(a914) % 177.41/177.18 [3276]P105(a912) % 177.41/177.18 [3277]P105(a100) % 177.41/177.18 [3278]P105(a323) % 177.41/177.18 [3279]P104(a914) % 177.41/177.18 [3280]P104(a1) % 177.41/177.18 [3281]P121(a915) % 177.41/177.18 [3282]P121(a1) % 177.41/177.18 [3283]P121(a100) % 177.41/177.18 [3284]P118(a1) % 177.41/177.18 [3285]P99(a910) % 177.41/177.18 [3301]P35(a915,a240) % 177.41/177.18 [3302]P35(a915,a317) % 177.41/177.18 [3303]P36(a915,a240) % 177.41/177.18 [4647]~E(a98,a83) % 177.41/177.18 [4648]~P1(a239) % 177.41/177.18 [3093]E(f2(a1),a83) % 177.41/177.18 [3094]E(f101(a100),a3) % 177.41/177.18 [3095]E(f23(a100),a24) % 177.41/177.18 [3286]E(f189(a915),f102(a915)) % 177.41/177.18 [3287]E(f238(a915),f103(a915)) % 177.41/177.18 [3288]E(f190(a915),f2(a915)) % 177.41/177.18 [3289]E(f28(a25),f2(a915)) % 177.41/177.18 [3290]E(f104(a1),f31(a1)) % 177.41/177.18 [3291]E(f84(a239),f2(a915)) % 177.41/177.18 [3292]E(f84(a188),f2(a915)) % 177.41/177.18 [3293]P4(f78(a1)) % 177.41/177.18 [3294]P4(f2(a1)) % 177.41/177.18 [3350]P35(f921(a915,a915),a32) % 177.41/177.18 [3696]E(f320(a915,a915,a240,a240),a32) % 177.41/177.18 [4649]~E(f78(a1),f2(a1)) % 177.41/177.18 [3295]E(f4(f2(a100)),f2(a915)) % 177.41/177.18 [3296]E(f112(f2(a915)),f2(a915)) % 177.41/177.18 [3305]E(f327(f79(a1),a83),a83) % 177.41/177.18 [3308]E(f327(a113,f2(a915)),f78(a915)) % 177.41/177.18 [3309]E(f327(a106,f78(a1)),f78(a915)) % 177.41/177.18 [3310]E(f327(a3,f78(a915)),f78(a100)) % 177.41/177.18 [3312]E(f327(a3,f2(a915)),f2(a100)) % 177.41/177.18 [3314]E(f327(f105(a1),a83),f2(a1)) % 177.41/177.18 [3315]E(f327(f105(a100),a83),f2(a100)) % 177.41/177.18 [3316]E(f327(a106,f2(a1)),f2(a915)) % 177.41/177.18 [3317]E(f327(f191(a910),a239),f2(a915)) % 177.41/177.18 [3318]E(f327(f191(a910),a188),f2(a915)) % 177.41/177.18 [3319]E(f327(f191(a912),a25),f2(a915)) % 177.41/177.18 [3320]E(f327(f105(a915),a83),f2(a915)) % 177.41/177.18 [3326]E(f327(f79(a1),f78(a1)),a98) % 177.41/177.18 [3333]E(f327(f79(a1),f2(a1)),f2(a1)) % 177.41/177.18 [3335]E(f327(f191(a100),f2(a100)),f2(a915)) % 177.41/177.18 [3336]E(f327(f101(a1),f78(a915)),f78(a1)) % 177.41/177.18 [3337]E(f327(f101(a1),f2(a915)),f2(a1)) % 177.41/177.18 [3347]E(f327(a106,f78(a1)),f327(a113,f2(a915))) % 177.41/177.18 [3348]E(f318(f921(a915,a915),a32),a33) % 177.41/177.18 [3349]E(f319(f921(a915,a915),a32),a34) % 177.41/177.18 [3351]P1(f327(f35(a908),a923)) % 177.41/177.18 [3377]E(f327(f282(a915),f2(a915)),f190(f922(a915,a910))) % 177.41/177.18 [3378]E(f327(f283(a915),f2(a915)),f242(f922(a915,a910))) % 177.41/177.18 [3386]P38(f190(f922(a1,a910))) % 177.41/177.18 [3420]E(f327(f327(f23(a100),f2(a100)),f78(a100)),f2(a100)) % 177.41/177.18 [3495]P1(f327(f327(f235(a1),a98),f2(a1))) % 177.41/177.18 [3519]P1(f327(f327(f234(a1),f2(a1)),f78(a1))) % 177.41/177.18 [3521]P1(f327(f327(f235(a1),f2(a1)),f78(a1))) % 177.41/177.18 [3727]E(f327(f327(f289(a915,a915,a915),a317),f307(a915,a317)),a240) % 177.41/177.18 [3766]P39(a1,a915,a106,f327(f234(a1),f2(a1))) % 177.41/177.18 [3770]E(f327(f327(f40(a915,f922(a915,a910)),f242(f922(a915,a910))),f282(a915)),f242(f922(a915,a910))) % 177.41/177.18 [3771]E(f327(f327(f40(a915,f922(a915,a910)),f242(f922(a915,a910))),f283(a915)),f242(f922(a915,a910))) % 177.41/177.18 [3772]E(f327(f327(f40(a915,f922(a915,a910)),f242(f922(a915,a910))),f301(a915)),f242(f922(a915,a910))) % 177.41/177.18 [3773]E(f327(f327(f41(a915,f922(a915,a910)),f242(f922(a915,a910))),f304(a915)),f190(f922(a915,a910))) % 177.41/177.18 [3789]P23(a915,a1,f101(a1),f242(f922(a915,a910))) % 177.41/177.18 [3803]P39(a915,a1,f101(a1),f327(f16(a910,a915),a188)) % 177.41/177.18 [3940]E(f327(f72(a915,a100,a1,a3),a106),f105(a100)) % 177.41/177.18 [4163]P54(a100,a915,a20,a3,f242(f922(a915,a910))) % 177.41/177.18 [4170]P54(a1,f922(f921(a915,a915),a910),a108,a89,a99) % 177.41/177.18 [4425]E(f258(a1,a1,a1,a1,f31(a1),f79(a1)),a52) % 177.41/177.18 [4664]~E(f327(f105(a1),a98),f327(f105(a1),a83)) % 177.41/177.18 [4665]~P1(f327(a195,f78(a1))) % 177.41/177.18 [4666]~P1(f327(a195,f2(a1))) % 177.41/177.18 [4704]~P1(f327(f327(f235(a1),a83),f2(a1))) % 177.41/177.18 [3369]E(f327(f327(f23(a1),a98),a98),a83) % 177.41/177.18 [3384]E(f327(f101(a1),f327(a113,f2(a915))),f78(a1)) % 177.41/177.18 [3449]E(f327(f36(a914),f242(f922(a914,a910))),f78(a915)) % 177.41/177.18 [3469]P1(f327(a195,f327(f105(a1),a98))) % 177.41/177.18 [3471]P1(f327(f327(f234(a1),a98),a83)) % 177.41/177.18 [3473]P1(f327(f327(f235(a1),a98),a83)) % 177.41/177.18 [3530]E(f327(f327(f309(a915),f2(a915)),f190(f922(a915,a910))),f327(f301(a915),f2(a915))) % 177.41/177.18 [3585]P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),a83))) % 177.41/177.18 [3597]E(f327(f310(a915,a915,a113),f242(f922(a915,a910))),f327(f304(a915),f2(a915))) % 177.41/177.18 [3634]P6(f921(a915,a915),f242(f922(f921(a915,a915),a910)),a110) % 177.41/177.18 [3947]E(f327(f72(a915,a1,a100,f101(a1)),a20),a22) % 177.41/177.18 [4008]P35(a915,f327(f262(f921(a915,a915)),f327(f257(a915,a915,a910),f235(a915)))) % 177.41/177.18 [4694]~P1(f327(a195,f327(f105(a1),a83))) % 177.41/177.18 [4695]~P1(f327(f327(f329(a908),a927),a923)) % 177.41/177.18 [4696]~P1(f327(f327(f234(a1),a83),a98)) % 177.41/177.18 [4697]~P1(f327(f327(f235(a1),a83),a83)) % 177.41/177.18 [4698]~P1(f327(f327(f235(a1),a83),a98)) % 177.41/177.18 [4699]~P1(f327(f327(f235(a1),a98),a98)) % 177.41/177.18 [4710]~P1(f327(f35(a915),f242(f922(a915,a910)))) % 177.41/177.18 [4711]~P1(f327(f35(a1),f242(f922(a1,a910)))) % 177.41/177.18 [4317]P22(a909,a924,f327(f327(f309(f913(a909)),f327(f327(f327(f91(a909),f327(a925,a927)),f327(a928,a927)),f327(a929,a927))),f190(f922(f913(a909),a910)))) % 177.41/177.18 [4591]E(f327(f257(a1,a1,a910),f327(f327(f8(f922(a1,a910),f922(a1,a910),a1),f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f235(a1),f2(a1))))),f327(f327(f7(a1,a1,f922(a1,a910)),f327(f327(f8(f922(a1,f922(a1,a910)),f922(a1,f922(a1,a910)),a1),f7(a1,a1,a910)),f327(f327(f8(f922(a1,a1),f922(a1,f922(a1,a910)),a1),f327(f8(a1,f922(a1,a910),a1),a324)),a219))),f78(a1)))),a215) % 177.41/177.18 [3671]E(f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98),f327(f79(a1),a98)) % 177.41/177.18 [3709]E(f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98),f327(f327(f23(a1),a83),a98)) % 177.41/177.18 [3873]E(f327(f327(f61(f921(a915,a915)),f242(f922(f921(a915,a915),a910))),a110),a99) % 177.41/177.18 [3902]E(f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f78(a1)) % 177.41/177.18 [3903]E(f327(f105(a100),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f78(a100)) % 177.41/177.18 [3904]E(f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f78(a915)) % 177.41/177.18 [3908]E(f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(a113,f2(a915))) % 177.41/177.18 [4292]E(f327(f327(f102(f922(f921(f921(a915,a915),f921(a915,a915)),a910)),a32),f307(f921(a915,a915),f190(f922(f921(f921(a915,a915),f921(a915,a915)),a910)))),a70) % 177.41/177.18 [4359]E(f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),f78(a915)),f2(a915))),f190(f922(f921(a915,a915),a910))))),f78(a1)) % 177.41/177.18 [4360]E(f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),f2(a915)),f2(a915))),f190(f922(f921(a915,a915),a910))))),f2(a1)) % 177.41/177.18 [4373]E(f327(f262(f921(a915,a915)),f327(f257(a915,a915,a910),f327(f327(f8(a915,f922(a915,a910),a915),f327(f7(a915,a915,a910),a324)),a113))),a317) % 177.41/177.18 [4345]E(f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),f327(a113,f327(a113,f2(a915)))) % 177.41/177.18 [4348]E(f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),f327(f327(f80(a915),f78(a915)),f78(a915))) % 177.41/177.18 [4349]E(f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),f327(f36(a910),f242(f922(a910,a910)))) % 177.41/177.18 [4412]P4(f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))) % 177.41/177.18 [4481]P25(f922(f921(a915,a915),a910),f327(f327(f252(f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910),f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910)),a33),a71)) % 177.41/177.18 [4482]P25(f922(f921(a915,a915),a910),f327(f327(f252(f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910),f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910)),a34),a69)) % 177.41/177.18 [4522]E(f327(f327(f102(f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910)),f319(f921(a915,a915),a70)),f327(f327(f309(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),f190(f922(f921(a915,a915),a910))),f190(f922(f921(a915,a915),a910)))),f190(f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910)))),a69) % 177.41/177.18 [4523]E(f327(f327(f102(f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910)),f318(f921(a915,a915),a70)),f327(f327(f309(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),f190(f922(f921(a915,a915),a910))),f190(f922(f921(a915,a915),a910)))),f190(f922(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a910)))),a71) % 177.41/177.18 [4414]E(f327(a106,f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(a113,f327(a113,f2(a915)))) % 177.41/177.18 [4459]E(f327(f101(a1),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))) % 177.41/177.18 [4492]P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.18 [4493]E(f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98)),f327(a113,f327(a113,f327(a113,f2(a915))))) % 177.41/177.18 [4537]P4(f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))) % 177.41/177.18 [4623]P22(a909,a924,f327(f310(a908,f913(a909),f327(f327(f18(a908,f922(a909,f922(a911,a910)),f913(a909)),f327(f327(f18(a908,a912,f922(f922(a909,f922(a911,a910)),f913(a909))),f327(f327(f8(f922(a909,f922(a911,a910)),f922(a912,f922(f922(a909,f922(a911,a910)),f913(a909))),a908),f91(a909)),a925)),a928)),a929)),a923)) % 177.41/177.18 [4563]E(f327(f101(a1),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))) % 177.41/177.18 [4576]P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98)))) % 177.41/177.18 [4737]~P22(a909,a924,f327(f327(f309(f913(a909)),f327(f327(f327(f91(a909),f327(a926,a927)),f327(a928,a927)),f327(a930,a927))),f327(f310(a908,f913(a909),f327(f327(f18(a908,f922(a909,f922(a911,a910)),f913(a909)),f327(f327(f18(a908,a912,f922(f922(a909,f922(a911,a910)),f913(a909))),f327(f327(f8(f922(a909,f922(a911,a910)),f922(a912,f922(f922(a909,f922(a911,a910)),f913(a909))),a908),f91(a909)),a926)),a928)),a930)),a923))) % 177.41/177.18 [3304]P5(x33041,a324) % 177.41/177.18 [3697]P23(a915,a915,a113,x36971) % 177.41/177.18 [3297]P105(f913(x32971)) % 177.41/177.18 [3298]P105(f918(x32981)) % 177.41/177.18 [3299]P105(f916(x32991)) % 177.41/177.18 [3300]P105(f917(x33001)) % 177.41/177.18 [3321]P35(a1,f107(x33211)) % 177.41/177.18 [3322]P35(a1,f109(x33221)) % 177.41/177.18 [3373]P35(f922(x33731,a910),f314(x33731)) % 177.41/177.18 [3374]P36(f922(x33741,a910),f314(x33741)) % 177.41/177.18 [3398]E(f243(x33981,x33981,a324),a324) % 177.41/177.18 [3413]E(f46(a1,x34131,x34131),f2(a1)) % 177.41/177.18 [3466]P12(x34661,f922(x34661,a910),f309(x34661)) % 177.41/177.18 [4651]~E(f327(a113,x46511),x46511) % 177.41/177.18 [4661]~E(f327(a113,x46611),f2(a915)) % 177.41/177.18 [3306]E(f327(f191(a915),x33061),x33061) % 177.41/177.18 [3307]E(f327(f105(a1),x33071),x33071) % 177.41/177.18 [3323]E(f327(a89,f328(x33231)),x33231) % 177.41/177.18 [3324]E(f327(a3,f572(x33241)),x33241) % 177.41/177.18 [3325]E(f241(x33251,f2(a100)),f2(a100)) % 177.41/177.18 [3338]E(f115(x33381,f114(x33381)),f114(x33381)) % 177.41/177.18 [3339]E(f153(x33391,f114(x33391)),f114(x33391)) % 177.41/177.18 [3344]E(f327(f168(x33441),f114(x33441)),f114(x33441)) % 177.41/177.18 [3345]E(f327(f172(x33451),f114(x33451)),f114(x33451)) % 177.41/177.18 [3346]E(f327(f169(x33461),f114(x33461)),f114(x33461)) % 177.41/177.18 [3352]E(f327(f105(a1),x33521),f327(f104(a1),x33521)) % 177.41/177.18 [3353]E(f327(a89,f327(a108,x33531)),x33531) % 177.41/177.18 [3355]E(f327(a3,f327(a20,x33551)),x33551) % 177.41/177.18 [3356]E(f327(a20,f327(a3,x33561)),x33561) % 177.41/177.18 [3358]P4(f327(f101(a1),x33581)) % 177.41/177.18 [3367]E(f327(f191(f916(x33671)),f114(x33671)),f2(a915)) % 177.41/177.18 [3368]E(f327(f191(f917(x33681)),f120(x33681)),f2(a915)) % 177.41/177.18 [3389]E(f327(f327(f23(a915),x33891),f2(a915)),x33891) % 177.41/177.18 [3390]E(f327(f327(f80(a915),x33901),f2(a915)),x33901) % 177.41/177.18 [3391]E(f327(f327(f80(a1),x33911),f2(a1)),x33911) % 177.41/177.18 [3392]E(f327(f327(f81(a915),x33921),f78(a915)),x33921) % 177.41/177.18 [3393]E(f327(f327(f81(a1),x33931),f78(a1)),x33931) % 177.41/177.18 [3394]E(f327(f327(f189(a915),x33941),f2(a915)),x33941) % 177.41/177.18 [3395]E(f327(f327(f81(a915),x33951),f2(a915)),f2(a915)) % 177.41/177.18 [3396]E(f327(f327(f238(a915),x33961),f2(a915)),f2(a915)) % 177.41/177.18 [3397]E(f327(f327(f37(a1),x33971),f2(a1)),f2(a1)) % 177.41/177.18 [3404]E(f327(f173(x34041),f114(x34041)),f190(f922(x34041,a910))) % 177.41/177.18 [3408]P1(f327(f138(x34081),f114(x34081))) % 177.41/177.18 [3414]E(f327(f155(x34141,x34141),f5(x34141)),f31(f916(x34141))) % 177.41/177.18 [3415]E(f327(f155(x34151,x34151),f31(x34151)),f31(f916(x34151))) % 177.41/177.18 [3416]E(f46(a1,x34161,f2(a1)),x34161) % 177.41/177.18 [3417]E(f327(f234(a915),f327(a113,x34171)),f327(f235(a915),x34171)) % 177.41/177.18 [3418]E(f327(f282(a915),f327(a113,x34181)),f327(f301(a915),x34181)) % 177.41/177.18 [3419]E(f327(f283(a915),f327(a113,x34191)),f327(f304(a915),x34191)) % 177.41/177.18 [3421]E(f46(a1,f2(a1),x34211),f2(a1)) % 177.41/177.18 [3434]E(f327(f327(f80(a915),x34341),f78(a915)),f327(a113,x34341)) % 177.41/177.18 [3443]E(f327(f302(a915,x34431),f2(a915)),f190(f922(a915,a910))) % 177.41/177.18 [3455]E(f303(a915,f2(a915),x34551),f327(f301(a915),x34551)) % 177.41/177.18 [3498]E(f327(f327(f23(a915),f327(a113,x34981)),f78(a915)),x34981) % 177.41/177.18 [3510]E(f48(f2(a1),x35101),f327(f327(f252(a1,a1),f2(a1)),f2(a1))) % 177.41/177.18 [3560]P1(f327(f327(f235(a915),x35601),f327(a113,x35601))) % 177.41/177.18 [3572]P1(f327(f327(f235(a915),f2(a915)),f327(a113,x35721))) % 177.41/177.18 [3802]E(f92(x38021,x38021,f242(f922(x38021,a910)),f31(x38021)),f31(x38021)) % 177.41/177.18 [3860]E(f327(f327(f23(a100),f327(a3,f327(a113,f327(a20,x38601)))),f78(a100)),x38601) % 177.41/177.18 [3931]P1(f327(f327(f234(a1),f327(f79(a1),f327(f101(a1),x39311))),f2(a1))) % 177.41/177.18 [4078]P1(f327(f327(f235(a1),f327(f79(a1),f327(f101(a1),f327(a113,x40781)))),f2(a1))) % 177.41/177.18 [4671]~E(f242(f922(x46711,a910)),f190(f922(x46711,a910))) % 177.41/177.18 [4707]~P1(f327(f327(f235(a915),x47071),f2(a915))) % 177.41/177.18 [4720]~P1(f327(f327(f235(a1),f327(f101(a1),x47201)),f2(a1))) % 177.41/177.18 [3357]E(f121(x33571,f120(f917(x33571))),f120(x33571)) % 177.41/177.18 [3372]E(f180(x33721,f114(f916(x33721))),f114(f916(x33721))) % 177.41/177.18 [3375]E(f327(f327(f81(a1),a83),x33751),a83) % 177.41/177.18 [3376]E(f327(f327(f80(a1),a83),x33761),x33761) % 177.41/177.18 [3379]E(f327(a106,f327(f101(a1),x33791)),x33791) % 177.41/177.18 [3380]E(f327(f327(f23(a1),x33801),a83),x33801) % 177.41/177.18 [3381]E(f327(f327(f80(a1),x33811),a83),x33811) % 177.41/177.18 [3383]E(f327(f327(f23(a915),x33831),x33831),f2(a915)) % 177.41/177.18 [3387]E(f327(f79(a1),f327(f79(a1),x33871)),x33871) % 177.41/177.18 [3388]E(f327(f36(a915),f327(f282(a915),x33881)),x33881) % 177.41/177.18 [3399]E(f327(f327(f80(a915),f2(a915)),x33991),x33991) % 177.41/177.18 [3400]E(f327(f327(f80(a1),f2(a1)),x34001),x34001) % 177.41/177.18 [3401]E(f327(f327(f81(a915),f78(a915)),x34011),x34011) % 177.41/177.18 [3402]E(f327(f327(f81(a1),f78(a1)),x34021),x34021) % 177.41/177.18 [3403]E(f327(f327(f189(a915),f2(a915)),x34031),x34031) % 177.41/177.18 [3409]E(f327(f327(f23(a915),f2(a915)),x34091),f2(a915)) % 177.41/177.18 [3410]E(f327(f327(f81(a915),f2(a915)),x34101),f2(a915)) % 177.41/177.18 [3411]E(f327(f327(f238(a915),f2(a915)),x34111),f2(a915)) % 177.41/177.18 [3412]E(f327(f327(f37(a1),f2(a1)),x34121),f2(a1)) % 177.41/177.18 [3422]E(f129(x34221,f327(f79(a1),x34221)),f133(a1,x34221)) % 177.41/177.18 [3427]E(f327(f302(a915,f2(a915)),x34271),f327(f282(a915),x34271)) % 177.41/177.18 [3428]E(f327(f327(f81(a1),a98),x34281),f327(f79(a1),x34281)) % 177.41/177.18 [3436]E(f327(a106,f327(f105(a1),x34361)),f327(f105(a915),x34361)) % 177.41/177.18 [3437]E(f327(a20,f327(f105(a100),x34371)),f327(f105(a915),x34371)) % 177.41/177.18 [3438]E(f327(f36(a915),f327(f301(a915),x34381)),f327(a113,x34381)) % 177.41/177.18 [3447]E(f327(f327(f80(a915),f78(a915)),x34471),f327(a113,x34471)) % 177.41/177.18 [3451]E(f327(f104(a1),f327(f101(a1),x34511)),f327(f101(a1),x34511)) % 177.41/177.18 [3452]E(f327(f75(a1),f327(f101(a1),x34521)),f327(f101(a1),x34521)) % 177.41/177.18 [3456]E(f327(f36(x34561),f190(f922(x34561,a910))),f2(a915)) % 177.41/177.18 [3458]E(f327(f327(f37(a915),x34581),f327(a113,f2(a915))),x34581) % 177.41/177.18 [3467]E(f46(a915,x34671,f327(a113,f2(a915))),f2(a915)) % 177.41/177.18 [3468]E(f46(a1,x34681,f327(f105(a1),a98)),f2(a1)) % 177.41/177.18 [3482]E(f327(f327(f37(a1),x34821),f327(f105(a1),a98)),f327(f79(a1),x34821)) % 177.41/177.18 [3486]E(f140(a915,f327(f302(a915,x34861),f2(a915))),f114(a915)) % 177.41/177.18 [3487]E(f327(f327(f80(a1),x34871),f78(a1)),f327(f327(f23(a1),x34871),a98)) % 177.41/177.18 [3488]E(f327(f327(f23(a1),x34881),f78(a1)),f327(f327(f80(a1),x34881),a98)) % 177.41/177.18 [3492]P1(f327(f327(f234(a915),x34921),x34921)) % 177.41/177.18 [3493]P1(f327(f327(f234(a1),x34931),x34931)) % 177.41/177.18 [3494]P1(f327(f327(f287(a915),x34941),x34941)) % 177.41/177.18 [3499]E(f327(f79(a1),f327(f105(a1),x34991)),f327(f105(a1),f327(f79(a1),x34991))) % 177.41/177.18 [3500]P1(f327(f35(a915),f327(f282(a915),x35001))) % 177.41/177.18 [3501]P1(f327(f35(a915),f327(f301(a915),x35011))) % 177.41/177.18 [3508]E(f162(x35081,f242(f922(x35081,a910))),f242(f922(f916(x35081),a910))) % 177.41/177.18 [3513]P1(f327(f327(f234(a915),f2(a915)),x35131)) % 177.41/177.18 [3523]E(f327(f327(f80(a915),f112(x35231)),f327(a113,f2(a915))),f112(f327(a113,x35231))) % 177.41/177.18 [3524]E(f327(f262(x35241),f327(f16(a910,x35241),a239)),f190(f922(x35241,a910))) % 177.41/177.18 [3525]E(f327(f262(x35251),f327(f16(a910,x35251),a188)),f242(f922(x35251,a910))) % 177.41/177.18 [3529]E(f327(f327(f309(a915),x35291),f327(f282(a915),x35291)),f327(f282(a915),f327(a113,x35291))) % 177.41/177.18 [3541]E(f327(f327(f80(a1),f78(a1)),f327(f101(a1),x35411)),f327(f101(a1),f327(a113,x35411))) % 177.41/177.18 [3543]E(f327(f327(f152(f916(x35431)),f114(x35431)),f114(f916(x35431))),f55(x35431,f114(x35431))) % 177.41/177.18 [3563]E(f190(f922(f921(x35631,x35631),a910)),f263(x35631,f190(f922(x35631,a910)))) % 177.41/177.18 [3564]E(f327(f308(x35641),f242(f922(x35641,a910))),f242(f922(f922(x35641,a910),a910))) % 177.41/177.18 [3565]E(f327(f79(f922(x35651,a910)),f190(f922(x35651,a910))),f242(f922(x35651,a910))) % 177.41/177.18 [3566]E(f327(f79(f922(x35661,a910)),f242(f922(x35661,a910))),f190(f922(x35661,a910))) % 177.41/177.18 [3568]P1(f327(f35(x35681),f190(f922(x35681,a910)))) % 177.41/177.18 [3570]E(f327(f302(a915,x35701),f327(a113,x35701)),f327(f327(f309(a915),x35701),f190(f922(a915,a910)))) % 177.41/177.18 [3571]E(f85(f921(a915,a915),f49(x35711,f2(a915))),f327(f327(f252(a915,a915),f2(a915)),x35711)) % 177.41/177.18 [3584]E(f327(f327(f309(a915),f327(a113,x35841)),f327(f301(a915),x35841)),f327(f301(a915),f327(a113,x35841))) % 177.41/177.18 [3588]P35(x35881,f190(f922(f921(x35881,x35881),a910))) % 177.41/177.18 [3589]P37(x35891,f190(f922(f921(x35891,x35891),a910))) % 177.41/177.18 [3592]P1(f327(f327(f234(a1),f2(a1)),f327(f101(a1),x35921))) % 177.41/177.18 [3599]E(f327(f327(f80(a915),f327(f191(a915),x35991)),f327(a113,f2(a915))),f327(f191(a915),f327(a113,x35991))) % 177.41/177.18 [3704]P38(f327(f310(a915,a1,f101(a1)),x37041)) % 177.41/177.18 [3742]P50(x37421,f190(f922(x37421,a910)),f190(f922(f921(x37421,x37421),a910))) % 177.41/177.18 [3762]E(f327(f327(f252(a1,a1),f327(f105(a1),a98)),f327(f327(f23(a1),x37621),f78(a1))),f51(f327(f105(a1),a98),x37621)) % 177.41/177.18 [3815]P57(x38151,f327(f16(f922(x38151,a910),x38151),f327(f16(a910,x38151),a239))) % 177.41/177.18 [3827]E(f290(a915,f287(a915),x38271,x38271),f327(f327(f309(a915),x38271),f190(f922(a915,a910)))) % 177.41/177.18 [4020]P1(f327(f327(f329(f922(f921(a915,a915),a910)),f328(x40201)),a99)) % 177.41/177.18 [4046]P1(f327(f327(f329(f922(f921(a915,a915),a910)),f327(a108,x40461)),a99)) % 177.41/177.18 [4179]P23(x41791,f922(x41791,a910),f327(f327(f7(x41791,f922(x41791,a910),f922(x41791,a910)),f309(x41791)),f190(f922(x41791,a910))),f242(f922(x41791,a910))) % 177.41/177.18 [4668]~E(f327(f327(f80(a1),x46681),x46681),a98) % 177.41/177.18 [4693]~E(f327(a3,f327(a113,f327(a20,x46931))),f2(a100)) % 177.41/177.18 [4700]~P1(f327(a195,f327(f101(a1),x47001))) % 177.41/177.18 [4703]~P1(f327(f327(f235(a915),x47031),x47031)) % 177.41/177.18 [4713]~P1(f327(f327(f234(a915),f327(a113,x47131)),x47131)) % 177.41/177.18 [3515]E(f327(a106,f327(f79(a1),f327(f101(a1),x35151))),f2(a915)) % 177.41/177.18 [3518]E(f327(f327(f80(a1),f327(f79(a1),x35181)),x35181),f2(a1)) % 177.41/177.18 [3522]E(f327(f36(a1),f327(f302(a1,f2(a1)),x35221)),f327(a106,x35221)) % 177.41/177.18 [3534]E(f327(f327(f244(a915),f327(a113,f2(a915))),x35341),f327(a113,f2(a915))) % 177.41/177.18 [3631]E(f327(f281(x36311),f190(f922(f921(x36311,x36311),a910))),f190(f922(x36311,a910))) % 177.41/177.18 [3639]E(f39(f922(x36391,a910),f190(f922(f922(x36391,a910),a910))),f242(f922(x36391,a910))) % 177.41/177.18 [3640]E(f39(f922(x36401,a910),f242(f922(f922(x36401,a910),a910))),f190(f922(x36401,a910))) % 177.41/177.18 [3641]E(f38(f922(x36411,a910),f190(f922(f922(x36411,a910),a910))),f190(f922(x36411,a910))) % 177.41/177.18 [3642]E(f38(f922(x36421,a910),f242(f922(f922(x36421,a910),a910))),f242(f922(x36421,a910))) % 177.41/177.18 [3646]P1(f327(f327(f287(a915),f327(a113,f2(a915))),x36461)) % 177.41/177.18 [3687]E(f327(f327(f309(f916(x36871)),f114(x36871)),f190(f922(f916(x36871),a910))),f162(x36871,f190(f922(x36871,a910)))) % 177.41/177.18 [3688]E(f327(f327(f309(f916(x36881)),f114(x36881)),f190(f922(f916(x36881),a910))),f163(x36881,f114(f922(x36881,a910)))) % 177.41/177.18 [3726]E(f327(f327(f80(a915),f4(x37261)),f327(a113,f2(a915))),f4(f327(a3,f327(a113,f327(a20,x37261))))) % 177.41/177.18 [3753]E(f327(f36(a1),f327(f310(a915,a1,f101(a1)),x37531)),f327(f36(a915),x37531)) % 177.41/177.18 [3756]P1(f327(f327(f234(a915),x37561),f327(f327(f81(a915),x37561),x37561))) % 177.41/177.18 [3793]E(f327(f310(a1,a915,a106),f303(a1,f2(a1),f327(f101(a1),x37931))),f327(f301(a915),x37931)) % 177.41/177.18 [3810]E(f327(f327(f37(a915),f327(a113,f2(a915))),f327(f105(a915),x38101)),f327(a106,f327(f327(f37(a1),f78(a1)),f327(f105(a1),x38101)))) % 177.41/177.18 [3812]E(f327(f173(a915),f140(a915,f327(f302(a915,f2(a915)),f327(a113,x38121)))),f327(f301(a915),x38121)) % 177.41/177.18 [3813]E(f327(f327(f80(a915),f327(f191(a100),x38131)),f327(a113,f2(a915))),f327(f191(a100),f327(a3,f327(a113,f327(a20,x38131))))) % 177.41/177.18 [3833]P37(x38331,f307(x38331,f190(f922(f921(x38331,x38331),a910)))) % 177.41/177.18 [3834]P49(x38341,f307(x38341,f190(f922(f921(x38341,x38341),a910)))) % 177.41/177.18 [3835]E(f327(f310(a1,a915,a106),f327(f310(a915,a1,f101(a1)),x38351)),x38351) % 177.41/177.18 [3866]E(f327(f327(f309(a915),f2(a915)),f327(f310(a915,a915,a113),f327(f282(a915),x38661))),f327(f282(a915),f327(a113,x38661))) % 177.41/177.18 [3872]P52(x38721,x38721,f307(x38721,f190(f922(f921(x38721,x38721),a910)))) % 177.41/177.18 [3878]P1(f327(a195,f327(f79(a1),f327(f101(a1),f327(a113,x38781))))) % 177.41/177.18 [3888]E(f327(f327(f23(f922(a915,a910)),f327(f283(a915),x38881)),f327(f327(f309(a915),x38881),f190(f922(a915,a910)))),f327(f283(a915),f327(a113,x38881))) % 177.41/177.18 [3905]E(f327(f327(f80(a1),f327(f327(f23(a1),a83),x39051)),f327(f327(f23(a1),a83),x39051)),f327(f327(f23(a1),a83),f327(f327(f80(a1),x39051),x39051))) % 177.41/177.18 [3920]E(f327(f327(f309(f922(x39201,a910)),f190(f922(x39201,a910))),f190(f922(f922(x39201,a910),a910))),f327(f308(x39201),f190(f922(x39201,a910)))) % 177.41/177.18 [3948]E(f327(f327(f23(f922(a915,a910)),f327(f304(a915),x39481)),f327(f327(f309(a915),f327(a113,x39481)),f190(f922(a915,a910)))),f327(f304(a915),f327(a113,x39481))) % 177.41/177.18 [4058]E(f327(f105(a915),f327(f327(f80(a1),x40581),x40581)),f327(f327(f86(a915,a915),f327(f105(a915),x40581)),f327(f327(f18(a915,a915,a915),f80(a915)),f5(a915)))) % 177.41/177.18 [4434]P12(x44341,f922(x44341,a910),f327(f327(f8(f922(x44341,a910),f922(f922(x44341,a910),f922(x44341,a910)),x44341),f327(f7(f922(x44341,a910),f922(x44341,a910),f922(x44341,a910)),f23(f922(x44341,a910)))),f327(f327(f7(x44341,f922(x44341,a910),f922(x44341,a910)),f309(x44341)),f190(f922(x44341,a910))))) % 177.41/177.18 [4521]E(f327(f262(f921(a1,a1)),f327(f257(a1,a1,a910),f327(f327(f8(f922(a1,a910),f922(a1,a910),a1),f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),x45211)))),f235(a1)))),f109(x45211)) % 177.41/177.18 [4554]E(f327(f262(f921(a1,a1)),f327(f257(a1,a1,a910),f327(f327(f18(a1,f922(a1,a910),f922(a1,a910)),f327(f327(f8(f922(a910,a910),f922(f922(a1,a910),f922(a1,a910)),a1),f8(a910,a910,a1)),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),x45541)))),f235(a1)))),f107(x45541)) % 177.41/177.18 [4607]E(f327(f262(f921(f922(x46071,a910),f922(x46071,a910))),f327(f257(f922(x46071,a910),f922(x46071,a910),a910),f327(f327(f7(f922(x46071,a910),f922(f922(x46071,a910),a910),f922(f922(x46071,a910),a910)),f327(f327(f8(f922(f922(x46071,a910),f922(a910,a910)),f922(f922(f922(x46071,a910),a910),f922(f922(x46071,a910),a910)),f922(x46071,a910)),f18(f922(x46071,a910),a910,a910)),f327(f327(f8(f922(f922(x46071,a910),a910),f922(f922(x46071,a910),f922(a910,a910)),f922(x46071,a910)),f327(f8(a910,f922(a910,a910),f922(x46071,a910)),a325)),f235(f922(x46071,a910))))),f35(x46071)))),f314(x46071)) % 177.41/177.18 [4717]~P1(f327(f35(f916(x47171)),f242(f922(f916(x47171),a910)))) % 177.41/177.18 [4729]~P1(f327(f327(f234(a1),f2(a1)),f327(f79(a1),f327(f101(a1),f327(a113,x47291))))) % 177.41/177.18 [3666]E(f327(f327(f23(a1),f327(f327(f80(a1),x36661),a98)),a98),x36661) % 177.41/177.18 [3680]E(f327(f173(a915),f140(a915,f327(f302(a915,f2(a915)),x36801))),f327(f282(a915),x36801)) % 177.41/177.18 [3927]E(f327(f327(f80(a1),f327(f327(f80(a1),f78(a1)),x39271)),x39271),f327(f327(f23(a1),f327(f327(f80(a1),x39271),x39271)),a98)) % 177.41/177.18 [3975]E(f327(f286(x39751,x39751),f307(x39751,f190(f922(f921(x39751,x39751),a910)))),f307(x39751,f190(f922(f921(x39751,x39751),a910)))) % 177.41/177.18 [4023]P1(f327(f327(f234(a915),x40231),f327(f327(f81(a915),x40231),f327(f327(f81(a915),x40231),x40231)))) % 177.41/177.18 [4296]P1(f327(f35(a915),f327(f262(a915),f327(f327(f7(a915,a915,a910),f234(a915)),x42961)))) % 177.41/177.18 [4297]P1(f327(f35(a915),f327(f262(a915),f327(f327(f7(a915,a915,a910),f235(a915)),x42971)))) % 177.41/177.18 [4570]E(f327(f262(f921(x45701,x45701)),f327(f327(f8(f922(x45701,a910),a910,f921(x45701,x45701)),f87(x45701)),f327(f327(f7(f921(x45701,x45701),f922(x45701,f921(x45701,x45701)),f922(x45701,a910)),f327(f327(f8(f922(f921(x45701,x45701),a910),f922(f922(x45701,f921(x45701,x45701)),f922(x45701,a910)),f921(x45701,x45701)),f8(f921(x45701,x45701),a910,x45701)),a324)),f327(f327(f18(x45701,x45701,f921(x45701,x45701)),f252(x45701,x45701)),f5(x45701))))),f307(x45701,f190(f922(f921(x45701,x45701),a910)))) % 177.41/177.18 [4719]~E(f327(f327(f23(a1),f327(f327(f80(a1),x47191),x47191)),a98),a83) % 177.41/177.18 [4721]~E(f327(f327(f80(a1),f327(f327(f80(a1),f78(a1)),x47211)),x47211),f2(a1)) % 177.41/177.18 [4069]E(f327(f327(f80(a1),f327(f327(f23(a1),a98),x40691)),f327(f327(f23(a1),a98),x40691)),f327(f327(f23(a1),a98),f327(f327(f23(a1),f327(f327(f80(a1),x40691),x40691)),a98))) % 177.41/177.18 [4187]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),a98),x41871)),f327(f327(f23(a1),a98),x41871))),a98),f327(f327(f23(a1),a98),f327(f327(f80(a1),x41871),x41871))) % 177.41/177.18 [4219]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f80(a1),x42191),a98)),f327(f327(f80(a1),x42191),a98))),a98),f327(f327(f80(a1),f327(f327(f80(a1),x42191),x42191)),a98)) % 177.41/177.18 [4257]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),a98),x42571)),f327(f327(f23(a1),a98),x42571))),a98),f327(f327(f23(a1),a83),f327(f327(f23(a1),f327(f327(f80(a1),x42571),x42571)),a98))) % 177.41/177.18 [4355]E(f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x43551),f2(a915))),f190(f922(f921(a915,a915),a910))))),f327(f101(a1),x43551)) % 177.41/177.18 [4365]E(f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),f332(x43651)),f534(x43651))),f190(f922(f921(a915,a915),a910))))),x43651) % 177.41/177.18 [4398]E(f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x43981)),f327(f310(a915,a1,f101(a1)),f327(f262(a915),f327(f327(f8(a1,a910,a915),x43981),f101(a1))))) % 177.41/177.18 [4442]P38(f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x44421))) % 177.41/177.18 [4462]P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x44621),f190(f922(f921(a915,a915),a910)))),a71)) % 177.41/177.18 [4467]E(f327(f310(a1,a915,a106),f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),f327(f327(f8(a915,a910,a1),x44671),a106)))),f327(f262(a915),x44671)) % 177.41/177.18 [4622]E(f312(a915,f327(f327(f40(f921(a915,a915),f922(a915,a910)),f327(a108,x46221)),f327(f257(a915,a915,f922(a915,a910)),f327(f327(f7(a915,f922(a915,a910),f922(a915,f922(a915,a910))),f327(f327(f8(f922(a915,f922(f922(a915,a910),f922(a915,a910))),f922(f922(a915,a910),f922(a915,f922(a915,a910))),a915),f7(a915,f922(a915,a910),f922(a915,a910))),f327(f327(f8(f922(a915,a915),f922(a915,f922(f922(a915,a910),f922(a915,a910))),a915),f327(f8(a915,f922(f922(a915,a910),f922(a915,a910)),a915),f309(a915))),f23(a915)))),f190(f922(a915,a910)))))),f327(a106,x46221)) % 177.41/177.18 [4114]E(f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),x41141),x41141)),a98)),a98),f327(f327(f80(a1),x41141),x41141)) % 177.41/177.18 [4164]E(f327(f327(f23(a1),f327(f327(f23(a1),f327(f327(f80(a1),x41641),x41641)),a98)),a98),f327(f327(f80(a1),f327(f327(f23(a1),x41641),a98)),f327(f327(f23(a1),x41641),a98))) % 177.41/177.18 [4371]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f80(a1),f327(f79(a1),x43711)),a98)),f327(f327(f80(a1),f327(f79(a1),x43711)),a98))),a98),f327(f79(a1),f327(f327(f23(a1),f327(f327(f80(a1),x43711),x43711)),a98))) % 177.41/177.18 [4415]E(f327(f327(f80(a915),x44151),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(a113,f327(a113,x44151))) % 177.41/177.18 [4416]E(f327(f327(f81(a915),x44161),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f80(a915),x44161),x44161)) % 177.41/177.18 [4417]E(f327(f327(f37(a915),f327(f327(f80(a915),x44171),x44171)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x44171) % 177.41/177.18 [4495]E(f46(a915,f327(a113,f327(a113,x44951)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f46(a915,x44951,f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.18 [4638]E(f327(a89,f327(f327(f40(f921(a915,a915),f922(f921(a915,a915),a910)),f327(a108,x46381)),f327(f257(a915,a915,f922(f921(a915,a915),a910)),f327(f327(f8(f922(a915,f922(f921(a915,a915),a910)),f922(a915,f922(f921(a915,a915),a910)),a915),f327(f8(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910),a915),f285(f921(a915,a915),f921(a915,a915),a110))),f327(f327(f7(a915,f922(f921(a915,a915),a910),f922(a915,f922(f921(a915,a915),a910))),f327(f327(f8(f922(a915,f922(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f922(f922(f921(a915,a915),a910),f922(a915,f922(f921(a915,a915),a910))),a915),f7(a915,f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f8(f922(a915,f921(a915,a915)),f922(a915,f922(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),a915),f327(f8(f921(a915,a915),f922(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),a915),f309(f921(a915,a915)))),f327(f7(a915,a915,f921(a915,a915)),f252(a915,a915))))),f190(f922(f921(a915,a915),a910))))))),f327(f79(a1),x46381)) % 177.41/177.18 [4490]E(f327(f327(f80(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x44901),f327(a113,f327(a113,x44901))) % 177.41/177.18 [4491]E(f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x44911),f327(f327(f80(a915),x44911),x44911)) % 177.41/177.18 [4527]E(f327(f327(f37(a915),f327(a113,f327(a113,x45271))),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(a113,f327(f327(f37(a915),x45271),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.18 [4577]E(f327(f327(f80(a915),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),x45771),f327(a113,f327(a113,f327(a113,x45771)))) % 177.41/177.18 [4645]E(f327(f257(a1,a1,f921(a1,a1)),f327(f327(f18(a1,f922(a1,f921(a1,a1)),f922(a1,f921(a1,a1))),f327(f327(f8(f922(a1,f922(f921(a1,a1),f921(a1,a1))),f922(f922(a1,f921(a1,a1)),f922(a1,f921(a1,a1))),a1),f18(a1,f921(a1,a1),f921(a1,a1))),f327(f327(f8(f922(a1,f921(a1,a1)),f922(a1,f922(f921(a1,a1),f921(a1,a1))),a1),f327(f18(a1,f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),f327(f327(f8(a910,f922(f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),a1),f97(f921(a1,a1))),f327(f327(f8(a1,a910,a1),f327(f234(a1),f2(a1))),f327(f327(f7(a1,a1,a1),f23(a1)),x46451))))),f327(f327(f7(a1,f922(a1,a1),f922(a1,f921(a1,a1))),f327(f327(f8(f922(a1,f921(a1,a1)),f922(f922(a1,a1),f922(a1,f921(a1,a1))),a1),f8(a1,f921(a1,a1),a1)),f327(f327(f8(a1,f922(a1,f921(a1,a1)),a1),f252(a1,a1)),f327(f327(f7(a1,a1,a1),f327(f327(f8(a1,f922(a1,a1),a1),f80(a1)),f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f78(a1))))),f327(f327(f7(a1,a1,a1),f23(a1)),x46451))))),f327(f327(f8(a1,f922(a1,f921(a1,a1)),a1),f252(a1,a1)),f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))))),f44(x46451)) % 177.41/177.18 [3341]P105(f920(x33411,x33412)) % 177.41/177.18 [3342]P105(f921(x33421,x33422)) % 177.41/177.18 [3343]P105(f919(x33431,x33432)) % 177.41/177.18 [3361]P11(a1,f179(x33611,x33612)) % 177.41/177.18 [3362]P35(x33621,f154(x33621,x33622)) % 177.41/177.18 [3363]P36(x33631,f263(x33631,x33632)) % 177.41/177.18 [3364]P36(x33641,f307(x33641,x33642)) % 177.41/177.18 [3365]P37(x33651,f263(x33651,x33652)) % 177.41/177.18 [3366]P49(x33661,f263(x33661,x33662)) % 177.41/177.18 [3429]P29(x34291,x34292,f114(x34291)) % 177.41/177.18 [3462]P50(x34621,x34622,f263(x34621,x34622)) % 177.41/177.18 [3463]P52(x34631,x34631,f263(x34631,x34632)) % 177.41/177.18 [3729]P23(x37291,x37291,f5(x37291),x37292) % 177.41/177.18 [3730]P23(x37301,x37301,f31(x37301),x37302) % 177.41/177.18 [3738]P30(x37381,x37382,f114(x37381),f114(x37381)) % 177.41/177.18 [3747]P23(f916(x37471),f916(x37471),f169(x37471),x37472) % 177.41/177.18 [4154]P24(x41541,x41541,f31(x41541),x41542,x41542) % 177.41/177.18 [4654]~E(f30(x46541,x46542),a25) % 177.41/177.18 [4655]~E(f29(x46551,x46552),a25) % 177.41/177.18 [4680]~P31(x46801,x46802,f114(x46801)) % 177.41/177.18 [4681]~P33(x46811,x46812,f114(x46811)) % 177.41/177.18 [3327]E(f327(f5(x33271),x33272),x33272) % 177.41/177.18 [3328]E(f327(f262(x33281),x33282),x33282) % 177.41/177.18 [3330]E(f327(f31(x33301),x33302),x33302) % 177.41/177.18 [3340]E(f327(f193(x33401),x33402),f116(x33401)) % 177.41/177.18 [3359]E(f85(x33591,f327(a324,x33592)),x33592) % 177.41/177.18 [3360]E(f90(x33601,f327(a324,x33602)),x33602) % 177.41/177.18 [3382]E(f327(f126(x33821,x33822),f120(x33821)),f2(a915)) % 177.41/177.18 [3385]E(f327(f137(x33851,x33852),f114(x33851)),f114(x33851)) % 177.41/177.18 [3405]E(f307(x34051,f307(x34051,x34052)),f307(x34051,x34052)) % 177.41/177.18 [3406]E(f153(x34061,f153(x34061,x34062)),f153(x34061,x34062)) % 177.41/177.18 [3424]E(f327(f327(f135(x34241),x34242),f114(x34241)),x34242) % 177.41/177.18 [3430]E(f174(x34301,x34302,f114(x34301)),x34302) % 177.41/177.18 [3431]E(f174(x34311,f114(x34311),x34312),x34312) % 177.41/177.18 [3432]E(f117(x34321,f120(x34321),x34322),x34322) % 177.41/177.18 [3433]E(f170(x34331,f2(a915),x34332),f114(x34331)) % 177.41/177.18 [3439]E(f327(f327(f176(x34391),x34392),f114(x34391)),f114(x34391)) % 177.41/177.18 [3440]E(f327(f327(f139(x34401),x34402),f114(x34401)),f114(x34401)) % 177.41/177.18 [3442]E(f156(x34421,x34422,f114(x34421)),f2(a915)) % 177.41/177.18 [3444]E(f171(x34441,x34442,f114(x34441)),f114(x34441)) % 177.41/177.18 [3445]E(f178(x34451,x34452,f114(x34451)),f114(x34451)) % 177.41/177.18 [3446]E(f177(x34461,f114(x34461),x34462),f114(x34461)) % 177.41/177.18 [3450]E(f327(f173(x34501),f153(x34501,x34502)),f327(f173(x34501),x34502)) % 177.41/177.18 [3453]E(f327(f284(x34531,x34531),f263(x34531,x34532)),x34532) % 177.41/177.18 [3454]E(f327(f264(x34541,x34541),f263(x34541,x34542)),x34542) % 177.41/177.18 [3461]E(f327(f286(x34611,x34611),f263(x34611,x34612)),f263(x34611,x34612)) % 177.41/177.18 [3474]E(f307(f916(x34741),f158(x34741,x34742)),f159(x34741,f307(x34741,x34742))) % 177.41/177.18 [3476]P1(f327(f138(a1),f179(x34761,x34762))) % 177.41/177.18 [3484]E(f327(f284(x34841,x34841),f307(x34841,x34842)),f242(f922(x34841,a910))) % 177.41/177.18 [3485]E(f327(f264(x34851,x34851),f307(x34851,x34852)),f242(f922(x34851,a910))) % 177.41/177.18 [3489]P1(f327(f138(x34891),f153(x34891,x34892))) % 177.41/177.18 [3491]P1(f327(f161(x34911,x34912),f114(x34911))) % 177.41/177.18 [3497]E(f327(f173(a1),f179(x34971,x34972)),f303(a1,x34971,x34972)) % 177.41/177.18 [3511]P53(x35111,f190(f922(x35111,a910)),x35112) % 177.41/177.18 [3516]E(f327(f256(a1,a1),f47(x35161,x35162)),f46(a1,x35161,x35162)) % 177.41/177.18 [3517]E(f327(f302(a915,x35171),f327(a113,x35172)),f303(a915,x35171,x35172)) % 177.41/177.18 [3533]E(f327(f327(f152(x35331),x35332),f114(x35331)),f141(x35331,x35332,f114(x35331))) % 177.41/177.18 [3545]E(f303(a915,f327(a113,x35451),x35452),f305(a915,x35451,x35452)) % 177.41/177.18 [3548]P50(x35481,f242(f922(x35481,a910)),f307(x35481,x35482)) % 177.41/177.18 [3611]E(f327(f327(f23(a915),x36111),f327(a113,x36112)),f327(f36(a915),f306(a915,x36112,x36111))) % 177.41/177.18 [3667]E(f167(x36671,x36672,f114(x36671)),f327(f327(f252(f916(x36671),f916(x36671)),f114(x36671)),f114(x36671))) % 177.41/177.18 [3685]E(f327(f257(x36851,x36852,f921(x36851,x36852)),f252(x36851,x36852)),f31(f921(x36851,x36852))) % 177.41/177.18 [3689]P1(f327(f327(f329(f916(x36891)),f114(x36891)),f162(x36891,x36892))) % 177.41/177.18 [3690]E(f327(f191(f916(x36901)),f115(x36901,x36902)),f327(f327(f23(a915),f327(f191(f916(x36901)),x36902)),f78(a915))) % 177.41/177.18 [3698]P1(f327(f35(a915),f306(a915,x36981,x36982))) % 177.41/177.18 [3699]P1(f327(f35(a915),f305(a915,x36991,x36992))) % 177.41/177.18 [3700]P1(f327(f35(a915),f303(a915,x37001,x37002))) % 177.41/177.18 [3701]P1(f327(f35(a1),f306(a1,x37011,x37012))) % 177.41/177.18 [3702]P1(f327(f35(a1),f305(a1,x37021,x37022))) % 177.41/177.18 [3703]P1(f327(f35(a1),f303(a1,x37031,x37032))) % 177.41/177.18 [3809]E(f327(f310(a915,a915,a113),f303(a915,x38091,x38092)),f303(a915,f327(a113,x38091),f327(a113,x38092))) % 177.41/177.18 [3829]E(f327(f327(f289(x38291,x38291,x38291),f307(x38291,x38292)),f307(x38291,x38292)),f307(x38291,x38292)) % 177.41/177.18 [3864]E(f327(f327(f252(a1,a1),f327(f327(f37(a1),x38641),x38642)),f46(a1,x38641,x38642)),f47(x38641,x38642)) % 177.41/177.18 [3865]E(f327(f327(f252(a100,a100),f327(f327(f37(a100),x38651),x38652)),f46(a100,x38651,x38652)),f21(x38651,x38652)) % 177.41/177.18 [3892]E(f327(f327(f252(a915,a915),f327(f327(f37(a915),x38921),x38922)),f46(a915,x38921,x38922)),f85(f921(a915,a915),f49(x38921,x38922))) % 177.41/177.18 [3944]P1(f327(f327(f235(a915),f327(f327(f23(a915),x39441),x39442)),f327(a113,x39441))) % 177.41/177.18 [3994]P36(x39941,f327(f327(f289(x39941,x39941,x39941),x39942),f307(x39941,x39942))) % 177.41/177.18 [4045]E(f327(f327(f80(a1),f327(f327(f81(a1),x40451),f327(f327(f37(a1),x40452),x40451))),f46(a1,x40452,x40451)),x40452) % 177.41/177.18 [4049]E(f327(f327(f40(a915,f922(f921(f916(x40491),f916(x40491)),a910)),f242(f922(a915,a910))),f144(x40491,x40492)),f146(x40491,x40492)) % 177.41/177.18 [4273]P1(f327(f327(f329(f921(f916(x42731),f916(x42731))),f327(f327(f252(f916(x42731),f916(x42731)),f114(x42731)),f114(x42731))),f159(x42731,x42732))) % 177.41/177.18 [4383]E(f253(x43831,x43831,x43831,a324,f253(x43831,x43831,x43831,x43832,a324)),x43832) % 177.41/177.18 [4427]E(f258(x44271,x44271,x44272,x44272,f5(x44271),f5(x44272)),f31(f921(x44271,x44272))) % 177.41/177.18 [4429]E(f258(x44291,x44291,x44292,x44292,f31(x44291),f31(x44292)),f31(f921(x44291,x44292))) % 177.41/177.18 [3423]E(f327(f169(x34231),f327(f169(x34231),x34232)),x34232) % 177.41/177.18 [3425]E(f327(f327(f139(x34251),f2(a915)),x34252),x34252) % 177.41/177.18 [3441]E(f327(f327(f176(x34411),f2(a915)),x34412),f114(x34411)) % 177.41/177.18 [3448]E(f327(f327(f135(x34481),f114(x34481)),x34482),x34482) % 177.41/177.18 [3457]E(f38(f922(x34571,a910),f327(f308(x34571),x34572)),x34572) % 177.41/177.18 [3459]E(f327(f173(x34591),f327(f168(x34591),x34592)),f327(f173(x34591),x34592)) % 177.41/177.18 [3460]E(f327(f173(x34601),f327(f169(x34601),x34602)),f327(f173(x34601),x34602)) % 177.41/177.18 [3465]E(f327(f327(f23(a100),x34651),x34652),f327(f327(a24,x34651),x34652)) % 177.41/177.18 [3478]E(f327(f327(f80(a915),x34781),x34782),f327(f327(f80(a915),x34782),x34781)) % 177.41/177.18 [3479]E(f327(f327(f80(a1),x34791),x34792),f327(f327(f80(a1),x34792),x34791)) % 177.41/177.18 [3480]E(f327(f327(f81(a915),x34801),x34802),f327(f327(f81(a915),x34802),x34801)) % 177.41/177.18 [3481]E(f327(f327(f81(a1),x34811),x34812),f327(f327(f81(a1),x34812),x34811)) % 177.41/177.18 [3503]E(f327(f327(f184(x35031,x35031),f2(a915)),x35032),f31(x35031)) % 177.41/177.18 [3504]E(f327(f191(f916(x35041)),f327(f168(x35041),x35042)),f327(f191(f916(x35041)),x35042)) % 177.41/177.18 [3505]E(f327(f191(f916(x35051)),f327(f169(x35051),x35052)),f327(f191(f916(x35051)),x35052)) % 177.41/177.18 [3506]E(f177(x35061,x35062,f190(f922(a915,a910))),f114(x35061)) % 177.41/177.18 [3507]E(f327(f327(f155(x35071,x35071),f5(x35071)),x35072),x35072) % 177.41/177.18 [3509]E(f327(f251(a1,a1),f47(x35091,x35092)),f327(f327(f37(a1),x35091),x35092)) % 177.41/177.18 [3526]E(f327(f191(f916(x35261)),f153(x35261,x35262)),f327(f36(x35261),f327(f173(x35261),x35262))) % 177.41/177.18 [3527]E(f28(f29(x35271,x35272)),f327(f327(f80(a915),f28(x35272)),f327(a113,f2(a915)))) % 177.41/177.18 [3528]E(f327(f281(x35281),f327(f286(x35281,x35281),x35282)),f327(f281(x35281),x35282)) % 177.41/177.18 [3532]P1(f327(f35(x35321),f327(f173(x35321),x35322))) % 177.41/177.18 [3540]E(f327(f327(f80(a1),x35401),f327(f79(a1),x35402)),f327(f327(f23(a1),x35401),x35402)) % 177.41/177.18 [3547]P22(x35471,x35472,f190(f922(f913(x35471),a910))) % 177.41/177.18 [3549]E(f327(f310(x35491,x35491,f5(x35491)),x35492),x35492) % 177.41/177.18 [3550]E(f327(f310(x35501,x35501,f31(x35501)),x35502),x35502) % 177.41/177.18 [3551]E(f327(f311(x35511,x35511,f5(x35511)),x35512),x35512) % 177.41/177.18 [3552]E(f327(f311(x35521,x35521,f31(x35521)),x35522),x35522) % 177.41/177.18 [3553]P1(f327(f242(f922(x35531,a910)),x35532)) % 177.41/177.18 [3555]E(f327(f36(a915),f327(f302(a915,x35551),x35552)),f327(f327(f23(a915),x35552),x35551)) % 177.41/177.18 [3556]E(f327(f302(a915,f327(a113,x35561)),x35562),f306(a915,x35561,x35562)) % 177.41/177.18 [3569]E(f327(f327(f309(x35691),x35692),f190(f922(x35691,a910))),f327(f262(x35691),f327(a324,x35692))) % 177.41/177.18 [3574]E(f307(x35741,f327(f286(x35741,x35741),x35742)),f327(f286(x35741,x35741),f307(x35741,x35742))) % 177.41/177.18 [3579]E(f327(f327(f80(a915),f327(a113,x35791)),x35792),f327(f327(f80(a915),x35791),f327(a113,x35792))) % 177.41/177.18 [3580]E(f327(f327(f23(a915),f327(a113,x35801)),f327(a113,x35802)),f327(f327(f23(a915),x35801),x35802)) % 177.41/177.18 [3586]E(f56(x35861,f2(a915),x35862),f327(f327(f152(f916(x35861)),f114(x35861)),f114(f916(x35861)))) % 177.41/177.18 [3587]E(f327(f36(a915),f305(a915,x35871,x35872)),f327(f327(f23(a915),x35872),x35871)) % 177.41/177.18 [3596]P35(x35961,f327(f327(f288(a915,x35961),a240),x35962)) % 177.41/177.18 [3598]P11(a915,f140(a915,f327(f302(a915,x35981),x35982))) % 177.41/177.18 [3600]P1(f327(f35(a915),f327(f302(a915,x36001),x36002))) % 177.41/177.18 [3601]P1(f327(f35(a1),f327(f302(a1,x36011),x36012))) % 177.41/177.18 [3604]E(f327(f286(f916(x36041),f916(x36041)),f158(x36041,x36042)),f158(x36041,f327(f286(x36041,x36041),x36042))) % 177.41/177.18 [3605]E(f327(f191(a912),f29(x36051,x36052)),f327(f327(f80(a915),f327(f191(a912),x36052)),f327(a113,f2(a915)))) % 177.41/177.18 [3607]E(f327(f302(a1,x36071),f327(f327(f80(a1),x36072),f78(a1))),f303(a1,x36071,x36072)) % 177.41/177.18 [3610]E(f327(f327(f37(a1),f327(f79(a1),x36101)),f327(f79(a1),x36102)),f327(f327(f37(a1),x36101),x36102)) % 177.41/177.18 [3618]E(f327(f327(f184(f921(x36181,x36181),a910),f78(a915)),x36182),x36182) % 177.41/177.18 [3620]E(f327(f327(f23(f922(x36201,a910)),x36202),f190(f922(x36201,a910))),x36202) % 177.41/177.18 [3621]E(f327(f327(f102(f922(x36211,a910)),x36212),f190(f922(x36211,a910))),x36212) % 177.41/177.18 [3622]E(f327(f327(f103(f922(x36221,a910)),x36222),f242(f922(x36221,a910))),x36222) % 177.41/177.18 [3623]E(f327(f251(a915,a915),f85(f921(a915,a915),f49(x36231,x36232))),f327(f327(f37(a915),x36231),x36232)) % 177.41/177.18 [3630]E(f303(a1,f327(f327(f80(a1),x36301),f78(a1)),x36302),f305(a1,x36301,x36302)) % 177.41/177.18 [3635]E(f327(f256(a915,a915),f85(f921(a915,a915),f49(x36351,x36352))),f46(a915,x36351,x36352)) % 177.41/177.18 [3645]P1(f327(f327(f329(x36451),x36452),f242(f922(x36451,a910)))) % 177.41/177.18 [3650]E(f327(f327(f23(a915),f327(a113,x36501)),x36502),f327(f36(a915),f303(a915,x36502,x36501))) % 177.41/177.18 [3676]E(f327(f327(f23(f922(x36761,a910)),x36762),f242(f922(x36761,a910))),f190(f922(x36761,a910))) % 177.41/177.18 [3677]E(f327(f327(f102(f922(x36771,a910)),x36772),f242(f922(x36771,a910))),f242(f922(x36771,a910))) % 177.41/177.18 [3678]E(f327(f327(f103(f922(x36781,a910)),x36782),f190(f922(x36781,a910))),f190(f922(x36781,a910))) % 177.41/177.18 [3693]E(f46(a1,f327(f79(a1),x36931),f327(f79(a1),x36932)),f327(f79(a1),f46(a1,x36931,x36932))) % 177.41/177.18 [3694]E(f46(a1,f327(f101(a1),x36941),f327(f101(a1),x36942)),f327(f101(a1),f46(a915,x36941,x36942))) % 177.41/177.18 [3705]E(f327(f191(f916(x37051)),f327(f172(x37051),x37052)),f327(f327(f23(a915),f327(f191(f916(x37051)),x37052)),f78(a915))) % 177.41/177.18 [3731]E(f327(f327(f37(a1),f46(a1,x37311,x37312)),x37312),f2(a1)) % 177.41/177.18 [3740]E(f327(a3,f46(a915,f327(a20,x37401),f327(a20,x37402))),f46(a100,x37401,x37402)) % 177.41/177.18 [3775]E(f327(a3,f327(f327(f23(a915),f327(a20,x37751)),f327(a20,x37752))),f327(f327(f23(a100),x37751),x37752)) % 177.41/177.18 [3776]E(f327(a3,f327(f327(f80(a915),f327(a20,x37761)),f327(a20,x37762))),f327(f327(f80(a100),x37761),x37762)) % 177.41/177.18 [3777]E(f327(a3,f327(f327(f81(a915),f327(a20,x37771)),f327(a20,x37772))),f327(f327(f81(a100),x37771),x37772)) % 177.41/177.18 [3778]E(f327(a3,f327(f327(f37(a915),f327(a20,x37781)),f327(a20,x37782))),f327(f327(f37(a100),x37781),x37782)) % 177.41/177.18 [3787]E(f327(f310(a915,a915,a113),f327(f302(a915,x37871),x37872)),f327(f302(a915,f327(a113,x37871)),f327(a113,x37872))) % 177.41/177.18 [3814]P1(f327(f49(x38141,x38142),f85(f921(a915,a915),f49(x38141,x38142)))) % 177.41/177.18 [3838]E(f327(f327(f80(a915),f327(f327(f80(a915),f28(x38381)),f28(x38382))),f327(a113,f2(a915))),f28(f30(x38381,x38382))) % 177.41/177.18 [3839]E(f46(a915,f327(a113,f46(a915,x38391,x38392)),x38392),f46(a915,f327(a113,x38391),x38392)) % 177.41/177.18 [3851]E(f327(f327(f41(f922(x38511,a910),f922(x38511,a910)),x38512),f5(f922(x38511,a910))),f39(f922(x38511,a910),x38512)) % 177.41/177.18 [3852]E(f327(f327(f40(f922(x38521,a910),f922(x38521,a910)),x38522),f5(f922(x38521,a910))),f38(f922(x38521,a910),x38522)) % 177.41/177.18 [3853]E(f327(f310(f916(x38531),f922(x38531,a910),f173(x38531)),f327(f173(f916(x38531)),f55(x38531,x38532))),f327(f308(x38531),f327(f173(x38531),x38532))) % 177.41/177.18 [3857]P1(f327(f327(f329(f922(x38571,a910)),x38572),f327(f308(x38571),x38572))) % 177.41/177.18 [3863]E(f46(a1,f327(f79(a1),f46(a1,x38631,x38632)),x38632),f46(a1,f327(f79(a1),x38631),x38632)) % 177.41/177.18 [3874]P1(f327(f327(f234(f922(x38741,a910)),x38742),f242(f922(x38741,a910)))) % 177.41/177.18 [3876]E(f327(f327(f289(x38761,x38761,x38761),f307(x38761,x38762)),f307(x38761,f307(x38761,x38762))),f307(x38761,x38762)) % 177.41/177.18 [3877]E(f327(f327(f102(f922(x38771,a910)),f327(f264(x38771,x38771),x38772)),f327(f284(x38771,x38771),x38772)),f327(f281(x38771),x38772)) % 177.41/177.18 [3898]E(f313(x38981,x38982,f242(f922(x38981,a910)),f242(f922(x38982,a910))),f242(f922(f920(x38981,x38982),a910))) % 177.41/177.18 [3949]P1(f327(f327(f234(a915),f46(a915,x39491,x39492)),x39491)) % 177.41/177.18 [3973]P1(f327(f327(f234(a1),f327(f79(a1),f327(f101(a1),x39731))),f327(f101(a1),x39732))) % 177.41/177.18 [3999]P1(f327(f327(f329(f922(x39991,a910)),f190(f922(x39991,a910))),f327(f308(x39991),x39992))) % 177.41/177.18 [4004]E(f307(x40041,f327(f327(f289(x40041,x40041,x40041),x40042),f307(x40041,x40042))),f307(x40041,x40042)) % 177.41/177.18 [4007]E(f327(f327(f289(x40071,x40071,x40071),f307(x40071,x40072)),x40072),f327(f327(f289(x40071,x40071,x40071),x40072),f307(x40071,x40072))) % 177.41/177.18 [4009]E(f327(a106,f327(f327(f80(a1),f327(f327(f23(a1),x40091),x40092)),f78(a1))),f327(f36(a1),f303(a1,x40092,x40091))) % 177.41/177.18 [4024]E(f327(f284(x40241,x40241),f327(f327(f289(x40241,x40241,x40241),x40242),f307(x40241,x40242))),f327(f284(x40241,x40241),x40242)) % 177.41/177.18 [4025]E(f327(f264(x40251,x40251),f327(f327(f289(x40251,x40251,x40251),x40252),f307(x40251,x40252))),f327(f264(x40251,x40251),x40252)) % 177.41/177.18 [4041]E(f327(f327(f80(a915),f327(f327(f80(a915),f327(f191(a912),x40411)),f327(f191(a912),x40412))),f327(a113,f2(a915))),f327(f191(a912),f30(x40411,x40412))) % 177.41/177.18 [4044]E(f327(f143(f916(x40441),f916(x40441),f135(x40441),f114(x40441)),f170(f916(x40441),x40442,f114(x40441))),f114(x40441)) % 177.41/177.18 [4053]P23(a915,a915,f327(f327(f7(a915,a915,a915),f80(a915)),x40531),x40532) % 177.41/177.18 [4055]P11(a915,f327(f169(a915),f327(f327(f155(f916(x40551),a915),f191(f916(x40551))),f180(x40551,x40552)))) % 177.41/177.18 [4086]P49(x40861,f327(f327(f102(f922(f921(x40861,x40861),a910)),x40862),f327(f286(x40861,x40861),x40862))) % 177.41/177.18 [4087]P49(x40871,f327(f327(f103(f922(f921(x40871,x40871),a910)),x40872),f327(f286(x40871,x40871),x40872))) % 177.41/177.18 [4098]P1(f327(f327(f235(a1),f327(f79(a1),f327(f101(a1),f327(a113,x40981)))),f327(f101(a1),x40982))) % 177.41/177.18 [4143]E(f327(f143(f916(x41431),x41431,f327(f7(x41431,f916(x41431),f916(x41431)),f152(x41431)),f114(x41431)),x41432),f327(f169(x41431),x41432)) % 177.41/177.18 [4194]P1(f327(f327(f234(f922(f921(f916(x41941),f916(x41941)),a910)),f159(x41941,x41942)),f307(f916(x41941),f158(x41941,x41942)))) % 177.41/177.18 [4223]P1(f327(f49(x42231,x42232),f327(f327(f252(a915,a915),f327(f327(f37(a915),x42231),x42232)),f46(a915,x42231,x42232)))) % 177.41/177.18 [4235]P1(f327(f327(f234(f922(f921(f916(x42351),f916(x42351)),a910)),f158(x42351,f307(x42351,x42352))),f307(f916(x42351),f158(x42351,x42352)))) % 177.41/177.18 [4452]E(f327(f327(f259(f921(a100,a100),a100,f921(a100,a100),f921(x44521,f921(a100,a100))),f267(f327(f166(a100),f327(f327(f155(f921(a100,x44521),a100),f251(a100,x44521)),x44522)))),f327(f327(f8(x44521,f922(f921(a100,a100),f921(x44521,f921(a100,a100))),a100),f252(x44521,f921(a100,a100))),f268(x44521,x44522))),f266(x44521,x44522)) % 177.41/177.18 [4529]E(f225(a915,f921(x45291,f917(x45291)),f2(a915),f327(f257(x45291,f917(x45291),a915),f327(f16(f922(f917(x45291),a915),x45291),f327(f327(f7(f917(x45291),a915,a915),f327(f327(f8(a915,f922(a915,a915),f917(x45291)),f80(a915)),f191(f917(x45291)))),f78(a915)))),f327(f136(x45291),x45292)),f327(f191(f917(x45291)),x45292)) % 177.41/177.18 [4637]E(f327(f257(f922(f921(x46371,x46371),a910),f922(f921(x46371,x46371),a910),f922(f922(x46372,x46371),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910)))),f327(f327(f7(f922(f921(x46371,x46371),a910),f922(f922(f921(x46371,x46371),a910),f922(f922(x46372,x46371),f922(f921(x46372,x46372),a910))),f922(f922(f921(x46371,x46371),a910),f922(f922(x46372,x46371),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910))))),f327(f327(f8(f922(f922(f922(x46372,x46371),f922(f921(x46372,x46372),a910)),f922(f922(x46372,x46371),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910)))),f922(f922(f922(f921(x46371,x46371),a910),f922(f922(x46372,x46371),f922(f921(x46372,x46372),a910))),f922(f922(f921(x46371,x46371),a910),f922(f922(x46372,x46371),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910))))),f922(f921(x46371,x46371),a910)),f8(f922(f922(x46372,x46371),f922(f921(x46372,x46372),a910)),f922(f922(x46372,x46371),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910))),f922(f921(x46371,x46371),a910))),f327(f327(f8(f922(f922(x46372,x46371),f922(f922(f921(x46372,x46372),a910),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910)))),f922(f922(f922(x46372,x46371),f922(f921(x46372,x46372),a910)),f922(f922(x46372,x46371),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910)))),f922(f921(x46371,x46371),a910)),f18(f922(x46372,x46371),f922(f921(x46372,x46372),a910),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910)))),f327(f327(f8(f922(f922(x46372,x46371),f922(f921(x46372,x46372),a910)),f922(f922(x46372,x46371),f922(f922(f921(x46372,x46372),a910),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910)))),f922(f921(x46371,x46371),a910)),f327(f8(f922(f921(x46372,x46372),a910),f922(f922(f921(x46372,x46372),a910),f921(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910))),f922(x46372,x46371)),f252(f922(f921(x46372,x46372),a910),f922(f921(x46372,x46372),a910)))),f288(x46371,x46372))))),f288(x46371,x46372))),f73(x46371,x46372)) % 177.41/177.18 [4701]~E(f327(f308(x47011),x47012),f190(f922(f922(x47011,a910),a910))) % 177.41/177.18 [4712]~P1(f327(f327(f173(x47121),f114(x47121)),x47122)) % 177.41/177.18 [4716]~P1(f327(f327(f329(x47161),x47162),f190(f922(x47161,a910)))) % 177.41/177.18 [4724]~P1(f327(f327(f235(f922(x47241,a910)),x47242),f190(f922(x47241,a910)))) % 177.41/177.18 [3558]E(f327(f327(f23(a915),x35581),f327(f327(f80(a915),x35581),x35582)),f2(a915)) % 177.41/177.18 [3561]E(f327(f327(f102(f922(x35611,a910)),x35612),x35612),x35612) % 177.41/177.18 [3562]E(f327(f327(f103(f922(x35621,a910)),x35622),x35622),x35622) % 177.41/177.18 [3590]E(f327(f327(f23(f922(x35901,a910)),x35902),x35902),f190(f922(x35901,a910))) % 177.41/177.18 [3593]E(f327(f144(x35931,x35932),f2(a915)),f190(f922(f921(f916(x35931),f916(x35931)),a910))) % 177.41/177.18 [3594]E(f327(f327(f80(a915),x35941),f327(a113,x35942)),f327(a113,f327(f327(f80(a915),x35941),x35942))) % 177.41/177.18 [3606]E(f196(f327(f101(a1),x36061),f327(f101(a1),x36062)),f327(f101(a1),f327(f327(f23(a915),x36061),x36062))) % 177.41/177.18 [3609]E(f327(f327(f37(a1),f327(f79(a1),x36091)),x36092),f327(f327(f37(a1),x36091),f327(f79(a1),x36092))) % 177.41/177.18 [3613]E(f327(f36(a1),f327(f302(a1,x36131),x36132)),f327(a106,f327(f327(f23(a1),x36132),x36131))) % 177.41/177.18 [3616]E(f327(f327(f80(a915),f327(a113,x36161)),x36162),f327(a113,f327(f327(f80(a915),x36161),x36162))) % 177.41/177.18 [3619]E(f327(f79(f922(x36191,a910)),f327(f79(f922(x36191,a910)),x36192)),x36192) % 177.41/177.18 [3632]E(f180(x36321,f327(f327(f152(f916(x36321)),f114(x36321)),x36322)),f180(x36321,x36322)) % 177.41/177.18 [3636]E(f327(f327(f80(a915),x36361),f327(f327(f81(a915),x36361),x36362)),f327(f327(f81(a915),x36361),f327(a113,x36362))) % 177.41/177.18 [3643]E(f327(f327(a24,f327(a3,x36431)),f327(a3,x36432)),f327(a3,f327(f327(f23(a915),x36431),x36432))) % 177.41/177.18 [3658]E(f327(f327(f81(a1),f327(f79(a1),x36581)),x36582),f327(f79(a1),f327(f327(f81(a1),x36581),x36582))) % 177.41/177.18 [3660]E(f327(f327(f244(a1),f327(f101(a1),x36601)),x36602),f327(f101(a1),f327(f327(f244(a915),x36601),x36602))) % 177.41/177.18 [3661]E(f327(f327(f80(a100),f327(a3,x36611)),f327(a3,x36612)),f327(a3,f327(f327(f80(a915),x36611),x36612))) % 177.41/177.18 [3662]E(f327(f327(f81(a100),f327(a3,x36621)),f327(a3,x36622)),f327(a3,f327(f327(f81(a915),x36621),x36622))) % 177.41/177.18 [3663]E(f327(f327(f238(a915),f327(a113,x36631)),f327(a113,x36632)),f327(a113,f327(f327(f238(a915),x36631),x36632))) % 177.41/177.18 [3664]E(f327(f327(f189(a915),f327(a113,x36641)),f327(a113,x36642)),f327(a113,f327(f327(f189(a915),x36641),x36642))) % 177.41/177.18 [3669]E(f327(f173(a915),f140(a915,f327(f302(a915,x36691),x36692))),f327(f302(a915,x36691),x36692)) % 177.41/177.18 [3670]E(f312(x36701,f327(f327(f309(x36701),x36702),f190(f922(x36701,a910)))),x36702) % 177.41/177.18 [3674]E(f327(f284(x36741,x36742),f190(f922(f921(x36741,x36742),a910))),f190(f922(x36742,a910))) % 177.41/177.18 [3675]E(f327(f264(x36751,x36752),f190(f922(f921(x36751,x36752),a910))),f190(f922(x36751,a910))) % 177.41/177.18 [3679]E(f327(a106,f327(f327(f23(a1),x36791),x36792)),f327(f36(a1),f305(a1,x36792,x36791))) % 177.41/177.18 [3684]E(f327(f327(f80(a915),x36841),f327(f327(f81(a915),x36842),x36841)),f327(f327(f81(a915),f327(a113,x36842)),x36841)) % 177.41/177.18 [3686]E(f327(f327(f61(x36861),f190(f922(x36861,a910))),x36862),f190(f922(f922(x36861,a910),a910))) % 177.41/177.18 [3695]E(f327(f191(f916(a915)),f140(a915,f327(f302(a915,x36951),x36952))),f327(f327(f23(a915),x36952),x36951)) % 177.41/177.18 [3710]E(f327(f327(f102(f922(x37101,a910)),f190(f922(x37101,a910))),x37102),x37102) % 177.41/177.18 [3711]E(f327(f327(f103(f922(x37111,a910)),f242(f922(x37111,a910))),x37112),x37112) % 177.41/177.18 [3712]E(f327(f327(f80(a1),f327(f79(a1),x37121)),f327(f79(a1),x37122)),f327(f79(a1),f327(f327(f80(a1),x37121),x37122))) % 177.41/177.18 [3717]E(f327(f327(f80(a1),f327(f101(a1),x37171)),f327(f101(a1),x37172)),f327(f101(a1),f327(f327(f80(a915),x37171),x37172))) % 177.41/177.18 [3718]E(f327(f327(f80(a1),f327(f105(a1),x37181)),f327(f105(a1),x37182)),f327(f105(a1),f327(f327(f80(a1),x37181),x37182))) % 177.41/177.18 [3720]E(f327(f327(f81(a1),f327(f101(a1),x37201)),f327(f101(a1),x37202)),f327(f101(a1),f327(f327(f81(a915),x37201),x37202))) % 177.41/177.18 [3721]E(f327(f327(f81(a1),f327(f105(a1),x37211)),f327(f105(a1),x37212)),f327(f105(a1),f327(f327(f81(a1),x37211),x37212))) % 177.41/177.18 [3722]E(f327(f327(f37(a1),f327(f101(a1),x37221)),f327(f101(a1),x37222)),f327(f101(a1),f327(f327(f37(a915),x37221),x37222))) % 177.41/177.18 [3741]E(f327(f327(f6(x37411,a915),f327(f16(a915,x37411),f78(a915))),x37412),f327(f36(x37411),x37412)) % 177.41/177.18 [3748]E(f327(f79(a1),f46(a1,f327(f79(a1),x37481),x37482)),f46(a1,x37481,f327(f79(a1),x37482))) % 177.41/177.18 [3750]E(f327(f173(a1),f179(x37501,f327(f327(f23(a1),x37502),f78(a1)))),f327(f302(a1,x37501),x37502)) % 177.41/177.18 [3754]P1(f327(f327(f234(a915),x37541),f327(f327(f80(a915),x37542),x37541))) % 177.41/177.18 [3755]P1(f327(f327(f234(a915),x37551),f327(f327(f80(a915),x37551),x37552))) % 177.41/177.18 [3758]E(f327(f327(f23(f922(x37581,a910)),f190(f922(x37581,a910))),x37582),f190(f922(x37581,a910))) % 177.41/177.18 [3759]E(f327(f327(f102(f922(x37591,a910)),f242(f922(x37591,a910))),x37592),f242(f922(x37591,a910))) % 177.41/177.18 [3760]E(f327(f327(f103(f922(x37601,a910)),f190(f922(x37601,a910))),x37602),f190(f922(x37601,a910))) % 177.41/177.18 [3767]E(f327(f327(f252(a1,a1),x37671),f327(f79(a1),x37672)),f327(a52,f327(f327(f252(a1,a1),x37671),x37672))) % 177.41/177.18 [3768]E(f327(f302(a1,f327(f327(f80(a1),x37681),f78(a1))),x37682),f306(a1,x37681,x37682)) % 177.41/177.18 [3779]E(f327(f327(f81(a915),x37791),f327(f327(f37(a915),x37792),x37791)),f327(f327(f23(a915),x37792),f46(a915,x37792,x37791))) % 177.41/177.18 [3780]E(f327(f327(f81(a1),x37801),f327(f327(f37(a1),x37802),x37801)),f327(f327(f23(a1),x37802),f46(a1,x37802,x37801))) % 177.41/177.18 [3784]E(f327(f173(a1),f179(f327(f327(f80(a1),x37841),f78(a1)),x37842)),f305(a1,x37841,x37842)) % 177.41/177.18 [3788]P1(f327(f327(f234(f922(x37881,a910)),x37882),x37882)) % 177.41/177.18 [3791]E(f327(f327(f102(f922(x37911,a910)),x37912),f327(f79(f922(x37911,a910)),x37912)),f242(f922(x37911,a910))) % 177.41/177.18 [3792]E(f327(f327(f103(f922(x37921,a910)),x37922),f327(f79(f922(x37921,a910)),x37922)),f190(f922(x37921,a910))) % 177.41/177.18 [3800]E(f327(f327(f23(a915),f327(f327(f23(a915),x38001),f78(a915))),x38002),f327(f327(f23(a915),x38001),f327(a113,x38002))) % 177.41/177.18 [3806]E(f327(f327(f23(f922(x38061,a910)),f242(f922(x38061,a910))),x38062),f327(f79(f922(x38061,a910)),x38062)) % 177.41/177.18 [3807]E(f327(f327(f23(a1),f327(f105(a1),x38071)),f327(f105(a1),x38072)),f327(f105(a1),f327(f327(f80(a1),x38071),f327(f79(a1),x38072)))) % 177.41/177.18 [3820]E(f327(f173(a915),f140(a915,f327(f302(a915,x38201),f327(a113,x38202)))),f303(a915,x38201,x38202)) % 177.41/177.18 [3836]E(f327(f191(f916(f916(x38361))),f55(x38361,x38362)),f327(f327(f244(a915),f327(a113,f327(a113,f2(a915)))),f327(f191(f916(x38361)),x38362))) % 177.41/177.18 [3855]E(f327(f327(f184(f921(x38551,x38551),a910),f2(a915)),x38552),f307(x38551,f190(f922(f921(x38551,x38551),a910)))) % 177.41/177.18 [3859]P1(f327(f138(a915),f140(a915,f327(f302(a915,x38591),x38592)))) % 177.41/177.18 [3875]E(f327(f310(a1,a915,a106),f303(a1,f327(f101(a1),x38751),f327(f101(a1),x38752))),f303(a915,x38751,x38752)) % 177.41/177.18 [3884]E(f186(a915,f2(a915),f5(a915),f327(f327(f23(a915),x38841),x38842)),f327(f327(f23(a915),x38841),f327(a113,x38842))) % 177.41/177.18 [3885]E(f327(a106,f327(f327(f23(a1),x38851),f327(f327(f80(a1),x38852),f78(a1)))),f327(f36(a1),f306(a1,x38852,x38851))) % 177.41/177.18 [3921]E(f327(f327(f155(a915,a915),a113),f140(a915,f327(f302(a915,x39211),x39212))),f140(a915,f327(f302(a915,f327(a113,x39211)),f327(a113,x39212)))) % 177.41/177.18 [3929]E(f327(f173(a1),f179(f327(f327(f80(a1),x39291),f78(a1)),f327(f327(f23(a1),x39292),f78(a1)))),f306(a1,x39291,x39292)) % 177.41/177.18 [3941]P1(f327(f327(f234(f922(x39411,a910)),f190(f922(x39411,a910))),x39412)) % 177.41/177.18 [3945]E(f85(x39451,f327(f327(f7(x39451,x39451,a910),a324),x39452)),x39452) % 177.41/177.18 [3946]E(f90(x39461,f327(f327(f7(x39461,x39461,a910),a324),x39462)),x39462) % 177.41/177.18 [3950]E(f327(f173(a915),f140(a915,f327(f302(a915,f327(a113,x39501)),f327(a113,x39502)))),f305(a915,x39501,x39502)) % 177.41/177.18 [3976]E(f327(f327(f254(x39761,x39762),f242(f922(x39761,a910))),f327(f16(f922(x39762,a910),x39761),f242(f922(x39762,a910)))),f242(f922(f921(x39761,x39762),a910))) % 177.41/177.18 [4011]E(f327(f262(x40111),f327(f327(f8(a910,a910,x40111),a322),x40112)),f327(f79(f922(x40111,a910)),f327(f262(x40111),x40112))) % 177.41/177.18 [4014]E(f327(f262(x40141),f327(f327(f7(x40141,x40141,a910),a324),x40142)),f327(f327(f309(x40141),x40142),f190(f922(x40141,a910)))) % 177.41/177.18 [4021]E(f327(f327(f80(a1),f327(f327(f23(a1),x40211),x40212)),f327(f327(f23(a1),x40211),x40212)),f327(f327(f23(a1),f327(f327(f80(a1),x40211),x40211)),f327(f327(f80(a1),x40212),x40212))) % 177.41/177.18 [4022]E(f327(f327(f80(a1),f327(f327(f80(a1),x40221),x40221)),f327(f327(f80(a1),x40222),x40222)),f327(f327(f80(a1),f327(f327(f80(a1),x40221),x40222)),f327(f327(f80(a1),x40221),x40222))) % 177.41/177.18 [4038]P1(f327(f327(f234(a915),f327(f36(x40381),f327(f173(x40381),x40382))),f327(f191(f916(x40381)),x40382))) % 177.41/177.18 [4039]P1(f327(f327(f234(a915),f327(f191(f916(x40391)),f153(x40391,x40392))),f327(f191(f916(x40391)),x40392))) % 177.41/177.18 [4050]E(f327(f262(x40501),f327(f327(f7(x40501,f922(x40501,a910),a910),f329(x40501)),x40502)),x40502) % 177.41/177.18 [4064]E(f327(f327(f176(x40641),f327(f327(f23(a915),f327(f191(f916(x40641)),x40642)),f78(a915))),x40642),f115(x40641,x40642)) % 177.41/177.18 [4085]E(f186(a915,f2(a915),f327(f327(f8(a915,a915,a915),a113),f327(f238(a915),x40851)),x40852),f327(f327(f238(a915),f327(a113,x40851)),x40852)) % 177.41/177.18 [4090]E(f38(f922(x40901,a910),f327(f310(f922(f921(x40901,x40901),a910),f922(x40901,a910),f281(x40901)),x40902)),f327(f281(x40901),f38(f922(f921(x40901,x40901),a910),x40902))) % 177.41/177.18 [4091]E(f186(a915,f327(a113,x40911),f327(f327(f8(a915,a915,a915),a113),f327(f189(a915),x40911)),x40912),f327(f327(f189(a915),f327(a113,x40911)),x40912)) % 177.41/177.18 [4093]E(f327(f327(f252(a1,a1),f327(f327(f37(a1),f327(f75(a1),x40931)),f327(f75(a1),x40932))),f46(a1,f327(f75(a1),x40931),f327(f75(a1),x40932))),f54(x40931,x40932)) % 177.41/177.18 [4116]P1(f327(f327(f234(f922(f922(x41161,a910),a910)),x41162),f327(f308(x41161),f38(f922(x41161,a910),x41162)))) % 177.41/177.18 [4148]E(f327(f327(f40(x41481,f922(x41481,a910)),x41482),f327(f327(f7(x41481,f922(x41481,a910),f922(x41481,a910)),f309(x41481)),f190(f922(x41481,a910)))),x41482) % 177.41/177.18 [4149]E(f327(f327(f289(x41491,x41491,x41491),f327(f286(x41491,x41491),x41492)),f307(x41491,f327(f286(x41491,x41491),x41492))),f327(f286(x41491,x41491),f327(f327(f289(x41491,x41491,x41491),x41492),f307(x41491,x41492)))) % 177.41/177.18 [4215]E(f327(f173(x42151),f327(f143(f916(x42151),f916(x42151),f135(x42151),f114(x42151)),x42152)),f327(f327(f40(f916(x42151),f922(x42151,a910)),f327(f173(f916(x42151)),x42152)),f173(x42151))) % 177.41/177.18 [4246]E(f327(f327(f102(f922(f921(x42461,x42461),a910)),f307(x42461,f190(f922(f921(x42461,x42461),a910)))),f327(f327(f289(x42461,x42461,x42461),f307(x42461,x42462)),x42462)),f307(x42461,x42462)) % 177.41/177.18 [4282]E(f327(f327(f182(x42821,x42821),x42822),x42822),f327(f327(f155(x42821,f921(x42821,x42821)),f327(f327(f18(x42821,x42821,f921(x42821,x42821)),f252(x42821,x42821)),f5(x42821))),x42822)) % 177.41/177.18 [4394]E(f327(f143(a915,f916(x43941),f327(f7(f916(x43941),a915,a915),f327(f327(f8(a915,f922(a915,a915),f916(x43941)),f189(a915)),f191(f916(x43941)))),f2(a915)),f327(f169(f916(x43941)),x43942)),f327(f191(f916(f916(x43941))),f180(x43941,x43942))) % 177.41/177.18 [4466]E(f327(f327(f288(f921(a915,f916(x44661)),f916(x44661)),f320(a915,f916(x44661),a240,f146(x44661,x44662))),f327(f327(f18(f916(x44661),f916(x44661),f921(a915,f916(x44661))),f327(f327(f8(a915,f922(f916(x44661),f921(a915,f916(x44661))),f916(x44661)),f252(a915,f916(x44661))),f191(f916(x44661)))),f5(f916(x44661)))),f147(x44661,x44662)) % 177.41/177.18 [4593]E(f327(f262(x45931),f327(f327(f8(f922(f922(x45931,a910),a910),a910,x45931),f88(f922(x45931,a910))),f327(f327(f8(f922(f922(x45931,a910),a910),f922(f922(x45931,a910),a910),x45931),f327(f18(f922(x45931,a910),a910,a910),f327(f327(f8(a910,f922(a910,a910),f922(x45931,a910)),a330),f327(f327(f7(f922(x45931,a910),f922(f922(x45931,a910),a910),a910),f329(f922(x45931,a910))),x45932)))),f329(x45931)))),f39(f922(x45931,a910),x45932)) % 177.41/177.18 [4594]E(f327(f262(x45941),f327(f327(f8(f922(f922(x45941,a910),a910),a910,x45941),f87(f922(x45941,a910))),f327(f327(f8(f922(f922(x45941,a910),a910),f922(f922(x45941,a910),a910),x45941),f327(f18(f922(x45941,a910),a910,a910),f327(f327(f8(a910,f922(a910,a910),f922(x45941,a910)),a325),f327(f327(f7(f922(x45941,a910),f922(f922(x45941,a910),a910),a910),f329(f922(x45941,a910))),x45942)))),f329(x45941)))),f38(f922(x45941,a910),x45942)) % 177.41/177.18 [4725]~P1(f327(f327(f235(a1),f327(f101(a1),x47251)),f327(f79(a1),f327(f101(a1),x47252)))) % 177.41/177.18 [3682]E(f327(f327(f23(a915),f327(f327(f80(a915),x36821),x36822)),x36822),x36821) % 177.41/177.18 [3683]E(f327(f327(f23(a915),f327(f327(f80(a915),x36831),x36832)),x36831),x36832) % 177.41/177.18 [3749]E(f327(f327(f80(a915),f327(f327(f23(a915),x37491),x37492)),x37492),f327(f327(f189(a915),x37491),x37492)) % 177.41/177.18 [3862]E(f327(f327(f81(a915),f327(f327(f37(a915),x38621),x38622)),x38622),f327(f327(f23(a915),x38621),f46(a915,x38621,x38622))) % 177.41/177.18 [3889]E(f327(f173(a915),f140(a915,f327(f302(a915,f327(a113,x38891)),x38892))),f306(a915,x38891,x38892)) % 177.41/177.18 [3897]E(f327(f101(a1),f218(f327(a106,f327(f75(a1),x38971)),f327(a106,f327(f75(a1),x38972)))),f327(f327(a219,x38971),x38972)) % 177.41/177.18 [3899]E(f327(f327(f102(f922(x38991,a910)),f327(f79(f922(x38991,a910)),x38992)),x38992),f242(f922(x38991,a910))) % 177.41/177.18 [3900]E(f327(f327(f103(f922(x39001,a910)),f327(f79(f922(x39001,a910)),x39002)),x39002),f190(f922(x39001,a910))) % 177.41/177.18 [3917]P1(f327(f327(f234(a915),f327(f327(f23(a915),x39171),x39172)),x39171)) % 177.41/177.18 [3918]P1(f327(f327(f234(a915),f327(f327(f37(a915),x39181),x39182)),x39181)) % 177.41/177.18 [3942]P1(f327(f327(f235(a915),x39421),f327(a113,f327(f327(f80(a915),x39422),x39421)))) % 177.41/177.18 [3943]P1(f327(f327(f235(a915),x39431),f327(a113,f327(f327(f80(a915),x39431),x39432)))) % 177.41/177.18 [3960]E(f327(f327(f81(a915),f327(a106,f327(f75(a1),x39601))),f327(a106,f327(f75(a1),x39602))),f327(a106,f327(f75(a1),f327(f327(f81(a1),x39601),x39602)))) % 177.41/177.18 [3972]P1(f327(f327(f234(a1),f2(a1)),f327(f327(f244(a1),f327(f75(a1),x39721)),x39722))) % 177.41/177.18 [4043]E(f327(f285(f916(x40431),f916(x40431),f159(x40431,x40432)),f327(f327(f309(f916(x40431)),f114(x40431)),f190(f922(f916(x40431),a910)))),f327(f327(f309(f916(x40431)),f114(x40431)),f190(f922(f916(x40431),a910)))) % 177.41/177.18 [4062]E(f327(f327(f102(f922(f921(x40621,x40621),a910)),f307(x40621,x40622)),f307(x40621,f190(f922(f921(x40621,x40621),a910)))),f307(x40621,x40622)) % 177.41/177.18 [4075]E(f327(f327(f37(a1),f327(f105(a1),f327(f327(f80(a1),x40751),x40751))),f327(f105(a1),f327(f327(f80(a1),x40752),x40752))),f327(f327(f37(a1),f327(f105(a1),x40751)),f327(f105(a1),x40752))) % 177.41/177.18 [4138]E(f327(f327(f244(a1),x41381),f327(f105(a915),f327(f327(f80(a1),x41382),x41382))),f327(f327(f86(a1,a1),f327(f327(f244(a1),x41381),f327(f105(a915),x41382))),f327(f327(f18(a1,a1,a1),f81(a1)),f5(a1)))) % 177.41/177.18 [4144]E(f327(f262(f922(x41441,a910)),f327(f327(f7(f922(x41441,a910),f922(x41441,a910),a910),f234(f922(x41441,a910))),x41442)),f327(f308(x41441),x41442)) % 177.41/177.18 [4160]E(f327(f327(f155(a1,a915),a106),f327(f327(f135(a1),f327(f327(f155(a915,a1),f101(a1)),x41601)),f327(f327(f155(a915,a1),f101(a1)),x41602))),f327(f327(f135(a915),x41601),x41602)) % 177.41/177.18 [4193]E(f327(f310(a1,a1,f327(f327(f7(a1,a1,a1),f80(a1)),x41931)),f327(f302(a1,f2(a1)),f327(f327(f23(a1),x41932),x41931))),f327(f302(a1,x41931),x41932)) % 177.41/177.18 [4195]P51(x41951,f327(f327(f23(f922(f921(x41951,x41951),a910)),x41952),f307(x41951,f190(f922(f921(x41951,x41951),a910))))) % 177.41/177.18 [4213]E(f327(f191(f916(x42131)),f327(f143(f916(x42131),f916(x42131),f135(x42131),f114(x42131)),x42132)),f327(f166(a915),f327(f327(f155(f916(x42131),a915),f191(f916(x42131))),x42132))) % 177.41/177.18 [4217]P50(x42171,f242(f922(x42171,a910)),f327(f327(f102(f922(f921(x42171,x42171),a910)),x42172),f307(x42171,f190(f922(f921(x42171,x42171),a910))))) % 177.41/177.18 [4262]E(f186(a915,f2(a915),f327(f327(f8(a915,a915,a915),a113),f327(f327(f7(a915,a915,a915),f238(a915)),x42621)),x42622),f327(f327(f238(a915),x42622),f327(a113,x42621))) % 177.41/177.18 [4265]E(f186(a915,f327(a113,x42651),f327(f327(f8(a915,a915,a915),a113),f327(f327(f7(a915,a915,a915),f189(a915)),x42651)),x42652),f327(f327(f189(a915),x42652),f327(a113,x42651))) % 177.41/177.18 [4268]E(f327(f310(x42681,f916(x42681),f327(f327(f7(x42681,f916(x42681),f916(x42681)),f152(x42681)),f114(x42681))),x42682),f175(x42681,x42682,f327(f327(f309(f916(x42681)),f114(x42681)),f190(f922(f916(x42681),a910))))) % 177.41/177.18 [4270]E(f327(f327(f102(f922(f921(x42701,x42701),a910)),f327(f327(f289(x42701,x42701,x42701),x42702),f307(x42701,x42702))),f307(x42701,f190(f922(f921(x42701,x42701),a910)))),f307(x42701,x42702)) % 177.41/177.18 [4277]P1(f327(f327(f234(f922(f921(x42771,x42771),a910)),f263(x42771,x42772)),f327(f327(f254(x42771,x42771),x42772),f327(f16(f922(x42771,a910),x42771),x42772)))) % 177.41/177.18 [4280]E(f327(f310(a1,a915,a106),f327(f327(f102(f922(a1,a910)),f327(f310(a915,a1,f101(a1)),x42801)),f327(f310(a915,a1,f101(a1)),x42802))),f327(f327(f102(f922(a915,a910)),x42801),x42802)) % 177.41/177.18 [4281]E(f327(f310(a1,a915,a106),f327(f327(f103(f922(a1,a910)),f327(f310(a915,a1,f101(a1)),x42811)),f327(f310(a915,a1,f101(a1)),x42812))),f327(f327(f103(f922(a915,a910)),x42811),x42812)) % 177.41/177.18 [4284]E(f327(f262(x42841),f327(f327(f8(a910,a910,x42841),a322),f327(f327(f7(x42841,f922(x42841,a910),a910),f329(x42841)),x42842))),f327(f79(f922(x42841,a910)),x42842)) % 177.41/177.18 [4311]E(f327(f143(f916(x43111),f916(x43111),f135(x43111),f114(x43111)),f327(f327(f155(f916(x43111),f916(x43111)),f169(x43111)),f327(f169(f916(x43111)),x43112))),f327(f169(x43111),f327(f143(f916(x43111),f916(x43111),f135(x43111),f114(x43111)),x43112))) % 177.41/177.18 [4338]E(f327(f327(f40(a915,f922(f921(x43381,x43381),a910)),f242(f922(a915,a910))),f327(f327(f7(a915,f922(f921(x43381,x43381),a910),f922(f921(x43381,x43381),a910)),f184(f921(x43381,x43381),a910)),x43382)),f307(x43381,x43382)) % 177.41/177.18 [4356]E(f85(x43561,f327(f327(f8(f922(x43561,a910),a910,x43561),f327(a324,x43562)),f327(f327(f7(x43561,f922(x43561,a910),f922(x43561,a910)),f309(x43561)),f190(f922(x43561,a910))))),f312(x43561,x43562)) % 177.41/177.18 [4364]E(f327(f191(f916(x43641)),f153(x43641,f327(f143(f916(x43641),f916(x43641),f135(x43641),f114(x43641)),x43642))),f327(f36(x43641),f327(f327(f40(f916(x43641),f922(x43641,a910)),f327(f173(f916(x43641)),x43642)),f173(x43641)))) % 177.41/177.18 [4378]E(f327(f327(f102(f922(f921(x43781,x43781),a910)),x43782),f327(f327(f289(x43781,x43781,x43781),f327(f327(f289(x43781,x43781,x43781),x43782),f307(x43781,x43782))),x43782)),f327(f327(f289(x43781,x43781,x43781),x43782),f307(x43781,x43782))) % 177.41/177.18 [4402]P1(f327(f327(f234(f922(f921(x44021,x44021),a910)),f327(f327(f289(x44021,x44021,x44021),x44022),f307(x44021,x44022))),f327(f327(f254(x44021,x44021),f327(f281(x44021),x44022)),f327(f16(f922(x44021,a910),x44021),f327(f281(x44021),x44022))))) % 177.41/177.18 [4443]E(f327(f262(f916(x44431)),f327(f327(f7(f916(x44431),f922(x44431,a910),a910),f327(f327(f8(f922(x44431,a910),f922(f922(x44431,a910),a910),f916(x44431)),f234(f922(x44431,a910))),f173(x44431))),x44432)),f162(x44431,x44432)) % 177.41/177.18 [4454]E(f327(f157(f916(x44541),x44541,f114(x44541),f327(f327(f8(f916(x44541),f922(f916(x44541),f916(x44541)),x44541),f327(f7(f916(x44541),f916(x44541),f916(x44541)),f135(x44541))),f327(f327(f7(x44541,f916(x44541),f916(x44541)),f152(x44541)),f114(x44541)))),x44542),f327(f168(x44541),x44542)) % 177.41/177.18 [4494]P23(f922(x44941,x44942),f922(f921(x44941,x44942),a910),f327(f327(f8(f922(f921(x44941,x44942),a910),f922(f921(x44941,x44942),a910),f922(x44941,x44942)),f262(f921(x44941,x44942))),f327(f327(f8(f922(x44941,f922(x44942,a910)),f922(f921(x44941,x44942),a910),f922(x44941,x44942)),f257(x44941,x44942,a910)),f327(f8(x44942,f922(x44942,a910),x44941),f327(f7(x44942,x44942,a910),a324)))),f242(f922(f922(x44941,x44942),a910))) % 177.41/177.18 [4499]E(f46(a1,f327(f105(a1),f327(f327(f80(a1),x44991),x44991)),f327(f105(a1),f327(f327(f80(a1),x44992),x44992))),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f46(a1,f327(f105(a1),x44991),f327(f105(a1),x44992)))) % 177.41/177.18 [4543]E(f327(f327(f40(x45431,f922(f921(x45431,x45431),a910)),x45432),f327(f327(f7(x45431,f922(f921(x45431,x45431),a910),f922(f921(x45431,x45431),a910)),f327(f327(f8(f921(x45431,x45431),f922(f922(f921(x45431,x45431),a910),f922(f921(x45431,x45431),a910)),x45431),f309(f921(x45431,x45431))),f327(f327(f18(x45431,x45431,f921(x45431,x45431)),f252(x45431,x45431)),f5(x45431)))),f190(f922(f921(x45431,x45431),a910)))),f263(x45431,x45432)) % 177.41/177.18 [4551]E(f204(x45511,f327(f327(f252(a1,a1),f327(f79(a1),f327(f327(f72(f921(a1,a1),a1,x45511,f251(a1,a1)),f214(x45511)),x45512))),f327(f327(f72(f921(a1,a1),a1,x45511,f256(a1,a1)),f214(x45511)),x45512))),f229(x45511,x45512)) % 177.41/177.18 [4633]E(f327(f262(f922(x46331,a910)),f327(f327(f8(f922(f922(x46331,a910),a910),a910,f922(x46331,a910)),f87(f922(x46331,a910))),f327(f327(f7(f922(x46331,a910),f922(f922(x46331,a910),a910),f922(f922(x46331,a910),a910)),f327(f327(f8(f922(f922(x46331,a910),f922(a910,a910)),f922(f922(f922(x46331,a910),a910),f922(f922(x46331,a910),a910)),f922(x46331,a910)),f18(f922(x46331,a910),a910,a910)),f327(f327(f8(f922(f922(x46331,a910),a910),f922(f922(x46331,a910),f922(a910,a910)),f922(x46331,a910)),f327(f8(a910,f922(a910,a910),f922(x46331,a910)),a325)),f327(f327(f7(f922(x46331,a910),f922(f922(x46331,a910),f922(x46331,a910)),f922(f922(x46331,a910),a910)),f327(f327(f8(f922(f922(x46331,a910),a910),f922(f922(f922(x46331,a910),f922(x46331,a910)),f922(f922(x46331,a910),a910)),f922(x46331,a910)),f8(f922(x46331,a910),a910,f922(x46331,a910))),a324)),f79(f922(x46331,a910)))))),f327(f327(f8(f922(f922(x46331,a910),a910),a910,f922(x46331,a910)),f327(f329(f922(x46331,a910)),x46332)),f308(x46331))))),f327(f308(x46331),f327(f79(f922(x46331,a910)),x46332))) % 177.41/177.18 [4723]~E(f327(f327(f80(a1),x47231),x47231),f327(f327(f23(a1),f327(f327(f80(a1),x47232),x47232)),a98)) % 177.41/177.18 [4727]~P1(f327(f327(f235(a915),f327(f327(f80(a915),x47271),x47272)),x47272)) % 177.41/177.18 [4728]~P1(f327(f327(f235(a915),f327(f327(f80(a915),x47281),x47282)),x47281)) % 177.41/177.18 [3977]E(f327(f327(f23(a915),x39771),f327(f327(f81(a915),f327(f327(f37(a915),x39771),x39772)),x39772)),f46(a915,x39771,x39772)) % 177.41/177.18 [3978]E(f327(f327(f23(a1),x39781),f327(f327(f81(a1),f327(f327(f37(a1),x39781),x39782)),x39782)),f46(a1,x39781,x39782)) % 177.41/177.18 [4012]E(f327(f327(f155(a915,x40121),f327(f165(x40121),x40122)),f140(a915,f327(f302(a915,f2(a915)),f327(f191(f916(x40121)),x40122)))),x40122) % 177.41/177.18 [4071]E(f327(f285(x40711,x40711,f307(x40711,f190(f922(f921(x40711,x40711),a910)))),x40712),x40712) % 177.41/177.18 [4198]E(f307(x41981,f327(f327(f23(f922(f921(x41981,x41981),a910)),x41982),f307(x41981,f190(f922(f921(x41981,x41981),a910))))),f307(x41981,x41982)) % 177.41/177.18 [4199]E(f307(x41991,f327(f327(f102(f922(f921(x41991,x41991),a910)),x41992),f307(x41991,f190(f922(f921(x41991,x41991),a910))))),f307(x41991,x41992)) % 177.41/177.18 [4249]E(f327(f327(f23(a1),f327(f327(f23(a1),f327(f327(f80(a1),x42491),x42491)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),x42492),x42492)),a98)),f327(f327(f80(a1),f327(f327(f23(a1),x42491),x42492)),f327(f327(f23(a1),x42491),x42492))) % 177.41/177.18 [4289]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f80(a1),x42891),x42892)),f327(f327(f80(a1),x42891),x42892))),a98),f327(f327(f80(a1),f327(f327(f80(a1),x42891),x42891)),f327(f327(f23(a1),f327(f327(f80(a1),x42892),x42892)),a98))) % 177.41/177.18 [4314]E(f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),x43141),x43141)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),x43142),x43142)),a98)),f327(f327(f80(a1),f327(f327(f80(a1),x43141),f327(f327(f23(a1),x43142),a98))),f327(f327(f80(a1),x43141),f327(f327(f23(a1),x43142),a98)))) % 177.41/177.18 [4326]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),x43261),x43262)),f327(f327(f23(a1),x43261),x43262))),a98),f327(f327(f23(a1),f327(f327(f23(a1),f327(f327(f80(a1),x43261),x43261)),a98)),f327(f327(f80(a1),x43262),x43262))) % 177.41/177.18 [4327]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f80(a1),x43271),x43272)),f327(f327(f80(a1),x43271),x43272))),a98),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),x43271),x43271)),a98)),f327(f327(f80(a1),x43272),x43272))) % 177.41/177.18 [4375]E(f327(f101(a1),f327(f327(f37(a915),f327(f327(f81(a915),f327(a106,f327(f75(a1),x43751))),f327(a106,f327(f75(a1),x43752)))),f218(f327(a106,f327(f75(a1),x43751)),f327(a106,f327(f75(a1),x43752))))),f220(x43751,x43752)) % 177.41/177.18 [4420]E(f327(f327(f259(f921(a100,a100),a100,f921(a100,a100),f921(x44201,f921(a100,a100))),f267(f327(a3,f327(f191(f916(x44201)),x44202)))),f327(f327(f8(x44201,f922(f921(a100,a100),f921(x44201,f921(a100,a100))),a100),f252(x44201,f921(a100,a100))),f327(f327(f8(a915,x44201,a100),f327(f165(x44201),x44202)),a20))),f275(x44201,x44202)) % 177.41/177.18 [4500]E(f327(f143(a915,f916(x45001),f327(f7(f916(x45001),a915,a915),f327(f327(f8(a915,f922(a915,a915),f916(x45001)),f189(a915)),f191(f916(x45001)))),f2(a915)),f327(f169(f916(x45001)),f180(x45001,x45002))),f327(f191(f916(f916(x45001))),f327(f137(f916(x45001),f327(f327(f8(a910,a910,f916(x45001)),a322),f327(f327(f7(f916(x45001),f916(x45001),a910),a324),f114(x45001)))),x45002))) % 177.41/177.18 [4506]E(f327(f327(f40(a915,f922(x45061,a910)),f242(f922(a915,a910))),f327(f327(f7(a915,f922(a915,f922(x45061,a910)),f922(x45061,a910)),f327(f327(f8(f922(a915,a910),f922(f922(a915,f922(x45061,a910)),f922(x45061,a910)),a915),f40(a915,f922(x45061,a910))),f302(a915,f2(a915)))),x45062)),f327(f327(f40(a915,f922(x45061,a910)),f242(f922(a915,a910))),x45062)) % 177.41/177.18 [4528]P1(f327(f35(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),x45281)),f327(f327(f7(a915,a915,a910),f235(a915)),x45282))))) % 177.41/177.18 [4642]E(f327(f262(f921(f916(x46421),f916(x46421))),f327(f257(f916(x46421),f916(x46421),a910),f327(f327(f18(f916(x46421),f922(f916(x46421),a910),f922(f916(x46421),a910)),f327(f327(f8(f922(f916(x46421),f922(a910,a910)),f922(f922(f916(x46421),a910),f922(f916(x46421),a910)),f916(x46421)),f18(f916(x46421),a910,a910)),f327(f327(f8(f922(f916(x46421),a910),f922(f916(x46421),f922(a910,a910)),f916(x46421)),f327(f8(a910,f922(a910,a910),f916(x46421)),a326)),f327(f327(f7(f916(x46421),f922(f916(x46421),a915),f922(f916(x46421),a910)),f327(f327(f8(f922(a915,a910),f922(f922(f916(x46421),a915),f922(f916(x46421),a910)),f916(x46421)),f8(a915,a910,f916(x46421))),f327(f327(f8(a915,f922(a915,a910),f916(x46421)),f235(a915)),f191(f916(x46421))))),f191(f916(x46421)))))),f327(f327(f18(f916(x46421),f922(f916(x46421),a910),f922(f916(x46421),a910)),f327(f327(f8(f922(f916(x46421),f922(a910,a910)),f922(f922(f916(x46421),a910),f922(f916(x46421),a910)),f916(x46421)),f18(f916(x46421),a910,a910)),f327(f327(f8(f922(f916(x46421),a910),f922(f916(x46421),f922(a910,a910)),f916(x46421)),f327(f8(a910,f922(a910,a910),f916(x46421)),a325)),f327(f327(f7(f916(x46421),f922(f916(x46421),a915),f922(f916(x46421),a910)),f327(f327(f8(f922(a915,a910),f922(f922(f916(x46421),a915),f922(f916(x46421),a910)),f916(x46421)),f8(a915,a910,f916(x46421))),f327(f327(f8(a915,f922(a915,a910),f916(x46421)),a324),f191(f916(x46421))))),f191(f916(x46421)))))),f327(f327(f7(f916(x46421),f922(f921(f916(x46421),f916(x46421)),a910),f922(f916(x46421),a910)),f327(f327(f8(f922(f916(x46421),f922(f922(f921(f916(x46421),f916(x46421)),a910),a910)),f922(f922(f921(f916(x46421),f916(x46421)),a910),f922(f916(x46421),a910)),f916(x46421)),f7(f916(x46421),f922(f921(f916(x46421),f916(x46421)),a910),a910)),f327(f327(f8(f922(f916(x46421),f921(f916(x46421),f916(x46421))),f922(f916(x46421),f922(f922(f921(f916(x46421),f916(x46421)),a910),a910)),f916(x46421)),f327(f8(f921(f916(x46421),f916(x46421)),f922(f922(f921(f916(x46421),f916(x46421)),a910),a910),f916(x46421)),f329(f921(f916(x46421),f916(x46421))))),f252(f916(x46421),f916(x46421))))),f146(x46421,x46422)))))),f147(x46421,x46422)) % 177.41/177.18 [4318]E(f327(f327(f80(a1),f327(f327(f80(a1),f327(f327(f81(a1),x43181),x43182)),f327(f327(f81(a1),x43181),x43182))),x43182),f327(f327(f81(a1),f327(f327(f23(a1),f327(f327(f80(a1),x43181),x43181)),a98)),x43182)) % 177.41/177.18 [4419]E(f327(a106,f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x44191),x44192)),f190(f922(f921(a915,a915),a910)))))),f327(f327(f23(a915),x44191),x44192)) % 177.41/177.18 [4423]E(f327(f327(f289(x44231,x44231,x44231),f327(f327(f102(f922(f921(x44231,x44231),a910)),x44232),f307(x44231,f190(f922(f921(x44231,x44231),a910))))),f307(x44231,f327(f327(f102(f922(f921(x44231,x44231),a910)),x44232),f307(x44231,f190(f922(f921(x44231,x44231),a910)))))),f307(x44231,x44232)) % 177.41/177.18 [4460]E(f268(x44601,f327(f137(f921(a100,x44601),f327(f257(a100,x44601,a910),f327(f327(f8(a910,f922(x44601,a910),a100),f16(a910,x44601)),f327(f235(a100),f2(a100))))),x44602)),f268(x44601,x44602)) % 177.41/177.18 [4461]E(f266(x44611,f327(f137(f921(a100,x44611),f327(f257(a100,x44611,a910),f327(f327(f8(a910,f922(x44611,a910),a100),f16(a910,x44611)),f327(f235(a100),f2(a100))))),x44612)),f266(x44611,x44612)) % 177.41/177.18 [4463]E(f327(f79(a1),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x44631),x44632)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x44632),x44631)),f190(f922(f921(a915,a915),a910)))))) % 177.41/177.18 [4519]E(f327(f327(f288(f916(a915),x45191),f146(a915,a240)),f327(f327(f7(x45191,f916(f922(x45191,a915)),f916(a915)),f327(f327(f8(f922(f922(x45191,a915),a915),f922(f916(f922(x45191,a915)),f916(a915)),x45191),f155(f922(x45191,a915),a915)),f327(f7(f922(x45191,a915),x45191,a915),f5(f922(x45191,a915))))),x45192)),f154(x45191,x45192)) % 177.41/177.18 [4540]E(f327(f327(f86(a1,a915),f327(f105(a1),f327(f327(f80(a1),x45401),a98))),f327(f327(f18(a1,a915,a915),f327(f327(f7(a1,a915,f922(a915,a915)),f327(f327(f8(a910,f922(a915,f922(a915,a915)),a1),f97(a915)),a195)),f2(a915))),f327(f327(f8(a915,a915,a1),a113),f327(f327(f8(a915,a915,a1),f327(f238(a915),x45402)),a106)))),f327(f327(f238(a915),f327(a113,x45402)),f327(f105(a915),x45401))) % 177.41/177.18 [4541]E(f327(f327(f86(a1,a915),f327(f105(a1),f327(f327(f80(a1),x45411),a98))),f327(f327(f18(a1,a915,a915),f327(f327(f7(a1,a915,f922(a915,a915)),f327(f327(f8(a910,f922(a915,f922(a915,a915)),a1),f97(a915)),a195)),f327(a113,x45412))),f327(f327(f8(a915,a915,a1),a113),f327(f327(f8(a915,a915,a1),f327(f189(a915),x45412)),a106)))),f327(f327(f189(a915),f327(a113,x45412)),f327(f105(a915),x45411))) % 177.41/177.18 [4561]E(f327(f143(f916(x45611),f916(x45611),f135(x45611),f114(x45611)),f327(f327(f155(f916(x45611),f916(x45611)),f157(f916(x45611),x45611,f114(x45611),f327(f327(f8(f916(x45611),f922(f916(x45611),f916(x45611)),x45611),f16(f916(x45611),f916(x45611))),f327(f327(f7(x45611,f916(x45611),f916(x45611)),f152(x45611)),f114(x45611))))),x45612)),f327(f327(f155(f916(x45611),x45611),f142(x45611)),f327(f137(f916(x45611),f327(f327(f8(a910,a910,f916(x45611)),a322),f327(f327(f7(f916(x45611),f916(x45611),a910),a324),f114(x45611)))),x45612))) % 177.41/177.18 [4624]E(f327(f257(a1,a1,a910),f327(f327(f7(a1,f922(a1,a910),f922(a1,a910)),f327(f327(f8(f922(a1,f922(a910,a910)),f922(f922(a1,a910),f922(a1,a910)),a1),f18(a1,a910,a910)),f327(f327(f8(f922(a1,a910),f922(a1,f922(a910,a910)),a1),f327(f8(a910,f922(a910,a910),a1),a325)),f327(f327(f8(f922(a1,a1),f922(a1,a910),a1),f327(f8(a1,a910,a1),f327(a324,x46241))),f327(f327(f8(a1,f922(a1,a1),a1),f80(a1)),f327(f81(a1),x46242)))))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),f327(a330,f327(f327(f235(a1),f2(a1)),x46242))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),f327(f327(f7(a1,a1,a910),f235(a1)),x46242))))),f327(f327(f8(a910,a910,a1),f327(a330,f327(a322,f327(f327(f235(a1),f2(a1)),x46242)))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f235(a1),x46242))),f327(f327(f7(a1,a1,a910),f234(a1)),f2(a1))))))),f50(x46241,x46242)) % 177.41/177.18 [4627]E(f327(f262(x46271),f327(f327(f8(f922(a915,a910),a910,x46271),f87(a915)),f327(f327(f7(x46271,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),x46271),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),x46271),f327(f8(a910,f922(a910,a910),a915),a325)),f327(f327(f7(x46271,f922(a915,x46271),f922(a915,a910)),f327(f327(f8(f922(x46271,a910),f922(f922(a915,x46271),f922(a915,a910)),x46271),f8(x46271,a910,a915)),a324)),f327(f165(x46271),x46272))))),f327(f327(f7(a915,a915,a910),f235(a915)),f327(f191(f916(x46271)),x46272))))),f327(f173(x46271),x46272)) % 177.41/177.18 [4433]E(f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),x44331),a98)),x44332)),f327(f327(f23(a1),f327(f327(f80(a1),x44331),a98)),x44332))),a98),f327(f327(f23(a1),f327(f327(f80(a1),x44331),x44331)),f327(f327(f23(a1),f327(f327(f80(a1),x44332),x44332)),a98))) % 177.41/177.18 [4556]E(f327(f143(f916(f916(x45561)),f916(f916(x45561)),f135(f916(x45561)),f114(f916(x45561))),f327(f327(f155(f916(x45561),f916(f916(x45561))),f157(f916(f916(x45561)),x45561,f114(f916(x45561)),f327(f16(f922(f916(x45561),f916(f916(x45561))),x45561),f327(f327(f7(f916(x45561),f916(f916(x45561)),f916(f916(x45561))),f152(f916(x45561))),f114(f916(x45561)))))),x45562)),f327(f327(f155(f916(x45561),f916(x45561)),f172(x45561)),f327(f137(f916(x45561),f327(f327(f8(a910,a910,f916(x45561)),a322),f327(f327(f7(f916(x45561),f916(x45561),a910),a324),f114(x45561)))),x45562))) % 177.41/177.18 [4566]E(f327(f327(f86(a1,a915),f327(f105(a1),f327(f327(f80(a1),x45661),a98))),f327(f327(f18(a1,a915,a915),f327(f327(f7(a1,a915,f922(a915,a915)),f327(f327(f8(a910,f922(a915,f922(a915,a915)),a1),f97(a915)),a195)),f2(a915))),f327(f327(f8(a915,a915,a1),a113),f327(f327(f7(a1,a915,a915),f327(f327(f8(a915,f922(a915,a915),a1),f238(a915)),a106)),x45662)))),f327(f327(f238(a915),f327(f105(a915),x45661)),f327(a113,x45662))) % 177.41/177.18 [4567]E(f327(f327(f86(a1,a915),f327(f105(a1),f327(f327(f80(a1),x45671),a98))),f327(f327(f18(a1,a915,a915),f327(f327(f7(a1,a915,f922(a915,a915)),f327(f327(f8(a910,f922(a915,f922(a915,a915)),a1),f97(a915)),a195)),f327(a113,x45672))),f327(f327(f8(a915,a915,a1),a113),f327(f327(f7(a1,a915,a915),f327(f327(f8(a915,f922(a915,a915),a1),f189(a915)),a106)),x45672)))),f327(f327(f189(a915),f327(f105(a915),x45671)),f327(a113,x45672))) % 177.41/177.18 [4555]E(f327(f257(x45551,x45551,a910),f327(f327(f18(x45551,a910,f922(x45551,a910)),f327(f327(f8(f922(x45551,f922(a910,a910)),f922(a910,f922(x45551,a910)),x45551),f7(x45551,a910,a910)),f327(f327(f8(f922(x45551,a910),f922(x45551,f922(a910,a910)),x45551),f327(f8(a910,f922(a910,a910),x45551),a325)),a324))),x45552)),f263(x45551,x45552)) % 177.41/177.18 [4600]E(f327(f327(f37(a915),x46001),f327(f327(f80(a915),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),x46002)),f327(f327(f37(a915),x46001),f327(a113,f327(a113,f327(a113,x46002))))) % 177.41/177.18 [4601]E(f46(a915,x46011,f327(f327(f80(a915),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),x46012)),f46(a915,x46011,f327(a113,f327(a113,f327(a113,x46012))))) % 177.41/177.18 [4602]E(f46(a915,f327(f327(f80(a915),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),x46021),x46022),f46(a915,f327(a113,f327(a113,f327(a113,x46021))),x46022)) % 177.41/177.18 [4614]E(f124(f327(x46141,f327(f327(f81(a100),f327(f105(a100),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),x46142))),f327(f202(x46141),x46142)) % 177.41/177.18 [4615]E(f327(f327(f37(a915),f327(f327(f80(a915),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),x46151)),x46152),f327(f327(f37(a915),f327(a113,f327(a113,f327(a113,x46151)))),x46152)) % 177.41/177.18 [4674]~E(f27(x46741,x46742,x46743),a25) % 177.41/177.18 [4675]~E(f26(x46751,x46752,x46753),a25) % 177.41/177.18 [4679]~E(f127(x46791,x46792,x46793),f120(x46791)) % 177.41/177.18 [3407]E(f327(f194(x34071,x34072),x34073),f122(x34071,x34072)) % 177.41/177.18 [3426]E(f327(f201(x34261,x34262),x34263),f327(f130(x34261),x34262)) % 177.41/177.18 [3502]E(f327(f327(f155(x35021,x35022),x35023),f114(x35021)),f114(x35022)) % 177.41/177.18 [3542]E(f327(f185(x35421,x35422,x35423),f2(a915)),x35422) % 177.41/177.18 [3544]E(f327(f327(f182(x35441,x35442),x35443),f114(x35442)),f114(f921(x35441,x35442))) % 177.41/177.18 [3559]E(f327(f191(f916(x35591)),f170(x35591,x35592,x35593)),x35592) % 177.41/177.18 [3578]E(f85(x35781,f62(x35781,x35782,x35783)),f327(f63(x35781,x35782),x35783)) % 177.41/177.18 [3582]E(f243(x35821,x35822,f243(x35822,x35821,x35823)),x35823) % 177.41/177.18 [3602]E(f327(f169(x36021),f170(x36021,x36022,x36023)),f170(x36021,x36022,x36023)) % 177.41/177.18 [3629]E(f141(x36291,x36292,f153(x36291,x36293)),f153(x36291,f141(x36291,x36292,x36293))) % 177.41/177.18 [3648]E(f327(f251(f916(x36481),f916(x36481)),f167(x36481,x36482,x36483)),f327(f137(x36481,x36482),x36483)) % 177.41/177.18 [3691]E(f327(f327(f152(x36911),x36912),f170(x36911,x36913,x36912)),f170(x36911,f327(a113,x36913),x36912)) % 177.41/177.18 [3723]E(f186(x37231,x37232,x37233,f2(a915)),x37232) % 177.41/177.18 [3724]E(f17(x37241,x37242,x37243,f2(a100)),x37242) % 177.41/177.18 [3725]E(f19(x37251,x37252,x37253,f2(a100)),x37252) % 177.41/177.18 [3732]E(f164(x37321,x37322,x37323,f114(x37321)),f114(x37322)) % 177.41/177.18 [3733]E(f131(x37331,x37332,x37333,f120(x37331)),f120(x37332)) % 177.41/177.18 [3739]E(f327(f327(f165(x37391),f327(f327(f152(x37391),x37392),x37393)),f2(a915)),x37392) % 177.41/177.18 [3769]E(f60(x37691,x37692,f114(x37691),x37693),f114(f921(x37691,x37692))) % 177.41/177.18 [3790]P23(x37901,x37902,x37903,f190(f922(x37901,a910))) % 177.41/177.18 [3893]E(f265(x38931,x38932,x38933),f327(f252(f922(a100,f922(a910,f918(f917(x38931)))),f921(a100,a100)),f42(x38931))) % 177.41/177.18 [3951]E(f327(f72(x39511,x39512,x39511,x39513),f31(x39511)),x39513) % 177.41/177.18 [4130]P1(f327(f327(f329(f921(x41301,x41301)),f327(f327(f252(x41301,x41301),x41302),x41302)),f307(x41301,x41303))) % 177.41/177.18 [4732]~P1(f327(f327(f329(f921(f916(x47321),f916(x47321))),f327(f327(f252(f916(x47321),f916(x47321)),x47322),f114(x47321))),f146(x47321,x47323))) % 177.41/177.18 [4733]~P1(f327(f327(f329(f921(f916(x47331),f916(x47331))),f327(f327(f252(f916(x47331),f916(x47331)),x47332),f114(x47331))),f148(x47331,x47333))) % 177.41/177.18 [4734]~P1(f327(f327(f329(f921(f916(x47341),f916(x47341))),f327(f327(f252(f916(x47341),f916(x47341)),x47342),f114(x47341))),f158(x47341,x47343))) % 177.41/177.18 [4735]~P1(f327(f327(f329(f921(f916(x47351),f916(x47351))),f327(f327(f252(f916(x47351),f916(x47351)),f114(x47351)),x47352)),f146(x47351,x47353))) % 177.41/177.18 [4736]~P1(f327(f327(f329(f921(f916(x47361),f916(x47361))),f327(f327(f252(f916(x47361),f916(x47361)),f114(x47361)),x47362)),f158(x47361,x47363))) % 177.41/177.18 [3477]E(f327(f327(f203(x34771),x34772),x34773),f204(x34771,f217(x34772,x34773))) % 177.41/177.18 [3531]E(f327(f286(x35311,x35312),f327(f286(x35312,x35311),x35313)),x35313) % 177.41/177.18 [3554]E(f327(f327(f182(x35541,x35542),f114(x35541)),x35543),f114(f921(x35541,x35542))) % 177.41/177.18 [3557]E(f177(x35571,x35572,f327(f282(a915),x35573)),f327(f327(f176(x35571),x35573),x35572)) % 177.41/177.18 [3575]E(f153(x35751,f327(f137(x35751,x35752),x35753)),f327(f137(x35751,x35752),f153(x35751,x35753))) % 177.41/177.18 [3576]E(f327(f284(x35761,x35762),f327(f286(x35762,x35761),x35763)),f327(f264(x35762,x35761),x35763)) % 177.41/177.18 [3577]E(f327(f264(x35771,x35772),f327(f286(x35772,x35771),x35773)),f327(f284(x35772,x35771),x35773)) % 177.41/177.18 [3595]E(f327(f137(x35951,x35952),f327(f169(x35951),x35953)),f327(f169(x35951),f327(f137(x35951,x35952),x35953))) % 177.41/177.18 [3608]E(f327(f327(f139(x36081),x36082),f327(f172(x36081),x36083)),f327(f327(f139(x36081),f327(a113,x36082)),x36083)) % 177.41/177.18 [3624]E(f28(f26(x36241,x36242,x36243)),f327(f327(f80(a915),f28(x36243)),f327(a113,f2(a915)))) % 177.41/177.18 [3625]E(f327(f310(x36251,x36252,x36253),f190(f922(x36251,a910))),f190(f922(x36252,a910))) % 177.41/177.18 [3626]E(f327(f311(x36261,x36262,x36263),f190(f922(x36262,a910))),f190(f922(x36261,a910))) % 177.41/177.18 [3627]E(f327(f311(x36271,x36272,x36273),f242(f922(x36272,a910))),f242(f922(x36271,a910))) % 177.41/177.18 [3628]E(f327(f285(x36281,x36282,x36283),f190(f922(x36281,a910))),f190(f922(x36282,a910))) % 177.41/177.18 [3654]E(f121(x36541,f127(f917(x36541),x36542,x36543)),f117(x36541,x36542,f121(x36541,x36543))) % 177.41/177.18 [3656]E(f327(f327(f309(x36561),x36562),f327(f173(x36561),x36563)),f327(f173(x36561),f141(x36561,x36562,x36563))) % 177.41/177.18 [3743]E(f327(f191(a912),f26(x37431,x37432,x37433)),f327(f327(f80(a915),f327(f191(a912),x37433)),f327(a113,f2(a915)))) % 177.41/177.18 [3744]E(f327(f310(f921(x37441,x37442),x37442,f256(x37441,x37442)),x37443),f327(f284(x37441,x37442),x37443)) % 177.41/177.18 [3745]E(f327(f310(f921(x37451,x37452),x37451,f251(x37451,x37452)),x37453),f327(f264(x37451,x37452),x37453)) % 177.41/177.18 [3761]E(f327(f173(x37611),f170(x37611,f327(a113,x37612),x37613)),f327(f327(f309(x37611),x37613),f190(f922(x37611,a910)))) % 177.41/177.18 [3819]E(f327(f327(f252(x38191,x38192),f327(f251(x38191,x38192),x38193)),f327(f256(x38191,x38192),x38193)),x38193) % 177.41/177.18 [3826]E(f327(f191(f917(x38261)),f127(x38261,x38262,x38263)),f327(f327(f80(a915),f327(f191(f917(x38261)),x38263)),f327(a113,f2(a915)))) % 177.41/177.18 [3828]E(f327(f327(f257(x38281,x38282,x38281),f16(x38281,x38282)),x38283),f327(f251(x38281,x38282),x38283)) % 177.41/177.18 [3906]E(f28(f27(x39061,x39062,x39063)),f327(f327(f80(a915),f327(f327(f80(a915),f28(x39062)),f28(x39063))),f327(a113,f2(a915)))) % 177.41/177.18 [3956]E(f327(f72(x39561,x39561,x39562,f31(x39561)),x39563),x39563) % 177.41/177.18 [3963]E(f327(f327(f135(x39631),f170(x39631,x39632,x39633)),f327(f327(f152(x39631),x39633),f114(x39631))),f327(f327(f152(x39631),x39633),f170(x39631,x39632,x39633))) % 177.41/177.18 [4065]E(f327(f191(a912),f27(x40651,x40652,x40653)),f327(f327(f80(a915),f327(f327(f80(a915),f327(f191(a912),x40652)),f327(f191(a912),x40653))),f327(a113,f2(a915)))) % 177.41/177.18 [4139]P1(f327(f327(f234(f922(x41391,a910)),f327(f173(x41391),f327(f137(x41391,x41392),x41393))),f327(f173(x41391),x41393))) % 177.41/177.18 [4184]P1(f327(f327(f234(f922(x41841,a910)),f327(f173(x41841),f327(f327(f176(x41841),x41842),x41843))),f327(f173(x41841),x41843))) % 177.41/177.18 [4185]P1(f327(f327(f234(f922(x41851,a910)),f327(f173(x41851),f327(f327(f139(x41851),x41852),x41853))),f327(f173(x41851),x41853))) % 177.41/177.18 [4189]P1(f327(f327(f234(f922(x41891,a910)),f327(f173(x41891),f177(x41891,x41892,x41893))),f327(f173(x41891),x41892))) % 177.41/177.18 [4190]P1(f327(f327(f234(f922(x41901,a910)),f327(f173(x41901),f171(x41901,x41902,x41903))),f327(f173(x41901),x41903))) % 177.41/177.18 [4211]P23(f921(x42111,x42112),f921(x42112,x42111),f327(f257(x42111,x42112,f921(x42112,x42111)),f327(f7(x42112,x42111,f921(x42112,x42111)),f252(x42112,x42111))),x42113) % 177.41/177.18 [4222]E(f327(f327(f327(f184(f916(x42221),f916(x42221)),f46(a915,x42222,f327(f191(f916(x42221)),x42223))),f168(x42221)),x42223),f327(f327(f327(f184(f916(x42221),f916(x42221)),x42222),f168(x42221)),x42223)) % 177.41/177.18 [4266]P1(f327(f327(f329(f921(f916(x42661),f916(x42661))),f327(f327(f252(f916(x42661),f916(x42661)),x42662),x42662)),f159(x42661,f307(x42661,x42663)))) % 177.41/177.18 [4406]E(f85(f921(x44061,x44062),f327(f327(f18(f921(x44061,x44062),x44062,a910),f327(f327(f8(x44061,f922(x44062,a910),f921(x44061,x44062)),x44063),f251(x44061,x44062))),f256(x44061,x44062))),f85(f921(x44061,x44062),f327(f257(x44061,x44062,a910),x44063))) % 177.41/177.18 [4407]E(f90(f921(x44071,x44072),f327(f327(f18(f921(x44071,x44072),x44072,a910),f327(f327(f8(x44071,f922(x44072,a910),f921(x44071,x44072)),x44073),f251(x44071,x44072))),f256(x44071,x44072))),f90(f921(x44071,x44072),f327(f257(x44071,x44072,a910),x44073))) % 177.41/177.18 [4440]E(f327(f327(f288(f921(a915,x44401),x44401),f320(a915,x44401,a240,x44402)),f327(f327(f18(x44401,x44401,f921(a915,x44401)),f327(f327(f8(a915,f922(x44401,f921(a915,x44401)),x44401),f252(a915,x44401)),x44403)),f5(x44401))),f321(x44401,x44403,x44402)) % 177.41/177.18 [4502]E(f327(f258(x45021,x45021,x45022,x45022,f5(x45021),f5(x45022)),x45023),x45023) % 177.41/177.18 [4575]E(f327(f143(f916(f916(x45751)),f916(f916(x45751)),f135(f916(x45751)),f114(f916(x45751))),f327(f327(f155(f916(x45751),f916(f916(x45751))),f327(f327(f7(f916(x45751),f916(x45751),f916(f916(x45751))),f327(f327(f8(f922(x45751,f916(x45751)),f922(f916(x45751),f916(f916(x45751))),f916(x45751)),f155(x45751,f916(x45751))),f327(f7(x45751,f916(x45751),f916(x45751)),f152(x45751)))),x45752)),f56(x45751,x45753,x45752))),f56(x45751,f327(a113,x45753),x45752)) % 177.41/177.18 [4632]E(f225(a915,f921(x46321,f917(x46321)),f2(a915),f327(f257(x46321,f917(x46321),a915),f327(f327(f7(x46321,a915,f922(f917(x46321),a915)),f327(f327(f8(f922(f917(x46321),f922(a915,a915)),f922(a915,f922(f917(x46321),a915)),x46321),f7(f917(x46321),a915,a915)),f327(f327(f8(f922(f917(x46321),a915),f922(f917(x46321),f922(a915,a915)),x46321),f327(f8(a915,f922(a915,a915),f917(x46321)),f80(a915))),f327(f327(f7(x46321,f922(f917(x46321),a915),f922(f917(x46321),a915)),f327(f327(f8(f922(a915,a915),f922(f922(f917(x46321),a915),f922(f917(x46321),a915)),x46321),f8(a915,a915,f917(x46321))),f327(f327(f8(a915,f922(a915,a915),x46321),f80(a915)),x46322))),f126(x46321,x46322))))),f78(a915))),f327(f136(x46321),x46323)),f327(f126(x46321,x46322),x46323)) % 177.41/177.18 [4641]E(f327(f327(f86(a1,x46411),f220(f327(f327(f72(f921(a1,a1),a1,x46411,f256(a1,a1)),f214(x46411)),x46412),f327(f327(f72(f921(a1,a1),a1,x46411,f256(a1,a1)),f214(x46411)),x46413))),f327(f327(f18(a1,a1,x46411),f327(f327(f8(a1,f922(a1,x46411),a1),f203(x46411)),f327(f327(f18(a1,a1,a1),f327(f327(f8(a1,f922(a1,a1),a1),f80(a1)),f327(f327(f8(a1,a1,a1),f327(f81(a1),f327(f327(f72(f921(a1,a1),a1,x46411,f251(a1,a1)),f214(x46411)),x46412))),f327(f327(f7(a1,a1,a1),f37(a1)),f327(f327(f72(f921(a1,a1),a1,x46411,f256(a1,a1)),f214(x46411)),x46412))))),f327(f327(f8(a1,a1,a1),f327(f81(a1),f327(f327(f72(f921(a1,a1),a1,x46411,f251(a1,a1)),f214(x46411)),x46413))),f327(f327(f7(a1,a1,a1),f37(a1)),f327(f327(f72(f921(a1,a1),a1,x46411,f256(a1,a1)),f214(x46411)),x46413)))))),f5(a1))),f232(x46411,x46412,x46413)) % 177.41/177.18 [4670]~E(f327(f327(f152(x46701),x46702),x46703),x46703) % 177.41/177.18 [4677]~E(f327(f327(f152(x46771),x46772),x46773),f114(x46771)) % 177.41/177.18 [4691]~E(f327(f327(f309(x46911),x46912),x46913),f190(f922(x46911,a910))) % 177.41/177.18 [4714]~E(f327(f310(x47141,f922(x47141,a910),x47142),x47143),f327(f308(x47141),x47143)) % 177.41/177.18 [3536]E(f327(f327(f160(x35361,f114(x35361)),x35362),x35363),f114(x35361)) % 177.41/177.18 [3537]E(f327(f142(x35371),f327(f327(f152(x35371),x35372),x35373)),x35372) % 177.41/177.18 [3538]E(f327(f172(x35381),f327(f327(f152(x35381),x35382),x35383)),x35383) % 177.41/177.18 [3581]E(f327(f327(f139(x35811),f78(a915)),f327(f327(f152(x35811),x35812),x35813)),x35813) % 177.41/177.18 [3615]E(f115(x36151,f327(f327(f139(x36151),x36152),x36153)),f327(f327(f139(x36151),x36152),f115(x36151,x36153))) % 177.41/177.18 [3617]E(f327(f327(f160(x36171,x36172),x36173),f327(f327(f165(x36171),x36172),x36173)),x36172) % 177.41/177.18 [3638]E(f327(f327(f309(x36381),x36382),f327(f327(f309(x36381),x36382),x36383)),f327(f327(f309(x36381),x36382),x36383)) % 177.41/177.18 [3651]E(f327(f327(f309(x36511),x36512),f327(f173(x36511),x36513)),f327(f173(x36511),f327(f327(f152(x36511),x36512),x36513))) % 177.41/177.18 [3653]E(f327(f327(f139(x36531),x36532),f327(f172(x36531),x36533)),f327(f172(x36531),f327(f327(f139(x36531),x36532),x36533))) % 177.41/177.18 [3665]E(f327(f327(f176(x36651),f78(a915)),f327(f327(f152(x36651),x36652),x36653)),f327(f327(f152(x36651),x36652),f114(x36651))) % 177.41/177.18 [3708]E(f327(f63(x37081,x37082),f327(f327(f309(x37081),x37083),f190(f922(x37081,a910)))),x37083) % 177.41/177.18 [3751]E(f327(f327(f80(a915),x37511),f327(f327(f80(a915),x37512),x37513)),f327(f327(f80(a915),x37512),f327(f327(f80(a915),x37511),x37513))) % 177.41/177.18 [3752]E(f327(f327(f80(a1),x37521),f327(f327(f80(a1),x37522),x37523)),f327(f327(f80(a1),x37522),f327(f327(f80(a1),x37521),x37523))) % 177.41/177.18 [3757]E(f327(f327(f254(x37571,x37572),f190(f922(x37571,a910))),x37573),f190(f922(f921(x37571,x37572),a910))) % 177.41/177.18 [3782]E(f327(f327(f102(f922(x37821,a910)),x37822),x37823),f327(f327(f102(f922(x37821,a910)),x37823),x37822)) % 177.41/177.18 [3783]E(f327(f327(f103(f922(x37831,a910)),x37832),x37833),f327(f327(f103(f922(x37831,a910)),x37833),x37832)) % 177.41/177.18 [3785]E(f327(f327(f135(x37851),x37852),f327(f327(f152(x37851),x37853),f114(x37851))),f327(f168(x37851),f327(f327(f152(x37851),x37853),x37852))) % 177.41/177.18 [3786]E(f327(f327(f135(x37861),f327(f169(x37861),x37862)),f327(f169(x37861),x37863)),f327(f169(x37861),f327(f327(f135(x37861),x37863),x37862))) % 177.41/177.18 [3796]E(f327(f172(x37961),f327(f327(f176(x37961),f327(a113,x37962)),x37963)),f327(f327(f176(x37961),x37962),f327(f172(x37961),x37963))) % 177.41/177.18 [3804]P1(f327(f327(f329(x38041),x38042),f327(f327(f309(x38041),x38042),x38043))) % 177.41/177.18 [3808]E(f327(f327(f41(x38081,f922(x38082,a910)),f190(f922(x38081,a910))),x38083),f242(f922(x38082,a910))) % 177.41/177.18 [3811]E(f327(f285(x38111,x38111,f263(x38111,x38112)),x38113),f327(f327(f103(f922(x38111,a910)),x38112),x38113)) % 177.41/177.18 [3825]E(f327(f191(f916(x38251)),f327(f327(f152(x38251),x38252),x38253)),f327(f327(f80(a915),f327(f191(f916(x38251)),x38253)),f327(a113,f2(a915)))) % 177.41/177.18 [3830]E(f115(x38301,f327(f327(f135(x38301),x38302),f327(f327(f152(x38301),x38303),f114(x38301)))),x38302) % 177.41/177.18 [3831]E(f145(x38311,f327(f327(f135(x38311),x38312),f327(f327(f152(x38311),x38313),f114(x38311)))),x38313) % 177.41/177.18 [3840]E(f327(f327(f135(x38401),f327(f327(f176(x38401),x38402),x38403)),f327(f327(f139(x38401),x38402),x38403)),x38403) % 177.41/177.18 [3849]E(f327(f327(f23(a915),f327(f327(f80(a915),x38491),x38492)),f327(f327(f80(a915),x38493),x38492)),f327(f327(f23(a915),x38491),x38493)) % 177.41/177.18 [3850]E(f327(f327(f23(a915),f327(f327(f80(a915),x38501),x38502)),f327(f327(f80(a915),x38501),x38503)),f327(f327(f23(a915),x38502),x38503)) % 177.41/177.18 [3856]E(f327(f327(f135(x38561),f327(f169(x38561),x38562)),f327(f327(f152(x38561),x38563),f114(x38561))),f327(f169(x38561),f327(f327(f152(x38561),x38563),x38562))) % 177.41/177.18 [3858]E(f327(f327(f80(a915),f327(f191(f916(x38581)),x38582)),f327(f191(f916(x38581)),x38583)),f327(f191(f916(x38581)),f327(f327(f135(x38581),x38582),x38583))) % 177.41/177.18 [3861]E(f327(f327(f80(a915),f327(f191(f916(x38611)),x38612)),f327(f191(f916(x38611)),x38613)),f327(f191(f916(x38611)),f174(x38611,x38612,x38613))) % 177.41/177.18 [3868]E(f327(f327(f102(f922(x38681,a910)),f327(f173(x38681),x38682)),f327(f173(x38681),x38683)),f327(f173(x38681),f327(f327(f135(x38681),x38682),x38683))) % 177.41/177.18 [3869]E(f46(a915,f327(f327(f81(a915),x38691),x38692),f327(f327(f81(a915),x38691),x38693)),f327(f327(f81(a915),x38691),f46(a915,x38692,x38693))) % 177.41/177.18 [3881]E(f327(f327(f176(x38811),f327(f327(f23(a915),x38812),f78(a915))),f327(f172(x38811),x38813)),f327(f172(x38811),f327(f327(f176(x38811),x38812),x38813))) % 177.41/177.18 [3886]E(f327(f327(f103(f922(x38861,a910)),x38862),f327(f79(f922(x38861,a910)),x38863)),f327(f327(f23(f922(x38861,a910)),x38862),x38863)) % 177.41/177.18 [3887]E(f327(f327(f23(f922(x38871,a910)),x38872),f327(f79(f922(x38871,a910)),x38873)),f327(f327(f103(f922(x38871,a910)),x38872),x38873)) % 177.41/177.18 [3910]E(f327(f327(f254(x39101,x39102),x39103),f327(f16(f922(x39102,a910),x39101),f190(f922(x39102,a910)))),f190(f922(f921(x39101,x39102),a910))) % 177.41/177.18 [3912]E(f327(f327(f23(a915),f327(f327(f81(a915),x39121),x39122)),f327(f327(f81(a915),x39121),x39123)),f327(f327(f81(a915),x39121),f327(f327(f23(a915),x39122),x39123))) % 177.41/177.18 [3913]E(f327(f327(f80(a915),f327(f327(f81(a915),x39131),x39132)),f327(f327(f81(a915),x39131),x39133)),f327(f327(f81(a915),x39131),f327(f327(f80(a915),x39132),x39133))) % 177.41/177.18 [3914]E(f327(f327(f23(a1),f327(f327(f81(a1),x39141),x39142)),f327(f327(f81(a1),x39141),x39143)),f327(f327(f81(a1),x39141),f327(f327(f23(a1),x39142),x39143))) % 177.41/177.18 [3915]E(f327(f327(f80(a1),f327(f327(f81(a1),x39151),x39152)),f327(f327(f81(a1),x39151),x39153)),f327(f327(f81(a1),x39151),f327(f327(f80(a1),x39152),x39153))) % 177.41/177.18 [3916]E(f327(f327(f81(a1),f327(f327(f244(a1),x39161),x39162)),f327(f327(f244(a1),x39161),x39163)),f327(f327(f244(a1),x39161),f327(f327(f80(a915),x39162),x39163))) % 177.41/177.18 [3930]E(f327(f327(f40(x39301,f922(x39302,a910)),x39303),f327(f16(f922(x39302,a910),x39301),f190(f922(x39302,a910)))),f190(f922(x39302,a910))) % 177.41/177.18 [3932]E(f46(a915,f327(f327(f81(a915),x39321),x39322),f327(f327(f81(a915),x39323),x39322)),f327(f327(f81(a915),f46(a915,x39321,x39323)),x39322)) % 177.41/177.18 [3937]E(f46(a1,f327(f327(f23(a1),x39371),f46(a1,x39372,x39373)),x39373),f46(a1,f327(f327(f23(a1),x39371),x39372),x39373)) % 177.41/177.18 [3938]E(f46(a1,f327(f327(f81(a1),x39381),f46(a1,x39382,x39383)),x39383),f46(a1,f327(f327(f81(a1),x39381),x39382),x39383)) % 177.41/177.18 [3939]P1(f327(f327(f234(f922(x39391,a910)),x39392),f327(f327(f309(x39391),x39393),x39392))) % 177.41/177.18 [4016]E(f327(f327(f41(f922(x40161,a910),f922(x40161,a910)),x40162),f327(f102(f922(x40161,a910)),x40163)),f327(f327(f102(f922(x40161,a910)),x40163),f39(f922(x40161,a910),x40162))) % 177.41/177.18 [4017]E(f327(f327(f40(f922(x40171,a910),f922(x40171,a910)),x40172),f327(f103(f922(x40171,a910)),x40173)),f327(f327(f103(f922(x40171,a910)),x40173),f38(f922(x40171,a910),x40172))) % 177.41/177.18 [4029]E(f327(f173(x40291),f327(f327(f327(f184(f916(x40291),f916(x40291)),x40292),f168(x40291)),x40293)),f327(f173(x40291),x40293)) % 177.41/177.18 [4033]E(f327(f327(f176(x40331),f327(f191(f916(x40331)),f178(x40331,x40332,x40333))),x40333),f178(x40331,x40332,x40333)) % 177.41/177.18 [4037]E(f327(f191(f916(x40371)),f327(f327(f327(f184(f916(x40371),f916(x40371)),x40372),f168(x40371)),x40373)),f327(f191(f916(x40371)),x40373)) % 177.41/177.18 [4040]E(f327(f327(f257(x40401,x40402,x40402),f327(f16(f922(x40402,x40402),x40401),f5(x40402))),x40403),f327(f256(x40401,x40402),x40403)) % 177.41/177.18 [4047]E(f46(a1,f327(f327(f23(a1),f46(a1,x40471,x40472)),x40473),x40472),f46(a1,f327(f327(f23(a1),x40471),x40473),x40472)) % 177.41/177.18 [4048]E(f46(a1,f327(f327(f244(a1),f46(a1,x40481,x40482)),x40483),x40482),f46(a1,f327(f327(f244(a1),x40481),x40483),x40482)) % 177.41/177.18 [4051]E(f327(f327(f40(f922(f921(x40511,x40512),a910),f922(x40512,a910)),x40513),f284(x40511,x40512)),f327(f284(x40511,x40512),f38(f922(f921(x40511,x40512),a910),x40513))) % 177.41/177.18 [4052]E(f327(f327(f40(f922(f921(x40521,x40522),a910),f922(x40521,a910)),x40523),f264(x40521,x40522)),f327(f264(x40521,x40522),f38(f922(f921(x40521,x40522),a910),x40523))) % 177.41/177.18 [4076]E(f327(f72(x40761,x40761,x40761,x40762),f327(f327(f184(x40761,x40761),x40763),x40762)),f327(f327(f184(x40761,x40761),f327(a113,x40763)),x40762)) % 177.41/177.18 [4094]E(f327(f327(f139(x40941),f327(f327(f23(a915),f327(f191(f916(x40941)),x40942)),x40943)),f327(f169(x40941),x40942)),f327(f169(x40941),f327(f327(f176(x40941),x40943),x40942))) % 177.41/177.18 [4095]E(f327(f327(f176(x40951),f327(f327(f23(a915),f327(f191(f916(x40951)),x40952)),x40953)),f327(f169(x40951),x40952)),f327(f169(x40951),f327(f327(f139(x40951),x40953),x40952))) % 177.41/177.18 [4097]E(f327(f327(f80(a915),f327(f166(a915),f327(f327(f155(x40971,a915),x40972),x40973))),f327(f191(f916(x40971)),x40973)),f156(x40971,x40972,x40973)) % 177.41/177.18 [4117]E(f327(f168(x41171),f327(f327(f327(f184(f916(x41171),f916(x41171)),x41172),f168(x41171)),x41173)),f327(f327(f327(f184(f916(x41171),f916(x41171)),f327(a113,x41172)),f168(x41171)),x41173)) % 177.41/177.18 [4131]P1(f327(f327(f234(a915),f327(f191(f916(x41311)),f327(f137(x41311,x41312),x41313))),f327(f191(f916(x41311)),x41313))) % 177.41/177.18 [4147]E(f327(f327(f102(f922(f922(x41471,a910),a910)),f327(f308(x41471),x41472)),f327(f310(f922(x41471,a910),f922(x41471,a910),f327(f309(x41471),x41473)),f327(f308(x41471),x41472))),f327(f308(x41471),f327(f327(f309(x41471),x41473),x41472))) % 177.41/177.18 [4166]P22(x41661,x41662,f327(f327(f309(f913(x41661)),f327(f327(f327(f91(x41661),x41663),a25),x41663)),f190(f922(f913(x41661),a910)))) % 177.41/177.18 [4181]P1(f327(f327(f234(a915),f327(f191(f916(x41811)),f178(x41811,x41812,x41813))),f327(f191(f916(x41811)),x41813))) % 177.41/177.18 [4188]E(f327(f264(x41881,x41882),f327(f262(f921(x41881,x41882)),f327(f257(x41881,x41882,a910),x41883))),f327(f262(x41881),f327(f327(f8(f922(x41882,a910),a910,x41881),f87(x41882)),x41883))) % 177.41/177.18 [4200]E(f327(f310(a915,a915,f327(f327(f7(a915,a915,a915),f80(a915)),x42001)),f303(a915,x42002,x42003)),f303(a915,f327(f327(f80(a915),x42002),x42001),f327(f327(f80(a915),x42003),x42001))) % 177.41/177.18 [4214]E(f327(f310(a915,a915,f327(f327(f7(a915,a915,a915),f80(a915)),x42141)),f327(f302(a915,x42142),x42143)),f327(f302(a915,f327(f327(f80(a915),x42142),x42141)),f327(f327(f80(a915),x42143),x42141))) % 177.41/177.18 [4232]E(f327(f327(f182(x42321,x42322),f327(f327(f155(f921(x42321,x42322),x42321),f251(x42321,x42322)),x42323)),f327(f327(f155(f921(x42321,x42322),x42322),f256(x42321,x42322)),x42323)),x42323) % 177.41/177.18 [4237]E(f327(f327(f80(a915),f327(f327(f81(a915),x42371),f46(a915,f327(f327(f37(a915),x42372),x42371),x42373))),f46(a915,x42372,x42371)),f46(a915,x42372,f327(f327(f81(a915),x42371),x42373))) % 177.41/177.18 [4250]E(f327(f327(f135(x42501),x42502),f327(f143(f916(x42501),f916(x42501),f135(x42501),f114(x42501)),x42503)),f327(f143(f916(x42501),f916(x42501),f135(x42501),x42502),x42503)) % 177.41/177.18 [4271]P1(f327(f327(f329(f921(x42711,x42711)),f327(f327(f252(x42711,x42711),x42712),x42712)),f327(f327(f184(f921(x42711,x42711),a910),f2(a915)),x42713))) % 177.41/177.18 [4276]E(f327(f262(x42761),f327(f327(f8(f922(x42762,a910),a910,x42761),f87(x42762)),f327(f7(x42762,x42761,a910),x42763))),f327(f284(x42762,x42761),f327(f262(f921(x42762,x42761)),f327(f257(x42762,x42761,a910),x42763)))) % 177.41/177.18 [4293]E(f327(f327(f102(f922(x42931,a910)),f327(f327(f40(a915,f922(x42931,a910)),f303(a915,f78(a915),x42932)),x42933)),f327(x42933,f2(a915))),f327(f327(f40(a915,f922(x42931,a910)),f327(f301(a915),x42932)),x42933)) % 177.41/177.18 [4308]E(f327(f143(f916(x43081),f916(x43081),f135(x43081),f114(x43081)),f327(f327(f155(f916(x43081),f916(x43081)),f137(x43081,x43082)),x43083)),f327(f137(x43081,x43082),f327(f143(f916(x43081),f916(x43081),f135(x43081),f114(x43081)),x43083))) % 177.41/177.18 [4312]E(f327(f256(f916(x43121),f916(x43121)),f167(x43121,x43122,x43123)),f327(f137(x43121,f327(f72(a910,a910,x43121,a322),x43122)),x43123)) % 177.41/177.18 [4358]E(f327(f327(f80(a1),f327(f327(f80(a1),f327(f327(f81(a1),x43581),f327(f327(f37(a1),x43582),x43581))),f46(a1,x43582,x43581))),x43583),f327(f327(f80(a1),x43582),x43583)) % 177.41/177.18 [4395]E(f327(f327(f80(a1),f327(f327(f80(a1),f327(f327(f81(a1),f327(f327(f37(a1),x43951),x43952)),x43952)),f46(a1,x43951,x43952))),x43953),f327(f327(f80(a1),x43951),x43953)) % 177.41/177.18 [4421]E(f85(f921(x44211,x44212),f327(f257(x44211,x44212,a910),f327(f327(f8(f922(x44212,f921(x44211,x44212)),f922(x44212,a910),x44211),f327(f8(f921(x44211,x44212),a910,x44212),x44213)),f252(x44211,x44212)))),f85(f921(x44211,x44212),x44213)) % 177.41/177.18 [4422]E(f90(f921(x44221,x44222),f327(f257(x44221,x44222,a910),f327(f327(f8(f922(x44222,f921(x44221,x44222)),f922(x44222,a910),x44221),f327(f8(f921(x44221,x44222),a910,x44222),x44223)),f252(x44221,x44222)))),f90(f921(x44221,x44222),x44223)) % 177.41/177.18 [4449]P1(f327(f327(f234(f922(x44491,a910)),f38(f922(x44491,a910),f327(f327(f103(f922(f922(x44491,a910),a910)),x44492),x44493))),f327(f327(f103(f922(x44491,a910)),f38(f922(x44491,a910),x44492)),f38(f922(x44491,a910),x44493)))) % 177.41/177.18 [4450]E(f327(f169(x44501),f327(f327(f327(f184(f916(x44501),f916(x44501)),f327(f327(f23(a915),f327(f191(f916(x44501)),x44502)),f46(a915,x44503,f327(f191(f916(x44501)),x44502)))),f168(x44501)),x44502)),f327(f327(f327(f184(f916(x44501),f916(x44501)),x44503),f168(x44501)),f327(f169(x44501),x44502))) % 177.41/177.18 [4487]P1(f327(f327(f234(a915),f327(f191(f916(x44871)),f327(f327(f139(x44871),f327(f191(f916(x44871)),f178(x44871,x44872,x44873))),x44873))),f327(f191(f916(x44871)),x44873))) % 177.41/177.18 [4726]~P1(f327(f62(x47261,x47262,f190(f922(x47261,a910))),x47263)) % 177.41/177.18 [4731]~P1(f327(f327(f329(f921(x47311,x47311)),f327(f327(f252(x47311,x47311),x47312),x47313)),f154(x47311,f114(f922(x47311,a915))))) % 177.41/177.18 [3797]E(f327(f191(f916(x37971)),f327(f327(f176(x37971),x37972),x37973)),f327(f327(f238(a915),f327(f191(f916(x37971)),x37973)),x37972)) % 177.41/177.18 [3798]E(f327(f191(f916(x37981)),f327(f327(f139(x37981),x37982),x37983)),f327(f327(f23(a915),f327(f191(f916(x37981)),x37983)),x37982)) % 177.41/177.18 [3824]E(f327(f191(f916(f916(x38241))),f56(x38241,x38242,x38243)),f327(f327(f244(a915),f327(f191(f916(x38241)),x38243)),x38242)) % 177.41/177.18 [3842]E(f327(f327(f37(a915),f327(f327(f37(a915),x38421),x38422)),x38423),f327(f327(f37(a915),x38421),f327(f327(f81(a915),x38422),x38423))) % 177.41/177.18 [3843]E(f327(f327(f23(a915),f327(f327(f23(a915),x38431),x38432)),x38433),f327(f327(f23(a915),x38431),f327(f327(f80(a915),x38432),x38433))) % 177.41/177.18 [3844]E(f327(f327(f80(a915),f327(f327(f80(a915),x38441),x38442)),x38443),f327(f327(f80(a915),x38441),f327(f327(f80(a915),x38442),x38443))) % 177.41/177.18 [3845]E(f327(f327(f80(a1),f327(f327(f80(a1),x38451),x38452)),x38453),f327(f327(f80(a1),x38451),f327(f327(f80(a1),x38452),x38453))) % 177.41/177.18 [3846]E(f327(f327(f81(a915),f327(f327(f81(a915),x38461),x38462)),x38463),f327(f327(f81(a915),x38461),f327(f327(f81(a915),x38462),x38463))) % 177.41/177.18 [3847]E(f327(f327(f81(a1),f327(f327(f81(a1),x38471),x38472)),x38473),f327(f327(f81(a1),x38471),f327(f327(f81(a1),x38472),x38473))) % 177.41/177.18 [3848]E(f327(f327(f244(a1),f327(f327(f244(a1),x38481),x38482)),x38483),f327(f327(f244(a1),x38481),f327(f327(f81(a915),x38482),x38483))) % 177.41/177.18 [3867]E(f163(x38671,f327(f327(f152(f922(x38671,a910)),x38672),x38673)),f175(x38671,x38672,f163(x38671,x38673))) % 177.41/177.18 [3911]E(f327(f327(f23(a915),f327(f327(f23(a915),x39111),x39112)),x39113),f327(f327(f23(a915),f327(f327(f23(a915),x39111),x39113)),x39112)) % 177.41/177.18 [3919]E(f327(f327(f103(f922(x39191,a910)),x39192),f327(f327(f23(f922(x39191,a910)),x39193),x39192)),f190(f922(x39191,a910))) % 177.41/177.18 [3923]E(f327(f327(f155(a915,x39231),f327(f16(x39231,a915),x39232)),f140(a915,f327(f302(a915,f2(a915)),x39233))),f170(x39231,x39233,x39232)) % 177.41/177.18 [3961]E(f39(f922(x39611,a910),f327(f327(f309(f922(x39611,a910)),x39612),x39613)),f327(f327(f103(f922(x39611,a910)),x39612),f39(f922(x39611,a910),x39613))) % 177.41/177.18 [3962]E(f38(f922(x39621,a910),f327(f327(f309(f922(x39621,a910)),x39622),x39623)),f327(f327(f102(f922(x39621,a910)),x39622),f38(f922(x39621,a910),x39623))) % 177.41/177.18 [3964]E(f170(x39641,f327(f191(f916(x39641)),f327(f137(x39641,f327(a324,x39642)),x39643)),x39642),f327(f137(x39641,f327(a324,x39642)),x39643)) % 177.41/177.18 [3966]E(f327(f327(f23(a915),f327(f327(f81(a915),x39661),x39662)),f327(f327(f81(a915),x39663),x39662)),f327(f327(f81(a915),f327(f327(f23(a915),x39661),x39663)),x39662)) % 177.41/177.18 [3967]E(f327(f327(f80(a915),f327(f327(f81(a915),x39671),x39672)),f327(f327(f81(a915),x39673),x39672)),f327(f327(f81(a915),f327(f327(f80(a915),x39671),x39673)),x39672)) % 177.41/177.18 [3968]E(f327(f327(f23(a1),f327(f327(f81(a1),x39681),x39682)),f327(f327(f81(a1),x39683),x39682)),f327(f327(f81(a1),f327(f327(f23(a1),x39681),x39683)),x39682)) % 177.41/177.18 [3969]E(f327(f327(f80(a1),f327(f327(f81(a1),x39691),x39692)),f327(f327(f81(a1),x39693),x39692)),f327(f327(f81(a1),f327(f327(f80(a1),x39691),x39693)),x39692)) % 177.41/177.18 [3971]E(f327(f327(f238(a915),f327(f327(f23(a915),x39711),x39712)),f327(f327(f23(a915),x39713),x39712)),f327(f327(f23(a915),f327(f327(f238(a915),x39711),x39713)),x39712)) % 177.41/177.18 [3993]E(f327(f327(f103(f922(f916(x39931),a910)),f161(x39931,x39932)),f161(x39931,x39933)),f161(x39931,f327(f327(f103(f922(x39931,a910)),x39932),x39933))) % 177.41/177.18 [3996]E(f327(f327(f102(f922(x39961,a910)),x39962),f327(f327(f23(f922(x39961,a910)),x39963),x39962)),f327(f327(f102(f922(x39961,a910)),x39962),x39963)) % 177.41/177.18 [3997]E(f327(f327(f102(f922(x39971,a910)),x39972),f327(f327(f102(f922(x39971,a910)),x39972),x39973)),f327(f327(f102(f922(x39971,a910)),x39972),x39973)) % 177.41/177.18 [3998]E(f327(f327(f103(f922(x39981,a910)),x39982),f327(f327(f103(f922(x39981,a910)),x39982),x39983)),f327(f327(f103(f922(x39981,a910)),x39982),x39983)) % 177.41/177.18 [4010]E(f327(f327(f289(x40101,x40102,x40102),x40103),f307(x40102,f190(f922(f921(x40102,x40102),a910)))),x40103) % 177.41/177.18 [4013]E(f327(f327(f102(f922(x40131,a910)),f327(f327(f309(x40131),x40132),f190(f922(x40131,a910)))),x40133),f327(f327(f309(x40131),x40132),x40133)) % 177.41/177.18 [4032]E(f327(f327(f23(a915),f327(f327(f23(a915),f327(a113,x40321)),x40322)),f327(a113,x40323)),f327(f327(f23(a915),f327(f327(f23(a915),x40321),x40322)),x40323)) % 177.41/177.18 [4060]E(f327(f327(f103(f922(f922(x40601,a910),a910)),f327(f308(x40601),x40602)),f327(f308(x40601),x40603)),f327(f308(x40601),f327(f327(f103(f922(x40601,a910)),x40602),x40603))) % 177.41/177.18 [4063]E(f327(f327(f102(f922(x40631,a910)),f327(f79(f922(x40631,a910)),x40632)),x40633),f327(f79(f922(x40631,a910)),f327(f327(f23(f922(x40631,a910)),x40632),x40633))) % 177.41/177.18 [4073]E(f327(f327(f309(x40731),x40732),f327(f327(f23(f922(x40731,a910)),x40733),f327(f327(f309(x40731),x40732),f190(f922(x40731,a910))))),f327(f327(f309(x40731),x40732),x40733)) % 177.41/177.18 [4083]P1(f327(f327(f234(f922(x40831,a910)),x40832),f327(f327(f102(f922(x40831,a910)),x40833),x40832))) % 177.41/177.18 [4084]P1(f327(f327(f234(f922(x40841,a910)),x40842),f327(f327(f102(f922(x40841,a910)),x40842),x40843))) % 177.41/177.18 [4088]E(f327(f327(f103(f922(x40881,a910)),f327(f79(f922(x40881,a910)),x40882)),f327(f79(f922(x40881,a910)),x40883)),f327(f79(f922(x40881,a910)),f327(f327(f102(f922(x40881,a910)),x40882),x40883))) % 177.41/177.18 [4089]E(f327(f327(f102(f922(x40891,a910)),f327(f79(f922(x40891,a910)),x40892)),f327(f79(f922(x40891,a910)),x40893)),f327(f79(f922(x40891,a910)),f327(f327(f103(f922(x40891,a910)),x40892),x40893))) % 177.41/177.18 [4103]P1(f327(f327(f234(f922(x41031,a910)),f327(f173(x41031),x41032)),f327(f173(x41031),f327(f327(f152(x41031),x41033),x41032)))) % 177.41/177.18 [4115]E(f327(f327(f102(f922(x41151,a910)),f327(f327(f23(f922(x41151,a910)),x41152),x41153)),f327(f327(f103(f922(x41151,a910)),x41152),x41153)),x41152) % 177.41/177.18 [4168]E(f327(f327(f6(x41681,a1),f327(f327(f8(a915,a1,x41681),f101(a1)),x41682)),x41683),f327(f101(a1),f327(f327(f6(x41681,a915),x41682),x41683))) % 177.41/177.18 [4169]E(f327(f327(f9(x41691,a1),f327(f327(f8(a915,a1,x41691),f101(a1)),x41692)),x41693),f327(f101(a1),f327(f327(f9(x41691,a915),x41692),x41693))) % 177.41/177.18 [4216]E(f327(f327(f135(x42161),f178(x42161,x42162,x42163)),f327(f327(f139(x42161),f327(f191(f916(x42161)),f178(x42161,x42162,x42163))),x42163)),x42163) % 177.41/177.18 [4220]E(f327(f79(f922(f921(x42201,x42202),a910)),f327(f327(f254(x42201,x42202),x42203),f327(f16(f922(x42202,a910),x42201),f242(f922(x42202,a910))))),f327(f327(f254(x42201,x42202),f327(f79(f922(x42201,a910)),x42203)),f327(f16(f922(x42202,a910),x42201),f242(f922(x42202,a910))))) % 177.41/177.18 [4221]E(f327(f79(f922(f921(x42211,x42212),a910)),f327(f327(f254(x42211,x42212),f242(f922(x42211,a910))),f327(f16(f922(x42212,a910),x42211),x42213))),f327(f327(f254(x42211,x42212),f242(f922(x42211,a910))),f327(f16(f922(x42212,a910),x42211),f327(f79(f922(x42212,a910)),x42213)))) % 177.41/177.18 [4272]E(f327(f327(f40(f922(x42721,a910),f922(x42721,a910)),x42722),f327(f327(f7(f922(x42721,a910),f922(x42721,a910),f922(x42721,a910)),f103(f922(x42721,a910))),x42723)),f327(f327(f103(f922(x42721,a910)),f38(f922(x42721,a910),x42722)),x42723)) % 177.41/177.18 [4278]E(f327(f143(f916(x42781),f916(x42781),f135(x42781),f114(x42781)),f327(f327(f152(f916(x42781)),x42782),x42783)),f327(f327(f135(x42781),x42782),f327(f143(f916(x42781),f916(x42781),f135(x42781),f114(x42781)),x42783))) % 177.41/177.18 [4299]E(f327(f327(f309(f922(x42991,a910)),f327(f285(x42991,x42991,x42992),f327(f327(f309(x42991),x42993),f190(f922(x42991,a910))))),f190(f922(f922(x42991,a910),a910))),f327(f327(f61(x42991),f327(f327(f309(x42991),x42993),f190(f922(x42991,a910)))),x42992)) % 177.41/177.18 [4309]E(f327(f327(f80(a915),f327(f327(f81(a915),x43091),f327(f327(f37(a915),x43092),x43093))),f327(f327(f37(a915),f327(f327(f81(a915),x43091),f46(a915,x43092,x43093))),x43093)),f327(f327(f37(a915),f327(f327(f81(a915),x43091),x43092)),x43093)) % 177.41/177.18 [4310]E(f327(f327(f80(a1),f327(f327(f81(a1),x43101),f327(f327(f37(a1),x43102),x43103))),f327(f327(f37(a1),f327(f327(f81(a1),x43101),f46(a1,x43102,x43103))),x43103)),f327(f327(f37(a1),f327(f327(f81(a1),x43101),x43102)),x43103)) % 177.41/177.18 [4343]E(f327(f327(f23(f922(x43431,a910)),f327(f173(x43431),x43432)),f327(f327(f309(x43431),x43433),f190(f922(x43431,a910)))),f327(f173(x43431),f327(f137(x43431,f327(f327(f8(a910,a910,x43431),a322),f327(a324,x43433))),x43432))) % 177.41/177.18 [4393]E(f327(f327(f135(x43931),f327(f143(f916(x43931),f916(x43931),f135(x43931),f114(x43931)),x43932)),f327(f143(f916(x43931),f916(x43931),f135(x43931),f114(x43931)),x43933)),f327(f143(f916(x43931),f916(x43931),f135(x43931),f114(x43931)),f327(f327(f135(f916(x43931)),x43932),x43933))) % 177.41/177.18 [4396]E(f327(f327(f252(f916(x43961),f916(x43961)),f327(f137(x43961,x43962),x43963)),f327(f137(x43961,f327(f72(a910,a910,x43961,a322),x43962)),x43963)),f167(x43961,x43962,x43963)) % 177.41/177.18 [4399]E(f327(f327(f80(a915),f327(f327(f80(a915),f327(f327(f37(a915),x43991),x43992)),f327(f327(f37(a915),x43993),x43992))),f327(f327(f37(a915),f327(f327(f80(a915),f46(a915,x43991,x43992)),f46(a915,x43993,x43992))),x43992)),f327(f327(f37(a915),f327(f327(f80(a915),x43991),x43993)),x43992)) % 177.41/177.18 [4400]E(f327(f327(f80(a1),f327(f327(f80(a1),f327(f327(f37(a1),x44001),x44002)),f327(f327(f37(a1),x44003),x44002))),f327(f327(f37(a1),f327(f327(f80(a1),f46(a1,x44001,x44002)),f46(a1,x44003,x44002))),x44002)),f327(f327(f37(a1),f327(f327(f80(a1),x44001),x44003)),x44002)) % 177.41/177.18 [4453]E(f327(f327(f103(f922(f916(x44531),a910)),f327(f327(f7(f916(x44531),f922(f916(x44531),a910),a910),f329(f916(x44531))),f162(x44531,x44532))),f327(f327(f7(f916(x44531),f922(f916(x44531),a910),a910),f329(f916(x44531))),f162(x44531,x44533))),f161(x44531,f327(f327(f103(f922(x44531,a910)),f327(f327(f7(x44531,f922(x44531,a910),a910),f329(x44531)),x44532)),f327(f327(f7(x44531,f922(x44531,a910),a910),f329(x44531)),x44533)))) % 177.41/177.18 [4465]E(f327(f262(x44651),f327(f327(f18(x44651,a910,a910),f327(f327(f8(a910,f922(a910,a910),x44651),a326),f327(f327(f7(x44651,x44651,a910),a324),x44652))),f327(f327(f7(x44651,f922(x44651,a910),a910),f329(x44651)),x44653))),f327(f327(f309(x44651),x44652),x44653)) % 177.41/177.18 [4485]E(f327(f327(f86(f916(f916(x44851)),f916(f916(x44851))),f55(x44851,x44852)),f327(f327(f18(f916(f916(x44851)),f916(f916(x44851)),f916(f916(x44851))),f327(f327(f8(f916(f916(x44851)),f922(f916(f916(x44851)),f916(f916(x44851))),f916(f916(x44851))),f135(f916(x44851))),f327(f155(f916(x44851),f916(x44851)),f327(f152(x44851),x44853)))),f5(f916(f916(x44851))))),f55(x44851,f327(f327(f152(x44851),x44853),x44852))) % 177.41/177.18 [4488]E(f327(f262(x44881),f327(f327(f18(x44881,a910,a910),f327(f327(f8(a910,f922(a910,a910),x44881),a326),f327(f327(f7(x44881,f922(x44881,a910),a910),f329(x44881)),x44882))),f327(f327(f7(x44881,f922(x44881,a910),a910),f329(x44881)),x44883))),f327(f327(f102(f922(x44881,a910)),x44882),x44883)) % 177.41/177.18 [4489]E(f327(f262(x44891),f327(f327(f18(x44891,a910,a910),f327(f327(f8(a910,f922(a910,a910),x44891),a325),f327(f327(f7(x44891,f922(x44891,a910),a910),f329(x44891)),x44892))),f327(f327(f7(x44891,f922(x44891,a910),a910),f329(x44891)),x44893))),f327(f327(f103(f922(x44891,a910)),x44892),x44893)) % 177.41/177.18 [4578]E(f327(f327(f40(x45781,f922(f922(x45781,a910),a910)),x45782),f327(f327(f7(x45781,f922(f922(x45781,a910),a910),f922(f922(x45781,a910),a910)),f327(f327(f8(f922(x45781,a910),f922(f922(f922(x45781,a910),a910),f922(f922(x45781,a910),a910)),x45781),f309(f922(x45781,a910))),f327(f327(f8(f922(x45781,a910),f922(x45781,a910),x45781),f285(x45781,x45781,x45783)),f327(f327(f7(x45781,f922(x45781,a910),f922(x45781,a910)),f309(x45781)),f190(f922(x45781,a910)))))),f190(f922(f922(x45781,a910),a910)))),f327(f327(f61(x45781),x45782),x45783)) % 177.41/177.18 [4580]E(f327(f327(f203(x45801),f327(f327(f81(a1),f327(f327(f72(f921(a1,a1),a1,x45801,f251(a1,a1)),f214(x45801)),x45802)),f327(f327(f72(f921(a1,a1),a1,x45801,f251(a1,a1)),f214(x45801)),x45803))),f327(f327(f81(a1),f327(f327(f72(f921(a1,a1),a1,x45801,f256(a1,a1)),f214(x45801)),x45802)),f327(f327(f72(f921(a1,a1),a1,x45801,f256(a1,a1)),f214(x45801)),x45803))),f230(x45801,x45802,x45803)) % 177.41/177.18 [4583]E(f327(f262(f916(x45831)),f327(f327(f18(f916(x45831),a910,a910),f327(f327(f8(a910,f922(a910,a910),f916(x45831)),a325),f327(f327(f7(f916(x45831),a915,a910),f327(f327(f8(a915,f922(a915,a910),f916(x45831)),a324),f191(f916(x45831)))),x45832))),f327(f327(f7(f916(x45831),f922(x45831,a910),a910),f327(f327(f8(f922(x45831,a910),f922(f922(x45831,a910),a910),f916(x45831)),f234(f922(x45831,a910))),f173(x45831))),f327(f173(x45831),x45833)))),f327(f173(f916(x45831)),f56(x45831,x45832,x45833))) % 177.41/177.18 [3984]E(f46(a915,f327(f327(f80(a915),f327(f327(f81(a915),x39841),x39842)),x39843),x39842),f46(a915,x39843,x39842)) % 177.41/177.18 [4031]E(f140(a915,f327(f302(a915,f327(f327(f80(a915),x40311),x40312)),x40313)),f327(f327(f139(a915),x40312),f140(a915,f327(f302(a915,x40311),x40313)))) % 177.41/177.18 [4072]E(f327(f327(f80(a1),f327(f101(a1),x40721)),f327(f327(f80(a1),f327(f101(a1),x40722)),x40723)),f327(f327(f80(a1),f327(f101(a1),f327(f327(f80(a915),x40721),x40722))),x40723)) % 177.41/177.18 [4079]E(f327(f327(f23(f922(x40791,a910)),f327(f327(f23(f922(x40791,a910)),x40792),x40793)),x40793),f327(f327(f23(f922(x40791,a910)),x40792),x40793)) % 177.41/177.18 [4080]E(f327(f327(f102(f922(x40801,a910)),f327(f327(f23(f922(x40801,a910)),x40802),x40803)),x40803),f327(f327(f102(f922(x40801,a910)),x40802),x40803)) % 177.41/177.18 [4104]E(f327(f327(f289(x41041,x41041,x41042),f307(x41041,f190(f922(f921(x41041,x41041),a910)))),x41043),x41043) % 177.41/177.18 [4112]E(f327(f327(f102(f922(x41121,a910)),f327(f281(x41121),x41122)),f327(f281(x41121),x41123)),f327(f281(x41121),f327(f327(f102(f922(f921(x41121,x41121),a910)),x41122),x41123))) % 177.41/177.18 [4122]E(f266(x41221,f327(f327(f152(f921(a100,x41221)),f327(f327(f252(a100,x41221),f2(a100)),x41222)),x41223)),f266(x41221,x41223)) % 177.41/177.18 [4124]E(f327(f327(f103(f922(x41241,a910)),f39(f922(x41241,a910),x41242)),f39(f922(x41241,a910),x41243)),f39(f922(x41241,a910),f327(f327(f102(f922(f922(x41241,a910),a910)),x41242),x41243))) % 177.41/177.18 [4125]E(f327(f327(f102(f922(x41251,a910)),f38(f922(x41251,a910),x41252)),f38(f922(x41251,a910),x41253)),f38(f922(x41251,a910),f327(f327(f102(f922(f922(x41251,a910),a910)),x41252),x41253))) % 177.41/177.18 [4162]E(f327(f327(f289(x41621,x41621,x41621),f327(f327(f184(f921(x41621,x41621),a910),x41622),x41623)),x41623),f327(f327(f184(f921(x41621,x41621),a910),f327(a113,x41622)),x41623)) % 177.41/177.18 [4208]P1(f327(f327(f234(f922(x42081,a910)),f327(f327(f23(f922(x42081,a910)),x42082),x42083)),x42082)) % 177.41/177.18 [4209]P1(f327(f327(f234(f922(x42091,a910)),f327(f327(f103(f922(x42091,a910)),x42092),x42093)),x42093)) % 177.41/177.18 [4210]P1(f327(f327(f234(f922(x42101,a910)),f327(f327(f103(f922(x42101,a910)),x42102),x42103)),x42102)) % 177.41/177.18 [4234]E(f307(x42341,f327(f327(f102(f922(f921(x42341,x42341),a910)),f307(x42341,x42342)),f307(x42341,x42343))),f307(x42341,f327(f327(f102(f922(f921(x42341,x42341),a910)),x42342),x42343))) % 177.41/177.18 [4238]E(f38(f922(x42381,a910),f327(f327(f309(f922(x42381,a910)),x42382),f327(f327(f309(f922(x42381,a910)),x42383),f190(f922(f922(x42381,a910),a910))))),f327(f327(f102(f922(x42381,a910)),x42382),x42383)) % 177.41/177.18 [4239]E(f39(f922(x42391,a910),f327(f327(f309(f922(x42391,a910)),x42392),f327(f327(f309(f922(x42391,a910)),x42393),f190(f922(f922(x42391,a910),a910))))),f327(f327(f103(f922(x42391,a910)),x42392),x42393)) % 177.41/177.18 [4244]E(f327(f327(f289(x42441,x42441,x42441),f327(f327(f184(f921(x42441,x42441),a910),x42442),x42443)),x42443),f327(f327(f289(x42441,x42441,x42441),x42443),f327(f327(f184(f921(x42441,x42441),a910),x42442),x42443))) % 177.41/177.18 [4313]E(f327(f327(f102(f922(x43131,a910)),f327(f262(x43131),f327(f327(f7(x43131,x43131,a910),a324),x43132))),x43133),f327(f327(f309(x43131),x43132),x43133)) % 177.41/177.18 [4315]E(f327(a106,f327(f327(f6(x43151,a1),f327(f327(f8(a915,a1,x43151),f101(a1)),x43152)),x43153)),f327(f327(f6(x43151,a915),x43152),x43153)) % 177.41/177.18 [4316]E(f327(a106,f327(f327(f9(x43161,a1),f327(f327(f8(a915,a1,x43161),f101(a1)),x43162)),x43163)),f327(f327(f9(x43161,a915),x43162),x43163)) % 177.41/177.18 [4390]E(f327(f157(f916(x43901),x43901,f327(f172(x43901),x43902),f327(f16(f922(f916(x43901),f916(x43901)),x43901),f327(f327(f7(f916(x43901),f916(x43901),f916(x43901)),f135(x43901)),x43902))),x43903),f327(f172(x43901),f327(f327(f135(x43901),x43903),x43902))) % 177.41/177.18 [4418]P1(f327(f327(f234(f922(f922(x44181,a910),a910)),f327(f327(f102(f922(f922(x44181,a910),a910)),f327(f308(x44181),x44182)),f327(f308(x44181),x44183))),f327(f308(x44181),f327(f327(f102(f922(x44181,a910)),x44182),x44183)))) % 177.41/177.18 [4507]E(f327(f262(x45071),f327(f327(f18(x45071,a910,a910),f327(f327(f8(a910,f922(a910,a910),x45071),a325),f327(f327(f7(x45071,f922(x45071,a910),a910),f329(x45071)),x45072))),f327(f327(f8(a910,a910,x45071),a322),f327(f327(f7(x45071,f922(x45071,a910),a910),f329(x45071)),x45073)))),f327(f327(f23(f922(x45071,a910)),x45072),x45073)) % 177.41/177.18 [4531]E(f327(f36(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,a915,a910),f235(a915)),f327(f191(f916(x45311)),x45312)))),f327(f327(f8(x45311,a910,a915),x45313),f327(f165(x45311),x45312))))),f327(f191(f916(x45311)),f327(f137(x45311,x45313),x45312))) % 177.41/177.18 [4533]E(f327(f191(f916(x45331)),f177(x45331,x45332,x45333)),f327(f36(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,a915,a910),f235(a915)),f327(f191(f916(x45331)),x45332)))),f327(f327(f7(a915,f922(a915,a910),a910),f329(a915)),x45333))))) % 177.41/177.18 [4630]E(f327(f327(f103(f922(f921(f916(x46301),f916(x46301)),a910)),f327(f310(f921(f921(x46301,f916(x46301)),f921(x46301,f916(x46301))),f921(f916(x46301),f916(x46301)),f258(f921(x46301,f916(x46301)),f916(x46301),f921(x46301,f916(x46301)),f916(x46301),f327(f257(x46301,f916(x46301),f916(x46301)),f152(x46301)),f327(f257(x46301,f916(x46301),f916(x46301)),f152(x46301)))),f320(x46301,f916(x46301),x46302,f327(f144(x46301,x46302),x46303)))),f327(f262(f921(f916(x46301),f916(x46301))),f327(f257(f916(x46301),f916(x46301),a910),f327(f327(f7(f916(x46301),f922(f916(x46301),a910),f922(f916(x46301),a910)),f327(f327(f8(f922(a910,a910),f922(f922(f916(x46301),a910),f922(f916(x46301),a910)),f916(x46301)),f8(a910,a910,f916(x46301))),f327(f327(f8(a910,f922(a910,a910),f916(x46301)),a325),f327(f327(f7(f916(x46301),a915,a910),f327(f327(f8(a915,f922(a915,a910),f916(x46301)),a324),f191(f916(x46301)))),f327(a113,x46303))))),f327(f327(f7(f916(x46301),a915,a910),f327(f327(f8(a915,f922(a915,a910),f916(x46301)),a324),f191(f916(x46301)))),f327(a113,x46303)))))),f327(f144(x46301,x46302),f327(a113,x46303))) % 177.41/177.18 [4126]E(f46(a915,f327(a113,f327(f327(f80(a915),f327(f327(f81(a915),x41261),x41262)),x41263)),x41262),f46(a915,f327(a113,x41263),x41262)) % 177.41/177.18 [4376]E(f327(f262(x43761),f327(f327(f18(x43761,a910,a910),f327(f327(f8(a910,f922(a910,a910),x43761),a325),x43762)),x43763)),f327(f327(f103(f922(x43761,a910)),f327(f262(x43761),x43762)),f327(f262(x43761),x43763))) % 177.41/177.18 [4377]E(f327(f262(x43771),f327(f327(f18(x43771,a910,a910),f327(f327(f8(a910,f922(a910,a910),x43771),a326),x43772)),x43773)),f327(f327(f102(f922(x43771,a910)),f327(f262(x43771),x43772)),f327(f262(x43771),x43773))) % 177.41/177.18 [4379]E(f327(f327(f135(x43791),f327(f327(f139(x43791),f46(a915,x43792,f327(f191(f916(x43791)),x43793))),x43793)),f327(f327(f176(x43791),f46(a915,x43792,f327(f191(f916(x43791)),x43793))),x43793)),f327(f327(f327(f184(f916(x43791),f916(x43791)),x43792),f168(x43791)),x43793)) % 177.41/177.18 [4385]E(f327(f262(x43851),f327(f327(f18(x43851,a910,a910),f327(f327(f8(a910,f922(a910,a910),x43851),a330),x43852)),x43853)),f327(f327(f102(f922(x43851,a910)),f327(f79(f922(x43851,a910)),f327(f262(x43851),x43852))),f327(f262(x43851),x43853))) % 177.41/177.18 [4401]E(f327(f327(f80(a915),f327(f191(f916(x44011)),f327(f137(x44011,x44012),x44013))),f327(f191(f916(x44011)),f327(f137(x44011,f327(f327(f8(a910,a910,x44011),a322),x44012)),x44013))),f327(f191(f916(x44011)),x44013)) % 177.41/177.18 [4424]P1(f327(f327(f234(f922(x44241,a910)),f327(f327(f102(f922(x44241,a910)),f39(f922(x44241,a910),x44242)),f39(f922(x44241,a910),x44243))),f39(f922(x44241,a910),f327(f327(f103(f922(f922(x44241,a910),a910)),x44242),x44243)))) % 177.41/177.18 [4438]E(f327(f173(x44381),f327(f137(x44381,f327(f327(f8(a910,a910,x44381),a322),f327(f327(f7(x44381,x44381,a910),a324),x44382))),x44383)),f327(f327(f23(f922(x44381,a910)),f327(f173(x44381),x44383)),f327(f327(f309(x44381),x44382),f190(f922(x44381,a910))))) % 177.41/177.18 [4447]P1(f327(f327(f234(f922(f921(x44471,x44471),a910)),f327(f327(f102(f922(f921(x44471,x44471),a910)),f307(x44471,x44472)),f307(x44471,x44473))),f307(x44471,f327(f327(f102(f922(f921(x44471,x44471),a910)),x44472),x44473)))) % 177.41/177.18 [4470]E(f327(f327(f81(a915),f327(a113,f327(a113,f2(a915)))),f327(f327(f6(a915,a915),f327(f327(f8(a915,a915,a915),f327(f80(a915),x44701)),f327(f327(f7(a915,a915,a915),f81(a915)),x44702))),f327(f282(a915),x44703))),f327(f327(f81(a915),x44703),f327(f327(f80(a915),x44701),f327(f327(f80(a915),x44701),f327(f327(f81(a915),f327(f327(f23(a915),x44703),f78(a915))),x44702))))) % 177.41/177.18 [4480]E(f327(f262(x44801),f327(f327(f18(x44801,a910,a910),f327(f327(f8(a910,f922(a910,a910),x44801),a325),f327(f327(f7(x44801,f922(x44801,a910),a910),f329(x44801)),f327(f173(x44801),x44802)))),x44803)),f327(f173(x44801),f327(f137(x44801,x44803),x44802))) % 177.41/177.18 [4629]E(f327(f262(x46291),f327(f327(f8(f922(a915,a910),a910,x46291),f87(a915)),f327(f327(f7(x46291,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),x46291),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),x46291),f327(f8(a910,f922(a910,a910),a915),a325)),f327(f327(f7(x46291,f922(a915,x46291),f922(a915,a910)),f327(f327(f8(f922(x46291,a910),f922(f922(a915,x46291),f922(a915,a910)),x46291),f8(x46291,a910,a915)),a324)),f327(f165(x46291),x46292))))),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,a915,a910),f235(a915)),f327(f191(f916(x46291)),x46292)))),f327(f327(f7(a915,f922(a915,a910),a910),f329(a915)),x46293))))),f327(f173(x46291),f177(x46291,x46292,x46293))) % 177.41/177.18 [4520]E(f327(f262(x45201),f327(f327(f18(x45201,a910,a910),f327(f327(f8(a910,f922(a910,a910),x45201),a330),f327(f327(f8(a910,a910,x45201),a322),f327(f327(f7(x45201,x45201,a910),a324),x45202)))),x45203)),f327(f327(f309(x45201),x45202),f327(f262(x45201),x45203))) % 177.41/177.18 [4552]E(f327(f327(f155(f921(x45521,a915),x45521),f251(x45521,a915)),f327(f137(f921(x45521,a915),f327(f327(f7(f921(x45521,a915),f922(a915,a910),a910),f327(f327(f8(a915,f922(f922(a915,a910),a910),f921(x45521,a915)),f329(a915)),f256(x45521,a915))),x45522)),f327(f327(f182(x45521,a915),x45523),f140(a915,f327(f302(a915,f2(a915)),f327(f191(f916(x45521)),x45523)))))),f177(x45521,x45523,x45522)) % 177.41/177.18 [4579]E(f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f6(a915,a1),f327(f327(f8(a1,a1,a915),f327(f80(a1),x45791)),f327(f327(f7(a915,a1,a1),f327(f327(f8(a1,f922(a1,a1),a915),f81(a1)),f101(a1))),x45792))),f327(f282(a915),x45793))),f327(f327(f81(a1),f327(f101(a1),x45793)),f327(f327(f80(a1),x45791),f327(f327(f80(a1),x45791),f327(f327(f81(a1),f327(f101(a1),f327(f327(f23(a915),x45793),f78(a915)))),x45792))))) % 177.41/177.18 [4621]E(f327(f262(f921(x46211,x46212)),f327(f257(x46211,x46212,a910),f327(f327(f7(x46211,f922(f921(x46212,x46211),a910),f922(x46212,a910)),f327(f327(f8(f922(x46212,f922(f922(f921(x46212,x46211),a910),a910)),f922(f922(f921(x46212,x46211),a910),f922(x46212,a910)),x46211),f7(x46212,f922(f921(x46212,x46211),a910),a910)),f327(f327(f8(f922(x46212,f921(x46212,x46211)),f922(x46212,f922(f922(f921(x46212,x46211),a910),a910)),x46211),f327(f8(f921(x46212,x46211),f922(f922(f921(x46212,x46211),a910),a910),x46212),f329(f921(x46212,x46211)))),f327(f7(x46212,x46211,f921(x46212,x46211)),f252(x46212,x46211))))),x46213))),f327(f286(x46212,x46211),x46213)) % 177.41/177.18 [4643]E(f327(f262(f916(x46431)),f327(f327(f8(f922(x46431,a910),a910,f916(x46431)),f87(x46431)),f327(f327(f8(f922(x46431,f922(f916(x46431),a910)),f922(x46431,a910),f916(x46431)),f327(f8(f922(f916(x46431),a910),a910,x46431),f87(f916(x46431)))),f327(f327(f7(f916(x46431),f922(x46431,f922(f916(x46431),a910)),f922(x46431,f922(f916(x46431),a910))),f327(f327(f8(f922(x46431,f922(f922(f916(x46431),a910),f922(f916(x46431),a910))),f922(f922(x46431,f922(f916(x46431),a910)),f922(x46431,f922(f916(x46431),a910))),f916(x46431)),f18(x46431,f922(f916(x46431),a910),f922(f916(x46431),a910))),f327(f327(f8(f922(x46431,f922(f916(x46431),f922(a910,a910))),f922(x46431,f922(f922(f916(x46431),a910),f922(f916(x46431),a910))),f916(x46431)),f327(f8(f922(f916(x46431),f922(a910,a910)),f922(f922(f916(x46431),a910),f922(f916(x46431),a910)),x46431),f18(f916(x46431),a910,a910))),f327(f327(f8(f922(x46431,f922(f916(x46431),a910)),f922(x46431,f922(f916(x46431),f922(a910,a910))),f916(x46431)),f327(f8(f922(f916(x46431),a910),f922(f916(x46431),f922(a910,a910)),x46431),f327(f8(a910,f922(a910,a910),f916(x46431)),a325))),f327(f327(f7(f916(x46431),f922(x46431,f922(f916(x46431),f916(x46431))),f922(x46431,f922(f916(x46431),a910))),f327(f327(f8(f922(f922(f916(x46431),f916(x46431)),f922(f916(x46431),a910)),f922(f922(x46431,f922(f916(x46431),f916(x46431))),f922(x46431,f922(f916(x46431),a910))),f916(x46431)),f8(f922(f916(x46431),f916(x46431)),f922(f916(x46431),a910),x46431)),f327(f327(f8(f922(f916(x46431),a910),f922(f922(f916(x46431),f916(x46431)),f922(f916(x46431),a910)),f916(x46431)),f8(f916(x46431),a910,f916(x46431))),a324))),f152(x46431)))))),f327(f327(f7(x46431,f922(f916(x46431),a910),f922(f916(x46431),a910)),f327(f327(f8(f922(a910,a910),f922(f922(f916(x46431),a910),f922(f916(x46431),a910)),x46431),f8(a910,a910,f916(x46431))),f327(f327(f8(a910,f922(a910,a910),x46431),a325),f327(f327(f7(x46431,f922(x46431,a910),a910),f329(x46431)),x46432)))),f327(f327(f7(f916(x46431),f922(f916(x46431),a910),a910),f329(f916(x46431))),x46433)))))),f175(x46431,x46432,x46433)) % 177.41/177.18 [4640]E(f327(f327(f86(a1,f921(a1,a1)),f327(f327(f23(a1),x46401),x46402)),f327(f327(f7(a1,f921(a1,a1),f921(a1,a1)),f327(f327(f18(a1,f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),f327(f327(f8(a910,f922(f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),a1),f97(f921(a1,a1))),f327(f234(a1),f2(a1)))),f327(f252(a1,a1),f327(f327(f80(a1),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x46403)),f78(a1))))),f327(f327(f252(a1,a1),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x46403)),x46401))),f327(f44(x46402),f327(f327(f252(a1,a1),x46403),x46401))) % 177.41/177.18 [4663]~E(f29(x46631,x46632),f30(x46633,x46634)) % 177.41/177.18 [3681]E(f117(x36811,f327(x36812,x36813),f327(x36814,x36813)),f327(f205(x36811,x36812,x36814),x36813)) % 177.41/177.18 [3734]E(f327(f327(f245(x37341,x37342,x37343),x37344),f2(a915)),x37342) % 177.41/177.18 [3774]E(f186(x37741,x37742,x37743,f327(a113,x37744)),f327(x37743,x37744)) % 177.41/177.18 [3816]E(f171(x38161,x38162,f171(x38161,x38163,x38164)),f171(x38161,x38163,f171(x38161,x38162,x38164))) % 177.41/177.18 [3817]E(f127(x38171,x38172,f117(x38171,x38173,x38174)),f117(x38171,f127(x38171,x38172,x38173),x38174)) % 177.41/177.18 [3952]E(f327(f157(x39521,x39522,x39523,x39524),f114(x39522)),x39523) % 177.41/177.18 [3953]E(f327(f143(x39531,x39532,x39533,x39534),f114(x39532)),x39534) % 177.41/177.18 [3990]E(f327(f191(f919(x39901,x39902)),f222(x39901,x39902,x39903,x39904)),f2(a915)) % 177.41/177.18 [4015]E(f327(f257(x40151,x40152,x40153),f255(x40151,x40152,x40153,x40154)),x40154) % 177.41/177.18 [4059]E(f327(f327(f135(x40591),f170(x40591,x40592,x40593)),f170(x40591,x40594,x40593)),f327(f327(f135(x40591),f170(x40591,x40594,x40593)),f170(x40591,x40592,x40593))) % 177.41/177.18 [4145]E(f327(f327(f259(x41451,x41452,x41453,f921(x41452,x41453)),x41454),f252(x41452,x41453)),x41454) % 177.41/177.18 [4155]E(f128(x41551,x41552,x41553,x41554,f120(x41552)),x41553) % 177.41/177.18 [4161]E(f74(x41611,x41612,x41613,x41614,f327(x41613,x41614)),x41613) % 177.41/177.18 [4431]P40(x44311,x44312,x44313,x44314,f190(f922(x44311,a910)),x44314) % 177.41/177.18 [3483]E(f327(f327(f16(x34831,x34832),x34833),x34834),x34833) % 177.41/177.18 [3764]E(f171(x37641,x37642,f327(f137(x37641,x37643),x37644)),f327(f137(x37641,x37643),f171(x37641,x37642,x37644))) % 177.41/177.18 [3799]E(f327(f327(f64(x37991,x37992,x37993),x37994),f190(f922(x37991,a910))),x37994) % 177.41/177.18 [3823]E(f327(f327(f165(x38231),f327(f327(f152(x38231),x38232),x38233)),f327(a113,x38234)),f327(f327(f165(x38231),x38233),x38234)) % 177.41/177.18 [3891]E(f327(f327(x38911,x38912),f327(f185(x38913,x38914,x38911),x38912)),f327(f185(x38913,x38914,x38911),f327(a113,x38912))) % 177.41/177.18 [3933]E(f255(x39331,x39332,x39333,f327(f257(x39331,x39332,x39333),x39334)),x39334) % 177.41/177.18 [3988]E(f327(f327(f160(x39881,f327(f327(f152(x39881),x39882),x39883)),f2(a915)),x39884),f327(f327(f152(x39881),x39884),x39883)) % 177.41/177.18 [4000]E(f327(f327(f40(f922(x40001,a910),f922(x40002,a910)),x40003),f310(x40001,x40002,x40004)),f327(f310(x40001,x40002,x40004),f38(f922(x40001,a910),x40003))) % 177.41/177.18 [4001]E(f327(f327(f40(f922(x40011,a910),f922(x40012,a910)),x40013),f311(x40012,x40011,x40014)),f327(f311(x40012,x40011,x40014),f38(f922(x40011,a910),x40013))) % 177.41/177.18 [4026]E(f121(x40261,f131(x40262,f917(x40261),x40263,x40264)),f327(f119(x40262,x40261,x40264),x40263)) % 177.41/177.18 [4100]E(f327(f126(x41001,x41002),f127(x41001,x41003,x41004)),f327(f327(f80(a915),f327(f327(f80(a915),f327(x41002,x41003)),f327(f126(x41001,x41002),x41004))),f327(a113,f2(a915)))) % 177.41/177.18 [4121]E(f327(f143(x41211,x41212,f327(f7(x41212,x41211,x41211),x41213),x41214),f327(f169(x41212),f114(x41212))),x41214) % 177.41/177.18 [4167]E(f76(x41671,x41672,x41673,x41674,f190(f922(x41671,a910))),x41673) % 177.41/177.18 [4228]E(f225(x42281,f921(x42282,f917(x42282)),x42283,f327(f257(x42282,f917(x42282),x42281),x42284),f327(f136(x42282),f120(x42282))),x42283) % 177.41/177.18 [4361]E(f327(f257(x43611,x43612,x43613),f327(f327(f8(f922(x43612,f921(x43611,x43612)),f922(x43612,x43613),x43611),f327(f8(f921(x43611,x43612),x43613,x43612),x43614)),f252(x43611,x43612))),x43614) % 177.41/177.18 [3672]E(f327(f256(x36721,x36722),f327(f327(f252(x36721,x36722),x36723),x36724)),x36724) % 177.41/177.18 [3673]E(f327(f251(x36731,x36732),f327(f327(f252(x36731,x36732),x36733),x36734)),x36733) % 177.41/177.18 [3706]E(f327(f191(f916(x37061)),f327(f327(f160(x37061,x37062),x37063),x37064)),f327(f191(f916(x37061)),x37062)) % 177.41/177.18 [3707]E(f327(f191(f916(x37071)),f327(f327(f155(x37072,x37071),x37073),x37074)),f327(f191(f916(x37072)),x37074)) % 177.41/177.18 [3728]E(f327(f327(f139(x37281),f327(a113,x37282)),f327(f327(f152(x37281),x37283),x37284)),f327(f327(f139(x37281),x37282),x37284)) % 177.41/177.18 [3794]E(f327(f327(f176(x37941),x37942),f170(x37941,x37943,x37944)),f170(x37941,f327(f327(f238(a915),x37942),x37943),x37944)) % 177.41/177.18 [3795]E(f327(f327(f139(x37951),x37952),f170(x37951,x37953,x37954)),f170(x37951,f327(f327(f23(a915),x37953),x37952),x37954)) % 177.41/177.18 [3801]E(f327(f327(f309(x38011),x38012),f327(f327(f309(x38011),x38013),x38014)),f327(f327(f309(x38011),x38013),f327(f327(f309(x38011),x38012),x38014))) % 177.41/177.18 [3805]E(f327(f327(f155(x38051,x38052),x38053),f115(x38051,x38054)),f115(x38052,f327(f327(f155(x38051,x38052),x38053),x38054))) % 177.41/177.18 [3821]E(f327(f169(x38211),f327(f327(f155(x38212,x38211),x38213),x38214)),f327(f327(f155(x38212,x38211),x38213),f327(f169(x38212),x38214))) % 177.41/177.18 [3822]E(f327(f327(f155(x38221,x38222),x38223),f327(f172(x38221),x38224)),f327(f172(x38222),f327(f327(f155(x38221,x38222),x38223),x38224))) % 177.41/177.18 [3837]E(f327(f327(f176(x38371),f327(a113,x38372)),f327(f327(f152(x38371),x38373),x38374)),f327(f327(f152(x38371),x38373),f327(f327(f176(x38371),x38372),x38374))) % 177.41/177.18 [3841]E(f327(f173(x38411),f327(f327(f155(x38412,x38411),x38413),x38414)),f327(f310(x38412,x38411,x38413),f327(f173(x38412),x38414))) % 177.41/177.18 [3854]E(f327(f327(f155(x38541,x38542),f327(f16(x38542,x38541),x38543)),x38544),f170(x38542,f327(f191(f916(x38541)),x38544),x38543)) % 177.41/177.18 [3890]E(f17(x38901,x38902,x38903,f327(a3,f327(a113,f327(a20,x38904)))),f327(x38903,x38904)) % 177.41/177.18 [3894]E(f327(f327(f135(x38941),f327(f137(x38941,x38942),x38943)),f327(f137(x38941,x38942),x38944)),f327(f137(x38941,x38942),f327(f327(f135(x38941),x38943),x38944))) % 177.41/177.18 [3907]E(f153(x39071,f327(f327(f155(x39072,x39071),x39073),f153(x39072,x39074))),f153(x39071,f327(f327(f155(x39072,x39071),x39073),x39074))) % 177.41/177.18 [3922]E(f327(f286(x39221,x39221),f327(f327(f288(x39222,x39221),x39223),x39224)),f327(f327(f288(x39222,x39221),f327(f286(x39222,x39222),x39223)),x39224)) % 177.41/177.18 [3934]E(f327(f327(f289(x39341,x39342,x39343),x39344),f190(f922(f921(x39342,x39343),a910))),f190(f922(f921(x39341,x39343),a910))) % 177.41/177.18 [3935]E(f327(f327(f176(x39351),f327(f327(f23(a915),x39352),x39353)),f327(f327(f139(x39351),x39353),x39354)),f327(f327(f139(x39351),x39353),f327(f327(f176(x39351),x39352),x39354))) % 177.41/177.18 [3954]E(f327(f327(f135(x39541),f170(x39541,x39542,x39543)),f170(x39541,x39544,x39543)),f170(x39541,f327(f327(f80(a915),x39542),x39544),x39543)) % 177.41/177.18 [3955]E(f327(f327(f327(f278(x39551),x39552),x39553),x39554),f327(f252(f922(a100,f922(a910,f918(f917(x39551)))),f921(a100,a100)),f327(f43(x39551),x39552))) % 177.41/177.18 [3981]E(f39(f922(x39811,a910),f327(f310(x39812,f922(x39811,a910),x39813),x39814)),f327(f327(f41(x39812,f922(x39811,a910)),x39814),x39813)) % 177.41/177.18 [3982]E(f38(f922(x39821,a910),f327(f310(x39822,f922(x39821,a910),x39823),x39824)),f327(f327(f40(x39822,f922(x39821,a910)),x39824),x39823)) % 177.41/177.18 [3983]E(f327(f191(f916(f921(x39831,x39832))),f327(f327(f182(x39831,x39832),x39833),x39834)),f327(f327(f238(a915),f327(f191(f916(x39831)),x39833)),f327(f191(f916(x39832)),x39834))) % 177.41/177.18 [3985]E(f327(f311(x39851,x39852,x39853),f327(f79(f922(x39852,a910)),x39854)),f327(f79(f922(x39851,a910)),f327(f311(x39851,x39852,x39853),x39854))) % 177.41/177.18 [4036]E(f327(f311(x40361,x40362,x40363),f327(f262(x40362),x40364)),f327(f262(x40361),f327(f327(f8(x40362,a910,x40361),x40364),x40363))) % 177.41/177.18 [4054]E(f327(f327(f165(x40541),f327(f327(f135(x40541),x40542),f327(f327(f152(x40541),x40543),x40544))),f327(f191(f916(x40541)),x40542)),x40543) % 177.41/177.18 [4077]E(f327(f310(x40771,x40772,x40773),f327(f311(x40771,x40772,x40773),x40774)),f327(f327(f103(f922(x40772,a910)),x40774),f327(f310(x40771,x40772,x40773),f242(f922(x40771,a910))))) % 177.41/177.18 [4096]P1(f327(f327(f329(x40961),f327(x40962,x40963)),f327(f310(x40964,x40961,x40962),f242(f922(x40964,a910))))) % 177.41/177.18 [4105]E(f19(x41051,x41052,x41053,f327(a3,f327(a113,f327(a20,x41054)))),f327(f327(x41053,x41054),f19(x41051,x41052,x41053,x41054))) % 177.41/177.18 [4109]E(f327(f327(f135(x41091),f170(x41091,x41092,x41093)),f327(f327(f152(x41091),x41093),x41094)),f327(f327(f152(x41091),x41093),f327(f327(f135(x41091),f170(x41091,x41092,x41093)),x41094))) % 177.41/177.18 [4111]E(f327(f327(f254(x41111,x41112),f327(f173(x41111),x41113)),f327(f16(f922(x41112,a910),x41111),f327(f173(x41112),x41114))),f327(f173(f921(x41111,x41112)),f60(x41111,x41112,x41113,x41114))) % 177.41/177.18 [4123]E(f156(x41231,x41232,f327(f327(f152(x41231),x41233),x41234)),f327(f327(f80(a915),f327(f327(f80(a915),f327(x41232,x41233)),f156(x41231,x41232,x41234))),f327(a113,f2(a915)))) % 177.41/177.18 [4136]E(f186(f916(x41361),f327(f327(f152(x41361),x41362),x41363),f327(f327(f7(a915,f916(x41361),f916(x41361)),f139(x41361)),x41363),x41364),f327(f327(f139(x41361),x41364),f327(f327(f152(x41361),x41362),x41363))) % 177.41/177.18 [4137]P23(x41371,f921(x41372,x41371),f331(x41373,x41374,x41372,x41371),f327(f327(f40(x41372,f922(x41371,a910)),x41374),x41373)) % 177.41/177.18 [4146]E(f327(f327(f23(f922(x41461,a910)),f327(f327(f23(f922(x41461,a910)),x41462),x41463)),f327(f327(f309(x41461),x41464),f190(f922(x41461,a910)))),f327(f327(f23(f922(x41461,a910)),x41462),f327(f327(f309(x41461),x41464),x41463))) % 177.41/177.18 [4159]E(f327(f327(f184(f922(x41591,x41592),f922(x41591,x41592)),x41593),f72(x41592,x41592,x41591,x41594)),f72(x41592,x41592,x41591,f327(f327(f184(x41592,x41592),x41593),x41594))) % 177.41/177.18 [4233]E(f327(f327(f327(f184(f916(x42331),f916(x42331)),x42332),f168(x42331)),f327(f327(f327(f184(f916(x42331),f916(x42331)),x42333),f168(x42331)),x42334)),f327(f327(f327(f184(f916(x42331),f916(x42331)),f327(f327(f80(a915),x42332),x42333)),f168(x42331)),x42334)) % 177.41/177.18 [4319]P1(f327(f327(f234(f922(x43191,a910)),f327(f173(x43191),f327(f327(f160(x43191,x43192),x43193),x43194))),f327(f327(f309(x43191),x43194),f327(f173(x43191),x43192)))) % 177.41/177.18 [4351]E(f327(f327(f40(f922(x43511,a910),f922(f921(x43511,x43512),a910)),x43513),f327(f327(f7(f922(x43511,a910),f922(x43511,f922(x43512,a910)),f922(f921(x43511,x43512),a910)),f254(x43511,x43512)),x43514)),f327(f327(f254(x43511,x43512),f38(f922(x43511,a910),x43513)),x43514)) % 177.41/177.18 [4389]E(f211(x43891,x43892,x43893,f327(f72(x43892,f922(a100,f922(a100,f922(f921(a100,a100),f922(a100,f917(x43892))))),x43891,f210(x43892)),x43894)),f212(x43891,x43892,x43894,x43893)) % 177.41/177.18 [4404]E(f207(x44041,x44042,x44043,f327(f72(x44042,f922(a100,f922(a100,f922(f921(a100,a100),f922(a100,f917(f918(x44042)))))),x44041,f206(x44042)),x44044)),f208(x44041,x44042,x44044,x44043)) % 177.41/177.18 [4409]P1(f327(f66(x44091,x44092,x44093,x44094,f190(f922(x44091,a910))),x44094)) % 177.41/177.18 [4448]E(f327(f327(f40(x44481,f922(x44482,a910)),x44483),f327(f327(f7(x44481,f922(x44482,a910),f922(x44482,a910)),f327(f327(f8(x44482,f922(f922(x44482,a910),f922(x44482,a910)),x44481),f309(x44482)),x44484)),f190(f922(x44482,a910)))),f327(f310(x44481,x44482,x44484),x44483)) % 177.41/177.18 [4455]P1(f327(f327(f234(f922(x44551,a910)),f327(f284(x44552,x44551),f327(f327(f103(f922(f921(x44552,x44551),a910)),x44553),x44554))),f327(f327(f103(f922(x44551,a910)),f327(f284(x44552,x44551),x44553)),f327(f284(x44552,x44551),x44554)))) % 177.41/177.18 [4456]P1(f327(f327(f234(f922(x44561,a910)),f327(f264(x44561,x44562),f327(f327(f103(f922(f921(x44561,x44562),a910)),x44563),x44564))),f327(f327(f103(f922(x44561,a910)),f327(f264(x44561,x44562),x44563)),f327(f264(x44561,x44562),x44564)))) % 177.41/177.18 [4516]P1(f327(f327(f234(f922(f921(x45161,x45162),a910)),f327(f310(x45162,f921(x45161,x45162),f331(x45163,x45164,x45161,x45162)),f327(f327(f40(x45161,f922(x45162,a910)),x45164),x45163))),f327(f327(f254(x45161,x45162),x45164),x45163))) % 177.41/177.18 [4517]E(f327(f119(x45171,f921(x45171,x45172),x45173),f327(f327(f8(f922(x45172,f917(f921(x45171,x45172))),f917(f921(x45171,x45172)),x45171),f119(x45172,f921(x45171,x45172),x45174)),f327(f327(f8(f922(x45172,f921(x45171,x45172)),f922(x45172,f917(f921(x45171,x45172))),x45171),f327(f8(f921(x45171,x45172),f917(f921(x45171,x45172)),x45172),f130(f921(x45171,x45172)))),f252(x45171,x45172)))),f132(x45171,x45172,x45173,x45174)) % 177.41/177.18 [4518]E(f276(x45181,x45182,x45183,f327(f72(x45182,f922(a100,f922(a100,f922(f921(a100,a100),f921(f922(a100,f922(a910,f918(f917(x45182)))),f921(a100,a100))))),x45181,f278(x45182)),x45184)),f279(x45181,x45182,x45184,x45183)) % 177.41/177.18 [4558]E(f85(f921(x45581,x45582),f327(f257(x45581,x45582,a910),f327(f327(f7(x45581,f922(x45582,a910),f922(x45582,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x45582,a910),f922(x45582,a910)),x45581),f8(a910,a910,x45582)),f327(f327(f8(a910,f922(a910,a910),x45581),a325),f327(a324,x45583)))),f327(a324,x45584)))),f327(f327(f252(x45581,x45582),x45583),x45584)) % 177.41/177.18 [4559]E(f90(f921(x45591,x45592),f327(f257(x45591,x45592,a910),f327(f327(f7(x45591,f922(x45592,a910),f922(x45592,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x45592,a910),f922(x45592,a910)),x45591),f8(a910,a910,x45592)),f327(f327(f8(a910,f922(a910,a910),x45591),a325),f327(a324,x45593)))),f327(a324,x45594)))),f327(f327(f252(x45591,x45592),x45593),x45594)) % 177.41/177.18 [4631]E(f327(f327(f257(f916(x46311),f916(x46311),f921(f916(x46311),f916(x46311))),f327(f327(f18(f916(x46311),f922(f916(x46311),f921(f916(x46311),f916(x46311))),f922(f916(x46311),f921(f916(x46311),f916(x46311)))),f327(f327(f8(f922(f916(x46311),f922(f921(f916(x46311),f916(x46311)),f921(f916(x46311),f916(x46311)))),f922(f922(f916(x46311),f921(f916(x46311),f916(x46311))),f922(f916(x46311),f921(f916(x46311),f916(x46311)))),f916(x46311)),f18(f916(x46311),f921(f916(x46311),f916(x46311)),f921(f916(x46311),f916(x46311)))),f327(f327(f8(f922(f916(x46311),f921(f916(x46311),f916(x46311))),f922(f916(x46311),f922(f921(f916(x46311),f916(x46311)),f921(f916(x46311),f916(x46311)))),f916(x46311)),f327(f8(f921(f916(x46311),f916(x46311)),f922(f921(f916(x46311),f916(x46311)),f921(f916(x46311),f916(x46311))),f916(x46311)),f327(f97(f921(f916(x46311),f916(x46311))),f327(x46312,x46313)))),f327(f327(f8(f916(x46311),f922(f916(x46311),f921(f916(x46311),f916(x46311))),f916(x46311)),f252(f916(x46311),f916(x46311))),f327(f152(x46311),x46313))))),f327(f327(f7(f916(x46311),f922(f916(x46311),f916(x46311)),f922(f916(x46311),f921(f916(x46311),f916(x46311)))),f327(f327(f8(f922(f916(x46311),f921(f916(x46311),f916(x46311))),f922(f922(f916(x46311),f916(x46311)),f922(f916(x46311),f921(f916(x46311),f916(x46311)))),f916(x46311)),f8(f916(x46311),f921(f916(x46311),f916(x46311)),f916(x46311))),f252(f916(x46311),f916(x46311)))),f327(f152(x46311),x46313)))),f167(x46311,x46312,x46314)),f167(x46311,x46312,f327(f327(f152(x46311),x46313),x46314))) % 177.41/177.18 [3746]E(f327(f191(f913(x37461)),f327(f327(f327(f91(x37461),x37462),x37463),x37464)),f2(a915)) % 177.41/177.18 [3870]E(f327(f327(f176(x38701),x38702),f327(f327(f176(x38701),x38703),x38704)),f327(f327(f176(x38701),f327(f327(f238(a915),x38702),x38703)),x38704)) % 177.41/177.18 [3871]E(f327(f327(f139(x38711),x38712),f327(f327(f139(x38711),x38713),x38714)),f327(f327(f139(x38711),f327(f327(f80(a915),x38712),x38713)),x38714)) % 177.41/177.18 [3882]E(f327(f327(f135(x38821),f327(f327(f152(x38821),x38822),x38823)),x38824),f327(f327(f152(x38821),x38822),f327(f327(f135(x38821),x38823),x38824))) % 177.41/177.18 [3883]E(f327(f327(f135(x38831),f327(f327(f135(x38831),x38832),x38833)),x38834),f327(f327(f135(x38831),x38832),f327(f327(f135(x38831),x38833),x38834))) % 177.41/177.18 [3965]E(f327(f327(f165(x39651),f327(f327(f152(x39651),x39652),x39653)),x39654),f186(x39651,x39652,f327(f165(x39651),x39653),x39654)) % 177.41/177.18 [3974]E(f327(f327(f184(x39741,x39741),x39742),f327(f327(f184(x39741,x39741),x39743),x39744)),f327(f327(f184(x39741,x39741),f327(f327(f81(a915),x39743),x39742)),x39744)) % 177.41/177.18 [4003]E(f327(f327(f102(f922(x40031,a910)),x40032),f327(f327(f309(x40031),x40033),x40034)),f327(f327(f309(x40031),x40033),f327(f327(f102(f922(x40031,a910)),x40032),x40034))) % 177.41/177.18 [4018]E(f327(f327(f327(f184(x40181,x40181),x40182),x40183),f327(x40183,x40184)),f327(x40183,f327(f327(f327(f184(x40181,x40181),x40182),x40183),x40184))) % 177.41/177.18 [4027]E(f327(f327(f289(x40271,x40272,x40273),f190(f922(f921(x40271,x40272),a910))),x40274),f190(f922(f921(x40271,x40273),a910))) % 177.41/177.18 [4042]E(f327(f327(f102(f922(x40421,a910)),f327(f327(f309(x40421),x40422),x40423)),x40424),f327(f327(f309(x40421),x40422),f327(f327(f102(f922(x40421,a910)),x40423),x40424))) % 177.41/177.18 [4061]E(f327(f36(f921(x40611,x40612)),f327(f327(f254(x40611,x40612),x40613),f327(f16(f922(x40612,a910),x40611),x40614))),f327(f327(f81(a915),f327(f36(x40611),x40613)),f327(f36(x40612),x40614))) % 177.41/177.18 [4068]E(f327(f327(f103(f922(x40681,a910)),f327(f327(f309(x40681),x40682),x40683)),f327(f327(f309(x40681),x40682),x40684)),f327(f327(f309(x40681),x40682),f327(f327(f103(f922(x40681,a910)),x40683),x40684))) % 177.41/177.18 [4081]E(f327(f327(f102(f922(x40811,a910)),x40812),f327(f327(f102(f922(x40811,a910)),x40813),x40814)),f327(f327(f102(f922(x40811,a910)),x40813),f327(f327(f102(f922(x40811,a910)),x40812),x40814))) % 177.41/177.18 [4082]E(f327(f327(f103(f922(x40821,a910)),x40822),f327(f327(f103(f922(x40821,a910)),x40823),x40824)),f327(f327(f103(f922(x40821,a910)),x40823),f327(f327(f103(f922(x40821,a910)),x40822),x40824))) % 177.41/177.18 [4092]E(f64(x40921,x40922,f327(f327(f8(x40922,f922(x40922,x40922),x40921),x40923),x40924)),f327(f65(x40922,x40921,x40923),x40924)) % 177.41/177.18 [4101]E(f180(x41011,f327(f327(f155(f916(x41012),f916(x41011)),f327(f155(x41012,x41011),x41013)),x41014)),f327(f327(f155(f916(x41012),f916(x41011)),f327(f155(x41012,x41011),x41013)),f180(x41012,x41014))) % 177.41/177.18 [4120]E(f327(f143(f916(x41201),f916(x41201),f135(x41201),f114(x41201)),f327(f327(f155(x41202,f916(x41201)),x41203),x41204)),f164(x41202,x41201,x41203,x41204)) % 177.41/177.18 [4180]E(f327(f72(x41801,x41801,x41801,f327(f327(f184(x41801,x41801),x41802),x41803)),f327(f327(f184(x41801,x41801),x41804),x41803)),f327(f327(f184(x41801,x41801),f327(f327(f80(a915),x41802),x41804)),x41803)) % 177.41/177.18 [4203]E(f327(f327(f103(f922(x42031,a910)),f327(f327(f23(f922(x42031,a910)),x42032),x42033)),f327(f327(f23(f922(x42031,a910)),x42032),x42034)),f327(f327(f23(f922(x42031,a910)),x42032),f327(f327(f102(f922(x42031,a910)),x42033),x42034))) % 177.41/177.18 [4204]E(f327(f327(f102(f922(x42041,a910)),f327(f327(f23(f922(x42041,a910)),x42042),x42043)),f327(f327(f23(f922(x42041,a910)),x42042),x42044)),f327(f327(f23(f922(x42041,a910)),x42042),f327(f327(f103(f922(x42041,a910)),x42043),x42044))) % 177.41/177.18 [4205]E(f327(f327(f103(f922(x42051,a910)),f327(f327(f102(f922(x42051,a910)),x42052),x42053)),f327(f327(f102(f922(x42051,a910)),x42052),x42054)),f327(f327(f102(f922(x42051,a910)),x42052),f327(f327(f103(f922(x42051,a910)),x42053),x42054))) % 177.41/177.18 [4206]E(f327(f327(f23(f922(x42061,a910)),f327(f327(f103(f922(x42061,a910)),x42062),x42063)),f327(f327(f103(f922(x42061,a910)),x42062),x42064)),f327(f327(f103(f922(x42061,a910)),x42062),f327(f327(f23(f922(x42061,a910)),x42063),x42064))) % 177.41/177.18 [4207]E(f327(f327(f102(f922(x42071,a910)),f327(f327(f103(f922(x42071,a910)),x42072),x42073)),f327(f327(f103(f922(x42071,a910)),x42072),x42074)),f327(f327(f103(f922(x42071,a910)),x42072),f327(f327(f102(f922(x42071,a910)),x42073),x42074))) % 177.41/177.18 [4212]E(f327(f36(f921(x42121,x42122)),f327(f327(f254(x42121,x42122),f327(f327(f309(x42121),x42123),f190(f922(x42121,a910)))),f327(f16(f922(x42122,a910),x42121),x42124))),f327(f36(x42122),x42124)) % 177.41/177.18 [4247]E(f327(f327(f41(x42471,f922(x42472,a910)),x42473),f327(f327(f8(f922(x42472,a910),f922(x42472,a910),x42471),f79(f922(x42472,a910))),x42474)),f327(f79(f922(x42472,a910)),f327(f327(f40(x42471,f922(x42472,a910)),x42473),x42474))) % 177.41/177.18 [4248]E(f327(f327(f40(x42481,f922(x42482,a910)),x42483),f327(f327(f8(f922(x42482,a910),f922(x42482,a910),x42481),f79(f922(x42482,a910))),x42484)),f327(f79(f922(x42482,a910)),f327(f327(f41(x42481,f922(x42482,a910)),x42483),x42484))) % 177.41/177.18 [4264]E(f327(f327(f289(x42641,x42641,x42641),f327(f327(f184(f921(x42641,x42641),a910),x42642),x42643)),f327(f327(f184(f921(x42641,x42641),a910),x42644),x42643)),f327(f327(f184(f921(x42641,x42641),a910),f327(f327(f80(a915),x42642),x42644)),x42643)) % 177.41/177.18 [4294]E(f327(f327(f41(x42941,f922(f922(x42942,a910),a910)),x42943),f327(f327(f8(f922(x42942,a910),f922(f922(x42942,a910),a910),x42941),f308(x42942)),x42944)),f327(f308(x42942),f327(f327(f41(x42941,f922(x42942,a910)),x42943),x42944))) % 177.41/177.18 [4324]E(f327(f327(f40(f922(x43241,a910),f922(x43242,a910)),x43243),f327(f327(f7(f922(x43241,a910),f922(x43241,f922(x43242,a910)),f922(x43242,a910)),f40(x43241,f922(x43242,a910))),x43244)),f327(f327(f40(x43241,f922(x43242,a910)),f38(f922(x43241,a910),x43243)),x43244)) % 177.41/177.18 [4325]E(f327(f327(f41(f922(x43251,a910),f922(x43252,a910)),x43253),f327(f327(f7(f922(x43251,a910),f922(x43251,f922(x43252,a910)),f922(x43252,a910)),f41(x43251,f922(x43252,a910))),x43254)),f327(f327(f41(x43251,f922(x43252,a910)),f38(f922(x43251,a910),x43253)),x43254)) % 177.41/177.18 [4330]E(f327(f327(f155(x43301,x43302),x43303),f327(f143(f916(x43301),f916(x43301),f135(x43301),f114(x43301)),x43304)),f327(f143(f916(x43302),f916(x43302),f135(x43302),f114(x43302)),f327(f327(f155(f916(x43301),f916(x43302)),f327(f155(x43301,x43302),x43303)),x43304))) % 177.41/177.18 [4332]E(f186(f916(x43321),f114(x43321),f327(f327(f8(f916(x43321),f916(x43321),a915),f327(f152(x43321),x43322)),f327(f327(f7(a915,f916(x43321),f916(x43321)),f176(x43321)),x43323)),x43324),f327(f327(f176(x43321),x43324),f327(f327(f152(x43321),x43322),x43323))) % 177.41/177.18 [4370]P1(f327(f327(f234(f922(x43701,a910)),f327(f310(x43702,x43701,x43703),f327(f311(x43702,x43701,x43703),x43704))),x43704)) % 177.41/177.18 [4372]E(f327(f310(f921(x43721,x43722),f921(x43722,x43721),f327(f257(x43721,x43722,f921(x43722,x43721)),f327(f7(x43722,x43721,f921(x43722,x43721)),f252(x43722,x43721)))),f327(f327(f254(x43721,x43722),x43723),f327(f16(f922(x43722,a910),x43721),x43724))),f327(f327(f254(x43722,x43721),x43724),f327(f16(f922(x43721,a910),x43722),x43723))) % 177.41/177.18 [4381]E(f327(f327(f40(x43811,f922(x43812,a910)),x43813),f327(f327(f8(f922(x43811,a910),f922(x43812,a910),x43811),f311(x43812,x43811,x43814)),f327(f327(f7(x43811,f922(x43811,a910),f922(x43811,a910)),f309(x43811)),f190(f922(x43811,a910))))),f327(f311(x43812,x43811,x43814),x43813)) % 177.41/177.18 [4382]E(f327(f327(f40(x43821,f922(x43822,a910)),x43823),f327(f327(f8(f922(x43821,a910),f922(x43822,a910),x43821),f285(x43821,x43822,x43824)),f327(f327(f7(x43821,f922(x43821,a910),f922(x43821,a910)),f309(x43821)),f190(f922(x43821,a910))))),f327(f285(x43821,x43822,x43824),x43823)) % 177.41/177.18 [4469]E(f327(f327(f103(f922(x44691,a910)),f327(f327(f103(f922(x44691,a910)),f327(f327(f102(f922(x44691,a910)),x44692),x44693)),f327(f327(f102(f922(x44691,a910)),x44693),x44694))),f327(f327(f102(f922(x44691,a910)),x44694),x44692)),f327(f327(f102(f922(x44691,a910)),f327(f327(f102(f922(x44691,a910)),f327(f327(f103(f922(x44691,a910)),x44692),x44693)),f327(f327(f103(f922(x44691,a910)),x44693),x44694))),f327(f327(f103(f922(x44691,a910)),x44694),x44692))) % 177.41/177.18 [4532]E(f327(f143(f916(x45321),f916(x45321),f135(x45321),f114(x45321)),f327(f327(f155(x45322,f916(x45321)),f327(f327(f7(x45322,f916(x45321),f916(x45321)),f327(f327(f8(x45321,f922(f916(x45321),f916(x45321)),x45322),f152(x45321)),x45323)),f114(x45321))),x45324)),f327(f327(f155(x45322,x45321),x45323),x45324)) % 177.41/177.18 [4542]E(f327(f327(f86(a1,x45421),f327(f105(a1),f327(f327(f80(a1),x45422),a98))),f327(f327(f18(a1,x45421,x45421),f327(f327(f7(a1,x45421,f922(x45421,x45421)),f327(f327(f8(a910,f922(x45421,f922(x45421,x45421)),a1),f97(x45421)),a195)),x45423)),f327(f327(f8(a915,x45421,a1),x45424),a106))),f186(x45421,x45423,x45424,f327(f105(a915),x45422))) % 177.41/177.18 [4573]E(f327(f262(x45731),f327(f327(f8(f922(x45732,a910),a910,x45731),f87(x45732)),f327(f327(f8(f922(x45732,a910),f922(x45732,a910),x45731),f327(f18(x45732,a910,a910),f327(f327(f8(a910,f922(a910,a910),x45732),a325),f327(f327(f7(x45732,f922(x45732,a910),a910),f329(x45732)),x45733)))),f327(f7(x45732,x45731,a910),x45734)))),f327(f285(x45732,x45731,f327(f262(f921(x45732,x45731)),f327(f257(x45732,x45731,a910),x45734))),x45733)) % 177.41/177.18 [4730]~P1(f327(f327(f190(f922(x47301,f922(x47302,a910))),x47303),x47304)) % 177.41/177.18 [4030]E(f327(f327(f165(x40301),f327(f327(f135(x40301),x40302),x40303)),f327(f327(f80(a915),f327(f191(f916(x40301)),x40302)),x40304)),f327(f327(f165(x40301),x40303),x40304)) % 177.41/177.18 [4035]E(f327(f327(f139(x40351),x40352),f327(f327(f176(x40351),f327(f327(f80(a915),x40353),x40352)),x40354)),f327(f327(f176(x40351),x40353),f327(f327(f139(x40351),x40352),x40354))) % 177.41/177.18 [4134]E(f327(f327(f102(f922(x41341,a910)),f327(f284(x41342,x41341),x41343)),f327(f284(x41342,x41341),x41344)),f327(f284(x41342,x41341),f327(f327(f102(f922(f921(x41342,x41341),a910)),x41343),x41344))) % 177.41/177.18 [4135]E(f327(f327(f102(f922(x41351,a910)),f327(f264(x41351,x41352),x41353)),f327(f264(x41351,x41352),x41354)),f327(f264(x41351,x41352),f327(f327(f102(f922(f921(x41351,x41352),a910)),x41353),x41354))) % 177.41/177.18 [4140]E(f327(f327(f23(f922(x41401,a910)),f327(f327(f103(f922(x41401,a910)),x41402),x41403)),x41404),f327(f327(f103(f922(x41401,a910)),x41402),f327(f327(f23(f922(x41401,a910)),x41403),x41404))) % 177.41/177.18 [4141]E(f327(f327(f102(f922(x41411,a910)),f327(f327(f102(f922(x41411,a910)),x41412),x41413)),x41414),f327(f327(f102(f922(x41411,a910)),x41412),f327(f327(f102(f922(x41411,a910)),x41413),x41414))) % 177.41/177.18 [4142]E(f327(f327(f103(f922(x41421,a910)),f327(f327(f103(f922(x41421,a910)),x41422),x41423)),x41424),f327(f327(f103(f922(x41421,a910)),x41422),f327(f327(f103(f922(x41421,a910)),x41423),x41424))) % 177.41/177.18 [4182]E(f327(f327(f102(f922(f921(x41821,x41822),a910)),f327(f286(x41822,x41821),x41823)),f327(f286(x41822,x41821),x41824)),f327(f286(x41822,x41821),f327(f327(f102(f922(f921(x41822,x41821),a910)),x41823),x41824))) % 177.41/177.18 [4183]E(f327(f327(f103(f922(f921(x41831,x41832),a910)),f327(f286(x41832,x41831),x41833)),f327(f286(x41832,x41831),x41834)),f327(f286(x41832,x41831),f327(f327(f103(f922(f921(x41832,x41831),a910)),x41833),x41834))) % 177.41/177.18 [4196]E(f327(f327(f102(f922(x41961,f922(x41962,a910))),f243(x41962,x41961,x41963)),f243(x41962,x41961,x41964)),f243(x41962,x41961,f327(f327(f102(f922(x41962,f922(x41961,a910))),x41963),x41964))) % 177.41/177.18 [4197]E(f327(f327(f103(f922(x41971,f922(x41972,a910))),f243(x41972,x41971,x41973)),f243(x41972,x41971,x41974)),f243(x41972,x41971,f327(f327(f103(f922(x41972,f922(x41971,a910))),x41973),x41974))) % 177.41/177.18 [4251]E(f327(f327(f102(f922(x42511,a910)),f327(f327(f23(f922(x42511,a910)),x42512),x42513)),f327(f327(f23(f922(x42511,a910)),x42514),x42513)),f327(f327(f23(f922(x42511,a910)),f327(f327(f102(f922(x42511,a910)),x42512),x42514)),x42513)) % 177.41/177.18 [4252]E(f327(f327(f103(f922(x42521,a910)),f327(f327(f102(f922(x42521,a910)),x42522),x42523)),f327(f327(f102(f922(x42521,a910)),x42524),x42523)),f327(f327(f102(f922(x42521,a910)),f327(f327(f103(f922(x42521,a910)),x42522),x42524)),x42523)) % 177.41/177.18 [4253]E(f327(f327(f23(f922(x42531,a910)),f327(f327(f103(f922(x42531,a910)),x42532),x42533)),f327(f327(f103(f922(x42531,a910)),x42534),x42533)),f327(f327(f103(f922(x42531,a910)),f327(f327(f23(f922(x42531,a910)),x42532),x42534)),x42533)) % 177.41/177.18 [4254]E(f327(f327(f102(f922(x42541,a910)),f327(f327(f103(f922(x42541,a910)),x42542),x42543)),f327(f327(f103(f922(x42541,a910)),x42544),x42543)),f327(f327(f103(f922(x42541,a910)),f327(f327(f102(f922(x42541,a910)),x42542),x42544)),x42543)) % 177.41/177.18 [4255]E(f327(f327(f23(f922(x42551,a910)),f327(f327(f103(f922(x42551,a910)),x42552),x42553)),f327(f327(f103(f922(x42551,a910)),x42554),x42553)),f327(f327(f23(f922(x42551,a910)),f327(f327(f103(f922(x42551,a910)),x42552),x42553)),x42554)) % 177.41/177.18 [4267]E(f327(f327(f23(f922(x42671,a910)),f327(f327(f23(f922(x42671,a910)),x42672),f327(f327(f309(x42671),x42673),f190(f922(x42671,a910))))),x42674),f327(f327(f23(f922(x42671,a910)),x42672),f327(f327(f309(x42671),x42673),x42674))) % 177.41/177.18 [4321]E(f327(f327(f102(f922(x43211,a910)),f327(f327(f309(x43211),x43212),f327(f327(f309(x43211),x43213),f190(f922(x43211,a910))))),f327(f281(x43211),x43214)),f327(f281(x43211),f327(f327(f309(f921(x43211,x43211)),f327(f327(f252(x43211,x43211),x43212),x43213)),x43214))) % 177.41/177.18 [4346]E(f327(f327(f40(a915,f922(x43461,a910)),f327(f301(a915),x43462)),f327(f327(f8(a915,f922(x43461,a910),a915),x43463),f327(f327(f7(a915,a915,a915),f80(a915)),x43464))),f327(f327(f40(a915,f922(x43461,a910)),f303(a915,x43464,f327(f327(f80(a915),x43462),x43464))),x43463)) % 177.41/177.18 [4347]E(f175(x43471,f327(f285(x43471,x43471,x43472),f327(f327(f309(x43471),x43473),f190(f922(x43471,a910)))),f327(f285(f916(x43471),f916(x43471),f159(x43471,x43472)),f327(f327(f309(f916(x43471)),x43474),f190(f922(f916(x43471),a910))))),f327(f285(f916(x43471),f916(x43471),f159(x43471,x43472)),f327(f327(f309(f916(x43471)),f327(f327(f152(x43471),x43473),x43474)),f190(f922(f916(x43471),a910))))) % 177.41/177.18 [4411]E(f327(f262(x44111),f327(f327(f7(x44111,f922(x44112,a910),a910),f327(f327(f8(x44112,f922(f922(x44112,a910),a910),x44111),f329(x44112)),x44113)),x44114)),f327(f311(x44111,x44112,x44113),x44114)) % 177.41/177.18 [4501]E(f327(f262(x45011),f327(f327(f7(x45011,f922(f921(x45012,x45011),a910),a910),f327(f327(f8(f921(x45012,x45011),f922(f922(f921(x45012,x45011),a910),a910),x45011),f329(f921(x45012,x45011))),f327(f252(x45012,x45011),x45013))),x45014)),f327(f285(x45012,x45011,x45014),f327(f327(f309(x45012),x45013),f190(f922(x45012,a910))))) % 177.41/177.18 [4515]E(f327(f327(f155(f921(x45151,a915),x45151),f251(x45151,a915)),f327(f137(f921(x45151,a915),f327(f327(f8(a915,a910,f921(x45151,a915)),x45152),f327(f327(f8(a915,a915,f921(x45151,a915)),a113),f256(x45151,a915)))),f327(f327(f182(x45151,a915),x45153),x45154))),f327(f327(f155(f921(x45151,a915),x45151),f251(x45151,a915)),f327(f137(f921(x45151,a915),f327(f327(f8(a915,a910,f921(x45151,a915)),x45152),f256(x45151,a915))),f327(f327(f182(x45151,a915),x45153),f327(f327(f155(a915,a915),a113),x45154))))) % 177.41/177.18 [4524]P1(f327(f327(f234(f922(f922(x45241,a910),a910)),f327(f327(f40(x45242,f922(f922(x45241,a910),a910)),x45243),f327(f327(f8(f922(x45241,a910),f922(f922(x45241,a910),a910),x45242),f308(x45241)),x45244))),f327(f308(x45241),f327(f327(f40(x45242,f922(x45241,a910)),x45243),x45244)))) % 177.41/177.18 [4565]E(f327(f327(f86(a1,x45651),f327(f105(a1),f327(f327(f80(a1),x45652),a98))),f327(f327(f18(a1,x45651,x45651),f327(f327(f7(a1,x45651,f922(x45651,x45651)),f327(f327(f8(a910,f922(x45651,f922(x45651,x45651)),a1),f97(x45651)),a195)),x45653)),f327(f327(f18(a1,x45651,x45651),f327(f327(f8(a915,f922(x45651,x45651),a1),x45654),a106)),f327(f327(f8(a915,x45651,a1),f185(x45651,x45653,x45654)),a106)))),f327(f185(x45651,x45653,x45654),f327(f105(a915),x45652))) % 177.41/177.18 [4589]E(f327(f262(f921(x45891,x45892)),f327(f257(x45891,x45892,a910),f327(f327(f7(x45891,f922(x45892,a910),f922(x45892,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x45892,a910),f922(x45892,a910)),x45891),f8(a910,a910,x45892)),f327(f327(f8(a910,f922(a910,a910),x45891),a325),f327(f327(f7(x45891,f922(x45891,a910),a910),f329(x45891)),x45893)))),f327(f327(f7(x45892,f922(x45892,a910),a910),f329(x45892)),x45894)))),f231(x45891,x45892,x45893,x45894)) % 177.41/177.18 [4626]E(f327(f327(f40(x46261,f922(f921(x46261,x46262),a910)),x46263),f327(f327(f18(x46261,f922(x46262,f922(f921(x46261,x46262),a910)),f922(f921(x46261,x46262),a910)),f327(f327(f8(f922(x46262,a910),f922(f922(x46262,f922(f921(x46261,x46262),a910)),f922(f921(x46261,x46262),a910)),x46261),f40(x46262,f922(f921(x46261,x46262),a910))),x46264)),f327(f327(f7(x46261,f922(f921(x46261,x46262),a910),f922(x46262,f922(f921(x46261,x46262),a910))),f327(f327(f8(f922(x46262,f922(f922(f921(x46261,x46262),a910),f922(f921(x46261,x46262),a910))),f922(f922(f921(x46261,x46262),a910),f922(x46262,f922(f921(x46261,x46262),a910))),x46261),f7(x46262,f922(f921(x46261,x46262),a910),f922(f921(x46261,x46262),a910))),f327(f327(f8(f922(x46262,f921(x46261,x46262)),f922(x46262,f922(f922(f921(x46261,x46262),a910),f922(f921(x46261,x46262),a910))),x46261),f327(f8(f921(x46261,x46262),f922(f922(f921(x46261,x46262),a910),f922(f921(x46261,x46262),a910)),x46262),f309(f921(x46261,x46262)))),f252(x46261,x46262)))),f190(f922(f921(x46261,x46262),a910))))),f327(f327(f254(x46261,x46262),x46263),x46264)) % 177.41/177.18 [4191]E(f327(f327(f135(x41911),f327(f327(f176(x41911),x41912),x41913)),f327(f327(f176(x41911),f327(f327(f23(a915),x41912),f327(f191(f916(x41911)),x41913))),x41914)),f327(f327(f176(x41911),x41912),f327(f327(f135(x41911),x41913),x41914))) % 177.41/177.18 [4192]E(f327(f327(f135(x41921),f327(f327(f139(x41921),x41922),x41923)),f327(f327(f139(x41921),f327(f327(f23(a915),x41922),f327(f191(f916(x41921)),x41923))),x41924)),f327(f327(f139(x41921),x41922),f327(f327(f135(x41921),x41923),x41924))) % 177.41/177.18 [4241]E(f327(f327(f80(a915),f327(f327(f81(a915),x42411),x42412)),f327(f327(f80(a915),f327(f327(f81(a915),x42413),x42412)),x42414)),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f80(a915),x42411),x42413)),x42412)),x42414)) % 177.41/177.18 [4387]E(f90(x43871,f327(f327(f7(x43871,x43872,a910),f327(f327(f8(x43872,f922(x43872,a910),x43871),a324),x43873)),x43874)),f327(f92(x43871,x43872,f242(f922(x43871,a910)),x43873),x43874)) % 177.41/177.18 [4435]P1(f327(f327(f234(f922(x44351,a910)),f327(f327(f23(f922(x44351,a910)),f327(f284(x44352,x44351),x44353)),f327(f284(x44352,x44351),x44354))),f327(f284(x44352,x44351),f327(f327(f23(f922(f921(x44352,x44351),a910)),x44353),x44354)))) % 177.41/177.18 [4436]P1(f327(f327(f234(f922(x44361,a910)),f327(f327(f23(f922(x44361,a910)),f327(f264(x44361,x44362),x44363)),f327(f264(x44361,x44362),x44364))),f327(f264(x44361,x44362),f327(f327(f23(f922(f921(x44361,x44362),a910)),x44363),x44364)))) % 177.41/177.18 [4544]E(f327(f327(f80(a1),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x45441),x45442)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x45443),x45444)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),f327(f327(f80(a915),x45441),x45443)),f327(f327(f80(a915),x45442),x45444))),f190(f922(f921(a915,a915),a910)))))) % 177.41/177.18 [4584]E(f327(f327(f81(a1),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x45841),x45842)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x45843),x45844)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),f327(f327(f80(a915),f327(f327(f81(a915),x45841),x45843)),f327(f327(f81(a915),x45842),x45844))),f327(f327(f80(a915),f327(f327(f81(a915),x45841),x45844)),f327(f327(f81(a915),x45842),x45843)))),f190(f922(f921(a915,a915),a910)))))) % 177.41/177.18 [4605]E(f327(f262(x46051),f327(f327(f8(f922(x46052,a910),a910,x46051),f88(x46052)),f327(f327(f8(f922(x46052,a910),f922(x46052,a910),x46051),f327(f18(x46052,a910,a910),f327(f327(f8(a910,f922(a910,a910),x46052),a330),f327(f327(f7(x46052,f922(x46052,a910),a910),f329(x46052)),x46053)))),f327(f327(f7(x46051,f922(x46052,f922(x46051,a910)),f922(x46052,a910)),f327(f327(f8(f922(f922(x46051,a910),a910),f922(f922(x46052,f922(x46051,a910)),f922(x46052,a910)),x46051),f8(f922(x46051,a910),a910,x46052)),f329(x46051))),x46054)))),f327(f327(f41(x46052,f922(x46051,a910)),x46053),x46054)) % 177.41/177.18 [4639]E(f327(f327(f289(x46391,x46391,x46391),f327(f327(f309(f921(x46391,x46391)),f327(f327(f252(x46391,x46391),x46392),x46393)),x46394)),f307(x46391,f327(f327(f309(f921(x46391,x46391)),f327(f327(f252(x46391,x46391),x46392),x46393)),x46394))),f327(f327(f102(f922(f921(x46391,x46391),a910)),f327(f327(f289(x46391,x46391,x46391),x46394),f307(x46391,x46394))),f327(f262(f921(x46391,x46391)),f327(f257(x46391,x46391,a910),f327(f327(f7(x46391,f922(x46391,a910),f922(x46391,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x46391,a910),f922(x46391,a910)),x46391),f8(a910,a910,x46391)),f327(f327(f8(a910,f922(a910,a910),x46391),a325),f327(f327(f7(x46391,f922(f921(x46391,x46391),a910),a910),f327(f327(f8(f921(x46391,x46391),f922(f922(f921(x46391,x46391),a910),a910),x46391),f329(f921(x46391,x46391))),f327(f327(f7(x46391,x46391,f921(x46391,x46391)),f252(x46391,x46391)),x46392))),f307(x46391,x46394))))),f327(f327(f7(x46391,f922(f921(x46391,x46391),a910),a910),f327(f327(f8(f921(x46391,x46391),f922(f922(f921(x46391,x46391),a910),a910),x46391),f329(f921(x46391,x46391))),f327(f252(x46391,x46391),x46393))),f307(x46391,x46394))))))) % 177.41/177.18 [4437]E(f327(f137(x44371,f327(f327(f18(x44371,a910,a910),f327(f327(f8(a910,f922(a910,a910),x44371),a325),x44372)),x44373)),x44374),f327(f137(x44371,x44373),f327(f137(x44371,x44372),x44374))) % 177.41/177.18 [4538]E(f327(f327(f135(x45381),f327(f327(f327(f97(f916(x45381)),f327(f327(f329(a915),f2(a915)),x45382)),f327(f327(f152(x45381),x45383),f114(x45381))),f114(x45381))),f177(x45381,x45384,f327(f262(a915),f327(f327(f7(a915,f922(a915,a910),a910),f327(f327(f8(a915,f922(f922(a915,a910),a910),a915),f329(a915)),a113)),x45382)))),f177(x45381,f327(f327(f152(x45381),x45383),x45384),x45382)) % 177.41/177.18 [4635]E(f327(f262(f921(x46351,x46352)),f327(f327(f8(f922(a915,a910),a910,f921(x46351,x46352)),f87(a915)),f327(f327(f7(f921(x46351,x46352),f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),f921(x46351,x46352)),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),f921(x46351,x46352)),f327(f8(a910,f922(a910,a910),a915),a325)),f327(f327(f7(f921(x46351,x46352),f922(a915,f921(x46351,x46352)),f922(a915,a910)),f327(f327(f8(f922(f921(x46351,x46352),a910),f922(f922(a915,f921(x46351,x46352)),f922(a915,a910)),f921(x46351,x46352)),f8(f921(x46351,x46352),a910,a915)),a324)),f327(f327(f18(a915,x46352,f921(x46351,x46352)),f327(f327(f8(x46351,f922(x46352,f921(x46351,x46352)),a915),f252(x46351,x46352)),f327(f165(x46351),x46353))),f327(f165(x46352),x46354)))))),f327(f327(f7(a915,a915,a910),f235(a915)),f327(f327(f238(a915),f327(f191(f916(x46351)),x46353)),f327(f191(f916(x46352)),x46354)))))),f327(f173(f921(x46351,x46352)),f327(f327(f182(x46351,x46352),x46353),x46354))) % 177.41/177.18 [4557]E(f327(f262(f921(x45571,x45572)),f327(f257(x45571,x45572,a910),f327(f327(f7(x45571,f922(x45572,a910),f922(x45572,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x45572,a910),f922(x45572,a910)),x45571),f8(a910,a910,x45572)),f327(f327(f8(a910,f922(a910,a910),x45571),a325),x45573))),x45574))),f327(f327(f254(x45571,x45572),f327(f262(x45571),x45573)),f327(f16(f922(x45572,a910),x45571),f327(f262(x45572),x45574)))) % 177.41/177.18 [4560]E(f327(f262(f921(x45601,x45602)),f327(f257(x45601,x45602,a910),f327(f327(f18(x45601,f922(x45602,a910),f922(x45602,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x45602,a910),f922(x45602,a910)),x45601),f8(a910,a910,x45602)),f327(f327(f8(a910,f922(a910,a910),x45601),a325),x45603))),x45604))),f327(f327(f254(x45601,x45602),f327(f262(x45601),x45603)),f327(f327(f8(f922(x45602,a910),f922(x45602,a910),x45601),f262(x45602)),x45604))) % 177.41/177.18 [4572]E(f327(f262(x45721),f327(f327(f8(f922(x45722,a910),a910,x45721),f88(x45722)),f327(f327(f8(f922(x45722,a910),f922(x45722,a910),x45721),f327(f18(x45722,a910,a910),f327(f327(f8(a910,f922(a910,a910),x45722),a330),f327(f327(f7(x45722,f922(x45722,a910),a910),f329(x45722)),x45723)))),x45724))),f327(f327(f41(x45722,f922(x45721,a910)),x45723),f327(f327(f8(f922(x45721,a910),f922(x45721,a910),x45722),f262(x45721)),f327(f7(x45721,x45722,a910),x45724)))) % 177.41/177.18 [4617]E(f327(f327(f155(f921(x46171,a915),x46171),f251(x46171,a915)),f327(f137(f921(x46171,a915),f327(f327(f7(f921(x46171,a915),f922(a915,a910),a910),f327(f327(f8(a915,f922(f922(a915,a910),a910),f921(x46171,a915)),f329(a915)),f256(x46171,a915))),x46172)),f327(f327(f182(x46171,a915),x46173),f140(a915,f327(f302(a915,x46174),f327(f327(f80(a915),x46174),f327(f191(f916(x46171)),x46173))))))),f327(f327(f155(f921(x46171,a915),x46171),f251(x46171,a915)),f327(f137(f921(x46171,a915),f327(f327(f7(f921(x46171,a915),f922(a915,a910),a910),f327(f327(f8(a915,f922(f922(a915,a910),a910),f921(x46171,a915)),f329(a915)),f327(f327(f7(f921(x46171,a915),a915,a915),f327(f327(f8(a915,f922(a915,a915),f921(x46171,a915)),f80(a915)),f256(x46171,a915))),x46174))),x46172)),f327(f327(f182(x46171,a915),x46173),f140(a915,f327(f302(a915,f2(a915)),f327(f191(f916(x46171)),x46173))))))) % 177.41/177.18 [4618]E(f327(a113,f327(f327(f189(a915),f327(f191(f916(x46181)),x46182)),f327(f143(a915,f916(x46183),f327(f7(f916(x46183),a915,a915),f327(f327(f8(a915,f922(a915,a915),f916(x46183)),f189(a915)),f327(f327(f7(f916(x46183),a915,a915),f327(f327(f8(a915,f922(a915,a915),f916(x46183)),f23(a915)),f191(f916(x46183)))),f327(a113,f2(a915))))),f2(a915)),f327(f169(f916(x46183)),f327(f137(f916(x46183),f327(f327(f8(a910,a910,f916(x46183)),a322),f327(f327(f7(f916(x46183),f916(x46183),a910),a324),f114(x46183)))),x46184))))),f327(f327(f189(a915),f327(a113,f327(f191(f916(x46181)),x46182))),f327(f143(a915,f916(x46183),f327(f7(f916(x46183),a915,a915),f327(f327(f8(a915,f922(a915,a915),f916(x46183)),f189(a915)),f191(f916(x46183)))),f2(a915)),f327(f169(f916(x46183)),x46184)))) % 177.41/177.18 [4571]E(f327(f327(f135(x45711),f177(x45711,x45712,x45713)),f177(x45711,x45714,f327(f262(a915),f327(f327(f7(a915,f922(a915,a910),a910),f327(f327(f8(a915,f922(f922(a915,a910),a910),a915),f329(a915)),f327(f327(f7(a915,a915,a915),f80(a915)),f327(f191(f916(x45711)),x45712)))),x45713)))),f177(x45711,f327(f327(f135(x45711),x45712),x45714),x45713)) % 177.41/177.18 [4619]E(f38(f922(x46191,a910),f327(f262(f922(x46191,a910)),f327(f327(f8(f922(x46192,a910),a910,f922(x46191,a910)),f87(x46192)),f327(f327(f8(f922(x46192,a910),f922(x46192,a910),f922(x46191,a910)),f327(f18(x46192,a910,a910),f327(f327(f8(a910,f922(a910,a910),x46192),a325),f327(f327(f7(x46192,f922(x46192,a910),a910),f329(x46192)),x46193)))),f327(f327(f7(f922(x46191,a910),f922(x46192,f922(x46191,a910)),f922(x46192,a910)),f327(f327(f8(f922(f922(x46191,a910),a910),f922(f922(x46192,f922(x46191,a910)),f922(x46192,a910)),f922(x46191,a910)),f8(f922(x46191,a910),a910,x46192)),a324)),x46194))))),f327(f327(f40(x46192,f922(x46191,a910)),x46193),x46194)) % 177.41/177.18 [4620]E(f39(f922(x46201,a910),f327(f262(f922(x46201,a910)),f327(f327(f8(f922(x46202,a910),a910,f922(x46201,a910)),f87(x46202)),f327(f327(f8(f922(x46202,a910),f922(x46202,a910),f922(x46201,a910)),f327(f18(x46202,a910,a910),f327(f327(f8(a910,f922(a910,a910),x46202),a325),f327(f327(f7(x46202,f922(x46202,a910),a910),f329(x46202)),x46203)))),f327(f327(f7(f922(x46201,a910),f922(x46202,f922(x46201,a910)),f922(x46202,a910)),f327(f327(f8(f922(f922(x46201,a910),a910),f922(f922(x46202,f922(x46201,a910)),f922(x46202,a910)),f922(x46201,a910)),f8(f922(x46201,a910),a910,x46202)),a324)),x46204))))),f327(f327(f41(x46202,f922(x46201,a910)),x46203),x46204)) % 177.41/177.18 [4628]E(f327(f327(f152(f916(x46281)),f327(f327(f152(x46281),x46282),f327(f143(f916(x46281),f916(x46281),f135(x46281),f114(x46281)),f327(f327(f155(f916(x46281),f916(x46281)),f157(f916(x46281),x46281,f114(x46281),f327(f327(f8(f916(x46281),f922(f916(x46281),f916(x46281)),x46281),f16(f916(x46281),f916(x46281))),f327(f327(f7(x46281,f916(x46281),f916(x46281)),f152(x46281)),f114(x46281))))),x46283)))),f180(x46281,f327(f327(f152(f916(x46281)),x46284),f327(f143(f916(f916(x46281)),f916(f916(x46281)),f135(f916(x46281)),f114(f916(x46281))),f327(f327(f155(f916(x46281),f916(f916(x46281))),f157(f916(f916(x46281)),x46281,f114(f916(x46281)),f327(f16(f922(f916(x46281),f916(f916(x46281))),x46281),f327(f327(f7(f916(x46281),f916(f916(x46281)),f916(f916(x46281))),f152(f916(x46281))),f114(f916(x46281)))))),x46283))))),f180(x46281,f327(f327(f152(f916(x46281)),f327(f327(f152(x46281),x46282),x46284)),x46283))) % 177.41/177.18 [4636]E(f327(f262(f921(x46361,x46361)),f327(f257(x46361,x46361,a910),f327(f327(f7(x46361,f922(f921(x46362,x46362),a910),f922(x46361,a910)),f327(f327(f8(f922(x46361,f922(f922(f921(x46362,x46362),a910),a910)),f922(f922(f921(x46362,x46362),a910),f922(x46361,a910)),x46361),f7(x46361,f922(f921(x46362,x46362),a910),a910)),f327(f327(f8(f922(x46361,f921(x46362,x46362)),f922(x46361,f922(f922(f921(x46362,x46362),a910),a910)),x46361),f327(f8(f921(x46362,x46362),f922(f922(f921(x46362,x46362),a910),a910),x46361),f329(f921(x46362,x46362)))),f327(f327(f7(x46361,f922(x46361,x46362),f922(x46361,f921(x46362,x46362))),f327(f327(f8(f922(x46362,f921(x46362,x46362)),f922(f922(x46361,x46362),f922(x46361,f921(x46362,x46362))),x46361),f8(x46362,f921(x46362,x46362),x46361)),f327(f327(f8(x46362,f922(x46362,f921(x46362,x46362)),x46361),f252(x46362,x46362)),x46363))),x46363)))),x46364))),f327(f327(f288(x46362,x46361),x46364),x46363)) % 177.41/177.18 [4682]~E(f30(x46821,x46822),f27(x46823,x46824,x46825)) % 177.41/177.18 [4683]~E(f30(x46831,x46832),f26(x46833,x46834,x46835)) % 177.41/177.18 [4684]~E(f29(x46841,x46842),f27(x46843,x46844,x46845)) % 177.41/177.18 [4685]~E(f29(x46851,x46852),f26(x46853,x46854,x46855)) % 177.41/177.18 [4686]~E(f27(x46861,x46862,x46863),f30(x46864,x46865)) % 177.41/177.18 [4687]~E(f27(x46871,x46872,x46873),f29(x46874,x46875)) % 177.41/177.18 [4688]~E(f26(x46881,x46882,x46883),f30(x46884,x46885)) % 177.41/177.18 [4689]~E(f26(x46891,x46892,x46893),f29(x46894,x46895)) % 177.41/177.18 [3765]E(f327(f327(f155(x37651,x37652),x37653),f170(x37651,x37654,x37655)),f170(x37652,x37654,f327(x37653,x37655))) % 177.41/177.18 [4102]E(f131(x41021,x41022,x41023,f127(x41021,x41024,x41025)),f127(x41022,f327(x41023,x41024),f131(x41021,x41022,x41023,x41025))) % 177.41/177.18 [4336]E(f327(f74(x43361,x43362,x43363,x43364,x43365),x43364),x43365) % 177.41/177.18 [4388]E(f253(x43881,x43882,x43883,f243(x43882,x43881,x43884),f243(x43883,x43882,x43885)),f243(x43883,x43881,f253(x43883,x43882,x43881,x43885,x43884))) % 177.41/177.18 [3959]E(f327(f327(f257(x39591,x39592,x39593),x39594),x39595),f327(f327(x39594,f327(f251(x39591,x39592),x39595)),f327(f256(x39591,x39592),x39595))) % 177.41/177.18 [3995]E(f327(f327(f327(f65(x39951,x39952,x39953),x39954),x39955),f190(f922(x39952,a910))),x39955) % 177.41/177.18 [4275]E(f327(f72(f916(x42751),f916(x42752),f916(x42753),f327(f155(x42751,x42752),x42754)),f327(f155(x42753,x42751),x42755)),f327(f155(x42753,x42752),f327(f72(x42751,x42752,x42753,x42754),x42755))) % 177.41/177.18 [4350]E(f85(x43501,f66(x43502,x43501,x43503,x43504,x43505)),f327(f327(f64(x43502,x43501,x43503),x43504),x43505)) % 177.41/177.18 [4384]E(f327(f327(f80(a915),f327(f327(f80(a915),f327(x43841,f327(f251(x43842,x43843),x43844))),f327(x43845,f327(f256(x43842,x43843),x43844)))),f327(a113,f2(a915))),f261(x43842,x43843,x43841,x43845,x43844)) % 177.41/177.18 [3895]E(f327(f327(f176(x38951),x38952),f327(f327(f155(x38953,x38951),x38954),x38955)),f327(f327(f155(x38953,x38951),x38954),f327(f327(f176(x38953),x38952),x38955))) % 177.41/177.18 [3896]E(f327(f327(f139(x38961),x38962),f327(f327(f155(x38963,x38961),x38964),x38965)),f327(f327(f155(x38963,x38961),x38964),f327(f327(f139(x38963),x38962),x38965))) % 177.41/177.18 [3928]E(f327(f327(f155(x39281,x39282),x39283),f327(f327(f152(x39281),x39284),x39285)),f327(f327(f152(x39282),f327(x39283,x39284)),f327(f327(f155(x39281,x39282),x39283),x39285))) % 177.41/177.18 [3989]E(f327(f310(x39891,x39892,x39893),f327(f327(f309(x39891),x39894),x39895)),f327(f327(f309(x39892),f327(x39893,x39894)),f327(f310(x39891,x39892,x39893),x39895))) % 177.41/177.18 [4019]E(f174(x40191,f327(f327(f152(x40191),x40192),x40193),f327(f327(f152(x40191),x40194),x40195)),f327(f327(f152(x40191),x40192),f327(f327(f152(x40191),x40194),f174(x40191,x40193,x40195)))) % 177.41/177.18 [4056]E(f327(f327(f182(x40561,x40562),f327(f327(f176(x40561),x40563),x40564)),f327(f327(f176(x40562),x40563),x40565)),f327(f327(f176(f921(x40561,x40562)),x40563),f327(f327(f182(x40561,x40562),x40564),x40565))) % 177.41/177.18 [4057]E(f327(f327(f182(x40571,x40572),f327(f327(f139(x40571),x40573),x40574)),f327(f327(f139(x40572),x40573),x40575)),f327(f327(f139(f921(x40571,x40572)),x40573),f327(f327(f182(x40571,x40572),x40574),x40575))) % 177.41/177.18 [4067]E(f327(f327(f160(x40671,f327(f327(f152(x40671),x40672),x40673)),f327(a113,x40674)),x40675),f327(f327(f152(x40671),x40672),f327(f327(f160(x40671,x40673),x40674),x40675))) % 177.41/177.18 [4070]E(f327(f327(f135(x40701),f327(f327(f155(x40702,x40701),x40703),x40704)),f327(f327(f155(x40702,x40701),x40703),x40705)),f327(f327(f155(x40702,x40701),x40703),f327(f327(f135(x40702),x40704),x40705))) % 177.41/177.18 [4074]E(f327(f327(x40741,x40742),f327(f327(f245(x40743,x40744,x40741),x40742),x40745)),f327(f327(f245(x40743,x40744,x40741),x40742),f327(a113,x40745))) % 177.41/177.18 [4106]E(f164(x41061,x41062,x41063,f327(f327(f152(x41061),x41064),x41065)),f327(f327(f135(x41062),f327(x41063,x41064)),f164(x41061,x41062,x41063,x41065))) % 177.41/177.18 [4118]E(f327(f327(f289(x41181,x41182,x41183),f327(f286(x41182,x41181),x41184)),f327(f286(x41183,x41182),x41185)),f327(f286(x41183,x41181),f327(f327(f289(x41183,x41182,x41181),x41185),x41184))) % 177.41/177.18 [4150]E(f327(f327(f327(f184(f916(x41501),f916(x41501)),x41502),f168(x41501)),f327(f327(f155(x41503,x41501),x41504),x41505)),f327(f327(f155(x41503,x41501),x41504),f327(f327(f327(f184(f916(x41503),f916(x41503)),x41502),f168(x41503)),x41505))) % 177.41/177.18 [4151]E(f327(f327(f259(x41511,x41512,x41511,x41513),f327(f252(x41512,x41511),x41514)),x41515),f327(x41515,x41514)) % 177.41/177.18 [4177]E(f156(x41771,x41772,f327(f327(f155(x41773,x41771),x41774),x41775)),f156(x41773,f327(f72(x41771,a915,x41773,x41772),x41774),x41775)) % 177.41/177.18 [4240]E(f178(f921(x42401,x42402),f327(f72(x42402,a910,f921(x42401,x42402),x42403),f256(x42401,x42402)),f327(f327(f182(x42401,x42402),x42404),x42405)),f327(f327(f182(x42401,x42402),x42404),f178(x42402,x42403,x42405))) % 177.41/177.18 [4245]E(f327(f310(x42451,x42452,f327(f327(f8(x42453,x42452,x42451),x42454),x42455)),f242(f922(x42451,a910))),f327(f310(x42453,x42452,x42454),f327(f310(x42451,x42453,x42455),f242(f922(x42451,a910))))) % 177.41/177.18 [4258]E(f178(f921(x42581,x42582),f327(f72(x42581,a910,f921(x42581,x42582),x42583),f251(x42581,x42582)),f327(f327(f182(x42581,x42582),x42584),x42585)),f327(f327(f182(x42581,x42582),f178(x42581,x42583,x42584)),x42585)) % 177.41/177.18 [4279]E(f327(f327(f102(f922(x42791,a910)),f327(f311(x42791,x42792,x42793),f327(f327(f309(x42792),x42794),f190(f922(x42792,a910))))),f327(f311(x42791,x42792,x42793),x42795)),f327(f311(x42791,x42792,x42793),f327(f327(f309(x42792),x42794),x42795))) % 177.41/177.18 [4335]E(f327(f327(f135(f921(x43351,x43352)),f327(f327(f155(x43352,f921(x43351,x43352)),f327(f252(x43351,x43352),x43353)),x43354)),f60(x43351,x43352,x43355,x43354)),f60(x43351,x43352,f327(f327(f152(x43351),x43353),x43355),x43354)) % 177.41/177.18 [4337]E(f327(f327(f155(x43371,x43372),x43373),f178(x43371,f327(f72(x43372,a910,x43371,x43374),x43373),x43375)),f178(x43372,x43374,f327(f327(f155(x43371,x43372),x43373),x43375))) % 177.41/177.18 [4342]E(f327(f143(x43421,x43422,f327(f7(x43422,x43421,x43421),f327(f7(x43421,x43422,x43421),x43423)),x43424),f327(f169(x43422),f327(f169(x43422),x43425))),f327(f143(x43421,x43422,x43423,x43424),x43425)) % 177.41/177.18 [4445]P1(f327(f327(f234(f922(x44451,a910)),f327(f310(x44452,x44451,x44453),f327(f327(f103(f922(x44452,a910)),x44454),x44455))),f327(f327(f103(f922(x44451,a910)),f327(f310(x44452,x44451,x44453),x44454)),f327(f310(x44452,x44451,x44453),x44455)))) % 177.41/177.18 [4446]P1(f327(f327(f234(f922(x44461,a910)),f327(f285(x44462,x44461,x44463),f327(f327(f103(f922(x44462,a910)),x44464),x44465))),f327(f327(f103(f922(x44461,a910)),f327(f285(x44462,x44461,x44463),x44464)),f327(f285(x44462,x44461,x44463),x44465)))) % 177.41/177.18 [4545]E(f327(f256(x45451,x45452),f327(f258(x45453,x45451,x45452,x45452,x45454,f31(x45452)),x45455)),f327(f256(x45453,x45452),x45455)) % 177.41/177.18 [4546]E(f327(f251(x45461,x45462),f327(f258(x45461,x45461,x45463,x45462,f31(x45461),x45464),x45465)),f327(f251(x45461,x45463),x45465)) % 177.41/177.18 [4634]P22(x46341,x46342,f327(f327(f309(f913(x46341)),f327(f327(f327(f91(x46341),f327(f327(f7(x46341,f922(a911,a910),f922(a911,a910)),f327(f327(f8(f922(a911,f922(a910,a910)),f922(f922(a911,a910),f922(a911,a910)),x46341),f18(a911,a910,a910)),f327(f327(f8(f922(a911,a910),f922(a911,f922(a910,a910)),x46341),f327(f8(a910,f922(a910,a910),a911),a325)),x46343))),f327(f327(f8(a910,a910,a911),a322),x46344))),f29(x46344,x46345)),x46343)),f190(f922(f913(x46341),a910)))) % 177.41/177.18 [3735]E(f327(f327(f327(f327(f206(x37351),x37352),x37353),x37354),x37355),f194(x37351,x37352)) % 177.41/177.18 [3736]E(f327(f327(f327(f327(f210(x37361),x37362),x37363),x37364),x37365),f201(x37361,x37362)) % 177.41/177.18 [3781]E(f94(x37811,x37812,f327(f327(f327(f91(x37811),x37813),x37814),x37815)),f2(a915)) % 177.41/177.18 [4107]E(f327(f327(f40(x41071,f922(x41072,a910)),f327(f327(f309(x41071),x41073),x41074)),x41075),f327(f327(f102(f922(x41072,a910)),f327(x41075,x41073)),f327(f327(f40(x41071,f922(x41072,a910)),x41074),x41075))) % 177.41/177.18 [4108]E(f327(f327(f41(x41081,f922(x41082,a910)),f327(f327(f309(x41081),x41083),x41084)),x41085),f327(f327(f103(f922(x41082,a910)),f327(x41085,x41083)),f327(f327(f41(x41081,f922(x41082,a910)),x41084),x41085))) % 177.41/177.18 [4158]E(f327(f119(x41581,x41582,f327(x41583,x41584)),f327(f327(f7(x41581,a100,f917(x41582)),x41585),x41584)),f327(f199(x41581,x41582,x41583,x41585),x41584)) % 177.41/177.18 [4171]E(f327(f327(f102(f922(x41711,a910)),f327(f310(x41712,x41711,x41713),x41714)),f327(f310(x41712,x41711,x41713),x41715)),f327(f310(x41712,x41711,x41713),f327(f327(f102(f922(x41712,a910)),x41714),x41715))) % 177.41/177.18 [4172]E(f327(f327(f23(f922(x41721,a910)),f327(f311(x41721,x41722,x41723),x41724)),f327(f311(x41721,x41722,x41723),x41725)),f327(f311(x41721,x41722,x41723),f327(f327(f23(f922(x41722,a910)),x41724),x41725))) % 177.41/177.18 [4173]E(f327(f327(f102(f922(x41731,a910)),f327(f311(x41731,x41732,x41733),x41734)),f327(f311(x41731,x41732,x41733),x41735)),f327(f311(x41731,x41732,x41733),f327(f327(f102(f922(x41732,a910)),x41734),x41735))) % 177.41/177.18 [4174]E(f327(f327(f103(f922(x41741,a910)),f327(f311(x41741,x41742,x41743),x41744)),f327(f311(x41741,x41742,x41743),x41745)),f327(f311(x41741,x41742,x41743),f327(f327(f103(f922(x41742,a910)),x41744),x41745))) % 177.41/177.18 [4175]E(f327(f327(f102(f922(x41751,a910)),f327(f285(x41752,x41751,x41753),x41754)),f327(f285(x41752,x41751,x41753),x41755)),f327(f285(x41752,x41751,x41753),f327(f327(f102(f922(x41752,a910)),x41754),x41755))) % 177.41/177.18 [4236]E(f327(f327(f160(x42361,f327(f327(f135(x42361),x42362),f327(f327(f152(x42361),x42363),x42364))),f327(f191(f916(x42361)),x42362)),x42365),f327(f327(f135(x42361),x42362),f327(f327(f152(x42361),x42365),x42364))) % 177.41/177.18 [4243]E(f327(f327(f41(x42431,f922(x42432,a910)),x42433),f327(f327(f8(f922(x42432,a910),f922(x42432,a910),x42431),f327(f309(x42432),x42434)),x42435)),f327(f327(f309(x42432),x42434),f327(f327(f41(x42431,f922(x42432,a910)),x42433),x42435))) % 177.41/177.18 [4397]E(f327(f327(f155(x43971,x43972),x43973),f327(f137(x43971,f327(f72(x43972,a910,x43971,x43974),x43973)),x43975)),f327(f137(x43972,x43974),f327(f327(f155(x43971,x43972),x43973),x43975))) % 177.41/177.18 [4403]E(f327(f191(f916(x44031)),f327(f137(x44031,x44032),f327(f327(f155(x44033,x44031),x44034),x44035))),f327(f191(f916(x44033)),f327(f137(x44033,f327(f72(x44031,a910,x44033,x44032),x44034)),x44035))) % 177.41/177.18 [4610]E(f327(f157(f916(f921(x46101,x46102)),x46102,f114(f921(x46101,x46102)),f327(f327(f7(x46102,f922(f916(x46102),f916(f921(x46101,x46102))),f922(f916(x46102),f916(f921(x46101,x46102)))),f327(f327(f8(f922(f916(f921(x46101,x46102)),f916(f921(x46101,x46102))),f922(f922(f916(x46102),f916(f921(x46101,x46102))),f922(f916(x46102),f916(f921(x46101,x46102)))),x46102),f8(f916(f921(x46101,x46102)),f916(f921(x46101,x46102)),f916(x46102))),f327(f327(f8(f921(x46101,x46102),f922(f916(f921(x46101,x46102)),f916(f921(x46101,x46102))),x46102),f152(f921(x46101,x46102))),f327(f252(x46101,x46102),x46103)))),f327(f182(x46101,x46102),x46104))),x46105),f327(f327(f182(x46101,x46102),f327(f327(f152(x46101),x46103),x46104)),x46105)) % 177.41/177.18 [4099]E(f327(f327(f160(x40991,f327(f327(f160(x40991,x40992),x40993),x40994)),x40993),x40995),f327(f327(f160(x40991,x40992),x40993),x40995)) % 177.41/177.18 [4152]E(f327(f284(x41521,x41522),f327(f327(f309(f921(x41521,x41522)),f327(f327(f252(x41521,x41522),x41523),x41524)),x41525)),f327(f327(f309(x41522),x41524),f327(f284(x41521,x41522),x41525))) % 177.41/177.18 [4153]E(f327(f264(x41531,x41532),f327(f327(f309(f921(x41531,x41532)),f327(f327(f252(x41531,x41532),x41533),x41534)),x41535)),f327(f327(f309(x41531),x41533),f327(f264(x41531,x41532),x41535))) % 177.41/177.18 [4201]E(f123(x42011,x42012,f327(x42013,x42014),f327(f327(f7(x42011,a100,f917(f918(x42012))),x42015),x42014)),f327(f197(x42011,x42012,x42013,x42015),x42014)) % 177.41/177.18 [4229]E(f327(f327(f23(f922(f921(x42291,x42292),a910)),f327(f327(f254(x42291,x42292),x42293),x42294)),f327(f327(f254(x42291,x42292),x42295),x42294)),f327(f327(f254(x42291,x42292),f327(f327(f23(f922(x42291,a910)),x42293),x42295)),x42294)) % 177.41/177.18 [4230]E(f327(f327(f102(f922(f921(x42301,x42302),a910)),f327(f327(f254(x42301,x42302),x42303),x42304)),f327(f327(f254(x42301,x42302),x42305),x42304)),f327(f327(f254(x42301,x42302),f327(f327(f102(f922(x42301,a910)),x42303),x42305)),x42304)) % 177.41/177.18 [4231]E(f327(f327(f103(f922(f921(x42311,x42312),a910)),f327(f327(f254(x42311,x42312),x42313),x42314)),f327(f327(f254(x42311,x42312),x42315),x42314)),f327(f327(f254(x42311,x42312),f327(f327(f103(f922(x42311,a910)),x42313),x42315)),x42314)) % 177.41/177.18 [4290]E(f327(f327(f102(f922(x42901,a910)),f327(f327(f40(x42902,f922(x42901,a910)),x42903),x42904)),f327(f327(f40(x42902,f922(x42901,a910)),x42905),x42904)),f327(f327(f40(x42902,f922(x42901,a910)),f327(f327(f102(f922(x42902,a910)),x42903),x42905)),x42904)) % 177.41/177.18 [4291]E(f327(f327(f103(f922(x42911,a910)),f327(f327(f41(x42912,f922(x42911,a910)),x42913),x42914)),f327(f327(f41(x42912,f922(x42911,a910)),x42915),x42914)),f327(f327(f41(x42912,f922(x42911,a910)),f327(f327(f102(f922(x42912,a910)),x42913),x42915)),x42914)) % 177.41/177.18 [4305]E(f327(f327(f40(x43051,f922(x43052,a910)),x43053),f327(f327(f8(f922(x43052,a910),f922(x43052,a910),x43051),f327(f23(f922(x43052,a910)),x43054)),x43055)),f327(f327(f23(f922(x43052,a910)),x43054),f327(f327(f41(x43051,f922(x43052,a910)),x43053),x43055))) % 177.41/177.18 [4306]E(f327(f327(f40(x43061,f922(x43062,a910)),x43063),f327(f327(f8(f922(x43062,a910),f922(x43062,a910),x43061),f327(f103(f922(x43062,a910)),x43064)),x43065)),f327(f327(f103(f922(x43062,a910)),x43064),f327(f327(f40(x43061,f922(x43062,a910)),x43063),x43065))) % 177.41/177.18 [4307]E(f327(f327(f41(x43071,f922(x43072,a910)),x43073),f327(f327(f8(f922(x43072,a910),f922(x43072,a910),x43071),f327(f102(f922(x43072,a910)),x43074)),x43075)),f327(f327(f102(f922(x43072,a910)),x43074),f327(f327(f41(x43071,f922(x43072,a910)),x43073),x43075))) % 177.41/177.18 [4362]E(f186(f916(x43621),f327(f327(f152(x43621),x43622),x43623),f327(f327(f8(f916(x43621),f916(x43621),a915),f327(f152(x43621),x43624)),f327(f327(f7(a915,x43621,f916(x43621)),f160(x43621,x43623)),x43622)),x43625),f327(f327(f160(x43621,f327(f327(f152(x43621),x43624),x43623)),x43625),x43622)) % 177.41/177.18 [4366]E(f327(f327(f40(x43661,f922(f921(x43662,x43663),a910)),x43664),f327(f327(f8(f922(f921(x43663,x43662),a910),f922(f921(x43662,x43663),a910),x43661),f286(x43663,x43662)),x43665)),f327(f286(x43663,x43662),f327(f327(f40(x43661,f922(f921(x43663,x43662),a910)),x43664),x43665))) % 177.41/177.18 [4367]E(f327(f327(f41(x43671,f922(f921(x43672,x43673),a910)),x43674),f327(f327(f8(f922(f921(x43673,x43672),a910),f922(f921(x43672,x43673),a910),x43671),f286(x43673,x43672)),x43675)),f327(f286(x43673,x43672),f327(f327(f41(x43671,f922(f921(x43673,x43672),a910)),x43674),x43675))) % 177.41/177.18 [4468]P1(f327(f327(f234(f922(x44681,a910)),f327(f327(f23(f922(x44681,a910)),f327(f310(x44682,x44681,x44683),x44684)),f327(f310(x44682,x44681,x44683),x44685))),f327(f310(x44682,x44681,x44683),f327(f327(f23(f922(x44682,a910)),x44684),x44685)))) % 177.41/177.18 [4613]E(f327(f157(f916(f921(x46131,x46132)),x46131,f114(f921(x46131,x46132)),f327(f327(f7(x46131,f922(f916(x46131),f916(f921(x46131,x46132))),f922(f916(x46131),f916(f921(x46131,x46132)))),f327(f327(f8(f922(f916(f921(x46131,x46132)),f916(f921(x46131,x46132))),f922(f922(f916(x46131),f916(f921(x46131,x46132))),f922(f916(x46131),f916(f921(x46131,x46132)))),x46131),f8(f916(f921(x46131,x46132)),f916(f921(x46131,x46132)),f916(x46131))),f327(f327(f8(f921(x46131,x46132),f922(f916(f921(x46131,x46132)),f916(f921(x46131,x46132))),x46131),f152(f921(x46131,x46132))),f327(f327(f7(x46131,x46132,f921(x46131,x46132)),f252(x46131,x46132)),x46133)))),f327(f327(f7(f916(x46131),f916(x46132),f916(f921(x46131,x46132))),f182(x46131,x46132)),x46134))),x46135),f327(f327(f182(x46131,x46132),x46135),f327(f327(f152(x46132),x46133),x46134))) % 177.41/177.18 [4331]E(f327(f327(f102(f922(x43311,a910)),f327(f285(x43312,x43311,x43313),x43314)),f327(f285(x43312,x43311,x43315),x43314)),f327(f285(x43312,x43311,f327(f327(f102(f922(f921(x43312,x43311),a910)),x43313),x43315)),x43314)) % 177.41/177.18 [4368]E(f327(f327(f135(f921(x43681,x43682)),f327(f327(f182(x43681,x43682),x43683),f327(f327(f176(x43682),f327(f191(f916(x43681)),x43683)),x43684))),f327(f327(f182(x43681,x43682),x43685),f327(f327(f139(x43682),f327(f191(f916(x43681)),x43683)),x43684))),f327(f327(f182(x43681,x43682),f327(f327(f135(x43681),x43683),x43685)),x43684)) % 177.41/177.18 [4471]E(f327(f327(f254(x44711,x44712),x44713),f327(f327(f18(x44711,f922(x44712,a910),f922(x44712,a910)),f327(f327(f8(f922(x44712,a910),f922(f922(x44712,a910),f922(x44712,a910)),x44711),f23(f922(x44712,a910))),x44714)),x44715)),f327(f327(f23(f922(f921(x44711,x44712),a910)),f327(f327(f254(x44711,x44712),x44713),x44714)),f327(f327(f254(x44711,x44712),x44713),x44715))) % 177.41/177.18 [4472]E(f327(f327(f254(x44721,x44722),x44723),f327(f327(f18(x44721,f922(x44722,a910),f922(x44722,a910)),f327(f327(f8(f922(x44722,a910),f922(f922(x44722,a910),f922(x44722,a910)),x44721),f102(f922(x44722,a910))),x44724)),x44725)),f327(f327(f102(f922(f921(x44721,x44722),a910)),f327(f327(f254(x44721,x44722),x44723),x44724)),f327(f327(f254(x44721,x44722),x44723),x44725))) % 177.41/177.18 [4473]E(f327(f327(f254(x44731,x44732),x44733),f327(f327(f18(x44731,f922(x44732,a910),f922(x44732,a910)),f327(f327(f8(f922(x44732,a910),f922(f922(x44732,a910),f922(x44732,a910)),x44731),f103(f922(x44732,a910))),x44734)),x44735)),f327(f327(f103(f922(f921(x44731,x44732),a910)),f327(f327(f254(x44731,x44732),x44733),x44734)),f327(f327(f254(x44731,x44732),x44733),x44735))) % 177.41/177.18 [4477]E(f327(f327(f40(x44771,f922(x44772,a910)),x44773),f327(f327(f7(x44771,f922(x44772,a910),f922(x44772,a910)),f327(f327(f8(f922(x44772,a910),f922(f922(x44772,a910),f922(x44772,a910)),x44771),f23(f922(x44772,a910))),x44774)),x44775)),f327(f327(f23(f922(x44772,a910)),f327(f327(f40(x44771,f922(x44772,a910)),x44773),x44774)),x44775)) % 177.41/177.18 [4478]E(f327(f327(f40(x44781,f922(x44782,a910)),x44783),f327(f327(f7(x44781,f922(x44782,a910),f922(x44782,a910)),f327(f327(f8(f922(x44782,a910),f922(f922(x44782,a910),f922(x44782,a910)),x44781),f103(f922(x44782,a910))),x44784)),x44785)),f327(f327(f103(f922(x44782,a910)),f327(f327(f40(x44781,f922(x44782,a910)),x44783),x44784)),x44785)) % 177.41/177.18 [4479]E(f327(f327(f41(x44791,f922(x44792,a910)),x44793),f327(f327(f7(x44791,f922(x44792,a910),f922(x44792,a910)),f327(f327(f8(f922(x44792,a910),f922(f922(x44792,a910),f922(x44792,a910)),x44791),f102(f922(x44792,a910))),x44794)),x44795)),f327(f327(f102(f922(x44792,a910)),f327(f327(f41(x44791,f922(x44792,a910)),x44793),x44794)),x44795)) % 177.41/177.18 [4483]E(f327(f327(f40(x44831,f922(x44832,a910)),x44833),f327(f327(f18(x44831,f922(x44832,a910),f922(x44832,a910)),f327(f327(f8(f922(x44832,a910),f922(f922(x44832,a910),f922(x44832,a910)),x44831),f102(f922(x44832,a910))),x44834)),x44835)),f327(f327(f102(f922(x44832,a910)),f327(f327(f40(x44831,f922(x44832,a910)),x44833),x44834)),f327(f327(f40(x44831,f922(x44832,a910)),x44833),x44835))) % 177.41/177.18 [4484]E(f327(f327(f41(x44841,f922(x44842,a910)),x44843),f327(f327(f18(x44841,f922(x44842,a910),f922(x44842,a910)),f327(f327(f8(f922(x44842,a910),f922(f922(x44842,a910),f922(x44842,a910)),x44841),f103(f922(x44842,a910))),x44844)),x44845)),f327(f327(f103(f922(x44842,a910)),f327(f327(f41(x44841,f922(x44842,a910)),x44843),x44844)),f327(f327(f41(x44841,f922(x44842,a910)),x44843),x44845))) % 177.41/177.18 [4497]E(f327(f327(f40(x44971,f922(x44972,a910)),x44973),f327(f327(f18(x44971,f922(x44972,a910),f922(x44972,a910)),f327(f327(f8(f922(x44972,a910),f922(f922(x44972,a910),f922(x44972,a910)),x44971),f102(f922(x44972,a910))),x44974)),x44975)),f327(f327(f102(f922(x44972,a910)),f38(f922(x44972,a910),f327(f310(x44971,f922(x44972,a910),x44974),x44973))),f38(f922(x44972,a910),f327(f310(x44971,f922(x44972,a910),x44975),x44973)))) % 177.41/177.18 [4498]E(f327(f327(f41(x44981,f922(x44982,a910)),x44983),f327(f327(f18(x44981,f922(x44982,a910),f922(x44982,a910)),f327(f327(f8(f922(x44982,a910),f922(f922(x44982,a910),f922(x44982,a910)),x44981),f103(f922(x44982,a910))),x44984)),x44985)),f327(f327(f103(f922(x44982,a910)),f39(f922(x44982,a910),f327(f310(x44981,f922(x44982,a910),x44984),x44983))),f39(f922(x44982,a910),f327(f310(x44981,f922(x44982,a910),x44985),x44983)))) % 177.41/177.18 [4534]E(f327(f327(f139(x45341),f327(f191(f916(x45341)),f178(x45341,x45342,f327(f327(f155(x45343,x45341),x45344),x45345)))),f327(f327(f155(x45343,x45341),x45344),x45345)),f327(f327(f155(x45343,x45341),x45344),f327(f327(f139(x45343),f327(f191(f916(x45343)),f178(x45343,f327(f72(x45341,a910,x45343,x45342),x45344),x45345))),x45345))) % 177.41/177.18 [4410]E(f327(f327(f135(f921(x44101,x44102)),f327(f327(f182(x44101,x44102),f327(f327(f176(x44101),f327(f191(f916(x44102)),x44103)),x44104)),x44103)),f327(f327(f182(x44101,x44102),f327(f327(f139(x44101),f327(f191(f916(x44102)),x44103)),x44104)),x44105)),f327(f327(f182(x44101,x44102),x44104),f327(f327(f135(x44102),x44103),x44105))) % 177.41/177.18 [4525]E(f85(x45251,f327(f327(f18(x45251,a910,a910),f327(f327(f8(a910,f922(a910,a910),x45251),a325),f327(f327(f7(x45251,f922(x45251,a910),a910),f329(x45251)),x45252))),f327(f327(f7(x45251,x45253,a910),f327(f327(f8(x45253,f922(x45253,a910),x45251),a324),x45254)),x45255))),f327(f77(x45251,x45253,x45252,x45254),x45255)) % 177.41/177.18 [4526]E(f90(x45261,f327(f327(f18(x45261,a910,a910),f327(f327(f8(a910,f922(a910,a910),x45261),a325),f327(f327(f7(x45261,f922(x45261,a910),a910),f329(x45261)),x45262))),f327(f327(f7(x45261,x45263,a910),f327(f327(f8(x45263,f922(x45263,a910),x45261),a324),x45264)),x45265))),f327(f92(x45261,x45263,x45262,x45264),x45265)) % 177.41/177.18 [4574]E(f327(f327(f86(a1,x45741),f327(f105(a1),f327(f327(f80(a1),x45742),a98))),f327(f327(f18(a1,x45741,x45741),f327(f327(f7(a1,x45741,f922(x45741,x45741)),f327(f327(f8(a910,f922(x45741,f922(x45741,x45741)),a1),f97(x45741)),a195)),f186(x45741,x45743,x45744,x45745))),f327(f327(f8(a915,x45741,a1),x45744),f327(f327(f7(a1,a915,a915),f327(f327(f8(a915,f922(a915,a915),a1),f80(a915)),a106)),x45745)))),f186(x45741,x45743,x45744,f327(f327(f80(a915),f327(f105(a915),x45742)),x45745))) % 177.41/177.18 [4609]E(f327(f327(f86(a1,x46091),f327(f105(a1),f327(f327(f80(a1),x46092),a98))),f327(f327(f18(a1,x46091,x46091),f327(f327(f7(a1,x46091,f922(x46091,x46091)),f327(f327(f8(a910,f922(x46091,f922(x46091,x46091)),a1),f97(x46091)),a195)),f327(f185(x46091,x46093,x46094),x46095))),f327(f327(f18(a1,x46091,x46091),f327(f327(f8(a915,f922(x46091,x46091),a1),x46094),f327(f327(f7(a1,a915,a915),f327(f327(f8(a915,f922(a915,a915),a1),f80(a915)),a106)),x46095))),f327(f327(f8(a915,x46091,a1),f185(x46091,x46093,x46094)),f327(f327(f7(a1,a915,a915),f327(f327(f8(a915,f922(a915,a915),a1),f80(a915)),a106)),x46095))))),f327(f185(x46091,x46093,x46094),f327(f327(f80(a915),f327(f105(a915),x46092)),x46095))) % 177.41/177.18 [4644]E(f327(f262(f921(x46441,x46442)),f327(f257(x46441,x46442,a910),f327(f327(f8(f922(x46442,f922(x46443,a910)),f922(x46442,a910),x46441),f327(f8(f922(x46443,a910),a910,x46442),f87(x46443))),f327(f327(f7(x46441,f922(x46442,f922(x46443,a910)),f922(x46442,f922(x46443,a910))),f327(f327(f8(f922(f922(x46443,a910),f922(x46443,a910)),f922(f922(x46442,f922(x46443,a910)),f922(x46442,f922(x46443,a910))),x46441),f8(f922(x46443,a910),f922(x46443,a910),x46442)),f327(f327(f8(f922(x46443,f922(a910,a910)),f922(f922(x46443,a910),f922(x46443,a910)),x46441),f18(x46443,a910,a910)),f327(f327(f8(f922(x46443,a910),f922(x46443,f922(a910,a910)),x46441),f327(f8(a910,f922(a910,a910),x46443),a325)),f327(f327(f7(x46441,f922(f921(x46441,x46443),a910),f922(x46443,a910)),f327(f327(f8(f922(x46443,f922(f922(f921(x46441,x46443),a910),a910)),f922(f922(f921(x46441,x46443),a910),f922(x46443,a910)),x46441),f7(x46443,f922(f921(x46441,x46443),a910),a910)),f327(f327(f8(f922(x46443,f921(x46441,x46443)),f922(x46443,f922(f922(f921(x46441,x46443),a910),a910)),x46441),f327(f8(f921(x46441,x46443),f922(f922(f921(x46441,x46443),a910),a910),x46443),f329(f921(x46441,x46443)))),f252(x46441,x46443)))),x46444))))),f327(f327(f7(x46442,f922(f921(x46443,x46442),a910),f922(x46443,a910)),f327(f327(f8(f922(x46443,f922(f922(f921(x46443,x46442),a910),a910)),f922(f922(f921(x46443,x46442),a910),f922(x46443,a910)),x46442),f7(x46443,f922(f921(x46443,x46442),a910),a910)),f327(f327(f8(f922(x46443,f921(x46443,x46442)),f922(x46443,f922(f922(f921(x46443,x46442),a910),a910)),x46442),f327(f8(f921(x46443,x46442),f922(f922(f921(x46443,x46442),a910),a910),x46443),f329(f921(x46443,x46442)))),f327(f7(x46443,x46442,f921(x46443,x46442)),f252(x46443,x46442))))),x46445))))),f327(f327(f289(x46441,x46443,x46442),x46444),x46445)) % 177.41/177.18 [4709]~E(f26(x47091,x47092,x47093),f27(x47094,x47095,x47096)) % 177.41/177.18 [4259]E(f226(x42591,x42592,x42593,x42594,f222(x42591,x42592,x42595,x42596)),f327(f327(x42594,x42595),x42596)) % 177.41/177.18 [4260]E(f227(x42601,x42602,x42603,x42604,f222(x42601,x42602,x42605,x42606)),f327(f327(x42604,x42605),x42606)) % 177.41/177.18 [4386]E(f128(x43861,x43862,x43863,x43864,f127(x43862,x43865,x43866)),f327(f327(f327(x43864,x43865),x43866),f128(x43861,x43862,x43863,x43864,x43866))) % 177.41/177.18 [4405]E(f74(x44051,x44052,f74(x44051,x44052,x44053,x44054,x44055),x44054,x44056),f74(x44051,x44052,x44053,x44054,x44056)) % 177.41/177.18 [4513]E(f327(f72(f921(x45131,x45132),x45132,f921(x45133,x45134),f256(x45131,x45132)),f258(x45133,x45131,x45134,x45132,x45135,x45136)),f327(f72(x45134,x45132,f921(x45133,x45134),x45136),f256(x45133,x45134))) % 177.41/177.18 [4514]E(f327(f72(f921(x45141,x45142),x45141,f921(x45143,x45144),f251(x45141,x45142)),f258(x45143,x45141,x45144,x45142,x45145,x45146)),f327(f72(x45143,x45141,f921(x45143,x45144),x45145),f251(x45143,x45144))) % 177.41/177.18 [4128]E(f327(f327(f72(x41281,x41282,x41283,x41284),x41285),x41286),f327(x41284,f327(x41285,x41286))) % 177.41/177.18 [4269]E(f225(x42691,f921(x42692,f917(x42692)),x42693,f327(f257(x42692,f917(x42692),x42691),x42694),f327(f136(x42692),f127(x42692,x42695,x42696))),f327(f327(x42694,x42695),x42696)) % 177.41/177.18 [4320]E(f228(x43201,x43202,x43203,x43204,f222(x43201,x43202,x43205,x43206)),f327(f327(f80(a915),f327(f327(f80(a915),f327(x43203,x43205)),f327(x43204,x43206))),f327(a113,f2(a915)))) % 177.41/177.18 [3926]E(f327(f327(f257(x39261,x39262,x39263),x39264),f327(f327(f252(x39261,x39262),x39265),x39266)),f327(f327(x39264,x39265),x39266)) % 177.41/177.18 [3986]E(f327(f327(f327(f8(x39861,x39862,x39863),x39864),x39865),x39866),f327(x39864,f327(x39865,x39866))) % 177.41/177.18 [3987]E(f327(f327(f327(f7(x39871,x39872,x39873),x39874),x39875),x39876),f327(f327(x39874,x39876),x39875)) % 177.41/177.18 [4005]E(f327(f327(f327(f18(x40051,x40052,x40053),x40054),x40055),x40056),f327(f327(x40054,x40056),f327(x40055,x40056))) % 177.41/177.18 [4028]E(f327(f157(x40281,x40282,x40283,x40284),f327(f327(f152(x40282),x40285),x40286)),f327(f327(x40284,x40285),x40286)) % 177.41/177.18 [4066]E(f170(f921(x40661,x40662),f327(f327(f238(a915),x40663),x40664),f327(f327(f252(x40661,x40662),x40665),x40666)),f327(f327(f182(x40661,x40662),f170(x40661,x40663,x40665)),f170(x40662,x40664,x40666))) % 177.41/177.18 [4132]E(f327(f327(f152(f921(x41321,x41322)),f327(f327(f252(x41321,x41322),x41323),x41324)),f327(f327(f182(x41321,x41322),x41325),x41326)),f327(f327(f182(x41321,x41322),f327(f327(f152(x41321),x41323),x41325)),f327(f327(f152(x41322),x41324),x41326))) % 177.41/177.18 [4133]E(f327(f327(f155(x41331,x41332),x41333),f327(f327(f160(x41331,x41334),x41335),x41336)),f327(f327(f160(x41332,f327(f327(f155(x41331,x41332),x41333),x41334)),x41335),f327(x41333,x41336))) % 177.41/177.18 [4157]E(f327(f327(f255(x41571,x41572,x41573,x41574),x41575),x41576),f327(x41574,f327(f327(f252(x41571,x41572),x41575),x41576))) % 177.41/177.18 [4176]E(f327(f143(x41761,x41762,x41763,x41764),f327(f327(f152(x41762),x41765),x41766)),f327(f143(x41761,x41762,x41763,f327(f327(x41763,x41764),x41765)),x41766)) % 177.41/177.18 [4202]E(f260(x42021,x42022,x42023,x42024,f327(f327(f252(x42021,x42022),x42025),x42026)),f327(f327(x42024,x42025),x42026)) % 177.41/177.18 [4283]E(f327(f327(f40(x42831,f922(x42832,a910)),x42833),f327(f72(x42834,f922(x42832,a910),x42831,x42835),x42836)),f327(f327(f40(x42834,f922(x42832,a910)),f327(f310(x42831,x42834,x42836),x42833)),x42835)) % 177.41/177.18 [4334]E(f327(f327(f155(x43341,x43342),x43343),f327(f327(f155(x43344,x43341),x43345),x43346)),f327(f327(f155(x43344,x43342),f327(f72(x43341,x43342,x43344,x43343),x43345)),x43346)) % 177.41/177.18 [4340]E(f327(f310(x43401,x43402,f327(f72(x43403,x43402,x43401,x43404),x43405)),x43406),f327(f310(x43403,x43402,x43404),f327(f310(x43401,x43403,x43405),x43406))) % 177.41/177.18 [4341]E(f327(f311(x43411,x43412,f327(f72(x43413,x43412,x43411,x43414),x43415)),x43416),f327(f311(x43411,x43413,x43415),f327(f311(x43413,x43412,x43414),x43416))) % 177.41/177.18 [4369]E(f327(f143(x43691,x43692,x43693,f327(f143(x43691,x43692,x43693,x43694),x43695)),x43696),f327(f143(x43691,x43692,x43693,x43694),f327(f327(f135(x43692),x43695),x43696))) % 177.41/177.18 [4503]E(f327(f258(x45031,x45031,x45032,x45033,f31(x45031),x45034),f327(f327(f252(x45031,x45032),x45035),x45036)),f327(f327(f252(x45031,x45033),x45035),f327(x45034,x45036))) % 177.41/177.18 [4504]E(f327(f258(x45041,x45042,x45043,x45043,x45044,f31(x45043)),f327(f327(f252(x45041,x45043),x45045),x45046)),f327(f327(f252(x45042,x45043),f327(x45044,x45045)),x45046)) % 177.41/177.18 [4592]E(f327(f327(f155(f921(x45921,x45922),f921(x45921,x45923)),f327(f257(x45921,x45922,f921(x45921,x45923)),f327(f327(f7(x45921,f922(x45922,x45923),f922(x45922,f921(x45921,x45923))),f327(f327(f8(f922(x45923,f921(x45921,x45923)),f922(f922(x45922,x45923),f922(x45922,f921(x45921,x45923))),x45921),f8(x45923,f921(x45921,x45923),x45922)),f252(x45921,x45923))),x45924))),f327(f327(f182(x45921,x45922),x45925),x45926)),f327(f327(f182(x45921,x45923),x45925),f327(f327(f155(x45922,x45923),x45924),x45926))) % 177.41/177.18 [3991]E(f95(x39911,x39912,x39913,f327(f327(f327(f91(x39911),x39914),x39915),x39916)),f327(f327(f327(x39913,x39914),x39915),x39916)) % 177.41/177.18 [3992]E(f96(x39921,x39922,x39923,f327(f327(f327(f91(x39921),x39924),x39925),x39926)),f327(f327(f327(x39923,x39924),x39925),x39926)) % 177.41/177.18 [4186]E(f327(f327(f72(x41861,x41862,x41863,f327(f16(x41862,x41861),x41864)),x41865),x41866),x41864) % 177.41/177.18 [4218]E(f327(f310(x42181,x42182,x42183),f327(f310(x42184,x42181,x42185),x42186)),f327(f310(x42184,x42182,f327(f327(f8(x42181,x42182,x42184),x42183),x42185)),x42186)) % 177.41/177.18 [4224]E(f327(f327(f40(x42241,f922(x42242,a910)),f327(f310(x42243,x42241,x42244),x42245)),x42246),f327(f327(f40(x42243,f922(x42242,a910)),x42245),f327(f327(f8(x42241,f922(x42242,a910),x42243),x42246),x42244))) % 177.41/177.18 [4225]E(f327(f327(f41(x42251,f922(x42252,a910)),f327(f310(x42253,x42251,x42254),x42255)),x42256),f327(f327(f41(x42253,f922(x42252,a910)),x42255),f327(f327(f8(x42251,f922(x42252,a910),x42253),x42256),x42254))) % 177.41/177.18 [4226]E(f327(f327(f40(x42261,f922(x42262,a910)),x42263),f327(f327(f8(x42264,f922(x42262,a910),x42261),x42265),x42266)),f327(f327(f40(x42264,f922(x42262,a910)),f327(f310(x42261,x42264,x42266),x42263)),x42265)) % 177.41/177.18 [4227]E(f327(f327(f41(x42271,f922(x42272,a910)),x42273),f327(f327(f8(x42274,f922(x42272,a910),x42271),x42275),x42276)),f327(f327(f41(x42274,f922(x42272,a910)),f327(f310(x42271,x42274,x42276),x42273)),x42275)) % 177.41/177.18 [4285]E(f327(f327(f40(x42851,f922(x42852,a910)),x42853),f327(f327(f8(f922(x42854,a910),f922(x42852,a910),x42851),f310(x42854,x42852,x42855)),x42856)),f327(f310(x42854,x42852,x42855),f327(f327(f40(x42851,f922(x42854,a910)),x42853),x42856))) % 177.41/177.18 [4286]E(f327(f327(f40(x42861,f922(x42862,a910)),x42863),f327(f327(f8(f922(x42864,a910),f922(x42862,a910),x42861),f311(x42862,x42864,x42865)),x42866)),f327(f311(x42862,x42864,x42865),f327(f327(f40(x42861,f922(x42864,a910)),x42863),x42866))) % 177.41/177.18 [4287]E(f327(f327(f41(x42871,f922(x42872,a910)),x42873),f327(f327(f8(f922(x42874,a910),f922(x42872,a910),x42871),f311(x42872,x42874,x42875)),x42876)),f327(f311(x42872,x42874,x42875),f327(f327(f41(x42871,f922(x42874,a910)),x42873),x42876))) % 177.41/177.18 [4288]E(f327(f327(f40(x42881,f922(x42882,a910)),x42883),f327(f327(f8(f922(x42884,a910),f922(x42882,a910),x42881),f285(x42884,x42882,x42885)),x42886)),f327(f285(x42884,x42882,x42885),f327(f327(f40(x42881,f922(x42884,a910)),x42883),x42886))) % 177.41/177.18 [4374]E(f327(f143(x43741,x43742,f327(f7(x43742,x43741,x43741),x43743),x43744),f327(f169(x43742),f327(f327(f152(x43742),x43745),x43746))),f327(f327(x43743,x43745),f327(f143(x43741,x43742,f327(f7(x43742,x43741,x43741),x43743),x43744),f327(f169(x43742),x43746)))) % 177.41/177.18 [4432]E(f327(f327(f18(f921(x44321,x44322),x44322,x44323),f327(f327(f8(x44324,f922(x44322,x44323),f921(x44321,x44322)),x44325),f327(f327(f8(x44321,x44324,f921(x44321,x44322)),x44326),f251(x44321,x44322)))),f256(x44321,x44322)),f327(f257(x44321,x44322,x44323),f327(f327(f8(x44324,f922(x44322,x44323),x44321),x44325),x44326))) % 177.41/177.18 [4439]E(f327(f143(x44391,x44392,f327(f7(x44392,x44391,x44391),x44393),f327(f143(x44391,x44392,f327(f7(x44392,x44391,x44391),x44393),x44394),f327(f169(x44392),x44395))),f327(f169(x44392),x44396)),f327(f143(x44391,x44392,f327(f7(x44392,x44391,x44391),x44393),x44394),f327(f169(x44392),f327(f327(f135(x44392),x44396),x44395)))) % 177.41/177.18 [4441]E(f327(f327(f155(f921(x44411,x44412),f921(x44413,x44412)),f327(f257(x44411,x44412,f921(x44413,x44412)),f327(f327(f8(x44413,f922(x44412,f921(x44413,x44412)),x44411),f252(x44413,x44412)),x44414))),f327(f327(f182(x44411,x44412),x44415),x44416)),f327(f327(f182(x44413,x44412),f327(f327(f155(x44411,x44413),x44414),x44415)),x44416)) % 177.41/177.18 [4486]P1(f327(f327(f234(f922(x44861,a910)),f327(f285(x44862,x44861,x44863),f327(f327(f41(x44864,f922(x44862,a910)),x44865),x44866))),f327(f327(f41(x44864,f922(x44861,a910)),x44865),f327(f327(f8(f922(x44862,a910),f922(x44861,a910),x44864),f285(x44862,x44861,x44863)),x44866)))) % 177.41/177.18 [4298]E(f327(f327(f182(x42981,x42982),f327(f327(f160(x42981,x42983),x42984),f327(f251(x42981,x42982),x42985))),f327(f327(f160(x42982,x42986),x42984),f327(f256(x42981,x42982),x42985))),f327(f327(f160(f921(x42981,x42982),f327(f327(f182(x42981,x42982),x42983),x42986)),x42984),x42985)) % 177.41/177.18 [4357]E(f327(f327(f102(f922(f921(x43571,x43572),a910)),f327(f327(f289(x43571,x43573,x43572),x43574),x43575)),f327(f327(f289(x43571,x43573,x43572),x43574),x43576)),f327(f327(f289(x43571,x43573,x43572),x43574),f327(f327(f102(f922(f921(x43573,x43572),a910)),x43575),x43576))) % 177.41/177.18 [4451]E(f327(f327(f309(f921(x44511,x44512)),f327(f327(f252(x44511,x44512),x44513),x44514)),f327(f327(f102(f922(f921(x44511,x44512),a910)),f327(f327(f254(x44511,x44512),x44515),f327(f16(f922(x44512,a910),x44511),f327(f327(f309(x44512),x44514),x44516)))),f327(f327(f254(x44511,x44512),f327(f327(f309(x44511),x44513),x44515)),f327(f16(f922(x44512,a910),x44511),x44516)))),f327(f327(f254(x44511,x44512),f327(f327(f309(x44511),x44513),x44515)),f327(f16(f922(x44512,a910),x44511),f327(f327(f309(x44512),x44514),x44516)))) % 177.41/177.18 [4530]E(f327(f327(f103(f922(x45301,a910)),f327(f311(x45301,x45302,f327(f72(f921(x45302,x45303),x45302,x45301,f251(x45302,x45303)),x45304)),x45305)),f327(f311(x45301,x45303,f327(f72(f921(x45302,x45303),x45303,x45301,f256(x45302,x45303)),x45304)),x45306)),f327(f311(x45301,f921(x45302,x45303),x45304),f327(f327(f254(x45302,x45303),x45305),f327(f16(f922(x45303,a910),x45302),x45306)))) % 177.41/177.18 [4380]E(f327(f327(f102(f922(f921(x43801,x43802),a910)),f327(f327(f289(x43801,x43803,x43802),x43804),x43805)),f327(f327(f289(x43801,x43803,x43802),x43806),x43805)),f327(f327(f289(x43801,x43803,x43802),f327(f327(f102(f922(f921(x43801,x43803),a910)),x43804),x43806)),x43805)) % 177.41/177.18 [4511]E(f327(f327(f40(x45111,f922(x45112,a910)),x45113),f327(f327(f7(x45111,f922(x45114,f922(x45112,a910)),f922(x45112,a910)),f327(f327(f8(f922(x45114,a910),f922(f922(x45114,f922(x45112,a910)),f922(x45112,a910)),x45111),f40(x45114,f922(x45112,a910))),x45115)),x45116)),f327(f327(f40(x45114,f922(x45112,a910)),f327(f327(f40(x45111,f922(x45114,a910)),x45113),x45115)),x45116)) % 177.41/177.18 [4512]E(f327(f327(f41(x45121,f922(x45122,a910)),x45123),f327(f327(f7(x45121,f922(x45124,f922(x45122,a910)),f922(x45122,a910)),f327(f327(f8(f922(x45124,a910),f922(f922(x45124,f922(x45122,a910)),f922(x45122,a910)),x45121),f41(x45124,f922(x45122,a910))),x45125)),x45126)),f327(f327(f41(x45124,f922(x45122,a910)),f327(f327(f40(x45121,f922(x45124,a910)),x45123),x45125)),x45126)) % 177.41/177.18 [4564]E(f327(f257(x45641,x45642,f921(x45643,x45644)),f327(f327(f7(x45641,f922(x45642,x45644),f922(x45642,f921(x45643,x45644))),f327(f327(f8(f922(x45644,f921(x45643,x45644)),f922(f922(x45642,x45644),f922(x45642,f921(x45643,x45644))),x45641),f8(x45644,f921(x45643,x45644),x45642)),f327(f327(f8(x45643,f922(x45644,f921(x45643,x45644)),x45641),f252(x45643,x45644)),x45645))),x45646)),f258(x45641,x45643,x45642,x45644,x45645,x45646)) % 177.41/177.18 [4587]E(f327(f310(x45871,x45872,f327(f327(f18(x45871,x45872,x45872),f327(f327(f18(x45871,x45872,f922(x45872,x45872)),f327(f327(f8(a910,f922(x45872,f922(x45872,x45872)),x45871),f97(x45872)),x45873)),x45874)),x45875)),x45876),f327(f327(f102(f922(x45872,a910)),f327(f310(x45871,x45872,x45874),f327(f327(f103(f922(x45871,a910)),x45876),f327(f262(x45871),x45873)))),f327(f310(x45871,x45872,x45875),f327(f327(f103(f922(x45871,a910)),x45876),f327(f262(x45871),f327(f327(f8(a910,a910,x45871),a322),x45873)))))) % 177.41/177.18 [4599]E(f327(f310(x45991,f921(x45992,x45993),f327(f327(f18(x45991,x45993,f921(x45992,x45993)),f327(f327(f8(x45992,f922(x45993,f921(x45992,x45993)),x45991),f252(x45992,x45993)),x45994)),x45995)),x45996),f327(f327(f254(x45992,x45993),f327(f310(x45991,x45992,x45994),x45996)),f327(f327(f8(f922(x45991,a910),f922(x45993,a910),x45992),f310(x45991,x45993,x45995)),f327(f327(f7(x45992,f922(x45991,a910),f922(x45991,a910)),f327(f327(f8(f922(x45991,a910),f922(f922(x45991,a910),f922(x45991,a910)),x45992),f103(f922(x45991,a910))),f327(f327(f8(f922(x45992,a910),f922(x45991,a910),x45992),f311(x45991,x45992,x45994)),f327(f327(f7(x45992,f922(x45992,a910),f922(x45992,a910)),f309(x45992)),f190(f922(x45992,a910)))))),x45996)))) % 177.41/177.18 [4625]E(f246(x46251,x46252,x46253,x46254,x46255,x46256),f327(x46254,f327(f262(x46251),f327(f327(f8(f922(f922(x46253,x46251),a910),a910,x46251),f87(f922(x46253,x46251))),f327(f327(f8(f922(f922(x46253,x46251),a910),f922(f922(x46253,x46251),a910),x46251),f327(f18(f922(x46253,x46251),a910,a910),f327(f327(f8(a910,f922(a910,a910),f922(x46253,x46251)),a325),f327(f327(f7(f922(x46253,x46251),f922(f922(x46253,x46251),a910),a910),f329(f922(x46253,x46251))),x46255)))),f327(f327(f7(x46251,f922(f922(x46253,x46251),x46251),f922(f922(x46253,x46251),a910)),f327(f327(f8(f922(x46251,a910),f922(f922(f922(x46253,x46251),x46251),f922(f922(x46253,x46251),a910)),x46251),f8(x46251,a910,f922(x46253,x46251))),a324)),f327(f327(f7(f922(x46253,x46251),x46253,x46251),f5(f922(x46253,x46251))),x46256))))))) % 177.41/177.18 [4413]E(f327(f72(x44131,x44132,x44133,x44134),f74(x44133,x44131,x44135,x44136,x44137)),f74(x44133,x44132,f327(f72(x44131,x44132,x44133,x44134),x44135),x44136,f327(x44134,x44137))) % 177.41/177.18 [4547]E(f327(f256(x45471,x45472),f327(f258(x45473,x45471,x45474,x45472,x45475,x45476),x45477)),f327(x45476,f327(f256(x45473,x45474),x45477))) % 177.41/177.18 [4548]E(f327(f251(x45481,x45482),f327(f258(x45483,x45481,x45484,x45482,x45485,x45486),x45487)),f327(x45485,f327(f251(x45483,x45484),x45487))) % 177.41/177.18 [4261]E(f327(f327(f182(x42611,x42612),f327(f327(f160(x42611,x42613),x42614),x42615)),f327(f327(f160(x42612,x42616),x42614),x42617)),f327(f327(f160(f921(x42611,x42612),f327(f327(f182(x42611,x42612),x42613),x42616)),x42614),f327(f327(f252(x42611,x42612),x42615),x42617))) % 177.41/177.18 [4329]E(f327(f327(f327(f259(x43291,x43292,x43293,x43294),x43295),x43296),x43297),f327(f327(f257(x43292,x43293,x43294),x43296),f327(x43295,x43297))) % 177.41/177.18 [4339]E(f327(f327(f327(f259(x43391,x43392,x43393,x43394),x43395),x43396),x43397),f327(f327(x43396,f327(f251(x43392,x43393),f327(x43395,x43397))),f327(f256(x43392,x43393),f327(x43395,x43397)))) % 177.41/177.18 [4391]E(f327(f72(x43911,x43912,x43913,x43914),f327(f72(x43915,x43911,x43913,x43916),x43917)),f327(f72(x43915,x43912,x43913,f327(f72(x43911,x43912,x43915,x43914),x43916)),x43917)) % 177.41/177.18 [4568]E(f327(f258(x45681,x45682,x45683,x45683,x45684,f31(x45683)),f327(f258(x45681,x45681,x45685,x45683,f31(x45681),x45686),x45687)),f327(f327(f252(x45682,x45683),f327(x45684,f327(f251(x45681,x45685),x45687))),f327(x45686,f327(f256(x45681,x45685),x45687)))) % 177.41/177.18 [4569]E(f327(f258(x45691,x45691,x45692,x45693,f31(x45691),x45694),f327(f258(x45695,x45691,x45692,x45692,x45696,f31(x45692)),x45697)),f327(f327(f252(x45691,x45693),f327(x45696,f327(f251(x45695,x45692),x45697))),f327(x45694,f327(f256(x45695,x45692),x45697)))) % 177.41/177.18 [4585]E(f327(f258(x45851,x45852,x45853,x45853,x45854,f31(x45853)),f327(f258(x45855,x45851,x45853,x45853,x45856,f31(x45853)),x45857)),f327(f258(x45855,x45852,x45853,x45853,f327(f72(x45851,x45852,x45855,x45854),x45856),f31(x45853)),x45857)) % 177.41/177.18 [4586]E(f327(f258(x45861,x45861,x45862,x45863,f31(x45861),x45864),f327(f258(x45861,x45861,x45865,x45862,f31(x45861),x45866),x45867)),f327(f258(x45861,x45861,x45865,x45863,f31(x45861),f327(f72(x45862,x45863,x45865,x45864),x45866)),x45867)) % 177.41/177.18 [4596]E(f327(f258(x45961,x45962,x45963,x45963,x45964,f31(x45963)),f327(f258(x45961,x45961,x45965,x45963,f31(x45961),x45966),x45967)),f327(f258(x45962,x45962,x45965,x45963,f31(x45962),x45966),f327(f258(x45961,x45962,x45965,x45965,x45964,f31(x45965)),x45967))) % 177.41/177.18 [4295]E(f327(f327(f289(x42951,x42952,x42953),f327(f327(f289(x42951,x42954,x42952),x42955),x42956)),x42957),f327(f327(f289(x42951,x42954,x42953),x42955),f327(f327(f289(x42954,x42952,x42953),x42956),x42957))) % 177.41/177.18 [4363]E(f327(f327(f257(x43631,x43632,x43633),f327(f72(x43634,f922(x43632,x43633),x43631,x43635),x43636)),x43637),f327(f327(x43635,f327(x43636,f327(f251(x43631,x43632),x43637))),f327(f256(x43631,x43632),x43637))) % 177.41/177.18 [4444]E(f327(f143(x44441,x44442,f327(f7(x44442,x44441,x44441),x44443),x44444),f327(f169(x44442),f327(f327(f155(x44445,x44442),x44446),x44447))),f327(f143(x44441,x44445,f327(f7(x44445,x44441,x44441),f327(f72(x44442,f922(x44441,x44441),x44445,x44443),x44446)),x44444),f327(f169(x44445),x44447))) % 177.41/177.18 [4392]E(f327(f327(f40(x43921,f922(f921(x43922,x43923),a910)),x43924),f327(f327(f8(f922(f921(x43925,x43923),a910),f922(f921(x43922,x43923),a910),x43921),f327(f289(x43922,x43925,x43923),x43926)),x43927)),f327(f327(f289(x43922,x43925,x43923),x43926),f327(f327(f40(x43921,f922(f921(x43925,x43923),a910)),x43924),x43927))) % 177.41/177.18 [4535]E(f327(f327(f40(x45351,f922(f921(x45352,x45353),a910)),x45354),f327(f327(f7(x45351,f922(f921(x45355,x45353),a910),f922(f921(x45352,x45353),a910)),f327(f327(f8(f922(f921(x45352,x45355),a910),f922(f922(f921(x45355,x45353),a910),f922(f921(x45352,x45353),a910)),x45351),f289(x45352,x45355,x45353)),x45356)),x45357)),f327(f327(f289(x45352,x45355,x45353),f327(f327(f40(x45351,f922(f921(x45352,x45355),a910)),x45354),x45356)),x45357)) % 177.41/177.18 [4536]E(f327(f143(x45361,x45362,f327(f327(f7(x45361,f922(x45362,x45363),f922(x45362,x45361)),f327(f327(f8(f922(x45363,x45361),f922(f922(x45362,x45363),f922(x45362,x45361)),x45361),f8(x45363,x45361,x45362)),x45364)),x45365),x45366),x45367),f327(f143(x45361,x45363,x45364,x45366),f327(f327(f155(x45362,x45363),x45365),x45367))) % 177.41/177.18 [4597]E(f327(f327(f41(x45971,f922(x45972,a910)),x45973),f327(f327(f8(f922(x45974,f922(x45972,a910)),f922(x45972,a910),x45971),f327(f41(x45974,f922(x45972,a910)),x45975)),f327(f327(f7(x45971,f922(x45974,f922(x45972,a910)),f922(x45974,f922(x45972,a910))),f327(f327(f8(f922(f922(x45972,a910),f922(x45972,a910)),f922(f922(x45974,f922(x45972,a910)),f922(x45974,f922(x45972,a910))),x45971),f8(f922(x45972,a910),f922(x45972,a910),x45974)),f327(f327(f8(f922(x45972,a910),f922(f922(x45972,a910),f922(x45972,a910)),x45971),f102(f922(x45972,a910))),x45976))),x45977))),f327(f327(f102(f922(x45972,a910)),f327(f327(f41(x45971,f922(x45972,a910)),x45973),x45976)),f327(f327(f41(x45974,f922(x45972,a910)),x45975),x45977))) % 177.41/177.18 [4598]E(f327(f327(f40(x45981,f922(x45982,a910)),x45983),f327(f327(f8(f922(x45984,f922(x45982,a910)),f922(x45982,a910),x45981),f327(f40(x45984,f922(x45982,a910)),x45985)),f327(f327(f7(x45981,f922(x45984,f922(x45982,a910)),f922(x45984,f922(x45982,a910))),f327(f327(f8(f922(f922(x45982,a910),f922(x45982,a910)),f922(f922(x45984,f922(x45982,a910)),f922(x45984,f922(x45982,a910))),x45981),f8(f922(x45982,a910),f922(x45982,a910),x45984)),f327(f327(f8(f922(x45982,a910),f922(f922(x45982,a910),f922(x45982,a910)),x45981),f103(f922(x45982,a910))),x45986))),x45987))),f327(f327(f103(f922(x45982,a910)),f327(f327(f40(x45981,f922(x45982,a910)),x45983),x45986)),f327(f327(f40(x45984,f922(x45982,a910)),x45985),x45987))) % 177.41/177.18 [4590]E(f199(x45901,x45902,f327(f327(f327(x45903,x45904),x45905),x45906),f327(f327(f7(x45901,f921(a100,a100),f922(a100,f917(x45902))),f327(f327(f7(x45901,a100,f922(f921(a100,a100),f922(a100,f917(x45902)))),f327(f327(f7(x45901,a100,f922(a100,f922(f921(a100,a100),f922(a100,f917(x45902))))),x45907),x45904)),x45905)),x45906)),f327(f327(f327(f211(x45901,x45902,x45903,x45907),x45904),x45905),x45906)) % 177.41/177.18 [4604]E(f200(x46041,x46042,f327(f327(f327(x46043,x46044),x46045),x46046),f327(f327(f7(x46041,f921(a100,a100),f922(a100,f917(x46042))),f327(f327(f7(x46041,a100,f922(f921(a100,a100),f922(a100,f917(x46042)))),f327(f327(f7(x46041,a100,f922(a100,f922(f921(a100,a100),f922(a100,f917(x46042))))),x46047),x46044)),x46045)),x46046)),f213(x46041,x46042,x46043,x46047,x46044,x46045,x46046)) % 177.41/177.18 [4595]E(f197(x45951,x45952,f327(f327(f327(x45953,x45954),x45955),x45956),f327(f327(f7(x45951,f921(a100,a100),f922(a100,f917(f918(x45952)))),f327(f327(f7(x45951,a100,f922(f921(a100,a100),f922(a100,f917(f918(x45952))))),f327(f327(f7(x45951,a100,f922(a100,f922(f921(a100,a100),f922(a100,f917(f918(x45952)))))),x45957),x45954)),x45955)),x45956)),f327(f327(f327(f207(x45951,x45952,x45953,x45957),x45954),x45955),x45956)) % 177.41/177.18 [4606]E(f198(x46061,x46062,f327(f327(f327(x46063,x46064),x46065),x46066),f327(f327(f7(x46061,f921(a100,a100),f922(a100,f917(f918(x46062)))),f327(f327(f7(x46061,a100,f922(f921(a100,a100),f922(a100,f917(f918(x46062))))),f327(f327(f7(x46061,a100,f922(a100,f922(f921(a100,a100),f922(a100,f917(f918(x46062)))))),x46067),x46064)),x46065)),x46066)),f209(x46061,x46062,x46063,x46067,x46064,x46065,x46066)) % 177.41/177.18 [4505]E(f327(f258(x45051,x45052,x45053,x45054,x45055,x45056),f327(f327(f252(x45051,x45053),x45057),x45058)),f327(f327(f252(x45052,x45054),f327(x45055,x45057)),f327(x45056,x45058))) % 177.41/177.18 [4608]E(f327(f327(f155(f921(x46081,x46082),f921(x46083,x46084)),f327(f257(x46081,x46082,f921(x46083,x46084)),f327(f327(f7(x46081,f922(x46082,x46084),f922(x46082,f921(x46083,x46084))),f327(f327(f8(f922(x46084,f921(x46083,x46084)),f922(f922(x46082,x46084),f922(x46082,f921(x46083,x46084))),x46081),f8(x46084,f921(x46083,x46084),x46082)),f327(f327(f8(x46083,f922(x46084,f921(x46083,x46084)),x46081),f252(x46083,x46084)),x46085))),x46086))),f327(f327(f182(x46081,x46082),x46087),x46088)),f327(f327(f182(x46083,x46084),f327(f327(f155(x46081,x46083),x46085),x46087)),f327(f327(f155(x46082,x46084),x46086),x46088))) % 177.41/177.18 [4611]E(f327(f327(f155(f921(x46111,x46112),x46113),f327(f257(x46111,x46112,x46113),f327(f327(f8(f922(x46112,f921(x46111,x46114)),f922(x46112,x46113),x46111),f327(f8(f921(x46111,x46114),x46113,x46112),x46115)),f327(f327(f7(x46111,f922(x46112,x46114),f922(x46112,f921(x46111,x46114))),f327(f327(f8(f922(x46114,f921(x46111,x46114)),f922(f922(x46112,x46114),f922(x46112,f921(x46111,x46114))),x46111),f8(x46114,f921(x46111,x46114),x46112)),f252(x46111,x46114))),x46116)))),f327(f327(f182(x46111,x46112),x46117),x46118)),f327(f327(f155(f921(x46111,x46114),x46113),x46115),f327(f327(f182(x46111,x46114),x46117),f327(f327(f155(x46112,x46114),x46116),x46118)))) % 177.41/177.18 [4539]E(f327(f327(f155(f921(x45391,x45392),x45393),f327(f257(x45391,x45392,x45393),f327(f327(f8(f922(x45392,f921(x45394,x45392)),f922(x45392,x45393),x45391),f327(f8(f921(x45394,x45392),x45393,x45392),x45395)),f327(f327(f8(x45394,f922(x45392,f921(x45394,x45392)),x45391),f252(x45394,x45392)),x45396)))),f327(f327(f182(x45391,x45392),x45397),x45398)),f327(f327(f155(f921(x45394,x45392),x45393),x45395),f327(f327(f182(x45394,x45392),f327(f327(f155(x45391,x45394),x45396),x45397)),x45398))) % 177.41/177.18 [4496]E(f327(f327(f257(x44961,x44962,x44963),f327(f327(f8(f922(x44962,f921(x44964,x44965)),f922(x44962,x44963),x44961),f327(f8(f921(x44964,x44965),x44963,x44962),f327(f257(x44964,x44965,x44963),x44966))),x44967)),x44968),f327(f327(f257(x44964,x44965,x44963),x44966),f327(f327(f257(x44961,x44962,f921(x44964,x44965)),x44967),x44968))) % 177.41/177.18 [4612]E(f327(f327(f40(f921(x46121,x46122),f922(f921(x46123,x46124),a910)),f327(f327(f254(x46121,x46122),x46125),f327(f16(f922(x46122,a910),x46121),x46126))),f327(f257(x46121,x46122,f922(f921(x46123,x46124),a910)),f327(f327(f7(x46121,f922(x46122,f922(x46123,f922(x46124,a910))),f922(x46122,f922(f921(x46123,x46124),a910))),f327(f327(f8(f922(f922(x46123,f922(x46124,a910)),f922(f921(x46123,x46124),a910)),f922(f922(x46122,f922(x46123,f922(x46124,a910))),f922(x46122,f922(f921(x46123,x46124),a910))),x46121),f8(f922(x46123,f922(x46124,a910)),f922(f921(x46123,x46124),a910),x46122)),f327(f327(f8(f922(x46123,a910),f922(f922(x46123,f922(x46124,a910)),f922(f921(x46123,x46124),a910)),x46121),f254(x46123,x46124)),x46127))),f327(f327(f8(f922(x46124,a910),f922(x46123,f922(x46124,a910)),x46122),f16(f922(x46124,a910),x46123)),x46128)))),f327(f327(f254(x46123,x46124),f327(f327(f40(x46121,f922(x46123,a910)),x46125),x46127)),f327(f16(f922(x46124,a910),x46123),f327(f327(f40(x46122,f922(x46124,a910)),x46126),x46128)))) % 177.41/177.18 [4553]E(f327(f327(f259(x45531,x45532,x45533,x45534),f327(f327(f259(x45531,x45535,x45536,f921(x45532,x45533)),x45537),x45538)),x45539),f327(f327(f259(x45531,x45535,x45536,x45534),x45537),f327(f327(f7(x45535,f922(x45532,f922(x45533,x45534)),f922(x45536,x45534)),f327(f327(f8(f922(x45536,f921(x45532,x45533)),f922(f922(x45532,f922(x45533,x45534)),f922(x45536,x45534)),x45535),f259(x45536,x45532,x45533,x45534)),x45538)),x45539))) % 177.41/177.18 [4582]E(f327(f72(f921(x45821,x45822),f921(x45823,x45824),f921(x45825,x45826),f258(x45821,x45823,x45822,x45824,x45827,x45828)),f258(x45825,x45821,x45826,x45822,x45829,x458210)),f258(x45825,x45823,x45826,x45824,f327(f72(x45821,x45823,x45825,x45827),x45829),f327(f72(x45822,x45824,x45826,x45828),x458210))) % 177.41/177.18 [4588]E(f327(f258(x45881,x45882,x45883,x45884,x45885,x45886),f327(f258(x45887,x45881,x45888,x45883,x45889,x458810),x458811)),f327(f258(x45887,x45882,x45888,x45884,f327(f72(x45881,x45882,x45887,x45885),x45889),f327(f72(x45883,x45884,x45888,x45886),x458810)),x458811)) % 177.41/177.18 [10390]P22(a909,a924,f327(f310(a908,f913(a909),f327(f327(f18(a908,f922(a909,f922(a911,a910)),f913(a909)),f327(f327(f18(a908,a912,f922(f922(a909,f922(a911,a910)),f913(a909))),f327(f327(f8(f922(a909,f922(a911,a910)),f922(a912,f922(f922(a909,f922(a911,a910)),f913(a909))),a908),f91(a909)),a926)),a928)),a930)),a923))+~P22(a909,a924,f327(f310(a908,f913(a909),f327(f327(f18(a908,f922(a909,f922(a911,a910)),f913(a909)),f327(f327(f18(a908,a912,f922(f922(a909,f922(a911,a910)),f913(a909))),f327(f327(f8(f922(a909,f922(a911,a910)),f922(a912,f922(f922(a909,f922(a911,a910)),f913(a909))),a908),f91(a909)),a925)),a928)),a929)),a923)) % 177.41/177.18 [4738]~P2(x47381)+P2(f918(x47381)) % 177.41/177.18 [4739]~P60(x47391)+P60(f918(x47391)) % 177.41/177.18 [4740]~P104(x47401)+P104(f916(x47401)) % 177.41/177.18 [4743]~P145(x47431)+~E(f78(x47431),f2(x47431)) % 177.41/177.18 [4745]~E(x47451,f2(a100))+E(f327(a22,x47451),f2(a1)) % 177.41/177.18 [4746]~E(x47461,f2(a1))+E(f82(a1,x47461),f2(a1)) % 177.41/177.18 [4752]~P146(x47521)+P26(x47521,f2(x47521)) % 177.41/177.18 [4754]~P108(x47541)+P11(x47541,f114(x47541)) % 177.41/177.18 [4763]P1(x47631)+P1(f327(a322,x47631)) % 177.41/177.18 [4817]~P146(x48171)+~P26(x48171,f78(x48171)) % 177.41/177.18 [4858]~P1(x48581)+~P1(f327(a322,x48581)) % 177.41/177.18 [4879]E(f327(a106,x48791),f2(a915))+~P1(f327(a195,x48791)) % 177.41/177.18 [4945]~P95(x49451)+P12(x49451,x49451,f81(x49451)) % 177.41/177.18 [4946]~P108(x49461)+P12(x49461,x49461,f238(x49461)) % 177.41/177.18 [4947]~P108(x49471)+P12(x49471,x49471,f189(x49471)) % 177.41/177.18 [4948]~P101(x49481)+P12(x49481,x49481,f102(x49481)) % 177.41/177.18 [4949]~P102(x49491)+P12(x49491,x49491,f103(x49491)) % 177.41/177.18 [4950]~P72(x49501)+P14(x49501,x49501,f81(x49501)) % 177.41/177.18 [4749]~E(x47491,f2(a915))+E(f327(f101(a1),x47491),f2(a1)) % 177.41/177.18 [4756]~P93(x47561)+E(f327(f105(x47561),a83),f2(x47561)) % 177.41/177.18 [4759]~E(f573(x47591),f2(a915))+E(f327(f166(a915),x47591),f2(a915)) % 177.41/177.18 [4760]~P109(x47601)+E(f236(x47601,f234(x47601)),f238(x47601)) % 177.41/177.18 [4761]~P109(x47611)+E(f237(x47611,f234(x47611)),f189(x47611)) % 177.41/177.18 [4762]~P89(x47621)+E(f82(x47621,f2(x47621)),f2(x47621)) % 177.41/177.18 [4771]~P146(x47711)+E(f327(f101(x47711),f78(a915)),f78(x47711)) % 177.41/177.18 [4772]~P146(x47721)+E(f327(f101(x47721),f2(a915)),f2(x47721)) % 177.41/177.18 [4773]~P142(x47731)+E(f327(f104(x47731),f78(a1)),f78(x47731)) % 177.41/177.18 [4774]~P142(x47741)+E(f327(f104(x47741),f2(a1)),f2(x47741)) % 177.41/177.18 [4775]E(x47751,f2(a915))+~E(f327(f101(a1),x47751),f2(a1)) % 177.41/177.18 [4811]~P86(x48111)+E(f327(f79(x48111),f190(x48111)),f242(x48111)) % 177.41/177.18 [4812]~P86(x48121)+E(f327(f79(x48121),f242(x48121)),f190(x48121)) % 177.41/177.18 [4813]~P74(x48131)+E(f327(f79(x48131),f2(x48131)),f2(x48131)) % 177.41/177.18 [4814]~P119(x48141)+E(f327(f75(x48141),f78(x48141)),f78(x48141)) % 177.41/177.18 [4815]~P84(x48151)+E(f327(f75(x48151),f2(x48151)),f2(x48151)) % 177.41/177.18 [4816]~P81(x48161)+E(f327(f166(x48161),f114(x48161)),f2(x48161)) % 177.41/177.18 [4834]~P34(x48341)+P38(f327(f173(a1),x48341)) % 177.41/177.18 [4863]~P93(x48631)+E(f327(f79(x48631),f78(x48631)),f327(f105(x48631),a98)) % 177.41/177.18 [4878]~P93(x48781)+P26(x48781,f327(f105(x48781),a83)) % 177.41/177.18 [4904]P34(x49041)+~P38(f327(f173(a1),x49041)) % 177.41/177.18 [4951]E(f327(f101(a1),f327(a106,x49511)),x49511)+P1(f327(a195,x49511)) % 177.41/177.18 [5021]~P116(x50211)+E(f245(x50211,f78(x50211),f81(x50211)),f244(x50211)) % 177.41/177.18 [5054]~P93(x50541)+~P26(x50541,f327(f105(x50541),a98)) % 177.41/177.18 [5202]E(f327(f75(a1),x52021),x52021)+P1(f327(f327(f235(a1),x52021),f2(a1))) % 177.41/177.18 [5220]~E(f327(a106,x52201),f2(a915))+P1(f327(f327(f234(a1),x52201),f2(a1))) % 177.41/177.18 [5285]~P1(f327(a195,x52851))+P1(f327(f327(f235(a1),x52851),f2(a1))) % 177.41/177.18 [5325]~P142(x53251)+P1(f327(f327(f329(x53251),f78(x53251)),f111(x53251))) % 177.41/177.18 [5326]~P146(x53261)+P1(f327(f327(f329(x53261),f78(x53261)),f187(x53261))) % 177.41/177.18 [5327]~P142(x53271)+P1(f327(f327(f329(x53271),f2(x53271)),f111(x53271))) % 177.41/177.18 [5328]~P146(x53281)+P1(f327(f327(f329(x53281),f2(x53281)),f187(x53281))) % 177.41/177.18 [5329]~P126(x53291)+P1(f327(f327(f234(x53291),f2(x53291)),f78(x53291))) % 177.41/177.18 [5330]~P126(x53301)+P1(f327(f327(f235(x53301),f2(x53301)),f78(x53301))) % 177.41/177.18 [5382]E(x53821,f2(a915))+~P1(f327(f327(f234(a915),x53821),f2(a915))) % 177.41/177.18 [5424]E(f327(a106,x54241),f2(a915))+~P1(f327(f327(f234(a1),x54241),f2(a1))) % 177.41/177.18 [5486]P1(f327(a195,x54861))+~P1(f327(f327(f235(a1),x54861),f2(a1))) % 177.41/177.18 [5493]~P108(x54931)+P14(x54931,f916(x54931),f149(x54931,x54931,f5(x54931))) % 177.41/177.18 [5511]P38(x55111)+~P1(f327(f327(f234(a1),f2(a1)),f335(x55111))) % 177.41/177.18 [5516]E(f327(f75(a1),x55161),f327(f79(a1),x55161))+~P1(f327(f327(f235(a1),x55161),f2(a1))) % 177.41/177.18 [5689]~P126(x56891)+~P1(f327(f327(f234(x56891),f78(x56891)),f2(x56891))) % 177.41/177.18 [5690]~P126(x56901)+~P1(f327(f327(f235(x56901),f78(x56901)),f2(x56901))) % 177.41/177.18 [5706]~E(x57061,f2(a915))+P1(f327(f327(f234(a1),f327(f101(a1),x57061)),f2(a1))) % 177.41/177.18 [5707]~E(x57071,f2(a1))+P1(f327(f327(f235(a1),f327(f75(a1),x57071)),f78(a1))) % 177.41/177.18 [5829]~P81(x58291)+E(f143(x58291,x58291,f80(x58291),f2(x58291)),f166(x58291)) % 177.41/177.18 [6003]~P103(x60031)+P23(a915,x60031,f101(x60031),f242(f922(a915,a910))) % 177.41/177.18 [6208]E(x62081,f2(a915))+~P1(f327(f327(f234(a1),f327(f101(a1),x62081)),f2(a1))) % 177.41/177.18 [6209]E(x62091,f2(a1))+~P1(f327(f327(f235(a1),f327(f75(a1),x62091)),f78(a1))) % 177.41/177.18 [7016]~P1(f327(f327(f235(a1),x70161),f2(a1)))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x70161),x70161)),f2(a1))) % 177.41/177.18 [7574]P1(f327(f327(f235(a1),x75741),f2(a1)))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),x75741),x75741)),f2(a1))) % 177.41/177.18 [8121]E(x81211,f327(a3,f2(a915)))+P1(f327(f327(f235(a915),f327(f327(f23(a915),f327(a20,x81211)),f327(a113,f2(a915)))),f327(a20,x81211))) % 177.41/177.18 [8885]~P1(f327(f327(f235(a1),x88851),f2(a1)))+P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x88851),x88851)),a98)),f2(a1))) % 177.41/177.18 [8982]~P1(f327(f327(f235(a1),x89821),f2(a1)))+P1(f327(f327(f235(a1),f327(f327(f80(a1),f327(f327(f80(a1),f78(a1)),x89821)),x89821)),f2(a1))) % 177.41/177.18 [9304]P1(f327(f327(f235(a1),x93041),f2(a1)))+~P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x93041),x93041)),a98)),f2(a1))) % 177.41/177.18 [9365]P1(f327(f327(f235(a1),x93651),f2(a1)))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),f327(f327(f80(a1),f78(a1)),x93651)),x93651)),f2(a1))) % 177.41/177.18 [4852]~E(a83,x48521)+E(f327(f327(f80(a1),x48521),x48521),a83) % 177.41/177.18 [4853]~E(x48531,a83)+E(f327(f327(f80(a1),x48531),x48531),a83) % 177.41/177.18 [4864]E(x48641,f2(a1))+E(f327(f327(f37(a1),x48641),x48641),f78(a1)) % 177.41/177.18 [4998]E(x49981,a83)+~E(f327(f327(f80(a1),x49981),x49981),a83) % 177.41/177.18 [4999]E(a83,x49991)+~E(f327(f327(f80(a1),x49991),x49991),a83) % 177.41/177.18 [5011]~P3(x50111)+E(f39(x50111,f190(f922(x50111,a910))),f242(x50111)) % 177.41/177.18 [5012]~P3(x50121)+E(f39(x50121,f242(f922(x50121,a910))),f190(x50121)) % 177.41/177.18 [5013]~P3(x50131)+E(f38(x50131,f190(f922(x50131,a910))),f190(x50131)) % 177.41/177.18 [5014]~P3(x50141)+E(f38(x50141,f242(f922(x50141,a910))),f242(x50141)) % 177.41/177.18 [5015]~P108(x50151)+E(f140(x50151,f190(f922(x50151,a910))),f114(x50151)) % 177.41/177.18 [5157]E(x51571,f2(a915))+P1(f327(f327(f235(a915),f2(a915)),x51571)) % 177.41/177.18 [5177]~P4(x51771)+P1(f327(f327(f234(a1),f2(a1)),x51771)) % 177.41/177.18 [5211]~E(f327(f105(a915),x52111),f2(a915))+P1(f327(f327(f234(a1),x52111),a83)) % 177.41/177.18 [5216]P38(x52161)+P1(f327(f327(f329(a1),f335(x52161)),x52161)) % 177.41/177.18 [5217]E(x52171,f327(a3,f2(a915)))+P1(f327(f327(f234(a100),f78(a100)),x52171)) % 177.41/177.18 [5258]P1(f327(a195,x52581))+P1(f327(f327(f234(a1),f2(a1)),x52581)) % 177.41/177.18 [5307]E(f327(f101(a1),f327(a106,x53071)),f2(a1))+P1(f327(f327(f234(a1),f2(a1)),x53071)) % 177.41/177.18 [5364]E(f327(f101(a1),f327(f105(a915),x53641)),f327(f105(a1),x53641))+P1(f327(a195,f327(f105(a1),x53641))) % 177.41/177.18 [5388]E(f327(f105(a915),x53881),f2(a915))+~P1(f327(a195,f327(f105(a1),x53881))) % 177.41/177.18 [5389]E(f327(f105(a915),x53891),f2(a915))+~P1(f327(f327(f234(a1),x53891),a83)) % 177.41/177.18 [5421]P4(x54211)+~P1(f327(f327(f234(a1),f2(a1)),x54211)) % 177.41/177.18 [5462]~E(x54621,f327(a113,f2(a915)))+P1(f327(f327(f287(a915),x54621),f327(a113,f2(a915)))) % 177.41/177.18 [5496]E(f327(a113,f337(x54961)),x54961)+~P1(f327(f327(f235(a915),f2(a915)),x54961)) % 177.41/177.18 [5505]E(f327(a113,f327(f105(a915),x55051)),f78(a915))+~P1(f327(a195,f327(f105(a1),x55051))) % 177.41/177.18 [5512]E(f327(f101(a1),f448(x55121)),x55121)+~P1(f327(f327(f235(a1),f2(a1)),x55121)) % 177.41/177.18 [5519]~E(x55191,f327(a3,f2(a915)))+~P1(f327(f327(f234(a100),f78(a100)),x55191)) % 177.41/177.18 [5526]E(f327(f101(a1),f327(f105(a915),x55261)),f2(a1))+~P1(f327(a195,f327(f105(a1),x55261))) % 177.41/177.18 [5552]E(f327(f166(a915),x55521),f2(a915))+P1(f327(f327(f329(a915),f573(x55521)),f327(f173(a915),x55521))) % 177.41/177.18 [5573]E(f327(f101(a1),f327(a106,x55731)),x55731)+~P1(f327(f327(f234(a1),f2(a1)),x55731)) % 177.41/177.18 [5581]~P1(f327(a195,x55811))+~P1(f327(f327(f234(a1),f2(a1)),x55811)) % 177.41/177.18 [5682]E(f327(f327(f80(a915),f78(a915)),f327(f105(a915),x56821)),f78(a915))+~P1(f327(f327(f235(a1),x56821),a83)) % 177.41/177.18 [5748]E(x57481,f2(a915))+~P1(f327(f327(f235(a915),x57481),f327(a113,f2(a915)))) % 177.41/177.18 [5770]E(x57701,f327(a113,f2(a915)))+~P1(f327(f327(f287(a915),x57701),f327(a113,f2(a915)))) % 177.41/177.18 [5788]E(f327(f327(f23(a915),f327(f105(a915),x57881)),f78(a915)),f2(a915))+~P1(f327(f327(f234(a1),x57881),a83)) % 177.41/177.18 [5789]E(f327(f327(f80(a915),f327(f105(a915),x57891)),f78(a915)),f78(a915))+~P1(f327(f327(f235(a1),x57891),a83)) % 177.41/177.18 [5801]~P38(x58011)+E(f327(f36(a915),f327(f310(a1,a915,a106),x58011)),f327(f36(a1),x58011)) % 177.41/177.18 [5830]~P108(x58301)+E(f236(x58301,f327(f7(x58301,x58301,a910),f234(x58301))),f189(x58301)) % 177.41/177.18 [5831]~P108(x58311)+E(f237(x58311,f327(f7(x58311,x58311,a910),f234(x58311))),f238(x58311)) % 177.41/177.18 [5841]E(f46(a915,f327(a113,f2(a915)),f327(f105(a915),x58411)),f327(a113,f2(a915)))+~P1(f327(a195,f327(f105(a1),x58411))) % 177.41/177.18 [5850]~P1(f327(f327(f235(a1),f2(a1)),x58501))+P1(f327(f327(f234(a1),f78(a1)),x58501)) % 177.41/177.18 [5851]P1(f327(f327(f235(a1),f2(a1)),x58511))+~P1(f327(f327(f234(a1),f78(a1)),x58511)) % 177.41/177.18 [5862]E(f327(a113,f327(f327(f23(a915),x58621),f78(a915))),x58621)+~P1(f327(f327(f235(a915),f2(a915)),x58621)) % 177.41/177.18 [5918]P1(f327(f327(f235(a915),f2(a915)),f448(x59181)))+~P1(f327(f327(f235(a1),f2(a1)),x59181)) % 177.41/177.18 [5979]E(f46(a1,f327(f105(a1),a98),x59791),f327(f327(f23(a1),x59791),f78(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x59791)) % 177.41/177.18 [6016]~P1(f327(f327(f235(a1),a83),x60161))+P1(f327(f327(f235(a915),f2(a915)),f327(f105(a915),x60161))) % 177.41/177.18 [6021]E(f327(a20,f804(x60211)),x60211)+~P1(f327(f327(f329(a915),x60211),f242(f922(a915,a910)))) % 177.41/177.18 [6074]P1(f327(f327(f235(a915),f2(a915)),f327(a106,x60741)))+~P1(f327(f327(f235(a1),f2(a1)),x60741)) % 177.41/177.18 [6124]~P1(f327(f327(f235(a915),f2(a915)),x61241))+P1(f327(f327(f235(a1),f2(a1)),f327(f101(a1),x61241))) % 177.41/177.18 [6160]~P1(f327(f327(f235(a915),f2(a915)),f327(a106,x61601)))+P1(f327(f327(f235(a1),f2(a1)),x61601)) % 177.41/177.18 [6175]~P38(x61751)+E(f327(f310(a915,a1,f101(a1)),f327(f310(a1,a915,a106),x61751)),x61751) % 177.41/177.18 [6188]P1(f327(f327(f235(a1),a83),x61881))+~P1(f327(f327(f235(a915),f2(a915)),f327(f105(a915),x61881))) % 177.41/177.18 [6249]P1(f327(f327(f235(a915),f2(a915)),x62491))+~P1(f327(f327(f235(a1),f2(a1)),f327(f101(a1),x62491))) % 177.41/177.18 [6366]E(f327(f310(a915,a1,f101(a1)),f327(f282(a915),f327(a106,x63661))),f327(f302(a1,f2(a1)),x63661))+~P1(f327(f327(f234(a1),f2(a1)),x63661)) % 177.41/177.18 [6383]~P126(x63831)+P1(f327(f327(f235(x63831),f2(x63831)),f327(f327(f80(x63831),f78(x63831)),f78(x63831)))) % 177.41/177.18 [6432]P1(f327(f327(f235(a915),f327(a113,f2(a915))),f327(a106,x64321)))+~P1(f327(f327(f235(a1),f78(a1)),x64321)) % 177.41/177.18 [6532]E(x65321,f2(a1))+P1(f327(f50(f2(a1),x65321),f327(f327(f252(a1,a1),f2(a1)),f2(a1)))) % 177.41/177.18 [6700]~P1(f327(f327(f235(a915),f327(a113,f2(a915))),f327(a106,x67001)))+P1(f327(f327(f235(a1),f78(a1)),x67001)) % 177.41/177.18 [7129]~P117(x71291)+P35(x71291,f327(f262(f921(x71291,x71291)),f327(f257(x71291,x71291,a910),f235(x71291)))) % 177.41/177.18 [5735]E(f327(f105(a915),f327(f327(f23(a1),x57351),a98)),f327(a113,f327(f105(a915),x57351)))+P1(f327(a195,f327(f105(a1),x57351))) % 177.41/177.18 [5751]~P34(x57511)+E(f327(f327(f155(a915,a1),f101(a1)),f327(f327(f155(a1,a915),a106),x57511)),x57511) % 177.41/177.18 [5868]E(f327(f79(a1),f327(f101(a1),f327(a113,f406(x58681)))),x58681)+~P1(f327(f327(f235(a1),x58681),f2(a1))) % 177.41/177.18 [5878]E(f327(f327(f80(a915),f78(a915)),f327(f105(a915),x58781)),f327(f105(a915),f327(f327(f23(a1),x58781),a98)))+P1(f327(f327(f235(a1),x58781),a83)) % 177.41/177.18 [5920]E(f327(f327(f37(a1),f327(f105(a1),a98)),x59201),f327(f105(a1),a98))+~P1(f327(f327(f235(a1),f2(a1)),x59201)) % 177.41/177.18 [6012]E(f327(f327(f23(a915),f327(f105(a915),x60121)),f78(a915)),f327(f105(a915),f327(f327(f80(a1),x60121),a98)))+P1(f327(f327(f234(a1),x60121),a83)) % 177.41/177.18 [6013]E(f327(f327(f80(a915),f327(f105(a915),x60131)),f78(a915)),f327(f105(a915),f327(f327(f23(a1),x60131),a98)))+P1(f327(f327(f235(a1),x60131),a83)) % 177.41/177.18 [6059]E(f327(a106,f327(f327(f80(a1),f78(a1)),x60591)),f327(a113,f327(a106,x60591)))+~P1(f327(f327(f234(a1),f2(a1)),x60591)) % 177.41/177.18 [6095]E(f327(a113,f327(f327(f23(a915),x60951),f327(a113,f2(a915)))),x60951)+~P1(f327(f327(f235(a915),f2(a915)),x60951)) % 177.41/177.18 [6316]E(f46(a915,f327(a113,f2(a915)),f327(f105(a915),x63161)),f327(a106,f46(a1,f78(a1),f327(f105(a1),x63161))))+P1(f327(a195,f327(f105(a1),x63161))) % 177.41/177.18 [6359]~P1(f327(f327(f234(a1),a83),x63591))+P1(f327(f327(f234(a1),a83),f327(f327(f80(a1),x63591),x63591))) % 177.41/177.18 [6360]~P1(f327(f327(f235(a1),a98),x63601))+P1(f327(f327(f234(a1),a98),f327(f327(f80(a1),x63601),x63601))) % 177.41/177.18 [6361]~P1(f327(f327(f235(a1),a83),x63611))+P1(f327(f327(f235(a1),a83),f327(f327(f80(a1),x63611),x63611))) % 177.41/177.18 [6362]~P1(f327(f327(f235(a1),a98),x63621))+P1(f327(f327(f235(a1),a98),f327(f327(f80(a1),x63621),x63621))) % 177.41/177.18 [6546]~P1(f327(f35(x65461),f242(f922(x65461,a910))))+P1(f327(f35(f918(x65461)),f242(f922(f918(x65461),a910)))) % 177.41/177.18 [6630]~P1(f327(f327(f234(a1),f2(a1)),x66301))+P1(f327(f327(f235(a1),f2(a1)),f327(f327(f80(a1),f78(a1)),x66301))) % 177.41/177.18 [6637]E(f327(f251(a1,a1),f48(f78(a1),f327(f105(a1),x66371))),f327(f327(f37(a1),f78(a1)),f327(f105(a1),x66371)))+~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x66371))) % 177.41/177.18 [6659]E(f327(f256(a1,a1),f48(f78(a1),f327(f105(a1),x66591))),f46(a1,f78(a1),f327(f105(a1),x66591)))+~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x66591))) % 177.41/177.18 [6671]P1(f327(f35(x66711),f242(f922(x66711,a910))))+~P1(f327(f35(f918(x66711)),f242(f922(f918(x66711),a910)))) % 177.41/177.18 [6701]P1(f327(f327(f234(a1),a83),x67011))+~P1(f327(f327(f234(a1),a83),f327(f327(f80(a1),x67011),x67011))) % 177.41/177.18 [6702]P1(f327(f327(f235(a1),a83),x67021))+~P1(f327(f327(f235(a1),a83),f327(f327(f80(a1),x67021),x67021))) % 177.41/177.18 [6703]P1(f327(f327(f235(a1),a98),x67031))+~P1(f327(f327(f234(a1),a98),f327(f327(f80(a1),x67031),x67031))) % 177.41/177.18 [6704]P1(f327(f327(f235(a1),a98),x67041))+~P1(f327(f327(f235(a1),a98),f327(f327(f80(a1),x67041),x67041))) % 177.41/177.18 [7020]~P1(f327(f35(x70201),f242(f922(x70201,a910))))+P1(f327(f327(f235(a915),f2(a915)),f327(f36(x70201),f242(f922(x70201,a910))))) % 177.41/177.18 [7613]P1(f327(f35(a915),x76131))+~P1(f327(f35(a1),f327(f310(a915,a1,f101(a1)),x76131))) % 177.41/177.18 [9707]~P22(a909,a924,f327(f327(f309(f913(a909)),f327(f327(f327(f91(a909),f327(a925,x97071)),f327(a928,x97071)),f327(a929,x97071))),f190(f922(f913(a909),a910))))+P22(a909,a924,f327(f327(f309(f913(a909)),f327(f327(f327(f91(a909),f327(a926,x97071)),f327(a928,x97071)),f327(a930,x97071))),f190(f922(f913(a909),a910)))) % 177.41/177.18 [5657]~E(a98,x56571)+E(f327(f327(f23(a1),f327(f327(f80(a1),x56571),x56571)),a98),a98) % 177.41/177.18 [5658]~E(x56581,a98)+E(f327(f327(f23(a1),f327(f327(f80(a1),x56581),x56581)),a98),a98) % 177.41/177.18 [6183]E(x61831,a98)+~E(f327(f327(f23(a1),f327(f327(f80(a1),x61831),x61831)),a98),a98) % 177.41/177.18 [6184]E(a98,x61841)+~E(f327(f327(f23(a1),f327(f327(f80(a1),x61841),x61841)),a98),a98) % 177.41/177.18 [6599]~E(f327(f105(a915),x65991),f2(a915))+P1(f327(a195,f327(f105(a1),f327(f327(f80(a1),x65991),a98)))) % 177.41/177.18 [6950]~P1(f327(a195,f327(f105(a1),x69501)))+P1(f327(a195,f327(f105(a1),f327(f327(f80(a1),x69501),x69501)))) % 177.41/177.18 [6951]~P1(f327(f327(f234(a1),x69511),a83))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x69511),x69511)),a83)) % 177.41/177.18 [6952]~P1(f327(f327(f234(a1),x69521),a98))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x69521),x69521)),a98)) % 177.41/177.18 [6953]~P1(f327(f327(f235(a1),x69531),a83))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x69531),x69531)),a83)) % 177.41/177.18 [6954]~P1(f327(f327(f234(a1),x69541),a98))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x69541),x69541)),a98)) % 177.41/177.18 [7277]E(f327(f105(a915),x72771),f2(a915))+~P1(f327(a195,f327(f105(a1),f327(f327(f80(a1),x72771),a98)))) % 177.41/177.18 [7530]~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x75301)))+P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),f327(f327(f80(a1),x75301),x75301)))) % 177.41/177.18 [7531]P1(f327(a195,f327(f105(a1),x75311)))+~P1(f327(a195,f327(f105(a1),f327(f327(f80(a1),x75311),x75311)))) % 177.41/177.18 [7532]P1(f327(f327(f234(a1),x75321),a83))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),x75321),x75321)),a83)) % 177.41/177.18 [7533]P1(f327(f327(f234(a1),x75331),a98))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),x75331),x75331)),a98)) % 177.41/177.18 [7534]P1(f327(f327(f234(a1),x75341),a98))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),x75341),x75341)),a98)) % 177.41/177.18 [7535]P1(f327(f327(f235(a1),x75351),a83))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),x75351),x75351)),a83)) % 177.41/177.18 [7892]E(f327(a108,f567(x78921)),x78921)+~P1(f327(f327(f329(f922(f921(a915,a915),a910)),x78921),a99)) % 177.41/177.18 [6519]~P93(x65191)+E(f327(f105(x65191),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f78(x65191)) % 177.41/177.18 [7000]~P1(f327(a195,f327(f105(a1),x70001)))+E(f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),x70001),x70001)),a98)),f2(a915)) % 177.41/177.18 [8066]~P1(f327(f327(f235(a1),f327(f105(a1),x80661)),f2(a1)))+E(f327(f251(a1,a1),f327(a52,f51(f327(f79(a1),f78(a1)),f327(f79(a1),f327(f105(a1),x80661))))),f327(f327(f37(a1),f78(a1)),f327(f105(a1),x80661))) % 177.41/177.18 [8079]~P1(f327(f327(f235(a1),f327(f105(a1),x80791)),f2(a1)))+E(f327(f256(a1,a1),f327(a52,f51(f327(f79(a1),f78(a1)),f327(f79(a1),f327(f105(a1),x80791))))),f46(a1,f78(a1),f327(f105(a1),x80791))) % 177.41/177.18 [8128]~P1(f327(f327(f234(a1),a83),x81281))+P1(f327(f327(f234(a1),a83),f327(f327(f23(a1),f327(f327(f80(a1),x81281),x81281)),a98))) % 177.41/177.18 [8129]~P1(f327(f327(f234(a1),a98),x81291))+P1(f327(f327(f234(a1),a98),f327(f327(f23(a1),f327(f327(f80(a1),x81291),x81291)),a98))) % 177.41/177.18 [8130]~P1(f327(f327(f234(a1),a83),x81301))+P1(f327(f327(f235(a1),a83),f327(f327(f23(a1),f327(f327(f80(a1),x81301),x81301)),a98))) % 177.41/177.18 [8131]~P1(f327(f327(f235(a1),a98),x81311))+P1(f327(f327(f235(a1),a98),f327(f327(f23(a1),f327(f327(f80(a1),x81311),x81311)),a98))) % 177.41/177.18 [8428]~P93(x84281)+~P26(x84281,f327(f105(x84281),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))) % 177.41/177.18 [8610]P1(f327(f327(f234(a1),a83),x86101))+~P1(f327(f327(f234(a1),a83),f327(f327(f23(a1),f327(f327(f80(a1),x86101),x86101)),a98))) % 177.41/177.18 [8611]P1(f327(f327(f234(a1),a83),x86111))+~P1(f327(f327(f235(a1),a83),f327(f327(f23(a1),f327(f327(f80(a1),x86111),x86111)),a98))) % 177.41/177.18 [8612]P1(f327(f327(f234(a1),a98),x86121))+~P1(f327(f327(f234(a1),a98),f327(f327(f23(a1),f327(f327(f80(a1),x86121),x86121)),a98))) % 177.41/177.18 [8613]P1(f327(f327(f235(a1),a98),x86131))+~P1(f327(f327(f235(a1),a98),f327(f327(f23(a1),f327(f327(f80(a1),x86131),x86131)),a98))) % 177.41/177.18 [8932]E(f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),x89321),x89321)),a98)),f327(f327(f86(a915,a915),f327(f105(a915),x89321)),f327(f327(f8(a915,a915,a915),a113),f327(f327(f18(a915,a915,a915),f80(a915)),f5(a915)))))+P1(f327(a195,f327(f105(a1),x89321))) % 177.41/177.18 [9790]E(x97901,f190(f922(f921(a915,a915),a910)))+P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x97901),f190(f922(f921(a915,a915),a910)))),a33)) % 177.41/177.18 [8859]~P1(f327(a195,f327(f105(a1),x88591)))+P1(f327(a195,f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),x88591),x88591)),a98)))) % 177.41/177.18 [8860]~P1(f327(f327(f235(a1),x88601),a83))+P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x88601),x88601)),a98)),a83)) % 177.41/177.18 [8861]~P1(f327(f327(f234(a1),x88611),a98))+P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x88611),x88611)),a98)),a98)) % 177.41/177.18 [8862]~P1(f327(f327(f235(a1),x88621),a83))+P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x88621),x88621)),a98)),a83)) % 177.41/177.18 [8863]~P1(f327(f327(f235(a1),x88631),a98))+P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x88631),x88631)),a98)),a98)) % 177.41/177.18 [8973]~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x89731)))+P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),x89731),x89731)),a98)))) % 177.41/177.18 [9135]~P93(x91351)+E(f327(f327(f80(x91351),f78(x91351)),f78(x91351)),f327(f105(x91351),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))) % 177.41/177.18 [9288]P1(f327(a195,f327(f105(a1),x92881)))+~P1(f327(a195,f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92881),x92881)),a98)))) % 177.41/177.18 [9289]P1(f327(f327(f234(a1),x92891),a98))+~P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92891),x92891)),a98)),a98)) % 177.41/177.18 [9290]P1(f327(f327(f235(a1),x92901),a83))+~P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92901),x92901)),a98)),a83)) % 177.41/177.18 [9291]P1(f327(f327(f235(a1),x92911),a83))+~P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92911),x92911)),a98)),a83)) % 177.41/177.18 [9292]P1(f327(f327(f235(a1),x92921),a98))+~P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92921),x92921)),a98)),a98)) % 177.41/177.18 [9835]~P1(f327(f35(f921(a915,a915)),x98351))+P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),f190(f922(f921(a915,a915),a910))),x98351)),a69)) % 177.41/177.18 [9618]~P146(x96181)+E(f327(f327(f244(x96181),f78(x96181)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f78(x96181)) % 177.41/177.18 [9619]~P146(x96191)+E(f327(f327(f244(x96191),f2(x96191)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f2(x96191)) % 177.41/177.18 [10060]~P1(f327(f327(f235(a915),f78(a915)),x100601))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f37(a915),x100601),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.18 [10066]~P1(f327(f327(f235(a915),f2(a915)),x100661))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f37(a915),f327(f327(f80(a915),x100661),f78(a915))),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.18 [10105]~E(f46(a915,x101051,f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f78(a915))+P1(f327(f327(f235(a915),f2(a915)),f46(a915,x101051,f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.18 [10135]E(f46(a915,x101351,f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f78(a915))+~P1(f327(f327(f235(a915),f2(a915)),f46(a915,x101351,f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.18 [4780]~P5(x47801,x47802)+P41(x47801,x47802) % 177.41/177.18 [4781]~P35(x47811,x47812)+P55(x47811,x47812) % 177.41/177.18 [4782]~P42(x47821,x47822)+P55(x47821,x47822) % 177.41/177.18 [4784]~P5(x47841,x47842)+P47(x47841,x47842) % 177.41/177.18 [4786]~P13(x47861,x47862)+P47(x47861,x47862) % 177.41/177.18 [4788]~P5(x47881,x47882)+P48(x47881,x47882) % 177.41/177.18 [4790]~P13(x47901,x47902)+P48(x47901,x47902) % 177.41/177.18 [4791]~P5(x47911,x47912)+P13(x47911,x47912) % 177.41/177.18 [4741]~E(x47411,x47412)+E(f269(x47411,x47412),f78(a100)) % 177.41/177.18 [4744]E(f218(x47441,x47442),x47441)+~E(x47442,f2(a915)) % 177.41/177.18 [4751]~E(x47512,f114(x47511))+E(f153(x47511,x47512),f114(x47511)) % 177.41/177.18 [4770]~E(f153(x47702,x47701),f114(x47702))+E(x47701,f114(x47702)) % 177.41/177.18 [4795]~P65(x47952)+P65(f922(x47951,x47952)) % 177.41/177.18 [4796]~P66(x47962)+P66(f922(x47961,x47962)) % 177.41/177.18 [4797]~P107(x47972)+P107(f922(x47971,x47972)) % 177.41/177.18 [4798]~P109(x47982)+P109(f922(x47981,x47982)) % 177.41/177.18 [4799]~P110(x47992)+P110(f922(x47991,x47992)) % 177.41/177.18 [4800]~P86(x48002)+P86(f922(x48001,x48002)) % 177.41/177.18 [4801]~P87(x48012)+P87(f922(x48011,x48012)) % 177.41/177.18 [4802]~P96(x48022)+P96(f922(x48021,x48022)) % 177.41/177.18 [4803]~P115(x48032)+P115(f922(x48031,x48032)) % 177.41/177.18 [4804]~P99(x48042)+P97(f922(x48041,x48042)) % 177.41/177.18 [4805]~P96(x48052)+P101(f922(x48051,x48052)) % 177.41/177.18 [4806]~P99(x48062)+P98(f922(x48061,x48062)) % 177.41/177.18 [4807]~P3(x48072)+P3(f922(x48071,x48072)) % 177.41/177.18 [4808]~P96(x48082)+P102(f922(x48081,x48082)) % 177.41/177.18 [4809]~P100(x48092)+P100(f922(x48091,x48092)) % 177.41/177.18 [4810]~P99(x48102)+P99(f922(x48101,x48102)) % 177.41/177.18 [4823]E(x48231,x48232)+~E(f327(a113,x48231),f327(a113,x48232)) % 177.41/177.18 [4824]E(x48241,x48242)+~E(f327(a108,x48241),f327(a108,x48242)) % 177.41/177.18 [4825]E(x48251,x48252)+~E(f327(a3,x48251),f327(a3,x48252)) % 177.41/177.18 [4827]E(x48271,x48272)+~E(f327(a20,x48271),f327(a20,x48272)) % 177.41/177.18 [4880]P37(x48801,x48802)+~E(f701(x48802,x48801),f702(x48802,x48801)) % 177.41/177.18 [4910]~P55(x49101,x49102)+P37(x49101,f307(x49101,x49102)) % 177.41/177.18 [4911]~P49(x49111,x49112)+P49(x49111,f307(x49111,x49112)) % 177.41/177.18 [4924]~P58(x49241)+E(f46(x49241,x49242,x49242),f2(x49241)) % 177.41/177.18 [4958]~P35(x49581,x49582)+P35(f916(x49581),f147(x49581,x49582)) % 177.41/177.18 [4959]~P35(x49591,x49592)+P35(f916(x49591),f146(x49591,x49592)) % 177.41/177.18 [4960]~P36(x49601,x49602)+P36(f916(x49601),f148(x49601,x49602)) % 177.41/177.18 [4961]~P36(x49611,x49612)+P36(f916(x49611),f159(x49611,x49612)) % 177.41/177.18 [4962]~P49(x49621,x49622)+P49(f916(x49621),f159(x49621,x49622)) % 177.41/177.18 [5059]~P35(x50591,x50592)+P35(f922(x50591,a910),f318(x50591,x50592)) % 177.41/177.18 [5060]~P35(x50601,x50602)+P35(f922(x50601,a910),f319(x50601,x50602)) % 177.41/177.18 [5186]~P4(x51861)+P38(f303(a1,x51861,x51862)) % 177.41/177.18 [5288]~P35(x52881,x52882)+P57(x52881,f67(x52881,x52881,x52882)) % 177.41/177.18 [5795]~P78(x57951)+P23(x57951,x57951,f79(x57951),x57952) % 177.41/177.18 [4765]~E(x47652,f114(x47651))+E(f327(f168(x47651),x47652),f114(x47651)) % 177.41/177.18 [4766]~E(x47662,f114(x47661))+E(f327(f169(x47661),x47662),f114(x47661)) % 177.41/177.18 [4829]E(x48291,f327(a106,x48292))+~E(f327(f101(a1),x48291),x48292) % 177.41/177.18 [4832]E(x48321,f114(x48322))+~E(f327(f168(x48322),x48321),f114(x48322)) % 177.41/177.18 [4833]E(x48331,f114(x48332))+~E(f327(f169(x48332),x48331),f114(x48332)) % 177.41/177.18 [4849]~P93(x48491)+E(f327(f105(x48491),x48492),f327(f104(x48491),x48492)) % 177.41/177.18 [4857]~P2(x48571)+P1(f327(f35(x48571),x48572)) % 177.41/177.18 [4865]~E(f660(x48652,x48651),f114(x48651))+E(f180(x48651,x48652),f114(f916(x48651))) % 177.41/177.18 [4874]~E(x48742,f114(x48741))+E(f327(f173(x48741),x48742),f190(f922(x48741,a910))) % 177.41/177.18 [4875]~E(x48752,f114(x48751))+E(f190(f922(x48751,a910)),f327(f173(x48751),x48752)) % 177.41/177.18 [4877]E(x48771,x48772)+~E(f327(f101(a1),x48771),f327(f101(a1),x48772)) % 177.41/177.18 [4881]E(f216(x48811,x48812),f2(a915))+P1(f327(f35(x48811),x48812)) % 177.41/177.18 [4899]~P119(x48991)+E(f82(x48991,f82(x48991,x48992)),f82(x48991,x48992)) % 177.41/177.18 [4913]~P112(x49131)+E(f327(f327(f244(x49131),x49132),f78(a915)),x49132) % 177.41/177.18 [4914]~P80(x49141)+E(f327(f327(f244(x49141),x49142),f78(a915)),x49142) % 177.41/177.18 [4915]~P49(x49151,x49152)+E(f327(f286(x49151,x49151),x49152),x49152) % 177.41/177.18 [4919]E(x49191,x49192)+E(f269(x49191,x49192),f327(f327(f80(a100),x49192),f78(a100))) % 177.41/177.18 [4922]E(f327(f36(x49221),x49222),f2(a915))+P1(f327(f35(x49221),x49222)) % 177.41/177.18 [4925]~E(f153(x49251,x49252),x49252)+P1(f327(f138(x49251),x49252)) % 177.41/177.18 [4928]~P74(x49281)+E(f327(f327(f23(x49281),x49282),f2(x49281)),x49282) % 177.41/177.18 [4929]~P68(x49291)+E(f327(f327(f80(x49291),x49292),f2(x49291)),x49292) % 177.41/177.18 [4930]~P112(x49301)+E(f327(f327(f80(x49301),x49302),f2(x49301)),x49302) % 177.41/177.18 [4931]~P81(x49311)+E(f327(f327(f80(x49311),x49312),f2(x49311)),x49312) % 177.41/177.18 [4932]~P112(x49321)+E(f327(f327(f81(x49321),x49322),f78(x49321)),x49322) % 177.41/177.18 [4933]~P75(x49331)+E(f327(f327(f81(x49331),x49332),f78(x49331)),x49332) % 177.41/177.18 [4934]~P80(x49341)+E(f327(f327(f81(x49341),x49342),f78(x49341)),x49342) % 177.41/177.18 [4935]~P98(x49351)+E(f327(f327(f102(x49351),x49352),f190(x49351)),x49352) % 177.41/177.18 [4936]~P97(x49361)+E(f327(f327(f103(x49361),x49362),f242(x49361)),x49362) % 177.41/177.18 [4937]~P58(x49371)+E(f327(f327(f37(x49371),x49372),f78(x49371)),x49372) % 177.41/177.18 [4938]~P122(x49381)+E(f327(f327(f291(x49381),x49382),f78(x49381)),x49382) % 177.41/177.18 [4939]~P112(x49391)+E(f327(f327(f244(x49391),x49392),f2(a915)),f78(x49391)) % 177.41/177.18 [4940]~P116(x49401)+E(f327(f327(f244(x49401),x49402),f2(a915)),f78(x49401)) % 177.41/177.18 [4941]~E(x49412,f190(f922(x49411,a910)))+E(f327(f36(x49411),x49412),f2(a915)) % 177.41/177.18 [4952]~P58(x49521)+E(f46(x49521,x49522,f2(x49521)),x49522) % 177.41/177.18 [4963]~P112(x49631)+E(f327(f327(f81(x49631),x49632),f2(x49631)),f2(x49631)) % 177.41/177.18 [4964]~P129(x49641)+E(f327(f327(f81(x49641),x49642),f2(x49641)),f2(x49641)) % 177.41/177.18 [4965]~P97(x49651)+E(f327(f327(f102(x49651),x49652),f242(x49651)),f242(x49651)) % 177.41/177.18 [4966]~P98(x49661)+E(f327(f327(f103(x49661),x49662),f190(x49661)),f190(x49661)) % 177.41/177.18 [4967]~P58(x49671)+E(f327(f327(f37(x49671),x49672),f2(x49671)),f2(x49671)) % 177.41/177.18 [4968]~P123(x49681)+E(f327(f327(f291(x49681),x49682),f2(x49681)),f2(x49681)) % 177.41/177.18 [4970]~P58(x49701)+E(f46(x49701,x49702,f78(x49701)),f2(x49701)) % 177.41/177.18 [4971]~P58(x49711)+E(f46(x49711,f2(x49711),x49712),f2(x49711)) % 177.41/177.18 [5000]E(x50001,f2(a915))+E(f56(x50002,x50001,f114(x50002)),f114(f916(x50002))) % 177.41/177.18 [5023]P49(x50231,x50232)+~E(f327(f286(x50231,x50231),x50232),x50232) % 177.41/177.18 [5024]P35(x50241,x50242)+~E(f574(x50242,x50241),f190(f922(x50241,a910))) % 177.41/177.18 [5025]E(x50251,f114(x50252))+~E(f327(f173(x50252),x50251),f190(f922(x50252,a910))) % 177.41/177.18 [5026]E(x50261,f114(x50262))+~E(f190(f922(x50262,a910)),f327(f173(x50262),x50261)) % 177.41/177.18 [5029]~E(x50291,x50292)+P1(f327(f327(a324,x50291),x50292)) % 177.41/177.18 [5039]P1(x50391)+P1(f327(f327(a330,x50391),x50392)) % 177.41/177.18 [5040]E(x50401,f114(x50402))+E(f327(f327(f165(x50402),x50401),f2(a915)),f327(f142(x50402),x50401)) % 177.41/177.18 [5043]E(f153(x50431,x50432),x50432)+~P1(f327(f138(x50431),x50432)) % 177.41/177.18 [5050]~P1(x50502)+P1(f327(f327(a326,x50501),x50502)) % 177.41/177.18 [5051]~P1(x50511)+P1(f327(f327(a326,x50511),x50512)) % 177.41/177.18 [5052]~P1(x50522)+P1(f327(f327(a330,x50521),x50522)) % 177.41/177.18 [5062]~E(f661(x50622,x50621),f667(x50622,x50621))+P1(f327(f138(x50621),x50622)) % 177.41/177.18 [5069]E(f327(f262(x50691),x50692),f190(f922(x50691,a910)))+P1(f327(x50692,f333(x50692))) % 177.41/177.18 [5070]E(f190(f922(x50701,a910)),f327(f262(x50701),x50702))+P1(f327(x50702,f334(x50702))) % 177.41/177.18 [5139]~P119(x51391)+E(f327(f327(f81(x51391),x51392),f82(x51391,x51392)),f327(f75(x51391),x51392)) % 177.41/177.18 [5150]~E(x51501,f2(a1))+E(f47(x51501,x51502),f327(f327(f252(a1,a1),f2(a1)),f2(a1))) % 177.41/177.18 [5182]~P55(x51821,x51822)+P55(x51821,f327(f286(x51821,x51821),x51822)) % 177.41/177.18 [5183]~P36(x51831,x51832)+P36(x51831,f327(f286(x51831,x51831),x51832)) % 177.41/177.18 [5184]~P37(x51841,x51842)+P37(x51841,f327(f286(x51841,x51841),x51842)) % 177.41/177.18 [5185]~P49(x51851,x51852)+P49(x51851,f327(f286(x51851,x51851),x51852)) % 177.41/177.18 [5207]E(x52071,x52072)+~P1(f327(f327(a324,x52071),x52072)) % 177.41/177.18 [5218]P1(x52181)+~P1(f327(f327(a325,x52182),x52181)) % 177.41/177.18 [5219]P1(x52191)+~P1(f327(f327(a325,x52191),x52192)) % 177.41/177.18 [5224]~P115(x52241)+P1(f327(f327(f234(x52241),x52242),f242(x52241))) % 177.41/177.18 [5225]~P112(x52251)+P1(f327(f327(f287(x52251),x52252),f2(x52251))) % 177.41/177.18 [5229]E(x52291,x52292)+~E(f327(x52291,f405(x52292,x52291)),f327(x52292,f405(x52292,x52291))) % 177.41/177.18 [5260]E(x52601,f2(a915))+E(f218(x52601,f46(a915,x52602,x52601)),f218(x52602,x52601)) % 177.41/177.18 [5265]~P108(x52651)+P11(x52651,f327(f327(f152(x52651),x52652),f114(x52651))) % 177.41/177.18 [5267]E(x52671,f2(a1))+P1(f327(f50(x52672,x52671),f47(x52672,x52671))) % 177.41/177.18 [5283]~P13(x52832,x52831)+P1(f327(f327(x52831,f796(x52831)),f796(x52831))) % 177.41/177.18 [5286]~E(x52861,x52862)+P1(f327(f327(f235(a915),x52861),f327(a113,x52862))) % 177.41/177.18 [5296]~E(x52961,f2(a915))+P1(f327(f327(f235(a915),x52961),f327(a113,x52962))) % 177.41/177.18 [5306]P1(f327(x53061,x53062))+P1(f327(f327(f234(a1),f2(a1)),f378(x53061))) % 177.41/177.18 [5369]P55(x53691,x53692)+~P55(x53691,f327(f286(x53691,x53691),x53692)) % 177.41/177.18 [5370]P36(x53701,x53702)+~P36(x53701,f327(f286(x53701,x53701),x53702)) % 177.41/177.18 [5371]P37(x53711,x53712)+~P37(x53711,f327(f286(x53711,x53711),x53712)) % 177.41/177.18 [5372]P49(x53721,x53722)+~P49(x53721,f327(f286(x53721,x53721),x53722)) % 177.41/177.18 [5375]~E(f46(a915,x53752,x53751),f2(a915))+E(f327(f327(f81(a915),x53751),f446(x53751,x53752)),x53752) % 177.41/177.18 [5376]~E(f46(a1,x53762,x53761),f2(a1))+E(f327(f327(f81(a1),x53761),f447(x53761,x53762)),x53762) % 177.41/177.18 [5402]~P1(f327(x54021,x54022))+P1(f327(f327(f234(a1),f2(a1)),f377(x54021))) % 177.41/177.18 [5413]E(f327(f327(f23(a915),f327(a106,x54131)),f327(a106,x54132)),f327(a106,x54131))+~P1(f327(a195,x54132)) % 177.41/177.18 [5442]E(f272(x54421,x54422),f78(a100))+~P1(f327(f327(f234(a100),x54421),f78(a100))) % 177.41/177.18 [5538]E(f327(f327(f165(x55381),x55382),f661(x55382,x55381)),f327(f327(f165(x55381),x55382),f667(x55382,x55381)))+P1(f327(f138(x55381),x55382)) % 177.41/177.18 [5582]~P1(f327(x55821,f90(x55822,x55821)))+P1(f327(x55821,f585(x55822,x55821))) % 177.41/177.18 [5647]P57(x56471,x56472)+~P1(f327(f315(x56471,x56472),f554(x56472,x56471))) % 177.41/177.18 [5792]~P13(x57922,x57921)+P1(f327(f327(x57921,f797(x57921,x57922)),f797(x57921,x57922))) % 177.41/177.18 [5793]~P13(x57932,x57931)+P1(f327(f327(x57931,f801(x57931,x57932)),f801(x57931,x57932))) % 177.41/177.18 [5802]~E(f327(a113,f46(a915,x58021,x58022)),x58022)+E(f46(a915,f327(a113,x58021),x58022),f2(a915)) % 177.41/177.18 [5857]P35(x58571,x58572)+P1(f327(f327(f329(x58571),f607(x58572,x58571)),f608(x58572,x58571))) % 177.41/177.18 [5864]~P142(x58641)+P1(f327(f327(f329(x58641),f327(f101(x58641),x58642)),f111(x58641))) % 177.41/177.18 [5865]~P146(x58651)+P1(f327(f327(f329(x58651),f327(f101(x58651),x58652)),f187(x58651))) % 177.41/177.18 [5866]~P142(x58661)+P1(f327(f327(f329(x58661),f327(f104(x58661),x58662)),f111(x58661))) % 177.41/177.18 [5867]~P93(x58671)+P1(f327(f327(f329(x58671),f327(f105(x58671),x58672)),f111(x58671))) % 177.41/177.18 [6001]~P36(x60011,x60012)+E(f327(f327(f289(x60011,x60011,x60011),x60012),f307(x60011,x60012)),x60012) % 177.41/177.18 [6015]E(f327(a113,f46(a915,x60151,x60152)),x60152)+E(f46(a915,f327(a113,x60151),x60152),f327(a113,f46(a915,x60151,x60152))) % 177.41/177.18 [6445]P35(x64451,x64452)+~P1(f327(f327(f329(x64451),f536(x64452,x64451)),f316(x64451,x64452))) % 177.41/177.18 [6483]~P126(x64831)+~P1(f327(f327(f235(x64831),f327(f101(x64831),x64832)),f2(x64831))) % 177.41/177.18 [6484]~P84(x64841)+~P1(f327(f327(f235(x64841),f327(f75(x64841),x64842)),f2(x64841))) % 177.41/177.18 [6573]P1(f327(f327(f235(a1),x65731),f46(a1,x65732,x65731)))+~P1(f327(f327(f235(a1),x65731),f2(a1))) % 177.41/177.18 [6673]E(f327(f327(f309(a915),f327(a113,x66731)),f303(a915,x66732,x66731)),f303(a915,x66732,f327(a113,x66731)))+~P1(f327(f327(f234(a915),x66732),f327(a113,x66731))) % 177.41/177.18 [6763]~P108(x67631)+P11(x67631,f151(x67631,x67631,f5(x67631),x67632)) % 177.41/177.18 [6892]E(f327(f168(x68921),x68922),x68922)+~P1(f327(f327(f234(a915),f327(f191(f916(x68921)),x68922)),f78(a915))) % 177.41/177.18 [6914]~P84(x69141)+P1(f327(f327(f234(x69141),f327(f79(x69141),f327(f75(x69141),x69142))),f2(x69141))) % 177.41/177.18 [6946]~P35(x69461,x69462)+P35(x69461,f327(f327(f289(x69461,x69461,x69461),x69462),f307(x69461,x69462))) % 177.41/177.18 [6947]~P49(x69471,x69472)+P49(x69471,f327(f327(f289(x69471,x69471,x69471),x69472),f307(x69471,x69472))) % 177.41/177.18 [7170]~P1(f327(f327(f235(a1),x71702),f2(a1)))+P1(f327(f327(f234(a1),f46(a1,x71701,x71702)),f2(a1))) % 177.41/177.18 [7571]~P146(x75711)+E(f192(x75711,f327(f327(f7(x75711,x75711,x75711),f80(x75711)),f78(x75711)),x75712,f2(x75711)),f327(f101(x75711),x75712)) % 177.41/177.18 [7599]~P128(x75991)+~P1(f327(f327(f235(x75991),f327(f327(f81(x75991),x75992),x75992)),f2(x75991))) % 177.41/177.18 [10227]~P119(x102271)+~P1(f327(f327(f235(x102271),f327(f327(f244(x102271),x102272),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f2(x102271))) % 177.41/177.18 [4830]~E(x48302,f114(x48301))+E(f327(f191(f916(x48301)),x48302),f2(a915)) % 177.41/177.18 [4866]~E(x48661,f2(a915))+E(f327(f327(f80(a915),x48661),x48662),x48662) % 177.41/177.18 [4867]~E(x48672,f2(a915))+E(f327(f327(f81(a915),x48671),x48672),f2(a915)) % 177.41/177.18 [4869]~E(x48691,f2(a915))+E(f327(f327(f81(a915),x48691),x48692),f2(a915)) % 177.41/177.18 [4870]~E(x48702,f2(a915))+E(f327(f327(f244(a915),x48701),x48702),f78(a915)) % 177.41/177.18 [4871]~E(x48712,f2(a1))+E(f327(f327(f37(a1),x48711),x48712),f2(a1)) % 177.41/177.18 [4882]E(x48821,f114(x48822))+~E(f327(f191(f916(x48822)),x48821),f2(a915)) % 177.41/177.18 [4884]~P95(x48841)+E(f327(f327(f81(x48841),x48842),x48842),x48842) % 177.41/177.18 [4886]~P108(x48861)+E(f327(f327(f238(x48861),x48862),x48862),x48862) % 177.41/177.18 [4888]~P108(x48881)+E(f327(f327(f189(x48881),x48882),x48882),x48882) % 177.41/177.18 [4889]~P96(x48891)+E(f327(f327(f102(x48891),x48892),x48892),x48892) % 177.41/177.18 [4891]~P101(x48911)+E(f327(f327(f102(x48911),x48912),x48912),x48912) % 177.41/177.18 [4892]~P96(x48921)+E(f327(f327(f103(x48921),x48922),x48922),x48922) % 177.41/177.18 [4894]~P102(x48941)+E(f327(f327(f103(x48941),x48942),x48942),x48942) % 177.41/177.18 [4912]~P74(x49121)+E(f327(f327(f23(x49121),x49122),x49122),f2(x49121)) % 177.41/177.18 [4926]~P74(x49261)+E(f327(f79(x49261),f327(f79(x49261),x49262)),x49262) % 177.41/177.18 [4927]~P86(x49271)+E(f327(f79(x49271),f327(f79(x49271),x49272)),x49272) % 177.41/177.18 [4944]~E(x49442,f2(a915))+E(f327(f327(f244(a915),x49441),x49442),f327(a113,f2(a915))) % 177.41/177.18 [4979]~P68(x49791)+E(f327(f327(f80(x49791),f2(x49791)),x49792),x49792) % 177.41/177.18 [4980]~P112(x49801)+E(f327(f327(f80(x49801),f2(x49801)),x49802),x49802) % 177.41/177.18 [4981]~P81(x49811)+E(f327(f327(f80(x49811),f2(x49811)),x49812),x49812) % 177.41/177.18 [4982]~P112(x49821)+E(f327(f327(f81(x49821),f78(x49821)),x49822),x49822) % 177.41/177.18 [4983]~P75(x49831)+E(f327(f327(f81(x49831),f78(x49831)),x49832),x49832) % 177.41/177.18 [4984]~P80(x49841)+E(f327(f327(f81(x49841),f78(x49841)),x49842),x49842) % 177.41/177.18 [4985]~P98(x49851)+E(f327(f327(f102(x49851),f190(x49851)),x49852),x49852) % 177.41/177.18 [4986]~P97(x49861)+E(f327(f327(f103(x49861),f242(x49861)),x49862),x49862) % 177.41/177.18 [5004]~P112(x50041)+E(f327(f327(f81(x50041),f2(x50041)),x50042),f2(x50041)) % 177.41/177.18 [5005]~P129(x50051)+E(f327(f327(f81(x50051),f2(x50051)),x50052),f2(x50051)) % 177.41/177.18 [5006]~P97(x50061)+E(f327(f327(f102(x50061),f242(x50061)),x50062),f242(x50061)) % 177.41/177.18 [5007]~P80(x50071)+E(f327(f327(f244(x50071),f78(x50071)),x50072),f78(x50071)) % 177.41/177.18 [5008]~P98(x50081)+E(f327(f327(f103(x50081),f190(x50081)),x50082),f190(x50081)) % 177.41/177.18 [5009]~P58(x50091)+E(f327(f327(f37(x50091),f2(x50091)),x50092),f2(x50091)) % 177.41/177.18 [5010]~P122(x50101)+E(f327(f327(f291(x50101),f2(x50101)),x50102),f2(x50101)) % 177.41/177.18 [5018]E(x50181,f114(x50182))+E(f145(x50182,f327(f169(x50182),x50181)),f327(f142(x50182),x50181)) % 177.41/177.18 [5019]E(x50191,f114(x50192))+E(f327(f142(x50192),f327(f169(x50192),x50191)),f145(x50192,x50191)) % 177.41/177.18 [5020]E(x50201,f2(a915))+~E(f327(f327(f80(a915),x50202),x50201),x50202) % 177.41/177.18 [5027]~P142(x50271)+E(f327(f104(x50271),f327(f101(a1),x50272)),f327(f101(x50271),x50272)) % 177.41/177.18 [5028]~P93(x50281)+E(f327(f104(x50281),f327(f105(a1),x50282)),f327(f105(x50281),x50282)) % 177.41/177.18 [5035]E(x50351,f78(a915))+~E(f327(f327(f81(a915),x50352),x50351),f78(a915)) % 177.41/177.18 [5036]E(x50361,f78(a915))+~E(f327(f327(f81(a915),x50361),x50362),f78(a915)) % 177.41/177.18 [5037]E(x50371,f2(a915))+~E(f327(f327(f80(a915),x50372),x50371),f2(a915)) % 177.41/177.18 [5038]E(x50381,f2(a915))+~E(f327(f327(f80(a915),x50381),x50382),f2(a915)) % 177.41/177.18 [5055]~P84(x50551)+E(f327(f75(x50551),f327(f79(x50551),x50552)),f327(f75(x50551),x50552)) % 177.41/177.18 [5056]~P119(x50561)+E(f327(f75(x50561),f327(f101(x50561),x50562)),f327(f101(x50561),x50562)) % 177.41/177.18 [5057]~P84(x50571)+E(f327(f75(x50571),f327(f75(x50571),x50572)),f327(f75(x50571),x50572)) % 177.41/177.18 [5058]~P68(x50581)+E(f327(f166(x50581),f327(f169(x50581),x50582)),f327(f166(x50581),x50582)) % 177.41/177.18 [5063]~E(x50631,f327(a113,f2(a915)))+E(f327(f327(f244(a915),x50631),x50632),f327(a113,f2(a915))) % 177.41/177.18 [5072]~P74(x50721)+E(f327(f327(f23(x50721),f2(x50721)),x50722),f327(f79(x50721),x50722)) % 177.41/177.18 [5073]~E(x50732,f2(a915))+E(f140(a915,f327(f302(a915,x50731),x50732)),f114(a915)) % 177.41/177.18 [5082]~P93(x50821)+E(f327(f327(f80(x50821),x50822),f327(f105(x50821),a83)),x50822) % 177.41/177.18 [5083]E(x50831,f2(a1))+E(f48(f327(f75(a1),x50832),f327(f75(a1),x50831)),f54(x50832,x50831)) % 177.41/177.18 [5099]~E(x50991,x50992)+P1(f327(f327(f234(a915),x50991),x50992)) % 177.41/177.18 [5106]~E(x51061,f2(a100))+E(f327(f327(f80(a915),f327(a20,x51061)),x51062),x51062) % 177.41/177.18 [5107]~E(f327(f105(a1),x51072),f327(f101(a1),x51071))+E(x51071,f327(a106,f327(f105(a1),x51072))) % 177.41/177.18 [5120]~P4(x51201)+P4(f327(f327(f244(a1),x51201),x51202)) % 177.41/177.18 [5121]~P74(x51211)+E(f327(f327(f80(x51211),x51212),f327(f79(x51211),x51212)),f2(x51211)) % 177.41/177.18 [5122]~P86(x51221)+E(f327(f327(f102(x51221),x51222),f327(f79(x51221),x51222)),f242(x51221)) % 177.41/177.18 [5123]~P86(x51231)+E(f327(f327(f103(x51231),x51232),f327(f79(x51231),x51232)),f190(x51231)) % 177.41/177.18 [5147]E(x51471,f2(a915))+~E(f327(f79(a1),f327(f101(a1),x51472)),f327(f101(a1),x51471)) % 177.41/177.18 [5148]E(x51481,f2(a915))+~E(f327(f79(a1),f327(f101(a1),x51481)),f327(f101(a1),x51482)) % 177.41/177.18 [5158]E(f196(x51581,x51582),f2(a1))+P1(f327(f327(f234(a1),x51582),x51581)) % 177.41/177.18 [5159]E(f179(x51591,x51592),f114(a1))+P1(f327(f327(f234(a1),x51591),x51592)) % 177.41/177.18 [5160]E(f241(x51601,x51602),f2(a100))+P1(f327(f327(f235(a100),x51601),x51602)) % 177.41/177.18 [5173]E(x51731,f327(a113,f2(a915)))+~E(f327(f327(f81(a915),x51732),x51731),f327(a113,f2(a915))) % 177.41/177.18 [5174]E(x51741,f327(a113,f2(a915)))+~E(f327(f327(f81(a915),x51741),x51742),f327(a113,f2(a915))) % 177.41/177.18 [5175]~P107(x51751)+P1(f327(f327(f234(x51751),x51752),x51752)) % 177.41/177.18 [5176]~P112(x51761)+P1(f327(f327(f287(x51761),x51762),x51762)) % 177.41/177.18 [5179]~P93(x51791)+E(f327(f327(f81(x51791),x51792),f327(f105(x51791),a98)),f327(f79(x51791),x51792)) % 177.41/177.18 [5199]~P142(x51991)+E(f327(f79(x51991),f327(f104(x51991),x51992)),f327(f104(x51991),f327(f79(a1),x51992))) % 177.41/177.18 [5200]~P93(x52001)+E(f327(f79(x52001),f327(f105(x52001),x52002)),f327(f105(x52001),f327(f79(a1),x52002))) % 177.41/177.18 [5230]~E(x52301,f327(a113,x52302))+P1(f327(f327(f235(a915),f2(a915)),x52301)) % 177.41/177.18 [5248]~P108(x52481)+E(f327(f79(f922(x52481,a910)),f327(f282(x52481),x52482)),f327(f283(x52481),x52482)) % 177.41/177.18 [5249]~P108(x52491)+E(f327(f79(f922(x52491,a910)),f327(f304(x52491),x52492)),f327(f301(x52491),x52492)) % 177.41/177.18 [5250]~P108(x52501)+E(f327(f79(f922(x52501,a910)),f327(f283(x52501),x52502)),f327(f282(x52501),x52502)) % 177.41/177.18 [5251]~P108(x52511)+E(f327(f79(f922(x52511,a910)),f327(f301(x52511),x52512)),f327(f304(x52511),x52512)) % 177.41/177.18 [5259]~E(f327(f101(a1),x52592),x52591)+P1(f327(f327(f234(a1),f2(a1)),x52591)) % 177.41/177.18 [5266]~E(x52662,f2(a1))+E(f54(x52661,x52662),f327(f327(f252(a1,a1),f2(a1)),f327(f75(a1),x52661))) % 177.41/177.18 [5268]~P65(x52681)+P1(f327(f327(f234(x52681),f190(x52681)),x52682)) % 177.41/177.18 [5301]E(x53011,x53012)+~E(f327(f327(f80(a1),x53011),x53011),f327(f327(f80(a1),x53012),x53012)) % 177.41/177.18 [5305]~P1(f327(x53051,x53052))+P1(f327(x53051,f327(a106,f377(x53051)))) % 177.41/177.18 [5331]~P119(x53311)+E(f327(f327(f81(x53311),f82(x53311,x53312)),f327(f75(x53311),x53312)),x53312) % 177.41/177.18 [5338]~E(x53382,f2(a915))+E(f85(f921(a915,a915),f49(x53381,x53382)),f327(f327(f252(a915,a915),f2(a915)),x53381)) % 177.41/177.18 [5343]~E(x53431,x53432)+~P1(f327(f327(f235(a915),x53431),x53432)) % 177.41/177.18 [5344]~E(x53441,x53442)+~P1(f327(f327(f235(a1),x53441),x53442)) % 177.41/177.18 [5347]~P146(x53471)+E(f327(f327(f80(x53471),f78(x53471)),f327(f101(x53471),x53472)),f327(f101(x53471),f327(a113,x53472))) % 177.41/177.18 [5351]~E(x53511,f2(a915))+~P1(f327(f327(f235(a915),x53512),x53511)) % 177.41/177.18 [5365]E(f153(x53651,x53652),x53652)+~E(f327(f191(f916(x53651)),f153(x53651,x53652)),f327(f191(f916(x53651)),x53652)) % 177.41/177.18 [5366]E(f327(f36(x53661),f327(f173(x53661),x53662)),f327(f191(f916(x53661)),x53662))+~P1(f327(f138(x53661),x53662)) % 177.41/177.18 [5380]~P1(f327(x53801,f379(x53801)))+P1(f327(x53801,f327(f101(a1),x53802))) % 177.41/177.18 [5390]E(f241(x53901,x53902),x53902)+~P1(f327(f327(f235(a100),x53901),x53902)) % 177.41/177.18 [5392]E(f272(x53921,x53922),f78(a100))+~P1(f327(f327(f235(a100),x53922),x53921)) % 177.41/177.18 [5393]E(f179(x53931,x53932),f114(a1))+~P1(f327(f327(f235(a1),x53932),x53931)) % 177.41/177.18 [5394]E(f129(x53941,x53942),f116(a1))+~P1(f327(f327(f235(a1),x53941),x53942)) % 177.41/177.18 [5396]~P110(x53961)+E(f303(x53961,x53962,x53962),f327(f327(f309(x53961),x53962),f190(f922(x53961,a910)))) % 177.41/177.18 [5416]~E(f327(f327(f23(a915),x54161),x54162),f2(a915))+P1(f327(f327(f234(a915),x54161),x54162)) % 177.41/177.18 [5439]~E(x54392,f2(a915))+E(f56(x54391,x54392,f114(x54391)),f327(f327(f152(f916(x54391)),f114(x54391)),f114(f916(x54391)))) % 177.41/177.18 [5443]~P107(x54431)+~P1(f327(f327(f235(x54431),x54432),x54432)) % 177.41/177.18 [5445]~E(f46(a1,x54451,x54452),f2(a1))+E(f46(a1,x54451,f327(f79(a1),x54452)),f2(a1)) % 177.41/177.18 [5447]~E(f46(a1,x54471,x54472),f2(a1))+E(f46(a1,f327(f79(a1),x54471),x54472),f2(a1)) % 177.41/177.18 [5454]E(f327(f302(a915,x54541),f327(a113,x54542)),f190(f922(a915,a910)))+P1(f327(f327(f234(a915),x54541),x54542)) % 177.41/177.18 [5478]E(f140(a915,f327(f302(a915,x54781),x54782)),f114(a915))+P1(f327(f327(f235(a915),x54781),x54782)) % 177.41/177.18 [5483]~E(f327(f36(x54831),f327(f173(x54831),x54832)),f327(f191(f916(x54831)),x54832))+P1(f327(f138(x54831),x54832)) % 177.41/177.18 [5487]~P1(f327(f138(x54871),x54872))+P1(f327(f138(x54871),f327(f168(x54871),x54872))) % 177.41/177.18 [5488]~P1(f327(f138(x54881),x54882))+P1(f327(f138(x54881),f327(f172(x54881),x54882))) % 177.41/177.18 [5489]~P1(f327(f138(x54891),x54892))+P1(f327(f138(x54891),f327(f169(x54891),x54892))) % 177.41/177.18 [5497]P1(f327(x54971,x54972))+~P1(f327(x54971,f327(a106,f378(x54971)))) % 177.41/177.18 [5498]P1(f327(f327(f234(a915),x54982),x54981))+P1(f327(f327(f234(a915),x54981),x54982)) % 177.41/177.18 [5499]P1(f327(f327(f234(a1),x54992),x54991))+P1(f327(f327(f234(a1),x54991),x54992)) % 177.41/177.18 [5503]~P84(x55031)+P1(f327(f327(f234(x55031),x55032),f327(f75(x55031),x55032))) % 177.41/177.18 [5506]P1(f327(x55061,f385(x55061)))+~P1(f327(x55061,f327(f101(a1),x55062))) % 177.41/177.18 [5530]E(f327(f327(f23(a915),x55301),x55302),f2(a915))+~P1(f327(f327(f234(a915),x55301),x55302)) % 177.41/177.18 [5531]E(f327(f327(f37(a915),x55311),x55312),f2(a915))+~P1(f327(f327(f235(a915),x55311),x55312)) % 177.41/177.18 [5550]E(f46(a915,x55501,x55502),x55501)+~P1(f327(f327(f235(a915),x55501),x55502)) % 177.41/177.18 [5558]E(f46(a1,x55581,f327(f79(a1),x55582)),f292(x55581,x55582))+P1(f327(f327(f234(a1),f2(a1)),x55582)) % 177.41/177.18 [5571]E(f327(f327(f23(a1),x55711),x55712),f196(x55711,x55712))+~P1(f327(f327(f234(a1),x55712),x55711)) % 177.41/177.18 [5591]P1(f327(f327(f234(a1),f2(a1)),f379(x55911)))+P1(f327(x55911,f327(f101(a1),x55912))) % 177.41/177.18 [5604]~P126(x56041)+P1(f327(f327(f234(x56041),f2(x56041)),f327(f101(x56041),x56042))) % 177.41/177.18 [5605]~P84(x56051)+P1(f327(f327(f234(x56051),f2(x56051)),f327(f75(x56051),x56052))) % 177.41/177.18 [5633]E(f327(f327(f80(a915),x56331),f813(x56332,x56331)),x56332)+~P1(f327(f327(f234(a915),x56331),x56332)) % 177.41/177.18 [5645]~E(f327(f105(a1),x56451),f327(f101(a1),x56452))+P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x56451))) % 177.41/177.18 [5648]E(f303(a1,x56481,x56482),f190(f922(a1,a910)))+~P1(f327(f327(f235(a1),x56482),x56481)) % 177.41/177.18 [5651]~P119(x56511)+E(f327(f327(f81(x56511),f327(f75(x56511),x56512)),f327(f75(x56511),x56512)),f327(f327(f81(x56511),x56512),x56512)) % 177.41/177.18 [5656]E(f140(a915,f327(f302(a915,x56561),f327(a113,x56562))),f114(a915))+P1(f327(f327(f234(a915),x56561),x56562)) % 177.41/177.18 [5660]E(f327(f327(f37(a1),x56601),x56602),f293(x56601,x56602))+~P1(f327(f327(f234(a1),f2(a1)),x56602)) % 177.41/177.18 [5680]P1(f327(f138(x56801),x56802))+~P1(f327(f138(x56801),f327(f168(x56801),x56802))) % 177.41/177.18 [5681]P1(f327(f138(x56811),x56812))+~P1(f327(f138(x56811),f327(f169(x56811),x56812))) % 177.41/177.18 [5708]P1(f327(f35(a915),x57081))+P1(f327(f327(f329(a915),f882(x57081,x57082)),x57081)) % 177.41/177.18 [5709]P1(f327(f35(a915),x57091))+P1(f327(f327(f329(a915),f884(x57091,x57092)),x57091)) % 177.41/177.18 [5712]P1(f327(f327(f235(a915),x57122),f327(a113,x57121)))+P1(f327(f327(f235(a915),x57121),x57122)) % 177.41/177.18 [5713]E(f46(a1,x57131,x57132),f292(x57131,x57132))+~P1(f327(f327(f234(a1),f2(a1)),x57132)) % 177.41/177.18 [5716]E(f140(a915,f327(f302(a915,x57161),x57162)),f114(a915))+~P1(f327(f327(f234(a915),x57162),x57161)) % 177.41/177.18 [5717]~P78(x57171)+E(f327(f310(x57171,x57171,f79(x57171)),f327(f282(x57171),x57172)),f327(f304(x57171),f327(f79(x57171),x57172))) % 177.41/177.18 [5718]~P78(x57181)+E(f327(f310(x57181,x57181,f79(x57181)),f327(f304(x57181),x57182)),f327(f282(x57181),f327(f79(x57181),x57182))) % 177.41/177.18 [5719]~P78(x57191)+E(f327(f310(x57191,x57191,f79(x57191)),f327(f283(x57191),x57192)),f327(f301(x57191),f327(f79(x57191),x57192))) % 177.41/177.18 [5720]~P78(x57201)+E(f327(f310(x57201,x57201,f79(x57201)),f327(f301(x57201),x57202)),f327(f283(x57201),f327(f79(x57201),x57202))) % 177.41/177.18 [5731]E(x57311,f190(f922(x57312,a910)))+P1(f327(f327(f329(x57312),f662(x57311,x57312)),x57311)) % 177.41/177.18 [5732]E(x57321,f190(f922(x57322,a910)))+P1(f327(f327(f329(x57322),f535(x57321,x57322)),x57321)) % 177.41/177.18 [5743]~P1(f327(f327(f235(a915),x57431),x57432))+P1(f327(f327(f234(a915),x57431),x57432)) % 177.41/177.18 [5744]~P1(f327(f327(f235(a1),x57441),x57442))+P1(f327(f327(f234(a1),x57441),x57442)) % 177.41/177.18 [5760]E(f48(x57601,x57602),f327(f327(f252(a1,a1),f2(a1)),x57601))+~P1(f327(f327(f235(a1),x57601),x57602)) % 177.41/177.18 [5762]E(f217(f327(f79(a1),x57621),f327(f79(a1),x57622)),f217(x57621,x57622))+~P1(f327(f327(f235(a1),x57622),f2(a1))) % 177.41/177.18 [5774]E(x57741,x57742)+~E(f327(a3,f327(a113,f327(a20,x57741))),f327(a3,f327(a113,f327(a20,x57742)))) % 177.41/177.18 [5779]E(f48(x57791,x57792),f327(f327(f252(a1,a1),f2(a1)),x57791))+~P1(f327(f327(f234(a1),x57792),f2(a1))) % 177.41/177.18 [5808]E(f46(a915,f327(f105(a915),x58081),f327(f105(a915),x58082)),f2(a915))+~P1(f327(a195,f327(f105(a1),x58081))) % 177.41/177.18 [5822]P1(f327(f327(f234(a1),f2(a1)),f385(x58221)))+~P1(f327(x58221,f327(f101(a1),x58222))) % 177.41/177.18 [5855]P38(f303(a1,x58551,x58552))+~P1(f327(f327(f234(a1),f2(a1)),x58551)) % 177.41/177.18 [5860]~P1(f327(f35(x58601),x58602))+P1(f327(f35(f922(x58601,a910)),f327(f308(x58601),x58602))) % 177.41/177.18 [5873]E(f327(f327(f80(a1),x58731),f327(f101(a1),f380(x58732,x58731))),x58732)+~P1(f327(f327(f234(a1),x58731),x58732)) % 177.41/177.18 [5881]P1(f327(f327(f234(a915),x58811),x58812))+P1(f327(f327(f234(a915),f327(a113,x58812)),x58811)) % 177.41/177.18 [5925]E(f327(f327(f37(a915),f327(f105(a915),x59251)),f327(f105(a915),x59252)),f2(a915))+~P1(f327(a195,f327(f105(a1),x59251))) % 177.41/177.18 [5926]E(f327(f327(f81(a915),f327(f105(a915),x59261)),f327(f105(a915),x59262)),f2(a915))+~P1(f327(f327(f235(a1),x59261),a83)) % 177.41/177.18 [5928]P1(f327(f327(f234(a915),x59281),f327(a113,x59282)))+~P1(f327(f327(f234(a915),x59281),x59282)) % 177.41/177.18 [5930]P1(f327(f327(f235(a915),x59301),f327(a113,x59302)))+~P1(f327(f327(f234(a915),x59301),x59302)) % 177.41/177.18 [5932]P1(f327(f327(f235(a915),x59321),f327(a113,x59322)))+~P1(f327(f327(f235(a915),x59321),x59322)) % 177.41/177.18 [5935]~E(x59351,x59352)+P1(f327(f327(f235(a1),x59351),f327(f327(f80(a1),x59352),f78(a1)))) % 177.41/177.18 [5938]E(f46(a1,x59381,x59382),f2(a1))+E(f327(f327(f23(a1),x59382),f46(a1,x59381,x59382)),f46(a1,f327(f79(a1),x59381),x59382)) % 177.41/177.18 [5947]E(x59471,f114(x59472))+P1(f327(f327(f329(x59472),f145(x59472,x59471)),f327(f173(x59472),x59471))) % 177.41/177.18 [5959]E(f85(f921(a915,a915),f49(x59591,x59592)),f327(f327(f252(a915,a915),f2(a915)),x59591))+~P1(f327(f327(f235(a915),x59591),x59592)) % 177.41/177.18 [5994]E(f327(f327(f23(a915),f327(f105(a915),x59941)),f327(f105(a915),x59942)),f327(f105(a915),x59941))+~P1(f327(f327(f235(a1),x59942),a83)) % 177.41/177.18 [5995]E(f327(f327(f80(a915),f327(f105(a915),x59951)),f327(f105(a915),x59952)),f327(f105(a915),x59952))+~P1(f327(f327(f235(a1),x59951),a83)) % 177.41/177.18 [6002]E(f327(a113,f327(f327(f80(a915),x60021),f338(x60022,x60021))),x60022)+~P1(f327(f327(f235(a915),x60021),x60022)) % 177.41/177.18 [6026]P1(f327(x60261,x60262))+~P1(f327(x60261,f327(a89,f566(x60262,x60261)))) % 177.41/177.18 [6027]P1(f327(x60271,x60272))+~P1(f327(x60271,f327(a3,f814(x60272,x60271)))) % 177.41/177.18 [6036]~P1(f327(f327(f235(a915),x60361),f327(a113,x60362)))+P1(f327(f327(f234(a915),x60361),x60362)) % 177.41/177.18 [6086]E(f327(f327(f309(a915),x60861),f327(f302(a915,x60862),x60861)),f327(f302(a915,x60862),f327(a113,x60861)))+~P1(f327(f327(f234(a915),x60862),x60861)) % 177.41/177.18 [6088]E(x60881,f114(x60882))+E(f327(f327(f135(x60882),f115(x60882,x60881)),f327(f327(f152(x60882),f145(x60882,x60881)),f114(x60882))),x60881) % 177.41/177.18 [6105]P1(f327(f35(x61051),x61052))+~P1(f327(f327(f235(a915),f2(a915)),f327(f36(x61051),x61052))) % 177.41/177.18 [6109]~E(x61091,f190(f922(x61092,a910)))+~P1(f327(f327(f235(a915),f2(a915)),f327(f36(x61092),x61091))) % 177.41/177.18 [6121]~P1(f327(f327(f235(a915),x61211),x61212))+P1(f327(f327(f234(a915),f327(a113,x61211)),x61212)) % 177.41/177.18 [6125]~P108(x61251)+E(f151(x61251,x61251,f5(x61251),f153(x61251,x61252)),f140(x61251,f327(f173(x61251),x61252))) % 177.41/177.18 [6128]E(x61281,f114(x61282))+P1(f327(f327(f329(x61282),f327(f142(x61282),x61281)),f327(f173(x61282),x61281))) % 177.41/177.18 [6134]~P126(x61341)+P1(f327(f327(f235(x61341),x61342),f327(f327(f80(x61341),x61342),f78(x61341)))) % 177.41/177.18 [6136]~P84(x61361)+P1(f327(f327(f234(x61361),f327(f79(x61361),x61362)),f327(f75(x61361),x61362))) % 177.41/177.18 [6150]~E(x61501,x61502)+E(f290(a915,f287(a915),x61501,x61502),f327(f327(f309(a915),x61501),f190(f922(a915,a910)))) % 177.41/177.18 [6168]P1(f327(f35(a915),x61681))+~P1(f327(f327(f234(a915),f882(x61681,x61682)),x61682)) % 177.41/177.18 [6169]P1(f327(f35(a915),x61691))+~P1(f327(f327(f235(a915),f884(x61691,x61692)),x61692)) % 177.41/177.18 [6172]~P1(f327(f35(f921(x61721,x61721)),x61722))+P1(f327(f35(x61721),f327(f281(x61721),x61722))) % 177.41/177.18 [6227]E(f290(a915,f287(a915),x62271,x62272),f190(f922(a915,a910)))+P1(f327(f327(f287(a915),x62271),x62272)) % 177.41/177.18 [6233]~P1(f327(f327(f235(a915),x62332),f327(a113,x62331)))+~P1(f327(f327(f235(a915),x62331),x62332)) % 177.41/177.18 [6234]~P110(x62341)+E(f327(f327(f103(f922(x62341,a910)),f327(f301(x62341),x62342)),f327(f283(x62341),x62342)),f327(f327(f309(x62341),x62342),f190(f922(x62341,a910)))) % 177.41/177.18 [6246]P1(f327(f35(x62461),x62462))+~P1(f327(f35(f922(x62461,a910)),f327(f308(x62461),x62462))) % 177.41/177.18 [6269]P1(f327(f327(f234(a915),f327(a113,x62691)),f327(a113,x62692)))+~P1(f327(f327(f234(a915),x62691),x62692)) % 177.41/177.18 [6270]P1(f327(f327(f234(a915),f327(a20,x62701)),f327(a20,x62702)))+~P1(f327(f327(f234(a100),x62701),x62702)) % 177.41/177.18 [6271]P1(f327(f327(f234(a100),f327(a3,x62711)),f327(a3,x62712)))+~P1(f327(f327(f234(a915),x62711),x62712)) % 177.41/177.18 [6273]P1(f327(f327(f235(a915),f327(a113,x62731)),f327(a113,x62732)))+~P1(f327(f327(f235(a915),x62731),x62732)) % 177.41/177.18 [6274]P1(f327(f327(f235(a915),f327(a20,x62741)),f327(a20,x62742)))+~P1(f327(f327(f235(a100),x62741),x62742)) % 177.41/177.18 [6275]P1(f327(f327(f235(a100),f327(a3,x62751)),f327(a3,x62752)))+~P1(f327(f327(f235(a915),x62751),x62752)) % 177.41/177.18 [6280]E(x62801,x62802)+~E(f327(f310(a915,a1,f101(a1)),x62801),f327(f310(a915,a1,f101(a1)),x62802)) % 177.41/177.18 [6296]P1(f327(f327(f234(a915),x62961),x62962))+~P1(f327(f327(f234(a915),f327(a113,x62961)),x62962)) % 177.41/177.18 [6299]P1(f327(f327(f235(a915),x62991),x62992))+~P1(f327(f327(f234(a915),f327(a113,x62991)),x62992)) % 177.41/177.18 [6300]P1(f327(f327(f235(a915),x63001),x63002))+~P1(f327(f327(f235(a915),f327(a113,x63001)),x63002)) % 177.41/177.18 [6319]E(f46(a1,x63191,x63192),f2(a1))+E(f327(f327(f23(a1),f46(a1,x63191,x63192)),x63192),f46(a1,x63191,f327(f79(a1),x63192))) % 177.41/177.18 [6386]E(f327(f36(f922(x63861,a910)),f327(f308(x63861),x63862)),f327(f327(f244(a915),f327(a113,f327(a113,f2(a915)))),f327(f36(x63861),x63862)))+~P1(f327(f35(x63861),x63862)) % 177.41/177.18 [6389]E(x63891,f114(x63892))+E(f327(f327(f165(x63892),x63891),f327(f327(f23(a915),f327(f191(f916(x63892)),x63891)),f78(a915))),f145(x63892,x63891)) % 177.41/177.18 [6411]E(x64111,f114(x64112))+E(f327(f327(f135(x64112),f327(f172(x64112),x64111)),f327(f327(f152(x64112),f327(f142(x64112),x64111)),f114(x64112))),f327(f168(x64112),x64111)) % 177.41/177.18 [6442]~P1(f327(f35(x64421),f38(f922(x64421,a910),x64422)))+P1(f327(f35(f922(x64421,a910)),x64422)) % 177.41/177.18 [6464]P1(f327(f327(f234(a915),f327(f105(a915),x64641)),f327(f105(a915),x64642)))+~P1(f327(f327(f234(a1),x64641),a83)) % 177.41/177.18 [6486]~P1(f327(f327(f235(a1),x64861),x64862))+P1(f327(f327(f234(a1),x64861),f327(f327(f23(a1),x64862),f78(a1)))) % 177.41/177.18 [6487]~P1(f327(f327(f234(a1),x64871),x64872))+P1(f327(f327(f235(a1),x64871),f327(f327(f80(a1),x64872),f78(a1)))) % 177.41/177.18 [6488]~P1(f327(f327(f235(a1),x64881),x64882))+P1(f327(f327(f235(a1),x64881),f327(f327(f80(a1),x64882),f78(a1)))) % 177.41/177.18 [6490]~P1(f327(f327(f234(a1),x64901),x64902))+P1(f327(f327(f234(a915),f327(f105(a915),x64901)),f327(f105(a915),x64902))) % 177.41/177.18 [6492]~P1(f327(f327(f234(a915),x64921),x64922))+P1(f327(f327(f234(a1),f327(f101(a1),x64921)),f327(f101(a1),x64922))) % 177.41/177.18 [6493]~P1(f327(f327(f234(a1),x64931),x64932))+P1(f327(f327(f234(a1),f327(f105(a1),x64931)),f327(f105(a1),x64932))) % 177.41/177.18 [6495]~P1(f327(f327(f235(a915),x64951),x64952))+P1(f327(f327(f235(a1),f327(f101(a1),x64951)),f327(f101(a1),x64952))) % 177.41/177.18 [6496]~P1(f327(f327(f235(a1),x64961),x64962))+P1(f327(f327(f235(a1),f327(f105(a1),x64961)),f327(f105(a1),x64962))) % 177.41/177.18 [6516]~P1(f327(f327(f234(a915),x65161),x65162))+~P1(f327(f327(f234(a915),f327(a113,x65162)),x65161)) % 177.41/177.18 [6559]~P1(f327(f327(f234(a915),f327(a113,x65591)),f327(a113,x65592)))+P1(f327(f327(f234(a915),x65591),x65592)) % 177.41/177.18 [6560]~P1(f327(f327(f234(a100),f327(a3,x65601)),f327(a3,x65602)))+P1(f327(f327(f234(a915),x65601),x65602)) % 177.41/177.18 [6561]~P1(f327(f327(f234(a915),f327(a20,x65611)),f327(a20,x65612)))+P1(f327(f327(f234(a100),x65611),x65612)) % 177.41/177.18 [6563]~P1(f327(f327(f235(a915),f327(a113,x65631)),f327(a113,x65632)))+P1(f327(f327(f235(a915),x65631),x65632)) % 177.41/177.18 [6564]~P1(f327(f327(f235(a100),f327(a3,x65641)),f327(a3,x65642)))+P1(f327(f327(f235(a915),x65641),x65642)) % 177.41/177.18 [6565]~P1(f327(f327(f235(a915),f327(a106,x65651)),f327(a106,x65652)))+P1(f327(f327(f235(a1),x65651),x65652)) % 177.41/177.18 [6566]~P1(f327(f327(f235(a915),f327(a20,x65661)),f327(a20,x65662)))+P1(f327(f327(f235(a100),x65661),x65662)) % 177.41/177.18 [6605]~P1(f327(f327(f235(a915),f327(a106,x66052)),f327(a106,x66051)))+P1(f327(f327(f235(a1),f2(a1)),x66051)) % 177.41/177.18 [6636]P1(f327(f327(f234(a1),f2(a1)),f46(a1,x66361,x66362)))+~P1(f327(f327(f235(a1),f2(a1)),x66362)) % 177.41/177.18 [6797]P35(x67971,x67972)+~E(f327(f327(f289(x67971,x67971,x67971),x67972),x67972),f190(f922(f921(x67971,x67971),a910))) % 177.41/177.18 [6811]~P35(x68111,x68112)+P35(x68111,f327(f327(f289(x68111,x68111,x68111),x68112),x68112)) % 177.41/177.18 [6822]P1(f327(f327(f234(a1),x68221),x68222))+~P1(f327(f327(f235(a1),x68221),f327(f327(f80(a1),x68222),f78(a1)))) % 177.41/177.18 [6823]P1(f327(f327(f235(a1),x68231),x68232))+~P1(f327(f327(f234(a1),x68231),f327(f327(f23(a1),x68232),f78(a1)))) % 177.41/177.18 [6826]P1(f327(f327(f234(a915),x68261),x68262))+~P1(f327(f327(f234(a1),f327(f101(a1),x68261)),f327(f101(a1),x68262))) % 177.41/177.18 [6827]P1(f327(f327(f234(a1),x68271),x68272))+~P1(f327(f327(f234(a1),f327(f105(a1),x68271)),f327(f105(a1),x68272))) % 177.41/177.18 [6829]P1(f327(f327(f235(a915),x68291),x68292))+~P1(f327(f327(f235(a1),f327(f101(a1),x68291)),f327(f101(a1),x68292))) % 177.41/177.18 [6830]P1(f327(f327(f235(a1),x68301),x68302))+~P1(f327(f327(f235(a915),f327(f105(a915),x68301)),f327(f105(a915),x68302))) % 177.41/177.18 [6831]P1(f327(f327(f235(a1),x68311),x68312))+~P1(f327(f327(f235(a1),f327(f105(a1),x68311)),f327(f105(a1),x68312))) % 177.41/177.18 [6903]~E(f290(a915,f287(a915),x69031,x69032),f190(f922(a915,a910)))+~P1(f327(f327(f287(a915),x69031),x69032)) % 177.41/177.18 [6928]~E(f692(x69282,x69281),f114(x69281))+E(f327(f143(f916(x69281),f916(x69281),f135(x69281),f114(x69281)),x69282),f114(x69281)) % 177.41/177.18 [6929]~E(f693(x69292,x69291),f114(x69291))+E(f327(f143(f916(x69291),f916(x69291),f135(x69291),f114(x69291)),x69292),f114(x69291)) % 177.41/177.18 [6933]~P3(x69331)+E(f327(f143(x69331,x69331,f103(x69331),f242(x69331)),x69332),f39(x69331,f327(f173(x69331),x69332))) % 177.41/177.18 [6934]~P3(x69341)+E(f327(f143(x69341,x69341,f102(x69341),f190(x69341)),x69342),f38(x69341,f327(f173(x69341),x69342))) % 177.41/177.18 [6948]E(x69481,f2(a100))+E(f327(f327(f80(a915),f327(a20,f327(f327(f23(a100),x69481),f78(a100)))),f327(a113,x69482)),f327(f327(f80(a915),f327(a20,x69481)),x69482)) % 177.41/177.18 [6997]P1(f327(f327(f235(a1),f327(f327(f23(a1),x69971),x69972)),f2(a1)))+~P1(f327(f327(f235(a1),x69971),x69972)) % 177.41/177.18 [7022]~P108(x70221)+E(f327(f327(f102(f922(x70221,a910)),f327(f327(f309(x70221),x70222),f190(f922(x70221,a910)))),f327(f304(x70221),x70222)),f327(f283(x70221),x70222)) % 177.41/177.18 [7099]~P57(x70991,x70992)+P35(x70991,f327(f262(f921(x70991,x70991)),f327(f257(x70991,x70991,a910),x70992))) % 177.41/177.18 [7100]~P57(x71001,x71002)+P55(x71001,f327(f262(f921(x71001,x71001)),f327(f257(x71001,x71001,a910),x71002))) % 177.41/177.18 [7101]~P47(x71011,x71012)+P36(x71011,f327(f262(f921(x71011,x71011)),f327(f257(x71011,x71011,a910),x71012))) % 177.41/177.18 [7102]~P48(x71021,x71022)+P49(x71021,f327(f262(f921(x71021,x71021)),f327(f257(x71021,x71021,a910),x71022))) % 177.41/177.18 [7103]E(x71031,f190(f922(x71032,a910)))+~P1(f327(f327(f234(f922(x71032,a910)),x71031),f190(f922(x71032,a910)))) % 177.41/177.18 [7185]~P1(f327(f327(f235(a915),f2(a915)),x71852))+P1(f327(f327(f234(a915),f46(a915,x71851,x71852)),x71852)) % 177.41/177.18 [7186]~P1(f327(f327(f234(a1),f2(a1)),x71861))+P1(f327(f327(f234(a1),f46(a1,x71861,x71862)),x71861)) % 177.41/177.18 [7187]~P1(f327(f327(f235(a915),f2(a915)),x71872))+P1(f327(f327(f235(a915),f46(a915,x71871,x71872)),x71872)) % 177.41/177.18 [7189]~P1(f327(f327(f235(a1),f2(a1)),x71892))+P1(f327(f327(f235(a1),f46(a1,x71891,x71892)),x71892)) % 177.41/177.18 [7267]~P110(x72671)+E(f327(f327(f23(f922(x72671,a910)),f327(f327(f309(x72671),x72672),f190(f922(x72671,a910)))),f327(f282(x72671),x72672)),f327(f327(f309(x72671),x72672),f190(f922(x72671,a910)))) % 177.41/177.18 [7342]~P41(x73421,x73422)+P50(x73421,f242(f922(x73421,a910)),f327(f262(f921(x73421,x73421)),f327(f257(x73421,x73421,a910),x73422))) % 177.41/177.18 [7343]P1(f327(x73431,x73432))+P1(f327(f327(f329(f922(f921(a915,a915),a910)),f566(x73432,x73431)),a99)) % 177.41/177.18 [7388]E(f327(f327(f135(a915),f140(a915,f327(f302(a915,x73881),x73882))),f327(f327(f152(a915),x73882),f114(a915))),f140(a915,f327(f302(a915,x73881),f327(a113,x73882))))+~P1(f327(f327(f234(a915),x73881),x73882)) % 177.41/177.18 [7539]E(x75391,f2(a915))+~E(f327(f143(a915,a915,f80(a915),x75391),x75392),f2(a915)) % 177.41/177.18 [7563]~P1(f327(f327(f235(a1),f327(f327(f23(a1),x75631),x75632)),f2(a1)))+P1(f327(f327(f235(a1),x75631),x75632)) % 177.41/177.18 [7590]P35(x75901,x75902)+~P35(x75901,f327(f327(f289(x75901,x75901,x75901),x75902),x75902)) % 177.41/177.18 [7616]~P1(f327(f327(f234(a915),f327(a113,x76161)),x76162))+P1(f186(a910,a239,f327(f234(a915),x76161),x76162)) % 177.41/177.18 [7769]P23(a915,a915,f327(f327(f7(a915,a915,a915),f23(a915)),x77691),x77692)+P1(f327(f327(f329(a915),f489(x77691,x77692)),x77692)) % 177.41/177.18 [7827]E(f327(f327(f327(f65(a915,x78271,f80(a915)),f327(f16(a915,x78271),f78(a915))),f2(a915)),x78272),f327(f36(x78271),x78272))+~P1(f327(f35(x78271),x78272)) % 177.41/177.18 [7869]P23(a915,a915,f327(f327(f7(a915,a915,a915),f23(a915)),x78691),x78692)+~P1(f327(f327(f234(a915),x78691),f489(x78691,x78692))) % 177.41/177.18 [7924]P35(x79241,x79242)+P1(f327(f327(f234(f922(x79241,a910)),f574(x79242,x79241)),f327(f285(x79241,x79241,x79242),f574(x79242,x79241)))) % 177.41/177.18 [7929]P57(x79291,x79292)+~P35(x79291,f327(f262(f921(x79291,x79291)),f327(f257(x79291,x79291,a910),x79292))) % 177.41/177.18 [7930]P47(x79301,x79302)+~P36(x79301,f327(f262(f921(x79301,x79301)),f327(f257(x79301,x79301,a910),x79302))) % 177.41/177.18 [7931]P48(x79311,x79312)+~P49(x79311,f327(f262(f921(x79311,x79311)),f327(f257(x79311,x79311,a910),x79312))) % 177.41/177.18 [7997]P1(f327(f327(f234(a915),f327(a113,x79971)),x79972))+~P1(f186(a910,a239,f327(f234(a915),x79971),x79972)) % 177.41/177.18 [8054]P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),x80541),x80542)),f307(a915,a317)))+~P1(f327(f327(f234(a915),x80541),x80542)) % 177.41/177.18 [8150]P41(x81501,x81502)+~P50(x81501,f242(f922(x81501,a910)),f327(f262(f921(x81501,x81501)),f327(f257(x81501,x81501,a910),x81502))) % 177.41/177.18 [8205]~P1(f327(f138(x82051),x82052))+P1(f327(f138(f922(x82051,a910)),f327(f327(f155(f916(x82051),f922(x82051,a910)),f173(x82051)),f55(x82051,x82052)))) % 177.41/177.18 [8406]~P35(x84061,f327(f286(x84061,x84061),x84062))+P35(x84061,f327(f286(x84061,x84061),f327(f327(f289(x84061,x84061,x84061),x84062),f307(x84061,x84062)))) % 177.41/177.18 [8504]P24(x85041,a915,f817(x85042,x85041),x85042,f327(f302(a915,f2(a915)),f327(f36(x85041),x85042)))+~P1(f327(f35(x85041),x85042)) % 177.41/177.18 [8505]P24(a915,x85051,f818(x85052,x85051),f327(f302(a915,f2(a915)),f327(f36(x85051),x85052)),x85052)+~P1(f327(f35(x85051),x85052)) % 177.41/177.18 [8522]P24(a915,x85221,f819(x85222,x85221),f303(a915,f78(a915),f327(f36(x85221),x85222)),x85222)+~P1(f327(f35(x85221),x85222)) % 177.41/177.18 [8531]P1(f327(f35(f921(x85311,x85311)),f327(f327(f289(x85311,x85311,x85311),x85312),f307(x85311,x85312))))+~P1(f327(f35(f921(x85311,x85311)),x85312)) % 177.41/177.18 [8558]E(x85581,f2(a1))+P1(f327(f50(x85582,x85581),f327(f327(f252(a1,a1),f327(f327(f37(a1),x85582),x85581)),f46(a1,x85582,x85581)))) % 177.41/177.18 [8571]~P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),x85711),x85712)),f307(a915,a317)))+P1(f327(f327(f234(a915),x85711),x85712)) % 177.41/177.18 [8588]~P81(x85881)+E(f327(f143(x85881,x85881,f327(f7(x85881,x85881,x85881),f80(x85881)),f2(x85881)),f327(f169(x85881),x85882)),f327(f143(x85881,x85881,f80(x85881),f2(x85881)),x85882)) % 177.41/177.18 [8759]~P108(x87591)+E(f327(f143(f916(x87591),x87591,f327(f7(x87591,f916(x87591),f916(x87591)),f149(x87591,x87591,f5(x87591))),f114(x87591)),x87592),f151(x87591,x87591,f5(x87591),x87592)) % 177.41/177.18 [8870]~P55(x88701,f327(f262(f921(x88701,x88701)),f327(f257(x88701,x88701,a910),x88702)))+P55(x88701,f327(f262(f921(x88701,x88701)),f327(f257(x88701,x88701,a910),f243(x88701,x88701,x88702)))) % 177.41/177.18 [8884]P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),x88841),x88842)),f327(f327(f289(a915,a915,a915),a317),f307(a915,a317))))+~P1(f327(f327(f235(a915),x88841),x88842)) % 177.41/177.18 [8930]~P1(f327(f35(f921(x89301,x89301)),f327(f327(f289(x89301,x89301,x89301),x89302),f307(x89301,x89302))))+P1(f327(f35(f921(x89301,x89301)),x89302)) % 177.41/177.18 [8988]~P55(x89881,f327(f262(f921(x89881,x89881)),f327(f257(x89881,x89881,a910),f243(x89881,x89881,x89882))))+P55(x89881,f327(f262(f921(x89881,x89881)),f327(f257(x89881,x89881,a910),x89882))) % 177.41/177.18 [9189]P55(x91891,x91892)+P1(f327(f327(f329(f921(x91891,x91891)),f327(f327(f252(x91891,x91891),f595(x91892,x91891)),f595(x91892,x91891))),f327(f327(f289(x91891,x91891,x91891),x91892),f307(x91891,x91892)))) % 177.41/177.18 [9190]P55(x91901,x91902)+P1(f327(f327(f329(f921(x91901,x91901)),f327(f327(f252(x91901,x91901),f611(x91902,x91901)),f611(x91902,x91901))),f327(f327(f289(x91901,x91901,x91901),x91902),f307(x91901,x91902)))) % 177.41/177.18 [9307]~P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),x93071),x93072)),f327(f327(f289(a915,a915,a915),a317),f307(a915,a317))))+P1(f327(f327(f235(a915),x93071),x93072)) % 177.41/177.18 [5244]~P93(x52441)+E(f327(f327(f80(x52441),f327(f105(x52441),a83)),x52442),x52442) % 177.41/177.18 [5273]~P67(x52731)+E(f327(f327(f80(x52731),f327(f79(x52731),x52732)),x52732),f2(x52731)) % 177.41/177.18 [5274]~P74(x52741)+E(f327(f327(f80(x52741),f327(f79(x52741),x52742)),x52742),f2(x52741)) % 177.41/177.18 [5275]~P86(x52751)+E(f327(f327(f102(x52751),f327(f79(x52751),x52752)),x52752),f242(x52751)) % 177.41/177.18 [5276]~P86(x52761)+E(f327(f327(f103(x52761),f327(f79(x52761),x52762)),x52762),f190(x52761)) % 177.41/177.18 [5309]~P93(x53091)+E(f327(f327(f81(x53091),f327(f105(x53091),a98)),x53092),f327(f79(x53091),x53092)) % 177.41/177.18 [5470]~P114(x54701)+E(f327(f327(f81(x54701),f327(f79(x54701),f78(x54701))),x54702),f327(f79(x54701),x54702)) % 177.41/177.18 [5515]E(f327(f75(a1),x55151),f78(a1))+~E(f327(f75(a1),f327(f327(f81(a1),x55151),x55152)),f78(a1)) % 177.41/177.18 [5607]~P93(x56071)+E(f327(f327(f80(x56071),f78(x56071)),f327(f105(x56071),x56072)),f327(f105(x56071),f327(f327(f23(a1),x56072),a98))) % 177.41/177.18 [5661]~P108(x56611)+E(f14(x56611,f327(f327(f309(x56611),x56612),f190(f922(x56611,a910)))),x56612) % 177.41/177.18 [5662]~P108(x56621)+E(f15(x56621,f327(f327(f309(x56621),x56622),f190(f922(x56621,a910)))),x56622) % 177.41/177.18 [5663]~P96(x56631)+E(f13(x56631,f327(f327(f309(x56631),x56632),f190(f922(x56631,a910)))),x56632) % 177.41/177.18 [5664]~P96(x56641)+E(f10(x56641,f327(f327(f309(x56641),x56642),f190(f922(x56641,a910)))),x56642) % 177.41/177.18 [5665]~P3(x56651)+E(f39(x56651,f327(f327(f309(x56651),x56652),f190(f922(x56651,a910)))),x56652) % 177.41/177.18 [5666]~P3(x56661)+E(f38(x56661,f327(f327(f309(x56661),x56662),f190(f922(x56661,a910)))),x56662) % 177.41/177.18 [5688]E(f327(f327(f80(a915),x56881),f327(f327(f23(a915),x56882),x56881)),x56882)+P1(f327(f327(f235(a915),x56882),x56881)) % 177.41/177.18 [5726]E(x57261,f114(x57262))+P1(f327(f327(f235(a915),f2(a915)),f327(f191(f916(x57262)),x57261))) % 177.41/177.18 [5852]~P108(x58521)+E(f11(x58521,f189(x58521),f327(f327(f309(x58521),x58522),f190(f922(x58521,a910)))),x58522) % 177.41/177.18 [5853]~P108(x58531)+E(f12(x58531,f238(x58531),f327(f327(f309(x58531),x58532),f190(f922(x58531,a910)))),x58532) % 177.41/177.18 [5914]E(f327(f327(f23(a915),x59141),f327(f327(f23(a915),x59141),x59142)),x59142)+~P1(f327(f327(f234(a915),x59142),x59141)) % 177.41/177.18 [5915]E(f327(f327(f80(a915),x59151),f327(f327(f23(a915),x59152),x59151)),x59152)+~P1(f327(f327(f234(a915),x59151),x59152)) % 177.41/177.18 [5937]E(f46(a915,f327(f327(f23(a915),x59371),x59372),x59372),f46(a915,x59371,x59372))+P1(f327(f327(f235(a915),x59371),x59372)) % 177.41/177.18 [5948]E(f327(f79(a1),f327(f327(f37(a1),x59481),f327(f79(a1),x59482))),f293(x59481,x59482))+P1(f327(f327(f234(a1),f2(a1)),x59482)) % 177.41/177.18 [5950]~E(x59502,f2(a915))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f244(a915),x59501),x59502))) % 177.41/177.18 [6004]~P93(x60041)+E(f327(f327(f80(x60041),f327(f79(x60041),f78(x60041))),f327(f105(x60041),x60042)),f327(f105(x60041),f327(f327(f80(a1),x60042),a98))) % 177.41/177.18 [6006]E(f327(f327(f244(a915),f327(f105(a915),x60061)),x60062),f327(f327(f244(a915),f2(a915)),x60062))+~P1(f327(a195,f327(f105(a1),x60061))) % 177.41/177.18 [6113]E(f327(f142(a915),f140(a915,f327(f302(a915,x61131),x61132))),x61131)+~P1(f327(f327(f235(a915),x61131),x61132)) % 177.41/177.18 [6129]E(f327(f327(f81(a915),f327(f105(a915),x61291)),f327(f105(a915),x61292)),f327(f105(a915),f327(f327(f81(a1),x61291),x61292)))+P1(f327(f327(f235(a1),x61291),a83)) % 177.41/177.18 [6135]~P128(x61351)+P1(f327(f327(f234(x61351),f2(x61351)),f327(f327(f81(x61351),x61352),x61352))) % 177.41/177.18 [6147]E(f327(f327(f23(a915),f327(a113,x61471)),x61472),f327(a113,f327(f327(f23(a915),x61471),x61472)))+~P1(f327(f327(f234(a915),x61472),x61471)) % 177.41/177.18 [6151]E(f46(a915,f327(f327(f23(a915),x61511),x61512),x61512),f46(a915,x61511,x61512))+~P1(f327(f327(f234(a915),x61512),x61511)) % 177.41/177.18 [6204]E(f327(f327(f244(a915),f327(a106,x62041)),x62042),f327(a106,f327(f327(f244(a1),x62041),x62042)))+~P1(f327(f327(f234(a1),f2(a1)),x62041)) % 177.41/177.18 [6222]P1(f327(f138(x62221),x62222))+P1(f327(f327(f235(a915),f661(x62222,x62221)),f327(f191(f916(x62221)),x62222))) % 177.41/177.18 [6223]P1(f327(f138(x62231),x62232))+P1(f327(f327(f235(a915),f667(x62232,x62231)),f327(f191(f916(x62231)),x62232))) % 177.41/177.18 [6240]~E(x62401,f114(x62402))+~P1(f327(f327(f235(a915),f2(a915)),f327(f191(f916(x62402)),x62401))) % 177.41/177.18 [6251]E(f145(a915,f140(a915,f327(f302(a915,x62511),x62512))),f327(f327(f23(a915),x62512),f78(a915)))+~P1(f327(f327(f235(a915),x62511),x62512)) % 177.41/177.18 [6254]E(f327(f327(f80(a1),x62541),f327(f101(a1),f327(a113,f381(x62542,x62541)))),x62542)+~P1(f327(f327(f235(a1),x62541),x62542)) % 177.41/177.18 [6261]E(x62611,f2(a915))+E(f327(f327(f81(a915),x62612),f327(f327(f244(a915),x62612),f327(f327(f23(a915),x62611),f78(a915)))),f327(f327(f244(a915),x62612),x62611)) % 177.41/177.18 [6290]E(f327(f327(f81(a915),f327(a106,x62901)),f327(a106,x62902)),f327(a106,f327(f327(f81(a1),x62901),x62902)))+~P1(f327(f327(f234(a1),f2(a1)),x62901)) % 177.41/177.18 [6291]E(f327(f327(f37(a915),f327(a106,x62911)),f327(a106,x62912)),f327(a106,f327(f327(f37(a1),x62911),x62912)))+~P1(f327(f327(f234(a1),f2(a1)),x62911)) % 177.41/177.18 [6306]~P112(x63061)+E(f327(f327(f80(x63061),x63062),x63062),f327(f327(f81(x63061),f327(f327(f80(x63061),f78(x63061)),f78(x63061))),x63062)) % 177.41/177.18 [6328]E(f327(f327(f23(a1),f327(f101(a1),x63281)),f327(f101(a1),x63282)),f327(f101(a1),f327(f327(f23(a915),x63281),x63282)))+~P1(f327(f327(f234(a915),x63282),x63281)) % 177.41/177.18 [6330]E(f327(f327(f252(a1,a1),f327(f105(a1),a98)),f327(f327(f80(a1),x63301),x63302)),f51(x63301,x63302))+~P1(f327(f327(f234(a1),x63302),f2(a1))) % 177.41/177.18 [6363]E(f180(x63631,x63632),f114(f916(x63631)))+P1(f327(f327(f329(f916(x63631)),f660(x63632,x63631)),f327(f173(f916(x63631)),x63632))) % 177.41/177.18 [6373]E(f117(a1,f327(f130(a1),x63731),f129(x63732,f327(f327(f80(a1),x63731),f78(a1)))),f129(x63732,x63731))+P1(f327(f327(f235(a1),x63732),x63731)) % 177.41/177.18 [6448]E(f327(f327(f152(a1),x64481),f179(f327(f327(f80(a1),x64481),f78(a1)),x64482)),f179(x64481,x64482))+~P1(f327(f327(f234(a1),x64481),x64482)) % 177.41/177.18 [6489]~P1(f327(f327(f235(a915),x64892),x64891))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f23(a915),x64891),x64892))) % 177.41/177.18 [6521]~P1(f327(f327(f235(a915),x65211),f327(a106,x65212)))+P1(f327(f327(f235(a1),f327(f101(a1),x65211)),x65212)) % 177.41/177.18 [6550]~P108(x65501)+E(f327(f327(f102(f922(x65501,a910)),f327(f282(x65501),x65502)),f327(f327(f309(x65501),x65502),f190(f922(x65501,a910)))),f327(f301(x65501),x65502)) % 177.41/177.18 [6551]~P1(f327(f327(f234(a1),f2(a1)),x65511))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f244(a1),x65511),x65512))) % 177.41/177.18 [6554]~P1(f327(f327(f235(a915),f2(a915)),x65541))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f244(a915),x65541),x65542))) % 177.41/177.18 [6581]~E(f327(x65811,f2(a915)),f2(a915))+E(f327(f327(f6(a915,a915),x65811),f303(a915,f327(a113,f2(a915)),x65812)),f327(f327(f6(a915,a915),x65811),f303(a915,f2(a915),x65812))) % 177.41/177.18 [6644]~P93(x66441)+E(f327(f327(f81(x66441),f327(f327(f80(x66441),f78(x66441)),f78(x66441))),f327(f105(x66441),x66442)),f327(f105(x66441),f327(f327(f80(a1),x66442),x66442))) % 177.41/177.18 [6661]E(f327(f327(f309(a1),x66611),f303(a1,f327(f327(f80(a1),x66611),f78(a1)),x66612)),f303(a1,x66611,x66612))+P1(f327(f327(f235(a1),x66612),x66611)) % 177.41/177.18 [6662]P1(f327(f327(f235(a915),x66621),f327(a106,x66622)))+~P1(f327(f327(f235(a1),f327(f101(a1),x66621)),x66622)) % 177.41/177.18 [6766]E(f327(a106,f327(f327(f37(a1),f327(f105(a1),x67661)),f327(f105(a1),x67662))),f327(f327(f37(a915),f327(f105(a915),x67661)),f327(f105(a915),x67662)))+P1(f327(a195,f327(f105(a1),x67661))) % 177.41/177.18 [6824]P1(f327(f327(f235(a915),x68241),x68242))+~P1(f327(f327(f235(a915),f2(a915)),f327(f327(f23(a915),x68242),x68241))) % 177.41/177.18 [6868]P1(f327(f327(f235(a915),f2(a915)),x68681))+~P1(f327(f327(f235(a915),f2(a915)),f327(f327(f81(a915),x68682),x68681))) % 177.41/177.18 [6869]P1(f327(f327(f235(a915),f2(a915)),x68691))+~P1(f327(f327(f235(a915),f2(a915)),f327(f327(f81(a915),x68691),x68692))) % 177.41/177.18 [6887]~P1(f327(f327(f234(a1),x68871),f2(a1)))+E(f327(f327(f81(a915),f327(a106,f327(f79(a1),x68871))),f327(a106,f327(f79(a1),x68872))),f327(a106,f327(f327(f81(a1),x68871),x68872))) % 177.41/177.18 [6945]~E(x69452,f190(f922(x69451,a910)))+P1(f327(f327(f234(f922(x69451,a910)),x69452),f327(f79(f922(x69451,a910)),x69452))) % 177.41/177.18 [7007]~P93(x70071)+E(f327(f327(f80(x70071),f327(f327(f80(x70071),f2(x70071)),f327(f105(x70071),x70072))),f327(f105(x70071),x70072)),f327(f105(x70071),f327(f327(f80(a1),x70072),x70072))) % 177.41/177.18 [7063]~P1(f327(f327(f235(a1),x70631),x70632))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x70631),f78(a1))),x70632)) % 177.41/177.18 [7130]E(x71301,f2(a915))+~P1(f327(f327(f234(a1),f327(f101(a1),x71302)),f327(f79(a1),f327(f101(a1),x71301)))) % 177.41/177.18 [7131]E(x71311,f2(a915))+~P1(f327(f327(f234(a1),f327(f101(a1),x71311)),f327(f79(a1),f327(f101(a1),x71312)))) % 177.41/177.18 [7235]E(f327(f327(f252(a1,a1),f327(f105(a1),a98)),f327(f327(f80(a1),x72351),x72352)),f51(x72351,x72352))+~P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),x72351),x72352))) % 177.41/177.18 [7279]~P25(x72791,x72792)+P35(x72791,f327(f251(f922(f921(x72791,x72791),a910),f922(f921(x72791,x72791),a910)),x72792)) % 177.41/177.18 [7298]~P1(f327(f327(f234(a915),f327(a113,f2(a915))),x72981))+P1(f327(f327(f234(a915),f327(a113,f2(a915))),f327(f327(f244(a915),x72981),x72982))) % 177.41/177.18 [7478]~P1(f327(f327(f234(a1),x74781),x74782))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x74781),x74781)),f327(f327(f80(a1),x74782),x74782))) % 177.41/177.18 [7483]~P1(f327(f327(f235(a1),x74831),x74832))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x74831),x74831)),f327(f327(f80(a1),x74832),x74832))) % 177.41/177.18 [7540]~P1(f327(f327(f235(a915),f2(a915)),x75401))+P1(f327(f327(f235(a915),f327(f327(f23(a915),x75401),f327(a113,x75402))),x75401)) % 177.41/177.18 [7572]P1(f327(f327(f234(a915),f327(a113,f2(a915))),x75721))+~P1(f327(f327(f234(a915),f327(a113,f2(a915))),f327(f327(f81(a915),x75722),x75721))) % 177.41/177.18 [7573]P1(f327(f327(f234(a915),f327(a113,f2(a915))),x75731))+~P1(f327(f327(f234(a915),f327(a113,f2(a915))),f327(f327(f81(a915),x75731),x75732))) % 177.41/177.18 [7577]P1(f327(f327(f234(a915),f327(f327(f165(a915),x75771),x75772)),f327(f166(a915),x75771)))+~P1(f327(f327(f235(a915),x75772),f327(f191(f916(a915)),x75771))) % 177.41/177.18 [7615]P1(f327(f327(f235(a1),x76151),x76152))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),x76151),f78(a1))),x76152)) % 177.41/177.18 [7657]P1(f327(f35(x76571),f242(f922(x76571,a910))))+~P1(f327(f35(f922(x76572,x76571)),f242(f922(f922(x76572,x76571),a910)))) % 177.41/177.18 [7658]P1(f327(f35(x76581),f242(f922(x76581,a910))))+~P1(f327(f35(f920(x76582,x76581)),f242(f922(f920(x76582,x76581),a910)))) % 177.41/177.18 [7659]P1(f327(f35(x76591),f242(f922(x76591,a910))))+~P1(f327(f35(f920(x76591,x76592)),f242(f922(f920(x76591,x76592),a910)))) % 177.41/177.18 [7697]E(x76971,f190(f922(x76972,a910)))+~P1(f327(f327(f234(f922(x76972,a910)),x76971),f327(f79(f922(x76972,a910)),x76971))) % 177.41/177.18 [7837]E(f327(f143(f916(x78371),f916(x78371),f135(x78371),f114(x78371)),x78372),f114(x78371))+P1(f327(f327(f329(f916(x78371)),f692(x78372,x78371)),f327(f173(f916(x78371)),x78372))) % 177.41/177.18 [7838]E(f327(f143(f916(x78381),f916(x78381),f135(x78381),f114(x78381)),x78382),f114(x78381))+P1(f327(f327(f329(f916(x78381)),f693(x78382,x78381)),f327(f173(f916(x78381)),x78382))) % 177.41/177.18 [8072]P1(f327(f327(f234(a1),x80721),x80722))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),x80721),x80721)),f327(f327(f80(a1),x80722),x80722))) % 177.41/177.18 [8077]P1(f327(f327(f235(a1),x80771),x80772))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),x80771),x80771)),f327(f327(f80(a1),x80772),x80772))) % 177.41/177.18 [8170]~P112(x81701)+E(f327(f327(f81(x81701),f327(f327(f80(x81701),f78(x81701)),f78(x81701))),f327(f327(f6(a915,x81701),f101(x81701)),f303(a915,f78(a915),x81702))),f327(f327(f81(x81701),f327(f101(x81701),x81702)),f327(f327(f80(x81701),f327(f101(x81701),x81702)),f78(x81701)))) % 177.41/177.18 [8219]P1(f327(f327(f329(a915),x82191),x82192))+~P1(f327(f327(f329(a1),f327(f101(a1),x82191)),f327(f310(a915,a1,f101(a1)),x82192))) % 177.41/177.18 [8378]~P1(f327(f35(x83781),x83782))+E(f327(f310(a915,x83781,f490(x83782,x83781)),f327(f262(a915),f327(f327(f7(a915,a915,a910),f235(a915)),f491(x83782,x83781)))),x83782) % 177.41/177.18 [8656]P51(x86561,x86562)+P1(f327(f327(f329(f921(x86561,x86561)),f327(f327(f252(x86561,x86561),f514(x86562,x86561)),f514(x86562,x86561))),x86562)) % 177.41/177.18 [8657]P36(x86571,x86572)+P1(f327(f327(f329(f921(x86571,x86571)),f327(f327(f252(x86571,x86571),f784(x86572,x86571)),f787(x86572,x86571))),x86572)) % 177.41/177.18 [8658]P36(x86581,x86582)+P1(f327(f327(f329(f921(x86581,x86581)),f327(f327(f252(x86581,x86581),f787(x86582,x86581)),f788(x86582,x86581))),x86582)) % 177.41/177.18 [8659]P37(x86591,x86592)+P1(f327(f327(f329(f921(x86591,x86591)),f327(f327(f252(x86591,x86591),f702(x86592,x86591)),f701(x86592,x86591))),x86592)) % 177.41/177.18 [8660]P37(x86601,x86602)+P1(f327(f327(f329(f921(x86601,x86601)),f327(f327(f252(x86601,x86601),f701(x86602,x86601)),f702(x86602,x86601))),x86602)) % 177.41/177.18 [8661]P49(x86611,x86612)+P1(f327(f327(f329(f921(x86611,x86611)),f327(f327(f252(x86611,x86611),f798(x86612,x86611)),f800(x86612,x86611))),x86612)) % 177.41/177.18 [8802]~P93(x88021)+E(f327(f327(f23(x88021),f78(x88021)),f327(f105(x88021),x88022)),f327(f105(x88021),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f79(a1),x88022)))) % 177.41/177.18 [8927]~P1(f327(f327(f235(f922(a915,a910)),x89271),x89272))+P1(f327(f327(f235(f922(a1,a910)),f327(f310(a915,a1,f101(a1)),x89271)),f327(f310(a915,a1,f101(a1)),x89272))) % 177.41/177.18 [8961]~P1(f327(f327(f235(a1),x89611),x89612))+P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x89611),x89611)),a98)),f327(f327(f80(a1),x89612),x89612))) % 177.41/177.18 [8963]~P1(f327(f327(f235(a1),x89631),x89632))+P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x89631),x89631)),a98)),f327(f327(f80(a1),x89632),x89632))) % 177.41/177.18 [9036]~P1(f327(f327(f329(a915),x90361),f327(f173(a915),x90362)))+P1(f327(f327(f234(a915),x90361),f327(f143(a915,a915,f80(a915),f2(a915)),x90362))) % 177.41/177.18 [9129]P44(x91291,x91292)+~P1(f327(f327(f329(f921(x91291,x91291)),f327(f327(f252(x91291,x91291),f516(x91292,x91291)),f516(x91292,x91291))),x91292)) % 177.41/177.18 [9130]P36(x91301,x91302)+~P1(f327(f327(f329(f921(x91301,x91301)),f327(f327(f252(x91301,x91301),f784(x91302,x91301)),f788(x91302,x91301))),x91302)) % 177.41/177.18 [9131]P49(x91311,x91312)+~P1(f327(f327(f329(f921(x91311,x91311)),f327(f327(f252(x91311,x91311),f800(x91312,x91311)),f798(x91312,x91311))),x91312)) % 177.41/177.18 [9270]~P1(f327(f327(f234(f922(a1,a910)),f327(f310(a915,a1,f101(a1)),x92701)),f327(f310(a915,a1,f101(a1)),x92702)))+P1(f327(f327(f234(f922(a915,a910)),x92701),x92702)) % 177.41/177.18 [9271]~P1(f327(f327(f235(f922(a1,a910)),f327(f310(a915,a1,f101(a1)),x92711)),f327(f310(a915,a1,f101(a1)),x92712)))+P1(f327(f327(f235(f922(a915,a910)),x92711),x92712)) % 177.41/177.18 [9355]P1(f327(f327(f235(a1),x93551),x93552))+~P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x93551),x93551)),a98)),f327(f327(f80(a1),x93552),x93552))) % 177.41/177.18 [9357]P1(f327(f327(f235(a1),x93571),x93572))+~P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x93571),x93571)),a98)),f327(f327(f80(a1),x93572),x93572))) % 177.41/177.18 [10247]~P104(x102471)+E(f117(f916(x102471),f327(f130(f916(x102471)),f114(x102471)),f327(f327(f327(f97(f917(f916(x102471))),f327(f327(f235(a1),f2(a1)),x102472)),f327(f119(f921(x102471,f916(x102471)),f916(x102471),f132(x102471,f916(x102471),f133(x102471,f327(f327(f23(a1),x102472),f78(a1))),f133(f916(x102471),f327(f327(f23(a1),x102472),f78(a1))))),f327(f257(x102471,f916(x102471),f917(f916(x102471))),f327(f327(f8(f922(f916(x102471),f916(x102471)),f922(f916(x102471),f917(f916(x102471))),x102471),f327(f8(f916(x102471),f917(f916(x102471)),f916(x102471)),f130(f916(x102471)))),f152(x102471))))),f116(f916(x102471)))),f133(f916(x102471),x102472)) % 177.41/177.18 [10269]~P1(f327(f35(x102691),x102692))+E(f327(f191(f916(x102691)),f90(f916(x102691),f327(f327(f18(f916(x102691),a910,a910),f327(f327(f8(a910,f922(a910,a910),f916(x102691)),a325),f327(f327(f7(f916(x102691),f922(x102691,a910),a910),f327(f327(f8(f922(x102691,a910),f922(f922(x102691,a910),a910),f916(x102691)),a324),f173(x102691))),x102692))),f138(x102691)))),f216(x102691,x102692)) % 177.41/177.18 [6250]E(f327(f327(f80(a915),f327(f327(f23(a915),x62501),x62502)),x62502),x62501)+~P1(f327(f327(f234(a915),x62502),x62501)) % 177.41/177.18 [6324]E(f327(f327(f37(a915),f327(f327(f81(a915),x63241),x63242)),x63242),x63241)+~P1(f327(f327(f235(a915),f2(a915)),x63242)) % 177.41/177.18 [6325]E(f327(f327(f37(a915),f327(f327(f81(a915),x63251),x63252)),x63251),x63252)+~P1(f327(f327(f235(a915),f2(a915)),x63251)) % 177.41/177.18 [6329]~P68(x63291)+E(f327(f327(f6(a915,x63291),f327(f165(x63291),x63292)),f327(f302(a915,f2(a915)),f327(f191(f916(x63291)),x63292))),f327(f166(x63291),x63292)) % 177.41/177.18 [6440]E(f46(a915,f327(a113,f327(f327(f81(a915),x64401),x64402)),x64401),f78(a915))+~P1(f327(f327(f235(a915),f78(a915)),x64401)) % 177.41/177.18 [6446]E(f327(a113,f327(f327(f80(a915),f327(f105(a915),x64461)),x64462)),f327(f327(f80(a915),f78(a915)),x64462))+~P1(f327(a195,f327(f105(a1),x64461))) % 177.41/177.18 [6475]E(f327(a106,f327(f327(f244(a1),f327(f105(a1),x64751)),x64752)),f327(f327(f244(a915),f327(f105(a915),x64751)),x64752))+P1(f327(a195,f327(f105(a1),x64751))) % 177.41/177.18 [6716]E(f327(f327(f23(a915),x67161),f327(f105(a915),f327(f327(f80(a1),x67162),a98))),f327(f327(f23(a915),f327(a113,x67161)),f327(f105(a915),x67162)))+~P1(f327(f327(f235(a1),a83),x67162)) % 177.41/177.18 [6796]E(x67961,f2(a915))+E(f327(a113,f327(f327(f80(a915),f327(f327(f23(a915),x67961),f78(a915))),x67962)),f327(f327(f80(a915),x67961),x67962)) % 177.41/177.18 [6837]E(x68371,f2(a1))+P1(f327(f327(f235(a1),f2(a1)),f327(f327(f244(a1),f327(f75(a1),x68371)),x68372))) % 177.41/177.18 [6852]~E(x68522,f2(a915))+P1(f327(f327(f235(a1),f2(a1)),f327(f327(f244(a1),f327(f75(a1),x68521)),x68522))) % 177.41/177.18 [6890]E(x68901,f2(a915))+E(f327(f327(f80(a915),x68902),f327(f327(f81(a915),f327(f327(f23(a915),x68901),f78(a915))),x68902)),f327(f327(f81(a915),x68901),x68902)) % 177.41/177.18 [6938]~P1(f327(f327(f234(a1),x69381),x69382))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x69381),a98)),x69382)) % 177.41/177.18 [7067]E(f327(f327(f152(a915),x70671),f140(a915,f327(f302(a915,f327(a113,x70671)),x70672))),f140(a915,f327(f302(a915,x70671),x70672)))+~P1(f327(f327(f235(a915),x70671),x70672)) % 177.41/177.18 [7270]E(x72701,x72702)+~E(f327(f327(f23(a1),f327(f327(f80(a1),x72701),x72701)),a98),f327(f327(f23(a1),f327(f327(f80(a1),x72702),x72702)),a98)) % 177.41/177.18 [7273]E(x72731,f114(x72732))+E(f266(x72732,f327(f327(f155(x72732,f921(a100,x72732)),f327(f252(a100,x72732),f78(a100))),x72731)),f275(x72732,x72731)) % 177.41/177.18 [7511]P1(f327(f327(f234(a1),x75111),x75112))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),x75111),a98)),x75112)) % 177.41/177.18 [7977]~P1(f327(f327(f235(a915),x79771),x79772))+P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),x79771),x79772)),a240)) % 177.41/177.18 [8196]~P1(f327(f327(f235(a100),f2(a100)),x81961))+P1(f327(f327(f235(a100),f327(f251(a100,f921(a100,a100)),f327(f267(x81961),x81962))),x81961)) % 177.41/177.18 [8459]~P36(x84591,x84592)+P36(x84591,f327(f327(f102(f922(f921(x84591,x84591),a910)),x84592),f307(x84591,f190(f922(f921(x84591,x84591),a910))))) % 177.41/177.18 [8460]~P37(x84601,x84602)+P37(x84601,f327(f327(f102(f922(f921(x84601,x84601),a910)),x84602),f307(x84601,f190(f922(f921(x84601,x84601),a910))))) % 177.41/177.18 [8508]~P84(x85081)+P1(f327(f327(f234(x85081),f327(f75(x85081),f327(f166(x85081),x85082))),f327(f166(x85081),f327(f327(f155(x85081,x85081),f75(x85081)),x85082)))) % 177.41/177.18 [8533]P1(f327(f327(f235(a915),x85331),x85332))+~P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),x85331),x85332)),a240)) % 177.41/177.18 [8680]E(f327(f327(f252(x86801,x86801),f610(x86802,x86801)),f610(x86802,x86801)),x86802)+~P1(f327(f327(f329(f921(x86801,x86801)),x86802),f307(x86801,f190(f922(f921(x86801,x86801),a910))))) % 177.41/177.18 [8724]E(f327(f302(a915,x87241),f327(f327(f80(a915),x87241),f327(f36(a915),x87242))),x87242)+~P1(f327(f327(f234(f922(a915,a910)),x87242),f327(f302(a915,x87241),f327(f327(f80(a915),x87241),f327(f36(a915),x87242))))) % 177.41/177.18 [8954]P37(x89541,x89542)+~P37(x89541,f327(f327(f102(f922(f921(x89541,x89541),a910)),x89542),f307(x89541,f190(f922(f921(x89541,x89541),a910))))) % 177.41/177.18 [9080]E(f327(f327(f37(a1),f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),x90801),x90801)),a98))),f327(f105(a1),f327(f327(f80(a1),x90802),x90802))),f327(f327(f37(a1),f327(f105(a1),x90801)),f327(f105(a1),x90802)))+~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x90802))) % 177.41/177.18 [9174]~P36(x91741,x91742)+P1(f327(f327(f234(f922(f921(x91741,x91741),a910)),f327(f327(f289(x91741,x91741,x91741),x91742),x91742)),x91742)) % 177.41/177.18 [9200]E(f178(f916(x92001),f327(f327(f8(a910,a910,f916(x92001)),a322),f327(f327(f7(f916(x92001),f916(x92001),a910),a324),f114(x92001))),x92002),f180(x92001,f180(x92001,x92002)))+~P11(a915,f327(f169(a915),f327(f327(f155(f916(x92001),a915),f191(f916(x92001))),x92002))) % 177.41/177.18 [9203]E(f327(f327(f37(a1),f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92031),x92031)),a98))),f327(f105(a1),f327(f327(f80(a1),x92032),x92032))),f327(f327(f37(a1),f327(f327(f80(a1),f327(f105(a1),x92031)),f78(a1))),f327(f105(a1),x92032)))+P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x92032))) % 177.41/177.18 [10041]P1(f327(a195,x100412))+E(f327(f327(f86(a1,a915),f327(f327(f23(a1),x100411),x100412)),f327(f327(f18(a1,a915,a915),f327(f327(f7(a1,a915,f922(a915,a915)),f327(f327(f8(a910,f922(a915,f922(a915,a915)),a1),f97(a915)),a195)),f2(a915))),a106)),f327(f327(f23(a915),f327(a106,x100411)),f327(a106,x100412))) % 177.41/177.18 [10049]E(f327(f327(f86(a1,a915),f327(f105(a1),f327(f327(f80(a1),x100491),f327(f79(a1),x100492)))),f327(f327(f18(a1,a915,a915),f327(f327(f7(a1,a915,f922(a915,a915)),f327(f327(f8(a910,f922(a915,f922(a915,a915)),a1),f97(a915)),a195)),f2(a915))),a106)),f327(f327(f23(a915),f327(f105(a915),x100491)),f327(f105(a915),x100492)))+P1(f327(f327(f235(a1),x100492),a83)) % 177.41/177.18 [10050]~P25(x100501,x100502)+P1(f327(f327(f234(f922(f921(x100501,x100501),a910)),f327(f327(f289(x100501,x100501,x100501),f327(f251(f922(f921(x100501,x100501),a910),f922(f921(x100501,x100501),a910)),x100502)),f327(f256(f922(f921(x100501,x100501),a910),f922(f921(x100501,x100501),a910)),x100502))),f327(f251(f922(f921(x100501,x100501),a910),f922(f921(x100501,x100501),a910)),x100502))) % 177.41/177.18 [10106]~E(f327(f36(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,f922(a915,a910),a910),f329(a915)),x101061))),f327(f327(f7(a915,a915,a910),f235(a915)),f327(a113,x101062))))),f2(a915))+~P1(f327(f327(f329(a915),f2(a915)),x101061)) % 177.41/177.18 [10117]E(f299(a915,f327(f327(f18(a915,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),a915),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),a915),f327(f8(a910,f922(a910,a910),a915),a325)),f287(a915)))),f327(f327(f8(f922(a915,a910),f922(a915,a910),a915),f327(f8(a910,a910,a915),a322)),f327(f7(a915,a915,a910),f287(a915)))),x101171,x101172),f190(f922(a915,a910)))+~P1(f327(f327(f287(a915),x101172),x101171)) % 177.41/177.18 [10122]E(f297(a915,f287(a915),f327(f327(f18(a915,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),a915),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),a915),f327(f8(a910,f922(a910,a910),a915),a325)),f287(a915)))),f327(f327(f8(f922(a915,a910),f922(a915,a910),a915),f327(f8(a910,a910,a915),a322)),f327(f7(a915,a915,a910),f287(a915)))),x101221,x101222),f190(f922(a915,a910)))+P1(f327(f327(f287(a915),x101221),x101222)) % 177.41/177.18 [10123]E(f300(a915,f287(a915),f327(f327(f18(a915,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),a915),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),a915),f327(f8(a910,f922(a910,a910),a915),a325)),f287(a915)))),f327(f327(f8(f922(a915,a910),f922(a915,a910),a915),f327(f8(a910,a910,a915),a322)),f327(f7(a915,a915,a910),f287(a915)))),x101231,x101232),f190(f922(a915,a910)))+P1(f327(f327(f287(a915),x101231),x101232)) % 177.41/177.18 [10127]E(f297(a915,f287(a915),f327(f327(f18(a915,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),a915),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),a915),f327(f8(a910,f922(a910,a910),a915),a325)),f287(a915)))),f327(f327(f8(f922(a915,a910),f922(a915,a910),a915),f327(f8(a910,a910,a915),a322)),f327(f7(a915,a915,a910),f287(a915)))),x101271,x101272),f190(f922(a915,a910)))+~P1(f327(f327(f287(a915),x101272),x101271)) % 177.41/177.18 [10129]E(f300(a915,f287(a915),f327(f327(f18(a915,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),a915),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),a915),f327(f8(a910,f922(a910,a910),a915),a325)),f287(a915)))),f327(f327(f8(f922(a915,a910),f922(a915,a910),a915),f327(f8(a910,a910,a915),a322)),f327(f7(a915,a915,a910),f287(a915)))),x101291,x101292),f190(f922(a915,a910)))+~P1(f327(f327(f287(a915),x101292),x101291)) % 177.41/177.18 [10172]E(f46(a1,f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),x101721),x101721)),a98)),f327(f105(a1),f327(f327(f80(a1),x101722),x101722))),f327(f327(f80(a1),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f46(a1,f327(f105(a1),x101721),f327(f105(a1),x101722)))),f78(a1)))+~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x101722))) % 177.41/177.18 [10181]E(f46(a1,f327(f105(a1),f327(f327(f23(a1),f327(f327(f80(a1),x101811),x101811)),a98)),f327(f105(a1),f327(f327(f80(a1),x101812),x101812))),f327(f327(f23(a1),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f46(a1,f327(f327(f80(a1),f327(f105(a1),x101811)),f78(a1)),f327(f105(a1),x101812)))),f78(a1)))+P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x101812))) % 177.41/177.18 [10236]~P3(x102361)+E(f38(x102361,f327(f262(x102361),f327(f327(f8(f922(x102361,a910),a910,x102361),f88(x102361)),f327(f327(f8(f922(x102361,a910),f922(x102361,a910),x102361),f327(f18(x102361,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102361),a330),f327(f327(f7(x102361,f922(x102361,a910),a910),f329(x102361)),x102362)))),f234(x102361))))),f39(x102361,x102362)) % 177.41/177.18 [10262]~P35(x102621,x102622)+P57(x102621,f327(f327(f7(x102621,f922(f921(x102621,x102621),a910),f922(x102621,a910)),f327(f327(f8(f922(x102621,f922(f922(f921(x102621,x102621),a910),a910)),f922(f922(f921(x102621,x102621),a910),f922(x102621,a910)),x102621),f7(x102621,f922(f921(x102621,x102621),a910),a910)),f327(f327(f8(f922(x102621,f921(x102621,x102621)),f922(x102621,f922(f922(f921(x102621,x102621),a910),a910)),x102621),f327(f8(f921(x102621,x102621),f922(f922(f921(x102621,x102621),a910),a910),x102621),f329(f921(x102621,x102621)))),f252(x102621,x102621)))),x102622)) % 177.41/177.18 [10263]~P6(x102631,f242(f922(x102631,a910)),x102632)+P5(x102631,f327(f327(f7(x102631,f922(f921(x102631,x102631),a910),f922(x102631,a910)),f327(f327(f8(f922(x102631,f922(f922(f921(x102631,x102631),a910),a910)),f922(f922(f921(x102631,x102631),a910),f922(x102631,a910)),x102631),f7(x102631,f922(f921(x102631,x102631),a910),a910)),f327(f327(f8(f922(x102631,f921(x102631,x102631)),f922(x102631,f922(f922(f921(x102631,x102631),a910),a910)),x102631),f327(f8(f921(x102631,x102631),f922(f922(f921(x102631,x102631),a910),a910),x102631),f329(f921(x102631,x102631)))),f252(x102631,x102631)))),x102632)) % 177.41/177.18 [10307]P35(x103071,x103072)+~P57(x103071,f327(f327(f7(x103071,f922(f921(x103071,x103071),a910),f922(x103071,a910)),f327(f327(f8(f922(x103071,f922(f922(f921(x103071,x103071),a910),a910)),f922(f922(f921(x103071,x103071),a910),f922(x103071,a910)),x103071),f7(x103071,f922(f921(x103071,x103071),a910),a910)),f327(f327(f8(f922(x103071,f921(x103071,x103071)),f922(x103071,f922(f922(f921(x103071,x103071),a910),a910)),x103071),f327(f8(f921(x103071,x103071),f922(f922(f921(x103071,x103071),a910),a910),x103071),f329(f921(x103071,x103071)))),f252(x103071,x103071)))),x103072)) % 177.41/177.18 [10308]P6(x103081,f242(f922(x103081,a910)),x103082)+~P5(x103081,f327(f327(f7(x103081,f922(f921(x103081,x103081),a910),f922(x103081,a910)),f327(f327(f8(f922(x103081,f922(f922(f921(x103081,x103081),a910),a910)),f922(f922(f921(x103081,x103081),a910),f922(x103081,a910)),x103081),f7(x103081,f922(f921(x103081,x103081),a910),a910)),f327(f327(f8(f922(x103081,f921(x103081,x103081)),f922(x103081,f922(f922(f921(x103081,x103081),a910),a910)),x103081),f327(f8(f921(x103081,x103081),f922(f922(f921(x103081,x103081),a910),a910),x103081),f329(f921(x103081,x103081)))),f252(x103081,x103081)))),x103082)) % 177.41/177.18 [7458]E(f327(f327(f80(a915),f327(f105(a915),f327(f327(f23(a1),x74581),a98))),x74582),f327(a113,f327(f327(f80(a915),f327(f105(a915),x74581)),x74582)))+P1(f327(a195,f327(f105(a1),x74581))) % 177.41/177.18 [7895]~P93(x78951)+E(f327(f327(f80(x78951),f327(f327(f80(x78951),f78(x78951)),f327(f105(x78951),x78952))),f327(f105(x78951),x78952)),f327(f105(x78951),f327(f327(f23(a1),f327(f327(f80(a1),x78952),x78952)),a98))) % 177.41/177.18 [8535]~P1(f327(f327(f234(a1),x85351),x85352))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x85351),x85351)),f327(f327(f23(a1),f327(f327(f80(a1),x85352),x85352)),a98))) % 177.41/177.18 [8537]~P1(f327(f327(f234(a1),x85371),x85372))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x85371),x85371)),f327(f327(f23(a1),f327(f327(f80(a1),x85372),x85372)),a98))) % 177.41/177.18 [8965]P1(f327(f327(f234(a1),x89651),x89652))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),x89651),x89651)),f327(f327(f23(a1),f327(f327(f80(a1),x89652),x89652)),a98))) % 177.41/177.18 [8967]P1(f327(f327(f234(a1),x89671),x89672))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),x89671),x89671)),f327(f327(f23(a1),f327(f327(f80(a1),x89672),x89672)),a98))) % 177.41/177.18 [9259]~P1(f327(f327(f234(a1),x92591),x92592))+P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92591),x92591)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),x92592),x92592)),a98))) % 177.41/177.18 [9261]~P1(f327(f327(f235(a1),x92611),x92612))+P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x92611),x92611)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),x92612),x92612)),a98))) % 177.41/177.18 [9527]P1(f327(f327(f234(a1),x95271),x95272))+~P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),x95271),x95271)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),x95272),x95272)),a98))) % 177.41/177.18 [9529]P1(f327(f327(f235(a1),x95291),x95292))+~P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),x95291),x95291)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),x95292),x95292)),a98))) % 177.41/177.18 [9562]~P1(f327(f35(x95621),x95622))+P1(f327(f35(f922(x95621,a910)),f327(f262(f922(x95621,a910)),f327(f327(f7(f922(x95621,a910),f922(x95621,a910),a910),f234(f922(x95621,a910))),x95622)))) % 177.41/177.18 [9613]~E(f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),x96131),f190(f922(f921(a915,a915),a910)))),f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),x96132),f190(f922(f921(a915,a915),a910)))))+P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),x96131),x96132)),a110)) % 177.41/177.18 [9700]E(f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),x97001),f190(f922(f921(a915,a915),a910)))),f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),x97002),f190(f922(f921(a915,a915),a910)))))+~P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),x97001),x97002)),a110)) % 177.41/177.18 [9737]P1(f327(f327(f234(a1),f2(a1)),f634(x97371,x97372)))+E(f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x97371)),f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x97372))) % 177.41/177.18 [10246]~P3(x102461)+E(f39(x102461,f327(f262(x102461),f327(f327(f8(f922(x102461,a910),a910,x102461),f88(x102461)),f327(f327(f8(f922(x102461,a910),f922(x102461,a910),x102461),f327(f18(x102461,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102461),a330),f327(f327(f7(x102461,f922(x102461,a910),a910),f329(x102461)),x102462)))),f327(f7(x102461,x102461,a910),f234(x102461)))))),f38(x102461,x102462)) % 177.41/177.18 [10268]P1(f327(f327(f329(a915),f2(a915)),x102681))+E(f327(f36(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,f922(a915,a910),a910),f327(f327(f8(a915,f922(f922(a915,a910),a910),a915),f329(a915)),a113)),x102681))),f327(f327(f7(a915,a915,a910),f235(a915)),x102682)))),f327(f36(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,f922(a915,a910),a910),f329(a915)),x102681))),f327(f327(f7(a915,a915,a910),f235(a915)),f327(a113,x102682)))))) % 177.41/177.18 [7763]~P93(x77631)+E(f327(f327(f81(x77631),x77632),f327(f105(x77631),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),x77632) % 177.41/177.18 [8024]~P93(x80241)+E(f327(f327(f80(x80241),f327(f105(x80241),x80242)),f78(x80241)),f327(f105(x80241),f327(f327(f80(a1),x80242),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))) % 177.41/177.18 [8168]P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x81682)))+E(f327(f327(f244(a1),x81681),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),x81682),x81682)),a98))),f78(a1)) % 177.41/177.18 [9589]~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x95892)))+E(f327(f327(f244(a1),x95891),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),x95892),x95892)),a98))),f327(f327(f86(a1,a1),f327(f327(f244(a1),x95891),f327(f105(a915),x95892))),f327(f327(f18(a1,a1,a1),f327(f327(f8(a1,f922(a1,a1),a1),f81(a1)),f327(f81(a1),x95891))),f5(a1)))) % 177.41/177.18 [9959]~P1(f327(f327(f234(a915),f646(x99592,x99591)),f327(x99591,f646(x99592,x99591))))+P1(f327(f35(a915),f327(f262(a915),f327(f327(f7(a915,a915,a910),f327(f327(f8(a915,f922(a915,a910),a915),f234(a915)),x99591)),x99592)))) % 177.41/177.18 [10096]~P1(f327(f327(f234(a915),f327(f105(a915),x100961)),f327(a113,x100962)))+P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x100961),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),f234(a915)),a106)),x100962)))) % 177.41/177.18 [10097]~P1(f327(f327(f235(a915),f327(f105(a915),x100971)),f327(a113,x100972)))+P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x100971),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),f235(a915)),a106)),x100972)))) % 177.41/177.18 [10156]P1(f327(f327(f234(a915),f327(f105(a915),x101561)),f327(a113,x101562)))+~P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x101561),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),f234(a915)),a106)),x101562)))) % 177.41/177.18 [10157]P1(f327(f327(f235(a915),f327(f105(a915),x101571)),f327(a113,x101572)))+~P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x101571),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),f235(a915)),a106)),x101572)))) % 177.41/177.18 [10187]~P1(f327(f327(f234(a915),f327(a113,x101872)),f327(f105(a915),x101871)))+P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x101871),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f8(a915,a910,a1),f327(f234(a915),x101872)),a106))))) % 177.41/177.18 [10188]~P1(f327(f327(f235(a915),f327(a113,x101882)),f327(f105(a915),x101881)))+P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x101881),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f8(a915,a910,a1),f327(f235(a915),x101882)),a106))))) % 177.41/177.18 [10234]P1(f327(f327(f234(a915),f327(a113,x102341)),f327(f105(a915),x102342)))+~P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x102342),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f8(a915,a910,a1),f327(f234(a915),x102341)),a106))))) % 177.41/177.18 [10235]P1(f327(f327(f235(a915),f327(a113,x102351)),f327(f105(a915),x102352)))+~P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x102352),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f8(a915,a910,a1),f327(f235(a915),x102351)),a106))))) % 177.41/177.18 [10317]~P1(f327(f327(f329(a915),f2(a915)),x103171))+E(f327(a113,f327(f36(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,f922(a915,a910),a910),f327(f327(f8(a915,f922(f922(a915,a910),a910),a915),f329(a915)),a113)),x103171))),f327(f327(f7(a915,a915,a910),f235(a915)),x103172))))),f327(f36(a915),f327(f262(a915),f327(f327(f18(a915,a910,a910),f327(f327(f8(a910,f922(a910,a910),a915),a325),f327(f327(f7(a915,f922(a915,a910),a910),f329(a915)),x103171))),f327(f327(f7(a915,a915,a910),f235(a915)),f327(a113,x103172)))))) % 177.41/177.18 [8707]~P93(x87071)+E(f327(f327(f81(x87071),f327(f105(x87071),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),x87072),x87072) % 177.41/177.18 [8768]~P93(x87681)+E(f327(f327(f80(x87681),f78(x87681)),f327(f105(x87681),x87682)),f327(f105(x87681),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),x87682))) % 177.41/177.18 [8830]~P93(x88301)+E(f327(f327(f23(x88301),f327(f105(x88301),x88302)),f78(x88301)),f327(f105(x88301),f327(f327(f80(a1),x88302),f327(f79(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.18 [8984]~P1(f327(f327(f235(a915),f327(f105(a915),a83)),x89842))+E(f327(f327(f23(a915),x89841),f327(f327(f23(a915),x89842),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f23(a915),f327(a113,x89841)),x89842)) % 177.41/177.18 [9631]~P112(x96311)+E(f327(f327(f81(x96311),x96312),x96312),f327(f327(f244(x96311),x96312),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.18 [9632]~P80(x96321)+E(f327(f327(f244(x96321),x96322),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f81(x96321),x96322),x96322)) % 177.41/177.18 [9634]~P93(x96341)+E(f327(f327(f81(x96341),x96342),f327(f105(x96341),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f80(x96341),x96342),x96342)) % 177.41/177.18 [9876]~P142(x98761)+E(f327(f327(f244(x98761),f327(f79(x98761),x98762)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f244(x98761),x98762),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.18 [9877]~P119(x98771)+E(f327(f327(f244(x98771),f327(f75(x98771),x98772)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f244(x98771),x98772),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.18 [9873]~P93(x98731)+E(f327(f327(f81(x98731),f327(f105(x98731),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x98732),f327(f327(f80(x98731),x98732),x98732)) % 177.41/177.18 [9992]~P119(x99921)+E(f327(f75(x99921),f327(f327(f244(x99921),x99922),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x99921),x99922),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.18 [10057]~P119(x100571)+P1(f327(f327(f234(x100571),f2(x100571)),f327(f327(f244(x100571),x100572),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.18 [10225]~E(f327(a113,x102252),f327(f105(a915),x102251))+P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x102251),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),a324),a106)),x102252))))) % 177.41/177.18 [10226]~E(f327(f105(a915),x102261),f327(a113,x102262))+P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x102261),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),a324),a106)),x102262))))) % 177.41/177.18 [10271]E(f327(a113,x102711),f327(f105(a915),x102712))+~P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x102712),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),a324),a106)),x102711))))) % 177.41/177.18 [10272]E(f327(f105(a915),x102721),f327(a113,x102722))+~P1(f327(f327(f86(a1,a910),f327(f105(a1),f327(f327(f80(a1),x102721),a98))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a330),f327(f327(f8(a910,a910,a1),a322),a195))),f327(f327(f7(a1,a915,a910),f327(f327(f8(a915,f922(a915,a910),a1),a324),a106)),x102722))))) % 177.41/177.18 [10318]~P13(x103181,x103182)+P1(f327(f327(f329(f922(x103181,a910)),f806(x103182,x103181)),f327(f327(f8(f922(x103181,a910),a910,f922(x103181,a910)),f87(x103181)),f327(f327(f8(f922(x103181,a910),f922(x103181,a910),f922(x103181,a910)),f327(f18(x103181,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103181),a325),f327(f327(f18(x103181,x103181,a910),x103182),f5(x103181))))),f327(f327(f7(f922(x103181,a910),f922(x103181,f922(x103181,a910)),f922(x103181,a910)),f327(f327(f8(f922(f922(x103181,a910),a910),f922(f922(x103181,f922(x103181,a910)),f922(x103181,a910)),f922(x103181,a910)),f8(f922(x103181,a910),a910,x103181)),a324)),x103182))))) % 177.41/177.18 [10055]~P93(x100551)+E(f327(f327(f244(x100551),f327(f105(x100551),a98)),f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x100552)),f78(x100551)) % 177.41/177.18 [10056]~P142(x100561)+E(f327(f327(f244(x100561),f327(f79(x100561),f78(x100561))),f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x100562)),f78(x100561)) % 177.41/177.18 [10059]~P80(x100591)+E(f327(f327(f244(x100591),x100592),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),a98))),f327(f327(f81(x100591),f327(f327(f81(x100591),x100592),x100592)),x100592)) % 177.41/177.18 [10251]~P1(f327(f327(f234(a1),f2(a1)),x102512))+E(f46(a1,f327(f327(f80(a1),f78(a1)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102511)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102512)),f327(f327(f80(a1),f78(a1)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f46(a1,x102511,x102512)))) % 177.41/177.18 [10274]~P1(f327(f327(f234(a1),f2(a1)),x102742))+E(f327(f327(f37(a1),f327(f327(f80(a1),f78(a1)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102741))),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102742)),f327(f327(f37(a1),x102741),x102742)) % 177.41/177.18 [10276]~P1(f327(f327(f234(a1),x102762),f2(a1)))+E(f327(f327(f37(a1),f327(f327(f80(a1),f78(a1)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102761))),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102762)),f327(f327(f37(a1),f327(f327(f80(a1),x102761),f78(a1))),x102762)) % 177.41/177.18 [10277]~P1(f327(f327(f234(a1),x102772),f2(a1)))+E(f46(a1,f327(f327(f80(a1),f78(a1)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102771)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102772)),f327(f327(f23(a1),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f46(a1,f327(f327(f80(a1),x102771),f78(a1)),x102772))),f78(a1))) % 177.41/177.18 [10147]~P93(x101471)+E(f327(f327(f244(x101471),f327(f105(x101471),a98)),f327(a113,f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101472))),f327(f105(x101471),a98)) % 177.41/177.18 [10149]~P142(x101491)+E(f327(f327(f244(x101491),f327(f79(x101491),f78(x101491))),f327(a113,f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101492))),f327(f79(x101491),f78(x101491))) % 177.41/177.18 [5109]P36(x51091,x51092)+~P6(x51091,x51093,x51092) % 177.41/177.18 [5111]P49(x51111,x51112)+~P6(x51111,x51113,x51112) % 177.41/177.18 [5282]~P6(x52821,x52822,x52823)+P50(x52821,x52822,x52823) % 177.41/177.18 [8234]~E(x82342,x82343)+P32(x82341,x82341,a324,x82342,x82343) % 177.41/177.18 [8781]E(x87811,x87812)+~P32(x87813,x87813,a324,x87811,x87812) % 177.41/177.18 [4917]E(f170(x49171,x49172,x49173),f114(x49171))+~E(x49172,f2(a915)) % 177.41/177.18 [5085]~E(f170(x50852,x50851,x50853),f114(x50852))+E(x50851,f2(a915)) % 177.41/177.18 [5287]~P35(x52871,x52873)+P35(x52871,f321(x52871,x52872,x52873)) % 177.41/177.18 [5395]~P27(x53951,x53952,x53953)+P29(a1,x53951,f179(x53952,x53953)) % 177.41/177.18 [5468]P27(x54681,x54682,x54683)+~P29(a1,x54681,f179(x54682,x54683)) % 177.41/177.18 [5539]~P6(x55391,x55392,x55393)+P6(f916(x55391),f162(x55391,x55392),f159(x55391,x55393)) % 177.41/177.18 [5540]~P50(x55401,x55402,x55403)+P50(f916(x55401),f162(x55401,x55402),f159(x55401,x55403)) % 177.41/177.18 [5653]P52(x56531,x56532,x56533)+~E(f586(x56533,x56532,x56531),f587(x56533,x56532,x56531)) % 177.41/177.18 [5654]P53(x56541,x56542,x56543)+~E(f603(x56543,x56542,x56541),f604(x56543,x56542,x56541)) % 177.41/177.18 [8240]~E(x82402,x82403)+P24(x82401,x82401,f31(x82401),x82402,x82403) % 177.41/177.18 [8789]E(x87891,x87892)+~P24(x87893,x87893,f31(x87893),x87891,x87892) % 177.41/177.18 [4872]~E(f327(f169(x48722),x48721),x48723)+E(x48721,f327(f169(x48722),x48723)) % 177.41/177.18 [4873]~E(x48732,f327(f169(x48731),x48733))+E(f327(f169(x48731),x48732),x48733) % 177.41/177.18 [4923]E(x49231,x49232)+~E(f327(f169(x49233),x49231),f327(f169(x49233),x49232)) % 177.41/177.18 [5135]~P5(x51353,x51351)+P1(f327(f327(x51351,x51352),x51352)) % 177.41/177.18 [5136]~P41(x51363,x51361)+P1(f327(f327(x51361,x51362),x51362)) % 177.41/177.18 [5138]~P57(x51381,x51382)+P1(f327(f315(x51381,x51382),x51383)) % 177.41/177.18 [5203]~P35(x52031,x52032)+P35(f916(x52031),f327(f144(x52031,x52032),x52033)) % 177.41/177.18 [5208]~P1(f327(x52082,x52083))+~E(f327(f262(x52081),x52082),f190(f922(x52081,a910))) % 177.41/177.18 [5209]~P1(f327(x52092,x52093))+~E(f190(f922(x52091,a910)),f327(f262(x52091),x52092)) % 177.41/177.18 [5221]E(x52211,f2(a915))+E(f145(x52212,f170(x52212,x52211,x52213)),x52213) % 177.41/177.18 [5240]~P1(f327(x52401,x52403))+P1(f327(x52401,f90(x52402,x52401))) % 177.41/177.18 [5241]~P1(f327(x52411,x52413))+P1(f327(x52411,f733(x52411,x52412))) % 177.41/177.18 [5253]E(x52531,f2(a915))+E(f327(f142(x52532),f170(x52532,x52531,x52533)),x52533) % 177.41/177.18 [5358]~E(x53582,x53583)+P1(f327(f327(f329(x53581),x53582),f327(a324,x53583))) % 177.41/177.18 [5373]~E(x53732,f2(a915))+E(f327(f173(x53731),f170(x53731,x53732,x53733)),f190(f922(x53731,a910))) % 177.41/177.18 [5417]E(f327(f169(x54171),x54172),f327(f327(f152(x54171),x54173),f114(x54171)))+~E(x54172,f327(f327(f152(x54171),x54173),f114(x54171))) % 177.41/177.18 [5418]~E(x54183,f327(f327(f152(x54181),x54182),f114(x54181)))+E(f327(f327(f152(x54181),x54182),f114(x54181)),f327(f169(x54181),x54183)) % 177.41/177.18 [5464]~P31(x54641,x54642,x54643)+P31(x54641,x54642,f327(f169(x54641),x54643)) % 177.41/177.18 [5465]~P29(x54651,x54652,x54653)+P29(x54651,x54652,f327(f169(x54651),x54653)) % 177.41/177.18 [5469]E(f327(f36(x54691),f336(x54692,x54693,x54691)),x54692)+~E(f327(f36(x54691),x54693),f327(a113,x54692)) % 177.41/177.18 [5476]~P35(x54761,x54763)+P1(f327(f327(f329(x54761),x54762),f316(x54761,x54763))) % 177.41/177.18 [5480]~E(f327(f169(x54802),x54801),f327(f327(f152(x54802),x54803),f114(x54802)))+E(x54801,f327(f327(f152(x54802),x54803),f114(x54802))) % 177.41/177.18 [5481]~E(f327(f327(f152(x54812),x54813),f114(x54812)),f327(f169(x54812),x54811))+E(x54811,f327(f327(f152(x54812),x54813),f114(x54812))) % 177.41/177.18 [5504]E(f85(f921(a915,a915),f49(x55041,x55042)),x55043)+~P1(f327(f49(x55041,x55042),x55043)) % 177.41/177.18 [5543]P31(x55431,x55432,x55433)+~P31(x55431,x55432,f327(f169(x55431),x55433)) % 177.41/177.18 [5544]P29(x55441,x55442,x55443)+~P29(x55441,x55442,f327(f169(x55441),x55443)) % 177.41/177.18 [5583]P1(f327(f327(x55831,x55832),x55832))+~P1(f327(f270(x55833,x55831),x55832)) % 177.41/177.18 [5584]~P1(f327(f327(x55842,x55843),x55843))+P1(f327(f270(x55841,x55842),x55843)) % 177.41/177.18 [5606]~E(x56062,f114(x56061))+P1(f327(f327(f329(f916(x56061)),x56062),f162(x56061,x56063))) % 177.41/177.18 [5616]~P50(x56161,x56162,x56163)+P50(x56161,x56162,f327(f286(x56161,x56161),x56163)) % 177.41/177.18 [5617]~P53(x56171,x56172,x56173)+P53(x56171,x56172,f327(f286(x56171,x56171),x56173)) % 177.41/177.18 [5634]~P58(x56341)+E(f46(x56341,f46(x56341,x56342,x56343),x56343),f46(x56341,x56342,x56343)) % 177.41/177.18 [5737]E(x57371,x57372)+~P1(f327(f327(f329(x57373),x57371),f327(a324,x57372))) % 177.41/177.18 [5784]~P146(x57841)+E(f192(x57841,x57842,f2(a915),x57843),x57843) % 177.41/177.18 [5806]P50(x58061,x58062,x58063)+~P50(x58061,x58062,f327(f286(x58061,x58061),x58063)) % 177.41/177.18 [5807]P53(x58071,x58072,x58073)+~P53(x58071,x58072,f327(f286(x58071,x58071),x58073)) % 177.41/177.18 [5811]~P108(x58112)+E(f151(x58111,x58112,x58113,f114(x58111)),f114(x58111)) % 177.41/177.18 [5823]E(f171(x58231,x58232,f153(x58231,x58233)),f153(x58231,f171(x58231,x58232,x58233)))+~P1(f327(f138(x58231),x58233)) % 177.41/177.18 [5922]~P1(f327(f327(x59223,x59222),x59222))+P1(f327(f327(f329(x59221),x59222),f270(x59221,x59223))) % 177.41/177.18 [5924]E(f327(f137(x59241,x59242),x59243),f114(x59241))+P1(f327(x59242,f668(x59243,x59242,x59241))) % 177.41/177.18 [5983]E(f68(x59831,x59832,x59833),x59832)+P1(f327(x59833,f734(x59832,x59831,x59833))) % 177.41/177.18 [6079]~P1(f327(f138(x60791),x60792))+P1(f327(f138(x60791),f177(x60791,x60792,x60793))) % 177.41/177.18 [6080]~P1(f327(f138(x60801),x60803))+P1(f327(f138(x60801),f171(x60801,x60802,x60803))) % 177.41/177.18 [6081]~P1(f327(f138(x60811),x60813))+P1(f327(f138(x60811),f178(x60811,x60812,x60813))) % 177.41/177.18 [6082]~P1(f327(f138(x60821),x60823))+P1(f327(f138(x60821),f141(x60821,x60822,x60823))) % 177.41/177.18 [6083]~P147(x60831,x60832,x60833)+P1(f327(x60831,f46(a1,x60832,x60833))) % 177.41/177.18 [6099]~P31(x60993,x60991,x60992)+P1(f327(x60991,f746(x60992,x60991,x60993))) % 177.41/177.18 [6100]~P33(x61003,x61001,x61002)+P1(f327(x61001,f752(x61002,x61001,x61003))) % 177.41/177.18 [6101]~P33(x61013,x61011,x61012)+P1(f327(x61011,f762(x61012,x61011,x61013))) % 177.41/177.18 [6102]~P31(x61023,x61021,x61022)+P1(f327(x61021,f791(x61021,x61022,x61023))) % 177.41/177.18 [6103]~P31(x61033,x61031,x61032)+P1(f327(x61031,f792(x61032,x61031,x61033))) % 177.41/177.18 [6108]P1(f327(f327(x61081,x61082),x61082))+~P1(f327(f327(f329(x61083),x61082),f270(x61083,x61081))) % 177.41/177.18 [6123]E(f327(f137(x61231,x61232),x61233),f178(x61231,x61232,x61233))+P1(f327(x61232,f717(x61233,x61232,x61231))) % 177.41/177.18 [6163]~P1(f327(f138(x61631),x61633))+P1(f327(f138(f916(x61631)),f56(x61631,x61632,x61633))) % 177.41/177.18 [6198]~P110(x61981)+E(f327(f327(f103(f922(x61981,a910)),f327(f282(x61981),x61982)),f303(x61981,x61982,x61983)),f190(f922(x61981,a910))) % 177.41/177.18 [6199]~P110(x61991)+E(f327(f327(f103(f922(x61991,a910)),f327(f301(x61991),x61992)),f306(x61991,x61992,x61993)),f190(f922(x61991,a910))) % 177.41/177.18 [6200]~P110(x62001)+E(f327(f327(f103(f922(x62001,a910)),f327(f301(x62001),x62002)),f305(x62001,x62002,x62003)),f190(f922(x62001,a910))) % 177.41/177.18 [6435]E(f327(f137(x64351,x64352),x64353),x64353)+~P1(f327(x64352,f669(x64353,x64352,x64351))) % 177.41/177.18 [6437]E(f327(f327(f309(x64371),f369(x64372,x64373,x64371)),f336(x64372,x64373,x64371)),x64373)+~E(f327(f36(x64371),x64373),f327(a113,x64372)) % 177.41/177.18 [6453]P147(x64531,x64532,x64533)+~P1(f327(x64531,f46(a1,x64532,x64533))) % 177.41/177.18 [6504]P29(x65041,x65042,x65043)+~P1(f327(x65042,f753(x65043,x65042,x65041))) % 177.41/177.18 [6505]P29(x65051,x65052,x65053)+~P1(f327(x65052,f760(x65052,x65053,x65051))) % 177.41/177.18 [6506]P29(x65061,x65062,x65063)+~P1(f327(x65062,f761(x65063,x65062,x65061))) % 177.41/177.18 [6507]P27(x65071,x65072,x65073)+~P1(f327(x65071,f774(x65073,x65072,x65071))) % 177.41/177.18 [6508]P28(x65081,x65082,x65083)+~P1(f327(x65081,f824(x65083,x65082,x65081))) % 177.41/177.18 [6510]E(f178(x65101,x65102,x65103),x65103)+~P1(f327(x65102,f713(x65103,x65102,x65101))) % 177.41/177.18 [6588]~P1(f327(x65882,f575(x65883,x65882,x65881)))+P1(f327(f248(x65881,x65882),x65883)) % 177.41/177.18 [6589]~P1(f327(x65892,f670(x65893,x65892,x65891)))+P1(f327(f161(x65891,x65892),x65893)) % 177.41/177.18 [6838]~P1(f327(f315(x68381,x68382),f503(x68383,x68382,x68381)))+P1(f327(f315(x68381,x68382),x68383)) % 177.41/177.18 [6839]~P1(f327(f315(x68391,x68392),f527(x68393,x68392,x68391)))+P1(f327(f315(x68391,x68392),x68393)) % 177.41/177.18 [7459]~P58(x74591)+E(f327(f327(f80(x74591),f327(f327(f81(x74591),x74592),f327(f327(f37(x74591),x74593),x74592))),f46(x74591,x74593,x74592)),x74593) % 177.41/177.18 [7489]P27(x74891,x74892,x74893)+P1(f327(f327(f329(a1),f774(x74893,x74892,x74891)),f303(a1,x74892,x74893))) % 177.41/177.18 [7916]E(f327(f327(f252(x79161,x79161),f531(x79162,x79163,x79161)),f531(x79162,x79163,x79161)),x79163)+~P1(f327(f327(f329(f921(x79161,x79161)),x79163),f263(x79161,x79162))) % 177.41/177.18 [8032]~P1(f327(f327(f329(x80321),f537(x80323,x80322,x80321)),f316(x80321,x80323)))+P1(f327(f327(f329(x80321),x80322),f316(x80321,x80323))) % 177.41/177.18 [8033]~P1(f327(f327(f329(x80331),f588(x80333,x80332,x80331)),f316(x80331,x80333)))+P1(f327(f327(f329(x80331),x80332),f316(x80331,x80333))) % 177.41/177.18 [8034]~P1(f327(f327(f329(x80341),f594(x80343,x80342,x80341)),f316(x80341,x80343)))+P1(f327(f327(f329(x80341),x80342),f316(x80341,x80343))) % 177.41/177.18 [8127]P31(a1,x81271,f179(x81272,x81273))+P27(f327(f72(a910,a910,a1,a322),x81271),x81272,x81273) % 177.41/177.18 [8215]~P58(x82151)+E(f327(f327(f80(x82151),f327(f327(f81(x82151),f327(f327(f37(x82151),x82152),x82153)),x82153)),f46(x82151,x82152,x82153)),x82152) % 177.41/177.18 [8261]~E(f327(f36(x82611),x82612),f327(a113,x82613))+~P1(f327(f327(f329(x82611),f369(x82613,x82612,x82611)),f336(x82613,x82612,x82611))) % 177.41/177.18 [8699]~P31(a1,x86991,f179(x86992,x86993))+~P27(f327(f72(a910,a910,a1,a322),x86991),x86992,x86993) % 177.41/177.18 [8886]P1(f327(f327(f234(f922(f921(x88861,x88861),a910)),f307(x88861,x88862)),f307(x88861,x88863)))+~P1(f327(f327(f234(f922(f921(x88861,x88861),a910)),x88862),f307(x88861,x88863))) % 177.41/177.18 [9170]E(x91701,f114(x91702))+~P1(f327(f327(f329(f921(f916(x91702),f916(x91702))),f327(f327(f252(f916(x91702),f916(x91702)),x91701),f114(x91702))),f159(x91702,x91703))) % 177.41/177.18 [9194]E(x91941,f114(x91942))+~P1(f327(f327(f329(f921(f916(x91942),f916(x91942))),f327(f327(f252(f916(x91942),f916(x91942)),f114(x91942)),x91941)),f159(x91942,x91943))) % 177.41/177.18 [9319]E(f327(f327(f152(x93191),f686(x93192,x93193,x93191)),f687(x93192,x93193,x93191)),x93193)+~P1(f327(f327(f329(f921(f916(x93191),f916(x93191))),f327(f327(f252(f916(x93191),f916(x93191)),f114(x93191)),x93193)),f148(x93191,x93192))) % 177.41/177.18 [9555]~P128(x95551)+~P1(f327(f327(f235(x95551),f327(f327(f80(x95551),f327(f327(f81(x95551),x95552),x95552)),f327(f327(f81(x95551),x95553),x95553))),f2(x95551))) % 177.41/177.18 [9606]P1(f327(f35(x96061),x96062))+~P1(f327(f327(f329(f921(f922(x96061,a910),f922(x96061,a910))),f327(f327(f252(f922(x96061,a910),f922(x96061,a910)),x96063),x96062)),f314(x96061))) % 177.41/177.18 [9903]~P45(x99031,x99032,x99033)+P1(f327(f327(f234(a1),f327(f327(f72(f921(a1,a1),a1,x99031,f251(a1,a1)),f214(x99031)),f232(x99031,x99032,f229(x99031,x99033)))),f2(a1))) % 177.41/177.18 [9904]~P46(x99041,x99042,x99043)+P1(f327(f327(f235(a1),f327(f327(f72(f921(a1,a1),a1,x99041,f251(a1,a1)),f214(x99041)),f232(x99041,x99042,f229(x99041,x99043)))),f2(a1))) % 177.41/177.18 [10023]P46(x100231,x100232,x100233)+~P1(f327(f327(f235(a1),f327(f327(f72(f921(a1,a1),a1,x100231,f251(a1,a1)),f214(x100231)),f232(x100231,x100232,f229(x100231,x100233)))),f2(a1))) % 177.41/177.18 [10024]P45(x100241,x100242,x100243)+~P1(f327(f327(f234(a1),f327(f327(f72(f921(a1,a1),a1,x100241,f251(a1,a1)),f214(x100241)),f232(x100241,x100242,f229(x100241,x100243)))),f2(a1))) % 177.41/177.18 [10376]~P119(x103761)+~P1(f327(f327(f235(x103761),f327(f327(f80(x103761),f327(f327(f244(x103761),x103762),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x103761),x103763),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f2(x103761))) % 177.41/177.18 [4902]~E(x49023,f114(x49021))+E(f327(f327(f135(x49021),x49022),x49023),x49022) % 177.41/177.18 [4903]~E(x49032,f114(x49031))+E(f327(f327(f135(x49031),x49032),x49033),x49033) % 177.41/177.18 [4909]~E(x49092,f2(a915))+E(f327(f327(f176(x49091),x49092),x49093),f114(x49091)) % 177.41/177.18 [4918]~E(x49183,f114(x49181))+E(f327(f327(f176(x49181),x49182),x49183),f114(x49181)) % 177.41/177.18 [4957]~E(x49571,x49573)+E(x49571,f327(f327(f135(x49572),f114(x49572)),x49573)) % 177.41/177.18 [5048]~P65(x50482)+E(f327(f190(f922(x50481,x50482)),x50483),f190(x50482)) % 177.41/177.18 [5049]~P115(x50492)+E(f327(f242(f922(x50491,x50492)),x50493),f242(x50492)) % 177.41/177.18 [5067]E(x50671,f114(x50672))+~E(f327(f327(f135(x50672),x50673),x50671),x50673) % 177.41/177.18 [5068]E(x50681,f114(x50682))+~E(f327(f327(f135(x50682),x50681),x50683),x50683) % 177.41/177.18 [5076]E(x50761,f114(x50762))+~E(f327(f327(f135(x50762),x50763),x50761),f114(x50762)) % 177.41/177.18 [5077]E(x50771,f114(x50772))+~E(f327(f327(f135(x50772),x50771),x50773),f114(x50772)) % 177.41/177.18 [5102]~E(x51022,f2(a915))+E(f327(f327(f81(a915),x51021),x51022),f327(f327(f81(a915),x51023),x51022)) % 177.41/177.18 [5104]~E(x51041,f2(a915))+E(f327(f327(f81(a915),x51041),x51042),f327(f327(f81(a915),x51041),x51043)) % 177.41/177.18 [5161]~P112(x51611)+E(f327(f327(f80(x51611),x51612),x51613),f327(f327(f80(x51611),x51613),x51612)) % 177.41/177.18 [5162]~P112(x51621)+E(f327(f327(f81(x51621),x51622),x51623),f327(f327(f81(x51621),x51623),x51622)) % 177.41/177.18 [5164]~P108(x51641)+E(f327(f327(f238(x51641),x51642),x51643),f327(f327(f238(x51641),x51643),x51642)) % 177.41/177.18 [5166]~P108(x51661)+E(f327(f327(f189(x51661),x51662),x51663),f327(f327(f189(x51661),x51663),x51662)) % 177.41/177.18 [5167]~P96(x51671)+E(f327(f327(f102(x51671),x51672),x51673),f327(f327(f102(x51671),x51673),x51672)) % 177.41/177.18 [5169]~P101(x51691)+E(f327(f327(f102(x51691),x51692),x51693),f327(f327(f102(x51691),x51693),x51692)) % 177.41/177.18 [5170]~P96(x51701)+E(f327(f327(f103(x51701),x51702),x51703),f327(f327(f103(x51701),x51703),x51702)) % 177.41/177.18 [5172]~P102(x51721)+E(f327(f327(f103(x51721),x51722),x51723),f327(f327(f103(x51721),x51723),x51722)) % 177.41/177.18 [5235]E(f46(a915,x52351,x52352),f2(a915))+~E(x52351,f327(f327(f81(a915),x52352),x52353)) % 177.41/177.18 [5236]E(f46(a1,x52361,x52362),f2(a1))+~E(x52361,f327(f327(f81(a1),x52362),x52363)) % 177.41/177.18 [5299]E(x52991,x52992)+~E(f327(f327(f80(a915),x52993),x52991),f327(f327(f80(a915),x52993),x52992)) % 177.41/177.18 [5300]E(x53001,x53002)+~E(f327(f327(f80(a915),x53001),x53003),f327(f327(f80(a915),x53002),x53003)) % 177.41/177.18 [5310]~P67(x53101)+E(f327(f327(f80(x53101),x53102),f327(f79(x53101),x53103)),f327(f327(f23(x53101),x53102),x53103)) % 177.41/177.18 [5311]~P74(x53111)+E(f327(f327(f80(x53111),x53112),f327(f79(x53111),x53113)),f327(f327(f23(x53111),x53112),x53113)) % 177.41/177.18 [5312]~P114(x53121)+E(f327(f327(f80(x53121),x53122),f327(f79(x53121),x53123)),f327(f327(f23(x53121),x53122),x53123)) % 177.41/177.18 [5313]~P86(x53131)+E(f327(f327(f103(x53131),x53132),f327(f79(x53131),x53133)),f327(f327(f23(x53131),x53132),x53133)) % 177.41/177.18 [5314]~P74(x53141)+E(f327(f327(f23(x53141),x53142),f327(f79(x53141),x53143)),f327(f327(f80(x53141),x53142),x53143)) % 177.41/177.18 [5352]~P1(f327(x53523,x53522))+P1(f327(f327(f329(x53521),x53522),x53523)) % 177.41/177.18 [5354]~P68(x53542)+E(f327(f327(f6(x53541,x53542),x53543),f190(f922(x53541,a910))),f2(x53542)) % 177.41/177.18 [5356]~P75(x53562)+E(f327(f327(f9(x53561,x53562),x53563),f190(f922(x53561,a910))),f78(x53562)) % 177.41/177.18 [5407]~E(x54072,f327(f327(f80(a915),x54071),x54073))+P1(f327(f327(f234(a915),x54071),x54072)) % 177.41/177.18 [5410]~E(x54102,f190(f922(x54101,a910)))+E(f327(f327(f61(x54101),x54102),x54103),f190(f922(f922(x54101,a910),a910))) % 177.41/177.18 [5411]~E(x54112,f190(f922(x54111,a910)))+E(f190(f922(f922(x54111,a910),a910)),f327(f327(f61(x54111),x54112),x54113)) % 177.41/177.18 [5484]~E(f327(f284(x54842,x54843),x54841),f190(f922(x54843,a910)))+E(x54841,f190(f922(f921(x54842,x54843),a910))) % 177.41/177.18 [5485]~E(f327(f264(x54852,x54853),x54851),f190(f922(x54852,a910)))+E(x54851,f190(f922(f921(x54852,x54853),a910))) % 177.41/177.18 [5517]E(f327(f284(x55171,x55172),x55173),f190(f922(x55172,a910)))+~E(x55173,f190(f922(f921(x55171,x55172),a910))) % 177.41/177.18 [5518]E(f327(f264(x55181,x55182),x55183),f190(f922(x55181,a910)))+~E(x55183,f190(f922(f921(x55181,x55182),a910))) % 177.41/177.18 [5521]E(f274(x55211,x55212,x55213),f327(f327(f23(a100),x55212),x55213))+P1(f327(f327(f235(a100),x55212),x55213)) % 177.41/177.18 [5537]P1(f327(x55371,x55372))+~P1(f327(f327(f329(x55373),x55372),x55371)) % 177.41/177.18 [5576]E(x55761,x55762)+~E(f327(f79(f922(x55763,a910)),x55761),f327(f79(f922(x55763,a910)),x55762)) % 177.41/177.18 [5587]~E(x55871,f190(f922(x55872,a910)))+~P1(f327(f327(f329(x55872),x55873),x55871)) % 177.41/177.18 [5618]~E(x56182,f327(f327(f80(a1),x56181),f327(f101(a1),x56183)))+P1(f327(f327(f234(a1),x56181),x56182)) % 177.41/177.18 [5632]E(f327(f327(f309(x56321),x56322),x56323),x56323)+~P1(f327(f327(f329(x56321),x56322),x56323)) % 177.41/177.18 [5643]E(x56431,f190(f922(x56432,a910)))+~E(f327(f327(f61(x56432),x56431),x56433),f190(f922(f922(x56432,a910),a910))) % 177.41/177.18 [5644]E(x56441,f190(f922(x56442,a910)))+~E(f190(f922(f922(x56442,a910),a910)),f327(f327(f61(x56442),x56441),x56443)) % 177.41/177.18 [5650]~P106(x56501)+E(f327(f327(f81(x56501),f327(f79(x56501),x56502)),f327(f79(x56501),x56503)),f327(f327(f81(x56501),x56502),x56503)) % 177.41/177.18 [5652]~P61(x56521)+E(f327(f327(f291(x56521),f327(f79(x56521),x56522)),f327(f79(x56521),x56523)),f327(f327(f291(x56521),x56522),x56523)) % 177.41/177.18 [5684]~P1(f327(x56843,x56842))+P1(f327(f327(f329(x56841),x56842),f327(f262(x56841),x56843))) % 177.41/177.18 [5711]E(x57111,f2(a915))+E(f327(f173(x57112),f170(x57112,x57111,x57113)),f327(f327(f309(x57112),x57113),f190(f922(x57112,a910)))) % 177.41/177.18 [5730]E(f171(x57301,x57302,x57303),x57303)+P1(f327(f327(f329(x57301),x57302),f327(f173(x57301),x57303))) % 177.41/177.18 [5815]~P1(f327(f138(x58151),x58153))+P1(f327(f138(x58151),f327(f137(x58151,x58152),x58153))) % 177.41/177.18 [5858]~P58(x58581)+E(f327(f327(f37(x58581),f46(x58581,x58582,x58583)),x58583),f2(x58581)) % 177.41/177.18 [5877]E(f177(x58771,f327(f327(f152(x58771),x58772),f114(x58771)),x58773),f114(x58771))+P1(f327(f327(f329(a915),f2(a915)),x58773)) % 177.41/177.18 [5883]E(x58831,f2(a915))+E(f327(f172(x58832),f170(x58832,x58831,x58833)),f170(x58832,f327(f327(f23(a915),x58831),f78(a915)),x58833)) % 177.41/177.18 [5934]E(f327(f327(f152(x59341),x59342),x59343),f141(x59341,x59342,x59343))+P1(f327(f327(f329(x59341),x59342),f327(f173(x59341),x59343))) % 177.41/177.18 [5943]E(x59431,x59432)+~E(f327(f327(f81(a915),f327(a113,x59433)),x59431),f327(f327(f81(a915),f327(a113,x59433)),x59432)) % 177.41/177.18 [5944]~E(x59442,f327(f327(f80(a1),x59441),f327(f101(a1),f327(a113,x59443))))+P1(f327(f327(f235(a1),x59441),x59442)) % 177.41/177.18 [6005]~P28(x60051,x60052,x60053)+P29(a915,x60051,f140(a915,f327(f302(a915,x60052),x60053))) % 177.41/177.18 [6058]~E(x60583,f114(x60581))+E(f327(f327(f327(f184(f916(x60581),f916(x60581)),x60582),f168(x60581)),x60583),f114(x60581)) % 177.41/177.18 [6062]P1(f327(x60621,x60622))+~P1(f327(f327(f329(x60623),x60622),f327(f262(x60623),x60621))) % 177.41/177.18 [6094]E(x60941,x60942)+~E(f327(f327(f309(x60943),x60941),f190(f922(x60943,a910))),f327(f327(f309(x60943),x60942),f190(f922(x60943,a910)))) % 177.41/177.18 [6110]~P110(x61101)+E(f327(f327(f103(f922(x61101,a910)),f327(f282(x61101),x61102)),f327(f302(x61101,x61102),x61103)),f190(f922(x61101,a910))) % 177.41/177.18 [6149]E(f141(x61491,x61492,x61493),x61493)+~P1(f327(f327(f329(x61491),x61492),f327(f173(x61491),x61493))) % 177.41/177.18 [6171]~P78(x61711)+E(f327(f310(x61711,x61711,f79(x61711)),f327(f302(x61711,x61712),x61713)),f305(x61711,f327(f79(x61711),x61713),f327(f79(x61711),x61712))) % 177.41/177.18 [6182]E(f327(f191(f916(x61821)),f171(x61821,x61822,x61823)),f327(f191(f916(x61821)),x61823))+P1(f327(f327(f329(x61821),x61822),f327(f173(x61821),x61823))) % 177.41/177.18 [6239]~P110(x62391)+E(f327(f327(f103(f922(x62391,a910)),f327(f302(x62391,x62392),x62393)),f327(f283(x62391),x62393)),f190(f922(x62391,a910))) % 177.41/177.18 [6259]~P78(x62591)+E(f327(f310(x62591,x62591,f79(x62591)),f306(x62591,x62592,x62593)),f306(x62591,f327(f79(x62591),x62593),f327(f79(x62591),x62592))) % 177.41/177.18 [6260]~P78(x62601)+E(f327(f310(x62601,x62601,f79(x62601)),f303(x62601,x62602,x62603)),f303(x62601,f327(f79(x62601),x62603),f327(f79(x62601),x62602))) % 177.41/177.18 [6326]E(f177(x63261,f327(f327(f152(x63261),x63262),f114(x63261)),x63263),f327(f327(f152(x63261),x63262),f114(x63261)))+~P1(f327(f327(f329(a915),f2(a915)),x63263)) % 177.41/177.18 [6331]P28(x63311,x63312,x63313)+~P29(a915,x63311,f140(a915,f327(f302(a915,x63312),x63313))) % 177.41/177.18 [6334]~P78(x63341)+E(f327(f310(x63341,x63341,f79(x63341)),f305(x63341,x63342,x63343)),f327(f302(x63341,f327(f79(x63341),x63343)),f327(f79(x63341),x63342))) % 177.41/177.18 [6355]~P59(x63551)+E(f46(x63551,f327(f79(x63551),f46(x63551,x63552,x63553)),x63553),f46(x63551,f327(f79(x63551),x63552),x63553)) % 177.41/177.18 [6451]~P1(f327(f35(f921(x64512,x64511)),x64513))+P1(f327(f35(x64511),f327(f284(x64512,x64511),x64513))) % 177.41/177.18 [6452]~P1(f327(f35(f921(x64521,x64522)),x64523))+P1(f327(f35(x64521),f327(f264(x64521,x64522),x64523))) % 177.41/177.18 [6457]~P110(x64571)+E(f327(f327(f103(f922(x64571,a910)),f306(x64571,x64572,x64573)),f327(f283(x64571),x64573)),f190(f922(x64571,a910))) % 177.41/177.18 [6458]~P110(x64581)+E(f327(f327(f103(f922(x64581,a910)),f305(x64581,x64582,x64583)),f327(f304(x64581),x64583)),f190(f922(x64581,a910))) % 177.41/177.18 [6459]~P110(x64591)+E(f327(f327(f103(f922(x64591,a910)),f303(x64591,x64592,x64593)),f327(f304(x64591),x64593)),f190(f922(x64591,a910))) % 177.41/177.18 [6530]E(f327(f327(f165(x65301),x65302),f629(x65302,x65303,x65301)),x65303)+~P1(f327(f327(f329(x65301),x65303),f327(f173(x65301),x65302))) % 177.41/177.18 [6672]E(x66721,f114(x66722))+~E(f327(f327(f327(f184(f916(x66722),f916(x66722)),x66723),f168(x66722)),x66721),f114(x66722)) % 177.41/177.18 [6776]~P1(f327(f35(f921(x67762,x67761)),x67763))+P1(f327(f35(f921(x67761,x67762)),f327(f286(x67762,x67761),x67763))) % 177.41/177.18 [6799]E(x67991,x67992)+~E(f290(a915,f287(a915),x67993,x67991),f327(f327(f309(a915),x67992),f190(f922(a915,a910)))) % 177.41/177.18 [6800]E(x68001,x68002)+~E(f290(a915,f287(a915),x68001,x68002),f327(f327(f309(a915),x68003),f190(f922(a915,a910)))) % 177.41/177.18 [6930]P53(x69301,x69302,x69303)+P1(f327(f327(f329(x69301),f604(x69303,x69302,x69301)),x69302)) % 177.41/177.18 [6931]P53(x69311,x69312,x69313)+P1(f327(f327(f329(x69311),f603(x69313,x69312,x69311)),x69312)) % 177.41/177.18 [6941]P1(f327(f315(x69411,x69412),x69413))+P1(f327(f327(x69412,f503(x69413,x69412,x69411)),x69413)) % 177.41/177.18 [6942]P1(f327(f315(x69421,x69422),x69423))+P1(f327(f327(x69422,f527(x69423,x69422,x69421)),x69423)) % 177.41/177.18 [6973]E(f327(f191(f916(x69731)),f171(x69731,x69732,x69733)),f327(f327(f23(a915),f327(f191(f916(x69731)),x69733)),f78(a915)))+~P1(f327(f327(f329(x69731),x69732),f327(f173(x69731),x69733))) % 177.41/177.18 [7012]P1(f327(f248(x70121,x70122),x70123))+P1(f327(f327(f329(x70121),f575(x70123,x70122,x70121)),x70123)) % 177.41/177.18 [7021]~P1(f327(f35(f921(x70212,x70211)),f327(f286(x70211,x70212),x70213)))+P1(f327(f35(f921(x70211,x70212)),x70213)) % 177.41/177.18 [7079]~P1(f327(f327(f329(x70791),x70792),f327(f173(x70791),f115(x70791,x70793))))+P1(f327(f327(f329(x70791),x70792),f327(f173(x70791),x70793))) % 177.41/177.18 [7114]E(f327(f137(x71141,x71142),x71143),x71143)+P1(f327(f327(f329(x71141),f669(x71143,x71142,x71141)),f327(f173(x71141),x71143))) % 177.41/177.18 [7128]E(f327(f137(x71281,x71282),x71283),f114(x71281))+P1(f327(f327(f329(x71281),f668(x71283,x71282,x71281)),f327(f173(x71281),x71283))) % 177.41/177.18 [7154]P29(x71541,x71542,x71543)+P1(f327(f327(f329(x71541),f753(x71543,x71542,x71541)),f327(f173(x71541),x71543))) % 177.41/177.18 [7155]P29(x71551,x71552,x71553)+P1(f327(f327(f329(x71551),f761(x71553,x71552,x71551)),f327(f173(x71551),x71553))) % 177.41/177.18 [7156]P29(x71561,x71562,x71563)+P1(f327(f327(f329(x71561),f760(x71562,x71563,x71561)),f327(f173(x71561),x71563))) % 177.41/177.18 [7159]E(f178(x71591,x71592,x71593),x71593)+P1(f327(f327(f329(x71591),f713(x71593,x71592,x71591)),f327(f173(x71591),x71593))) % 177.41/177.18 [7236]P1(f327(f161(x72361,x72362),x72363))+P1(f327(f327(f329(x72361),f670(x72363,x72362,x72361)),f327(f173(x72361),x72363))) % 177.41/177.18 [7245]~P31(x72451,x72453,x72452)+P1(f327(f327(f329(x72451),f746(x72452,x72453,x72451)),f327(f173(x72451),x72452))) % 177.41/177.18 [7246]~P33(x72461,x72463,x72462)+P1(f327(f327(f329(x72461),f752(x72462,x72463,x72461)),f327(f173(x72461),x72462))) % 177.41/177.18 [7247]~P33(x72471,x72473,x72472)+P1(f327(f327(f329(x72471),f762(x72472,x72473,x72471)),f327(f173(x72471),x72472))) % 177.41/177.18 [7248]~P31(x72481,x72482,x72483)+P1(f327(f327(f329(x72481),f791(x72482,x72483,x72481)),f327(f173(x72481),x72483))) % 177.41/177.18 [7249]~P31(x72491,x72493,x72492)+P1(f327(f327(f329(x72491),f792(x72492,x72493,x72491)),f327(f173(x72491),x72492))) % 177.41/177.18 [7283]P1(f327(f327(f329(x72831),x72832),f633(x72833,x72832,x72831)))+~P1(f327(f327(f329(x72831),x72832),f38(f922(x72831,a910),x72833))) % 177.41/177.18 [7284]~P68(x72841)+E(f327(f327(f80(x72841),f327(f327(f6(a915,x72841),x72842),f327(f282(a915),x72843))),f327(x72842,x72843)),f327(f327(f6(a915,x72841),x72842),f327(f282(a915),f327(a113,x72843)))) % 177.41/177.18 [7296]P28(x72961,x72962,x72963)+P1(f327(f327(f329(a915),f824(x72963,x72962,x72961)),f327(f302(a915,x72962),x72963))) % 177.41/177.18 [7376]~P31(x73762,x73761,x73763)+P1(f327(x73761,f327(f327(f165(x73762),x73763),f749(x73763,x73761,x73762)))) % 177.41/177.18 [7389]~P1(f327(f327(f329(x73891),x73892),f504(x73892,x73893,x73891)))+P1(f327(f327(f329(x73891),x73892),f39(f922(x73891,a910),x73893))) % 177.41/177.18 [7422]~P68(x74221)+E(f327(f327(f80(x74221),f327(f327(f6(a915,x74221),x74222),f327(f301(a915),x74223))),f327(x74222,f327(a113,x74223))),f327(f327(f6(a915,x74221),x74222),f327(f301(a915),f327(a113,x74223)))) % 177.41/177.18 [7561]P1(f327(f327(f329(f916(x75611)),x75612),f162(x75611,x75613)))+P1(f327(f327(f329(x75611),f654(x75613,x75612,x75611)),f327(f173(x75611),x75612))) % 177.41/177.18 [7575]~P1(f327(f327(f329(f916(x75751)),x75752),f162(x75751,f316(x75751,x75753))))+P1(f327(f327(f329(f916(x75751)),x75752),f316(f916(x75751),f158(x75751,x75753)))) % 177.41/177.18 [7600]~P1(f327(f327(f329(f916(x76001)),x76002),f316(f916(x76001),f158(x76001,x76003))))+P1(f327(f327(f329(f916(x76001)),x76002),f162(x76001,f316(x76001,x76003)))) % 177.41/177.18 [7633]E(f327(f327(f327(f184(f916(x76331),f916(x76331)),x76332),f168(x76331)),x76333),x76333)+~P1(f327(f327(f234(a915),f327(f191(f916(x76331)),x76333)),f78(a915))) % 177.41/177.18 [7666]E(f327(f327(f135(x76661),f750(x76662,x76663,x76661)),f327(f327(f152(x76661),x76663),f751(x76662,x76663,x76661))),x76662)+~P1(f327(f327(f329(x76661),x76663),f327(f173(x76661),x76662))) % 177.41/177.18 [7667]E(f327(f327(f135(x76671),f755(x76672,x76673,x76671)),f327(f327(f152(x76671),x76673),f756(x76672,x76673,x76671))),x76672)+~P1(f327(f327(f329(x76671),x76673),f327(f173(x76671),x76672))) % 177.41/177.18 [7668]E(f327(f327(f135(x76681),f757(x76682,x76683,x76681)),f327(f327(f152(x76681),x76683),f758(x76682,x76683,x76681))),x76682)+~P1(f327(f327(f329(x76681),x76683),f327(f173(x76681),x76682))) % 177.41/177.18 [7689]~P23(x76891,x76892,x76893,f242(f922(x76891,a910)))+P23(f916(x76891),f916(x76892),f327(f155(x76891,x76892),x76893),f242(f922(f916(x76891),a910))) % 177.41/177.18 [7839]E(x78391,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),x78392)),x78393)),f327(f256(a915,a915),x78392)))+~P1(f327(f49(x78391,x78393),x78392)) % 177.41/177.18 [7847]P23(x78471,x78472,x78473,f242(f922(x78471,a910)))+~P23(f916(x78471),f916(x78472),f327(f155(x78471,x78472),x78473),f242(f922(f916(x78471),a910))) % 177.41/177.18 [7891]P1(f327(f327(f329(f922(x78911,a910)),f504(x78912,x78913,x78911)),x78913))+P1(f327(f327(f329(x78911),x78912),f39(f922(x78911,a910),x78913))) % 177.41/177.18 [7980]P1(f327(f327(f329(f916(x79801)),x79802),f162(x79801,x79803)))+~P1(f327(f327(f329(x79801),f654(x79803,x79802,x79801)),x79803)) % 177.41/177.18 [8081]P29(x80811,x80812,x80813)+~P1(f327(x80812,f327(f327(f165(x80811),x80813),f754(x80813,x80812,x80811)))) % 177.41/177.18 [8106]E(x81061,x81062)+~E(f327(f327(f7(x81063,f922(x81063,a910),a910),f329(x81063)),x81061),f327(f327(f7(x81063,f922(x81063,a910),a910),f329(x81063)),x81062)) % 177.41/177.18 [8114]~P1(f327(f327(f329(f921(x81141,x81141)),x81143),f263(x81141,x81142)))+P1(f327(f327(f329(x81141),f531(x81142,x81143,x81141)),x81142)) % 177.41/177.18 [8116]~P1(f327(f327(f329(x81161),x81163),f38(f922(x81161,a910),x81162)))+P1(f327(f327(f329(f922(x81161,a910)),f633(x81162,x81163,x81161)),x81162)) % 177.41/177.18 [8235]P23(x82351,x82352,f92(x82352,x82351,f242(f922(x82352,a910)),x82353),f242(f922(x82351,a910)))+~E(f327(f310(x82352,x82351,x82353),f242(f922(x82352,a910))),f242(f922(x82351,a910))) % 177.41/177.18 [8289]~P1(f327(f327(f329(x82891),x82892),f327(f173(x82891),f755(x82893,x82892,x82891))))+~P1(f327(f327(f329(x82891),x82892),f327(f173(x82891),x82893))) % 177.41/177.18 [8290]~P1(f327(f327(f329(x82901),x82902),f327(f173(x82901),f758(x82903,x82902,x82901))))+~P1(f327(f327(f329(x82901),x82902),f327(f173(x82901),x82903))) % 177.41/177.18 [8319]P28(f327(f72(a910,a910,a915,a322),x83191),x83192,x83193)+P31(a915,x83191,f140(a915,f327(f302(a915,x83192),x83193))) % 177.41/177.18 [8479]E(x84791,f114(x84792))+P1(f327(f327(f329(x84792),f327(f251(x84792,f921(a100,a100)),f327(f275(x84792,x84791),x84793))),f327(f173(x84792),x84791))) % 177.41/177.18 [8577]~P71(x85771)+E(f327(f143(x85771,x85771,f327(f7(x85771,x85771,x85771),f80(x85771)),x85772),f327(f169(x85771),x85773)),f327(f143(x85771,x85771,f80(x85771),x85772),x85773)) % 177.41/177.18 [8769]~P23(x87692,x87691,x87693,f242(f922(x87692,a910)))+E(f327(f310(x87691,x87692,f92(x87692,x87691,f242(f922(x87692,a910)),x87693)),f242(f922(x87691,a910))),f242(f922(x87692,a910))) % 177.41/177.18 [8839]~P28(f327(f72(a910,a910,a915,a322),x88391),x88392,x88393)+~P31(a915,x88391,f140(a915,f327(f302(a915,x88392),x88393))) % 177.41/177.18 [9086]~P108(x90861)+E(f327(f173(x90861),f150(x90861,x90861,f5(x90861),x90862,x90863)),f327(f327(f309(x90861),x90862),f327(f173(x90861),x90863))) % 177.41/177.18 [9097]~E(f327(x90973,f327(f92(x90971,x90972,f242(f922(x90971,a910)),x90973),f805(x90973,x90972,x90971))),f805(x90973,x90972,x90971))+E(f327(f310(x90971,x90972,x90973),f242(f922(x90971,a910))),f242(f922(x90972,a910))) % 177.41/177.18 [9099]P1(f327(f327(f235(a915),f2(a915)),f606(x90991,x90992,x90993)))+~P1(f327(f327(f329(f921(x90993,x90993)),x90992),f327(f327(f289(x90993,x90993,x90993),x90991),f307(x90993,x90991)))) % 177.41/177.18 [9376]~P55(x93761,x93762)+~P1(f327(f327(f329(f921(x93761,x93761)),f327(f327(f252(x93761,x93761),x93763),x93763)),f327(f327(f289(x93761,x93761,x93761),x93762),f307(x93761,x93762)))) % 177.41/177.18 [9510]~E(f327(f327(f103(f922(f921(x95101,x95101),a910)),f327(f286(x95101,x95101),x95102)),f307(x95101,x95102)),f190(f922(f921(x95101,x95101),a910)))+~P1(f327(f327(f329(f921(x95101,x95101)),f327(f327(f252(x95101,x95101),x95103),x95103)),f327(f327(f289(x95101,x95101,x95101),x95102),f307(x95101,x95102)))) % 177.41/177.18 [9693]~P1(f327(f35(x96931),x96932))+P1(f327(f327(f234(a915),f327(f36(x96931),f327(f327(f23(f922(x96931,a910)),x96932),f327(f327(f309(x96931),x96933),f190(f922(x96931,a910)))))),f327(f36(x96931),x96932))) % 177.41/177.18 [5223]~E(x52233,f114(x52231))+E(f145(x52231,f327(f327(f152(x52231),x52232),x52233)),x52232) % 177.41/177.18 [5232]~E(x52323,f114(x52321))+E(f115(x52321,f327(f327(f152(x52321),x52322),x52323)),f114(x52321)) % 177.41/177.18 [5262]E(x52621,f114(x52622))+E(f145(x52622,f327(f327(f152(x52622),x52623),x52621)),f145(x52622,x52621)) % 177.41/177.18 [5264]E(x52641,f114(x52642))+E(f145(x52642,f327(f327(f135(x52642),x52643),x52641)),f145(x52642,x52641)) % 177.41/177.18 [5269]~E(x52693,f114(x52691))+E(f115(x52691,f327(f327(f135(x52691),x52692),x52693)),f115(x52691,x52692)) % 177.41/177.18 [5271]~E(x52713,f114(x52711))+E(f145(x52711,f327(f327(f135(x52711),x52712),x52713)),f145(x52711,x52712)) % 177.41/177.18 [5304]E(x53041,f114(x53042))+E(f327(f142(x53042),f327(f327(f135(x53042),x53041),x53043)),f327(f142(x53042),x53041)) % 177.41/177.18 [5332]~E(x53322,f114(x53321))+E(f327(f142(x53321),f327(f327(f135(x53321),x53322),x53323)),f327(f142(x53321),x53323)) % 177.41/177.18 [5383]~P108(x53831)+E(f327(f327(f238(x53831),x53832),f327(f327(f189(x53831),x53832),x53833)),x53832) % 177.41/177.18 [5384]~P108(x53841)+E(f327(f327(f189(x53841),x53842),f327(f327(f238(x53841),x53842),x53843)),x53842) % 177.41/177.18 [5385]~P96(x53851)+E(f327(f327(f102(x53851),x53852),f327(f327(f103(x53851),x53852),x53853)),x53852) % 177.41/177.18 [5386]~P96(x53861)+E(f327(f327(f103(x53861),x53862),f327(f327(f102(x53861),x53862),x53863)),x53862) % 177.41/177.18 [5405]~P58(x54051)+E(f46(x54051,f327(f327(f81(x54051),x54052),x54053),x54053),f2(x54051)) % 177.41/177.18 [5406]~P58(x54061)+E(f46(x54061,f327(f327(f81(x54061),x54062),x54063),x54062),f2(x54061)) % 177.41/177.18 [5479]~P67(x54791)+E(f327(f79(x54791),f327(f327(f23(x54791),x54792),x54793)),f327(f327(f23(x54791),x54793),x54792)) % 177.41/177.18 [5541]E(x55411,f114(x55412))+E(f115(x55412,f327(f327(f152(x55412),x55413),x55411)),f327(f327(f152(x55412),x55413),f115(x55412,x55411))) % 177.41/177.18 [5542]E(x55421,f114(x55422))+E(f115(x55422,f327(f327(f135(x55422),x55423),x55421)),f327(f327(f135(x55422),x55423),f115(x55422,x55421))) % 177.41/177.18 [5545]~P3(x55451)+E(f39(x55451,f327(f327(f309(x55451),x55452),x55453)),f327(f327(f103(x55451),x55452),f39(x55451,x55453))) % 177.41/177.18 [5546]~P3(x55461)+E(f38(x55461,f327(f327(f309(x55461),x55462),x55463)),f327(f327(f102(x55461),x55462),f38(x55461,x55463))) % 177.41/177.18 [5592]~P95(x55921)+E(f327(f327(f81(x55921),x55922),f327(f327(f81(x55921),x55922),x55923)),f327(f327(f81(x55921),x55922),x55923)) % 177.41/177.18 [5594]~P108(x55941)+E(f327(f327(f238(x55941),x55942),f327(f327(f238(x55941),x55942),x55943)),f327(f327(f238(x55941),x55942),x55943)) % 177.41/177.18 [5596]~P108(x55961)+E(f327(f327(f189(x55961),x55962),f327(f327(f189(x55961),x55962),x55963)),f327(f327(f189(x55961),x55962),x55963)) % 177.41/177.18 [5597]~P96(x55971)+E(f327(f327(f102(x55971),x55972),f327(f327(f102(x55971),x55972),x55973)),f327(f327(f102(x55971),x55972),x55973)) % 177.41/177.18 [5599]~P101(x55991)+E(f327(f327(f102(x55991),x55992),f327(f327(f102(x55991),x55992),x55993)),f327(f327(f102(x55991),x55992),x55993)) % 177.41/177.18 [5600]~P96(x56001)+E(f327(f327(f103(x56001),x56002),f327(f327(f103(x56001),x56002),x56003)),f327(f327(f103(x56001),x56002),x56003)) % 177.41/177.18 [5602]~P102(x56021)+E(f327(f327(f103(x56021),x56022),f327(f327(f103(x56021),x56022),x56023)),f327(f327(f103(x56021),x56022),x56023)) % 177.41/177.18 [5609]~P58(x56091)+E(f46(x56091,f327(f327(f80(x56091),x56092),x56093),x56093),f46(x56091,x56092,x56093)) % 177.41/177.18 [5610]~P58(x56101)+E(f46(x56101,f327(f327(f80(x56101),x56102),x56103),x56102),f46(x56101,x56103,x56102)) % 177.41/177.18 [5619]~P106(x56191)+E(f327(f327(f81(x56191),x56192),f327(f79(x56191),x56193)),f327(f79(x56191),f327(f327(f81(x56191),x56192),x56193))) % 177.41/177.18 [5620]~P61(x56201)+E(f327(f327(f291(x56201),x56202),f327(f79(x56201),x56203)),f327(f79(x56201),f327(f327(f291(x56201),x56202),x56203))) % 177.41/177.18 [5621]~P81(x56211)+E(f327(f327(f80(x56211),x56212),f327(f166(x56211),x56213)),f327(f166(x56211),f327(f327(f152(x56211),x56212),x56213))) % 177.41/177.18 [5649]~P106(x56491)+E(f327(f327(f81(x56491),f327(f79(x56491),x56492)),x56493),f327(f327(f81(x56491),x56492),f327(f79(x56491),x56493))) % 177.41/177.18 [5655]~P6(x56551,x56552,x56553)+E(f38(f922(x56551,a910),f327(f327(f61(x56551),x56552),x56553)),x56552) % 177.41/177.18 [5722]~P116(x57221)+E(f327(f327(f81(x57221),x57222),f327(f327(f244(x57221),x57222),x57223)),f327(f327(f244(x57221),x57222),f327(a113,x57223))) % 177.41/177.18 [5723]~P112(x57231)+E(f327(f327(f81(x57231),x57232),f327(f327(f244(x57231),x57232),x57233)),f327(f327(f244(x57231),x57232),f327(a113,x57233))) % 177.41/177.18 [5733]~P74(x57331)+E(f327(f327(f80(x57331),f327(f79(x57331),x57332)),f327(f327(f80(x57331),x57332),x57333)),x57333) % 177.41/177.18 [5756]~P146(x57561)+E(f327(f327(f244(x57561),f327(f101(x57561),x57562)),x57563),f327(f101(x57561),f327(f327(f244(a915),x57562),x57563))) % 177.41/177.18 [5757]~P142(x57571)+E(f327(f327(f244(x57571),f327(f104(x57571),x57572)),x57573),f327(f104(x57571),f327(f327(f244(a1),x57572),x57573))) % 177.41/177.18 [5763]~P84(x57631)+E(f327(f75(x57631),f327(f327(f23(x57631),x57632),x57633)),f327(f75(x57631),f327(f327(f23(x57631),x57633),x57632))) % 177.41/177.18 [5765]~P119(x57651)+E(f327(f327(f81(x57651),f82(x57651,x57652)),f82(x57651,x57653)),f82(x57651,f327(f327(f81(x57651),x57652),x57653))) % 177.41/177.18 [5769]E(x57691,f114(x57692))+E(f327(f327(f135(x57692),f327(f172(x57692),x57691)),x57693),f327(f172(x57692),f327(f327(f135(x57692),x57691),x57693))) % 177.41/177.18 [5775]~E(x57752,f327(a113,f327(f327(f80(a915),x57751),x57753)))+P1(f327(f327(f235(a915),x57751),x57752)) % 177.41/177.18 [5776]~P106(x57761)+E(f327(f327(f81(x57761),f327(f79(x57761),x57762)),x57763),f327(f79(x57761),f327(f327(f81(x57761),x57762),x57763))) % 177.41/177.18 [5777]~P122(x57771)+E(f327(f327(f291(x57771),f327(f79(x57771),x57772)),x57773),f327(f79(x57771),f327(f327(f291(x57771),x57772),x57773))) % 177.41/177.18 [5778]~P119(x57781)+E(f327(f327(f244(x57781),f327(f75(x57781),x57782)),x57783),f327(f75(x57781),f327(f327(f244(x57781),x57782),x57783))) % 177.41/177.18 [5876]E(f888(x58761,x58762,x58763),f896(x58761,x58762,x58763))+E(f327(f327(f103(f922(x58763,a910)),x58762),x58761),f190(f922(x58763,a910))) % 177.41/177.18 [5891]~P68(x58912)+E(f327(f327(f6(x58911,x58912),f327(f16(x58912,x58911),f2(x58912))),x58913),f2(x58912)) % 177.41/177.18 [5892]~P75(x58922)+E(f327(f327(f9(x58921,x58922),f327(f16(x58922,x58921),f78(x58922))),x58923),f78(x58922)) % 177.41/177.18 [5894]~P146(x58941)+E(f327(f327(f80(x58941),f327(f101(x58941),x58942)),f327(f101(x58941),x58943)),f327(f101(x58941),f327(f327(f80(a915),x58942),x58943))) % 177.41/177.18 [5895]~P146(x58951)+E(f327(f327(f81(x58951),f327(f101(x58951),x58952)),f327(f101(x58951),x58953)),f327(f101(x58951),f327(f327(f81(a915),x58952),x58953))) % 177.41/177.18 [5896]~P142(x58961)+E(f327(f327(f23(x58961),f327(f104(x58961),x58962)),f327(f104(x58961),x58963)),f327(f104(x58961),f327(f327(f23(a1),x58962),x58963))) % 177.41/177.18 [5897]~P142(x58971)+E(f327(f327(f80(x58971),f327(f104(x58971),x58972)),f327(f104(x58971),x58973)),f327(f104(x58971),f327(f327(f80(a1),x58972),x58973))) % 177.41/177.18 [5898]~P142(x58981)+E(f327(f327(f81(x58981),f327(f104(x58981),x58982)),f327(f104(x58981),x58983)),f327(f104(x58981),f327(f327(f81(a1),x58982),x58983))) % 177.41/177.18 [5899]~P93(x58991)+E(f327(f327(f23(x58991),f327(f105(x58991),x58992)),f327(f105(x58991),x58993)),f327(f105(x58991),f327(f327(f23(a1),x58992),x58993))) % 177.41/177.18 [5902]~P93(x59021)+E(f327(f327(f80(x59021),f327(f105(x59021),x59022)),f327(f105(x59021),x59023)),f327(f105(x59021),f327(f327(f80(a1),x59022),x59023))) % 177.41/177.18 [5903]~P93(x59031)+E(f327(f327(f81(x59031),f327(f105(x59031),x59032)),f327(f105(x59031),x59033)),f327(f105(x59031),f327(f327(f81(a1),x59032),x59033))) % 177.41/177.18 [5951]~E(x59513,x59512)+P1(f327(f327(f234(f922(x59511,a910)),x59512),x59513)) % 177.41/177.18 [5957]~E(x59572,x59573)+P1(f327(f327(f234(f922(x59571,a910)),x59572),x59573)) % 177.41/177.18 [5962]~P74(x59621)+E(f327(f327(f80(x59621),f327(f79(x59621),x59622)),f327(f79(x59621),x59623)),f327(f79(x59621),f327(f327(f80(x59621),x59623),x59622))) % 177.41/177.18 [5963]~P67(x59631)+E(f327(f327(f80(x59631),f327(f79(x59631),x59632)),f327(f79(x59631),x59633)),f327(f79(x59631),f327(f327(f80(x59631),x59632),x59633))) % 177.41/177.18 [5964]~P76(x59641)+E(f327(f327(f189(x59641),f327(f79(x59641),x59642)),f327(f79(x59641),x59643)),f327(f79(x59641),f327(f327(f238(x59641),x59642),x59643))) % 177.41/177.18 [5965]~P76(x59651)+E(f327(f327(f238(x59651),f327(f79(x59651),x59652)),f327(f79(x59651),x59653)),f327(f79(x59651),f327(f327(f189(x59651),x59652),x59653))) % 177.41/177.18 [5966]~P86(x59661)+E(f327(f327(f103(x59661),f327(f79(x59661),x59662)),f327(f79(x59661),x59663)),f327(f79(x59661),f327(f327(f102(x59661),x59662),x59663))) % 177.41/177.18 [5967]~P86(x59671)+E(f327(f327(f102(x59671),f327(f79(x59671),x59672)),f327(f79(x59671),x59673)),f327(f79(x59671),f327(f327(f103(x59671),x59672),x59673))) % 177.41/177.18 [5968]~P119(x59681)+E(f327(f327(f81(x59681),f327(f75(x59681),x59682)),f327(f75(x59681),x59683)),f327(f75(x59681),f327(f327(f81(x59681),x59682),x59683))) % 177.41/177.18 [5969]~P63(x59691)+E(f327(f327(f291(x59691),f327(f75(x59691),x59692)),f327(f75(x59691),x59693)),f327(f75(x59691),f327(f327(f291(x59691),x59692),x59693))) % 177.41/177.18 [5970]~P81(x59701)+E(f327(f327(f80(x59701),f327(f166(x59701),x59702)),f327(f166(x59701),x59703)),f327(f166(x59701),f327(f327(f135(x59701),x59702),x59703))) % 177.41/177.18 [5971]E(x59711,f190(f922(x59712,a910)))+~E(f327(f327(f102(f922(x59712,a910)),x59713),x59711),f190(f922(x59712,a910))) % 177.41/177.18 [5972]E(x59721,f190(f922(x59722,a910)))+~E(f327(f327(f102(f922(x59722,a910)),x59721),x59723),f190(f922(x59722,a910))) % 177.41/177.18 [5973]~P148(x59731,x59732,x59733)+P1(f327(x59731,f327(f327(f37(a1),x59732),x59733))) % 177.41/177.18 [6029]~P1(f327(f35(x60291),x60293))+P1(f327(f35(x60291),f327(f327(f309(x60291),x60292),x60293))) % 177.41/177.18 [6030]~P1(f327(f138(x60301),x60303))+P1(f327(f138(x60301),f327(f327(f176(x60301),x60302),x60303))) % 177.41/177.18 [6031]~P1(f327(f138(x60311),x60313))+P1(f327(f138(x60311),f327(f327(f139(x60311),x60312),x60313))) % 177.41/177.18 [6063]~P108(x60631)+P1(f327(f327(f234(x60631),x60632),f327(f327(f189(x60631),x60633),x60632))) % 177.41/177.18 [6064]~P108(x60641)+P1(f327(f327(f234(x60641),x60642),f327(f327(f189(x60641),x60642),x60643))) % 177.41/177.18 [6065]~P96(x60651)+P1(f327(f327(f234(x60651),x60652),f327(f327(f102(x60651),x60653),x60652))) % 177.41/177.18 [6066]~P101(x60661)+P1(f327(f327(f234(x60661),x60662),f327(f327(f102(x60661),x60663),x60662))) % 177.41/177.18 [6067]~P96(x60671)+P1(f327(f327(f234(x60671),x60672),f327(f327(f102(x60671),x60672),x60673))) % 177.41/177.18 [6068]~P101(x60681)+P1(f327(f327(f234(x60681),x60682),f327(f327(f102(x60681),x60682),x60683))) % 177.41/177.18 [6069]~P112(x60691)+P1(f327(f327(f287(x60691),x60692),f327(f327(f81(x60691),x60693),x60692))) % 177.41/177.18 [6070]~P112(x60701)+P1(f327(f327(f287(x60701),x60702),f327(f327(f81(x60701),x60702),x60703))) % 177.41/177.18 [6084]~E(x60841,f2(a915))+E(f327(f327(f37(a915),f327(f327(f81(a915),x60841),x60842)),f327(f327(f81(a915),x60841),x60843)),f2(a915)) % 177.41/177.18 [6165]~P93(x61651)+E(f327(f327(f23(x61651),f327(f105(x61651),x61652)),f327(f105(x61651),x61653)),f327(f105(x61651),f327(f327(f80(a1),x61652),f327(f79(a1),x61653)))) % 177.41/177.18 [6224]E(x62241,f2(a915))+E(f327(f327(f37(a915),f327(f327(f81(a915),x62241),x62242)),f327(f327(f81(a915),x62241),x62243)),f327(f327(f37(a915),x62242),x62243)) % 177.41/177.18 [6257]E(f153(x62571,f327(f327(f152(x62571),x62572),x62573)),f327(f327(f152(x62571),x62572),f153(x62571,x62573)))+P1(f327(f327(f329(x62571),x62572),f327(f173(x62571),x62573))) % 177.41/177.18 [6294]P148(x62941,x62942,x62943)+~P1(f327(x62941,f327(f327(f37(a1),x62942),x62943))) % 177.41/177.18 [6368]E(x63681,f114(x63682))+E(f327(f327(f152(x63682),f327(f142(x63682),x63681)),f327(f327(f176(x63682),x63683),f327(f172(x63682),x63681))),f327(f327(f176(x63682),f327(a113,x63683)),x63681)) % 177.41/177.18 [6376]E(f327(f327(f23(f922(x63761,a910)),x63762),x63763),x63762)+~E(f327(f327(f103(f922(x63761,a910)),x63762),x63763),f190(f922(x63761,a910))) % 177.41/177.18 [6390]E(f153(x63901,f327(f327(f152(x63901),x63902),x63903)),f153(x63901,x63903))+~P1(f327(f327(f329(x63901),x63902),f327(f173(x63901),x63903))) % 177.41/177.18 [6420]~P1(f327(f327(f234(a915),x64201),x64203))+P1(f327(f327(f234(a915),x64201),f327(f327(f80(a915),x64202),x64203))) % 177.41/177.18 [6422]~P1(f327(f327(f234(a915),x64221),x64222))+P1(f327(f327(f234(a915),x64221),f327(f327(f80(a915),x64222),x64223))) % 177.41/177.18 [6424]~P1(f327(f327(f235(a915),x64241),x64243))+P1(f327(f327(f235(a915),x64241),f327(f327(f80(a915),x64242),x64243))) % 177.41/177.18 [6426]~P1(f327(f327(f235(a915),x64261),x64262))+P1(f327(f327(f235(a915),x64261),f327(f327(f80(a915),x64262),x64263))) % 177.41/177.18 [6465]P1(f327(f35(x64651),x64652))+~P1(f327(f35(x64651),f327(f327(f309(x64651),x64653),x64652))) % 177.41/177.18 [6466]P1(f327(f138(x64661),x64662))+~P1(f327(f138(x64661),f327(f327(f152(x64661),x64663),x64662))) % 177.41/177.18 [6467]P1(f327(f138(x64671),x64672))+~P1(f327(f138(x64671),f327(f327(f135(x64671),x64673),x64672))) % 177.41/177.18 [6468]P1(f327(f138(x64681),x64682))+~P1(f327(f138(x64681),f327(f327(f135(x64681),x64682),x64683))) % 177.41/177.18 [6520]~P112(x65201)+E(f327(f327(f80(x65201),x65202),f327(f327(f81(x65201),x65203),x65202)),f327(f327(f81(x65201),f327(f327(f80(x65201),x65203),f78(x65201))),x65202)) % 177.41/177.18 [6567]~E(x65671,x65672)+~P1(f327(f327(f235(f922(x65673,a910)),x65671),x65672)) % 177.41/177.18 [6610]P1(f327(f327(f329(x66101),x66102),x66103))+P1(f327(f327(f329(x66101),x66102),f327(f79(f922(x66101,a910)),x66103))) % 177.41/177.18 [6616]E(f145(x66161,f327(f327(f139(x66161),x66162),x66163)),f145(x66161,x66163))+~P1(f327(f327(f235(a915),x66162),f327(f191(f916(x66161)),x66163))) % 177.41/177.18 [6617]E(f327(f327(f176(x66171),x66172),f115(x66171,x66173)),f327(f327(f176(x66171),x66172),x66173))+~P1(f327(f327(f235(a915),x66172),f327(f191(f916(x66171)),x66173))) % 177.41/177.18 [6674]E(f327(f327(f327(f184(f916(x66741),f916(x66741)),x66742),f168(x66741)),x66743),x66743)+~E(f46(a915,x66742,f327(f191(f916(x66741)),x66743)),f2(a915)) % 177.41/177.18 [6681]~P6(x66811,x66813,x66812)+E(f327(f327(f289(x66811,x66811,x66811),f327(f286(x66811,x66811),x66812)),x66812),x66812) % 177.41/177.18 [6724]~E(f327(f327(f102(f922(x67241,a910)),x67242),x67243),x67243)+P1(f327(f327(f234(f922(x67241,a910)),x67242),x67243)) % 177.41/177.18 [6729]~P52(x67291,x67291,x67293)+P52(x67291,x67291,f327(f327(f184(f921(x67291,x67291),a910),x67292),x67293)) % 177.41/177.18 [6732]~P1(f327(f327(f329(x67321),x67323),f327(f173(x67321),x67322)))+P1(f327(f327(f235(a915),f2(a915)),f327(f191(f916(x67321)),x67322))) % 177.41/177.18 [6759]~P84(x67591)+E(f327(f75(x67591),f327(f327(f80(x67591),f327(f75(x67591),x67592)),f327(f75(x67591),x67593))),f327(f327(f80(x67591),f327(f75(x67591),x67592)),f327(f75(x67591),x67593))) % 177.41/177.18 [6769]E(f327(f327(f37(a915),f327(f327(f81(a915),x67691),x67692)),f327(f327(f81(a915),x67691),x67693)),f327(f327(f37(a915),x67692),x67693))+~P1(f327(f327(f235(a915),f2(a915)),x67691)) % 177.41/177.18 [6909]~P1(f327(f35(x69091),x69093))+E(f327(f327(f64(x69091,f922(x69091,a910),f309(x69091)),x69092),x69093),f327(f327(f102(f922(x69091,a910)),x69093),x69092)) % 177.41/177.18 [6966]E(f327(f327(f102(f922(x69661,a910)),x69662),x69663),x69662)+~P1(f327(f327(f234(f922(x69661,a910)),x69663),x69662)) % 177.41/177.18 [6968]E(f327(f327(f102(f922(x69681,a910)),x69682),x69683),x69683)+~P1(f327(f327(f234(f922(x69681,a910)),x69682),x69683)) % 177.41/177.18 [6969]E(f327(f327(f103(f922(x69691,a910)),x69692),x69693),x69693)+~P1(f327(f327(f234(f922(x69691,a910)),x69693),x69692)) % 177.41/177.18 [6970]E(f327(f327(f103(f922(x69701,a910)),x69702),x69703),x69702)+~P1(f327(f327(f234(f922(x69701,a910)),x69702),x69703)) % 177.41/177.18 [7019]~P1(f327(f138(x70191),x70192))+E(f327(f327(f23(f922(x70191,a910)),f327(f173(x70191),x70192)),f327(f327(f309(x70191),x70193),f190(f922(x70191,a910)))),f327(f173(x70191),f171(x70191,x70193,x70192))) % 177.41/177.18 [7074]P35(x70741,x70742)+~P35(x70741,f327(f327(f184(f921(x70741,x70741),a910),x70743),x70742)) % 177.41/177.18 [7091]~E(x70911,f2(a915))+P1(f327(f327(f287(a915),f327(f327(f81(a915),x70911),x70912)),f327(f327(f81(a915),x70911),x70913))) % 177.41/177.18 [7140]P1(f327(f50(x71401,x71402),f327(a52,x71403)))+~P1(f327(f50(f327(f79(a1),x71401),f327(f79(a1),x71402)),x71403)) % 177.41/177.18 [7145]E(f327(f327(f23(f922(x71451,a910)),f327(f327(f309(x71451),x71452),x71453)),f327(f327(f309(x71451),x71452),f190(f922(x71451,a910)))),x71453)+P1(f327(f327(f329(x71451),x71452),x71453)) % 177.41/177.18 [7168]E(f327(f327(f103(f922(x71681,a910)),f327(f173(x71681),x71682)),f327(f173(x71681),x71683)),f190(f922(x71681,a910)))+~P1(f327(f138(x71681),f327(f327(f135(x71681),x71682),x71683))) % 177.41/177.18 [7183]~P1(f327(f327(f329(x71831),x71832),f327(f173(x71831),x71833)))+~P1(f327(f138(x71831),f327(f327(f152(x71831),x71832),x71833))) % 177.41/177.18 [7255]P29(x72551,x72552,x72553)+P1(f327(f327(f235(a915),f754(x72553,x72552,x72551)),f327(f191(f916(x72551)),x72553))) % 177.41/177.18 [7265]E(f327(f327(f103(f922(x72651,a910)),x72652),x72653),f190(f922(x72651,a910)))+P1(f327(f327(f329(x72651),f888(x72653,x72652,x72651)),x72652)) % 177.41/177.18 [7266]E(f327(f327(f103(f922(x72661,a910)),x72662),x72663),f190(f922(x72661,a910)))+P1(f327(f327(f329(x72661),f896(x72663,x72662,x72661)),x72663)) % 177.41/177.18 [7269]E(f115(x72691,f327(f327(f176(x72691),x72692),x72693)),f327(f327(f176(x72691),f327(f327(f23(a915),x72692),f78(a915))),x72693))+~P1(f327(f327(f234(a915),x72692),f327(f191(f916(x72691)),x72693))) % 177.41/177.18 [7329]~P31(x73293,x73292,x73291)+P1(f327(f327(f235(a915),f749(x73291,x73292,x73293)),f327(f191(f916(x73293)),x73291))) % 177.41/177.18 [7349]P1(f327(f327(f235(a915),f2(a915)),x73491))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x73492),x73491)),f327(f327(f81(a915),x73493),x73491))) % 177.41/177.18 [7350]P1(f327(f327(f235(a915),f2(a915)),x73501))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x73501),x73502)),f327(f327(f81(a915),x73501),x73503))) % 177.41/177.18 [7353]~P1(f327(f327(f329(x73531),x73532),x73533))+~P1(f327(f327(f329(x73531),x73532),f327(f79(f922(x73531,a910)),x73533))) % 177.41/177.18 [7359]~P1(f327(f327(f235(f922(x73591,a910)),x73592),x73593))+P1(f327(f327(f234(f922(x73591,a910)),x73592),x73593)) % 177.41/177.18 [7467]~P1(f327(f327(f234(a915),x74673),x74672))+P1(f327(f327(f234(a915),f327(f327(f23(a915),x74671),x74672)),f327(f327(f23(a915),x74671),x74673))) % 177.41/177.18 [7468]~P1(f327(f327(f234(a915),x74681),x74683))+P1(f327(f327(f234(a915),f327(f327(f23(a915),x74681),x74682)),f327(f327(f23(a915),x74683),x74682))) % 177.41/177.18 [7469]~P1(f327(f327(f234(a915),x74692),x74693))+P1(f327(f327(f234(a915),f327(f327(f80(a915),x74691),x74692)),f327(f327(f80(a915),x74691),x74693))) % 177.41/177.18 [7470]~P1(f327(f327(f234(a915),x74701),x74703))+P1(f327(f327(f234(a915),f327(f327(f80(a915),x74701),x74702)),f327(f327(f80(a915),x74703),x74702))) % 177.41/177.18 [7472]~P1(f327(f327(f234(a915),x74722),x74723))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x74721),x74722)),f327(f327(f81(a915),x74721),x74723))) % 177.41/177.18 [7474]~P1(f327(f327(f234(a915),x74741),x74743))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x74741),x74742)),f327(f327(f81(a915),x74743),x74742))) % 177.41/177.18 [7475]~P1(f327(f327(f234(a915),x74751),x74753))+P1(f327(f327(f234(a915),f327(f327(f37(a915),x74751),x74752)),f327(f327(f37(a915),x74753),x74752))) % 177.41/177.18 [7476]~P1(f327(f327(f234(a1),x74762),x74763))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x74761),x74762)),f327(f327(f80(a1),x74761),x74763))) % 177.41/177.18 [7479]~P1(f327(f327(f235(a915),x74792),x74793))+P1(f327(f327(f235(a915),f327(f327(f80(a915),x74791),x74792)),f327(f327(f80(a915),x74791),x74793))) % 177.41/177.18 [7480]~P1(f327(f327(f235(a915),x74801),x74803))+P1(f327(f327(f235(a915),f327(f327(f80(a915),x74801),x74802)),f327(f327(f80(a915),x74803),x74802))) % 177.41/177.18 [7481]~P1(f327(f327(f235(a1),x74811),x74813))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x74811),x74812)),f327(f327(f80(a1),x74813),x74812))) % 177.41/177.18 [7484]~P1(f327(f327(f287(a915),x74842),x74843))+P1(f327(f327(f287(a915),f327(f327(f81(a915),x74841),x74842)),f327(f327(f81(a915),x74841),x74843))) % 177.41/177.18 [7560]E(x75601,x75602)+~P1(f327(f327(f329(x75603),x75601),f327(f327(f309(x75603),x75602),f190(f922(x75603,a910))))) % 177.41/177.18 [7562]~E(f327(f327(f103(f922(x75621,a910)),x75622),x75623),f190(f922(x75621,a910)))+P1(f327(f327(f234(f922(x75621,a910)),x75622),f327(f79(f922(x75621,a910)),x75623))) % 177.41/177.18 [7567]P1(f327(f327(f329(f922(x75671,a910)),x75672),f327(f308(x75671),x75673)))+~P1(f327(f327(f234(f922(x75671,a910)),x75672),x75673)) % 177.41/177.18 [7617]E(f327(f327(f152(x76171),f327(f327(f165(x76171),x76172),x76173)),f327(f327(f139(x76171),f327(a113,x76173)),x76172)),f327(f327(f139(x76171),x76173),x76172))+~P1(f327(f327(f235(a915),x76173),f327(f191(f916(x76171)),x76172))) % 177.41/177.18 [7643]P1(f327(f327(f329(f921(x76431,x76431)),x76432),f307(x76431,x76433)))+~P1(f327(f327(f329(f921(x76431,x76431)),x76432),x76433)) % 177.41/177.18 [7652]~P1(f327(f327(f329(f922(x76521,a910)),x76522),f327(f308(x76521),x76523)))+P1(f327(f327(f234(f922(x76521,a910)),x76522),x76523)) % 177.41/177.18 [7695]P1(f327(f327(f234(f922(x76951,a910)),x76952),f38(f922(x76951,a910),x76953)))+~P1(f327(f327(f329(f922(x76951,a910)),x76952),x76953)) % 177.41/177.18 [7719]~P142(x77191)+E(f327(f327(f81(x77191),f327(f327(f244(x77191),f327(f79(x77191),f78(x77191))),x77192)),f327(f327(f244(x77191),x77193),x77192)),f327(f327(f244(x77191),f327(f79(x77191),x77193)),x77192)) % 177.41/177.18 [7741]E(f327(f327(f165(x77411),x77412),f327(f327(f23(a915),f327(f191(f916(x77411)),x77412)),f327(a113,x77413))),f327(f327(f165(x77411),f327(f169(x77411),x77412)),x77413))+~P1(f327(f327(f235(a915),x77413),f327(f191(f916(x77411)),x77412))) % 177.41/177.18 [7758]~E(f327(f327(f103(f922(x77581,a910)),f470(x77583,x77582,x77581)),x77583),f190(f922(x77581,a910)))+E(f327(f327(f103(f922(x77581,a910)),f38(f922(x77581,a910),x77582)),x77583),f190(f922(x77581,a910))) % 177.41/177.18 [7822]~P1(f327(f327(f329(x78223),x78222),f327(f173(x78223),x78221)))+P1(f327(f327(f235(a915),f629(x78221,x78222,x78223)),f327(f191(f916(x78223)),x78221))) % 177.41/177.18 [7830]P1(f327(f327(f329(x78301),f327(f327(f165(x78301),x78302),x78303)),f327(f173(x78301),x78302)))+~P1(f327(f327(f235(a915),x78303),f327(f191(f916(x78301)),x78302))) % 177.41/177.18 [7927]~P1(f327(x79272,f714(x79273,x79272,x79271)))+E(f327(f327(f139(x79271),f327(f191(f916(x79271)),f178(x79271,x79272,x79273))),x79273),f114(x79271)) % 177.41/177.18 [7940]P1(f327(f327(f234(f922(f916(x79401),a910)),f162(x79401,x79402)),f162(x79401,x79403)))+~P1(f327(f327(f234(f922(x79401,a910)),x79402),x79403)) % 177.41/177.18 [7941]P1(f327(f327(f234(f922(f916(x79411),a910)),f161(x79411,x79412)),f161(x79411,x79413)))+~P1(f327(f327(f234(f922(x79411,a910)),x79412),x79413)) % 177.41/177.18 [7967]E(f327(f327(f103(f922(x79671,a910)),f38(f922(x79671,a910),x79672)),x79673),f190(f922(x79671,a910)))+P1(f327(f327(f329(f922(x79671,a910)),f470(x79673,x79672,x79671)),x79672)) % 177.41/177.18 [7969]~P1(f327(f327(f329(f922(x79691,a910)),x79693),x79692))+P1(f327(f327(f234(f922(x79691,a910)),f39(f922(x79691,a910),x79692)),x79693)) % 177.41/177.18 [7971]E(f327(f327(f103(f922(x79711,a910)),x79712),x79713),f190(f922(x79711,a910)))+~P1(f327(f327(f234(f922(x79711,a910)),x79712),f327(f79(f922(x79711,a910)),x79713))) % 177.41/177.18 [8019]E(f327(f327(f23(a915),f327(f327(f80(a915),f327(f166(a915),x80191)),x80192)),f327(f327(f165(a915),x80191),x80193)),f327(f166(a915),f327(f327(f160(a915,x80191),x80193),x80192)))+~P1(f327(f327(f235(a915),x80193),f327(f191(f916(a915)),x80191))) % 177.41/177.18 [8070]P1(f327(f327(f234(a915),x80701),x80702))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),x80703),x80701)),f327(f327(f80(a915),x80703),x80702))) % 177.41/177.18 [8073]P1(f327(f327(f235(a915),x80731),x80732))+~P1(f327(f327(f235(a915),f327(f327(f80(a915),x80733),x80731)),f327(f327(f80(a915),x80733),x80732))) % 177.41/177.18 [8074]P1(f327(f327(f235(a915),x80741),x80742))+~P1(f327(f327(f235(a915),f327(f327(f81(a915),x80743),x80741)),f327(f327(f81(a915),x80743),x80742))) % 177.41/177.18 [8075]P1(f327(f327(f235(a915),x80751),x80752))+~P1(f327(f327(f235(a915),f327(f327(f81(a915),x80751),x80753)),f327(f327(f81(a915),x80752),x80753))) % 177.41/177.18 [8104]P1(f327(f327(f235(a915),f2(a915)),x81041))+~P1(f327(f327(f235(a915),f327(f327(f81(a915),x81042),x81041)),f327(f327(f81(a915),x81043),x81041))) % 177.41/177.18 [8105]P1(f327(f327(f235(a915),f2(a915)),x81051))+~P1(f327(f327(f235(a915),f327(f327(f81(a915),x81051),x81052)),f327(f327(f81(a915),x81051),x81053))) % 177.41/177.18 [8178]E(f247(x81781,x81782,x81783),x81782)+~P1(f327(f327(f234(f922(x81781,a910)),x81783),f327(f327(f309(x81781),x81782),f190(f922(x81781,a910))))) % 177.41/177.18 [8228]~P1(f327(f138(x82281),x82283))+E(f327(f137(x82281,f327(f327(f8(a910,a910,x82281),a322),f327(a324,x82282))),x82283),f171(x82281,x82282,x82283)) % 177.41/177.18 [8253]E(f327(f327(f139(x82531),f327(f191(f916(x82531)),f178(x82531,x82532,x82533))),x82533),f114(x82531))+P1(f327(f327(f329(x82531),f714(x82533,x82532,x82531)),f327(f173(x82531),x82533))) % 177.41/177.18 [8257]E(f327(f327(f135(x82571),f327(f327(f176(x82571),x82572),x82573)),f327(f327(f152(x82571),f327(f327(f165(x82571),x82573),x82572)),f114(x82571))),f327(f327(f176(x82571),f327(a113,x82572)),x82573))+~P1(f327(f327(f235(a915),x82572),f327(f191(f916(x82571)),x82573))) % 177.41/177.18 [8324]E(f327(f137(x83241,f327(f327(f8(a910,a910,x83241),a322),f327(a324,x83242))),x83243),x83243)+P1(f327(f327(f329(x83241),x83242),f327(f173(x83241),x83243))) % 177.41/177.18 [8330]P1(f327(f327(f234(f922(f922(x83301,a910),a910)),f248(x83301,x83302)),f248(x83301,x83303)))+~P1(f327(f327(f234(f922(x83301,a910)),x83302),x83303)) % 177.41/177.18 [8369]~P1(f327(f138(x83691),x83693))+P1(f327(f138(x83691),f327(f327(f327(f184(f916(x83691),f916(x83691)),x83692),f168(x83691)),x83693))) % 177.41/177.18 [8375]~P1(f327(f327(f235(a915),x83752),x83753))+P1(f327(f327(f235(a915),f327(f327(f81(a915),f327(a113,x83751)),x83752)),f327(f327(f81(a915),f327(a113,x83751)),x83753))) % 177.41/177.18 [8395]P1(f327(f327(f234(f922(f922(x83951,a910),a910)),f327(f308(x83951),x83952)),f327(f308(x83951),x83953)))+~P1(f327(f327(f234(f922(x83951,a910)),x83952),x83953)) % 177.41/177.18 [8464]~E(f327(f310(x84641,x84642,x84643),f242(f922(x84641,a910))),f242(f922(x84642,a910)))+E(f327(f72(x84641,x84642,x84642,x84643),f92(x84641,x84642,f242(f922(x84641,a910)),x84643)),f31(x84642)) % 177.41/177.18 [8557]~P1(f327(f327(f234(f922(x85571,a910)),x85573),x85572))+P1(f327(f327(f234(f922(x85571,a910)),f327(f79(f922(x85571,a910)),x85572)),f327(f79(f922(x85571,a910)),x85573))) % 177.41/177.18 [8591]E(f327(f310(a915,a915,f327(f327(f7(a915,a915,a915),f23(a915)),x85911)),f327(f302(a915,x85912),x85913)),f327(f302(a915,f327(f327(f23(a915),x85912),x85911)),f327(f327(f23(a915),x85913),x85911)))+~P1(f327(f327(f235(a915),x85911),x85913)) % 177.41/177.18 [8617]~P81(x86171)+E(f327(f327(f80(x86171),x86172),f327(f143(x86171,x86171,f80(x86171),f2(x86171)),x86173)),f327(f143(x86171,x86171,f80(x86171),x86172),x86173)) % 177.41/177.18 [8693]~P84(x86931)+P1(f327(f327(f234(x86931),f327(f75(x86931),f327(f327(f23(x86931),x86932),x86933))),f327(f327(f80(x86931),f327(f75(x86931),x86932)),f327(f75(x86931),x86933)))) % 177.41/177.18 [8694]~P84(x86941)+P1(f327(f327(f234(x86941),f327(f75(x86941),f327(f327(f80(x86941),x86942),x86943))),f327(f327(f80(x86941),f327(f75(x86941),x86942)),f327(f75(x86941),x86943)))) % 177.41/177.18 [8705]E(f327(f327(f80(a1),f327(f327(f81(a1),x87051),f46(a1,f327(f327(f37(a1),x87052),x87051),x87053))),f46(a1,x87052,x87051)),f46(a1,x87052,f327(f327(f81(a1),x87051),x87053)))+~P1(f327(f327(f235(a1),f2(a1)),x87053)) % 177.41/177.18 [8711]E(f327(f327(f135(x87111),f327(f327(f176(x87111),x87112),x87113)),f327(f327(f152(x87111),f327(f142(x87111),f327(f327(f139(x87111),x87112),x87113))),f114(x87111))),f327(f327(f176(x87111),f327(a113,x87112)),x87113))+~P1(f327(f327(f235(a915),x87112),f327(f191(f916(x87111)),x87113))) % 177.41/177.18 [8731]E(f327(f268(x87311,f327(f327(f155(x87311,f921(a100,x87311)),f327(f252(a100,x87311),f78(a100))),x87312)),f327(a3,x87313)),f327(f327(f165(x87311),x87312),x87313))+~P1(f327(f327(f235(a915),x87313),f327(f191(f916(x87311)),x87312))) % 177.41/177.18 [8799]P1(f327(f327(f329(f921(x87991,x87991)),x87992),f327(f327(f289(x87991,x87991,x87991),x87993),f307(x87991,x87993))))+~P1(f327(f327(f329(f921(x87991,x87991)),x87992),x87993)) % 177.41/177.18 [8810]E(f327(f310(x88101,x88102,x88103),f242(f922(x88101,a910))),f242(f922(x88102,a910)))+~E(f327(f72(x88101,x88102,x88102,x88103),f92(x88101,x88102,f242(f922(x88101,a910)),x88103)),f31(x88102)) % 177.41/177.18 [8819]P1(f327(f327(f234(a915),x88191),x88192))+~P1(f327(f327(f234(a915),f327(f327(f81(a915),f327(a113,x88193)),x88191)),f327(f327(f81(a915),f327(a113,x88193)),x88192))) % 177.41/177.18 [8835]P1(f327(f327(f234(f922(x88351,a910)),x88352),x88353))+~P1(f327(f327(f234(f922(x88351,a910)),f327(f79(f922(x88351,a910)),x88353)),f327(f79(f922(x88351,a910)),x88352))) % 177.41/177.18 [8858]P1(f327(f138(x88581),x88582))+~P1(f327(f138(x88581),f327(f327(f327(f184(f916(x88581),f916(x88581)),x88583),f168(x88581)),x88582))) % 177.41/177.18 [8931]E(f327(f285(x89311,x89311,f307(x89311,x89312)),x89313),x89313)+~P1(f327(f327(f234(f922(x89311,a910)),f327(f285(x89311,x89311,x89312),x89313)),x89313)) % 177.41/177.18 [8979]~P108(x89791)+P11(x89791,f327(f137(x89791,f327(f327(f7(x89791,x89791,a910),a324),f327(x89792,x89793))),x89793)) % 177.41/177.18 [8986]~P1(f327(f327(f234(a915),x89861),x89862))+P1(f327(f327(f234(a915),x89861),f327(f143(a915,a915,f80(a915),x89862),x89863))) % 177.41/177.18 [9072]~P1(f327(f327(f329(f921(x90721,x90721)),x90722),f307(x90721,x90723)))+P1(f327(f327(f329(f921(x90721,x90721)),x90722),f327(f327(f184(f921(x90721,x90721),a910),f605(x90723,x90722,x90721)),x90723))) % 177.41/177.18 [9157]~P81(x91571)+E(f327(f327(f80(x91571),x91572),f327(f143(x91571,x91571,f327(f7(x91571,x91571,x91571),f80(x91571)),f2(x91571)),f327(f169(x91571),x91573))),f327(f143(x91571,x91571,f80(x91571),x91572),x91573)) % 177.41/177.18 [9274]~P24(x92742,x92741,x92743,f242(f922(x92742,a910)),f242(f922(x92741,a910)))+E(f92(x92741,x92742,f242(f922(x92741,a910)),f92(x92742,x92741,f242(f922(x92742,a910)),x92743)),x92743) % 177.41/177.18 [9426]P52(x94261,x94262,x94263)+P1(f327(f327(f329(f921(x94261,x94262)),f327(f327(f252(x94261,x94262),f601(x94263,x94262,x94261)),f587(x94263,x94262,x94261))),x94263)) % 177.41/177.18 [9427]P52(x94271,x94272,x94273)+P1(f327(f327(f329(f921(x94271,x94272)),f327(f327(f252(x94271,x94272),f601(x94273,x94272,x94271)),f586(x94273,x94272,x94271))),x94273)) % 177.41/177.18 [9495]~P1(f327(f327(f329(f921(x94951,x94951)),x94952),f327(f327(f289(x94951,x94951,x94951),x94953),f307(x94951,x94953))))+P1(f327(f327(f329(f921(x94951,x94951)),x94952),f327(f327(f184(f921(x94951,x94951),a910),f606(x94953,x94952,x94951)),x94953))) % 177.41/177.18 [9496]~P1(f327(x94961,f327(f327(f165(x94962),x94963),f327(f191(f916(x94962)),f178(x94962,x94961,x94963)))))+~P1(f327(f327(f235(a915),f327(f191(f916(x94962)),f178(x94962,x94961,x94963))),f327(f191(f916(x94962)),x94963))) % 177.41/177.18 [9587]~P1(f327(f327(f234(f922(x95871,a910)),x95872),x95873))+P1(f327(f327(f234(f922(x95871,a910)),f327(f327(f7(x95871,f922(x95871,a910),a910),f329(x95871)),x95872)),f327(f327(f7(x95871,f922(x95871,a910),a910),f329(x95871)),x95873))) % 177.41/177.18 [9644]~P1(f327(f327(f329(f921(f922(x96441,a910),f922(x96441,a910))),f327(f327(f252(f922(x96441,a910),f922(x96441,a910)),x96442),x96443)),f314(x96441)))+P1(f327(f327(f235(f922(x96441,a910)),x96442),x96443)) % 177.41/177.18 [9668]P53(x96681,x96682,x96683)+~P1(f327(f327(f329(f921(x96681,x96681)),f327(f327(f252(x96681,x96681),f604(x96683,x96682,x96681)),f603(x96683,x96682,x96681))),x96683)) % 177.41/177.18 [9669]P53(x96691,x96692,x96693)+~P1(f327(f327(f329(f921(x96691,x96691)),f327(f327(f252(x96691,x96691),f603(x96693,x96692,x96691)),f604(x96693,x96692,x96691))),x96693)) % 177.41/177.18 [9708]~P1(f327(f327(f329(f921(f916(x97081),f916(x97081))),f327(f327(f252(f916(x97081),f916(x97081)),x97082),x97082)),f148(x97081,x97083)))+P1(f327(f327(f329(f921(x97081,x97081)),f327(f327(f252(x97081,x97081),f644(x97082,x97083,x97081)),f644(x97082,x97083,x97081))),x97083)) % 177.41/177.18 [9758]P1(f327(f327(f234(f922(x97581,a910)),x97582),x97583))+~P1(f327(f327(f234(f922(x97581,a910)),f327(f327(f7(x97581,f922(x97581,a910),a910),f329(x97581)),x97582)),f327(f327(f7(x97581,f922(x97581,a910),a910),f329(x97581)),x97583))) % 177.41/177.18 [9839]E(f327(f327(f23(a915),f327(f327(f6(a915,a915),x98391),f327(f282(a915),x98392))),f327(f327(f6(a915,a915),x98393),f327(f282(a915),x98392))),f327(f327(f6(a915,a915),f327(f327(f18(a915,a915,a915),f327(f327(f8(a915,f922(a915,a915),a915),f23(a915)),x98391)),x98393)),f327(f282(a915),x98392)))+~P1(f327(f327(f234(a915),f327(x98393,f415(x98392,x98391,x98393))),f327(x98391,f415(x98392,x98391,x98393)))) % 177.41/177.18 [5812]~P74(x58121)+E(f327(f327(f23(x58121),f327(f327(f80(x58121),x58122),x58123)),x58123),x58122) % 177.41/177.18 [5813]~P74(x58131)+E(f327(f327(f80(x58131),f327(f327(f23(x58131),x58132),x58133)),x58133),x58132) % 177.41/177.18 [6038]~P74(x60381)+E(f327(f327(f80(x60381),x60382),f327(f327(f80(x60381),f327(f79(x60381),x60382)),x60383)),x60383) % 177.41/177.18 [6126]~P80(x61261)+E(f327(f327(f81(x61261),f327(f327(f244(x61261),x61262),x61263)),x61262),f327(f327(f244(x61261),x61262),f327(a113,x61263))) % 177.41/177.18 [6127]~P112(x61271)+E(f327(f327(f81(x61271),f327(f327(f244(x61271),x61272),x61273)),x61272),f327(f327(f244(x61271),x61272),f327(a113,x61273))) % 177.41/177.18 [6352]~P119(x63521)+E(f327(f75(x63521),f327(f327(f244(x63521),f327(f79(x63521),x63522)),x63523)),f327(f75(x63521),f327(f327(f244(x63521),x63522),x63523))) % 177.41/177.18 [6398]~P80(x63981)+E(f327(f327(f81(x63981),f327(f327(f244(x63981),x63982),x63983)),x63982),f327(f327(f81(x63981),x63982),f327(f327(f244(x63981),x63982),x63983))) % 177.41/177.18 [6456]E(f327(f327(f23(a100),f327(f327(f80(a100),x64561),x64562)),x64563),f274(x64561,x64562,x64563))+~P1(f327(f327(f235(a100),x64562),x64563)) % 177.41/177.18 [6480]~E(f327(f327(f139(x64801),x64803),x64802),f114(x64801))+P1(f327(f327(f234(a915),f327(f191(f916(x64801)),x64802)),x64803)) % 177.41/177.18 [6615]E(f327(f327(f81(a915),f327(f105(a915),x66151)),f327(f327(f81(a915),f327(f105(a915),x66152)),x66153)),f2(a915))+~P1(f327(f327(f235(a1),x66151),a83)) % 177.41/177.18 [6631]~P61(x66311)+E(f327(f327(f244(x66311),f327(f327(f291(x66311),f78(x66311)),x66312)),x66313),f327(f327(f291(x66311),f78(x66311)),f327(f327(f244(x66311),x66312),x66313))) % 177.41/177.18 [6710]E(f327(f327(f23(a915),f327(f327(f80(a915),x67101),x67102)),x67103),f327(f327(f23(a915),x67101),f327(f327(f23(a915),x67103),x67102)))+~P1(f327(f327(f234(a915),x67102),x67103)) % 177.41/177.18 [6712]E(f327(f327(f23(a915),f327(f327(f80(a915),x67121),x67122)),x67123),f327(f327(f80(a915),x67121),f327(f327(f23(a915),x67122),x67123)))+~P1(f327(f327(f234(a915),x67123),x67122)) % 177.41/177.18 [6750]~P108(x67501)+P1(f327(f327(f234(x67501),f327(f327(f238(x67501),x67502),x67503)),x67503)) % 177.41/177.18 [6751]~P108(x67511)+P1(f327(f327(f234(x67511),f327(f327(f238(x67511),x67512),x67513)),x67512)) % 177.41/177.18 [6752]~P96(x67521)+P1(f327(f327(f234(x67521),f327(f327(f103(x67521),x67522),x67523)),x67523)) % 177.41/177.18 [6753]~P102(x67531)+P1(f327(f327(f234(x67531),f327(f327(f103(x67531),x67532),x67533)),x67533)) % 177.41/177.18 [6754]~P96(x67541)+P1(f327(f327(f234(x67541),f327(f327(f103(x67541),x67542),x67543)),x67542)) % 177.41/177.18 [6755]~P102(x67551)+P1(f327(f327(f234(x67551),f327(f327(f103(x67551),x67552),x67553)),x67552)) % 177.41/177.18 [6768]E(f327(f327(f37(a1),f327(f327(f37(a1),x67681),x67682)),x67683),f327(f327(f37(a1),x67681),f327(f327(f81(a1),x67682),x67683)))+~P1(f327(f327(f235(a1),f2(a1)),x67683)) % 177.41/177.18 [6820]~P112(x68201)+E(f327(f327(f80(x68201),f327(f327(f81(x68201),x68202),x68203)),x68203),f327(f327(f81(x68201),f327(f327(f80(x68201),x68202),f78(x68201))),x68203)) % 177.41/177.18 [6821]~P93(x68211)+E(f327(f327(f81(x68211),f327(f79(x68211),f327(f105(x68211),x68212))),x68213),f327(f327(f81(x68211),f327(f105(x68211),f327(f79(a1),x68212))),x68213)) % 177.41/177.18 [6893]~P81(x68931)+E(f327(f166(x68931),f327(f327(f155(x68932,x68931),f327(f16(x68931,x68932),f2(x68931))),x68933)),f2(x68931)) % 177.41/177.18 [6911]E(f327(f327(f80(a915),f327(f105(a915),x69111)),f327(f327(f80(a915),f327(f105(a915),x69112)),x69113)),f327(f327(f80(a915),f327(f105(a915),x69112)),x69113))+~P1(f327(a195,f327(f105(a1),x69111))) % 177.41/177.18 [6926]~P3(x69261)+E(f39(x69261,f327(f327(f309(x69261),x69262),f327(f327(f309(x69261),x69263),f190(f922(x69261,a910))))),f327(f327(f103(x69261),x69262),x69263)) % 177.41/177.18 [6927]~P3(x69271)+E(f38(x69271,f327(f327(f309(x69271),x69272),f327(f327(f309(x69271),x69273),f190(f922(x69271,a910))))),f327(f327(f102(x69271),x69272),x69273)) % 177.41/177.18 [6949]E(f327(f327(f176(x69491),x69492),x69493),x69493)+~P1(f327(f327(f234(a915),f327(f191(f916(x69491)),x69493)),x69492)) % 177.41/177.18 [6961]E(f327(f327(f139(x69611),x69612),x69613),f114(x69611))+~P1(f327(f327(f234(a915),f327(f191(f916(x69611)),x69613)),x69612)) % 177.41/177.18 [6972]E(f327(f327(f80(a915),f327(f327(f23(a915),x69721),x69722)),x69723),f327(f327(f23(a915),f327(f327(f80(a915),x69721),x69723)),x69722))+~P1(f327(f327(f234(a915),x69722),x69721)) % 177.41/177.18 [6986]~P1(f327(f327(f235(a915),x69861),x69863))+P1(f327(f327(f235(a915),f327(f327(f23(a915),x69861),x69862)),x69863)) % 177.41/177.18 [7013]~P108(x70131)+E(f171(x70131,x70132,f327(f327(f149(x70131,x70131,f5(x70131)),x70132),x70133)),x70133) % 177.41/177.18 [7104]E(f327(f327(f23(a915),f327(f327(f80(a915),x71041),x71042)),f327(a113,x71043)),f327(f327(f23(a915),x71041),f327(a113,f327(f327(f23(a915),x71043),x71042))))+~P1(f327(f327(f234(a915),x71042),x71043)) % 177.41/177.18 [7105]~P119(x71051)+P1(f327(f327(f234(x71051),f2(x71051)),f327(f327(f244(x71051),f327(f75(x71051),x71052)),x71053))) % 177.41/177.18 [7152]P22(x71521,x71522,x71523)+~P1(f327(f327(f234(f922(f913(x71521),a910)),x71523),x71522)) % 177.41/177.18 [7194]~P1(f327(f35(x71941),x71942))+P1(f327(f35(x71941),f327(f327(f23(f922(x71941,a910)),x71942),x71943))) % 177.41/177.18 [7195]~P1(f327(f35(x71951),x71953))+P1(f327(f35(x71951),f327(f327(f103(f922(x71951,a910)),x71952),x71953))) % 177.41/177.18 [7196]~P1(f327(f35(x71961),x71962))+P1(f327(f35(x71961),f327(f327(f103(f922(x71961,a910)),x71962),x71963))) % 177.41/177.18 [7339]~P35(x73391,x73393)+P35(x73391,f327(f327(f103(f922(f921(x73391,x73391),a910)),x73392),x73393)) % 177.41/177.18 [7340]~P35(x73401,x73402)+P35(x73401,f327(f327(f103(f922(f921(x73401,x73401),a910)),x73402),x73403)) % 177.41/177.18 [7463]~P108(x74631)+E(f14(x74631,f327(f173(x74631),f327(f327(f152(x74631),x74632),x74633))),f327(f143(x74631,x74631,f189(x74631),x74632),x74633)) % 177.41/177.18 [7464]~P108(x74641)+E(f15(x74641,f327(f173(x74641),f327(f327(f152(x74641),x74642),x74643))),f327(f143(x74641,x74641,f238(x74641),x74642),x74643)) % 177.41/177.18 [7465]~P96(x74651)+E(f13(x74651,f327(f173(x74651),f327(f327(f152(x74651),x74652),x74653))),f327(f143(x74651,x74651,f102(x74651),x74652),x74653)) % 177.41/177.18 [7466]~P96(x74661)+E(f10(x74661,f327(f173(x74661),f327(f327(f152(x74661),x74662),x74663))),f327(f143(x74661,x74661,f103(x74661),x74662),x74663)) % 177.41/177.18 [7529]~P1(f327(f35(x75291),x75292))+P1(f327(f327(f234(a915),f327(f36(x75291),x75292)),f327(f36(x75291),f327(f327(f309(x75291),x75293),x75292)))) % 177.41/177.18 [7536]E(f327(f327(f102(f922(a915,a910)),f327(f302(a915,x75361),x75362)),f327(f302(a915,x75362),f327(f327(f80(a915),x75362),x75363))),f327(f302(a915,x75361),f327(f327(f80(a915),x75362),x75363)))+~P1(f327(f327(f234(a915),x75361),x75362)) % 177.41/177.18 [7545]P1(f327(f327(f234(a915),x75451),x75452))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),x75453),x75451)),x75452)) % 177.41/177.18 [7546]P1(f327(f327(f234(a915),x75461),x75462))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),x75461),x75463)),x75462)) % 177.41/177.18 [7547]P1(f327(f327(f235(a915),x75471),x75472))+~P1(f327(f327(f235(a915),f327(f327(f80(a915),x75471),x75473)),x75472)) % 177.41/177.18 [7584]~P108(x75841)+E(f11(x75841,f189(x75841),f327(f173(x75841),f327(f327(f152(x75841),x75842),x75843))),f327(f143(x75841,x75841,f189(x75841),x75842),x75843)) % 177.41/177.18 [7585]~P108(x75851)+E(f12(x75851,f238(x75851),f327(f173(x75851),f327(f327(f152(x75851),x75852),x75853))),f327(f143(x75851,x75851,f238(x75851),x75852),x75853)) % 177.41/177.18 [7589]~E(x75892,f190(f922(f921(x75891,x75891),a910)))+P1(f327(f327(f234(f922(f921(x75891,x75891),a910)),x75892),x75893)) % 177.41/177.18 [7690]E(f327(f327(f102(f922(x76901,a910)),x76902),f327(f327(f23(f922(x76901,a910)),x76903),x76902)),x76903)+~P1(f327(f327(f234(f922(x76901,a910)),x76902),x76903)) % 177.41/177.18 [7691]~P1(f327(f327(f234(a915),x76911),f327(f327(f80(a915),x76913),x76912)))+P1(f327(f327(f234(a915),f327(f327(f23(a915),x76911),x76912)),x76913)) % 177.41/177.18 [7692]~P1(f327(f327(f235(a915),x76921),f327(f327(f23(a915),x76923),x76922)))+P1(f327(f327(f235(a915),f327(f327(f80(a915),x76921),x76922)),x76923)) % 177.41/177.18 [7748]E(x77481,f114(x77482))+E(f327(f142(x77482),f327(f327(f327(f184(f916(x77482),f916(x77482)),x77483),f168(x77482)),x77481)),f327(f327(f165(x77482),x77481),f46(a915,x77483,f327(f191(f916(x77482)),x77481)))) % 177.41/177.18 [7757]E(f327(f327(f309(x77571),x77572),f327(f327(f23(f922(x77571,a910)),x77573),f327(f327(f309(x77571),x77572),f190(f922(x77571,a910))))),x77573)+~P1(f327(f327(f329(x77571),x77572),x77573)) % 177.41/177.18 [7918]P1(f327(f327(f234(a915),x79181),f327(f327(f80(a915),x79182),x79183)))+~P1(f327(f327(f234(a915),f327(f327(f23(a915),x79181),x79183)),x79182)) % 177.41/177.18 [7919]P1(f327(f327(f235(a915),x79191),f327(f327(f23(a915),x79192),x79193)))+~P1(f327(f327(f235(a915),f327(f327(f80(a915),x79191),x79193)),x79192)) % 177.41/177.18 [7944]P1(f327(f35(x79441),x79442))+~P1(f327(f35(x79441),f327(f327(f102(f922(x79441,a910)),x79443),x79442))) % 177.41/177.18 [7945]P1(f327(f35(x79451),x79452))+~P1(f327(f35(x79451),f327(f327(f102(f922(x79451,a910)),x79452),x79453))) % 177.41/177.18 [8018]~P44(x80181,x80183)+P1(f327(f327(f329(f921(x80181,x80181)),f327(f327(f252(x80181,x80181),x80182),x80182)),x80183)) % 177.41/177.18 [8151]E(f327(f327(f165(a915),f140(a915,f327(f302(a915,x81511),x81512))),x81513),f327(f327(f80(a915),x81511),x81513))+~P1(f327(f327(f235(a915),f327(f327(f80(a915),x81511),x81513)),x81512)) % 177.41/177.18 [8217]E(f327(f327(f176(a915),x82171),f140(a915,f327(f302(a915,x82172),x82173))),f140(a915,f327(f302(a915,x82172),f327(f327(f80(a915),x82172),x82171))))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),x82172),x82171)),x82173)) % 177.41/177.18 [8274]~P93(x82741)+E(f327(f327(f244(x82741),x82742),f327(f105(a915),f327(f327(f80(a1),x82743),x82743))),f327(f327(f86(x82741,x82741),f327(f327(f244(x82741),x82742),f327(f105(a915),x82743))),f327(f327(f18(x82741,x82741,x82741),f81(x82741)),f5(x82741)))) % 177.41/177.18 [8538]E(f327(f327(f135(x85381),f327(f327(f176(x85381),x85382),x85383)),f327(f327(f152(x85381),f327(f327(f165(x85381),x85383),x85382)),f327(f327(f139(x85381),f327(a113,x85382)),x85383))),x85383)+~P1(f327(f327(f235(a915),x85382),f327(f191(f916(x85381)),x85383))) % 177.41/177.18 [8545]P1(f327(f327(f234(f922(x85451,a910)),f315(x85451,x85452)),f315(x85451,x85453)))+~P1(f327(f327(f234(f922(x85451,f922(x85451,a910))),x85453),x85452)) % 177.41/177.18 [8546]~P53(x85461,x85462,x85463)+P53(x85461,x85462,f327(f327(f23(f922(f921(x85461,x85461),a910)),x85463),f307(x85461,f190(f922(f921(x85461,x85461),a910))))) % 177.41/177.18 [8565]P1(f327(f327(f234(f922(x85651,a910)),f316(x85651,x85652)),f316(x85651,x85653)))+~P1(f327(f327(f234(f922(f921(x85651,x85651),a910)),x85653),x85652)) % 177.41/177.18 [8572]~P128(x85721)+P1(f327(f327(f234(x85721),f2(x85721)),f327(f327(f80(x85721),f327(f327(f81(x85721),x85722),x85722)),f327(f327(f81(x85721),x85723),x85723)))) % 177.41/177.18 [8606]P1(f327(f327(f234(f922(x86061,a910)),f327(f281(x86061),x86062)),f327(f281(x86061),x86063)))+~P1(f327(f327(f234(f922(f921(x86061,x86061),a910)),x86062),x86063)) % 177.41/177.18 [8635]~P51(x86351,x86352)+~P1(f327(f327(f329(f921(x86351,x86351)),f327(f327(f252(x86351,x86351),x86353),x86353)),x86352)) % 177.41/177.18 [8637]~P35(x86371,x86372)+~P1(f327(f327(f329(f921(x86371,x86371)),f327(f327(f252(x86371,x86371),x86373),x86373)),x86372)) % 177.41/177.18 [8695]P1(f327(f327(f234(f922(x86951,a910)),f39(f922(x86951,a910),x86952)),f39(f922(x86951,a910),x86953)))+~P1(f327(f327(f234(f922(f922(x86951,a910),a910)),x86953),x86952)) % 177.41/177.18 [8696]P1(f327(f327(f234(f922(x86961,a910)),f38(f922(x86961,a910),x86962)),f38(f922(x86961,a910),x86963)))+~P1(f327(f327(f234(f922(f922(x86961,a910),a910)),x86962),x86963)) % 177.41/177.18 [8750]~P6(x87501,x87503,x87502)+P1(f327(f327(f234(f922(f921(x87501,x87501),a910)),x87502),f327(f327(f254(x87501,x87501),x87503),f327(f16(f922(x87501,a910),x87501),x87503)))) % 177.41/177.18 [8751]~P50(x87511,x87513,x87512)+P1(f327(f327(f234(f922(f921(x87511,x87511),a910)),x87512),f327(f327(f254(x87511,x87511),x87513),f327(f16(f922(x87511,a910),x87511),x87513)))) % 177.41/177.18 [8800]~P84(x88001)+P1(f327(f327(f234(x88001),f327(f327(f23(x88001),f327(f75(x88001),x88002)),f327(f75(x88001),x88003))),f327(f75(x88001),f327(f327(f23(x88001),x88003),x88002)))) % 177.41/177.18 [8801]~P84(x88011)+P1(f327(f327(f234(x88011),f327(f327(f23(x88011),f327(f75(x88011),x88012)),f327(f75(x88011),x88013))),f327(f75(x88011),f327(f327(f23(x88011),x88012),x88013)))) % 177.41/177.18 [8833]P1(f327(f327(f234(f922(f921(x88331,x88331),a910)),f307(x88331,x88332)),f307(x88331,x88333)))+~P1(f327(f327(f234(f922(f921(x88331,x88331),a910)),x88332),x88333)) % 177.41/177.18 [8944]~P23(x89442,x89441,x89443,f242(f922(x89442,a910)))+E(f327(f72(x89441,x89442,x89442,f92(x89442,x89441,f242(f922(x89442,a910)),x89443)),x89443),f31(x89442)) % 177.41/177.18 [9004]P53(x90041,x90042,x90043)+~P53(x90041,x90042,f327(f327(f23(f922(f921(x90041,x90041),a910)),x90043),f307(x90041,f190(f922(f921(x90041,x90041),a910))))) % 177.41/177.18 [9024]P1(f327(f327(f234(f922(f921(f916(x90241),f916(x90241)),a910)),f158(x90241,x90242)),f158(x90241,x90243)))+~P1(f327(f327(f234(f922(f921(x90241,x90241),a910)),x90242),x90243)) % 177.41/177.18 [9025]P1(f327(f327(f234(f922(f921(f916(x90251),f916(x90251)),a910)),f159(x90251,x90252)),f159(x90251,x90253)))+~P1(f327(f327(f234(f922(f921(x90251,x90251),a910)),x90252),x90253)) % 177.41/177.18 [9046]~P50(x90461,x90463,x90462)+P1(f327(f327(f234(f922(f921(x90461,x90461),a910)),x90462),f327(f327(f289(x90461,x90461,x90461),f327(f286(x90461,x90461),x90462)),x90462))) % 177.41/177.18 [9100]~P1(f327(f138(x91001),x91002))+E(f327(f137(x91001,f327(f327(f7(x91001,f922(x91001,a910),a910),f329(x91001)),f327(f173(x91001),f177(x91001,x91002,x91003)))),x91002),f177(x91001,x91002,x91003)) % 177.41/177.18 [9155]E(x91551,x91552)+~P1(f327(f327(f329(f921(x91553,x91553)),f327(f327(f252(x91553,x91553),x91551),x91552)),f307(x91553,f190(f922(f921(x91553,x91553),a910))))) % 177.41/177.18 [9237]P1(f327(f327(f329(x92371),x92372),f316(x92371,x92373)))+P1(f327(f327(f329(f921(x92371,x92371)),f327(f327(f252(x92371,x92371),f537(x92373,x92372,x92371)),x92372)),x92373)) % 177.41/177.18 [9238]P1(f327(f327(f329(x92381),x92382),f316(x92381,x92383)))+P1(f327(f327(f329(f921(x92381,x92381)),f327(f327(f252(x92381,x92381),f588(x92383,x92382,x92381)),x92382)),x92383)) % 177.41/177.18 [9239]P1(f327(f327(f329(x92391),x92392),f316(x92391,x92393)))+P1(f327(f327(f329(f921(x92391,x92391)),f327(f327(f252(x92391,x92391),f594(x92393,x92392,x92391)),x92392)),x92393)) % 177.41/177.18 [9275]P23(x92751,x92752,x92753,f242(f922(x92751,a910)))+~E(f327(f72(x92752,x92751,x92751,f92(x92751,x92752,f242(f922(x92751,a910)),x92753)),x92753),f31(x92751)) % 177.41/177.18 [9328]~P1(f327(f327(f329(f916(x93281)),x93283),f162(x93281,x93282)))+P1(f327(f161(x93281,f327(f327(f7(x93281,f922(x93281,a910),a910),f329(x93281)),x93282)),x93283)) % 177.41/177.18 [9351]P1(f327(x93513,x93512))+E(f327(f262(x93511),f327(f327(f18(x93511,a910,a910),f327(f327(f8(a910,f922(a910,a910),x93511),a325),f327(a324,x93512))),x93513)),f190(f922(x93511,a910))) % 177.41/177.18 [9367]~P84(x93671)+P1(f327(f327(f234(x93671),f327(f75(x93671),f327(f327(f23(x93671),f327(f75(x93671),x93672)),f327(f75(x93671),x93673)))),f327(f75(x93671),f327(f327(f23(x93671),x93672),x93673)))) % 177.41/177.18 [9381]~P1(f327(x93813,x93812))+E(f327(f262(x93811),f327(f327(f18(x93811,a910,a910),f327(f327(f8(a910,f922(a910,a910),x93811),a325),f327(a324,x93812))),x93813)),f327(f327(f309(x93811),x93812),f190(f922(x93811,a910)))) % 177.41/177.18 [9390]~P1(f327(f327(f329(f922(x93901,a910)),x93903),f327(f308(x93901),x93902)))+P1(f327(f248(x93901,f327(f327(f7(x93901,f922(x93901,a910),a910),f329(x93901)),x93902)),x93903)) % 177.41/177.18 [9425]P35(x94251,x94252)+P1(f327(f327(f329(f921(x94251,x94251)),f327(f327(f252(x94251,x94251),f327(f546(x94252,x94251),f327(a113,x94253))),f327(f546(x94252,x94251),x94253))),x94252)) % 177.41/177.18 [9564]P1(f327(f327(f329(f916(x95641)),x95642),f162(x95641,x95643)))+~P1(f327(f161(x95641,f327(f327(f7(x95641,f922(x95641,a910),a910),f329(x95641)),x95643)),x95642)) % 177.41/177.18 [9579]P1(f327(f327(f329(f922(x95791,a910)),x95792),f327(f308(x95791),x95793)))+~P1(f327(f248(x95791,f327(f327(f7(x95791,f922(x95791,a910),a910),f329(x95791)),x95793)),x95792)) % 177.41/177.18 [9639]P1(f327(f327(f329(x96391),f327(f268(x96391,x96392),x96393)),f327(f173(x96391),f327(f327(f155(f921(a100,x96391),x96391),f256(a100,x96391)),x96392))))+~P1(f327(f327(f235(a100),x96393),f327(f166(a100),f327(f327(f155(f921(a100,x96391),a100),f251(a100,x96391)),x96392)))) % 177.41/177.18 [9686]P1(f327(f327(f234(f922(f921(f916(x96861),f916(x96861)),a910)),f159(x96861,x96862)),f327(f327(f254(f916(x96861),f916(x96861)),f162(x96861,x96863)),f327(f16(f922(f916(x96861),a910),f916(x96861)),f162(x96861,x96863)))))+~P1(f327(f327(f234(f922(f921(x96861,x96861),a910)),x96862),f327(f327(f254(x96861,x96861),x96863),f327(f16(f922(x96861,a910),x96861),x96863)))) % 177.41/177.18 [9711]P1(f327(f327(f329(x97111),f327(f251(x97111,f921(a100,a100)),f327(f266(x97111,x97112),x97113))),f327(f173(x97111),f327(f327(f155(f921(a100,x97111),x97111),f256(a100,x97111)),x97112))))+~P1(f327(f327(f235(a100),f2(a100)),f327(f166(a100),f327(f327(f155(f921(a100,x97111),a100),f251(a100,x97111)),x97112)))) % 177.41/177.18 [9726]~P1(f327(f327(f234(f922(f921(x97261,x97261),a910)),x97262),f327(f327(f254(x97261,x97261),x97263),f327(f16(f922(x97261,a910),x97261),x97263))))+P1(f327(f327(f234(f922(f921(x97261,x97261),a910)),f327(f327(f289(x97261,x97261,x97261),x97262),f307(x97261,x97262))),f327(f327(f254(x97261,x97261),x97263),f327(f16(f922(x97261,a910),x97261),x97263)))) % 177.41/177.18 [10026]~P35(x100261,x100262)+~P1(f327(f327(f329(f921(x100261,x100261)),f327(f327(f252(x100261,x100261),f327(x100263,f327(a113,f545(x100262,x100261,x100263)))),f327(x100263,f545(x100262,x100261,x100263)))),x100262)) % 177.41/177.18 [10027]~P35(x100271,x100272)+~P1(f327(f327(f329(f921(x100271,x100271)),f327(f327(f252(x100271,x100271),f327(x100273,f327(a113,f599(x100273,x100272,x100271)))),f327(x100273,f599(x100273,x100272,x100271)))),x100272)) % 177.41/177.18 [10288]P1(f327(f327(f234(f922(f921(f922(x102881,a910),f922(x102881,a910)),a910)),f327(f327(f289(f922(x102881,a910),f922(x102881,a910),f922(x102881,a910)),f318(x102881,x102882)),f327(f327(f102(f922(f921(f922(x102881,a910),f922(x102881,a910)),a910)),f318(x102881,x102883)),f327(f327(f309(f921(f922(x102881,a910),f922(x102881,a910))),f327(f327(f252(f922(x102881,a910),f922(x102881,a910)),f190(f922(x102881,a910))),f190(f922(x102881,a910)))),f190(f922(f921(f922(x102881,a910),f922(x102881,a910)),a910)))))),f318(x102881,x102882)))+~P1(f327(f327(f234(f922(f921(x102881,x102881),a910)),f327(f327(f289(x102881,x102881,x102881),x102882),x102883)),x102882)) % 177.41/177.18 [10289]P1(f327(f327(f234(f922(f921(f922(x102891,a910),f922(x102891,a910)),a910)),f327(f327(f289(f922(x102891,a910),f922(x102891,a910),f922(x102891,a910)),f319(x102891,x102892)),f327(f327(f102(f922(f921(f922(x102891,a910),f922(x102891,a910)),a910)),f319(x102891,x102893)),f327(f327(f309(f921(f922(x102891,a910),f922(x102891,a910))),f327(f327(f252(f922(x102891,a910),f922(x102891,a910)),f190(f922(x102891,a910))),f190(f922(x102891,a910)))),f190(f922(f921(f922(x102891,a910),f922(x102891,a910)),a910)))))),f319(x102891,x102892)))+~P1(f327(f327(f234(f922(f921(x102891,x102891),a910)),f327(f327(f289(x102891,x102891,x102891),x102892),x102893)),x102892)) % 177.41/177.18 [7462]~P1(f327(f327(f234(a915),x74622),x74621))+E(f327(f327(f23(a915),f327(a113,f327(f327(f23(a915),x74621),x74622))),x74623),f327(f327(f23(a915),f327(a113,x74621)),f327(f327(f80(a915),x74622),x74623))) % 177.41/177.18 [7502]~P58(x75021)+E(f327(f327(f80(x75021),f46(x75021,x75022,x75023)),f327(f327(f81(x75021),f327(f327(f37(x75021),x75022),x75023)),x75023)),x75022) % 177.41/177.18 [7696]E(f327(f327(f81(a915),f327(f105(a915),x76961)),f327(f327(f81(a915),f327(f105(a915),x76962)),x76963)),f327(f327(f81(a915),f327(f105(a915),f327(f327(f81(a1),x76961),x76962))),x76963))+P1(f327(f327(f235(a1),x76961),a83)) % 177.41/177.18 [8160]~P1(f327(f327(f234(a915),x81603),x81602))+P1(f327(f327(f234(a915),x81601),f327(f327(f23(a915),f327(f327(f80(a915),x81602),x81601)),x81603))) % 177.41/177.18 [8360]~P1(f327(f327(f234(a915),x83601),x83602))+E(f327(f327(f135(a915),f140(a915,f327(f302(a915,x83601),x83602))),f140(a915,f327(f302(a915,x83602),f327(f327(f80(a915),x83602),x83603)))),f140(a915,f327(f302(a915,x83601),f327(f327(f80(a915),x83602),x83603)))) % 177.41/177.18 [8614]~P1(f327(f35(x86141),x86142))+E(f327(a113,f327(f36(x86141),f327(f327(f23(f922(x86141,a910)),x86142),f327(f327(f309(x86141),x86143),f190(f922(x86141,a910)))))),f327(f36(x86141),f327(f327(f309(x86141),x86143),x86142))) % 177.41/177.18 [8653]~P1(f327(f35(x86531),x86532))+E(f327(f327(f80(a915),f78(a915)),f327(f36(x86531),f327(f327(f23(f922(x86531,a910)),x86532),f327(f327(f309(x86531),x86533),f190(f922(x86531,a910)))))),f327(f36(x86531),f327(f327(f309(x86531),x86533),x86532))) % 177.41/177.18 [8842]E(f327(f327(f23(a915),f327(f36(x88421),x88422)),f327(f36(x88421),f327(f327(f103(f922(x88421,a910)),x88422),x88423))),f327(f36(x88421),f327(f327(f23(f922(x88421,a910)),x88422),x88423)))+~P1(f327(f35(x88421),f327(f327(f103(f922(x88421,a910)),x88422),x88423))) % 177.41/177.18 [9095]~P4(f327(x90952,f411(x90952,x90953,x90951)))+E(f327(f101(a1),f327(f327(f6(x90951,a915),f327(f327(f8(a1,a915,x90951),a106),x90952)),x90953)),f327(f327(f6(x90951,a1),x90952),x90953)) % 177.41/177.18 [9096]~P4(f327(x90962,f412(x90962,x90963,x90961)))+E(f327(f101(a1),f327(f327(f9(x90961,a915),f327(f327(f8(a1,a915,x90961),a106),x90962)),x90963)),f327(f327(f9(x90961,a1),x90962),x90963)) % 177.41/177.18 [9138]~P1(f327(f35(x91381),x91383))+P1(f327(f327(f234(a915),f327(f327(f23(a915),f327(f36(x91381),x91382)),f327(f36(x91381),x91383))),f327(f36(x91381),f327(f327(f23(f922(x91381,a910)),x91382),x91383)))) % 177.41/177.18 [9165]P1(f327(f327(f329(x91651),f411(x91652,x91653,x91651)),x91653))+E(f327(f101(a1),f327(f327(f6(x91651,a915),f327(f327(f8(a1,a915,x91651),a106),x91652)),x91653)),f327(f327(f6(x91651,a1),x91652),x91653)) % 177.41/177.18 [9166]P1(f327(f327(f329(x91661),f412(x91662,x91663,x91661)),x91663))+E(f327(f101(a1),f327(f327(f9(x91661,a915),f327(f327(f8(a1,a915,x91661),a106),x91662)),x91663)),f327(f327(f9(x91661,a1),x91662),x91663)) % 177.41/177.18 [9229]E(f85(x92291,f327(f327(f7(x92291,f922(x92291,a910),a910),f329(x92291)),f327(f327(f23(f922(x92291,a910)),x92292),f327(f327(f309(x92291),x92293),f190(f922(x92291,a910)))))),f247(x92291,x92293,x92292))+P1(f327(f327(f234(f922(x92291,a910)),x92292),f327(f327(f309(x92291),x92293),f190(f922(x92291,a910))))) % 177.41/177.18 [9580]E(f327(f327(f155(f916(x95801),x95801),f327(f327(f7(f916(x95801),a915,x95801),f165(x95801)),x95802)),f327(f137(f916(x95801),f327(f327(f8(a915,a910,f916(x95801)),f327(f235(a915),x95802)),f191(f916(x95801)))),x95803)),f327(f327(f165(f916(x95801)),f180(x95801,x95803)),x95802))+~P1(f327(f327(f235(a915),x95802),f327(f191(f916(f916(x95801))),f180(x95801,x95803)))) % 177.41/177.18 [9659]E(f327(f137(x96591,x96592),x96593),f178(x96591,x96592,x96593))+P1(f327(f327(f329(x96591),f717(x96593,x96592,x96591)),f327(f173(x96591),f327(f327(f139(x96591),f327(f191(f916(x96591)),f178(x96591,x96592,x96593))),x96593)))) % 177.41/177.18 [9799]E(f327(f327(f139(x97991),f327(f191(f916(x97991)),f178(x97991,x97992,x97993))),x97993),f114(x97991))+~P1(f327(x97992,f327(f142(x97991),f327(f327(f139(x97991),f327(f191(f916(x97991)),f178(x97991,x97992,x97993))),x97993)))) % 177.41/177.18 [9891]~P1(f327(f327(f329(f921(x98911,x98911)),x98912),f307(x98911,x98913)))+P1(f327(f327(f329(f921(x98911,x98911)),x98912),f327(f327(f40(a915,f922(f921(x98911,x98911),a910)),f242(f922(a915,a910))),f327(f327(f7(a915,f922(f921(x98911,x98911),a910),f922(f921(x98911,x98911),a910)),f184(f921(x98911,x98911),a910)),x98913)))) % 177.41/177.18 [9952]~P1(f327(f327(f234(f922(x99521,a910)),f327(f327(f40(a915,f922(x99521,a910)),f327(f302(a915,f2(a915)),f395(x99523,x99522,x99521))),x99522)),x99523))+P1(f327(f327(f234(f922(x99521,a910)),f327(f327(f40(a915,f922(x99521,a910)),f242(f922(a915,a910))),x99522)),x99523)) % 177.41/177.18 [9999]~P1(f327(f327(f235(a1),f2(a1)),x99993))+P1(f327(f327(f235(a1),x99991),f327(f327(f80(a1),x99992),f327(f327(f81(a1),f327(f327(f80(a1),f327(f75(a1),f327(f327(f23(a1),x99992),x99991))),f78(a1))),x99993)))) % 177.41/177.18 [10013]~P35(x100131,f327(f327(f102(f922(f921(x100131,x100131),a910)),x100132),x100133))+P35(x100131,f327(f327(f102(f922(f921(x100131,x100131),a910)),f327(f327(f102(f922(f921(x100131,x100131),a910)),f327(f327(f289(x100131,x100131,x100131),x100132),x100132)),f327(f327(f289(x100131,x100131,x100131),x100133),x100132))),x100133)) % 177.41/177.18 [10088]P35(x100881,f327(f327(f102(f922(f921(x100881,x100881),a910)),x100882),x100883))+~P35(x100881,f327(f327(f102(f922(f921(x100881,x100881),a910)),f327(f327(f102(f922(f921(x100881,x100881),a910)),f327(f327(f289(x100881,x100881,x100881),x100882),x100882)),f327(f327(f289(x100881,x100881,x100881),x100883),x100882))),x100883)) % 177.41/177.19 [9662]~P142(x96621)+E(f327(f104(x96621),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x96622),x96623)),f190(f922(f921(a915,a915),a910)))))),f327(f327(f23(x96621),f327(f101(x96621),x96622)),f327(f101(x96621),x96623))) % 177.41/177.19 [9746]P1(f327(x97463,x97462))+E(f327(f262(x97461),f327(f327(f18(x97461,a910,a910),f327(f327(f8(a910,f922(a910,a910),x97461),a325),f327(f327(f7(x97461,x97461,a910),a324),x97462))),x97463)),f190(f922(x97461,a910))) % 177.41/177.19 [9748]~P1(f327(x97483,x97482))+E(f327(f262(x97481),f327(f327(f18(x97481,a910,a910),f327(f327(f8(a910,f922(a910,a910),x97481),a325),f327(f327(f7(x97481,x97481,a910),a324),x97482))),x97483)),f327(f327(f309(x97481),x97482),f190(f922(x97481,a910)))) % 177.41/177.19 [9978]E(x99781,x99782)+P1(f327(f327(f243(x99783,x99783,f327(f327(f8(f922(x99783,a910),f922(x99783,a910),x99783),f327(f8(a910,a910,x99783),a322)),a324)),x99781),x99782)) % 177.41/177.19 [10068]~E(x100681,x100682)+~P1(f327(f327(f243(x100683,x100683,f327(f327(f8(f922(x100683,a910),f922(x100683,a910),x100683),f327(f8(a910,a910,x100683),a322)),a324)),x100681),x100682)) % 177.41/177.19 [10080]~P1(f327(f35(x100801),x100803))+E(f327(f327(f64(x100801,f922(x100801,a910),f327(f327(f8(f922(x100801,a910),f922(f922(x100801,a910),f922(x100801,a910)),x100801),f327(f7(f922(x100801,a910),f922(x100801,a910),f922(x100801,a910)),f23(f922(x100801,a910)))),f327(f327(f7(x100801,f922(x100801,a910),f922(x100801,a910)),f309(x100801)),f190(f922(x100801,a910))))),x100802),x100803),f327(f327(f23(f922(x100801,a910)),x100802),x100803)) % 177.41/177.19 [10111]~P1(f327(f327(f235(a1),f2(a1)),x101113))+P1(f327(f327(f235(a1),f327(f327(f23(a1),x101111),f327(f327(f81(a1),f327(f327(f80(a1),f327(f75(a1),f327(f327(f23(a1),x101111),x101112))),f78(a1))),x101113))),x101112)) % 177.41/177.19 [10372]~P1(f327(f327(f329(x103721),x103723),f316(x103721,x103722)))+P1(f327(f315(x103721,f327(f327(f7(x103721,f922(f921(x103721,x103721),a910),f922(x103721,a910)),f327(f327(f8(f922(x103721,f922(f922(f921(x103721,x103721),a910),a910)),f922(f922(f921(x103721,x103721),a910),f922(x103721,a910)),x103721),f7(x103721,f922(f921(x103721,x103721),a910),a910)),f327(f327(f8(f922(x103721,f921(x103721,x103721)),f922(x103721,f922(f922(f921(x103721,x103721),a910),a910)),x103721),f327(f8(f921(x103721,x103721),f922(f922(f921(x103721,x103721),a910),a910),x103721),f329(f921(x103721,x103721)))),f252(x103721,x103721)))),x103722)),x103723)) % 177.41/177.19 [10385]P1(f327(f327(f329(x103851),x103852),f316(x103851,x103853)))+~P1(f327(f315(x103851,f327(f327(f7(x103851,f922(f921(x103851,x103851),a910),f922(x103851,a910)),f327(f327(f8(f922(x103851,f922(f922(f921(x103851,x103851),a910),a910)),f922(f922(f921(x103851,x103851),a910),f922(x103851,a910)),x103851),f7(x103851,f922(f921(x103851,x103851),a910),a910)),f327(f327(f8(f922(x103851,f921(x103851,x103851)),f922(x103851,f922(f922(f921(x103851,x103851),a910),a910)),x103851),f327(f8(f921(x103851,x103851),f922(f922(f921(x103851,x103851),a910),a910),x103851),f329(f921(x103851,x103851)))),f252(x103851,x103851)))),x103853)),x103852)) % 177.41/177.19 [9950]~P1(f327(f35(x99501),f327(f262(x99501),x99503)))+P1(f327(f35(x99501),f327(f262(x99501),f327(f327(f18(x99501,a910,a910),f327(f327(f8(a910,f922(a910,a910),x99501),a325),x99502)),x99503)))) % 177.41/177.19 [9951]~P1(f327(f35(x99511),f327(f262(x99511),x99512)))+P1(f327(f35(x99511),f327(f262(x99511),f327(f327(f18(x99511,a910,a910),f327(f327(f8(a910,f922(a910,a910),x99511),a325),x99512)),x99513)))) % 177.41/177.19 [10047]P1(f327(f35(x100471),f327(f262(x100471),x100472)))+~P1(f327(f35(x100471),f327(f262(x100471),f327(f327(f18(x100471,a910,a910),f327(f327(f8(a910,f922(a910,a910),x100471),a326),x100473)),x100472)))) % 177.41/177.19 [10048]P1(f327(f35(x100481),f327(f262(x100481),x100482)))+~P1(f327(f35(x100481),f327(f262(x100481),f327(f327(f18(x100481,a910,a910),f327(f327(f8(a910,f922(a910,a910),x100481),a326),x100482)),x100483)))) % 177.41/177.19 [10351]~P1(f327(f35(x103511),x103512))+P1(f327(f35(f916(x103511)),f327(f262(f916(x103511)),f327(f327(f18(f916(x103511),a910,a910),f327(f327(f8(a910,f922(a910,a910),f916(x103511)),a325),f327(f327(f7(f916(x103511),f922(x103511,a910),a910),f327(f327(f8(f922(x103511,a910),f922(f922(x103511,a910),a910),f916(x103511)),f234(f922(x103511,a910))),f173(x103511))),x103512))),f327(f327(f7(f916(x103511),a915,a910),f327(f327(f8(a915,f922(a915,a910),f916(x103511)),a324),f191(f916(x103511)))),x103513))))) % 177.41/177.19 [10352]~P1(f327(f35(x103521),x103522))+P1(f327(f35(f916(x103521)),f327(f262(f916(x103521)),f327(f327(f18(f916(x103521),a910,a910),f327(f327(f8(a910,f922(a910,a910),f916(x103521)),a325),f327(f327(f7(f916(x103521),f922(x103521,a910),a910),f327(f327(f8(f922(x103521,a910),f922(f922(x103521,a910),a910),f916(x103521)),f234(f922(x103521,a910))),f173(x103521))),x103522))),f327(f327(f7(f916(x103521),a915,a910),f327(f327(f8(a915,f922(a915,a910),f916(x103521)),f234(a915)),f191(f916(x103521)))),x103523))))) % 177.41/177.19 [10061]~P112(x100611)+E(f327(f327(f244(x100611),x100612),f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x100613)),f327(f327(f81(x100611),f327(f327(f244(x100611),x100612),x100613)),f327(f327(f244(x100611),x100612),x100613))) % 177.41/177.19 [10092]~P80(x100921)+E(f327(f327(f244(x100921),f327(f327(f244(x100921),x100922),x100923)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f244(x100921),x100922),f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x100923))) % 177.41/177.19 [10148]~P142(x101481)+E(f327(f327(f244(x101481),f327(f79(x101481),x101482)),f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101483)),f327(f327(f244(x101481),x101482),f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101483))) % 177.41/177.19 [10296]~P119(x102961)+P1(f327(f327(f234(x102961),f2(x102961)),f327(f327(f80(x102961),f327(f327(f244(x102961),x102962),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x102961),x102963),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))))) % 177.41/177.19 [10158]~P112(x101581)+E(f327(f327(f244(x101581),x101582),f327(a113,f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101583))),f327(f327(f81(x101581),x101582),f327(f327(f81(x101581),f327(f327(f244(x101581),x101582),x101583)),f327(f327(f244(x101581),x101582),x101583)))) % 177.41/177.19 [10209]~P80(x102091)+E(f327(f327(f81(x102091),x102092),f327(f327(f244(x102091),f327(f327(f244(x102091),x102092),x102093)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x102091),x102092),f327(a113,f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102093)))) % 177.41/177.19 [10250]~P119(x102501)+P1(f327(f327(f234(x102501),f2(x102501)),f327(f327(f244(x102501),x102502),f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x102503)))) % 177.41/177.19 [10327]~P93(x103271)+E(f327(f327(f23(x103271),f327(f327(f80(x103271),f327(f327(f244(x103271),x103272),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x103271),x103273),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f327(f327(f81(x103271),f327(f327(f81(x103271),f327(f105(x103271),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x103272)),x103273)),f327(f327(f244(x103271),f327(f327(f23(x103271),x103272),x103273)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.19 [10328]~P93(x103281)+E(f327(f327(f80(x103281),f327(f327(f80(x103281),f327(f327(f244(x103281),x103282),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x103281),x103283),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f327(f327(f81(x103281),f327(f327(f81(x103281),f327(f105(x103281),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x103282)),x103283)),f327(f327(f244(x103281),f327(f327(f80(x103281),x103282),x103283)),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.19 [4845]E(x48451,x48452)+~E(f30(x48453,x48451),f30(x48454,x48452)) % 177.41/177.19 [4846]E(x48461,x48462)+~E(f30(x48461,x48463),f30(x48462,x48464)) % 177.41/177.19 [4847]E(x48471,x48472)+~E(f29(x48473,x48471),f29(x48474,x48472)) % 177.41/177.19 [4848]E(x48481,x48482)+~E(f29(x48481,x48483),f29(x48482,x48484)) % 177.41/177.19 [7961]P23(x79611,x79612,x79613,x79614)+~E(f457(x79614,x79613,x79612,x79611),f469(x79614,x79613,x79612,x79611)) % 177.41/177.19 [8251]P32(x82511,x82512,x82513,x82514,f114(x82512))+~E(x82514,f114(x82511)) % 177.41/177.19 [8252]P32(x82521,x82522,x82523,f114(x82521),x82524)+~E(x82524,f114(x82522)) % 177.41/177.19 [8790]~P32(x87902,x87903,x87904,x87901,f114(x87903))+E(x87901,f114(x87902)) % 177.41/177.19 [8791]~P32(x87913,x87912,x87914,f114(x87913),x87911)+E(x87911,f114(x87912)) % 177.41/177.19 [5228]~P15(x52283,x52281,x52284)+E(f327(f327(x52281,x52282),x52282),x52282) % 177.41/177.19 [5477]P1(f327(x54772,x54774))+E(f327(f137(x54771,x54772),f170(x54771,x54773,x54774)),f114(x54771)) % 177.41/177.19 [5514]~E(x55144,f190(f922(x55141,a910)))+E(f327(f310(x55141,x55142,x55143),x55144),f190(f922(x55142,a910))) % 177.41/177.19 [5761]~P1(f327(x57612,x57614))+E(f327(f137(x57611,x57612),f170(x57611,x57613,x57614)),f170(x57611,x57613,x57614)) % 177.41/177.19 [5791]~E(f327(f310(x57912,x57913,x57914),x57911),f190(f922(x57913,a910)))+E(x57911,f190(f922(x57912,a910))) % 177.41/177.19 [5978]~P5(x59781,x59783)+E(f271(x59781,x59782,f270(x59781,x59783),x59784),x59784) % 177.41/177.19 [6085]~P108(x60852)+E(f327(f327(f149(x60851,x60852,x60853),x60854),f114(x60851)),f327(f327(f152(x60851),x60854),f114(x60851))) % 177.41/177.19 [6450]~E(x64501,f190(f922(x64502,a910)))+~P1(f327(f62(x64502,x64503,x64501),x64504)) % 177.41/177.19 [6472]~P56(x64721,x64723,x64724,x64722)+P1(f327(f35(x64721),x64722)) % 177.41/177.19 [6474]~P56(x64741,x64743,x64742,x64744)+P1(f327(f35(x64741),x64742)) % 177.41/177.19 [6482]~P56(x64822,x64823,x64824,x64821)+~E(x64821,f190(f922(x64822,a910))) % 177.41/177.19 [6515]~P110(x65151)+E(f327(f327(f103(f922(x65151,a910)),f327(f302(x65151,x65152),x65153)),f303(x65151,x65153,x65154)),f190(f922(x65151,a910))) % 177.41/177.19 [6542]~P1(f327(f327(x65423,x65424),x65422))+P1(f327(f327(f329(x65421),x65422),f294(x65421,x65423,x65424))) % 177.41/177.19 [6543]~P1(f327(f327(x65433,x65434),x65432))+P1(f327(f327(f329(x65431),x65432),f295(x65431,x65433,x65434))) % 177.41/177.19 [6544]~P1(f327(f327(x65443,x65442),x65444))+P1(f327(f327(f329(x65441),x65442),f296(x65441,x65443,x65444))) % 177.41/177.19 [6545]~P1(f327(f327(x65453,x65452),x65454))+P1(f327(f327(f329(x65451),x65452),f298(x65451,x65453,x65454))) % 177.41/177.19 [6685]~P110(x66851)+E(f327(f327(f103(f922(x66851,a910)),f306(x66851,x66852,x66853)),f303(x66851,x66853,x66854)),f190(f922(x66851,a910))) % 177.41/177.19 [6686]~P110(x66861)+E(f327(f327(f103(f922(x66861,a910)),f305(x66861,x66862,x66863)),f306(x66861,x66863,x66864)),f190(f922(x66861,a910))) % 177.41/177.19 [6687]~P110(x66871)+E(f327(f327(f103(f922(x66871,a910)),f305(x66871,x66872,x66873)),f305(x66871,x66873,x66874)),f190(f922(x66871,a910))) % 177.41/177.19 [6688]~P110(x66881)+E(f327(f327(f103(f922(x66881,a910)),f303(x66881,x66882,x66883)),f306(x66881,x66883,x66884)),f190(f922(x66881,a910))) % 177.41/177.19 [6689]~P110(x66891)+E(f327(f327(f103(f922(x66891,a910)),f303(x66891,x66892,x66893)),f305(x66891,x66893,x66894)),f190(f922(x66891,a910))) % 177.41/177.19 [6727]P1(f327(f327(x67271,x67272),f541(x67272,x67271)))+~P1(f327(f249(x67273,x67274,x67271),x67272)) % 177.41/177.19 [6807]~P108(x68072)+E(f327(f173(x68071),f151(x68071,x68072,x68073,x68074)),f327(f173(x68071),x68074)) % 177.41/177.19 [6857]~P146(x68571)+E(f192(x68571,x68572,f327(a113,x68573),x68574),f192(x68571,x68572,x68573,f327(x68572,x68574))) % 177.41/177.19 [6920]~P1(f327(f327(f329(x69204),x69203),f294(x69204,x69201,x69202)))+P1(f327(f327(x69201,x69202),x69203)) % 177.41/177.19 [6921]~P1(f327(f327(f329(x69214),x69213),f295(x69214,x69211,x69212)))+P1(f327(f327(x69211,x69212),x69213)) % 177.41/177.19 [6922]~P1(f327(f327(f329(x69224),x69222),f296(x69224,x69221,x69223)))+P1(f327(f327(x69221,x69222),x69223)) % 177.41/177.19 [6923]~P1(f327(f327(f329(x69234),x69232),f298(x69234,x69231,x69233)))+P1(f327(f327(x69231,x69232),x69233)) % 177.41/177.19 [6998]E(f327(f36(f920(x69981,x69982)),f313(x69981,x69982,x69983,x69984)),f2(a915))+P1(f327(f35(x69982),x69984)) % 177.41/177.19 [6999]E(f327(f36(f920(x69991,x69992)),f313(x69991,x69992,x69993,x69994)),f2(a915))+P1(f327(f35(x69991),x69993)) % 177.41/177.19 [7203]~P12(x72034,x72031,x72032)+E(f327(f72(x72031,x72031,x72031,f327(x72032,x72033)),f327(x72032,x72033)),f327(x72032,x72033)) % 177.41/177.19 [7447]E(f277(x74471,x74472,x74473,x74474),f327(f252(f922(a100,f922(a910,f918(f917(x74471)))),f921(a100,a100)),f42(x74471)))+~P1(f327(f327(f234(a100),x74473),f2(a100))) % 177.41/177.19 [8083]~E(x80832,x80833)+P1(f327(f327(f329(f921(x80831,x80831)),f327(f327(f252(x80831,x80831),x80832),x80833)),f307(x80831,x80834))) % 177.41/177.19 [8112]~P23(x81121,x81122,x81123,f242(f922(x81121,a910)))+E(f327(f77(x81121,x81122,f242(f922(x81121,a910)),x81123),f327(x81123,x81124)),x81124) % 177.41/177.19 [8113]~P23(x81131,x81132,x81133,f242(f922(x81131,a910)))+E(f327(f92(x81131,x81132,f242(f922(x81131,a910)),x81133),f327(x81133,x81134)),x81134) % 177.41/177.19 [8200]~P1(f327(f327(f329(f916(x82001)),f327(f327(f152(x82001),x82004),x82002)),f162(x82001,x82003)))+P1(f327(f327(f329(f916(x82001)),x82002),f162(x82001,x82003))) % 177.41/177.19 [8201]~P1(f327(f327(f329(f916(x82011)),f327(f327(f135(x82011),x82014),x82012)),f162(x82011,x82013)))+P1(f327(f327(f329(f916(x82011)),x82012),f162(x82011,x82013))) % 177.41/177.19 [8202]~P1(f327(f327(f329(f916(x82021)),f327(f327(f135(x82021),x82022),x82024)),f162(x82021,x82023)))+P1(f327(f327(f329(f916(x82021)),x82022),f162(x82021,x82023))) % 177.41/177.19 [8213]~P108(x82131)+P11(x82131,f327(f327(f155(x82132,x82131),x82133),f151(x82132,x82131,x82133,x82134))) % 177.41/177.19 [8318]P23(x83184,x83183,x83181,x83182)+E(f327(x83181,f457(x83182,x83181,x83183,x83184)),f327(x83181,f469(x83182,x83181,x83183,x83184))) % 177.41/177.19 [8424]~P23(x84242,x84241,x84244,x84243)+P23(x84241,x84242,f77(x84242,x84241,x84243,x84244),f327(f310(x84242,x84241,x84244),x84243)) % 177.41/177.19 [8563]P35(f921(x85632,x85634),f280(x85632,x85634,x85631,x85633))+P1(f327(x85631,f543(x85632,x85633,x85634,x85631))) % 177.41/177.19 [8678]E(x86781,x86782)+~P1(f327(f327(f329(f921(x86783,x86783)),f327(f327(f252(x86783,x86783),x86781),x86782)),f263(x86783,x86784))) % 177.41/177.19 [8742]~P1(f327(f35(f920(x87423,x87421)),f313(x87423,x87421,x87424,x87422)))+P1(f327(f35(x87421),x87422)) % 177.41/177.19 [8743]~P1(f327(f35(f920(x87431,x87433)),f313(x87431,x87433,x87432,x87434)))+P1(f327(f35(x87431),x87432)) % 177.41/177.19 [8752]~P23(x87521,x87522,x87523,x87524)+P24(x87521,x87522,x87523,x87524,f327(f310(x87521,x87522,x87523),x87524)) % 177.41/177.19 [8753]P9(x87531,x87532,x87533,x87534)+~E(f327(x87534,f825(x87532,x87534,x87533,x87531)),f327(x87534,f826(x87532,x87534,x87533,x87531))) % 177.41/177.19 [8843]~P24(x88432,x88433,x88434,x88431,f190(f922(x88433,a910)))+E(x88431,f190(f922(x88432,a910))) % 177.41/177.19 [8844]~P24(x88443,x88442,x88444,f190(f922(x88443,a910)),x88441)+E(x88441,f190(f922(x88442,a910))) % 177.41/177.19 [8936]P35(f921(x89361,x89362),f280(x89361,x89362,x89363,x89364))+~P35(x89362,f327(x89364,f543(x89361,x89364,x89362,x89363))) % 177.41/177.19 [9500]E(f327(f327(f160(x95001,x95002),f666(x95003,x95004,x95002,x95001)),f665(x95003,x95004,x95002,x95001)),x95004)+~P1(f327(f327(f329(f921(f916(x95001),f916(x95001))),f327(f327(f252(f916(x95001),f916(x95001)),x95002),x95004)),f158(x95001,x95003))) % 177.41/177.19 [9505]~P1(f327(f327(f329(f921(f916(x95051),f916(x95051))),f327(f327(f252(f916(x95051),f916(x95051)),x95052),x95053)),f146(x95051,x95054)))+P1(f327(f327(f329(f921(f916(x95051),f916(x95051))),f327(f327(f252(f916(x95051),f916(x95051)),x95052),x95053)),f148(x95051,x95054))) % 177.41/177.19 [9616]P1(f327(f35(x96161),x96162))+~P1(f327(f327(f329(f921(f922(x96161,a910),f922(x96161,a910))),f327(f327(f252(f922(x96161,a910),f922(x96161,a910)),x96163),x96162)),f319(x96161,x96164))) % 177.41/177.19 [9617]P1(f327(f35(x96171),x96172))+~P1(f327(f327(f329(f921(f922(x96171,a910),f922(x96171,a910))),f327(f327(f252(f922(x96171,a910),f922(x96171,a910)),x96172),x96173)),f319(x96171,x96174))) % 177.41/177.19 [9620]~E(x96201,f190(f922(x96202,a910)))+~P1(f327(f327(f329(f921(f922(x96202,a910),f922(x96202,a910))),f327(f327(f252(f922(x96202,a910),f922(x96202,a910)),x96203),x96201)),f319(x96202,x96204))) % 177.41/177.19 [10261]P9(x102611,x102612,x102613,x102614)+~P1(f327(f327(f257(x102611,x102611,a910),f327(f327(f7(x102611,f922(x102611,x102612),f922(x102611,a910)),f327(f327(f8(f922(x102612,a910),f922(f922(x102611,x102612),f922(x102611,a910)),x102611),f8(x102612,a910,x102611)),f327(f327(f8(x102612,f922(x102612,a910),x102611),a324),x102614))),x102614)),f578(x102614,x102613,x102612,x102611))) % 177.41/177.19 [5127]~E(x51272,f114(x51271))+E(f327(f327(f160(x51271,x51272),x51273),x51274),f114(x51271)) % 177.41/177.19 [5128]~E(x51284,f114(x51281))+E(f327(f327(f155(x51281,x51282),x51283),x51284),f114(x51282)) % 177.41/177.19 [5360]E(x53601,f114(x53602))+~E(f327(f327(f155(x53602,x53603),x53604),x53601),f114(x53603)) % 177.41/177.19 [5361]E(x53611,f114(x53612))+~E(f327(f327(f160(x53612,x53611),x53613),x53614),f114(x53612)) % 177.41/177.19 [5397]E(x53971,x53972)+~E(f327(f327(f135(x53973),x53974),x53971),f327(f327(f135(x53973),x53974),x53972)) % 177.41/177.19 [5398]E(x53981,x53982)+~E(f327(f327(f135(x53983),x53981),x53984),f327(f327(f135(x53983),x53982),x53984)) % 177.41/177.19 [5551]P1(f327(x55513,x55512))+E(f171(x55511,x55512,f327(f137(x55511,x55513),x55514)),f327(f137(x55511,x55513),x55514)) % 177.41/177.19 [5553]~P1(f327(x55532,x55533))+P31(x55531,x55532,f327(f327(f152(x55531),x55533),x55534)) % 177.41/177.19 [5563]E(x55631,x55632)+~E(f140(a915,f327(f302(a915,x55631),x55633)),f327(f327(f152(a915),x55632),x55634)) % 177.41/177.19 [5612]~P25(x56122,x56123)+P25(x56121,f327(f327(f73(x56122,x56121),x56123),x56124)) % 177.41/177.19 [5613]~P35(x56132,x56133)+P35(x56131,f327(f327(f288(x56132,x56131),x56133),x56134)) % 177.41/177.19 [5614]~P36(x56142,x56143)+P36(x56141,f327(f327(f288(x56142,x56141),x56143),x56144)) % 177.41/177.19 [5615]~P49(x56152,x56153)+P49(x56151,f327(f327(f288(x56152,x56151),x56153),x56154)) % 177.41/177.19 [5745]~P31(x57451,x57452,x57454)+P31(x57451,x57452,f327(f327(f152(x57451),x57453),x57454)) % 177.41/177.19 [5746]~P31(x57461,x57462,x57464)+P31(x57461,x57462,f327(f327(f135(x57461),x57463),x57464)) % 177.41/177.19 [5747]~P31(x57471,x57472,x57473)+P31(x57471,x57472,f327(f327(f135(x57471),x57473),x57474)) % 177.41/177.19 [5834]~E(x58341,f114(x58342))+~E(f327(f327(f135(x58342),x58343),f327(f327(f152(x58342),x58344),f114(x58342))),x58341) % 177.41/177.19 [5859]~P29(x58593,x58591,f327(f327(f152(x58593),x58592),x58594))+P1(f327(x58591,x58592)) % 177.41/177.19 [5869]E(f115(x58691,x58692),x58693)+~E(f327(f327(f135(x58691),x58693),f327(f327(f152(x58691),x58694),f114(x58691))),x58692) % 177.41/177.19 [5870]E(f145(x58701,x58702),x58703)+~E(f327(f327(f135(x58701),x58704),f327(f327(f152(x58701),x58703),f114(x58701))),x58702) % 177.41/177.19 [5980]~E(f140(a915,f327(f302(a915,x59801),x59802)),f327(f327(f152(a915),x59803),x59804))+P1(f327(f327(f235(a915),x59801),x59802)) % 177.41/177.19 [5989]P29(x59891,x59892,x59893)+~P29(x59891,x59892,f327(f327(f152(x59891),x59894),x59893)) % 177.41/177.19 [5990]P29(x59901,x59902,x59903)+~P29(x59901,x59902,f327(f327(f135(x59901),x59904),x59903)) % 177.41/177.19 [5991]P29(x59911,x59912,x59913)+~P29(x59911,x59912,f327(f327(f135(x59911),x59913),x59914)) % 177.41/177.19 [6189]E(x61891,f327(f327(f135(x61892),f327(f169(x61892),x61893)),f327(f327(f152(x61892),x61894),f114(x61892))))+~E(f327(f169(x61892),x61891),f327(f327(f152(x61892),x61894),x61893)) % 177.41/177.19 [6371]~P110(x63711)+E(f327(f327(f103(f922(x63711,a910)),f327(f302(x63711,x63712),x63713)),f327(f302(x63711,x63713),x63714)),f190(f922(x63711,a910))) % 177.41/177.19 [6382]E(f327(f327(f165(x63821),f170(x63821,x63822,x63823)),x63824),x63823)+~P1(f327(f327(f235(a915),x63824),x63822)) % 177.41/177.19 [6409]~P68(x64091)+E(f327(f166(x64091),f327(f327(f155(a1,x64091),x64092),f179(x64093,x64094))),f327(f327(f6(a1,x64091),x64092),f327(f173(a1),f179(x64093,x64094)))) % 177.41/177.19 [6410]~P68(x64101)+E(f327(f327(f6(a1,x64101),x64102),f327(f173(a1),f179(x64103,x64104))),f327(f166(x64101),f327(f327(f155(a1,x64101),x64102),f179(x64103,x64104)))) % 177.41/177.19 [6555]~E(x65552,f327(f327(f135(x65551),f327(f169(x65551),x65554)),f327(f327(f152(x65551),x65553),f114(x65551))))+E(f327(f169(x65551),x65552),f327(f327(f152(x65551),x65553),x65554)) % 177.41/177.19 [6571]~P17(x65712,x65713,x65714,x65711)+E(f327(x65711,f190(f922(x65712,a910))),f31(x65713)) % 177.41/177.19 [6596]~P110(x65961)+E(f327(f327(f103(f922(x65961,a910)),f306(x65961,x65962,x65963)),f327(f302(x65961,x65963),x65964)),f190(f922(x65961,a910))) % 177.41/177.19 [6808]E(x68081,f190(f922(x68082,a910)))+~E(f313(x68083,x68082,x68084,x68081),f190(f922(f920(x68083,x68082),a910))) % 177.41/177.19 [6809]E(x68091,f190(f922(x68092,a910)))+~E(f313(x68092,x68093,x68091,x68094),f190(f922(f920(x68092,x68093),a910))) % 177.41/177.19 [6878]~P108(x68782)+E(f327(f191(f916(x68781)),f151(x68781,x68782,x68783,x68784)),f327(f191(f916(x68781)),x68784)) % 177.41/177.19 [6889]~P1(f327(f250(x68893,x68894,x68891),x68892))+P1(f327(f327(x68891,f542(x68892,x68891)),x68892)) % 177.41/177.19 [6932]~P1(f327(f35(x69322),x69324))+P1(f327(f35(x69321),f327(f310(x69322,x69321,x69323),x69324))) % 177.41/177.19 [7164]~P23(x71642,x71641,x71643,x71644)+E(f327(f36(x71641),f327(f310(x71642,x71641,x71643),x71644)),f327(f36(x71642),x71644)) % 177.41/177.19 [7182]E(f327(f310(x71821,x71822,x71823),f327(f311(x71821,x71822,x71823),x71824)),x71824)+~E(f327(f310(x71821,x71822,x71823),f242(f922(x71821,a910))),f242(f922(x71822,a910))) % 177.41/177.19 [7598]~P23(x75981,x75982,x75983,f242(f922(x75981,a910)))+E(f327(f311(x75981,x75982,x75983),f327(f310(x75981,x75982,x75983),x75984)),x75984) % 177.41/177.19 [7879]E(x78791,x78792)+~P1(f327(f327(f329(x78793),x78791),f327(f173(x78793),f170(x78793,x78794,x78792)))) % 177.41/177.19 [7888]~E(x78881,f2(a915))+~P1(f327(f327(f329(x78882),x78883),f327(f173(x78882),f170(x78882,x78881,x78884)))) % 177.41/177.19 [7921]P1(f327(x79211,x79212))+~P1(f327(f327(f329(x79213),x79212),f327(f173(x79213),f178(x79213,x79211,x79214)))) % 177.41/177.19 [8029]~P1(f327(f327(f329(f916(x80291)),f327(f327(f152(x80291),x80292),x80294)),f162(x80291,x80293)))+P1(f327(f327(f329(x80291),x80292),x80293)) % 177.41/177.19 [8157]~P1(f327(f327(f329(x81571),x81572),f327(f173(x81571),f177(x81571,x81573,x81574))))+P1(f327(f327(f329(x81571),x81572),f327(f173(x81571),x81573))) % 177.41/177.19 [8158]~P1(f327(f327(f329(x81581),x81582),f327(f173(x81581),f171(x81581,x81584,x81583))))+P1(f327(f327(f329(x81581),x81582),f327(f173(x81581),x81583))) % 177.41/177.19 [8159]~P1(f327(f327(f329(x81591),x81592),f327(f173(x81591),f178(x81591,x81594,x81593))))+P1(f327(f327(f329(x81591),x81592),f327(f173(x81591),x81593))) % 177.41/177.19 [8169]E(f327(f191(f916(x81691)),x81692),x81693)+~P1(f327(f327(f329(f916(x81691)),x81692),f327(f173(f916(x81691)),f56(x81691,x81693,x81694)))) % 177.41/177.19 [8264]P1(f327(x82643,x82642))+E(f327(f137(x82641,f327(f327(f8(a910,a910,x82641),a322),f327(a324,x82642))),f327(f137(x82641,x82643),x82644)),f327(f137(x82641,x82643),x82644)) % 177.41/177.19 [8376]E(f327(f327(f165(x83761),f178(x83761,x83762,x83763)),x83764),f327(f327(f165(x83761),x83763),x83764))+~P1(f327(f327(f235(a915),x83764),f327(f191(f916(x83761)),f178(x83761,x83762,x83763)))) % 177.41/177.19 [8462]~P68(x84621)+E(f327(f327(f6(a915,x84621),f327(f327(f8(a915,x84621,a915),x84622),a113)),f327(f302(a915,x84623),x84624)),f327(f327(f6(a915,x84621),x84622),f327(f302(a915,f327(a113,x84623)),f327(a113,x84624)))) % 177.41/177.19 [8471]~P68(x84711)+E(f327(f327(f6(a915,x84711),f327(f327(f8(a915,x84711,a915),x84712),a113)),f303(a915,x84713,x84714)),f327(f327(f6(a915,x84711),x84712),f303(a915,f327(a113,x84713),f327(a113,x84714)))) % 177.41/177.19 [8599]~P23(x85991,x85993,x85994,f242(f922(x85991,a910)))+P23(x85991,f922(x85992,x85993),f327(f327(f8(x85993,f922(x85992,x85993),x85991),f16(x85993,x85992)),x85994),f242(f922(x85991,a910))) % 177.41/177.19 [8684]~P23(x86842,x86841,x86844,x86843)+E(f327(f310(x86841,x86842,f77(x86842,x86841,x86843,x86844)),f327(f310(x86842,x86841,x86844),x86843)),x86843) % 177.41/177.19 [8744]~P1(f327(f327(f329(f921(x87441,x87441)),f327(f327(f252(x87441,x87441),x87442),x87444)),f263(x87441,x87443)))+P1(f327(f327(f329(x87441),x87442),x87443)) % 177.41/177.19 [8867]~P23(x88672,x88671,x88673,f242(f922(x88672,a910)))+E(f327(f310(x88671,x88672,f92(x88672,x88671,f242(f922(x88672,a910)),x88673)),f327(f310(x88672,x88671,x88673),x88674)),x88674) % 177.41/177.19 [8942]~P24(x89421,x89422,x89423,x89424,f242(f922(x89422,a910)))+E(f327(f310(x89421,x89422,x89423),f242(f922(x89421,a910))),f242(f922(x89422,a910))) % 177.41/177.19 [8975]~E(f327(f327(f6(x89751,a915),x89754),x89753),f327(a113,x89752))+P1(f327(f327(f329(x89751),f498(x89752,x89753,x89754,x89751)),x89753)) % 177.41/177.19 [8996]~E(f327(f327(f6(x89964,a915),x89961),x89963),f327(a113,x89962))+P1(f327(f327(f235(a915),f2(a915)),f327(x89961,f498(x89962,x89963,x89961,x89964)))) % 177.41/177.19 [9007]~P1(f327(f35(x90072),x90074))+P1(f327(f327(f234(a915),f327(f36(x90071),f327(f310(x90072,x90071,x90073),x90074))),f327(f36(x90072),x90074))) % 177.41/177.19 [9008]E(f327(f327(f252(x90081,x90082),f636(x90083,x90084,x90082,x90081)),f637(x90083,x90084,x90082,x90081)),x90084)+~P1(f327(f327(f329(f921(x90081,x90082)),x90084),f327(f286(x90082,x90081),x90083))) % 177.41/177.19 [9016]P23(x90161,x90162,x90163,x90164)+P1(f327(f327(f329(x90161),f457(x90164,x90163,x90162,x90161)),x90164)) % 177.41/177.19 [9017]P23(x90171,x90172,x90173,x90174)+P1(f327(f327(f329(x90171),f469(x90174,x90173,x90172,x90171)),x90174)) % 177.41/177.19 [9085]P9(x90851,x90852,x90853,x90854)+P1(f327(f327(f329(f921(x90851,x90851)),f578(x90854,x90853,x90852,x90851)),x90853)) % 177.41/177.19 [9143]P1(f327(x91431,x91432))+~P1(f327(x91431,f327(f327(f252(x91433,x91434),f517(x91434,x91433,x91431)),f518(x91434,x91433,x91431)))) % 177.41/177.19 [9160]E(f327(f191(f916(x91601)),x91602),f327(f191(f916(x91601)),x91603))+~P1(f327(f327(f329(f921(f916(x91601),f916(x91601))),f327(f327(f252(f916(x91601),f916(x91601)),x91602),x91603)),f146(x91601,x91604))) % 177.41/177.19 [9161]E(f327(f191(f916(x91611)),x91612),f327(f191(f916(x91611)),x91613))+~P1(f327(f327(f329(f921(f916(x91611),f916(x91611))),f327(f327(f252(f916(x91611),f916(x91611)),x91612),x91613)),f158(x91611,x91614))) % 177.41/177.19 [9164]E(f327(f191(f916(x91641)),x91642),f327(f191(f916(x91641)),x91643))+~P1(f327(f327(f329(f921(f916(x91641),f916(x91641))),f327(f327(f252(f916(x91641),f916(x91641)),x91642),x91643)),f159(x91641,x91644))) % 177.41/177.19 [9233]P1(f327(f327(f234(a915),f156(x92331,x92332,x92333)),f156(x92331,x92334,x92333)))+P1(f327(f327(f329(x92331),f664(x92334,x92332,x92333,x92331)),f327(f173(x92331),x92333))) % 177.41/177.19 [9236]E(f327(f191(f916(x92361)),x92362),f327(f191(f916(x92361)),x92363))+~P1(f327(f327(f329(f921(f916(x92361),f916(x92361))),f327(f327(f252(f916(x92361),f916(x92361)),x92362),x92363)),f307(f916(x92361),f158(x92361,x92364)))) % 177.41/177.19 [9471]~P23(x94711,x94712,x94713,x94714)+~P1(f327(f327(f235(a915),f327(f36(x94712),f327(f310(x94711,x94712,x94713),x94714))),f327(f36(x94711),x94714))) % 177.41/177.19 [9518]~P1(f327(f327(f329(f921(f916(x95181),f916(x95181))),f327(f327(f252(f916(x95181),f916(x95181)),x95182),x95183)),f158(x95181,x95184)))+P1(f327(f327(f329(f921(f916(x95181),f916(x95181))),f327(f327(f252(f916(x95181),f916(x95181)),x95182),x95183)),f159(x95181,f307(x95181,x95184)))) % 177.41/177.19 [9522]~P1(f327(f327(f329(f921(f916(x95221),f916(x95221))),f327(f327(f252(f916(x95221),f916(x95221)),x95222),x95223)),f159(x95221,x95224)))+P1(f327(f327(f329(f921(f916(x95221),f916(x95221))),f327(f327(f252(f916(x95221),f916(x95221)),x95222),x95223)),f307(f916(x95221),f158(x95221,x95224)))) % 177.41/177.19 [9538]P1(f327(f327(f329(f921(x95381,x95381)),f327(f327(f252(x95381,x95381),x95382),x95383)),f307(x95381,x95384)))+~P1(f327(f327(f329(f921(x95381,x95381)),f327(f327(f252(x95381,x95381),x95382),x95383)),f327(f327(f289(x95381,x95381,x95381),x95384),f307(x95381,x95384)))) % 177.41/177.19 [9727]E(f327(f327(f135(x97271),f680(x97272,x97273,x97274,x97271)),f327(f327(f152(x97271),f681(x97272,x97273,x97274,x97271)),f683(x97272,x97273,x97274,x97271))),x97274)+~P1(f327(f327(f329(f921(f916(x97271),f916(x97271))),f327(f327(f252(f916(x97271),f916(x97271)),x97274),x97273)),f158(x97271,x97272))) % 177.41/177.19 [9728]E(f327(f327(f135(x97281),f680(x97282,x97283,x97284,x97281)),f327(f327(f152(x97281),f682(x97282,x97283,x97284,x97281)),f683(x97282,x97283,x97284,x97281))),x97283)+~P1(f327(f327(f329(f921(f916(x97281),f916(x97281))),f327(f327(f252(f916(x97281),f916(x97281)),x97284),x97283)),f158(x97281,x97282))) % 177.41/177.19 [9806]P1(f327(f327(f329(f921(x98061,x98061)),f327(f327(f252(x98061,x98061),x98062),f618(x98063,x98064,x98062,x98061))),f307(x98061,x98063)))+~P1(f327(f327(f329(f921(x98061,x98061)),f327(f327(f252(x98061,x98061),x98062),x98064)),f327(f327(f289(x98061,x98061,x98061),x98063),f307(x98061,x98063)))) % 177.41/177.19 [9874]P1(f327(f327(f234(a915),f156(x98741,x98742,x98743)),f156(x98741,x98744,x98743)))+~P1(f327(f327(f235(a915),f327(x98742,f664(x98744,x98742,x98743,x98741))),f327(x98744,f664(x98744,x98742,x98743,x98741)))) % 177.41/177.19 [9946]P1(f327(f327(f329(f921(x99461,x99461)),f327(f327(f252(x99461,x99461),f617(x99462,x99463,x99464,x99461)),x99463)),f307(x99461,x99462)))+~P1(f327(f327(f329(f921(x99461,x99461)),f327(f327(f252(x99461,x99461),x99464),x99463)),f327(f327(f289(x99461,x99461,x99461),x99462),f307(x99461,x99462)))) % 177.41/177.19 [5379]~E(x53792,x53793)+E(f171(x53791,x53792,f327(f327(f152(x53791),x53793),x53794)),x53794) % 177.41/177.19 [5507]P1(f327(x55072,x55073))+E(f178(x55071,x55072,f327(f327(f152(x55071),x55073),x55074)),f114(x55071)) % 177.41/177.19 [5575]~P87(x55752)+E(f327(f327(f79(f922(x55751,x55752)),x55753),x55754),f327(f79(x55752),f327(x55753,x55754))) % 177.41/177.19 [5588]~E(x55882,f2(a915))+E(f327(f327(f139(x55881),x55882),f327(f327(f152(x55881),x55883),x55884)),f327(f327(f152(x55881),x55883),x55884)) % 177.41/177.19 [5589]P1(f327(x55892,x55893))+E(f327(f137(x55891,x55892),f327(f327(f152(x55891),x55893),x55894)),f327(f137(x55891,x55892),x55894)) % 177.41/177.19 [5728]~E(x57282,x57284)+P1(f327(f327(f327(f309(x57281),x57282),x57283),x57284)) % 177.41/177.19 [5736]E(x57361,f114(x57362))+E(f145(x57363,f327(f327(f155(x57362,x57363),x57364),x57361)),f327(x57364,f145(x57362,x57361))) % 177.41/177.19 [5750]~E(x57501,f63(x57502,x57504))+E(f327(x57501,f327(f327(f309(x57502),x57503),f190(f922(x57502,a910)))),x57503) % 177.41/177.19 [5786]E(x57861,f114(x57862))+E(f327(f142(x57863),f327(f327(f155(x57862,x57863),x57864),x57861)),f327(x57864,f327(f142(x57862),x57861))) % 177.41/177.19 [5889]~P1(f327(x58893,x58894))+P1(f327(f327(f327(f309(x58891),x58892),x58893),x58894)) % 177.41/177.19 [6008]~P16(x60082,x60084,x60081)+E(f327(x60081,f327(f327(f309(x60082),x60083),f190(f922(x60082,a910)))),x60083) % 177.41/177.19 [6034]~E(x60342,x60343)+P1(f327(f327(f329(x60341),x60342),f327(f327(f309(x60341),x60343),x60344))) % 177.41/177.19 [6039]~P112(x60391)+E(f327(f327(f80(x60391),x60392),f327(f327(f80(x60391),x60393),x60394)),f327(f327(f80(x60391),x60393),f327(f327(f80(x60391),x60392),x60394))) % 177.41/177.19 [6040]~P112(x60401)+E(f327(f327(f81(x60401),x60402),f327(f327(f81(x60401),x60403),x60404)),f327(f327(f81(x60401),x60403),f327(f327(f81(x60401),x60402),x60404))) % 177.41/177.19 [6042]~P108(x60421)+E(f327(f327(f238(x60421),x60422),f327(f327(f238(x60421),x60423),x60424)),f327(f327(f238(x60421),x60423),f327(f327(f238(x60421),x60422),x60424))) % 177.41/177.19 [6044]~P108(x60441)+E(f327(f327(f189(x60441),x60442),f327(f327(f189(x60441),x60443),x60444)),f327(f327(f189(x60441),x60443),f327(f327(f189(x60441),x60442),x60444))) % 177.41/177.19 [6045]~P96(x60451)+E(f327(f327(f102(x60451),x60452),f327(f327(f102(x60451),x60453),x60454)),f327(f327(f102(x60451),x60453),f327(f327(f102(x60451),x60452),x60454))) % 177.41/177.19 [6047]~P101(x60471)+E(f327(f327(f102(x60471),x60472),f327(f327(f102(x60471),x60473),x60474)),f327(f327(f102(x60471),x60473),f327(f327(f102(x60471),x60472),x60474))) % 177.41/177.19 [6048]~P96(x60481)+E(f327(f327(f103(x60481),x60482),f327(f327(f103(x60481),x60483),x60484)),f327(f327(f103(x60481),x60483),f327(f327(f103(x60481),x60482),x60484))) % 177.41/177.19 [6050]~P102(x60501)+E(f327(f327(f103(x60501),x60502),f327(f327(f103(x60501),x60503),x60504)),f327(f327(f103(x60501),x60503),f327(f327(f103(x60501),x60502),x60504))) % 177.41/177.19 [6057]E(x60571,x60572)+E(f171(x60573,x60571,f327(f327(f152(x60573),x60572),x60574)),f327(f327(f152(x60573),x60572),f171(x60573,x60571,x60574))) % 177.41/177.19 [6072]~P1(f327(x60722,x60723))+E(f327(f137(x60721,x60722),f327(f327(f152(x60721),x60723),x60724)),f327(f327(f152(x60721),x60723),f327(f137(x60721,x60722),x60724))) % 177.41/177.19 [6210]~P1(f327(x62102,x62103))+E(f178(x62101,x62102,f327(f327(f152(x62101),x62103),x62104)),f327(f327(f152(x62101),x62103),f178(x62101,x62102,x62104))) % 177.41/177.19 [6262]P22(x62621,x62622,x62623)+~P22(x62621,x62622,f327(f327(f309(f913(x62621)),x62624),x62623)) % 177.41/177.19 [6278]E(x62781,f190(f922(x62782,a910)))+E(f327(f327(f40(x62782,f922(x62783,a910)),x62781),f327(f16(f922(x62783,a910),x62782),x62784)),x62784) % 177.41/177.19 [6279]E(x62791,f190(f922(x62792,a910)))+E(f327(f327(f41(x62792,f922(x62793,a910)),x62791),f327(f16(f922(x62793,a910),x62792),x62794)),x62794) % 177.41/177.19 [6288]~E(x62884,f190(f922(x62882,a910)))+E(f327(f327(f254(x62881,x62882),x62883),f327(f16(f922(x62882,a910),x62881),x62884)),f190(f922(f921(x62881,x62882),a910))) % 177.41/177.19 [6289]~E(x62893,f190(f922(x62891,a910)))+E(f327(f327(f254(x62891,x62892),x62893),f327(f16(f922(x62892,a910),x62891),x62894)),f190(f922(f921(x62891,x62892),a910))) % 177.41/177.19 [6343]E(x63431,f2(a915))+E(f327(f327(f139(x63432),x63431),f327(f327(f152(x63432),x63433),x63434)),f327(f327(f139(x63432),f327(f327(f23(a915),x63431),f78(a915))),x63434)) % 177.41/177.19 [6364]E(x63641,f190(f922(x63642,a910)))+E(f327(f310(x63642,x63643,f327(f16(x63643,x63642),x63644)),x63641),f327(f327(f309(x63643),x63644),f190(f922(x63643,a910)))) % 177.41/177.19 [6367]E(f327(f311(x63671,x63672,f327(f16(x63672,x63671),x63673)),x63674),f190(f922(x63671,a910)))+P1(f327(f327(f329(x63672),x63673),x63674)) % 177.41/177.19 [6433]~E(x64333,f190(f922(x64331,a910)))+E(f327(f327(f40(x64331,f922(x64332,a910)),x64333),f327(f16(f922(x64332,a910),x64331),x64334)),f190(f922(x64332,a910))) % 177.41/177.19 [6434]~E(x64343,f190(f922(x64341,a910)))+E(f327(f327(f41(x64341,f922(x64342,a910)),x64343),f327(f16(f922(x64342,a910),x64341),x64344)),f242(f922(x64342,a910))) % 177.41/177.19 [6436]~P58(x64361)+E(f46(x64361,f327(f327(f81(x64361),x64362),x64363),f327(f327(f81(x64361),x64362),x64364)),f327(f327(f81(x64361),x64362),f46(x64361,x64363,x64364))) % 177.41/177.19 [6606]E(f327(f311(x66061,x66062,f327(f16(x66062,x66061),x66063)),x66064),f242(f922(x66061,a910)))+~P1(f327(f327(f329(x66062),x66063),x66064)) % 177.41/177.19 [6629]~P1(f327(f327(f329(x66291),x66292),x66294))+P1(f327(f327(f329(x66291),x66292),f327(f327(f309(x66291),x66293),x66294))) % 177.41/177.19 [6634]P1(f327(x66341,x66342))+~P1(f327(f161(x66343,x66341),f327(f327(f152(x66343),x66342),x66344))) % 177.41/177.19 [6643]~E(x66433,f327(f327(f23(a915),f327(f191(f916(x66431)),x66432)),f78(a915)))+E(f115(x66431,f327(f327(f160(x66431,x66432),x66433),x66434)),f115(x66431,x66432)) % 177.41/177.19 [6663]~P108(x66631)+E(f327(f327(f103(f922(x66631,a910)),f327(f301(x66631),x66632)),f303(x66631,x66633,x66634)),f303(x66631,x66633,f327(f327(f238(x66631),x66632),x66634))) % 177.41/177.19 [6664]~P108(x66641)+E(f327(f327(f103(f922(x66641,a910)),f327(f283(x66641),x66642)),f303(x66641,x66643,x66644)),f303(x66641,f327(f327(f189(x66641),x66642),x66643),x66644)) % 177.41/177.19 [6680]E(f327(f327(f103(f922(x66801,a910)),x66802),f327(f327(f309(x66801),x66803),x66804)),f327(f327(f103(f922(x66801,a910)),x66802),x66804))+P1(f327(f327(f329(x66801),x66803),x66802)) % 177.41/177.19 [6692]E(f171(x66921,x66922,f327(f327(f135(x66921),x66923),x66924)),f327(f327(f135(x66921),x66923),f171(x66921,x66922,x66924)))+P1(f327(f327(f329(x66921),x66922),f327(f173(x66921),x66923))) % 177.41/177.19 [6697]~P80(x66971)+E(f327(f327(f81(x66971),f327(f327(f244(x66971),x66972),x66973)),f327(f327(f244(x66971),x66972),x66974)),f327(f327(f244(x66971),x66972),f327(f327(f80(a915),x66973),x66974))) % 177.41/177.19 [6698]~P112(x66981)+E(f327(f327(f81(x66981),f327(f327(f244(x66981),x66982),x66983)),f327(f327(f244(x66981),x66982),x66984)),f327(f327(f244(x66981),x66982),f327(f327(f80(a915),x66983),x66984))) % 177.41/177.19 [6735]~P112(x67351)+E(f327(f327(f80(x67351),f327(f327(f81(x67351),x67352),x67353)),f327(f327(f81(x67351),x67352),x67354)),f327(f327(f81(x67351),x67352),f327(f327(f80(x67351),x67353),x67354))) % 177.41/177.19 [6736]~P108(x67361)+E(f327(f327(f189(x67361),f327(f327(f238(x67361),x67362),x67363)),f327(f327(f238(x67361),x67362),x67364)),f327(f327(f238(x67361),x67362),f327(f327(f189(x67361),x67363),x67364))) % 177.41/177.19 [6737]~P108(x67371)+E(f327(f327(f238(x67371),f327(f327(f189(x67371),x67372),x67373)),f327(f327(f189(x67371),x67372),x67374)),f327(f327(f189(x67371),x67372),f327(f327(f238(x67371),x67373),x67374))) % 177.41/177.19 [6738]~P100(x67381)+E(f327(f327(f103(x67381),f327(f327(f102(x67381),x67382),x67383)),f327(f327(f102(x67381),x67382),x67384)),f327(f327(f102(x67381),x67382),f327(f327(f103(x67381),x67383),x67384))) % 177.41/177.19 [6739]~P100(x67391)+E(f327(f327(f102(x67391),f327(f327(f103(x67391),x67392),x67393)),f327(f327(f103(x67391),x67392),x67394)),f327(f327(f103(x67391),x67392),f327(f327(f102(x67391),x67393),x67394))) % 177.41/177.19 [6771]~P58(x67711)+E(f46(x67711,f327(f327(f81(x67711),x67712),x67713),f327(f327(f81(x67711),x67714),x67713)),f327(f327(f81(x67711),f46(x67711,x67712,x67714)),x67713)) % 177.41/177.19 [6774]~E(f327(f191(f916(x67741)),x67743),f327(f191(f916(x67742)),x67744))+E(f327(f327(f155(f921(x67741,x67742),x67742),f256(x67741,x67742)),f327(f327(f182(x67741,x67742),x67743),x67744)),x67744) % 177.41/177.19 [6775]~E(f327(f191(f916(x67751)),x67753),f327(f191(f916(x67752)),x67754))+E(f327(f327(f155(f921(x67751,x67752),x67751),f251(x67751,x67752)),f327(f327(f182(x67751,x67752),x67753),x67754)),x67753) % 177.41/177.19 [6780]P1(f327(f161(x67801,x67802),x67803))+~P1(f327(f161(x67801,x67802),f327(f327(f152(x67801),x67804),x67803))) % 177.41/177.19 [6781]P1(f327(f161(x67811,x67812),x67813))+~P1(f327(f161(x67811,x67812),f327(f327(f135(x67811),x67814),x67813))) % 177.41/177.19 [6782]P1(f327(f161(x67821,x67822),x67823))+~P1(f327(f161(x67821,x67822),f327(f327(f135(x67821),x67823),x67824))) % 177.41/177.19 [6787]~P59(x67871)+E(f46(x67871,f327(f327(f23(x67871),x67872),f46(x67871,x67873,x67874)),x67874),f46(x67871,f327(f327(f23(x67871),x67872),x67873),x67874)) % 177.41/177.19 [6789]~P58(x67891)+E(f46(x67891,f327(f327(f81(x67891),x67892),f46(x67891,x67893,x67894)),x67894),f46(x67891,f327(f327(f81(x67891),x67892),x67893),x67894)) % 177.41/177.19 [6790]~P58(x67901)+E(f46(x67901,f327(f327(f80(x67901),x67902),f46(x67901,x67903,x67904)),x67904),f46(x67901,f327(f327(f80(x67901),x67902),x67903),x67904)) % 177.41/177.19 [6871]~P108(x68711)+E(f327(f327(f103(f922(x68711,a910)),f303(x68711,x68712,x68713)),f327(f301(x68711),x68714)),f303(x68711,x68712,f327(f327(f238(x68711),x68713),x68714))) % 177.41/177.19 [6872]~P108(x68721)+E(f327(f327(f103(f922(x68721,a910)),f303(x68721,x68722,x68723)),f327(f283(x68721),x68724)),f303(x68721,f327(f327(f189(x68721),x68722),x68724),x68723)) % 177.41/177.19 [6875]~E(f327(f191(f916(x68751)),x68753),f327(f191(f916(x68752)),x68754))+E(f327(f327(f182(x68751,x68752),f327(f169(x68751),x68753)),f327(f169(x68752),x68754)),f327(f169(f921(x68751,x68752)),f327(f327(f182(x68751,x68752),x68753),x68754))) % 177.41/177.19 [6886]E(x68861,f327(f327(f23(a915),f327(f191(f916(x68862)),x68863)),f78(a915)))+E(f115(x68862,f327(f327(f160(x68862,x68863),x68861),x68864)),f327(f327(f160(x68862,f115(x68862,x68863)),x68861),x68864)) % 177.41/177.19 [6900]~P1(f327(f138(x69002),x69004))+P1(f327(f138(f921(x69001,x69002)),f327(f327(f182(x69001,x69002),x69003),x69004))) % 177.41/177.19 [6901]~P1(f327(f138(x69011),x69013))+P1(f327(f138(f921(x69011,x69012)),f327(f327(f182(x69011,x69012),x69013),x69014))) % 177.41/177.19 [7167]E(f327(f327(f37(a915),x71671),x71672),x71673)+~P1(f327(f49(x71671,x71672),f327(f327(f252(a915,a915),x71673),x71674))) % 177.41/177.19 [7190]E(f46(a915,x71901,x71902),x71903)+~P1(f327(f49(x71901,x71902),f327(f327(f252(a915,a915),x71904),x71903))) % 177.41/177.19 [7193]P1(f327(f138(x71931),x71932))+~P1(f327(f138(x71933),f327(f327(f155(x71931,x71933),x71934),x71932))) % 177.41/177.19 [7201]~P22(x72011,x72012,f327(f327(f309(f913(x72011)),x72013),x72014))+P22(x72011,x72012,f327(f327(f309(f913(x72011)),x72013),f190(f922(f913(x72011),a910)))) % 177.41/177.19 [7278]E(f171(x72781,x72782,f327(f327(f135(x72781),x72783),x72784)),f327(f327(f135(x72781),f171(x72781,x72782,x72783)),x72784))+~P1(f327(f327(f329(x72781),x72782),f327(f173(x72781),x72783))) % 177.41/177.19 [7371]~P59(x73711)+E(f46(x73711,f327(f327(f23(x73711),f46(x73711,x73712,x73713)),x73714),x73713),f46(x73711,f327(f327(f23(x73711),x73712),x73714),x73713)) % 177.41/177.19 [7374]~P58(x73741)+E(f46(x73741,f327(f327(f80(x73741),f46(x73741,x73742,x73743)),x73744),x73743),f46(x73741,f327(f327(f80(x73741),x73742),x73744),x73743)) % 177.41/177.19 [7375]~P58(x73751)+E(f46(x73751,f327(f327(f81(x73751),f46(x73751,x73752,x73753)),x73754),x73753),f46(x73751,f327(f327(f81(x73751),x73752),x73754),x73753)) % 177.41/177.19 [7569]~E(x75691,f327(f327(f152(x75692),x75693),x75694))+~P1(f327(f327(f234(a915),f327(f191(f916(x75692)),x75691)),f327(f191(f916(x75692)),x75694))) % 177.41/177.19 [7770]P23(x77701,x77702,x77703,f327(f173(x77701),x77704))+~P1(f327(f138(x77702),f327(f327(f155(x77701,x77702),x77703),x77704))) % 177.41/177.19 [7845]~P1(f327(f327(f234(f922(x78451,a910)),x78452),x78454))+P1(f327(f327(f234(f922(x78451,a910)),x78452),f327(f327(f309(x78451),x78453),x78454))) % 177.41/177.19 [7880]~P59(x78801)+E(f46(x78801,f327(f327(f23(x78801),f46(x78801,x78802,x78803)),f46(x78801,x78804,x78803)),x78803),f46(x78801,f327(f327(f23(x78801),x78802),x78804),x78803)) % 177.41/177.19 [7881]~P58(x78811)+E(f46(x78811,f327(f327(f80(x78811),f46(x78811,x78812,x78813)),f46(x78811,x78814,x78813)),x78813),f46(x78811,f327(f327(f80(x78811),x78812),x78814),x78813)) % 177.41/177.19 [7882]~P58(x78821)+E(f46(x78821,f327(f327(f81(x78821),f46(x78821,x78822,x78823)),f46(x78821,x78824,x78823)),x78823),f46(x78821,f327(f327(f81(x78821),x78822),x78824),x78823)) % 177.41/177.19 [7984]~E(f327(x79844,f899(x79844,x79843,x79841,x79842)),f190(f922(x79842,a910)))+E(f327(f327(f40(x79841,f922(x79842,a910)),x79843),x79844),f190(f922(x79842,a910))) % 177.41/177.19 [7985]~E(f327(x79854,f340(x79854,x79853,x79851,x79852)),f242(f922(x79852,a910)))+E(f327(f327(f41(x79851,f922(x79852,a910)),x79853),x79854),f242(f922(x79852,a910))) % 177.41/177.19 [7986]~E(f327(x79864,f900(x79864,x79863,x79862,x79861)),f190(f922(x79862,a910)))+E(f327(f327(f40(x79861,f922(x79862,a910)),x79863),x79864),f190(f922(x79862,a910))) % 177.41/177.19 [7987]~E(f327(x79874,f341(x79874,x79873,x79872,x79871)),f242(f922(x79872,a910)))+E(f327(f327(f41(x79871,f922(x79872,a910)),x79873),x79874),f242(f922(x79872,a910))) % 177.41/177.19 [8377]P1(f327(x83771,x83772))+~P1(f327(f327(f329(x83773),x83772),f327(f327(f103(f922(x83773,a910)),x83774),f327(f262(x83773),x83771)))) % 177.41/177.19 [8414]~P1(f327(f327(f234(f922(x84141,a910)),x84143),x84144))+P1(f327(f327(f234(f922(x84141,a910)),f327(f327(f309(x84141),x84142),x84143)),f327(f327(f309(x84141),x84142),x84144))) % 177.41/177.19 [8592]P1(f327(x85922,x85923))+E(f327(f327(f139(x85921),f327(f191(f916(x85921)),f178(x85921,x85922,f327(f327(f152(x85921),x85923),x85924)))),f327(f327(f152(x85921),x85923),x85924)),f327(f327(f152(x85921),x85923),x85924)) % 177.41/177.19 [8698]~P1(f327(f327(f235(a915),f327(x86984,x86982)),f327(x86984,x86983)))+P1(f327(f327(f329(f921(x86981,x86981)),f327(f327(f252(x86981,x86981),x86982),x86983)),f327(f327(f288(a915,x86981),a240),x86984))) % 177.41/177.19 [8794]~P1(f327(x87942,f736(x87944,x87942,x87943,x87941)))+E(f178(x87941,x87942,f327(f327(f135(x87941),x87943),x87944)),f327(f327(f135(x87941),x87943),f178(x87941,x87942,x87944))) % 177.41/177.19 [8871]P23(f916(x88711),f916(x88712),f327(f155(x88711,x88712),x88713),x88714)+~P23(x88711,x88712,x88713,f38(f922(x88711,a910),f327(f310(f916(x88711),f922(x88711,a910),f173(x88711)),x88714))) % 177.41/177.19 [8946]~P1(f327(x89462,x89463))+E(f327(f327(f139(x89461),f327(f191(f916(x89461)),f178(x89461,x89462,f327(f327(f152(x89461),x89463),x89464)))),f327(f327(f152(x89461),x89463),x89464)),f327(f327(f139(x89461),f327(f191(f916(x89461)),f178(x89461,x89462,x89464))),x89464)) % 177.41/177.19 [8987]~E(x89872,x89873)+E(f327(f137(x89871,f327(f327(f8(a910,a910,x89871),a322),f327(a324,x89872))),f327(f327(f152(x89871),x89873),x89874)),f327(f137(x89871,f327(f327(f8(a910,a910,x89871),a322),f327(a324,x89872))),x89874)) % 177.41/177.19 [8997]E(f327(f327(f40(x89971,f922(x89972,a910)),x89973),x89974),f190(f922(x89972,a910)))+P1(f327(f327(f329(x89971),f899(x89974,x89973,x89971,x89972)),x89973)) % 177.41/177.19 [8998]E(f327(f327(f41(x89981,f922(x89982,a910)),x89983),x89984),f242(f922(x89982,a910)))+P1(f327(f327(f329(x89981),f340(x89984,x89983,x89981,x89982)),x89983)) % 177.41/177.19 [8999]E(f327(f327(f40(x89991,f922(x89992,a910)),x89993),x89994),f190(f922(x89992,a910)))+P1(f327(f327(f329(x89991),f900(x89994,x89993,x89992,x89991)),x89993)) % 177.41/177.19 [9000]E(f327(f327(f41(x90001,f922(x90002,a910)),x90003),x90004),f242(f922(x90002,a910)))+P1(f327(f327(f329(x90001),f341(x90004,x90003,x90002,x90001)),x90003)) % 177.41/177.19 [9038]P1(f327(f327(f235(a915),f327(x90381,x90382)),f327(x90381,x90383)))+~P1(f327(f327(f329(f921(x90384,x90384)),f327(f327(f252(x90384,x90384),x90382),x90383)),f327(f327(f288(a915,x90384),a240),x90381))) % 177.41/177.19 [9064]E(f178(x90641,x90642,f327(f327(f135(x90641),x90643),x90644)),f327(f327(f135(x90641),x90643),f178(x90641,x90642,x90644)))+P1(f327(f327(f329(x90641),f736(x90644,x90642,x90643,x90641)),f327(f173(x90641),x90643))) % 177.41/177.19 [9119]~P24(x91191,x91192,x91193,f242(f922(x91191,a910)),f242(f922(x91192,a910)))+E(f327(f310(x91191,x91192,x91193),f327(f79(f922(x91191,a910)),x91194)),f327(f79(f922(x91192,a910)),f327(f310(x91191,x91192,x91193),x91194))) % 177.41/177.19 [9222]P1(f327(f327(f329(x92221),f499(x92222,x92223,x92224,x92221)),x92223))+~P1(f327(f327(f329(f922(x92221,a910)),x92224),f327(f327(f61(x92221),x92223),x92222))) % 177.41/177.19 [9225]E(x92251,x92252)+~P1(f327(f327(f329(f921(x92253,x92253)),f327(f327(f252(x92253,x92253),x92251),x92252)),f327(f327(f184(f921(x92253,x92253),a910),f2(a915)),x92254))) % 177.41/177.19 [9306]E(f327(f285(x93061,x93061,x93062),f327(f327(f309(x93061),f499(x93062,x93063,x93064,x93061)),f190(f922(x93061,a910)))),x93064)+~P1(f327(f327(f329(f922(x93061,a910)),x93064),f327(f327(f61(x93061),x93063),x93062))) % 177.41/177.19 [9311]~P1(f327(f327(f329(f921(x93111,x93111)),f327(f327(f252(x93111,x93111),x93113),x93112)),f307(x93111,x93114)))+P1(f327(f327(f329(f921(x93111,x93111)),f327(f327(f252(x93111,x93111),x93112),x93113)),f307(x93111,f327(f286(x93111,x93111),x93114)))) % 177.41/177.19 [9324]~P58(x93241)+E(f327(f327(f80(x93241),f327(f327(f80(x93241),f327(f327(f81(x93241),x93242),f327(f327(f37(x93241),x93243),x93242))),f46(x93241,x93243,x93242))),x93244),f327(f327(f80(x93241),x93243),x93244)) % 177.41/177.19 [9335]~P1(f327(f327(f329(x93351),x93353),x93354))+P1(f327(f327(f329(f922(x93351,a910)),f327(f285(x93351,x93351,x93352),f327(f327(f309(x93351),x93353),f190(f922(x93351,a910))))),f327(f327(f61(x93351),x93354),x93352))) % 177.41/177.19 [9347]P1(f327(f327(f329(f921(x93471,x93471)),f327(f327(f252(x93471,x93471),x93472),x93473)),f307(x93471,x93474)))+~P1(f327(f327(f329(f921(x93471,x93471)),f327(f327(f252(x93471,x93471),x93473),x93472)),f307(x93471,f327(f286(x93471,x93471),x93474)))) % 177.41/177.19 [9432]E(f327(f327(f160(x94321,f327(f169(x94321),x94322)),f327(f327(f23(a915),f327(f327(f23(a915),f327(f191(f916(x94321)),x94322)),x94323)),f78(a915))),x94324),f327(f169(x94321),f327(f327(f160(x94321,x94322),x94323),x94324)))+~P1(f327(f327(f235(a915),x94323),f327(f191(f916(x94321)),x94322))) % 177.41/177.19 [9435]~P1(f327(x94352,f730(x94354,x94352,x94353,x94351)))+E(f327(f327(f139(x94351),f327(f191(f916(x94351)),f178(x94351,x94352,f327(f327(f135(x94351),x94353),x94354)))),f327(f327(f135(x94351),x94353),x94354)),f327(f327(f139(x94351),f327(f191(f916(x94351)),f178(x94351,x94352,x94354))),x94354)) % 177.41/177.19 [9479]~P23(x94792,x94791,x94793,f242(f922(x94792,a910)))+P1(f327(f327(f234(f922(x94791,a910)),f327(f310(x94792,x94791,x94793),f327(f79(f922(x94792,a910)),x94794))),f327(f79(f922(x94791,a910)),f327(f310(x94792,x94791,x94793),x94794)))) % 177.41/177.19 [9491]~P3(x94911)+E(f327(f143(x94911,x94912,f327(f7(x94912,x94911,x94911),f327(f327(f8(x94911,f922(x94911,x94911),x94912),f102(x94911)),x94913)),f190(x94911)),x94914),f327(f327(f40(x94912,x94911),f327(f173(x94912),x94914)),x94913)) % 177.41/177.19 [9492]~P3(x94921)+E(f327(f143(x94921,x94922,f327(f7(x94922,x94921,x94921),f327(f327(f8(x94921,f922(x94921,x94921),x94922),f103(x94921)),x94923)),f242(x94921)),x94924),f327(f327(f41(x94922,x94921),f327(f173(x94922),x94924)),x94923)) % 177.41/177.19 [9502]E(f327(f327(f139(x95021),f327(f191(f916(x95021)),f178(x95021,x95022,f327(f327(f135(x95021),x95023),x95024)))),f327(f327(f135(x95021),x95023),x95024)),f327(f327(f139(x95021),f327(f191(f916(x95021)),f178(x95021,x95022,x95024))),x95024))+P1(f327(f327(f329(x95021),f730(x95024,x95022,x95023,x95021)),f327(f173(x95021),x95023))) % 177.41/177.19 [9572]~P1(f327(f327(f329(f921(f916(x95724),f916(x95724))),f327(f327(f252(f916(x95724),f916(x95724)),x95723),x95722)),f158(x95724,x95721)))+P1(f327(f327(f235(a915),f666(x95721,x95722,x95723,x95724)),f327(f191(f916(x95724)),x95723))) % 177.41/177.19 [9573]~P58(x95731)+E(f327(f327(f80(x95731),f327(f327(f80(x95731),f327(f327(f81(x95731),f327(f327(f37(x95731),x95732),x95733)),x95733)),f46(x95731,x95732,x95733))),x95734),f327(f327(f80(x95731),x95732),x95734)) % 177.41/177.19 [9602]~P1(f327(f327(f329(f921(f916(x96021),f916(x96021))),f327(f327(f252(f916(x96021),f916(x96021)),x96022),x96023)),f327(f286(f916(x96021),f916(x96021)),f158(x96021,x96024))))+P1(f327(f327(f329(f921(f916(x96021),f916(x96021))),f327(f327(f252(f916(x96021),f916(x96021)),x96022),x96023)),f158(x96021,f327(f286(x96021,x96021),x96024)))) % 177.41/177.19 [9603]P1(f327(f327(f329(f921(f916(x96031),f916(x96031))),f327(f327(f252(f916(x96031),f916(x96031)),x96032),x96033)),f327(f286(f916(x96031),f916(x96031)),f158(x96031,x96034))))+~P1(f327(f327(f329(f921(f916(x96031),f916(x96031))),f327(f327(f252(f916(x96031),f916(x96031)),x96032),x96033)),f158(x96031,f327(f286(x96031,x96031),x96034)))) % 177.41/177.19 [9642]~P1(f327(f327(f329(x96421),x96423),f327(f264(x96421,x96422),x96424)))+P1(f327(f327(f329(f921(x96421,x96422)),f327(f327(f252(x96421,x96422),x96423),f550(x96424,x96422,x96423,x96421))),x96424)) % 177.41/177.19 [9643]~P1(f327(f327(f329(x96431),x96433),f327(f264(x96431,x96432),x96434)))+P1(f327(f327(f329(f921(x96431,x96432)),f327(f327(f252(x96431,x96432),x96433),f552(x96434,x96432,x96433,x96431))),x96434)) % 177.41/177.19 [9801]~P1(f327(f327(f329(f921(x98011,x98011)),f327(f327(f252(x98011,x98011),x98012),x98014)),f327(f327(f289(x98011,x98011,x98011),x98013),f307(x98011,x98013))))+P1(f327(f327(f329(f921(x98011,x98011)),f327(f327(f252(x98011,x98011),x98012),f617(x98013,x98014,x98012,x98011))),x98013)) % 177.41/177.19 [9960]P9(x99601,x99602,x99603,x99604)+P1(f327(f327(f329(f921(x99601,x99601)),f327(f327(f252(x99601,x99601),f826(x99602,x99604,x99603,x99601)),f825(x99602,x99604,x99603,x99601))),x99603)) % 177.41/177.19 [9967]~P1(f327(f327(f329(f921(x99672,x99671)),x99674),f327(f286(x99671,x99672),x99673)))+P1(f327(f327(f329(f921(x99671,x99672)),f327(f327(f252(x99671,x99672),f637(x99673,x99674,x99671,x99672)),f636(x99673,x99674,x99671,x99672))),x99673)) % 177.41/177.19 [9991]~P1(f327(f327(f329(f921(f916(x99911),f916(x99911))),f327(f327(f252(f916(x99911),f916(x99911)),x99914),x99913)),f158(x99911,x99912)))+P1(f327(f327(f329(f921(x99911,x99911)),f327(f327(f252(x99911,x99911),f681(x99912,x99913,x99914,x99911)),f682(x99912,x99913,x99914,x99911))),x99912)) % 177.41/177.19 [10082]~P1(f327(f327(f329(f921(f916(x100821),f916(x100821))),f327(f327(f252(f916(x100821),f916(x100821)),x100822),x100824)),f158(x100821,x100823)))+P1(f327(f327(f329(f921(x100821,x100821)),f327(f327(f252(x100821,x100821),f327(f327(f165(x100821),x100822),f666(x100823,x100824,x100822,x100821))),f665(x100823,x100824,x100822,x100821))),x100823)) % 177.41/177.19 [10103]~P1(f327(f35(x101032),x101034))+E(f327(f327(f327(f65(f922(x101031,a910),x101032,f102(f922(x101031,a910))),f327(f327(f7(x101032,f922(x101031,a910),f922(x101031,a910)),f327(f327(f8(x101031,f922(f922(x101031,a910),f922(x101031,a910)),x101032),f309(x101031)),x101033)),f190(f922(x101031,a910)))),f190(f922(x101031,a910))),x101034),f327(f310(x101032,x101031,x101033),x101034)) % 177.41/177.19 [10214]~P23(x102141,x102142,x102143,f242(f922(x102141,a910)))+P1(f327(f327(f234(f922(x102141,a910)),f327(f311(x102141,x102142,x102143),f327(f327(f309(x102142),x102144),f190(f922(x102142,a910))))),f327(f327(f309(x102141),f85(x102141,f327(f327(f7(x102141,x102142,a910),f327(f327(f8(x102142,f922(x102142,a910),x102141),a324),x102143)),x102144))),f190(f922(x102141,a910))))) % 177.41/177.19 [5797]~E(f327(f327(f135(x57971),x57972),x57974),x57973)+E(f327(f327(f176(x57971),f327(f191(f916(x57971)),x57972)),x57973),x57972) % 177.41/177.19 [5798]~E(f327(f327(f135(x57982),x57983),x57981),x57984)+E(x57981,f327(f327(f139(x57982),f327(f191(f916(x57982)),x57983)),x57984)) % 177.41/177.19 [5809]~E(x58094,f2(a915))+E(f327(f327(f165(x58091),f327(f327(f152(x58091),x58092),x58093)),x58094),x58092) % 177.41/177.19 [6356]~P112(x63561)+E(f327(f327(f244(x63561),f327(f327(f244(x63561),x63562),x63563)),x63564),f327(f327(f244(x63561),x63562),f327(f327(f81(a915),x63563),x63564))) % 177.41/177.19 [6357]~P80(x63571)+E(f327(f327(f244(x63571),f327(f327(f244(x63571),x63572),x63573)),x63574),f327(f327(f244(x63571),x63572),f327(f327(f81(a915),x63573),x63574))) % 177.41/177.19 [6365]E(x63651,f2(a915))+E(f327(f327(f165(x63652),f327(f327(f152(x63652),x63653),x63654)),x63651),f327(f327(f165(x63652),x63654),f327(f327(f23(a915),x63651),f78(a915)))) % 177.41/177.19 [6393]~P122(x63931)+E(f327(f327(f291(x63931),f327(f327(f81(x63931),x63932),x63933)),x63934),f327(f327(f81(x63931),x63932),f327(f327(f291(x63931),x63933),x63934))) % 177.41/177.19 [6394]~P71(x63941)+E(f327(f327(f80(x63941),f327(f327(f80(x63941),x63942),x63943)),x63944),f327(f327(f80(x63941),x63942),f327(f327(f80(x63941),x63943),x63944))) % 177.41/177.19 [6395]~P112(x63951)+E(f327(f327(f80(x63951),f327(f327(f80(x63951),x63952),x63953)),x63954),f327(f327(f80(x63951),x63952),f327(f327(f80(x63951),x63953),x63954))) % 177.41/177.19 [6396]~P72(x63961)+E(f327(f327(f81(x63961),f327(f327(f81(x63961),x63962),x63963)),x63964),f327(f327(f81(x63961),x63962),f327(f327(f81(x63961),x63963),x63964))) % 177.41/177.19 [6397]~P112(x63971)+E(f327(f327(f81(x63971),f327(f327(f81(x63971),x63972),x63973)),x63974),f327(f327(f81(x63971),x63972),f327(f327(f81(x63971),x63973),x63974))) % 177.41/177.19 [6400]~P108(x64001)+E(f327(f327(f238(x64001),f327(f327(f238(x64001),x64002),x64003)),x64004),f327(f327(f238(x64001),x64002),f327(f327(f238(x64001),x64003),x64004))) % 177.41/177.19 [6402]~P108(x64021)+E(f327(f327(f189(x64021),f327(f327(f189(x64021),x64022),x64023)),x64024),f327(f327(f189(x64021),x64022),f327(f327(f189(x64021),x64023),x64024))) % 177.41/177.19 [6403]~P96(x64031)+E(f327(f327(f102(x64031),f327(f327(f102(x64031),x64032),x64033)),x64034),f327(f327(f102(x64031),x64032),f327(f327(f102(x64031),x64033),x64034))) % 177.41/177.19 [6405]~P101(x64051)+E(f327(f327(f102(x64051),f327(f327(f102(x64051),x64052),x64053)),x64054),f327(f327(f102(x64051),x64052),f327(f327(f102(x64051),x64053),x64054))) % 177.41/177.19 [6406]~P96(x64061)+E(f327(f327(f103(x64061),f327(f327(f103(x64061),x64062),x64063)),x64064),f327(f327(f103(x64061),x64062),f327(f327(f103(x64061),x64063),x64064))) % 177.41/177.19 [6408]~P102(x64081)+E(f327(f327(f103(x64081),f327(f327(f103(x64081),x64082),x64083)),x64084),f327(f327(f103(x64081),x64082),f327(f327(f103(x64081),x64083),x64084))) % 177.41/177.19 [6417]~P58(x64171)+E(f46(x64171,f327(f327(f80(x64171),x64172),f327(f327(f81(x64171),x64173),x64174)),x64174),f46(x64171,x64172,x64174)) % 177.41/177.19 [6418]~P58(x64181)+E(f46(x64181,f327(f327(f80(x64181),x64182),f327(f327(f81(x64181),x64183),x64184)),x64183),f46(x64181,x64182,x64183)) % 177.41/177.19 [6556]E(f327(f327(f165(x65561),f327(f327(f176(x65561),x65562),x65563)),x65564),f327(f327(f165(x65561),x65563),x65564))+~P1(f327(f327(f235(a915),x65564),x65562)) % 177.41/177.19 [6731]~E(x67312,x67314)+P1(f327(f327(f173(x67311),f327(f327(f152(x67311),x67312),x67313)),x67314)) % 177.41/177.19 [6733]~P112(x67331)+E(f327(f327(f80(x67331),f327(f327(f80(x67331),x67332),x67333)),x67334),f327(f327(f80(x67331),f327(f327(f80(x67331),x67332),x67334)),x67333)) % 177.41/177.19 [6734]~P112(x67341)+E(f327(f327(f81(x67341),f327(f327(f81(x67341),x67342),x67343)),x67344),f327(f327(f81(x67341),f327(f327(f81(x67341),x67342),x67344)),x67343)) % 177.41/177.19 [6793]~P146(x67932)+E(f327(f327(f6(x67931,x67932),f327(f16(x67932,x67931),x67933)),x67934),f327(f327(f81(x67932),f327(f101(x67932),f327(f36(x67931),x67934))),x67933)) % 177.41/177.19 [6964]E(f327(f327(f103(f922(x69641,a910)),f327(f327(f309(x69641),x69642),x69643)),x69644),f327(f327(f103(f922(x69641,a910)),x69643),x69644))+P1(f327(f327(f329(x69641),x69642),x69644)) % 177.41/177.19 [7033]~P78(x70331)+E(f327(f327(f238(x70331),f327(f327(f23(x70331),x70332),x70333)),f327(f327(f23(x70331),x70334),x70333)),f327(f327(f23(x70331),f327(f327(f238(x70331),x70332),x70334)),x70333)) % 177.41/177.19 [7034]~P78(x70341)+E(f327(f327(f189(x70341),f327(f327(f23(x70341),x70342),x70343)),f327(f327(f23(x70341),x70344),x70343)),f327(f327(f23(x70341),f327(f327(f189(x70341),x70342),x70344)),x70343)) % 177.41/177.19 [7035]~P82(x70351)+E(f327(f327(f238(x70351),f327(f327(f80(x70351),x70352),x70353)),f327(f327(f80(x70351),x70354),x70353)),f327(f327(f80(x70351),f327(f327(f238(x70351),x70352),x70354)),x70353)) % 177.41/177.19 [7036]~P82(x70361)+E(f327(f327(f189(x70361),f327(f327(f80(x70361),x70362),x70363)),f327(f327(f80(x70361),x70364),x70363)),f327(f327(f80(x70361),f327(f327(f189(x70361),x70362),x70364)),x70363)) % 177.41/177.19 [7038]~P113(x70381)+E(f327(f327(f80(x70381),f327(f327(f81(x70381),x70382),x70383)),f327(f327(f81(x70381),x70384),x70383)),f327(f327(f81(x70381),f327(f327(f80(x70381),x70382),x70384)),x70383)) % 177.41/177.19 [7039]~P108(x70391)+E(f327(f327(f189(x70391),f327(f327(f238(x70391),x70392),x70393)),f327(f327(f238(x70391),x70394),x70393)),f327(f327(f238(x70391),f327(f327(f189(x70391),x70392),x70394)),x70393)) % 177.41/177.19 [7040]~P108(x70401)+E(f327(f327(f238(x70401),f327(f327(f189(x70401),x70402),x70403)),f327(f327(f189(x70401),x70404),x70403)),f327(f327(f189(x70401),f327(f327(f238(x70401),x70402),x70404)),x70403)) % 177.41/177.19 [7041]~P100(x70411)+E(f327(f327(f103(x70411),f327(f327(f102(x70411),x70412),x70413)),f327(f327(f102(x70411),x70414),x70413)),f327(f327(f102(x70411),f327(f327(f103(x70411),x70412),x70414)),x70413)) % 177.41/177.19 [7042]~P112(x70421)+E(f327(f327(f81(x70421),f327(f327(f244(x70421),x70422),x70423)),f327(f327(f244(x70421),x70424),x70423)),f327(f327(f244(x70421),f327(f327(f81(x70421),x70422),x70424)),x70423)) % 177.41/177.19 [7043]~P75(x70431)+E(f327(f327(f81(x70431),f327(f327(f244(x70431),x70432),x70433)),f327(f327(f244(x70431),x70434),x70433)),f327(f327(f244(x70431),f327(f327(f81(x70431),x70432),x70434)),x70433)) % 177.41/177.19 [7044]~P61(x70441)+E(f327(f327(f291(x70441),f327(f327(f244(x70441),x70442),x70443)),f327(f327(f244(x70441),x70444),x70443)),f327(f327(f244(x70441),f327(f327(f291(x70441),x70442),x70444)),x70443)) % 177.41/177.19 [7045]~P100(x70451)+E(f327(f327(f102(x70451),f327(f327(f103(x70451),x70452),x70453)),f327(f327(f103(x70451),x70454),x70453)),f327(f327(f103(x70451),f327(f327(f102(x70451),x70452),x70454)),x70453)) % 177.41/177.19 [7046]~P122(x70461)+E(f327(f327(f23(x70461),f327(f327(f291(x70461),x70462),x70463)),f327(f327(f291(x70461),x70464),x70463)),f327(f327(f291(x70461),f327(f327(f23(x70461),x70462),x70464)),x70463)) % 177.41/177.19 [7047]~P122(x70471)+E(f327(f327(f80(x70471),f327(f327(f291(x70471),x70472),x70473)),f327(f327(f291(x70471),x70474),x70473)),f327(f327(f291(x70471),f327(f327(f80(x70471),x70472),x70474)),x70473)) % 177.41/177.19 [7048]~P112(x70481)+E(f327(f327(f80(x70481),f327(f327(f81(x70481),x70482),x70483)),f327(f327(f81(x70481),x70484),x70483)),f327(f327(f81(x70481),f327(f327(f80(x70481),x70482),x70484)),x70483)) % 177.41/177.19 [7080]E(f327(f327(f160(x70801,x70802),x70803),x70804),x70802)+~P1(f327(f327(f234(a915),f327(f191(f916(x70801)),x70802)),x70803)) % 177.41/177.19 [7107]~P1(f327(x71073,x71074))+P1(f327(f327(f327(f102(f922(x71071,a910)),x71072),x71073),x71074)) % 177.41/177.19 [7109]~P1(f327(x71092,x71094))+P1(f327(f327(f327(f102(f922(x71091,a910)),x71092),x71093),x71094)) % 177.41/177.19 [7127]E(f327(f327(f165(x71271),f327(f327(f135(x71271),x71272),x71273)),x71274),f327(f327(f165(x71271),x71272),x71274))+~P1(f327(f327(f235(a915),x71274),f327(f191(f916(x71271)),x71272))) % 177.41/177.19 [7138]E(f327(f327(f23(f922(x71381,a910)),f327(f327(f309(x71381),x71382),x71383)),x71384),f327(f327(f23(f922(x71381,a910)),x71383),x71384))+~P1(f327(f327(f329(x71381),x71382),x71384)) % 177.41/177.19 [7180]~E(f140(a915,f327(f302(a915,x71801),x71802)),f327(f327(f152(a915),x71804),x71803))+E(f140(a915,f327(f302(a915,f327(f327(f80(a915),x71801),f78(a915))),x71802)),x71803) % 177.41/177.19 [7202]~P1(f327(f327(f173(x72021),x72023),x72024))+P1(f327(f327(f173(x72021),f327(f327(f152(x72021),x72022),x72023)),x72024)) % 177.41/177.19 [7253]E(x72531,f2(a915))+E(f327(f327(f152(x72532),x72533),f327(f327(f176(x72532),f327(f327(f23(a915),x72531),f78(a915))),x72534)),f327(f327(f176(x72532),x72531),f327(f327(f152(x72532),x72533),x72534))) % 177.41/177.19 [7355]E(f327(f327(f165(x73551),x73552),f327(f327(f23(a915),x73553),f327(f191(f916(x73551)),x73554))),f327(f327(f165(x73551),f327(f327(f135(x73551),x73554),x73552)),x73553))+P1(f327(f327(f235(a915),x73553),f327(f191(f916(x73551)),x73554))) % 177.41/177.19 [7385]E(f327(f327(f103(f922(x73851,a910)),x73852),f327(f327(f309(x73851),x73853),x73854)),f327(f327(f309(x73851),x73853),f327(f327(f103(f922(x73851,a910)),x73852),x73854)))+~P1(f327(f327(f329(x73851),x73853),x73852)) % 177.41/177.19 [7423]E(f327(f327(f165(x74231),f327(f327(f160(x74231,x74232),x74233),x74234)),x74233),x74234)+~P1(f327(f327(f235(a915),x74233),f327(f191(f916(x74231)),x74232))) % 177.41/177.19 [7445]E(x74451,f190(f922(x74452,a910)))+E(f327(f310(f921(x74453,x74452),x74453,f251(x74453,x74452)),f327(f327(f254(x74453,x74452),x74454),f327(f16(f922(x74452,a910),x74453),x74451))),x74454) % 177.41/177.19 [7446]E(x74461,f190(f922(x74462,a910)))+E(f327(f310(f921(x74462,x74463),x74463,f256(x74462,x74463)),f327(f327(f254(x74462,x74463),x74461),f327(f16(f922(x74463,a910),x74462),x74464))),x74464) % 177.41/177.19 [7520]E(f327(f327(f23(f922(x75201,a910)),f327(f327(f309(x75201),x75202),x75203)),x75204),f327(f327(f309(x75201),x75202),f327(f327(f23(f922(x75201,a910)),x75203),x75204)))+P1(f327(f327(f329(x75201),x75202),x75204)) % 177.41/177.19 [7555]~E(x75554,f190(f922(x75552,a910)))+E(f327(f310(f921(x75551,x75552),x75551,f251(x75551,x75552)),f327(f327(f254(x75551,x75552),x75553),f327(f16(f922(x75552,a910),x75551),x75554))),f190(f922(x75551,a910))) % 177.41/177.19 [7556]~E(x75563,f190(f922(x75561,a910)))+E(f327(f310(f921(x75561,x75562),x75562,f256(x75561,x75562)),f327(f327(f254(x75561,x75562),x75563),f327(f16(f922(x75562,a910),x75561),x75564))),f190(f922(x75562,a910))) % 177.41/177.19 [7607]~P1(f327(f327(f329(x76071),x76072),x76074))+P1(f327(f327(f329(x76071),x76072),f327(f327(f102(f922(x76071,a910)),x76073),x76074))) % 177.41/177.19 [7610]~P1(f327(f327(f329(x76101),x76102),x76103))+P1(f327(f327(f329(x76101),x76102),f327(f327(f102(f922(x76101,a910)),x76103),x76104))) % 177.41/177.19 [7628]E(f327(f327(f103(f922(x76281,a910)),f327(f327(f309(x76281),x76282),x76283)),x76284),f327(f327(f309(x76281),x76282),f327(f327(f103(f922(x76281,a910)),x76283),x76284)))+~P1(f327(f327(f329(x76281),x76282),x76284)) % 177.41/177.19 [7902]P1(f327(x79021,x79022))+~P1(f327(f327(f327(f103(f922(x79023,a910)),x79024),x79021),x79022)) % 177.41/177.19 [7903]P1(f327(x79031,x79032))+~P1(f327(f327(f327(f103(f922(x79033,a910)),x79031),x79034),x79032)) % 177.41/177.19 [7904]E(f327(f327(f6(x79041,a915),x79042),f327(f327(f23(f922(x79041,a910)),x79043),f327(f327(f309(x79041),x79044),f190(f922(x79041,a910))))),f327(f327(f6(x79041,a915),x79042),x79043))+P1(f327(f327(f329(x79041),x79044),x79043)) % 177.41/177.19 [7909]~P68(x79091)+E(f327(f166(x79091),f327(f327(f155(a915,x79091),x79092),f140(a915,f327(f302(a915,x79093),x79094)))),f327(f327(f6(a915,x79091),x79092),f327(f173(a915),f140(a915,f327(f302(a915,x79093),x79094))))) % 177.41/177.19 [7910]~P68(x79101)+E(f327(f327(f6(a915,x79101),x79102),f327(f173(a915),f140(a915,f327(f302(a915,x79103),x79104)))),f327(f166(x79101),f327(f327(f155(a915,x79101),x79102),f140(a915,f327(f302(a915,x79103),x79104))))) % 177.41/177.19 [8022]~E(x80223,x80224)+P1(f327(f62(x80221,x80222,f327(f327(f309(x80221),x80223),f190(f922(x80221,a910)))),x80224)) % 177.41/177.19 [8119]P1(f327(f327(f329(x81191),x81192),f327(f173(x81191),x81193)))+~P1(f327(f327(f329(x81191),x81192),f327(f173(x81191),f327(f327(f176(x81191),x81194),x81193)))) % 177.41/177.19 [8120]P1(f327(f327(f329(x81201),x81202),f327(f173(x81201),x81203)))+~P1(f327(f327(f329(x81201),x81202),f327(f173(x81201),f327(f327(f139(x81201),x81204),x81203)))) % 177.41/177.19 [8190]P1(f327(f327(f329(x81901),x81902),x81903))+~P1(f327(f327(f329(x81901),x81902),f327(f327(f23(f922(x81901,a910)),x81903),x81904))) % 177.41/177.19 [8192]P1(f327(f327(f329(x81921),x81922),x81923))+~P1(f327(f327(f329(x81921),x81922),f327(f327(f103(f922(x81921,a910)),x81924),x81923))) % 177.41/177.19 [8195]P1(f327(f327(f329(x81951),x81952),x81953))+~P1(f327(f327(f329(x81951),x81952),f327(f327(f103(f922(x81951,a910)),x81953),x81954))) % 177.41/177.19 [8210]E(f327(f327(f135(x82101),f327(f327(f176(x82101),x82102),x82103)),f327(f327(f152(x82101),x82104),f327(f327(f139(x82101),f327(a113,x82102)),x82103))),f327(f327(f160(x82101,x82103),x82102),x82104))+~P1(f327(f327(f235(a915),x82102),f327(f191(f916(x82101)),x82103))) % 177.41/177.19 [8233]P1(f327(f327(f329(x82331),x82332),x82333))+~P1(f327(f327(f234(f922(x82331,a910)),f327(f327(f309(x82331),x82332),x82334)),x82333)) % 177.41/177.19 [8270]~P1(f327(f327(f329(x82701),x82702),x82703))+~P1(f327(f327(f329(x82701),x82702),f327(f327(f23(f922(x82701,a910)),x82704),x82703))) % 177.41/177.19 [8303]~P1(f327(f327(f235(a915),x83034),f327(f191(f916(x83031)),x83033)))+P1(f327(f327(f329(x83031),x83032),f327(f173(x83031),f327(f327(f160(x83031,x83033),x83034),x83032)))) % 177.41/177.19 [8356]E(f327(f327(f165(x83561),f327(f327(f139(x83561),x83562),x83563)),x83564),f327(f327(f165(x83561),x83563),f327(f327(f80(a915),x83562),x83564)))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),x83562),x83564)),f327(f191(f916(x83561)),x83563))) % 177.41/177.19 [8365]~P146(x83652)+E(f327(f327(f6(x83651,x83652),f327(f327(f8(a915,x83652,x83651),f101(x83652)),x83653)),x83654),f327(f101(x83652),f327(f327(f6(x83651,a915),x83653),x83654))) % 177.41/177.19 [8366]~P142(x83662)+E(f327(f327(f6(x83661,x83662),f327(f327(f8(a1,x83662,x83661),f104(x83662)),x83663)),x83664),f327(f104(x83662),f327(f327(f6(x83661,a1),x83663),x83664))) % 177.41/177.19 [8416]~P64(x84162)+E(f327(f327(f9(x84161,x84162),f327(f327(f8(x84162,x84162,x84161),f75(x84162)),x84163)),x84164),f327(f75(x84162),f327(f327(f9(x84161,x84162),x84163),x84164))) % 177.41/177.19 [8417]~P67(x84172)+E(f327(f327(f6(x84171,x84172),f327(f327(f8(x84172,x84172,x84171),f79(x84172)),x84173)),x84174),f327(f79(x84172),f327(f327(f6(x84171,x84172),x84173),x84174))) % 177.41/177.19 [8419]E(f327(f327(f6(x84191,a915),x84192),f327(f327(f23(f922(x84191,a910)),x84193),f327(f327(f309(x84191),x84194),f190(f922(x84191,a910))))),f327(f327(f23(a915),f327(f327(f6(x84191,a915),x84192),x84193)),f327(x84192,x84194)))+~P1(f327(f327(f329(x84191),x84194),x84193)) % 177.41/177.19 [8438]P1(f327(f327(f234(f922(x84381,a910)),x84382),x84383))+~P1(f327(f327(f234(f922(x84381,a910)),f327(f327(f309(x84381),x84384),x84382)),x84383)) % 177.41/177.19 [8561]~E(f327(f310(x85612,x85613,x85611),f242(f922(x85612,a910))),f242(f922(x85613,a910)))+E(f327(x85611,f327(f92(x85612,x85613,f242(f922(x85612,a910)),x85611),x85614)),x85614) % 177.41/177.19 [8644]P35(x86441,x86442)+~P35(x86441,f327(f327(f309(f921(x86441,x86441)),f327(f327(f252(x86441,x86441),x86443),x86444)),x86442)) % 177.41/177.19 [8645]P55(x86451,x86452)+~P55(x86451,f327(f327(f309(f921(x86451,x86451)),f327(f327(f252(x86451,x86451),x86453),x86454)),x86452)) % 177.41/177.19 [8650]~P108(x86501)+E(f327(f327(f149(x86501,x86501,f5(x86501)),x86502),f327(f327(f149(x86501,x86501,f5(x86501)),x86503),x86504)),f327(f327(f149(x86501,x86501,f5(x86501)),x86503),f327(f327(f149(x86501,x86501,f5(x86501)),x86502),x86504))) % 177.41/177.19 [8665]E(x86651,x86652)+~P1(f327(f62(x86653,x86654,f327(f327(f309(x86653),x86651),f190(f922(x86653,a910)))),x86652)) % 177.41/177.19 [8674]E(f327(f327(f135(x86741),f327(f327(f176(x86741),x86742),x86743)),f327(f327(f176(x86741),x86744),f327(f327(f139(x86741),x86742),x86743))),f327(f327(f176(x86741),f327(f327(f80(a915),x86742),x86744)),x86743))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),x86742),x86744)),f327(f191(f916(x86741)),x86743))) % 177.41/177.19 [8714]P1(f327(f35(x87141),x87142))+~E(x87142,f327(f310(a915,x87141,x87143),f327(f262(a915),f327(f327(f7(a915,a915,a910),f235(a915)),x87144)))) % 177.41/177.19 [8734]~P90(x87341)+E(f327(f143(x87341,x87341,f80(x87341),f327(f327(f80(x87341),x87342),x87343)),x87344),f327(f327(f80(x87341),x87342),f327(f143(x87341,x87341,f80(x87341),x87343),x87344))) % 177.41/177.19 [8770]P1(f327(f327(f234(f922(x87701,a910)),f327(f264(x87701,x87702),x87703)),f327(f264(x87701,x87702),x87704)))+~P1(f327(f327(f234(f922(f921(x87701,x87702),a910)),x87703),x87704)) % 177.41/177.19 [8782]~P1(f327(f327(f234(a915),x87822),x87824))+P1(f327(f327(f234(f922(x87821,a910)),f327(f173(x87821),f327(f327(f176(x87821),x87822),x87823))),f327(f173(x87821),f327(f327(f176(x87821),x87824),x87823)))) % 177.41/177.19 [8783]~P1(f327(f327(f234(a915),x87834),x87832))+P1(f327(f327(f234(f922(x87831,a910)),f327(f173(x87831),f327(f327(f139(x87831),x87832),x87833))),f327(f173(x87831),f327(f327(f139(x87831),x87834),x87833)))) % 177.41/177.19 [8840]~P1(f327(f35(x88401),f327(f327(f23(f922(x88401,a910)),x88402),x88404)))+P1(f327(f35(x88401),f327(f327(f23(f922(x88401,a910)),x88402),f327(f327(f309(x88401),x88403),x88404)))) % 177.41/177.19 [8882]P1(f327(f327(f329(f921(x88821,x88821)),x88822),f307(x88821,x88823)))+~P1(f327(f327(f329(f921(x88821,x88821)),x88822),f327(f327(f184(f921(x88821,x88821),a910),x88824),x88823))) % 177.41/177.19 [8968]~P1(f327(f35(x89681),f327(f327(f23(f922(x89681,a910)),x89682),f327(f327(f309(x89681),x89684),x89683))))+P1(f327(f35(x89681),f327(f327(f23(f922(x89681,a910)),x89682),x89683))) % 177.41/177.19 [9183]~P108(x91831)+P1(f327(f327(f234(x91831),f327(f327(f189(x91831),x91832),f327(f327(f238(x91831),x91833),x91834))),f327(f327(f238(x91831),f327(f327(f189(x91831),x91832),x91833)),f327(f327(f189(x91831),x91832),x91834)))) % 177.41/177.19 [9184]~P96(x91841)+P1(f327(f327(f234(x91841),f327(f327(f102(x91841),x91842),f327(f327(f103(x91841),x91843),x91844))),f327(f327(f103(x91841),f327(f327(f102(x91841),x91842),x91843)),f327(f327(f102(x91841),x91842),x91844)))) % 177.41/177.19 [9331]E(x93311,x93312)+~P1(f327(f327(f329(f921(x93313,x93313)),f327(f327(f252(x93313,x93313),x93311),x93312)),f327(f173(f921(x93313,x93313)),f327(f327(f182(x93313,x93313),x93314),x93314)))) % 177.41/177.19 [9361]~P1(f327(f327(f329(f921(x93611,x93611)),f327(f327(f252(x93611,x93611),x93613),x93612)),f307(x93611,x93614)))+~P35(x93611,f327(f327(f309(f921(x93611,x93611)),f327(f327(f252(x93611,x93611),x93612),x93613)),x93614)) % 177.41/177.19 [9362]~P1(f327(f327(f329(f921(x93621,x93621)),f327(f327(f252(x93621,x93621),x93623),x93622)),f307(x93621,x93624)))+~P55(x93621,f327(f327(f309(f921(x93621,x93621)),f327(f327(f252(x93621,x93621),x93622),x93623)),x93624)) % 177.41/177.19 [9366]E(x93661,x93662)+E(f327(f137(x93663,f327(f327(f8(a910,a910,x93663),a322),f327(a324,x93661))),f327(f327(f152(x93663),x93662),x93664)),f327(f327(f152(x93663),x93662),f327(f137(x93663,f327(f327(f8(a910,a910,x93663),a322),f327(a324,x93661))),x93664))) % 177.41/177.19 [9396]~P24(x93962,x93961,x93963,f242(f922(x93962,a910)),f242(f922(x93961,a910)))+E(f327(f310(x93961,x93962,f92(x93962,x93961,f242(f922(x93962,a910)),x93963)),x93964),f327(f311(x93962,x93961,x93963),x93964)) % 177.41/177.19 [9411]~P108(x94111)+P1(f327(f327(f234(x94111),f327(f327(f189(x94111),f327(f327(f238(x94111),x94112),x94113)),f327(f327(f238(x94111),x94112),x94114))),f327(f327(f238(x94111),x94112),f327(f327(f189(x94111),x94113),x94114)))) % 177.41/177.19 [9412]~P96(x94121)+P1(f327(f327(f234(x94121),f327(f327(f102(x94121),f327(f327(f103(x94121),x94122),x94123)),f327(f327(f103(x94121),x94122),x94124))),f327(f327(f103(x94121),x94122),f327(f327(f102(x94121),x94123),x94124)))) % 177.41/177.19 [9473]~P24(x94732,x94731,x94734,f242(f922(x94732,a910)),f242(f922(x94731,a910)))+E(f327(f262(x94731),f327(f327(f8(x94732,a910,x94731),x94733),f92(x94732,x94731,f242(f922(x94732,a910)),x94734))),f327(f310(x94732,x94731,x94734),f327(f262(x94732),x94733))) % 177.41/177.19 [9487]~E(f327(f310(x94872,x94871,x94873),f242(f922(x94872,a910))),f242(f922(x94871,a910)))+P1(f327(f327(f234(f922(x94871,a910)),f327(f79(f922(x94871,a910)),f327(f310(x94872,x94871,x94873),x94874))),f327(f310(x94872,x94871,x94873),f327(f79(f922(x94872,a910)),x94874)))) % 177.41/177.19 [9814]P1(f327(f327(f329(f921(x98141,x98141)),f327(f327(f252(x98141,x98141),x98142),x98143)),f327(f286(x98141,x98141),f327(f327(f289(x98141,x98141,x98141),x98144),f307(x98141,x98144)))))+~P1(f327(f327(f329(f921(x98141,x98141)),f327(f327(f252(x98141,x98141),x98142),x98143)),f327(f327(f289(x98141,x98141,x98141),f327(f286(x98141,x98141),x98144)),f307(x98141,f327(f286(x98141,x98141),x98144))))) % 177.41/177.19 [9815]~P1(f327(f327(f329(f921(x98151,x98151)),f327(f327(f252(x98151,x98151),x98152),x98153)),f327(f286(x98151,x98151),f327(f327(f289(x98151,x98151,x98151),x98154),f307(x98151,x98154)))))+P1(f327(f327(f329(f921(x98151,x98151)),f327(f327(f252(x98151,x98151),x98152),x98153)),f327(f327(f289(x98151,x98151,x98151),f327(f286(x98151,x98151),x98154)),f307(x98151,f327(f286(x98151,x98151),x98154))))) % 177.41/177.19 [9836]~P1(f327(f327(f329(x98362),x98364),f327(f284(x98361,x98362),x98363)))+P1(f327(f327(f329(f921(x98361,x98362)),f327(f327(f252(x98361,x98362),f549(x98363,x98361,x98364,x98362)),x98364)),x98363)) % 177.41/177.19 [9837]~P1(f327(f327(f329(x98372),x98374),f327(f284(x98371,x98372),x98373)))+P1(f327(f327(f329(f921(x98371,x98372)),f327(f327(f252(x98371,x98372),f551(x98373,x98371,x98374,x98372)),x98374)),x98373)) % 177.41/177.19 [9862]~P1(f327(f327(f329(x98621),x98624),f327(f327(f102(f922(x98621,a910)),x98622),x98623)))+P1(f327(f327(f327(f102(f922(x98621,a910)),f327(f327(f7(x98621,f922(x98621,a910),a910),f329(x98621)),x98622)),f327(f327(f7(x98621,f922(x98621,a910),a910),f329(x98621)),x98623)),x98624)) % 177.41/177.19 [9863]~P1(f327(f327(f329(x98631),x98634),f327(f327(f103(f922(x98631,a910)),x98632),x98633)))+P1(f327(f327(f327(f103(f922(x98631,a910)),f327(f327(f7(x98631,f922(x98631,a910),a910),f329(x98631)),x98632)),f327(f327(f7(x98631,f922(x98631,a910),a910),f329(x98631)),x98633)),x98634)) % 177.41/177.19 [9944]~P1(f327(f327(f329(f921(x99441,x99441)),f327(f327(f252(x99441,x99441),x99444),x99443)),f327(f327(f289(x99441,x99441,x99441),x99442),f307(x99441,x99442))))+P1(f327(f327(f329(f921(x99441,x99441)),f327(f327(f252(x99441,x99441),f618(x99442,x99443,x99444,x99441)),x99443)),x99442)) % 177.41/177.19 [9979]P1(f327(f327(f329(x99791),x99792),f327(f327(f102(f922(x99791,a910)),x99793),x99794)))+~P1(f327(f327(f327(f102(f922(x99791,a910)),f327(f327(f7(x99791,f922(x99791,a910),a910),f329(x99791)),x99793)),f327(f327(f7(x99791,f922(x99791,a910),a910),f329(x99791)),x99794)),x99792)) % 177.41/177.19 [9980]P1(f327(f327(f329(x99801),x99802),f327(f327(f103(f922(x99801,a910)),x99803),x99804)))+~P1(f327(f327(f327(f103(f922(x99801,a910)),f327(f327(f7(x99801,f922(x99801,a910),a910),f329(x99801)),x99803)),f327(f327(f7(x99801,f922(x99801,a910),a910),f329(x99801)),x99804)),x99802)) % 177.41/177.19 [10266]P30(x102661,f327(f327(f7(x102661,f922(f921(x102661,x102661),a910),f922(x102661,a910)),f327(f327(f8(f922(x102661,f922(f922(f921(x102661,x102661),a910),a910)),f922(f922(f921(x102661,x102661),a910),f922(x102661,a910)),x102661),f7(x102661,f922(f921(x102661,x102661),a910),a910)),f327(f327(f8(f922(x102661,f921(x102661,x102661)),f922(x102661,f922(f922(f921(x102661,x102661),a910),a910)),x102661),f327(f8(f921(x102661,x102661),f922(f922(f921(x102661,x102661),a910),a910),x102661),f329(f921(x102661,x102661)))),f252(x102661,x102661)))),x102662),x102663,x102664)+~P1(f327(f327(f329(f921(f916(x102661),f916(x102661))),f327(f327(f252(f916(x102661),f916(x102661)),x102663),x102664)),f159(x102661,x102662))) % 177.41/177.19 [10270]P56(x102701,f327(f327(f7(x102701,f922(f921(x102701,x102701),a910),f922(x102701,a910)),f327(f327(f8(f922(x102701,f922(f922(f921(x102701,x102701),a910),a910)),f922(f922(f921(x102701,x102701),a910),f922(x102701,a910)),x102701),f7(x102701,f922(f921(x102701,x102701),a910),a910)),f327(f327(f8(f922(x102701,f921(x102701,x102701)),f922(x102701,f922(f922(f921(x102701,x102701),a910),a910)),x102701),f327(f8(f921(x102701,x102701),f922(f922(f921(x102701,x102701),a910),a910),x102701),f329(f921(x102701,x102701)))),f252(x102701,x102701)))),x102702),x102703,x102704)+~P1(f327(f327(f329(f921(f922(x102701,a910),f922(x102701,a910))),f327(f327(f252(f922(x102701,a910),f922(x102701,a910)),x102703),x102704)),f319(x102701,x102702))) % 177.41/177.19 [10306]E(x103061,x103062)+~E(f327(f327(f7(x103063,f922(f921(x103063,x103064),a910),f922(x103064,a910)),f327(f327(f8(f922(x103064,f922(f922(f921(x103063,x103064),a910),a910)),f922(f922(f921(x103063,x103064),a910),f922(x103064,a910)),x103063),f7(x103064,f922(f921(x103063,x103064),a910),a910)),f327(f327(f8(f922(x103064,f921(x103063,x103064)),f922(x103064,f922(f922(f921(x103063,x103064),a910),a910)),x103063),f327(f8(f921(x103063,x103064),f922(f922(f921(x103063,x103064),a910),a910),x103064),f329(f921(x103063,x103064)))),f252(x103063,x103064)))),x103061),f327(f327(f7(x103063,f922(f921(x103063,x103064),a910),f922(x103064,a910)),f327(f327(f8(f922(x103064,f922(f922(f921(x103063,x103064),a910),a910)),f922(f922(f921(x103063,x103064),a910),f922(x103064,a910)),x103063),f7(x103064,f922(f921(x103063,x103064),a910),a910)),f327(f327(f8(f922(x103064,f921(x103063,x103064)),f922(x103064,f922(f922(f921(x103063,x103064),a910),a910)),x103063),f327(f8(f921(x103063,x103064),f922(f922(f921(x103063,x103064),a910),a910),x103064),f329(f921(x103063,x103064)))),f252(x103063,x103064)))),x103062)) % 177.41/177.19 [10309]~P30(x103091,f327(f327(f7(x103091,f922(f921(x103091,x103091),a910),f922(x103091,a910)),f327(f327(f8(f922(x103091,f922(f922(f921(x103091,x103091),a910),a910)),f922(f922(f921(x103091,x103091),a910),f922(x103091,a910)),x103091),f7(x103091,f922(f921(x103091,x103091),a910),a910)),f327(f327(f8(f922(x103091,f921(x103091,x103091)),f922(x103091,f922(f922(f921(x103091,x103091),a910),a910)),x103091),f327(f8(f921(x103091,x103091),f922(f922(f921(x103091,x103091),a910),a910),x103091),f329(f921(x103091,x103091)))),f252(x103091,x103091)))),x103094),x103092,x103093)+P1(f327(f327(f329(f921(f916(x103091),f916(x103091))),f327(f327(f252(f916(x103091),f916(x103091)),x103092),x103093)),f159(x103091,x103094))) % 177.41/177.19 [10310]~P56(x103101,f327(f327(f7(x103101,f922(f921(x103101,x103101),a910),f922(x103101,a910)),f327(f327(f8(f922(x103101,f922(f922(f921(x103101,x103101),a910),a910)),f922(f922(f921(x103101,x103101),a910),f922(x103101,a910)),x103101),f7(x103101,f922(f921(x103101,x103101),a910),a910)),f327(f327(f8(f922(x103101,f921(x103101,x103101)),f922(x103101,f922(f922(f921(x103101,x103101),a910),a910)),x103101),f327(f8(f921(x103101,x103101),f922(f922(f921(x103101,x103101),a910),a910),x103101),f329(f921(x103101,x103101)))),f252(x103101,x103101)))),x103104),x103102,x103103)+P1(f327(f327(f329(f921(f922(x103101,a910),f922(x103101,a910))),f327(f327(f252(f922(x103101,a910),f922(x103101,a910)),x103102),x103103)),f319(x103101,x103104))) % 177.41/177.19 [7677]~P93(x76771)+E(f327(f327(f80(x76771),f327(f105(x76771),x76772)),f327(f327(f23(x76771),f327(f105(x76771),x76773)),x76774)),f327(f327(f23(x76771),f327(f105(x76771),f327(f327(f80(a1),x76772),x76773))),x76774)) % 177.41/177.19 [7678]~P93(x76781)+E(f327(f327(f80(x76781),f327(f105(x76781),x76782)),f327(f327(f80(x76781),f327(f105(x76781),x76783)),x76784)),f327(f327(f80(x76781),f327(f105(x76781),f327(f327(f80(a1),x76782),x76783))),x76784)) % 177.41/177.19 [7679]~P93(x76791)+E(f327(f327(f81(x76791),f327(f105(x76791),x76792)),f327(f327(f81(x76791),f327(f105(x76791),x76793)),x76794)),f327(f327(f81(x76791),f327(f105(x76791),f327(f327(f81(a1),x76792),x76793))),x76794)) % 177.41/177.19 [7720]~P146(x77201)+E(f327(f166(x77201),f327(f327(f155(x77202,x77201),f327(f16(x77201,x77202),x77203)),x77204)),f327(f327(f81(x77201),f327(f101(x77201),f327(f191(f916(x77202)),x77204))),x77203)) % 177.41/177.19 [7958]E(f327(f268(x79581,f327(f327(f152(f921(a100,x79581)),x79582),x79583)),x79584),f327(f256(a100,x79581),x79582))+~P1(f327(f327(f235(a100),x79584),f327(f251(a100,x79581),x79582))) % 177.41/177.19 [7998]~P93(x79981)+E(f327(f327(f80(x79981),f327(f105(x79981),x79982)),f327(f327(f23(x79981),x79983),f327(f105(x79981),x79984))),f327(f327(f80(x79981),f327(f105(x79981),f327(f327(f80(a1),x79982),f327(f79(a1),x79984)))),x79983)) % 177.41/177.19 [8132]E(f327(f268(x81321,x81322),f327(f327(f23(a100),x81323),f327(f251(a100,x81321),x81324))),f327(f268(x81321,f327(f327(f152(f921(a100,x81321)),x81324),x81322)),x81323))+P1(f327(f327(f235(a100),x81323),f327(f251(a100,x81321),x81324))) % 177.41/177.19 [8567]~P1(f327(f327(f329(x85671),x85672),f327(f173(x85671),f115(x85671,x85674))))+P1(f327(f327(f329(x85671),x85672),f327(f173(x85671),f115(x85671,f327(f327(f135(x85671),x85673),x85674))))) % 177.41/177.19 [8568]~P1(f327(f327(f329(x85681),x85682),f327(f173(x85681),f115(x85681,x85683))))+P1(f327(f327(f329(x85681),x85682),f327(f173(x85681),f115(x85681,f327(f327(f135(x85681),x85683),x85684))))) % 177.41/177.19 [8587]E(f327(f327(f102(f922(x85871,a910)),f327(f327(f103(f922(x85871,a910)),x85872),x85873)),x85874),f327(f327(f103(f922(x85871,a910)),x85872),f327(f327(f102(f922(x85871,a910)),x85873),x85874)))+~P1(f327(f327(f234(f922(x85871,a910)),x85874),x85872)) % 177.41/177.19 [8896]~E(f327(f327(f102(f922(x88961,a910)),f327(f327(f103(f922(x88961,a910)),x88963),x88964)),x88962),f327(f327(f103(f922(x88961,a910)),x88963),f327(f327(f102(f922(x88961,a910)),x88964),x88962)))+P1(f327(f327(f234(f922(x88961,a910)),x88962),x88963)) % 177.41/177.19 [9188]~P1(f327(f327(f234(f922(x91881,a910)),x91882),f327(f327(f102(f922(x91881,a910)),x91883),x91884)))+P1(f327(f327(f234(f922(x91881,a910)),f327(f327(f23(f922(x91881,a910)),x91882),x91883)),x91884)) % 177.41/177.19 [9303]~E(f327(f310(x93031,x93032,x93033),f242(f922(x93031,a910))),f242(f922(x93032,a910)))+E(f327(f310(x93031,x93032,x93033),f327(f310(x93032,x93031,f92(x93031,x93032,f242(f922(x93031,a910)),x93033)),x93034)),x93034) % 177.41/177.19 [9308]P1(f327(f327(f234(f922(x93081,a910)),x93082),f327(f327(f102(f922(x93081,a910)),x93083),x93084)))+~P1(f327(f327(f234(f922(x93081,a910)),f327(f327(f23(f922(x93081,a910)),x93082),x93083)),x93084)) % 177.41/177.19 [9392]~P84(x93921)+E(f327(f75(x93921),f327(f327(f6(x93922,x93921),f327(f327(f8(x93921,x93921,x93922),f75(x93921)),x93923)),x93924)),f327(f327(f6(x93922,x93921),f327(f327(f8(x93921,x93921,x93922),f75(x93921)),x93923)),x93924)) % 177.41/177.19 [9563]~P84(x95631)+P1(f327(f327(f234(x95631),f2(x95631)),f327(f327(f6(x95632,x95631),f327(f327(f8(x95631,x95631,x95632),f75(x95631)),x95633)),x95634))) % 177.41/177.19 [9567]~P67(x95671)+E(f327(f166(x95671),f327(f327(f155(x95672,x95671),f327(f72(x95671,x95671,x95672,f79(x95671)),x95673)),x95674)),f327(f79(x95671),f327(f166(x95671),f327(f327(f155(x95672,x95671),x95673),x95674)))) % 177.41/177.19 [9710]~P84(x97101)+P1(f327(f327(f234(x97101),f327(f75(x97101),f327(f327(f6(x97102,x97101),x97103),x97104))),f327(f327(f6(x97102,x97101),f327(f327(f8(x97101,x97101,x97102),f75(x97101)),x97103)),x97104))) % 177.41/177.19 [9739]~E(f327(f327(f80(a915),x97391),x97394),f327(f327(f80(a915),x97393),x97392))+P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),f327(f327(f252(a915,a915),x97391),x97392)),f327(f327(f252(a915,a915),x97393),x97394))),a110)) % 177.41/177.19 [9740]~P1(f327(f327(f235(a915),x97401),x97403))+P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),f327(f327(f252(a915,a915),x97401),x97402)),f327(f327(f252(a915,a915),x97403),x97404))),a32)) % 177.41/177.19 [9741]~P1(f327(f327(f235(a915),x97411),x97413))+P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),f327(f327(f252(a915,a915),x97411),x97412)),f327(f327(f252(a915,a915),x97413),x97414))),a70)) % 177.41/177.19 [9887]E(f327(f327(f80(a915),x98871),x98872),f327(f327(f80(a915),x98873),x98874))+~P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),f327(f327(f252(a915,a915),x98871),x98874)),f327(f327(f252(a915,a915),x98873),x98872))),a110)) % 177.41/177.19 [9919]E(f327(f327(f165(x99191),f327(f327(f139(x99191),f327(f191(f916(x99191)),f178(x99191,x99192,x99193))),x99193)),x99194),f327(f327(f165(x99191),x99193),f327(f327(f80(a915),x99194),f327(f191(f916(x99191)),f178(x99191,x99192,x99193)))))+~P1(f327(f327(f235(a915),x99194),f327(f191(f916(x99191)),f327(f327(f139(x99191),f327(f191(f916(x99191)),f178(x99191,x99192,x99193))),x99193)))) % 177.41/177.19 [9935]~P1(f327(f327(f329(x99352),x99354),f327(f327(f40(x99351,f922(x99352,a910)),f242(f922(x99351,a910))),x99353)))+P1(f327(f327(f327(f40(x99351,f922(x99352,a910)),f242(f922(x99351,a910))),f327(f327(f8(f922(x99352,a910),f922(x99352,a910),x99351),f327(f7(x99352,f922(x99352,a910),a910),f329(x99352))),x99353)),x99354)) % 177.41/177.19 [9936]~P1(f327(f327(f329(x99362),x99364),f327(f327(f41(x99361,f922(x99362,a910)),f242(f922(x99361,a910))),x99363)))+P1(f327(f327(f327(f41(x99361,f922(x99362,a910)),f242(f922(x99361,a910))),f327(f327(f8(f922(x99362,a910),f922(x99362,a910),x99361),f327(f7(x99362,f922(x99362,a910),a910),f329(x99362))),x99363)),x99364)) % 177.41/177.19 [10006]~P1(f327(f50(x100061,x100062),f327(f327(f252(a1,a1),x100064),x100063)))+P1(f327(f50(f327(f79(a1),x100061),x100062),f327(f327(f252(a1,a1),f327(f327(f327(f97(a1),f327(f327(a324,x100063),f2(a1))),f327(f79(a1),x100064)),f327(f327(f23(a1),f327(f79(a1),x100064)),f78(a1)))),f327(f327(f327(f97(a1),f327(f327(a324,x100063),f2(a1))),f2(a1)),f327(f327(f23(a1),x100062),x100063))))) % 177.41/177.19 [10018]P1(f327(f327(f329(x100181),x100182),f327(f327(f40(x100183,f922(x100181,a910)),f242(f922(x100183,a910))),x100184)))+~P1(f327(f327(f327(f40(x100183,f922(x100181,a910)),f242(f922(x100183,a910))),f327(f327(f8(f922(x100181,a910),f922(x100181,a910),x100183),f327(f7(x100181,f922(x100181,a910),a910),f329(x100181))),x100184)),x100182)) % 177.41/177.19 [10019]P1(f327(f327(f329(x100191),x100192),f327(f327(f41(x100193,f922(x100191,a910)),f242(f922(x100193,a910))),x100194)))+~P1(f327(f327(f327(f41(x100193,f922(x100191,a910)),f242(f922(x100193,a910))),f327(f327(f8(f922(x100191,a910),f922(x100191,a910),x100193),f327(f7(x100191,f922(x100191,a910),a910),f329(x100191))),x100194)),x100192)) % 177.41/177.19 [10031]E(f327(f327(f40(a915,f922(x100311,a910)),f242(f922(a915,a910))),x100312),f327(f327(f40(a915,f922(x100311,a910)),f242(f922(a915,a910))),x100313))+~E(f327(f327(f40(a915,f922(x100311,a910)),f327(f302(a915,f2(a915)),f396(x100312,x100314,x100313,x100311))),x100313),f327(f327(f40(a915,f922(x100311,a910)),f327(f302(a915,f2(a915)),f327(f327(f80(a915),f396(x100312,x100314,x100313,x100311)),x100314))),x100312)) % 177.41/177.19 [10383]~P1(f327(f327(f234(f922(f921(x103831,x103832),a910)),x103833),x103834))+P1(f327(f327(f234(f922(x103831,f922(x103832,a910))),f327(f327(f7(x103831,f922(f921(x103831,x103832),a910),f922(x103832,a910)),f327(f327(f8(f922(x103832,f922(f922(f921(x103831,x103832),a910),a910)),f922(f922(f921(x103831,x103832),a910),f922(x103832,a910)),x103831),f7(x103832,f922(f921(x103831,x103832),a910),a910)),f327(f327(f8(f922(x103832,f921(x103831,x103832)),f922(x103832,f922(f922(f921(x103831,x103832),a910),a910)),x103831),f327(f8(f921(x103831,x103832),f922(f922(f921(x103831,x103832),a910),a910),x103832),f329(f921(x103831,x103832)))),f252(x103831,x103832)))),x103833)),f327(f327(f7(x103831,f922(f921(x103831,x103832),a910),f922(x103832,a910)),f327(f327(f8(f922(x103832,f922(f922(f921(x103831,x103832),a910),a910)),f922(f922(f921(x103831,x103832),a910),f922(x103832,a910)),x103831),f7(x103832,f922(f921(x103831,x103832),a910),a910)),f327(f327(f8(f922(x103832,f921(x103831,x103832)),f922(x103832,f922(f922(f921(x103831,x103832),a910),a910)),x103831),f327(f8(f921(x103831,x103832),f922(f922(f921(x103831,x103832),a910),a910),x103832),f329(f921(x103831,x103832)))),f252(x103831,x103832)))),x103834))) % 177.41/177.19 [10401]P1(f327(f327(f234(f922(f921(x104011,x104012),a910)),x104013),x104014))+~P1(f327(f327(f234(f922(x104011,f922(x104012,a910))),f327(f327(f7(x104011,f922(f921(x104011,x104012),a910),f922(x104012,a910)),f327(f327(f8(f922(x104012,f922(f922(f921(x104011,x104012),a910),a910)),f922(f922(f921(x104011,x104012),a910),f922(x104012,a910)),x104011),f7(x104012,f922(f921(x104011,x104012),a910),a910)),f327(f327(f8(f922(x104012,f921(x104011,x104012)),f922(x104012,f922(f922(f921(x104011,x104012),a910),a910)),x104011),f327(f8(f921(x104011,x104012),f922(f922(f921(x104011,x104012),a910),a910),x104012),f329(f921(x104011,x104012)))),f252(x104011,x104012)))),x104013)),f327(f327(f7(x104011,f922(f921(x104011,x104012),a910),f922(x104012,a910)),f327(f327(f8(f922(x104012,f922(f922(f921(x104011,x104012),a910),a910)),f922(f922(f921(x104011,x104012),a910),f922(x104012,a910)),x104011),f7(x104012,f922(f921(x104011,x104012),a910),a910)),f327(f327(f8(f922(x104012,f921(x104011,x104012)),f922(x104012,f922(f922(f921(x104011,x104012),a910),a910)),x104011),f327(f8(f921(x104011,x104012),f922(f922(f921(x104011,x104012),a910),a910),x104012),f329(f921(x104011,x104012)))),f252(x104011,x104012)))),x104014))) % 177.41/177.19 [9438]~P1(f327(f327(f329(f921(x94381,x94381)),x94382),f307(x94381,x94384)))+P1(f327(f327(f329(f921(x94381,x94381)),x94382),f307(x94381,f327(f327(f102(f922(f921(x94381,x94381),a910)),x94383),x94384)))) % 177.41/177.19 [9439]~P1(f327(f327(f329(f921(x94391,x94391)),x94392),f307(x94391,x94393)))+P1(f327(f327(f329(f921(x94391,x94391)),x94392),f307(x94391,f327(f327(f102(f922(f921(x94391,x94391),a910)),x94393),x94394)))) % 177.41/177.19 [10118]~P1(f327(f327(f234(a915),f327(f327(f80(a915),x101181),x101184)),f327(f327(f80(a915),x101183),x101182)))+P1(f327(f327(f234(a1),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x101181),x101182)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x101183),x101184)),f190(f922(f921(a915,a915),a910))))))) % 177.41/177.19 [10119]~P1(f327(f327(f235(a915),f327(f327(f80(a915),x101191),x101194)),f327(f327(f80(a915),x101193),x101192)))+P1(f327(f327(f235(a1),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x101191),x101192)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x101193),x101194)),f190(f922(f921(a915,a915),a910))))))) % 177.41/177.19 [10207]P1(f327(f327(f234(a915),f327(f327(f80(a915),x102071),x102072)),f327(f327(f80(a915),x102073),x102074)))+~P1(f327(f327(f234(a1),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x102071),x102074)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x102073),x102072)),f190(f922(f921(a915,a915),a910))))))) % 177.41/177.19 [10208]P1(f327(f327(f235(a915),f327(f327(f80(a915),x102081),x102082)),f327(f327(f80(a915),x102083),x102084)))+~P1(f327(f327(f235(a1),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x102081),x102084)),f190(f922(f921(a915,a915),a910)))))),f327(a89,f327(f285(f921(a915,a915),f921(a915,a915),a110),f327(f327(f309(f921(a915,a915)),f327(f327(f252(a915,a915),x102083),x102082)),f190(f922(f921(a915,a915),a910))))))) % 177.41/177.19 [10252]P1(f327(f327(f234(f922(x102521,a910)),f327(f327(f40(a915,f922(x102521,a910)),f242(f922(a915,a910))),x102522)),f327(f327(f40(a915,f922(x102521,a910)),f242(f922(a915,a910))),x102523)))+~P1(f327(f327(f234(f922(x102521,a910)),f327(f327(f40(a915,f922(x102521,a910)),f327(f302(a915,f2(a915)),f398(x102523,x102524,x102522,x102521))),x102522)),f327(f327(f40(a915,f922(x102521,a910)),f327(f302(a915,f2(a915)),f327(f327(f80(a915),f398(x102523,x102524,x102522,x102521)),x102524))),x102523))) % 177.41/177.19 [10313]P1(f327(f327(f234(a100),x103134),f2(a100)))+E(f327(f327(f259(f921(a100,a100),f921(x103131,f922(a914,a323)),f921(a100,a100),f921(f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100))),f327(x103132,x103133)),f327(f327(f8(f922(f922(a100,f922(a910,f918(f917(x103131)))),f922(f921(a100,a100),f921(f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100)))),f922(f921(a100,a100),f921(f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100))),f921(x103131,f922(a914,a323))),f327(f259(f921(a100,a100),f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100),f921(f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100))),f277(x103131,x103132,f327(f327(f23(a100),x103134),f78(a100)),x103133))),f327(f327(f8(f922(f922(a100,f922(a910,f918(f917(x103131)))),f922(a100,f922(a910,f918(f917(x103131))))),f922(f922(a100,f922(a910,f918(f917(x103131)))),f922(f921(a100,a100),f921(f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100)))),f921(x103131,f922(a914,a323))),f327(f8(f922(a100,f922(a910,f918(f917(x103131)))),f922(f921(a100,a100),f921(f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100))),f922(a100,f922(a910,f918(f917(x103131))))),f252(f922(a100,f922(a910,f918(f917(x103131)))),f921(a100,a100)))),f327(f327(f8(f922(a100,f922(a910,f918(f917(x103131)))),f922(f922(a100,f922(a910,f918(f917(x103131)))),f922(a100,f922(a910,f918(f917(x103131))))),f921(x103131,f922(a914,a323))),f45(x103131)),f327(f327(f8(x103131,f922(a100,f922(a910,f918(f917(x103131)))),f921(x103131,f922(a914,a323))),f43(x103131)),f251(x103131,f922(a914,a323))))))),f277(x103131,x103132,x103134,x103133)) % 177.41/177.19 [10373]~P1(f327(f327(f329(x103732),x103734),f327(f284(x103731,x103732),x103733)))+P1(f327(f250(x103731,x103732,f327(f327(f7(x103731,f922(f921(x103731,x103732),a910),f922(x103732,a910)),f327(f327(f8(f922(x103732,f922(f922(f921(x103731,x103732),a910),a910)),f922(f922(f921(x103731,x103732),a910),f922(x103732,a910)),x103731),f7(x103732,f922(f921(x103731,x103732),a910),a910)),f327(f327(f8(f922(x103732,f921(x103731,x103732)),f922(x103732,f922(f922(f921(x103731,x103732),a910),a910)),x103731),f327(f8(f921(x103731,x103732),f922(f922(f921(x103731,x103732),a910),a910),x103732),f329(f921(x103731,x103732)))),f252(x103731,x103732)))),x103733)),x103734)) % 177.41/177.19 [10374]~P1(f327(f327(f329(x103741),x103744),f327(f264(x103741,x103742),x103743)))+P1(f327(f249(x103741,x103742,f327(f327(f7(x103741,f922(f921(x103741,x103742),a910),f922(x103742,a910)),f327(f327(f8(f922(x103742,f922(f922(f921(x103741,x103742),a910),a910)),f922(f922(f921(x103741,x103742),a910),f922(x103742,a910)),x103741),f7(x103742,f922(f921(x103741,x103742),a910),a910)),f327(f327(f8(f922(x103742,f921(x103741,x103742)),f922(x103742,f922(f922(f921(x103741,x103742),a910),a910)),x103741),f327(f8(f921(x103741,x103742),f922(f922(f921(x103741,x103742),a910),a910),x103742),f329(f921(x103741,x103742)))),f252(x103741,x103742)))),x103743)),x103744)) % 177.41/177.19 [10386]P1(f327(f327(f329(x103861),x103862),f327(f284(x103863,x103861),x103864)))+~P1(f327(f250(x103863,x103861,f327(f327(f7(x103863,f922(f921(x103863,x103861),a910),f922(x103861,a910)),f327(f327(f8(f922(x103861,f922(f922(f921(x103863,x103861),a910),a910)),f922(f922(f921(x103863,x103861),a910),f922(x103861,a910)),x103863),f7(x103861,f922(f921(x103863,x103861),a910),a910)),f327(f327(f8(f922(x103861,f921(x103863,x103861)),f922(x103861,f922(f922(f921(x103863,x103861),a910),a910)),x103863),f327(f8(f921(x103863,x103861),f922(f922(f921(x103863,x103861),a910),a910),x103861),f329(f921(x103863,x103861)))),f252(x103863,x103861)))),x103864)),x103862)) % 177.41/177.19 [10387]P1(f327(f327(f329(x103871),x103872),f327(f264(x103871,x103873),x103874)))+~P1(f327(f249(x103871,x103873,f327(f327(f7(x103871,f922(f921(x103871,x103873),a910),f922(x103873,a910)),f327(f327(f8(f922(x103873,f922(f922(f921(x103871,x103873),a910),a910)),f922(f922(f921(x103871,x103873),a910),f922(x103873,a910)),x103871),f7(x103873,f922(f921(x103871,x103873),a910),a910)),f327(f327(f8(f922(x103873,f921(x103871,x103873)),f922(x103873,f922(f922(f921(x103871,x103873),a910),a910)),x103871),f327(f8(f921(x103871,x103873),f922(f922(f921(x103871,x103873),a910),a910),x103873),f329(f921(x103871,x103873)))),f252(x103871,x103873)))),x103874)),x103872)) % 177.41/177.19 [10042]P1(f327(f161(x100421,x100422),x100423))+~P1(f327(f161(x100421,f327(f327(f18(x100421,a910,a910),f327(f327(f8(a910,f922(a910,a910),x100421),a325),x100424)),x100422)),x100423)) % 177.41/177.19 [10043]P1(f327(f161(x100431,x100432),x100433))+~P1(f327(f161(x100431,f327(f327(f18(x100431,a910,a910),f327(f327(f8(a910,f922(a910,a910),x100431),a325),x100432)),x100434)),x100433)) % 177.41/177.19 [10130]~P112(x101301)+E(f327(f327(f81(x101301),f327(f327(f80(x101301),f78(x101301)),f78(x101301))),f327(f327(f6(a915,x101301),f327(f327(f8(x101301,x101301,a915),f327(f80(x101301),x101302)),f327(f327(f7(a915,x101301,x101301),f327(f327(f8(x101301,f922(x101301,x101301),a915),f81(x101301)),f101(x101301))),x101303))),f327(f282(a915),x101304))),f327(f327(f81(x101301),f327(f101(x101301),x101304)),f327(f327(f80(x101301),x101302),f327(f327(f80(x101301),x101302),f327(f327(f81(x101301),f327(f101(x101301),f327(f327(f23(a915),x101304),f78(a915)))),x101303))))) % 177.41/177.19 [10273]P1(f327(x102731,f548(x102732,x102733,x102734,x102731)))+P35(x102732,f327(f262(f921(x102732,x102732)),f327(f257(x102732,x102732,a910),f327(f327(f8(f922(x102732,a910),f922(x102732,a910),x102732),f327(f18(x102732,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102732),a325),x102731))),f327(f327(f7(x102732,f922(x102732,x102732),f922(x102732,a910)),f327(f327(f8(f922(x102732,a910),f922(f922(x102732,x102732),f922(x102732,a910)),x102732),f8(x102732,a910,x102732)),a324)),x102733))))) % 177.41/177.19 [10290]~P1(f327(f327(f235(a915),f327(x102904,f327(x102903,f548(x102901,x102903,x102904,x102902)))),f327(x102904,f548(x102901,x102903,x102904,x102902))))+P35(x102901,f327(f262(f921(x102901,x102901)),f327(f257(x102901,x102901,a910),f327(f327(f8(f922(x102901,a910),f922(x102901,a910),x102901),f327(f18(x102901,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102901),a325),x102902))),f327(f327(f7(x102901,f922(x102901,x102901),f922(x102901,a910)),f327(f327(f8(f922(x102901,a910),f922(f922(x102901,x102901),f922(x102901,a910)),x102901),f8(x102901,a910,x102901)),a324)),x102903))))) % 177.41/177.19 [10360]~P3(x103601)+E(f39(x103601,f327(f262(x103601),f327(f327(f8(f922(f922(x103602,x103601),a910),a910,x103601),f87(f922(x103602,x103601))),f327(f327(f8(f922(f922(x103602,x103601),a910),f922(f922(x103602,x103601),a910),x103601),f327(f18(f922(x103602,x103601),a910,a910),f327(f327(f8(a910,f922(a910,a910),f922(x103602,x103601)),a325),f327(f327(f7(f922(x103602,x103601),f922(f922(x103602,x103601),a910),a910),f329(f922(x103602,x103601))),x103603)))),f327(f327(f7(x103601,f922(f922(x103602,x103601),x103601),f922(f922(x103602,x103601),a910)),f327(f327(f8(f922(x103601,a910),f922(f922(f922(x103602,x103601),x103601),f922(f922(x103602,x103601),a910)),x103601),f8(x103601,a910,f922(x103602,x103601))),a324)),f327(f327(f7(f922(x103602,x103601),x103602,x103601),f5(f922(x103602,x103601))),x103604)))))),f327(f39(f922(x103602,x103601),x103603),x103604)) % 177.41/177.19 [10361]~P3(x103611)+E(f39(x103611,f327(f262(x103611),f327(f327(f8(f922(f922(x103612,x103611),a910),a910,x103611),f87(f922(x103612,x103611))),f327(f327(f8(f922(f922(x103612,x103611),a910),f922(f922(x103612,x103611),a910),x103611),f327(f18(f922(x103612,x103611),a910,a910),f327(f327(f8(a910,f922(a910,a910),f922(x103612,x103611)),a325),f327(f327(f7(f922(x103612,x103611),f922(f922(x103612,x103611),a910),a910),f329(f922(x103612,x103611))),x103613)))),f327(f327(f7(x103611,f922(f922(x103612,x103611),x103611),f922(f922(x103612,x103611),a910)),f327(f327(f8(f922(x103611,a910),f922(f922(f922(x103612,x103611),x103611),f922(f922(x103612,x103611),a910)),x103611),f8(x103611,a910,f922(x103612,x103611))),a324)),f327(f327(f7(f922(x103612,x103611),x103612,x103611),f5(f922(x103612,x103611))),x103614)))))),f327(f39(f922(x103612,x103611),x103613),x103614)) % 177.41/177.19 [10362]~P3(x103621)+E(f38(x103621,f327(f262(x103621),f327(f327(f8(f922(f922(x103622,x103621),a910),a910,x103621),f87(f922(x103622,x103621))),f327(f327(f8(f922(f922(x103622,x103621),a910),f922(f922(x103622,x103621),a910),x103621),f327(f18(f922(x103622,x103621),a910,a910),f327(f327(f8(a910,f922(a910,a910),f922(x103622,x103621)),a325),f327(f327(f7(f922(x103622,x103621),f922(f922(x103622,x103621),a910),a910),f329(f922(x103622,x103621))),x103623)))),f327(f327(f7(x103621,f922(f922(x103622,x103621),x103621),f922(f922(x103622,x103621),a910)),f327(f327(f8(f922(x103621,a910),f922(f922(f922(x103622,x103621),x103621),f922(f922(x103622,x103621),a910)),x103621),f8(x103621,a910,f922(x103622,x103621))),a324)),f327(f327(f7(f922(x103622,x103621),x103622,x103621),f5(f922(x103622,x103621))),x103624)))))),f327(f38(f922(x103622,x103621),x103623),x103624)) % 177.41/177.19 [10363]~P3(x103631)+E(f38(x103631,f327(f262(x103631),f327(f327(f8(f922(f922(x103632,x103631),a910),a910,x103631),f87(f922(x103632,x103631))),f327(f327(f8(f922(f922(x103632,x103631),a910),f922(f922(x103632,x103631),a910),x103631),f327(f18(f922(x103632,x103631),a910,a910),f327(f327(f8(a910,f922(a910,a910),f922(x103632,x103631)),a325),f327(f327(f7(f922(x103632,x103631),f922(f922(x103632,x103631),a910),a910),f329(f922(x103632,x103631))),x103633)))),f327(f327(f7(x103631,f922(f922(x103632,x103631),x103631),f922(f922(x103632,x103631),a910)),f327(f327(f8(f922(x103631,a910),f922(f922(f922(x103632,x103631),x103631),f922(f922(x103632,x103631),a910)),x103631),f8(x103631,a910,f922(x103632,x103631))),a324)),f327(f327(f7(f922(x103632,x103631),x103632,x103631),f5(f922(x103632,x103631))),x103634)))))),f327(f38(f922(x103632,x103631),x103633),x103634)) % 177.41/177.19 [10414]~P1(f327(f327(f329(f921(x104141,x104141)),f327(f327(f252(x104141,x104141),x104143),x104144)),f327(f327(f102(f922(f921(x104141,x104141),a910)),x104142),f307(x104141,f190(f922(f921(x104141,x104141),a910))))))+P1(f327(f327(f327(f327(f102(f922(x104141,f922(x104141,a910))),f327(f327(f7(x104141,f922(f921(x104141,x104141),a910),f922(x104141,a910)),f327(f327(f8(f922(x104141,f922(f922(f921(x104141,x104141),a910),a910)),f922(f922(f921(x104141,x104141),a910),f922(x104141,a910)),x104141),f7(x104141,f922(f921(x104141,x104141),a910),a910)),f327(f327(f8(f922(x104141,f921(x104141,x104141)),f922(x104141,f922(f922(f921(x104141,x104141),a910),a910)),x104141),f327(f8(f921(x104141,x104141),f922(f922(f921(x104141,x104141),a910),a910),x104141),f329(f921(x104141,x104141)))),f252(x104141,x104141)))),x104142)),a324),x104143),x104144)) % 177.41/177.19 [10424]P1(f327(f327(f329(f921(x104241,x104241)),f327(f327(f252(x104241,x104241),x104242),x104243)),f327(f327(f102(f922(f921(x104241,x104241),a910)),x104244),f307(x104241,f190(f922(f921(x104241,x104241),a910))))))+~P1(f327(f327(f327(f327(f102(f922(x104241,f922(x104241,a910))),f327(f327(f7(x104241,f922(f921(x104241,x104241),a910),f922(x104241,a910)),f327(f327(f8(f922(x104241,f922(f922(f921(x104241,x104241),a910),a910)),f922(f922(f921(x104241,x104241),a910),f922(x104241,a910)),x104241),f7(x104241,f922(f921(x104241,x104241),a910),a910)),f327(f327(f8(f922(x104241,f921(x104241,x104241)),f922(x104241,f922(f922(f921(x104241,x104241),a910),a910)),x104241),f327(f8(f921(x104241,x104241),f922(f922(f921(x104241,x104241),a910),a910),x104241),f329(f921(x104241,x104241)))),f252(x104241,x104241)))),x104244)),a324),x104242),x104243)) % 177.41/177.19 [10370]E(f327(f327(f152(f916(x103701)),f327(f327(f152(x103701),x103702),f327(f143(f916(x103701),f916(x103701),f135(x103701),f114(x103701)),f327(f327(f155(f916(x103701),f916(x103701)),f157(f916(x103701),x103701,f114(x103701),f327(f327(f8(f916(x103701),f922(f916(x103701),f916(x103701)),x103701),f16(f916(x103701),f916(x103701))),f327(f327(f7(x103701,f916(x103701),f916(x103701)),f152(x103701)),f114(x103701))))),x103703)))),f180(x103701,f327(f327(f152(f916(x103701)),x103704),f327(f143(f916(f916(x103701)),f916(f916(x103701)),f135(f916(x103701)),f114(f916(x103701))),f327(f327(f155(f916(x103701),f916(f916(x103701))),f157(f916(f916(x103701)),x103701,f114(f916(x103701)),f327(f16(f922(f916(x103701),f916(f916(x103701))),x103701),f327(f327(f7(f916(x103701),f916(f916(x103701)),f916(f916(x103701))),f152(f916(x103701))),f114(f916(x103701)))))),x103703))))),f180(x103701,f327(f327(f152(f916(x103701)),f327(f327(f152(x103701),x103702),x103704)),x103703)))+~P1(f327(f315(f916(f916(x103701)),f181(x103701)),f327(f327(f152(f916(x103701)),f327(f327(f152(x103701),x103702),x103704)),x103703))) % 177.41/177.19 [10413]~P1(f327(f35(x104132),f327(f262(x104132),x104134)))+P1(f327(f35(x104131),f327(f262(x104131),f327(f327(f8(f922(x104132,a910),a910,x104131),f87(x104132)),f327(f327(f7(x104131,f922(x104132,a910),f922(x104132,a910)),f327(f327(f8(f922(x104132,f922(a910,a910)),f922(f922(x104132,a910),f922(x104132,a910)),x104131),f18(x104132,a910,a910)),f327(f327(f8(f922(x104132,a910),f922(x104132,f922(a910,a910)),x104131),f327(f8(a910,f922(a910,a910),x104132),a325)),f327(f327(f7(x104131,f922(x104132,x104131),f922(x104132,a910)),f327(f327(f8(f922(x104131,a910),f922(f922(x104132,x104131),f922(x104132,a910)),x104131),f8(x104131,a910,x104132)),a324)),x104133)))),x104134))))) % 177.41/177.19 [8934]P23(x89341,x89342,x89343,x89344)+~P24(x89341,x89342,x89343,x89344,x89345) % 177.41/177.19 [5431]E(x54311,x54312)+~E(f170(x54313,x54311,x54314),f170(x54313,x54312,x54315)) % 177.41/177.19 [5432]E(x54321,x54322)+~E(f127(x54323,x54324,x54321),f127(x54323,x54325,x54322)) % 177.41/177.19 [5433]E(x54331,x54332)+~E(f127(x54333,x54331,x54334),f127(x54333,x54332,x54335)) % 177.41/177.19 [8263]~E(f327(x82633,x82634),x82635)+E(f74(x82631,x82632,x82633,x82634,x82635),x82633) % 177.41/177.19 [8792]~E(f74(x87924,x87925,x87921,x87922,x87923),x87921)+E(f327(x87921,x87922),x87923) % 177.41/177.19 [9409]~P24(x94092,x94091,x94094,x94093,x94095)+P24(x94091,x94092,f77(x94092,x94091,x94093,x94094),x94095,x94093) % 177.41/177.19 [9410]~P24(x94102,x94101,x94104,x94103,x94105)+P24(x94101,x94102,f92(x94102,x94101,x94103,x94104),x94105,x94103) % 177.41/177.19 [6243]P1(f327(f250(x62431,x62432,x62433),x62434))+~P1(f327(f327(x62433,x62435),x62434)) % 177.41/177.19 [6245]P1(f327(f249(x62451,x62452,x62453),x62454))+~P1(f327(f327(x62453,x62454),x62455)) % 177.41/177.19 [6722]~E(x67225,f2(a100))+E(f327(f198(x67221,x67222,x67223,x67224),x67225),f125(x67222)) % 177.41/177.19 [6723]~E(x67235,f2(a100))+E(f327(f200(x67231,x67232,x67233,x67234),x67235),f116(x67232)) % 177.41/177.19 [6859]~E(x68593,f2(a100))+E(f327(f273(x68591,x68592,x68593,x68594),x68595),f327(f252(x68591,x68592),x68595)) % 177.41/177.19 [7914]~P18(x79144,x79141,x79142,x79145)+E(f327(f72(x79141,x79141,x79141,f327(x79142,x79143)),f327(x79142,x79143)),f327(x79142,x79143)) % 177.41/177.19 [8304]~P14(x83045,x83041,x83042)+E(f327(f72(x83041,x83041,x83041,f327(x83042,x83043)),f327(x83042,x83044)),f327(f72(x83041,x83041,x83041,f327(x83042,x83044)),f327(x83042,x83043))) % 177.41/177.19 [8627]P1(f327(f327(f329(f921(x86271,x86271)),f327(f327(f252(x86271,x86271),x86272),x86273)),f321(x86271,x86274,x86275)))+~P1(f327(f327(f235(a915),f327(x86274,x86272)),f327(x86274,x86273))) % 177.41/177.19 [8720]~P1(f327(f327(f329(x87204),x87203),f290(x87204,x87201,x87202,x87205)))+P1(f327(f327(x87201,x87202),x87203)) % 177.41/177.19 [8721]~P1(f327(f327(f329(x87214),x87213),f299(x87214,x87211,x87212,x87215)))+P1(f327(f327(x87211,x87212),x87213)) % 177.41/177.19 [8722]~P1(f327(f327(f329(x87224),x87222),f290(x87224,x87221,x87225,x87223)))+P1(f327(f327(x87221,x87222),x87223)) % 177.41/177.19 [8723]~P1(f327(f327(f329(x87234),x87232),f299(x87234,x87231,x87235,x87233)))+P1(f327(f327(x87231,x87232),x87233)) % 177.41/177.19 [8804]~P24(x88041,x88043,x88045,x88042,x88044)+E(f327(f36(x88041),x88042),f327(f36(x88043),x88044)) % 177.41/177.19 [8852]~P24(x88521,x88522,x88523,x88524,x88525)+E(f327(f310(x88521,x88522,x88523),x88524),x88525) % 177.41/177.19 [8872]~P54(x88722,x88721,x88725,x88723,x88724)+E(f327(f310(x88721,x88722,x88723),x88724),f242(f922(x88722,a910))) % 177.41/177.19 [9320]~P32(x93201,x93202,x93203,x93204,x93205)+P32(x93201,x93202,x93203,f327(f169(x93201),x93204),f327(f169(x93202),x93205)) % 177.41/177.19 [9322]~P32(x93221,x93222,x93223,f327(f169(x93221),x93224),x93225)+P32(x93221,x93222,x93223,x93224,f327(f169(x93222),x93225)) % 177.41/177.19 [9323]~P32(x93231,x93232,x93233,x93234,f327(f169(x93232),x93235))+P32(x93231,x93232,x93233,f327(f169(x93231),x93234),x93235) % 177.41/177.19 [9329]P32(x93291,x93292,x93293,x93294,x93295)+~P32(x93291,x93292,x93293,f327(f169(x93291),x93294),f327(f169(x93292),x93295)) % 177.41/177.19 [9729]P1(f327(f327(f329(f921(f916(x97291),f916(x97291))),f327(f327(f252(f916(x97291),f916(x97291)),f327(f327(f152(x97291),x97292),x97293)),f327(f327(f152(x97291),x97292),x97294))),f158(x97291,x97295)))+~P1(f327(f327(f329(f921(f916(x97291),f916(x97291))),f327(f327(f252(f916(x97291),f916(x97291)),x97293),x97294)),f158(x97291,x97295))) % 177.41/177.19 [9730]P1(f327(f327(f329(f921(f916(x97301),f916(x97301))),f327(f327(f252(f916(x97301),f916(x97301)),f327(f327(f135(x97301),x97302),x97303)),f327(f327(f135(x97301),x97302),x97304))),f148(x97301,x97305)))+~P1(f327(f327(f329(f921(f916(x97301),f916(x97301))),f327(f327(f252(f916(x97301),f916(x97301)),x97303),x97304)),f148(x97301,x97305))) % 177.41/177.19 [9926]E(f327(f327(f152(x99261),f647(x99262,x99263,x99264,x99265,x99261)),f648(x99262,x99263,x99264,x99265,x99261)),x99265)+~P1(f327(f327(f329(f921(f916(x99261),f916(x99261))),f327(f327(f252(f916(x99261),f916(x99261)),x99265),f327(f327(f152(x99261),x99264),x99263))),f159(x99261,x99262))) % 177.41/177.19 [9947]E(f327(f327(f152(x99471),f649(x99472,x99473,x99474,x99475,x99471)),f650(x99472,x99473,x99474,x99475,x99471)),x99473)+~P1(f327(f327(f329(f921(f916(x99471),f916(x99471))),f327(f327(f252(f916(x99471),f916(x99471)),f327(f327(f152(x99471),x99475),x99474)),x99473)),f159(x99471,x99472))) % 177.41/177.19 [10093]~P1(f327(f327(f329(f921(f916(x100931),f916(x100931))),f327(f327(f252(f916(x100931),f916(x100931)),f327(f327(f152(x100931),x100935),x100932)),x100934)),f159(x100931,x100933)))+P1(f327(f327(f329(f921(f916(x100931),f916(x100931))),f327(f327(f252(f916(x100931),f916(x100931)),x100932),f650(x100933,x100934,x100932,x100935,x100931))),f159(x100931,x100933))) % 177.41/177.19 [10173]~P1(f327(f327(f329(f921(f916(x101731),f916(x101731))),f327(f327(f252(f916(x101731),f916(x101731)),x101735),f327(f327(f152(x101731),x101734),x101733))),f159(x101731,x101732)))+P1(f327(f327(f329(f921(f916(x101731),f916(x101731))),f327(f327(f252(f916(x101731),f916(x101731)),f648(x101732,x101733,x101734,x101735,x101731)),x101733)),f159(x101731,x101732))) % 177.41/177.19 [10364]P1(f327(f327(f329(f921(x103641,x103641)),f327(f327(f252(x103641,x103641),f327(x103642,f327(f327(f80(a915),x103643),x103644))),f327(x103642,x103643))),f307(x103641,x103645)))+~P1(f327(f327(f329(f921(x103641,x103641)),f327(f327(f252(x103641,x103641),f327(x103642,f327(a113,f602(x103644,x103643,x103645,x103642,x103641)))),f327(x103642,f602(x103644,x103643,x103645,x103642,x103641)))),f307(x103641,x103645))) % 177.41/177.19 [5399]E(x53991,x53992)+~E(f327(f327(f152(x53993),x53994),x53991),f327(f327(f152(x53993),x53995),x53992)) % 177.41/177.19 [5400]E(x54001,x54002)+~E(f327(f327(f152(x54003),x54001),x54004),f327(f327(f152(x54003),x54002),x54005)) % 177.41/177.19 [5448]P1(f327(x54481,x54482))+~E(f327(f137(x54483,x54481),x54484),f327(f327(f152(x54483),x54482),x54485)) % 177.41/177.19 [5449]P1(f327(x54491,x54492))+~E(f327(f327(f152(x54493),x54492),x54494),f327(f137(x54493,x54491),x54495)) % 177.41/177.19 [5608]~E(f327(f327(f139(x56081),x56083),x56082),f327(f327(f152(x56081),x56084),x56085))+E(f327(f327(f165(x56081),x56082),x56083),x56084) % 177.41/177.19 [5749]~P12(x57494,x57495,x57491)+E(f327(f327(x57491,x57492),f327(f327(x57491,x57492),x57493)),f327(f327(x57491,x57492),x57493)) % 177.41/177.19 [6303]~E(x63034,f2(a100))+E(f327(f327(f118(x63031,x63032,x63033),x63034),x63035),f327(f327(f252(f916(x63032),x63031),f114(x63032)),x63035)) % 177.41/177.19 [6375]~P108(x63752)+~E(f327(f327(f149(x63751,x63752,x63753),x63754),x63755),f114(x63751)) % 177.41/177.19 [6761]E(x67611,x67612)+~E(f327(f327(f135(x67613),x67614),f327(f327(f152(x67613),x67611),f114(x67613))),f327(f327(f135(x67613),x67615),f327(f327(f152(x67613),x67612),f114(x67613)))) % 177.41/177.19 [6762]E(x67621,x67622)+~E(f327(f327(f135(x67623),x67621),f327(f327(f152(x67623),x67624),f114(x67623))),f327(f327(f135(x67623),x67622),f327(f327(f152(x67623),x67625),f114(x67623)))) % 177.41/177.19 [7078]E(f327(f327(f309(x70781),f327(x70782,x70783)),f327(f310(x70784,x70781,x70782),x70785)),f327(f310(x70784,x70781,x70782),x70785))+~P1(f327(f327(f329(x70784),x70783),x70785)) % 177.41/177.19 [7085]~P1(f327(x70854,f327(x70853,x70855)))+P1(f327(f327(f311(x70851,x70852,x70853),x70854),x70855)) % 177.41/177.19 [7088]~P1(f327(f327(x70883,x70885),x70884))+P1(f327(f327(f243(x70881,x70882,x70883),x70884),x70885)) % 177.41/177.19 [7184]~E(f327(f310(x71841,x71842,x71843),x71844),x71845)+E(f327(f310(f922(x71841,a910),f922(x71842,a910),f310(x71841,x71842,x71843)),f327(f308(x71841),x71844)),f327(f308(x71842),x71845)) % 177.41/177.19 [7213]E(f327(f271(x72131,x72132,x72133,x72134),x72135),f327(x72134,x72135))+~P1(f327(f327(f329(x72131),x72135),x72133)) % 177.41/177.19 [7528]P23(x75281,x75282,x75283,x75284)+~P23(x75281,x75282,x75283,f327(f327(f309(x75281),x75285),x75284)) % 177.41/177.19 [7591]P1(f327(x75911,x75912))+~P1(f327(f327(f93(x75913,x75914,x75911),x75915),x75912)) % 177.41/177.19 [7632]~P1(f327(f327(f329(x76324),x76323),x76325))+P1(f327(f327(f329(x76321),f327(x76322,x76323)),f327(f310(x76324,x76321,x76322),x76325))) % 177.41/177.19 [7653]~P108(x76532)+E(f151(x76531,x76532,x76533,f327(f137(x76531,x76534),x76535)),f327(f137(x76531,x76534),f151(x76531,x76532,x76533,x76535))) % 177.41/177.19 [7683]P1(f327(x76831,f327(x76832,x76833)))+~P1(f327(f327(f311(x76834,x76835,x76832),x76831),x76833)) % 177.41/177.19 [7686]P1(f327(f327(x76861,x76862),x76863))+~P1(f327(f327(f243(x76864,x76865,x76861),x76863),x76862)) % 177.41/177.19 [7687]P1(f327(f327(x76871,x76872),x76873))+~P1(f327(f327(f93(x76874,x76871,x76875),x76872),x76873)) % 177.41/177.19 [7750]~P1(f327(f327(f329(x77503),f327(x77504,x77502)),x77505))+P1(f327(f327(f329(x77501),x77502),f327(f311(x77501,x77503,x77504),x77505))) % 177.41/177.19 [8145]~P1(f327(f327(f329(x81455),x81453),f327(f311(x81455,x81451,x81452),x81454)))+P1(f327(f327(f329(x81451),f327(x81452,x81453)),x81454)) % 177.41/177.19 [8443]~P14(x84432,x84431,x84433)+E(f327(f143(x84431,x84432,f327(f7(x84432,x84431,x84431),x84433),x84434),f153(x84432,x84435)),f327(f327(f64(x84432,x84431,x84433),x84434),f327(f173(x84432),x84435))) % 177.41/177.19 [8465]E(f327(x84651,f776(x84652,x84651,x84653,x84654)),x84654)+~P1(f327(f327(f329(x84655),x84654),f327(f310(x84653,x84655,x84651),x84652))) % 177.41/177.19 [8767]~E(x87672,f327(f327(f152(x87671),x87674),x87675))+P1(f327(f327(f329(f921(f916(x87671),f916(x87671))),f327(f327(f252(f916(x87671),f916(x87671)),f114(x87671)),x87672)),f148(x87671,x87673))) % 177.41/177.19 [8813]E(f327(x88131,f327(f92(x88132,x88133,x88134,x88131),x88135)),x88135)+~P1(f327(f327(f329(x88133),x88135),f327(f310(x88132,x88133,x88131),x88134))) % 177.41/177.19 [8816]P23(x88161,x88162,f92(x88162,x88161,x88163,x88164),x88165)+~P1(f327(f327(f234(f922(x88161,a910)),x88165),f327(f310(x88162,x88161,x88164),x88163))) % 177.41/177.19 [8823]~P32(x88231,x88233,x88235,x88232,x88234)+E(f327(f191(f916(x88231)),x88232),f327(f191(f916(x88233)),x88234)) % 177.41/177.19 [8834]P1(f327(f327(f234(f922(x88341,a910)),f327(f327(f41(x88342,f922(x88341,a910)),x88343),x88344)),f327(x88344,x88345)))+~P1(f327(f327(f329(x88342),x88345),x88343)) % 177.41/177.19 [8888]~P54(x88881,x88882,x88883,x88885,x88884)+E(f327(f310(x88881,x88882,x88883),f242(f922(x88881,a910))),x88884) % 177.41/177.19 [9115]E(f327(f137(x91151,x91152),f737(x91153,x91154,x91155,x91152,x91151)),x91153)+~E(f327(f137(x91151,x91152),x91155),f327(f327(f152(x91151),x91154),x91153)) % 177.41/177.19 [9116]E(f327(f137(x91161,x91162),f738(x91163,x91162,x91164,x91165,x91161)),x91164)+~E(f327(f327(f152(x91161),x91165),x91164),f327(f137(x91161,x91162),x91163)) % 177.41/177.19 [9209]E(f327(f191(f916(x92091)),x92092),x92093)+~P1(f327(f327(f329(f921(f916(x92091),f916(x92091))),f327(f327(f252(f916(x92091),f916(x92091)),x92094),x92092)),f327(f144(x92091,x92095),x92093))) % 177.41/177.19 [9210]E(f327(f191(f916(x92101)),x92102),x92103)+~P1(f327(f327(f329(f921(f916(x92101),f916(x92101))),f327(f327(f252(f916(x92101),f916(x92101)),x92102),x92104)),f327(f144(x92101,x92105),x92103))) % 177.41/177.19 [9279]P1(f327(f327(f329(x92791),f776(x92792,x92793,x92791,x92794)),x92792))+~P1(f327(f327(f329(x92795),x92794),f327(f310(x92791,x92795,x92793),x92792))) % 177.41/177.19 [9436]E(f327(f310(x94361,x94362,x94363),f481(x94364,x94363,x94361,x94365,x94362)),x94365)+~P1(f327(f327(f234(f922(x94362,a910)),x94365),f327(f310(x94361,x94362,x94363),x94364))) % 177.41/177.19 [9747]P1(f327(f327(f329(f921(f916(x97471),f916(x97471))),f327(f327(f252(f916(x97471),f916(x97471)),f327(f327(f152(x97471),x97472),x97473)),f327(f327(f152(x97471),x97472),x97474))),f307(f916(x97471),f158(x97471,x97475))))+~P1(f327(f327(f329(f921(f916(x97471),f916(x97471))),f327(f327(f252(f916(x97471),f916(x97471)),x97473),x97474)),f307(f916(x97471),f158(x97471,x97475)))) % 177.41/177.19 [9778]~E(f327(x97783,f690(x97785,x97784,x97783,x97782,x97781)),f327(x97785,f690(x97785,x97784,x97783,x97782,x97781)))+E(f327(f327(f155(x97781,x97782),x97783),x97784),f327(f327(f155(x97781,x97782),x97785),x97784)) % 177.41/177.19 [9853]~E(f327(f137(x98531,x98535),x98534),f327(f327(f152(x98531),x98533),x98532))+E(f327(f327(f135(x98531),f741(x98532,x98533,x98534,x98535,x98531)),f327(f327(f152(x98531),x98533),f737(x98532,x98533,x98534,x98535,x98531))),x98534) % 177.41/177.19 [9854]~E(f327(f327(f152(x98541),x98545),x98544),f327(f137(x98541,x98543),x98542))+E(f327(f327(f135(x98541),f739(x98542,x98543,x98544,x98545,x98541)),f327(f327(f152(x98541),x98545),f738(x98542,x98543,x98544,x98545,x98541))),x98542) % 177.41/177.19 [9858]E(f327(f327(f155(x98581,x98582),x98583),x98584),f327(f327(f155(x98581,x98582),x98585),x98584))+P1(f327(f327(f329(x98581),f690(x98583,x98584,x98585,x98582,x98581)),f327(f173(x98581),x98584))) % 177.41/177.19 [9888]~P1(f327(f327(f329(x98885),x98884),f327(f285(x98881,x98885,x98883),x98882)))+P1(f327(f327(f329(x98881),f509(x98882,x98883,x98881,x98884,x98885)),x98882)) % 177.41/177.19 [9889]~P1(f327(f327(f329(x98895),x98894),f327(f285(x98891,x98895,x98893),x98892)))+P1(f327(f327(f329(x98891),f533(x98892,x98893,x98891,x98894,x98895)),x98892)) % 177.41/177.19 [9920]~P1(f327(f327(f234(f922(x99205,a910)),x99204),f327(f310(x99201,x99205,x99203),x99202)))+P1(f327(f327(f234(f922(x99201,a910)),f481(x99202,x99203,x99201,x99204,x99205)),x99202)) % 177.41/177.19 [10365]E(x103651,f2(a100))+E(f225(f921(f916(x103652),x103653),f921(x103652,x103653),f327(f327(f252(f916(x103652),x103653),f114(x103652)),x103654),f327(f257(x103652,x103653,f921(f916(x103652),x103653)),f327(f327(f7(x103652,f922(x103653,f921(f916(x103652),x103653)),f922(x103653,f921(f916(x103652),x103653))),f327(f327(f8(f922(f921(f916(x103652),x103653),f921(f916(x103652),x103653)),f922(f922(x103653,f921(f916(x103652),x103653)),f922(x103653,f921(f916(x103652),x103653))),x103652),f8(f921(f916(x103652),x103653),f921(f916(x103652),x103653),x103653)),f327(f327(f8(f922(f916(x103652),f922(x103653,f921(f916(x103652),x103653))),f922(f921(f916(x103652),x103653),f921(f916(x103652),x103653)),x103652),f257(f916(x103652),x103653,f921(f916(x103652),x103653))),f327(f327(f8(f922(f916(x103652),f916(x103652)),f922(f916(x103652),f922(x103653,f921(f916(x103652),x103653))),x103652),f327(f8(f916(x103652),f922(x103653,f921(f916(x103652),x103653)),f916(x103652)),f252(f916(x103652),x103653))),f152(x103652))))),f327(f118(x103653,x103652,x103655),f327(f327(f23(a100),x103651),f78(a100))))),f327(x103655,x103654)),f327(f327(f118(x103653,x103652,x103655),x103651),x103654)) % 177.41/177.19 [6178]E(x61781,x61782)+~E(f327(f256(x61783,x61784),f327(f327(f252(x61783,x61784),x61785),x61781)),x61782) % 177.41/177.19 [6179]E(x61791,x61792)+~E(f327(f251(x61793,x61794),f327(f327(f252(x61793,x61794),x61791),x61795)),x61792) % 177.41/177.19 [6449]~E(x64493,f327(f327(f135(x64491),x64494),f327(f327(f152(x64491),x64492),x64495)))+P1(f327(f327(f329(x64491),x64492),f327(f173(x64491),x64493))) % 177.41/177.19 [6846]E(f327(f310(x68461,x68462,f327(f16(x68462,x68461),x68463)),x68464),f327(f327(f309(x68462),x68463),f190(f922(x68462,a910))))+~P1(f327(f327(f329(x68461),x68465),x68464)) % 177.41/177.19 [6919]E(f327(f327(f102(f922(x69191,a910)),f327(f173(x69191),x69192)),f327(f173(x69191),x69193)),f327(f173(x69191),x69194))+~E(f167(x69191,x69195,x69194),f327(f327(f252(f916(x69191),f916(x69191)),x69192),x69193)) % 177.41/177.19 [7018]~P108(x70182)+E(f327(f191(f916(x70181)),f327(f327(f149(x70181,x70182,x70183),x70184),x70185)),f327(a113,f327(f191(f916(x70181)),x70185))) % 177.41/177.19 [7032]~P108(x70322)+E(f327(f173(x70321),f327(f327(f149(x70321,x70322,x70323),x70324),x70325)),f327(f327(f309(x70321),x70324),f327(f173(x70321),x70325))) % 177.41/177.19 [7307]~P112(x73071)+E(f327(f327(f80(x73071),f327(f327(f80(x73071),x73072),x73073)),f327(f327(f80(x73071),x73074),x73075)),f327(f327(f80(x73071),f327(f327(f80(x73071),x73072),x73074)),f327(f327(f80(x73071),x73073),x73075))) % 177.41/177.19 [7308]~P112(x73081)+E(f327(f327(f81(x73081),f327(f327(f81(x73081),x73082),x73083)),f327(f327(f81(x73081),x73084),x73085)),f327(f327(f81(x73081),f327(f327(f81(x73081),x73082),x73084)),f327(f327(f81(x73081),x73083),x73085))) % 177.41/177.19 [7309]~P61(x73091)+E(f327(f327(f291(x73091),f327(f327(f81(x73091),x73092),x73093)),f327(f327(f81(x73091),x73094),x73095)),f327(f327(f81(x73091),f327(f327(f291(x73091),x73092),x73094)),f327(f327(f291(x73091),x73093),x73095))) % 177.41/177.19 [7323]~P108(x73231)+E(f306(x73231,f327(f327(f189(x73231),x73232),x73233),f327(f327(f238(x73231),x73234),x73235)),f327(f327(f103(f922(x73231,a910)),f306(x73231,x73232,x73234)),f306(x73231,x73233,x73235))) % 177.41/177.19 [7324]~P108(x73241)+E(f305(x73241,f327(f327(f189(x73241),x73242),x73243),f327(f327(f238(x73241),x73244),x73245)),f327(f327(f103(f922(x73241,a910)),f305(x73241,x73242,x73244)),f305(x73241,x73243,x73245))) % 177.41/177.19 [7325]~P108(x73251)+E(f303(x73251,f327(f327(f189(x73251),x73252),x73253),f327(f327(f238(x73251),x73254),x73255)),f327(f327(f103(f922(x73251,a910)),f303(x73251,x73252,x73254)),f303(x73251,x73253,x73255))) % 177.41/177.19 [7326]~P108(x73261)+E(f327(f327(f103(f922(x73261,a910)),f327(f302(x73261,x73262),x73263)),f327(f302(x73261,x73264),x73265)),f327(f302(x73261,f327(f327(f189(x73261),x73262),x73264)),f327(f327(f238(x73261),x73263),x73265))) % 177.41/177.19 [7448]~P1(f327(x74481,f505(x74483,x74482,x74481)))+P1(f327(x74481,f327(f327(f252(x74482,x74483),x74484),x74485))) % 177.41/177.19 [7558]~E(x75582,f327(x75584,x75585))+P1(f327(f327(f329(x75581),x75582),f327(f310(x75583,x75581,x75584),f242(f922(x75583,a910))))) % 177.41/177.19 [7629]~P12(x76293,x76292,x76294)+P12(x76291,x76292,f327(f327(f8(x76293,f922(x76292,x76292),x76291),x76294),x76295)) % 177.41/177.19 [7630]~P14(x76303,x76302,x76304)+P14(x76301,x76302,f327(f327(f8(x76303,f922(x76302,x76302),x76301),x76304),x76305)) % 177.41/177.19 [7767]~P23(x77671,x77672,x77673,x77674)+P23(x77671,x77672,x77673,f327(f327(f23(f922(x77671,a910)),x77674),x77675)) % 177.41/177.19 [7923]~P1(f327(f327(x79233,x79234),x79235))+P1(f327(f327(f257(x79231,x79232,a910),x79233),f327(f327(f252(x79231,x79232),x79234),x79235))) % 177.41/177.19 [8035]~P1(f327(x80352,x80354))+~E(f327(f327(f139(x80351),f327(f191(f916(x80351)),f178(x80351,x80352,x80353))),x80353),f327(f327(f152(x80351),x80354),x80355)) % 177.41/177.19 [8055]P23(x80551,x80552,x80553,x80554)+~P23(x80551,x80552,x80553,f327(f327(f102(f922(x80551,a910)),x80555),x80554)) % 177.41/177.19 [8056]P23(x80561,x80562,x80563,x80564)+~P23(x80561,x80562,x80563,f327(f327(f102(f922(x80561,a910)),x80564),x80565)) % 177.41/177.19 [8103]~P108(x81032)+E(f327(f327(f149(x81031,x81032,x81033),x81034),f151(x81031,x81032,x81033,x81035)),f151(x81031,x81032,x81033,f327(f327(f152(x81031),x81034),x81035))) % 177.41/177.19 [8420]~P12(x84202,x84201,x84203)+E(f327(f143(x84201,x84202,f327(f7(x84202,x84201,x84201),x84203),x84204),x84205),f327(f327(f64(x84202,x84201,x84203),x84204),f327(f173(x84202),x84205))) % 177.41/177.19 [8448]~E(f327(f327(f139(x84481),f327(f191(f916(x84481)),f178(x84481,x84482,x84483))),x84483),f327(f327(f152(x84481),x84484),x84485))+E(f327(f327(f135(x84481),f178(x84481,x84482,x84483)),f327(f327(f152(x84481),x84484),x84485)),x84483) % 177.41/177.19 [8475]P1(f327(f327(x84751,x84752),x84753))+~P1(f327(f327(f257(x84754,x84755,a910),x84751),f327(f327(f252(x84754,x84755),x84752),x84753))) % 177.41/177.19 [8951]P1(f327(f327(f234(f922(x89511,a910)),f327(f310(x89512,x89511,x89513),x89514)),f327(f310(x89512,x89511,x89513),x89515)))+~P1(f327(f327(f234(f922(x89512,a910)),x89514),x89515)) % 177.41/177.19 [8952]P1(f327(f327(f234(f922(x89521,a910)),f327(f311(x89521,x89522,x89523),x89524)),f327(f311(x89521,x89522,x89523),x89525)))+~P1(f327(f327(f234(f922(x89522,a910)),x89524),x89525)) % 177.41/177.19 [9031]E(x90311,f2(a100))+E(f327(f327(f259(x90312,x90313,x90312,f921(x90313,x90312)),f327(x90314,x90315)),f273(x90313,x90312,f327(f327(f23(a100),x90311),f78(a100)),x90314)),f327(f273(x90313,x90312,x90311,x90314),x90315)) % 177.41/177.19 [9142]P1(f327(f327(f255(x91421,x91422,a910,x91423),x91424),x91425))+~P1(f327(x91423,f327(f327(f252(x91421,x91422),x91424),x91425))) % 177.41/177.19 [9415]~P1(f327(f327(f255(x94152,x94153,a910,x94151),x94154),x94155))+P1(f327(x94151,f327(f327(f252(x94152,x94153),x94154),x94155))) % 177.41/177.19 [9597]~P1(f327(f327(f329(x95972),x95975),f327(f310(x95971,x95972,x95974),x95973)))+P1(f327(f327(f329(x95971),f327(f92(x95971,x95972,x95973,x95974),x95975)),x95973)) % 177.41/177.19 [9688]~P1(f327(f35(x96883),f327(f310(x96882,x96883,x96885),f242(f922(x96882,a910)))))+P1(f327(f35(x96881),f327(f310(x96882,x96881,f327(f327(f8(x96883,x96881,x96882),x96884),x96885)),f242(f922(x96882,a910))))) % 177.41/177.19 [9714]P1(f327(f327(f234(f922(f922(x97141,a910),a910)),f327(f310(f922(x97142,a910),f922(x97141,a910),f310(x97142,x97141,x97143)),f327(f308(x97142),x97144))),f327(f308(x97141),x97145)))+~P1(f327(f327(f234(f922(x97141,a910)),f327(f310(x97142,x97141,x97143),x97144)),x97145)) % 177.41/177.19 [9786]E(x97861,x97862)+~P1(f327(f66(x97863,x97864,x97865,x97861,f190(f922(x97863,a910))),x97862)) % 177.41/177.19 [9802]E(f327(f327(f252(x98021,x98022),f562(x98023,x98024,x98025,x98022,x98021)),f563(x98023,x98024,x98025,x98022,x98021)),x98025)+~P1(f327(f327(f329(f921(x98021,x98022)),x98025),f327(f327(f254(x98021,x98022),x98024),x98023))) % 177.41/177.19 [9894]P1(f327(f327(f329(x98941),f562(x98942,x98943,x98944,x98945,x98941)),x98943))+~P1(f327(f327(f329(f921(x98941,x98945)),x98944),f327(f327(f254(x98941,x98945),x98943),x98942))) % 177.41/177.19 [9995]P22(x99955,x99954,f327(f327(f309(f913(x99955)),f327(f327(f327(f91(x99955),x99951),x99953),x99952)),f190(f922(f913(x99955),a910))))+P1(f327(f327(x99951,f866(x99952,x99953,x99954,x99955,x99951)),f877(x99952,x99953,x99954,x99955,x99951))) % 177.41/177.19 [10051]P1(f327(f327(f329(x100511),f563(x100512,x100513,x100514,x100511,x100515)),f327(x100512,f562(x100512,x100513,x100514,x100511,x100515))))+~P1(f327(f327(f329(f921(x100515,x100511)),x100514),f327(f327(f254(x100515,x100511),x100513),x100512))) % 177.41/177.19 [10071]P1(f327(f327(f329(f921(x100711,x100711)),f327(f327(f252(x100711,x100711),x100712),f623(x100713,x100714,x100715,x100712,x100711))),x100713))+~P1(f327(f327(f329(f921(x100711,x100711)),f327(f327(f252(x100711,x100711),x100712),x100715)),f327(f327(f184(f921(x100711,x100711),a910),f327(a113,x100714)),x100713))) % 177.41/177.19 [10072]P1(f327(f327(f329(f921(x100721,x100721)),f327(f327(f252(x100721,x100721),x100722),f624(x100723,x100724,x100725,x100722,x100721))),x100723))+~P1(f327(f327(f329(f921(x100721,x100721)),f327(f327(f252(x100721,x100721),x100722),x100725)),f327(f327(f184(f921(x100721,x100721),a910),f327(a113,x100724)),x100723))) % 177.41/177.19 [10089]~P1(f327(f327(f329(f921(f916(x100891),f916(x100891))),f327(f327(f252(f916(x100891),f916(x100891)),f327(f327(f152(x100891),x100892),x100895)),x100894)),f159(x100891,x100893)))+P1(f327(f327(f329(f921(x100891,x100891)),f327(f327(f252(x100891,x100891),x100892),f649(x100893,x100894,x100895,x100892,x100891))),x100893)) % 177.41/177.19 [10091]~P22(x100911,x100912,f327(f327(f309(f913(x100911)),f327(f327(f327(f91(x100911),f93(x100911,x100913,x100914)),x100915),x100913)),f190(f922(f913(x100911),a910))))+P22(x100911,x100912,f327(f327(f309(f913(x100911)),f327(f327(f327(f91(x100911),x100913),f29(x100914,x100915)),f93(x100911,x100913,f327(f72(a910,a910,a911,a322),x100914)))),f190(f922(f913(x100911),a910)))) % 177.41/177.19 [10389]P22(x103891,x103892,f327(f327(f309(f913(x103891)),f327(f327(f327(f91(x103891),x103893),x103894),x103895)),f190(f922(f913(x103891),a910))))+~P22(x103891,x103892,f327(f327(f309(f913(x103891)),f327(f327(f327(f91(x103891),f327(f16(f922(a911,a910),x103891),f327(f327(f7(a911,a911,a910),a324),f877(x103895,x103894,x103892,x103891,x103893)))),x103894),f327(f16(f922(a911,a910),x103891),f327(x103895,f866(x103895,x103894,x103892,x103891,x103893))))),f190(f922(f913(x103891),a910)))) % 177.41/177.19 [6527]P1(f327(x65272,x65274))+E(f178(x65271,x65272,f327(f327(f135(x65271),x65273),f327(f327(f152(x65271),x65274),x65275))),f178(x65271,x65272,x65273)) % 177.41/177.19 [6576]~P66(x65762)+E(f327(f327(f327(f23(f922(x65761,x65762)),x65763),x65764),x65765),f327(f327(f23(x65762),f327(x65763,x65765)),f327(x65764,x65765))) % 177.41/177.19 [6578]~P96(x65782)+E(f327(f327(f327(f102(f922(x65781,x65782)),x65783),x65784),x65785),f327(f327(f102(x65782),f327(x65783,x65785)),f327(x65784,x65785))) % 177.41/177.19 [6580]~P96(x65802)+E(f327(f327(f327(f103(f922(x65801,x65802)),x65803),x65804),x65805),f327(f327(f103(x65802),f327(x65803,x65805)),f327(x65804,x65805))) % 177.41/177.19 [6597]E(x65971,x65972)+E(f327(f327(f165(x65973),f327(f327(f160(x65973,x65974),x65971),x65975)),x65972),f327(f327(f165(x65973),x65974),x65972)) % 177.41/177.19 [6865]~E(x68654,f190(f922(x68653,a910)))+E(f327(f327(f23(f922(x68651,a910)),x68652),f327(f327(f40(x68653,f922(x68651,a910)),x68654),x68655)),x68652) % 177.41/177.19 [6866]~E(x68664,f190(f922(x68663,a910)))+E(f327(f327(f102(f922(x68661,a910)),x68662),f327(f327(f40(x68663,f922(x68661,a910)),x68664),x68665)),x68662) % 177.41/177.19 [6867]~E(x68674,f190(f922(x68673,a910)))+E(f327(f327(f103(f922(x68671,a910)),x68672),f327(f327(f41(x68673,f922(x68671,a910)),x68674),x68675)),x68672) % 177.41/177.19 [6882]~E(x68824,f190(f922(x68823,a910)))+E(f327(f327(f309(x68821),x68822),f327(f327(f40(x68823,f922(x68821,a910)),x68824),x68825)),f327(f327(f309(x68821),x68822),f190(f922(x68821,a910)))) % 177.41/177.19 [7675]E(f327(f327(f165(x76751),f327(f327(f155(x76752,x76751),x76753),x76754)),x76755),f327(x76753,f327(f327(f165(x76752),x76754),x76755)))+~P1(f327(f327(f235(a915),x76755),f327(f191(f916(x76752)),x76754))) % 177.41/177.19 [7738]E(f327(f327(f102(f922(x77381,a910)),f327(x77382,x77383)),f327(f327(f40(x77384,f922(x77381,a910)),x77385),x77382)),f327(f327(f40(x77384,f922(x77381,a910)),x77385),x77382))+~P1(f327(f327(f329(x77384),x77383),x77385)) % 177.41/177.19 [7739]E(f327(f327(f103(f922(x77391,a910)),f327(x77392,x77393)),f327(f327(f41(x77394,f922(x77391,a910)),x77395),x77392)),f327(f327(f41(x77394,f922(x77391,a910)),x77395),x77392))+~P1(f327(f327(f329(x77394),x77393),x77395)) % 177.41/177.19 [8343]~E(x83433,f190(f922(x83431,a910)))+E(f327(f327(f40(x83431,f922(x83432,a910)),x83433),f327(f327(f8(f922(x83432,a910),f922(x83432,a910),x83431),f327(f309(x83432),x83434)),x83435)),f190(f922(x83432,a910))) % 177.41/177.19 [8348]~P1(f327(f327(f329(x83484),x83483),x83485))+P1(f327(f327(f234(f922(x83481,a910)),f327(x83482,x83483)),f327(f327(f40(x83484,f922(x83481,a910)),x83485),x83482))) % 177.41/177.19 [8474]~E(f327(x84744,x84742),x84745)+P1(f327(f327(f329(x84741),x84742),f327(f311(x84741,x84743,x84744),f327(f327(f309(x84743),x84745),f190(f922(x84743,a910)))))) % 177.41/177.19 [8521]~P52(x85211,x85212,f327(f286(x85212,x85211),x85213))+E(f327(f327(f103(f922(x85211,a910)),f327(f285(x85212,x85211,x85213),x85214)),f327(f285(x85212,x85211,x85213),x85215)),f327(f285(x85212,x85211,x85213),f327(f327(f103(f922(x85212,a910)),x85214),x85215))) % 177.41/177.19 [8596]E(x85961,f2(a100))+E(f327(f119(x85962,x85963,f327(x85964,f327(f327(f23(a100),x85961),f78(a100)))),f327(f327(f7(x85962,a100,f917(x85963)),x85965),x85961)),f327(f200(x85962,x85963,x85964,x85965),x85961)) % 177.41/177.19 [8634]E(x86341,f190(f922(x86342,a910)))+E(f327(f327(f40(x86342,f922(x86343,a910)),x86341),f327(f327(f8(f922(x86343,a910),f922(x86343,a910),x86342),f327(f309(x86343),x86344)),x86345)),f327(f327(f309(x86343),x86344),f327(f327(f40(x86342,f922(x86343,a910)),x86341),x86345))) % 177.41/177.19 [8685]~P23(x86852,x86851,x86853,f242(f922(x86852,a910)))+E(f327(f327(f23(f922(x86851,a910)),f327(f310(x86852,x86851,x86853),x86854)),f327(f310(x86852,x86851,x86853),x86855)),f327(f310(x86852,x86851,x86853),f327(f327(f23(f922(x86852,a910)),x86854),x86855))) % 177.41/177.19 [8686]~P23(x86862,x86861,x86863,f242(f922(x86862,a910)))+E(f327(f327(f103(f922(x86861,a910)),f327(f310(x86862,x86861,x86863),x86864)),f327(f310(x86862,x86861,x86863),x86865)),f327(f310(x86862,x86861,x86863),f327(f327(f103(f922(x86862,a910)),x86864),x86865))) % 177.41/177.19 [8754]~P1(f327(f327(f67(x87541,x87542,x87545),x87543),x87544))+P1(f327(f327(f329(f921(x87541,x87542)),f327(f327(f252(x87541,x87542),x87543),x87544)),x87545)) % 177.41/177.19 [8786]P1(f327(f327(f329(x87861),x87862),f327(f284(x87863,x87861),x87864)))+~P1(f327(f327(f329(f921(x87863,x87861)),f327(f327(f252(x87863,x87861),x87865),x87862)),x87864)) % 177.41/177.19 [8788]P1(f327(f327(f329(x87881),x87882),f327(f264(x87881,x87883),x87884)))+~P1(f327(f327(f329(f921(x87881,x87883)),f327(f327(f252(x87881,x87883),x87882),x87885)),x87884)) % 177.41/177.19 [8935]P1(f327(f327(f67(x89351,x89352,x89353),x89354),x89355))+~P1(f327(f327(f329(f921(x89351,x89352)),f327(f327(f252(x89351,x89352),x89354),x89355)),x89353)) % 177.41/177.19 [8974]E(f327(x89741,x89742),x89743)+~P1(f327(f327(f329(x89744),x89742),f327(f311(x89744,x89745,x89741),f327(f327(f309(x89745),x89743),f190(f922(x89745,a910)))))) % 177.41/177.19 [9206]P1(f327(f327(f329(f921(x92061,x92062)),f327(f327(f252(x92061,x92062),x92063),x92064)),f327(f286(x92062,x92061),x92065)))+~P1(f327(f327(f329(f921(x92062,x92061)),f327(f327(f252(x92062,x92061),x92064),x92063)),x92065)) % 177.41/177.19 [9224]~P1(f327(f327(x92241,x92245),x92244))+P1(f327(f327(x92241,f327(f256(x92242,x92243),f327(f327(f252(x92242,x92243),x92244),x92245))),f327(f251(x92242,x92243),f327(f327(f252(x92242,x92243),x92244),x92245)))) % 177.41/177.19 [9254]~P1(f327(f327(f329(f921(x92542,x92541)),f327(f327(f252(x92542,x92541),x92544),x92543)),f327(f286(x92541,x92542),x92545)))+P1(f327(f327(f329(f921(x92541,x92542)),f327(f327(f252(x92541,x92542),x92543),x92544)),x92545)) % 177.41/177.19 [9286]~P1(f327(f327(f329(f921(x92863,x92861)),f327(f327(f252(x92863,x92861),x92865),x92862)),x92864))+P1(f327(f327(f329(x92861),x92862),f327(f285(x92863,x92861,x92864),f327(f327(f309(x92863),x92865),f190(f922(x92863,a910)))))) % 177.41/177.19 [9333]P1(f327(f327(f329(f921(x93331,x93332)),f327(f327(f252(x93331,x93332),x93333),x93334)),x93335))+~P1(f327(f327(f329(x93332),x93334),f327(f285(x93331,x93332,x93335),f327(f327(f309(x93331),x93333),f190(f922(x93331,a910)))))) % 177.41/177.19 [9422]~P68(x94221)+E(f327(f327(f6(a915,x94221),x94222),f303(a915,f327(f327(f80(a915),x94223),x94224),f327(f327(f80(a915),x94225),x94224))),f327(f327(f6(a915,x94221),f327(f327(f8(a915,x94221,a915),x94222),f327(f327(f7(a915,a915,a915),f80(a915)),x94224))),f303(a915,x94223,x94225))) % 177.41/177.19 [9441]~P68(x94411)+E(f327(f327(f6(a915,x94411),x94412),f327(f302(a915,f327(f327(f80(a915),x94413),x94414)),f327(f327(f80(a915),x94415),x94414))),f327(f327(f6(a915,x94411),f327(f327(f8(a915,x94411,a915),x94412),f327(f327(f7(a915,a915,a915),f80(a915)),x94414))),f327(f302(a915,x94413),x94415))) % 177.41/177.19 [9497]~P23(x94971,x94972,x94973,f242(f922(x94971,a910)))+E(f327(f327(f155(x94971,x94972),x94973),f327(f137(x94971,f327(f327(f8(a910,a910,x94971),a322),f327(a324,x94974))),x94975)),f327(f137(x94972,f327(f327(f8(a910,a910,x94972),a322),f327(a324,f327(x94973,x94974)))),f327(f327(f155(x94971,x94972),x94973),x94975))) % 177.41/177.19 [9515]~P23(x95151,x95152,x95153,f327(f327(f309(x95151),x95154),f327(f173(x95151),x95155)))+E(f327(f327(f155(x95151,x95152),x95153),f327(f137(x95151,f327(f327(f8(a910,a910,x95151),a322),f327(a324,x95154))),x95155)),f327(f137(x95152,f327(f327(f8(a910,a910,x95152),a322),f327(a324,f327(x95153,x95154)))),f327(f327(f155(x95151,x95152),x95153),x95155))) % 177.41/177.19 [9676]P1(f327(f327(f329(f921(f916(x96761),f916(x96761))),f327(f327(f252(f916(x96761),f916(x96761)),f327(f327(f152(x96761),x96762),x96763)),f327(f327(f152(x96761),x96764),x96763))),f158(x96761,x96765)))+~P1(f327(f327(f329(f921(x96761,x96761)),f327(f327(f252(x96761,x96761),x96762),x96764)),x96765)) % 177.41/177.19 [9797]E(f327(f327(f309(x97971),f561(x97972,x97973,x97974,x97975,x97971)),f579(x97972,x97973,x97974,x97975,x97971)),f327(f327(f309(x97971),x97974),x97973))+~P1(f327(f62(x97971,x97975,f327(f327(f309(x97971),x97974),x97973)),x97972)) % 177.41/177.19 [9798]E(f327(f327(f309(x97981),f589(x97982,x97983,x97984,x97985,x97981)),f598(x97982,x97983,x97984,x97985,x97981)),f327(f327(f309(x97981),x97984),x97983))+~P1(f327(f62(x97981,x97985,f327(f327(f309(x97981),x97984),x97983)),x97982)) % 177.41/177.19 [9879]P1(f327(f327(f329(x98791),f359(x98792,x98793,x98794,x98795,x98791)),x98794))+P1(f327(f327(f327(f41(x98791,f922(x98795,a910)),x98794),x98793),x98792)) % 177.41/177.19 [9884]P1(f327(f327(f329(x98841),f348(x98842,x98843,x98841,x98844,x98845)),x98843))+P1(f327(f327(f329(x98845),x98844),f327(f327(f41(x98841,f922(x98845,a910)),x98843),x98842))) % 177.41/177.19 [9892]P1(f327(f327(f329(x98921),f349(x98922,x98923,x98921,x98924,x98925)),x98923))+P1(f327(f327(f234(f922(x98925,a910)),x98924),f327(f327(f41(x98921,f922(x98925,a910)),x98923),x98922))) % 177.41/177.19 [9893]P1(f327(f327(f329(x98931),f830(x98932,x98933,x98934,x98935,x98931)),x98935))+P1(f327(f327(f234(f922(x98934,a910)),x98933),f327(f327(f41(x98931,f922(x98934,a910)),x98935),x98932))) % 177.41/177.19 [9895]P1(f327(f327(x98951,f904(x98952,x98951,x98953,x98954,x98955)),x98952))+~P1(f327(f327(f327(f40(x98955,f922(x98954,a910)),x98953),x98951),x98952)) % 177.41/177.19 [9899]P1(f327(f327(f329(x98991),f904(x98992,x98993,x98994,x98995,x98991)),x98994))+~P1(f327(f327(f327(f40(x98991,f922(x98995,a910)),x98994),x98993),x98992)) % 177.41/177.19 [9900]P50(x99004,f327(f327(f41(x99001,f922(x99004,a910)),x99005),x99003),f327(f327(f41(x99001,f922(f921(x99004,x99004),a910)),x99005),x99002))+P1(f327(f327(f329(x99001),f770(x99002,x99003,x99004,x99005,x99001)),x99005)) % 177.41/177.19 [9901]P50(x99014,f327(f327(f40(x99011,f922(x99014,a910)),x99015),x99013),f327(f327(f40(x99011,f922(f921(x99014,x99014),a910)),x99015),x99012))+P1(f327(f327(f329(x99011),f823(x99012,x99013,x99014,x99015,x99011)),x99015)) % 177.41/177.19 [9912]P1(f327(f327(f329(x99121),f905(x99122,x99123,x99121,x99124,x99125)),x99123))+~P1(f327(f327(f329(x99125),x99124),f327(f327(f40(x99121,f922(x99125,a910)),x99123),x99122))) % 177.41/177.19 [9918]P1(f327(f327(f329(x99181),x99182),f327(x99183,f905(x99183,x99184,x99185,x99182,x99181))))+~P1(f327(f327(f329(x99181),x99182),f327(f327(f40(x99185,f922(x99181,a910)),x99184),x99183))) % 177.41/177.19 [10000]~P1(f327(f327(x100004,f359(x100005,x100004,x100003,x100002,x100001)),x100005))+P1(f327(f327(f327(f41(x100001,f922(x100002,a910)),x100003),x100004),x100005)) % 177.41/177.19 [10003]~P1(f327(f327(f329(x100031),x100032),f327(x100035,f348(x100035,x100034,x100033,x100032,x100031))))+P1(f327(f327(f329(x100031),x100032),f327(f327(f41(x100033,f922(x100031,a910)),x100034),x100035))) % 177.41/177.19 [10007]~P50(x100071,f327(x100074,f823(x100075,x100074,x100071,x100073,x100072)),f327(x100075,f823(x100075,x100074,x100071,x100073,x100072)))+P50(x100071,f327(f327(f40(x100072,f922(x100071,a910)),x100073),x100074),f327(f327(f40(x100072,f922(f921(x100071,x100071),a910)),x100073),x100075)) % 177.41/177.19 [10008]~P50(x100081,f327(x100084,f770(x100085,x100084,x100081,x100083,x100082)),f327(x100085,f770(x100085,x100084,x100081,x100083,x100082)))+P50(x100081,f327(f327(f41(x100082,f922(x100081,a910)),x100083),x100084),f327(f327(f41(x100082,f922(f921(x100081,x100081),a910)),x100083),x100085)) % 177.41/177.19 [10009]~P1(f327(f327(f234(f922(x100091,a910)),x100092),f327(x100095,f349(x100095,x100094,x100093,x100092,x100091))))+P1(f327(f327(f234(f922(x100091,a910)),x100092),f327(f327(f41(x100093,f922(x100091,a910)),x100094),x100095))) % 177.41/177.19 [10010]~P1(f327(f327(f234(f922(x100101,a910)),x100102),f327(x100105,f830(x100105,x100102,x100101,x100104,x100103))))+P1(f327(f327(f234(f922(x100101,a910)),x100102),f327(f327(f41(x100103,f922(x100101,a910)),x100104),x100105))) % 177.41/177.19 [10075]~P1(f327(f327(f329(x100751),f561(x100755,x100754,x100753,x100752,x100751)),f579(x100755,x100754,x100753,x100752,x100751)))+~P1(f327(f62(x100751,x100752,f327(f327(f309(x100751),x100753),x100754)),x100755)) % 177.41/177.19 [10076]~P1(f327(f327(f329(x100761),f589(x100765,x100764,x100763,x100762,x100761)),f598(x100765,x100764,x100763,x100762,x100761)))+~P1(f327(f62(x100761,x100762,f327(f327(f309(x100761),x100763),x100764)),x100765)) % 177.41/177.19 [10077]~P1(f327(f327(f329(f921(x100771,x100771)),f327(f327(f252(x100771,x100771),x100772),x100775)),f327(f327(f184(f921(x100771,x100771),a910),f327(a113,x100774)),x100773)))+P1(f327(f327(f329(f921(x100771,x100771)),f327(f327(f252(x100771,x100771),x100772),f625(x100773,x100774,x100775,x100772,x100771))),f327(f327(f184(f921(x100771,x100771),a910),x100774),x100773))) % 177.41/177.19 [10083]P1(f327(f66(x100831,x100831,x100832,f561(x100833,x100834,x100835,x100832,x100831),f579(x100833,x100834,x100835,x100832,x100831)),x100833))+~P1(f327(f62(x100831,x100832,f327(f327(f309(x100831),x100835),x100834)),x100833)) % 177.41/177.19 [10084]P1(f327(f66(x100841,x100841,x100842,f589(x100843,x100844,x100845,x100842,x100841),f598(x100843,x100844,x100845,x100842,x100841)),x100843))+~P1(f327(f62(x100841,x100842,f327(f327(f309(x100841),x100845),x100844)),x100843)) % 177.41/177.19 [10095]~P108(x100951)+P11(x100951,f327(f327(f155(x100952,x100951),x100953),f327(f137(x100952,f327(f327(f7(x100952,x100951,a910),f327(f327(f8(x100951,f922(x100951,a910),x100952),a324),x100953)),f327(x100954,x100955))),x100955))) % 177.41/177.19 [10145]~P1(f327(f327(f329(x101452),x101455),f327(f285(x101451,x101452,x101454),x101453)))+P1(f327(f327(f329(f921(x101451,x101452)),f327(f327(f252(x101451,x101452),f509(x101453,x101454,x101451,x101455,x101452)),x101455)),x101454)) % 177.41/177.19 [10146]~P1(f327(f327(f329(x101462),x101465),f327(f285(x101461,x101462,x101464),x101463)))+P1(f327(f327(f329(f921(x101461,x101462)),f327(f327(f252(x101461,x101462),f533(x101463,x101464,x101461,x101465,x101462)),x101465)),x101464)) % 177.41/177.19 [10166]~P1(f327(f327(f329(f921(x101661,x101661)),f327(f327(f252(x101661,x101661),x101665),x101664)),f327(f327(f184(f921(x101661,x101661),a910),f327(a113,x101663)),x101662)))+P1(f327(f327(f329(f921(x101661,x101661)),f327(f327(f252(x101661,x101661),f625(x101662,x101663,x101664,x101665,x101661)),x101664)),x101662)) % 177.41/177.19 [10169]~P1(f327(f327(f329(f921(x101691,x101691)),f327(f327(f252(x101691,x101691),x101695),x101694)),f327(f327(f184(f921(x101691,x101691),a910),f327(a113,x101693)),x101692)))+P1(f327(f327(f329(f921(x101691,x101691)),f327(f327(f252(x101691,x101691),f623(x101692,x101693,x101694,x101695,x101691)),x101694)),f327(f327(f184(f921(x101691,x101691),a910),x101693),x101692))) % 177.41/177.19 [10170]~P1(f327(f327(f329(f921(x101701,x101701)),f327(f327(f252(x101701,x101701),x101705),x101704)),f327(f327(f184(f921(x101701,x101701),a910),f327(a113,x101703)),x101702)))+P1(f327(f327(f329(f921(x101701,x101701)),f327(f327(f252(x101701,x101701),f624(x101702,x101703,x101704,x101705,x101701)),x101704)),f327(f327(f184(f921(x101701,x101701),a910),x101703),x101702))) % 177.41/177.19 [10171]~P1(f327(f327(f329(f921(f916(x101711),f916(x101711))),f327(f327(f252(f916(x101711),f916(x101711)),x101715),f327(f327(f152(x101711),x101714),x101713))),f159(x101711,x101712)))+P1(f327(f327(f329(f921(x101711,x101711)),f327(f327(f252(x101711,x101711),f647(x101712,x101713,x101714,x101715,x101711)),x101714)),x101712)) % 177.41/177.19 [7759]~E(x77593,f190(f922(x77592,a910)))+E(f327(f327(f102(f922(x77591,a910)),f327(f327(f40(x77592,f922(x77591,a910)),x77593),x77594)),x77595),x77595) % 177.41/177.19 [7760]~E(x77603,f190(f922(x77602,a910)))+E(f327(f327(f103(f922(x77601,a910)),f327(f327(f41(x77602,f922(x77601,a910)),x77603),x77604)),x77605),x77605) % 177.41/177.19 [8184]~E(x81843,f190(f922(x81842,a910)))+E(f327(f327(f23(f922(x81841,a910)),f327(f327(f41(x81842,f922(x81841,a910)),x81843),x81844)),x81845),f327(f327(f23(f922(x81841,a910)),f242(f922(x81841,a910))),x81845)) % 177.41/177.19 [8317]E(f327(f327(f160(x83171,f327(f327(f135(x83171),x83172),x83173)),x83174),x83175),f327(f327(f135(x83171),f327(f327(f160(x83171,x83172),x83174),x83175)),x83173))+~P1(f327(f327(f235(a915),x83174),f327(f191(f916(x83171)),x83172))) % 177.41/177.19 [8586]E(f327(f327(f165(x85861),f327(f327(f155(a915,x85861),x85862),f140(a915,f327(f302(a915,x85863),x85864)))),x85865),f327(x85862,f327(f327(f80(a915),x85863),x85865)))+~P1(f327(f327(f235(a915),x85865),f327(f327(f23(a915),x85864),x85863))) % 177.41/177.19 [8600]E(x86001,f2(a100))+E(f123(x86002,x86003,f327(x86004,f327(f327(f23(a100),x86001),f78(a100))),f327(f327(f7(x86002,a100,f917(f918(x86003))),x86005),x86001)),f327(f198(x86002,x86003,x86004,x86005),x86001)) % 177.41/177.19 [8624]~E(x86243,f190(f922(x86241,a910)))+E(f327(f327(f40(x86241,f922(x86242,a910)),x86243),f327(f327(f8(f922(x86242,a910),f922(x86242,a910),x86241),f327(f102(f922(x86242,a910)),x86244)),x86245)),f190(f922(x86242,a910))) % 177.41/177.19 [8625]~E(x86253,f190(f922(x86251,a910)))+E(f327(f327(f41(x86251,f922(x86252,a910)),x86253),f327(f327(f8(f922(x86252,a910),f922(x86252,a910),x86251),f327(f23(f922(x86252,a910)),x86254)),x86255)),f242(f922(x86252,a910))) % 177.41/177.19 [8626]~E(x86263,f190(f922(x86261,a910)))+E(f327(f327(f41(x86261,f922(x86262,a910)),x86263),f327(f327(f8(f922(x86262,a910),f922(x86262,a910),x86261),f327(f103(f922(x86262,a910)),x86264)),x86265)),f242(f922(x86262,a910))) % 177.41/177.19 [8628]~P139(x86282)+E(f327(f327(f6(x86281,x86282),f327(f327(f8(x86282,x86282,x86281),f327(f81(x86282),x86283)),x86284)),x86285),f327(f327(f81(x86282),x86283),f327(f327(f6(x86281,x86282),x86284),x86285))) % 177.41/177.19 [8919]E(x89191,f190(f922(x89192,a910)))+E(f327(f327(f40(x89192,f922(x89193,a910)),x89191),f327(f327(f8(f922(x89193,a910),f922(x89193,a910),x89192),f327(f102(f922(x89193,a910)),x89194)),x89195)),f327(f327(f102(f922(x89193,a910)),x89194),f327(f327(f40(x89192,f922(x89193,a910)),x89191),x89195))) % 177.41/177.19 [8920]E(x89201,f190(f922(x89202,a910)))+E(f327(f327(f41(x89202,f922(x89203,a910)),x89201),f327(f327(f8(f922(x89203,a910),f922(x89203,a910),x89202),f327(f23(f922(x89203,a910)),x89204)),x89205)),f327(f327(f23(f922(x89203,a910)),x89204),f327(f327(f40(x89202,f922(x89203,a910)),x89201),x89205))) % 177.41/177.19 [8921]E(x89211,f190(f922(x89212,a910)))+E(f327(f327(f41(x89212,f922(x89213,a910)),x89211),f327(f327(f8(f922(x89213,a910),f922(x89213,a910),x89212),f327(f103(f922(x89213,a910)),x89214)),x89215)),f327(f327(f103(f922(x89213,a910)),x89214),f327(f327(f41(x89212,f922(x89213,a910)),x89211),x89215))) % 177.41/177.19 [9124]~P1(f327(f327(f235(a915),f327(x91244,x91242)),f327(x91244,x91243)))+P1(f327(f327(f329(f921(x91241,x91241)),f327(f327(f252(x91241,x91241),x91242),x91243)),f154(x91241,f327(f327(f152(f922(x91241,a915)),x91244),x91245)))) % 177.41/177.19 [9388]~P23(x93882,x93881,x93883,f327(f327(f102(f922(x93882,a910)),x93884),x93885))+E(f327(f327(f103(f922(x93881,a910)),f327(f310(x93882,x93881,x93883),f327(f327(f23(f922(x93882,a910)),x93884),x93885))),f327(f310(x93882,x93881,x93883),f327(f327(f23(f922(x93882,a910)),x93885),x93884))),f190(f922(x93881,a910))) % 177.41/177.19 [9641]~P23(x96413,x96411,x96415,f242(f922(x96413,a910)))+E(f327(f72(x96411,x96412,x96413,f327(f72(x96413,x96412,x96411,x96414),f92(x96413,x96411,f242(f922(x96413,a910)),x96415))),x96415),x96414) % 177.41/177.19 [9672]~P1(f327(f327(f234(f922(x96723,a910)),f327(f285(x96721,x96723,x96724),x96722)),x96725))+P1(f327(f327(f234(f922(x96721,a910)),x96722),f327(f79(f922(x96721,a910)),f327(f285(x96723,x96721,f327(f286(x96721,x96723),x96724)),f327(f79(f922(x96723,a910)),x96725))))) % 177.41/177.19 [9697]~P23(x96971,x96972,x96973,f327(f327(f309(x96971),x96974),x96975))+~P1(f327(f327(f329(x96972),f327(x96973,x96974)),f327(f310(x96971,x96972,x96973),f327(f327(f23(f922(x96971,a910)),x96975),f327(f327(f309(x96971),x96974),f190(f922(x96971,a910))))))) % 177.41/177.19 [9751]P1(f327(f327(f234(f922(x97511,a910)),f327(f285(x97512,x97511,x97513),x97514)),x97515))+~P1(f327(f327(f234(f922(x97512,a910)),x97514),f327(f79(f922(x97512,a910)),f327(f285(x97511,x97512,f327(f286(x97512,x97511),x97513)),f327(f79(f922(x97511,a910)),x97515))))) % 177.41/177.19 [9824]~P84(x98241)+P1(f327(f327(f234(x98241),f327(f75(x98241),f327(f327(f23(x98241),f327(f327(f80(x98241),x98242),x98243)),f327(f327(f80(x98241),x98244),x98245)))),f327(f327(f80(x98241),f327(f75(x98241),f327(f327(f23(x98241),x98242),x98244))),f327(f75(x98241),f327(f327(f23(x98241),x98243),x98245))))) % 177.41/177.19 [9933]P1(f327(f327(f329(x99331),f346(x99332,x99333,x99334,x99331,x99335)),x99334))+P1(f327(f327(f234(f922(x99335,a910)),f327(f327(f40(x99331,f922(x99335,a910)),x99334),x99333)),x99332)) % 177.41/177.19 [10113]~P1(f327(f327(f234(f922(x101131,a910)),f327(x101134,f346(x101135,x101134,x101133,x101132,x101131))),x101135))+P1(f327(f327(f234(f922(x101131,a910)),f327(f327(f40(x101132,f922(x101131,a910)),x101133),x101134)),x101135)) % 177.41/177.19 [8733]E(f327(f327(f135(x87331),x87332),f327(f327(f160(x87331,x87333),f327(f327(f23(a915),x87334),f327(f191(f916(x87331)),x87332))),x87335)),f327(f327(f160(x87331,f327(f327(f135(x87331),x87332),x87333)),x87334),x87335))+P1(f327(f327(f235(a915),x87334),f327(f191(f916(x87331)),x87332))) % 177.41/177.19 [8761]~P140(x87611)+E(f327(f327(f80(x87611),f327(f327(f81(x87611),x87612),x87613)),f327(f327(f80(x87611),f327(f327(f81(x87611),x87614),x87613)),x87615)),f327(f327(f80(x87611),f327(f327(f81(x87611),f327(f327(f80(x87611),x87612),x87614)),x87613)),x87615)) % 177.41/177.19 [9342]~P139(x93421)+E(f327(f166(x93421),f327(f327(f155(x93422,x93421),f327(f327(f8(x93421,x93421,x93422),f327(f81(x93421),x93423)),x93424)),x93425)),f327(f327(f81(x93421),x93423),f327(f166(x93421),f327(f327(f155(x93422,x93421),x93424),x93425)))) % 177.41/177.19 [9514]E(f327(f191(f916(x95141)),f327(f327(f176(x95141),f327(f327(f238(a915),f327(f191(f916(x95141)),x95142)),f327(f191(f916(x95143)),x95144))),x95142)),f327(f191(f916(x95143)),f327(f327(f176(x95143),f327(f327(f238(a915),f327(f191(f916(x95141)),x95142)),f327(f191(f916(x95143)),x95144))),x95144)))+P1(f327(x95145,f327(f327(f182(x95141,x95143),x95142),x95144))) % 177.41/177.19 [9761]~P139(x97612)+E(f327(f327(f6(x97611,x97612),f327(f327(f7(x97611,x97612,x97612),f327(f327(f8(x97612,f922(x97612,x97612),x97611),f81(x97612)),x97613)),x97614)),x97615),f327(f327(f81(x97612),f327(f327(f6(x97611,x97612),x97613),x97615)),x97614)) % 177.41/177.19 [9762]~P62(x97622)+E(f327(f327(f6(x97621,x97622),f327(f327(f7(x97621,x97622,x97622),f327(f327(f8(x97622,f922(x97622,x97622),x97621),f291(x97622)),x97623)),x97624)),x97625),f327(f327(f291(x97622),f327(f327(f6(x97621,x97622),x97623),x97625)),x97624)) % 177.41/177.19 [9769]~P67(x97692)+E(f327(f327(f6(x97691,x97692),f327(f327(f18(x97691,x97692,x97692),f327(f327(f8(x97692,f922(x97692,x97692),x97691),f23(x97692)),x97693)),x97694)),x97695),f327(f327(f23(x97692),f327(f327(f6(x97691,x97692),x97693),x97695)),f327(f327(f6(x97691,x97692),x97694),x97695))) % 177.41/177.19 [9770]~P68(x97702)+E(f327(f327(f6(x97701,x97702),f327(f327(f18(x97701,x97702,x97702),f327(f327(f8(x97702,f922(x97702,x97702),x97701),f80(x97702)),x97703)),x97704)),x97705),f327(f327(f80(x97702),f327(f327(f6(x97701,x97702),x97703),x97705)),f327(f327(f6(x97701,x97702),x97704),x97705))) % 177.41/177.19 [9771]~P75(x97712)+E(f327(f327(f9(x97711,x97712),f327(f327(f18(x97711,x97712,x97712),f327(f327(f8(x97712,f922(x97712,x97712),x97711),f81(x97712)),x97713)),x97714)),x97715),f327(f327(f81(x97712),f327(f327(f9(x97711,x97712),x97713),x97715)),f327(f327(f9(x97711,x97712),x97714),x97715))) % 177.41/177.19 [9809]~E(x98093,f190(f922(x98091,a910)))+E(f327(f327(f40(x98091,f922(x98092,a910)),x98093),f327(f327(f7(x98091,f922(x98092,a910),f922(x98092,a910)),f327(f327(f8(f922(x98092,a910),f922(f922(x98092,a910),f922(x98092,a910)),x98091),f102(f922(x98092,a910))),x98094)),x98095)),f190(f922(x98092,a910))) % 177.41/177.19 [9810]~E(x98103,f190(f922(x98101,a910)))+E(f327(f327(f41(x98101,f922(x98102,a910)),x98103),f327(f327(f7(x98101,f922(x98102,a910),f922(x98102,a910)),f327(f327(f8(f922(x98102,a910),f922(f922(x98102,a910),f922(x98102,a910)),x98101),f23(f922(x98102,a910))),x98104)),x98105)),f242(f922(x98102,a910))) % 177.41/177.19 [9811]~E(x98113,f190(f922(x98111,a910)))+E(f327(f327(f41(x98111,f922(x98112,a910)),x98113),f327(f327(f7(x98111,f922(x98112,a910),f922(x98112,a910)),f327(f327(f8(f922(x98112,a910),f922(f922(x98112,a910),f922(x98112,a910)),x98111),f103(f922(x98112,a910))),x98114)),x98115)),f242(f922(x98112,a910))) % 177.41/177.19 [9832]E(x98321,f190(f922(x98322,a910)))+E(f327(f327(f40(x98322,f922(x98323,a910)),x98321),f327(f327(f7(x98322,f922(x98323,a910),f922(x98323,a910)),f327(f327(f8(f922(x98323,a910),f922(f922(x98323,a910),f922(x98323,a910)),x98322),f102(f922(x98323,a910))),x98324)),x98325)),f327(f327(f102(f922(x98323,a910)),f327(f327(f40(x98322,f922(x98323,a910)),x98321),x98324)),x98325)) % 177.41/177.19 [9833]E(x98331,f190(f922(x98332,a910)))+E(f327(f327(f41(x98332,f922(x98333,a910)),x98331),f327(f327(f7(x98332,f922(x98333,a910),f922(x98333,a910)),f327(f327(f8(f922(x98333,a910),f922(f922(x98333,a910),f922(x98333,a910)),x98332),f23(f922(x98333,a910))),x98334)),x98335)),f327(f327(f23(f922(x98333,a910)),f327(f327(f41(x98332,f922(x98333,a910)),x98331),x98334)),x98335)) % 177.41/177.19 [9834]E(x98341,f190(f922(x98342,a910)))+E(f327(f327(f41(x98342,f922(x98343,a910)),x98341),f327(f327(f7(x98342,f922(x98343,a910),f922(x98343,a910)),f327(f327(f8(f922(x98343,a910),f922(f922(x98343,a910),f922(x98343,a910)),x98342),f103(f922(x98343,a910))),x98344)),x98345)),f327(f327(f103(f922(x98343,a910)),f327(f327(f41(x98342,f922(x98343,a910)),x98341),x98344)),x98345)) % 177.41/177.19 [9393]~P1(f327(f327(f234(a915),x93931),x93934))+E(f327(f327(f23(a915),f327(f327(f80(a915),f327(f327(f81(a915),x93931),x93932)),x93933)),f327(f327(f80(a915),f327(f327(f81(a915),x93934),x93932)),x93935)),f327(f327(f23(a915),x93933),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x93934),x93931)),x93932)),x93935))) % 177.41/177.19 [9982]~P139(x99821)+E(f327(f166(x99821),f327(f327(f155(x99822,x99821),f327(f327(f7(x99822,x99821,x99821),f327(f327(f8(x99821,f922(x99821,x99821),x99822),f81(x99821)),x99823)),x99824)),x99825)),f327(f327(f81(x99821),f327(f166(x99821),f327(f327(f155(x99822,x99821),x99823),x99825))),x99824)) % 177.41/177.19 [9988]~P67(x99881)+E(f327(f166(x99881),f327(f327(f155(x99882,x99881),f327(f327(f18(x99882,x99881,x99881),f327(f327(f8(x99881,f922(x99881,x99881),x99882),f23(x99881)),x99883)),x99884)),x99885)),f327(f327(f23(x99881),f327(f166(x99881),f327(f327(f155(x99882,x99881),x99883),x99885))),f327(f166(x99881),f327(f327(f155(x99882,x99881),x99884),x99885)))) % 177.41/177.19 [9989]~P68(x99891)+E(f327(f166(x99891),f327(f327(f155(x99892,x99891),f327(f327(f18(x99892,x99891,x99891),f327(f327(f8(x99891,f922(x99891,x99891),x99892),f80(x99891)),x99893)),x99894)),x99895)),f327(f327(f80(x99891),f327(f166(x99891),f327(f327(f155(x99892,x99891),x99893),x99895))),f327(f166(x99891),f327(f327(f155(x99892,x99891),x99894),x99895)))) % 177.41/177.19 [10137]P1(f327(x101371,f327(f327(f182(x101372,x101373),x101374),x101375)))+~P1(f327(x101371,f327(f327(f182(x101372,x101373),f327(f327(f176(x101372),f327(f327(f238(a915),f327(f191(f916(x101372)),x101374)),f327(f191(f916(x101373)),x101375))),x101374)),f327(f327(f176(x101373),f327(f327(f238(a915),f327(f191(f916(x101372)),x101374)),f327(f191(f916(x101373)),x101375))),x101375)))) % 177.41/177.19 [10400]~P1(f327(f327(f329(f921(x104002,x104001)),f327(f327(f252(x104002,x104001),x104004),x104005)),f327(f286(x104001,x104002),x104003)))+P1(f327(f327(f243(x104001,x104002,f327(f327(f7(x104001,f922(f921(x104001,x104002),a910),f922(x104002,a910)),f327(f327(f8(f922(x104002,f922(f922(f921(x104001,x104002),a910),a910)),f922(f922(f921(x104001,x104002),a910),f922(x104002,a910)),x104001),f7(x104002,f922(f921(x104001,x104002),a910),a910)),f327(f327(f8(f922(x104002,f921(x104001,x104002)),f922(x104002,f922(f922(f921(x104001,x104002),a910),a910)),x104001),f327(f8(f921(x104001,x104002),f922(f922(f921(x104001,x104002),a910),a910),x104002),f329(f921(x104001,x104002)))),f252(x104001,x104002)))),x104003)),x104004),x104005)) % 177.41/177.19 [10410]P1(f327(f327(f329(f921(x104101,x104102)),f327(f327(f252(x104101,x104102),x104103),x104104)),f327(f286(x104102,x104101),x104105)))+~P1(f327(f327(f243(x104102,x104101,f327(f327(f7(x104102,f922(f921(x104102,x104101),a910),f922(x104101,a910)),f327(f327(f8(f922(x104101,f922(f922(f921(x104102,x104101),a910),a910)),f922(f922(f921(x104102,x104101),a910),f922(x104101,a910)),x104102),f7(x104101,f922(f921(x104102,x104101),a910),a910)),f327(f327(f8(f922(x104101,f921(x104102,x104101)),f922(x104101,f922(f922(f921(x104102,x104101),a910),a910)),x104102),f327(f8(f921(x104102,x104101),f922(f922(f921(x104102,x104101),a910),a910),x104101),f329(f921(x104102,x104101)))),f252(x104102,x104101)))),x104105)),x104103),x104104)) % 177.41/177.19 [9640]~P1(f327(f327(f234(a915),x96404),x96401))+E(f327(f327(f23(a915),f327(f327(f80(a915),f327(f327(f81(a915),x96401),x96402)),x96403)),f327(f327(f80(a915),f327(f327(f81(a915),x96404),x96402)),x96405)),f327(f327(f23(a915),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x96401),x96404)),x96402)),x96403)),x96405)) % 177.41/177.19 [5425]E(x54251,x54252)+~E(f27(x54253,x54254,x54251),f27(x54255,x54256,x54252)) % 177.41/177.19 [5426]E(x54261,x54262)+~E(f27(x54263,x54261,x54264),f27(x54265,x54262,x54266)) % 177.41/177.19 [5427]E(x54271,x54272)+~E(f27(x54271,x54273,x54274),f27(x54272,x54275,x54276)) % 177.41/177.19 [5428]E(x54281,x54282)+~E(f26(x54283,x54284,x54281),f26(x54285,x54286,x54282)) % 177.41/177.19 [5429]E(x54291,x54292)+~E(f26(x54293,x54291,x54294),f26(x54295,x54292,x54296)) % 177.41/177.19 [5430]E(x54301,x54302)+~E(f26(x54301,x54303,x54304),f26(x54302,x54305,x54306)) % 177.41/177.19 [7456]E(x74561,x74562)+~E(f222(x74563,x74564,x74565,x74561),f222(x74563,x74564,x74566,x74562)) % 177.41/177.19 [7457]E(x74571,x74572)+~E(f222(x74573,x74574,x74571,x74575),f222(x74573,x74574,x74572,x74576)) % 177.41/177.19 [8570]~P17(x85705,x85701,x85702,x85706)+E(f327(f72(x85701,x85701,x85701,f327(x85702,x85703)),f327(x85702,x85704)),f327(f72(x85701,x85701,x85701,f327(x85702,x85704)),f327(x85702,x85703))) % 177.41/177.19 [8805]~P54(x88054,x88055,x88052,x88051,x88056)+E(f327(x88051,f327(x88052,x88053)),x88053) % 177.41/177.19 [8972]P23(x89721,x89722,x89723,x89724)+~P23(x89721,x89725,f327(f72(x89722,x89725,x89721,x89726),x89723),x89724) % 177.41/177.19 [9045]~E(x90456,x90454)+E(f327(f74(x90451,x90452,x90453,x90454,x90455),x90456),x90455) % 177.41/177.19 [9051]E(x90511,x90512)+E(f327(f74(x90513,x90514,x90515,x90512,x90516),x90511),f327(x90515,x90511)) % 177.41/177.19 [9063]~P23(x90634,x90632,f327(f72(x90631,x90632,x90634,x90633),x90635),x90636)+P23(x90631,x90632,x90633,f327(f310(x90634,x90631,x90635),x90636)) % 177.41/177.19 [9772]P1(f327(f35(x97721),x97722))+~P1(f327(f66(x97721,x97723,x97724,x97725,x97722),x97726)) % 177.41/177.19 [9781]~P1(f327(f327(f329(x97814),x97813),f297(x97814,x97811,x97815,x97812,x97816)))+P1(f327(f327(x97811,x97812),x97813)) % 177.41/177.19 [9782]~P1(f327(f327(f329(x97824),x97823),f300(x97824,x97825,x97821,x97822,x97826)))+P1(f327(f327(x97821,x97822),x97823)) % 177.41/177.19 [9783]~P1(f327(f327(f329(x97834),x97832),f297(x97834,x97835,x97831,x97836,x97833)))+P1(f327(f327(x97831,x97832),x97833)) % 177.41/177.19 [9784]~P1(f327(f327(f329(x97844),x97842),f300(x97844,x97841,x97845,x97846,x97843)))+P1(f327(f327(x97841,x97842),x97843)) % 177.41/177.19 [10291]P10(x102911,x102912,x102913,x102914,x102915,x102916)+~E(f327(f327(x102916,f844(x102913,x102916,x102915,x102912,x102914,x102911)),f847(x102913,x102916,x102915,x102912,x102914,x102911)),f327(f327(x102916,f845(x102913,x102916,x102915,x102912,x102914,x102911)),f848(x102913,x102916,x102915,x102912,x102914,x102911))) % 177.41/177.19 [5940]E(x59401,x59402)+~E(f327(f327(f252(x59403,x59404),x59405),x59401),f327(f327(f252(x59403,x59404),x59406),x59402)) % 177.41/177.19 [5942]E(x59421,x59422)+~E(f327(f327(f252(x59423,x59424),x59421),x59425),f327(f327(f252(x59423,x59424),x59422),x59426)) % 177.41/177.19 [6078]~P14(x60785,x60786,x60781)+E(f327(f327(x60781,x60782),f327(f327(x60781,x60783),x60784)),f327(f327(x60781,x60783),f327(f327(x60781,x60782),x60784))) % 177.41/177.19 [7522]~P30(x75224,x75221,f327(f327(f152(x75224),x75222),x75225),f327(f327(f152(x75224),x75223),x75226))+P1(f327(f327(x75221,x75222),x75223)) % 177.41/177.19 [7876]P30(x78761,x78762,x78763,x78764)+~P30(x78761,x78762,f327(f327(f152(x78761),x78765),x78763),f327(f327(f152(x78761),x78766),x78764)) % 177.41/177.19 [8909]~P54(x89095,x89091,x89092,x89096,x89094)+P1(f327(f327(f329(x89091),f327(x89092,x89093)),x89094)) % 177.41/177.19 [9091]E(f327(f76(x90911,x90912,x90913,x90914,x90915),x90916),f327(x90913,x90916))+P1(f327(f327(f329(x90911),x90916),x90915)) % 177.41/177.19 [9113]~E(x91133,f327(f327(f152(x91131),x91135),x91136))+P1(f327(f327(f329(f921(f916(x91131),f916(x91131))),f327(f327(f252(f916(x91131),f916(x91131)),x91132),f327(f327(f135(x91131),x91132),x91133))),f148(x91131,x91134))) % 177.41/177.19 [9118]E(f327(f76(x91181,x91182,x91183,x91184,x91185),x91186),f327(x91184,x91186))+~P1(f327(f327(f329(x91181),x91186),x91185)) % 177.41/177.19 [9348]~P32(x93481,x93482,x93483,x93485,x93486)+P32(x93481,x93482,x93483,f327(f327(f176(x93481),x93484),x93485),f327(f327(f176(x93482),x93484),x93486)) % 177.41/177.19 [9349]~P32(x93491,x93492,x93493,x93495,x93496)+P32(x93491,x93492,x93493,f327(f327(f139(x93491),x93494),x93495),f327(f327(f139(x93492),x93494),x93496)) % 177.41/177.19 [9607]E(f327(f310(x96071,x96072,f74(x96071,x96072,x96073,x96074,x96075)),x96076),f327(f310(x96071,x96072,x96073),x96076))+P1(f327(f327(f329(x96071),x96074),x96076)) % 177.41/177.19 [9610]E(f327(f327(f155(x96101,x96102),f74(x96101,x96102,x96103,x96104,x96105)),x96106),f327(f327(f155(x96101,x96102),x96103),x96106))+P1(f327(f327(f329(x96101),x96104),f327(f173(x96101),x96106))) % 177.41/177.19 [9844]~P21(x98444,x98442,x98445,x98443,x98446,x98441)+E(f327(x98441,f190(f922(x98442,a910))),x98443) % 177.41/177.19 [10078]~E(f327(x100784,f327(f251(x100781,x100783),x100785)),f327(x100786,f327(f251(x100781,x100783),x100785)))+E(f327(f258(x100781,x100782,x100783,x100783,x100784,f31(x100783)),x100785),f327(f258(x100781,x100782,x100783,x100783,x100786,f31(x100783)),x100785)) % 177.41/177.19 [10079]~E(f327(x100794,f327(f256(x100791,x100792),x100795)),f327(x100796,f327(f256(x100791,x100792),x100795)))+E(f327(f258(x100791,x100791,x100792,x100793,f31(x100791),x100794),x100795),f327(f258(x100791,x100791,x100792,x100793,f31(x100791),x100796),x100795)) % 177.41/177.19 [10133]~E(f327(f258(x101332,x101336,x101333,x101333,x101331,f31(x101333)),x101334),f327(f258(x101332,x101336,x101333,x101333,x101335,f31(x101333)),x101334))+E(f327(x101331,f327(f251(x101332,x101333),x101334)),f327(x101335,f327(f251(x101332,x101333),x101334))) % 177.41/177.19 [10134]~E(f327(f258(x101342,x101342,x101343,x101346,f31(x101342),x101341),x101344),f327(f258(x101342,x101342,x101343,x101346,f31(x101342),x101345),x101344))+E(f327(x101341,f327(f256(x101342,x101343),x101344)),f327(x101345,f327(f256(x101342,x101343),x101344))) % 177.41/177.19 [9012]P1(f327(f327(f329(x90121),x90122),x90123))+~P1(f327(f327(f329(f921(x90121,x90124)),f327(f327(f252(x90121,x90124),x90122),x90125)),f327(f327(f254(x90121,x90124),x90123),x90126))) % 177.41/177.19 [9028]P1(f327(f327(f329(x90281),x90282),f327(x90283,x90284)))+~P1(f327(f327(f329(f921(x90285,x90281)),f327(f327(f252(x90285,x90281),x90284),x90282)),f327(f327(f254(x90285,x90281),x90286),x90283))) % 177.41/177.19 [9464]P1(f327(f327(f329(f921(x94641,x94641)),f327(f327(f252(x94641,x94641),f327(x94642,x94643)),f327(x94642,x94644))),x94645))+~P1(f327(f327(f329(f921(x94646,x94646)),f327(f327(f252(x94646,x94646),x94643),x94644)),f327(f327(f288(x94641,x94646),x94645),x94642))) % 177.41/177.19 [9484]~P1(f327(f327(f329(f921(x94844,x94844)),f327(f327(f252(x94844,x94844),f327(x94846,x94842)),f327(x94846,x94843))),x94845))+P1(f327(f327(f329(f921(x94841,x94841)),f327(f327(f252(x94841,x94841),x94842),x94843)),f327(f327(f288(x94844,x94841),x94845),x94846))) % 177.41/177.19 [10136]E(f327(f327(f252(x101361,x101362),f638(x101363,x101364,x101365,x101366,x101362,x101361)),f639(x101363,x101364,x101365,x101366,x101362,x101361)),x101366)+~P1(f327(f327(f329(f921(x101361,x101362)),x101366),f327(f327(f289(x101361,x101365,x101362),x101364),x101363))) % 177.41/177.19 [10356]~P1(f327(f327(f329(f921(x103561,x103566)),x103565),f327(f327(f289(x103561,x103562,x103566),x103564),x103563)))+P1(f327(f327(f329(f921(x103561,x103562)),f327(f327(f252(x103561,x103562),f638(x103563,x103564,x103562,x103565,x103566,x103561)),f640(x103563,x103564,x103562,x103565,x103566,x103561))),x103564)) % 177.41/177.19 [10357]~P1(f327(f327(f329(f921(x103576,x103572)),x103575),f327(f327(f289(x103576,x103571,x103572),x103574),x103573)))+P1(f327(f327(f329(f921(x103571,x103572)),f327(f327(f252(x103571,x103572),f640(x103573,x103574,x103571,x103575,x103572,x103576)),f639(x103573,x103574,x103571,x103575,x103572,x103576))),x103573)) % 177.41/177.19 [10358]P10(x103581,x103582,x103583,x103584,x103585,x103586)+P1(f327(f327(f329(f921(x103582,x103582)),f327(f327(f252(x103582,x103582),f848(x103583,x103586,x103585,x103582,x103584,x103581)),f847(x103583,x103586,x103585,x103582,x103584,x103581))),x103585)) % 177.41/177.19 [10359]P10(x103591,x103592,x103593,x103594,x103595,x103596)+P1(f327(f327(f329(f921(x103591,x103591)),f327(f327(f252(x103591,x103591),f845(x103593,x103596,x103595,x103592,x103594,x103591)),f844(x103593,x103596,x103595,x103592,x103594,x103591))),x103594)) % 177.41/177.19 [7946]~P3(x79462)+E(f327(f327(f40(x79461,x79462),x79463),f327(f327(f7(x79461,x79464,x79462),x79465),x79466)),f327(f327(f327(f40(x79461,f922(x79464,x79462)),x79463),x79465),x79466)) % 177.41/177.19 [7947]~P3(x79472)+E(f327(f327(f41(x79471,x79472),x79473),f327(f327(f7(x79471,x79474,x79472),x79475),x79476)),f327(f327(f327(f41(x79471,f922(x79474,x79472)),x79473),x79475),x79476)) % 177.41/177.19 [8715]E(f327(f327(f40(x87151,f922(x87152,a910)),x87153),f327(f327(f8(f922(x87152,a910),f922(x87152,a910),x87151),f327(f309(x87152),x87154)),x87155)),f327(f327(f309(x87152),x87154),f327(f327(f40(x87151,f922(x87152,a910)),x87153),x87155)))+~P1(f327(f327(f329(x87151),x87156),x87153)) % 177.41/177.19 [9168]~P3(x91682)+E(f327(f327(f40(x91681,x91682),x91683),f327(f327(f8(f922(x91684,x91682),x91682,x91681),f327(f40(x91684,x91682),x91685)),f327(f7(x91684,x91681,x91682),x91686))),f327(f327(f40(x91684,x91682),x91685),f327(f327(f8(f922(x91681,x91682),x91682,x91684),f327(f40(x91681,x91682),x91683)),x91686))) % 177.41/177.19 [9169]~P3(x91692)+E(f327(f327(f41(x91691,x91692),x91693),f327(f327(f8(f922(x91694,x91692),x91692,x91691),f327(f41(x91694,x91692),x91695)),f327(f7(x91694,x91691,x91692),x91696))),f327(f327(f41(x91694,x91692),x91695),f327(f327(f8(f922(x91691,x91692),x91692,x91694),f327(f41(x91691,x91692),x91693)),x91696))) % 177.41/177.19 [9373]P1(f327(f327(f329(x93731),x93732),f327(f173(x93731),x93733)))+~P1(f327(f327(f329(f921(x93734,x93731)),f327(f327(f252(x93734,x93731),x93735),x93732)),f327(f173(f921(x93734,x93731)),f327(f327(f182(x93734,x93731),x93736),x93733)))) % 177.41/177.19 [9374]P1(f327(f327(f329(x93741),x93742),f327(f173(x93741),x93743)))+~P1(f327(f327(f329(f921(x93741,x93744)),f327(f327(f252(x93741,x93744),x93742),x93745)),f327(f173(f921(x93741,x93744)),f327(f327(f182(x93741,x93744),x93743),x93746)))) % 177.41/177.19 [9480]P1(f327(f327(f234(f922(x94801,a910)),f327(f285(x94802,x94801,x94803),x94804)),x94805))+~P1(f327(f327(f234(f922(f921(x94802,x94801),a910)),x94803),f327(f327(f254(x94802,x94801),x94806),f327(f16(f922(x94801,a910),x94802),x94805)))) % 177.41/177.19 [9485]~P24(x94854,x94852,x94855,f242(f922(x94854,a910)),f242(f922(x94852,a910)))+E(f327(f327(f41(x94851,f922(x94852,a910)),x94853),f327(f327(f8(f922(x94854,a910),f922(x94852,a910),x94851),f310(x94854,x94852,x94855)),x94856)),f327(f310(x94854,x94852,x94855),f327(f327(f41(x94851,f922(x94854,a910)),x94853),x94856))) % 177.41/177.19 [9675]P1(f327(f327(f329(f921(f916(x96751),f916(x96751))),f327(f327(f252(f916(x96751),f916(x96751)),f327(f327(f152(x96751),x96752),x96753)),f327(f327(f152(x96751),x96754),x96755))),f148(x96751,x96756)))+~P1(f327(f327(f329(f921(x96751,x96751)),f327(f327(f252(x96751,x96751),x96752),x96754)),x96756)) % 177.41/177.19 [10132]E(f327(f327(f252(x101321,x101322),f581(x101323,x101324,x101325,x101322,x101321,x101326)),f582(x101323,x101324,x101325,x101322,x101321,x101326)),x101326)+P1(f327(f327(f329(x101325),x101324),f327(f327(f257(x101321,x101322,f922(x101325,a910)),x101323),x101326))) % 177.41/177.19 [10138]E(f327(f327(f252(x101381,x101382),f583(x101383,x101384,x101382,x101381,x101385,x101386)),f584(x101383,x101384,x101382,x101381,x101385,x101386)),x101383)+~P1(f327(f327(f329(x101386),x101385),f327(f327(f257(x101381,x101382,f922(x101386,a910)),x101384),x101383))) % 177.41/177.19 [10304]P1(f327(f327(f329(x103041),x103042),f327(f327(x103043,f583(x103044,x103043,x103045,x103046,x103042,x103041)),f584(x103044,x103043,x103045,x103046,x103042,x103041))))+~P1(f327(f327(f329(x103041),x103042),f327(f327(f257(x103046,x103045,f922(x103041,a910)),x103043),x103044))) % 177.41/177.19 [10329]~P1(f327(f327(f329(x103291),x103292),f327(f327(x103295,f581(x103295,x103292,x103291,x103294,x103293,x103296)),f582(x103295,x103292,x103291,x103294,x103293,x103296))))+P1(f327(f327(f329(x103291),x103292),f327(f327(f257(x103293,x103294,f922(x103291,a910)),x103295),x103296))) % 177.41/177.19 [8616]E(x86161,x86162)+E(f327(f327(f160(x86163,f327(f327(f160(x86163,x86164),x86161),x86165)),x86162),x86166),f327(f327(f160(x86163,f327(f327(f160(x86163,x86164),x86162),x86166)),x86161),x86165)) % 177.41/177.19 [9736]~P1(f327(f327(f329(x97363),x97366),x97365))+E(f327(f327(f309(x97361),x97362),f327(f310(x97363,x97361,x97364),f327(f327(f23(f922(x97363,a910)),x97365),f327(f327(f309(x97363),x97366),f190(f922(x97363,a910)))))),f327(f310(x97363,x97361,f74(x97363,x97361,x97364,x97366,x97362)),x97365)) % 177.41/177.19 [9247]~P1(f327(f327(x92474,x92475),x92476))+P1(f327(f327(f327(f327(f102(f922(x92471,f922(x92472,a910))),x92473),x92474),x92475),x92476)) % 177.41/177.19 [9249]~P1(f327(f327(x92493,x92495),x92496))+P1(f327(f327(f327(f327(f102(f922(x92491,f922(x92492,a910))),x92493),x92494),x92495),x92496)) % 177.41/177.19 [9535]P1(f327(f327(x95351,x95352),x95353))+~P1(f327(f327(f327(f327(f103(f922(x95354,f922(x95355,a910))),x95356),x95351),x95352),x95353)) % 177.41/177.19 [9536]P1(f327(f327(x95361,x95362),x95363))+~P1(f327(f327(f327(f327(f103(f922(x95364,f922(x95365,a910))),x95361),x95366),x95362),x95363)) % 177.41/177.19 [9970]~P68(x99702)+E(f327(f327(f6(x99701,x99702),f327(f327(f7(x99701,f922(x99703,a910),x99702),f327(f327(f8(f922(x99703,x99702),f922(f922(x99703,a910),x99702),x99701),f6(x99703,x99702)),x99704)),x99705)),x99706),f327(f327(f6(f921(x99701,x99703),x99702),f327(f257(x99701,x99703,x99702),x99704)),f327(f327(f254(x99701,x99703),x99706),f327(f16(f922(x99703,a910),x99701),x99705)))) % 177.41/177.19 [9971]~P75(x99712)+E(f327(f327(f9(x99711,x99712),f327(f327(f7(x99711,f922(x99713,a910),x99712),f327(f327(f8(f922(x99713,x99712),f922(f922(x99713,a910),x99712),x99711),f9(x99713,x99712)),x99714)),x99715)),x99716),f327(f327(f9(f921(x99711,x99713),x99712),f327(f257(x99711,x99713,x99712),x99714)),f327(f327(f254(x99711,x99713),x99716),f327(f16(f922(x99713,a910),x99711),x99715)))) % 177.41/177.19 [10104]~P68(x101042)+E(f327(f327(f6(x101041,x101042),f327(f327(f7(x101041,f922(x101043,a910),x101042),f327(f327(f8(f922(x101043,x101042),f922(f922(x101043,a910),x101042),x101041),f6(x101043,x101042)),f327(f7(x101043,x101041,x101042),x101044))),x101045)),x101046),f327(f327(f6(x101043,x101042),f327(f327(f7(x101043,f922(x101041,a910),x101042),f327(f327(f8(f922(x101041,x101042),f922(f922(x101041,a910),x101042),x101043),f6(x101041,x101042)),x101044)),x101046)),x101045)) % 177.41/177.19 [10422]~P1(f327(f327(f329(f921(x104221,x104222)),f327(f327(f252(x104221,x104222),x104225),x104226)),f327(f327(f102(f922(f921(x104221,x104222),a910)),x104223),x104224)))+P1(f327(f327(f327(f327(f102(f922(x104221,f922(x104222,a910))),f327(f327(f7(x104221,f922(f921(x104221,x104222),a910),f922(x104222,a910)),f327(f327(f8(f922(x104222,f922(f922(f921(x104221,x104222),a910),a910)),f922(f922(f921(x104221,x104222),a910),f922(x104222,a910)),x104221),f7(x104222,f922(f921(x104221,x104222),a910),a910)),f327(f327(f8(f922(x104222,f921(x104221,x104222)),f922(x104222,f922(f922(f921(x104221,x104222),a910),a910)),x104221),f327(f8(f921(x104221,x104222),f922(f922(f921(x104221,x104222),a910),a910),x104222),f329(f921(x104221,x104222)))),f252(x104221,x104222)))),x104223)),f327(f327(f7(x104221,f922(f921(x104221,x104222),a910),f922(x104222,a910)),f327(f327(f8(f922(x104222,f922(f922(f921(x104221,x104222),a910),a910)),f922(f922(f921(x104221,x104222),a910),f922(x104222,a910)),x104221),f7(x104222,f922(f921(x104221,x104222),a910),a910)),f327(f327(f8(f922(x104222,f921(x104221,x104222)),f922(x104222,f922(f922(f921(x104221,x104222),a910),a910)),x104221),f327(f8(f921(x104221,x104222),f922(f922(f921(x104221,x104222),a910),a910),x104222),f329(f921(x104221,x104222)))),f252(x104221,x104222)))),x104224)),x104225),x104226)) % 177.41/177.19 [10423]~P1(f327(f327(f329(f921(x104231,x104232)),f327(f327(f252(x104231,x104232),x104235),x104236)),f327(f327(f103(f922(f921(x104231,x104232),a910)),x104233),x104234)))+P1(f327(f327(f327(f327(f103(f922(x104231,f922(x104232,a910))),f327(f327(f7(x104231,f922(f921(x104231,x104232),a910),f922(x104232,a910)),f327(f327(f8(f922(x104232,f922(f922(f921(x104231,x104232),a910),a910)),f922(f922(f921(x104231,x104232),a910),f922(x104232,a910)),x104231),f7(x104232,f922(f921(x104231,x104232),a910),a910)),f327(f327(f8(f922(x104232,f921(x104231,x104232)),f922(x104232,f922(f922(f921(x104231,x104232),a910),a910)),x104231),f327(f8(f921(x104231,x104232),f922(f922(f921(x104231,x104232),a910),a910),x104232),f329(f921(x104231,x104232)))),f252(x104231,x104232)))),x104233)),f327(f327(f7(x104231,f922(f921(x104231,x104232),a910),f922(x104232,a910)),f327(f327(f8(f922(x104232,f922(f922(f921(x104231,x104232),a910),a910)),f922(f922(f921(x104231,x104232),a910),f922(x104232,a910)),x104231),f7(x104232,f922(f921(x104231,x104232),a910),a910)),f327(f327(f8(f922(x104232,f921(x104231,x104232)),f922(x104232,f922(f922(f921(x104231,x104232),a910),a910)),x104231),f327(f8(f921(x104231,x104232),f922(f922(f921(x104231,x104232),a910),a910),x104232),f329(f921(x104231,x104232)))),f252(x104231,x104232)))),x104234)),x104235),x104236)) % 177.41/177.19 [10432]P1(f327(f327(f329(f921(x104321,x104322)),f327(f327(f252(x104321,x104322),x104323),x104324)),f327(f327(f102(f922(f921(x104321,x104322),a910)),x104325),x104326)))+~P1(f327(f327(f327(f327(f102(f922(x104321,f922(x104322,a910))),f327(f327(f7(x104321,f922(f921(x104321,x104322),a910),f922(x104322,a910)),f327(f327(f8(f922(x104322,f922(f922(f921(x104321,x104322),a910),a910)),f922(f922(f921(x104321,x104322),a910),f922(x104322,a910)),x104321),f7(x104322,f922(f921(x104321,x104322),a910),a910)),f327(f327(f8(f922(x104322,f921(x104321,x104322)),f922(x104322,f922(f922(f921(x104321,x104322),a910),a910)),x104321),f327(f8(f921(x104321,x104322),f922(f922(f921(x104321,x104322),a910),a910),x104322),f329(f921(x104321,x104322)))),f252(x104321,x104322)))),x104325)),f327(f327(f7(x104321,f922(f921(x104321,x104322),a910),f922(x104322,a910)),f327(f327(f8(f922(x104322,f922(f922(f921(x104321,x104322),a910),a910)),f922(f922(f921(x104321,x104322),a910),f922(x104322,a910)),x104321),f7(x104322,f922(f921(x104321,x104322),a910),a910)),f327(f327(f8(f922(x104322,f921(x104321,x104322)),f922(x104322,f922(f922(f921(x104321,x104322),a910),a910)),x104321),f327(f8(f921(x104321,x104322),f922(f922(f921(x104321,x104322),a910),a910),x104322),f329(f921(x104321,x104322)))),f252(x104321,x104322)))),x104326)),x104323),x104324)) % 177.41/177.19 [10433]P1(f327(f327(f329(f921(x104331,x104332)),f327(f327(f252(x104331,x104332),x104333),x104334)),f327(f327(f103(f922(f921(x104331,x104332),a910)),x104335),x104336)))+~P1(f327(f327(f327(f327(f103(f922(x104331,f922(x104332,a910))),f327(f327(f7(x104331,f922(f921(x104331,x104332),a910),f922(x104332,a910)),f327(f327(f8(f922(x104332,f922(f922(f921(x104331,x104332),a910),a910)),f922(f922(f921(x104331,x104332),a910),f922(x104332,a910)),x104331),f7(x104332,f922(f921(x104331,x104332),a910),a910)),f327(f327(f8(f922(x104332,f921(x104331,x104332)),f922(x104332,f922(f922(f921(x104331,x104332),a910),a910)),x104331),f327(f8(f921(x104331,x104332),f922(f922(f921(x104331,x104332),a910),a910),x104332),f329(f921(x104331,x104332)))),f252(x104331,x104332)))),x104335)),f327(f327(f7(x104331,f922(f921(x104331,x104332),a910),f922(x104332,a910)),f327(f327(f8(f922(x104332,f922(f922(f921(x104331,x104332),a910),a910)),f922(f922(f921(x104331,x104332),a910),f922(x104332,a910)),x104331),f7(x104332,f922(f921(x104331,x104332),a910),a910)),f327(f327(f8(f922(x104332,f921(x104331,x104332)),f922(x104332,f922(f922(f921(x104331,x104332),a910),a910)),x104331),f327(f8(f921(x104331,x104332),f922(f922(f921(x104331,x104332),a910),a910),x104332),f329(f921(x104331,x104332)))),f252(x104331,x104332)))),x104336)),x104333),x104334)) % 177.41/177.19 [10416]~P1(f327(f327(f329(f921(x104162,x104163)),f327(f327(f252(x104162,x104163),x104165),x104166)),f327(f327(f40(x104161,f922(f921(x104162,x104163),a910)),f242(f922(x104161,a910))),x104164)))+P1(f327(f327(f327(f327(f40(x104161,f922(x104162,f922(x104163,a910))),f242(f922(x104161,a910))),f327(f327(f8(f922(f921(x104162,x104163),a910),f922(x104162,f922(x104163,a910)),x104161),f327(f7(x104162,f922(f921(x104162,x104163),a910),f922(x104163,a910)),f327(f327(f8(f922(x104163,f922(f922(f921(x104162,x104163),a910),a910)),f922(f922(f921(x104162,x104163),a910),f922(x104163,a910)),x104162),f7(x104163,f922(f921(x104162,x104163),a910),a910)),f327(f327(f8(f922(x104163,f921(x104162,x104163)),f922(x104163,f922(f922(f921(x104162,x104163),a910),a910)),x104162),f327(f8(f921(x104162,x104163),f922(f922(f921(x104162,x104163),a910),a910),x104163),f329(f921(x104162,x104163)))),f252(x104162,x104163))))),x104164)),x104165),x104166)) % 177.41/177.19 [10417]~P1(f327(f327(f329(f921(x104172,x104173)),f327(f327(f252(x104172,x104173),x104175),x104176)),f327(f327(f41(x104171,f922(f921(x104172,x104173),a910)),f242(f922(x104171,a910))),x104174)))+P1(f327(f327(f327(f327(f41(x104171,f922(x104172,f922(x104173,a910))),f242(f922(x104171,a910))),f327(f327(f8(f922(f921(x104172,x104173),a910),f922(x104172,f922(x104173,a910)),x104171),f327(f7(x104172,f922(f921(x104172,x104173),a910),f922(x104173,a910)),f327(f327(f8(f922(x104173,f922(f922(f921(x104172,x104173),a910),a910)),f922(f922(f921(x104172,x104173),a910),f922(x104173,a910)),x104172),f7(x104173,f922(f921(x104172,x104173),a910),a910)),f327(f327(f8(f922(x104173,f921(x104172,x104173)),f922(x104173,f922(f922(f921(x104172,x104173),a910),a910)),x104172),f327(f8(f921(x104172,x104173),f922(f922(f921(x104172,x104173),a910),a910),x104173),f329(f921(x104172,x104173)))),f252(x104172,x104173))))),x104174)),x104175),x104176)) % 177.41/177.19 [10426]P1(f327(f327(f329(f921(x104261,x104262)),f327(f327(f252(x104261,x104262),x104263),x104264)),f327(f327(f40(x104265,f922(f921(x104261,x104262),a910)),f242(f922(x104265,a910))),x104266)))+~P1(f327(f327(f327(f327(f40(x104265,f922(x104261,f922(x104262,a910))),f242(f922(x104265,a910))),f327(f327(f8(f922(f921(x104261,x104262),a910),f922(x104261,f922(x104262,a910)),x104265),f327(f7(x104261,f922(f921(x104261,x104262),a910),f922(x104262,a910)),f327(f327(f8(f922(x104262,f922(f922(f921(x104261,x104262),a910),a910)),f922(f922(f921(x104261,x104262),a910),f922(x104262,a910)),x104261),f7(x104262,f922(f921(x104261,x104262),a910),a910)),f327(f327(f8(f922(x104262,f921(x104261,x104262)),f922(x104262,f922(f922(f921(x104261,x104262),a910),a910)),x104261),f327(f8(f921(x104261,x104262),f922(f922(f921(x104261,x104262),a910),a910),x104262),f329(f921(x104261,x104262)))),f252(x104261,x104262))))),x104266)),x104263),x104264)) % 177.41/177.19 [10427]P1(f327(f327(f329(f921(x104271,x104272)),f327(f327(f252(x104271,x104272),x104273),x104274)),f327(f327(f41(x104275,f922(f921(x104271,x104272),a910)),f242(f922(x104275,a910))),x104276)))+~P1(f327(f327(f327(f327(f41(x104275,f922(x104271,f922(x104272,a910))),f242(f922(x104275,a910))),f327(f327(f8(f922(f921(x104271,x104272),a910),f922(x104271,f922(x104272,a910)),x104275),f327(f7(x104271,f922(f921(x104271,x104272),a910),f922(x104272,a910)),f327(f327(f8(f922(x104272,f922(f922(f921(x104271,x104272),a910),a910)),f922(f922(f921(x104271,x104272),a910),f922(x104272,a910)),x104271),f7(x104272,f922(f921(x104271,x104272),a910),a910)),f327(f327(f8(f922(x104272,f921(x104271,x104272)),f922(x104272,f922(f922(f921(x104271,x104272),a910),a910)),x104271),f327(f8(f921(x104271,x104272),f922(f922(f921(x104271,x104272),a910),a910),x104272),f329(f921(x104271,x104272)))),f252(x104271,x104272))))),x104276)),x104273),x104274)) % 177.41/177.19 [7625]E(f327(x76251,f327(x76252,x76253)),f327(x76254,x76253))+~E(f327(f72(x76255,x76256,x76257,x76251),x76252),x76254) % 177.41/177.19 [9752]E(x97521,x97522)+E(f74(x97523,x97524,f74(x97523,x97524,x97525,x97521,x97526),x97522,x97527),f74(x97523,x97524,f74(x97523,x97524,x97525,x97522,x97527),x97521,x97526)) % 177.41/177.19 [9843]~P20(x98433,x98434,x98431,x98435,x98436,x98437)+E(f327(f327(x98431,x98432),x98432),x98432) % 177.41/177.19 [6180]~E(f327(f327(f155(x61801,x61805),x61806),x61802),f327(f327(f155(x61803,x61805),x61807),x61804))+E(f327(f191(f916(x61801)),x61802),f327(f191(f916(x61803)),x61804)) % 177.41/177.19 [8647]E(f327(x86471,f327(x86472,x86473)),f327(x86474,x86473))+~E(f327(f72(x86475,x86476,x86477,x86471),x86472),f327(f72(x86476,x86476,x86477,f31(x86476)),x86474)) % 177.41/177.19 [9001]~P32(x90014,x90015,x90011,f327(f327(f152(x90014),x90012),x90016),f327(f327(f152(x90015),x90013),x90017))+P1(f327(f327(x90011,x90012),x90013)) % 177.41/177.19 [9380]P32(x93801,x93802,x93803,x93804,x93805)+~P32(x93801,x93802,x93803,f327(f327(f152(x93801),x93806),x93804),f327(f327(f152(x93802),x93807),x93805)) % 177.41/177.19 [10004]P1(f327(f327(x100041,x100042),f540(x100043,x100042,x100044,x100041)))+~P1(f327(f327(f253(x100045,x100046,x100047,x100041,x100044),x100042),x100043)) % 177.41/177.19 [10028]P1(f327(f327(x100281,f540(x100282,x100283,x100281,x100284)),x100282))+~P1(f327(f327(f253(x100285,x100286,x100287,x100284,x100281),x100283),x100282)) % 177.41/177.19 [6229]E(x62291,x62292)+~E(f327(f327(f327(f91(x62293),x62294),x62295),x62291),f327(f327(f327(f91(x62293),x62296),x62297),x62292)) % 177.41/177.19 [6230]E(x62301,x62302)+~E(f327(f327(f327(f91(x62303),x62304),x62301),x62305),f327(f327(f327(f91(x62303),x62306),x62302),x62307)) % 177.41/177.19 [6231]E(x62311,x62312)+~E(f327(f327(f327(f91(x62313),x62311),x62314),x62315),f327(f327(f327(f91(x62313),x62312),x62316),x62317)) % 177.41/177.19 [9122]~P18(x91226,x91221,x91223,x91227)+E(f327(f72(x91221,x91221,x91222,f327(x91223,x91224)),f327(f72(x91221,x91221,x91222,f327(x91223,x91224)),x91225)),f327(f72(x91221,x91221,x91222,f327(x91223,x91224)),x91225)) % 177.41/177.19 [9488]~P32(x94883,x94882,x94884,f327(f327(f155(x94881,x94883),x94885),x94886),x94887)+P32(x94881,x94882,f327(f327(f8(x94883,f922(x94882,a910),x94881),x94884),x94885),x94886,x94887) % 177.41/177.19 [9511]P32(x95111,x95112,x95113,f327(f327(f155(x95114,x95111),x95115),x95116),x95117)+~P32(x95114,x95112,f327(f327(f8(x95111,f922(x95112,a910),x95114),x95113),x95115),x95116,x95117) % 177.41/177.19 [9121]~P1(f327(f327(f329(x91211),x91212),f327(f327(x91215,x91216),x91217)))+P1(f327(f327(f329(x91211),x91212),f327(f327(f257(x91213,x91214,f922(x91211,a910)),x91215),f327(f327(f252(x91213,x91214),x91216),x91217)))) % 177.41/177.19 [9405]P1(f327(f327(f327(x94051,x94052),x94053),x94054))+~P1(f327(f327(f327(f257(x94055,x94056,f922(x94057,a910)),x94051),f327(f327(f252(x94055,x94056),x94052),x94053)),x94054)) % 177.41/177.19 [9550]P1(f327(f327(f329(x95501),f327(f327(x95502,x95503),x95504)),f327(f310(f921(x95505,x95506),x95501,f327(f257(x95505,x95506,x95501),x95502)),x95507)))+~P1(f327(f327(f329(f921(x95505,x95506)),f327(f327(f252(x95505,x95506),x95503),x95504)),x95507)) % 177.41/177.19 [9890]P1(f327(f327(f329(f921(f916(x98901),f916(x98901))),f327(f327(f252(f916(x98901),f916(x98901)),f327(f327(f135(x98901),x98902),f327(f327(f152(x98901),x98903),x98904))),f327(f327(f135(x98901),x98902),f327(f327(f152(x98901),x98905),x98906)))),f148(x98901,x98907)))+~P1(f327(f327(f329(f921(x98901,x98901)),f327(f327(f252(x98901,x98901),x98903),x98905)),x98907)) % 177.41/177.19 [9955]~P32(x99551,x99553,x99554,x99556,f327(f327(f155(x99552,x99553),x99555),x99557))+P32(x99551,x99552,f327(f327(f7(x99551,f922(x99552,x99553),f922(x99552,a910)),f327(f327(f8(f922(x99553,a910),f922(f922(x99552,x99553),f922(x99552,a910)),x99551),f8(x99553,a910,x99552)),x99554)),x99555),x99556,x99557) % 177.41/177.19 [10032]P32(x100321,x100322,x100323,x100324,f327(f327(f155(x100325,x100322),x100326),x100327))+~P32(x100321,x100325,f327(f327(f7(x100321,f922(x100325,x100322),f922(x100325,a910)),f327(f327(f8(f922(x100322,a910),f922(f922(x100325,x100322),f922(x100325,a910)),x100321),f8(x100322,a910,x100325)),x100323)),x100326),x100324,x100327) % 177.41/177.19 [10343]P1(f327(f327(f329(x103431),f361(x103432,x103433,x103434,x103435,x103436,x103437,x103431)),x103435))+P1(f327(f327(f327(f327(f41(x103431,f922(x103437,f922(x103436,a910))),x103435),x103434),x103433),x103432)) % 177.41/177.19 [10344]P1(f327(f327(f329(x103441),f782(x103442,x103443,x103444,x103445,x103446,x103447,x103441)),x103447))+P1(f327(f327(f327(f327(f41(x103441,f922(x103443,f922(x103442,a910))),x103447),x103446),x103445),x103444)) % 177.41/177.19 [10345]P1(f327(f327(f329(x103451),f906(x103452,x103453,x103454,x103455,x103456,x103457,x103451)),x103455))+~P1(f327(f327(f327(f327(f40(x103451,f922(x103457,f922(x103456,a910))),x103455),x103454),x103453),x103452)) % 177.41/177.19 [10346]P1(f327(f327(f329(x103461),f783(x103462,x103463,x103464,x103465,x103466,x103467,x103461)),x103465))+~P1(f327(f327(f327(f327(f40(x103461,f922(x103467,f922(x103466,a910))),x103465),x103464),x103463),x103462)) % 177.41/177.19 [10379]P1(f327(f327(f327(x103791,f906(x103792,x103793,x103791,x103794,x103795,x103796,x103797)),x103793),x103792))+~P1(f327(f327(f327(f327(f40(x103797,f922(x103796,f922(x103795,a910))),x103794),x103791),x103793),x103792)) % 177.41/177.19 [10380]P1(f327(f327(f327(x103801,f783(x103802,x103803,x103801,x103804,x103805,x103806,x103807)),x103803),x103802))+~P1(f327(f327(f327(f327(f40(x103807,f922(x103806,f922(x103805,a910))),x103804),x103801),x103803),x103802)) % 177.41/177.19 [10397]~P1(f327(f327(f327(x103975,f361(x103977,x103976,x103975,x103974,x103973,x103972,x103971)),x103976),x103977))+P1(f327(f327(f327(f327(f41(x103971,f922(x103972,f922(x103973,a910))),x103974),x103975),x103976),x103977)) % 177.41/177.19 [10398]~P1(f327(f327(f327(x103985,f782(x103983,x103982,x103987,x103986,x103985,x103984,x103981)),x103986),x103987))+P1(f327(f327(f327(f327(f41(x103981,f922(x103982,f922(x103983,a910))),x103984),x103985),x103986),x103987)) % 177.41/177.19 [10415]~P1(f327(f327(f329(f921(x104151,x104153)),f327(f327(f252(x104151,x104153),x104156),x104157)),f327(f327(f289(x104151,x104152,x104153),x104154),x104155)))+P1(f327(f327(f253(x104151,x104152,x104153,f327(f327(f7(x104151,f922(f921(x104151,x104152),a910),f922(x104152,a910)),f327(f327(f8(f922(x104152,f922(f922(f921(x104151,x104152),a910),a910)),f922(f922(f921(x104151,x104152),a910),f922(x104152,a910)),x104151),f7(x104152,f922(f921(x104151,x104152),a910),a910)),f327(f327(f8(f922(x104152,f921(x104151,x104152)),f922(x104152,f922(f922(f921(x104151,x104152),a910),a910)),x104151),f327(f8(f921(x104151,x104152),f922(f922(f921(x104151,x104152),a910),a910),x104152),f329(f921(x104151,x104152)))),f252(x104151,x104152)))),x104154),f327(f327(f7(x104152,f922(f921(x104152,x104153),a910),f922(x104153,a910)),f327(f327(f8(f922(x104153,f922(f922(f921(x104152,x104153),a910),a910)),f922(f922(f921(x104152,x104153),a910),f922(x104153,a910)),x104152),f7(x104153,f922(f921(x104152,x104153),a910),a910)),f327(f327(f8(f922(x104153,f921(x104152,x104153)),f922(x104153,f922(f922(f921(x104152,x104153),a910),a910)),x104152),f327(f8(f921(x104152,x104153),f922(f922(f921(x104152,x104153),a910),a910),x104153),f329(f921(x104152,x104153)))),f252(x104152,x104153)))),x104155)),x104156),x104157)) % 177.41/177.19 [10425]P1(f327(f327(f329(f921(x104251,x104252)),f327(f327(f252(x104251,x104252),x104253),x104254)),f327(f327(f289(x104251,x104255,x104252),x104256),x104257)))+~P1(f327(f327(f253(x104251,x104255,x104252,f327(f327(f7(x104251,f922(f921(x104251,x104255),a910),f922(x104255,a910)),f327(f327(f8(f922(x104255,f922(f922(f921(x104251,x104255),a910),a910)),f922(f922(f921(x104251,x104255),a910),f922(x104255,a910)),x104251),f7(x104255,f922(f921(x104251,x104255),a910),a910)),f327(f327(f8(f922(x104255,f921(x104251,x104255)),f922(x104255,f922(f922(f921(x104251,x104255),a910),a910)),x104251),f327(f8(f921(x104251,x104255),f922(f922(f921(x104251,x104255),a910),a910),x104255),f329(f921(x104251,x104255)))),f252(x104251,x104255)))),x104256),f327(f327(f7(x104255,f922(f921(x104255,x104252),a910),f922(x104252,a910)),f327(f327(f8(f922(x104252,f922(f922(f921(x104255,x104252),a910),a910)),f922(f922(f921(x104255,x104252),a910),f922(x104252,a910)),x104255),f7(x104252,f922(f921(x104255,x104252),a910),a910)),f327(f327(f8(f922(x104252,f921(x104255,x104252)),f922(x104252,f922(f922(f921(x104255,x104252),a910),a910)),x104255),f327(f8(f921(x104255,x104252),f922(f922(f921(x104255,x104252),a910),a910),x104252),f329(f921(x104255,x104252)))),f252(x104255,x104252)))),x104257)),x104253),x104254)) % 177.41/177.19 [10355]~P139(x103552)+E(f327(f327(f6(x103551,x103552),f327(f327(f7(x103551,f922(x103553,a910),x103552),f327(f327(f8(f922(x103553,x103552),f922(f922(x103553,a910),x103552),x103551),f6(x103553,x103552)),f327(f327(f7(x103551,f922(x103553,x103552),f922(x103553,x103552)),f327(f327(f8(f922(x103552,x103552),f922(f922(x103553,x103552),f922(x103553,x103552)),x103551),f8(x103552,x103552,x103553)),f327(f327(f8(x103552,f922(x103552,x103552),x103551),f81(x103552)),x103554))),x103555))),x103556)),x103557),f327(f327(f81(x103552),f327(f327(f6(x103551,x103552),x103554),x103557)),f327(f327(f6(x103553,x103552),x103555),x103556))) % 177.41/177.19 [9437]~P17(x94377,x94371,x94373,x94378)+E(f327(f72(x94371,x94371,x94372,f327(x94373,x94374)),f327(f72(x94371,x94371,x94372,f327(x94373,x94375)),x94376)),f327(f72(x94371,x94371,x94372,f327(x94373,x94375)),f327(f72(x94371,x94371,x94372,f327(x94373,x94374)),x94376))) % 177.41/177.19 [10420]E(f327(f327(f252(x104201,x104202),f327(x104203,f564(x104204,x104205,x104203,x104206,x104207,x104208,x104202,x104201))),f327(x104205,f565(x104204,x104205,x104203,x104206,x104207,x104208,x104202,x104201))),x104208)+~P1(f327(f327(f329(f921(x104201,x104202)),x104208),f327(f310(f921(x104207,x104206),f921(x104201,x104202),f258(x104207,x104201,x104206,x104202,x104203,x104205)),x104204))) % 177.41/177.19 [10438]~P1(f327(f327(f329(f921(x104388,x104387)),x104386),f327(f310(f921(x104381,x104382),f921(x104388,x104387),f258(x104381,x104388,x104382,x104387,x104385,x104384)),x104383)))+P1(f327(f327(f329(f921(x104381,x104382)),f327(f327(f252(x104381,x104382),f564(x104383,x104384,x104385,x104382,x104381,x104386,x104387,x104388)),f565(x104383,x104384,x104385,x104382,x104381,x104386,x104387,x104388))),x104383)) % 177.41/177.19 [9880]P1(f327(f327(f329(f921(f921(x98801,x98802),f921(x98801,x98802))),f327(f327(f252(f921(x98801,x98802),f921(x98801,x98802)),f327(f327(f252(x98801,x98802),x98803),x98804)),f327(f327(f252(x98801,x98802),x98805),x98806))),f320(x98801,x98802,x98807,x98808)))+~P1(f327(f327(f329(f921(x98801,x98801)),f327(f327(f252(x98801,x98801),x98803),x98805)),x98807)) % 177.41/177.19 [10409]E(f327(f143(x104091,x104092,f327(f7(x104092,x104091,x104091),x104093),f327(x104094,x104095)),x104096),f327(x104094,f327(f143(x104097,x104092,f327(f7(x104092,x104097,x104097),x104098),x104095),x104096)))+P1(f327(f327(f329(x104092),f728(x104095,x104098,x104094,x104093,x104097,x104091,x104096,x104092)),f327(f173(x104092),x104096))) % 177.41/177.19 [10428]~E(f327(f72(x104281,x104281,x104287,f327(x104283,f728(x104285,x104288,x104284,x104283,x104287,x104281,x104286,x104282))),x104284),f327(f72(x104287,x104281,x104287,x104284),f327(x104288,f728(x104285,x104288,x104284,x104283,x104287,x104281,x104286,x104282))))+E(f327(f143(x104281,x104282,f327(f7(x104282,x104281,x104281),x104283),f327(x104284,x104285)),x104286),f327(x104284,f327(f143(x104287,x104282,f327(f7(x104282,x104287,x104287),x104288),x104285),x104286))) % 177.41/177.19 [8652]E(f327(x86521,f327(x86522,x86523)),f327(x86524,f327(x86525,x86523)))+~E(f327(f72(x86526,x86527,x86528,x86521),x86522),f327(f72(x86529,x86527,x86528,x86524),x86525)) % 177.41/177.19 [10267]P1(f327(f327(f329(f921(x102671,x102672)),f327(f327(f252(x102671,x102672),f327(x102673,x102674)),f327(x102675,x102676))),f327(f310(f921(x102677,x102678),f921(x102671,x102672),f258(x102677,x102671,x102678,x102672,x102673,x102675)),x102679)))+~P1(f327(f327(f329(f921(x102677,x102678)),f327(f327(f252(x102677,x102678),x102674),x102676)),x102679)) % 177.41/177.19 [8947]~E(f327(x89474,f327(x89475,x89476)),f327(x89479,f327(x894710,x894711)))+E(f327(f327(f72(x89471,x89472,x89473,x89474),x89475),x89476),f327(f327(f72(x89477,x89472,x89478,x89479),x894710),x894711)) % 177.41/177.19 [4747]~P108(x47471)+~P101(x47471)+E(f189(x47471),f102(x47471)) % 177.41/177.19 [4748]~P108(x47481)+~P102(x47481)+E(f238(x47481),f103(x47481)) % 177.41/177.19 [4997]~P119(x49971)+~P93(x49971)+E(f327(f75(x49971),f327(f105(x49971),a98)),f78(x49971)) % 177.41/177.19 [5284]E(x52841,f2(a1))+E(f82(a1,x52841),f327(f79(a1),f78(a1)))+P1(f327(f327(f235(a1),f2(a1)),x52841)) % 177.41/177.19 [5492]E(x54921,f2(a1))+E(f82(a1,x54921),f78(a1))+~P1(f327(f327(f235(a1),f2(a1)),x54921)) % 177.41/177.19 [7526]~P38(x75261)+P1(f327(f35(a1),x75261))+~P1(f327(f35(a915),f327(f310(a1,a915,a106),x75261))) % 177.41/177.19 [9842]E(x98421,f190(f922(f921(a915,a915),a910)))+~P1(f327(f35(f921(a915,a915)),x98421))+P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),f190(f922(f921(a915,a915),a910))),x98421)),a34)) % 177.41/177.19 [10005]E(x100051,f2(a915))+E(x100051,f327(a113,f2(a915)))+~P1(f327(f327(f235(a915),x100051),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.19 [10299]E(x102991,f2(a100))+E(f327(f327(f80(a1),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(a22,f327(f327(f37(a100),x102991),f327(f105(a100),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))))),f78(a1)),f327(a22,x102991))+E(f46(a100,x102991,f327(f105(a100),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f2(a100)) % 177.41/177.19 [10142]E(x101421,f2(a100))+~E(f46(a100,x101421,f327(f105(a100),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f2(a100))+E(f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(a22,f327(f327(f37(a100),x101421),f327(f105(a100),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f327(a22,x101421)) % 177.41/177.19 [4828]~P55(x48281,x48282)+P42(x48281,x48282)+~P43(a910) % 177.41/177.19 [4757]~P146(x47571)+P26(x47571,x47572)+~E(x47572,f2(x47571)) % 177.41/177.19 [4758]~P108(x47581)+P11(x47581,x47582)+~E(x47582,f114(x47581)) % 177.41/177.19 [4767]~P119(x47671)+~E(x47672,f2(x47671))+E(f82(x47671,x47672),f2(x47671)) % 177.41/177.19 [4768]~P89(x47681)+~E(x47682,f2(x47681))+E(f82(x47681,x47682),f2(x47681)) % 177.41/177.19 [4776]~P146(x47762)+~P26(x47762,x47761)+E(x47761,f2(x47762)) % 177.41/177.19 [4821]~P119(x48212)+~E(f82(x48212,x48211),f2(x48212))+E(x48211,f2(x48212)) % 177.41/177.19 [4835]~P2(x48352)+~P2(x48351)+P2(f922(x48351,x48352)) % 177.41/177.19 [4836]~P2(x48362)+~P2(x48361)+P2(f920(x48361,x48362)) % 177.41/177.19 [4837]~P2(x48372)+~P2(x48371)+P2(f921(x48371,x48372)) % 177.41/177.19 [4838]~P4(x48382)+~P4(x48381)+P4(f196(x48381,x48382)) % 177.41/177.19 [4839]~P60(x48392)+~P60(x48391)+P60(f922(x48391,x48392)) % 177.41/177.19 [4840]~P60(x48402)+~P60(x48401)+P60(f920(x48401,x48402)) % 177.41/177.19 [4841]~P60(x48412)+~P60(x48411)+P60(f921(x48411,x48412)) % 177.41/177.19 [4842]~P104(x48422)+~P104(x48421)+P104(f921(x48421,x48422)) % 177.41/177.19 [4969]~P108(x49691)+~P11(x49691,x49692)+P11(x49691,f153(x49691,x49692)) % 177.41/177.19 [5212]~P4(x52122)+~P4(x52121)+P4(f46(a1,x52121,x52122)) % 177.41/177.19 [4778]~P76(x47781)+~E(x47782,f2(x47781))+E(f327(f79(x47781),x47782),x47782) % 177.41/177.19 [4793]~P142(x47931)+~E(x47932,f2(a1))+E(f327(f104(x47931),x47932),f2(x47931)) % 177.41/177.19 [4794]~P92(x47941)+~E(x47942,f2(a1))+E(f327(f104(x47941),x47942),f2(x47941)) % 177.41/177.19 [4818]~P74(x48181)+~E(f2(x48181),x48182)+E(f327(f79(x48181),x48182),f2(x48181)) % 177.41/177.19 [4819]~P74(x48191)+~E(x48192,f2(x48191))+E(f327(f79(x48191),x48192),f2(x48191)) % 177.41/177.19 [4820]~P84(x48201)+~E(x48202,f2(x48201))+E(f327(f75(x48201),x48202),f2(x48201)) % 177.41/177.19 [4844]~P76(x48442)+E(x48441,f2(x48442))+~E(f327(f79(x48442),x48441),x48441) % 177.41/177.19 [4850]E(x48501,f327(a106,x48502))+~E(x48501,f2(a915))+~E(x48502,f327(f101(a1),x48501)) % 177.41/177.19 [4851]E(f327(a106,x48511),x48512)+~E(x48512,f2(a915))+~E(x48511,f327(f101(a1),x48512)) % 177.41/177.19 [4855]~P92(x48552)+E(x48551,f2(a1))+~E(f327(f104(x48552),x48551),f2(x48552)) % 177.41/177.19 [4859]~P74(x48592)+E(x48591,f2(x48592))+~E(f327(f79(x48592),x48591),f2(x48592)) % 177.41/177.19 [4860]~P84(x48602)+E(x48601,f2(x48602))+~E(f327(f75(x48602),x48601),f2(x48602)) % 177.41/177.19 [4861]~P74(x48611)+E(f2(x48611),x48612)+~E(f327(f79(x48611),x48612),f2(x48611)) % 177.41/177.19 [5044]~P108(x50441)+~P11(x50441,x50442)+P11(x50441,f327(f172(x50441),x50442)) % 177.41/177.19 [5071]~P1(x50712)+~P1(x50711)+P1(f327(f327(a325,x50711),x50712)) % 177.41/177.19 [5105]~E(f78(a915),f2(a915))+E(f327(f36(x51051),x51052),f2(a915))+~P1(f327(f35(x51051),x51052)) % 177.41/177.19 [5141]~P139(x51411)+~P116(x51411)+E(f327(f327(f244(x51411),f2(x51411)),f327(a113,x51412)),f2(x51411)) % 177.41/177.19 [5180]~P108(x51801)+P11(x51801,f140(x51801,x51802))+~P1(f327(f35(x51801),x51802)) % 177.41/177.19 [5181]~P108(x51811)+P11(x51811,f720(x51812,x51811))+~P1(f327(f35(x51811),x51812)) % 177.41/177.19 [5204]~P108(x52041)+E(f327(f173(x52041),f140(x52041,x52042)),x52042)+~P1(f327(f35(x52041),x52042)) % 177.41/177.19 [5205]~P108(x52051)+E(f327(f173(x52051),f720(x52052,x52051)),x52052)+~P1(f327(f35(x52051),x52052)) % 177.41/177.19 [5234]P1(x52341)+P1(x52342)+~P1(f327(f327(a326,x52342),x52341)) % 177.41/177.19 [5247]E(x52471,f190(f922(x52472,a910)))+~E(f327(f36(x52472),x52471),f2(a915))+~P1(f327(f35(x52472),x52471)) % 177.41/177.19 [5252]P1(x52521)+~P1(x52522)+~P1(f327(f327(a330,x52522),x52521)) % 177.41/177.19 [5302]~P73(x53021)+E(f327(f75(x53021),x53022),x53022)+P1(f327(f327(f235(x53021),x53022),f2(x53021))) % 177.41/177.19 [5362]~P60(x53622)+~P1(f327(f57(x53622),x53621))+P1(f327(x53621,f721(x53621,x53622))) % 177.41/177.19 [5363]~P60(x53632)+~P1(f327(f57(x53632),x53631))+P1(f327(x53631,f729(x53631,x53632))) % 177.41/177.19 [5403]E(x54031,f114(x54032))+P1(f327(f138(x54032),f115(x54032,x54031)))+~P1(f327(f138(x54032),x54031)) % 177.41/177.19 [5408]~P108(x54081)+~P1(f327(f35(x54081),x54082))+P1(f327(f138(x54081),f140(x54081,x54082))) % 177.41/177.19 [5409]~P108(x54091)+~P1(f327(f35(x54091),x54092))+P1(f327(f138(x54091),f720(x54092,x54091))) % 177.41/177.19 [5414]~P142(x54141)+E(f327(f101(x54141),f327(a106,x54142)),f327(f104(x54141),x54142))+P1(f327(f327(f235(a1),x54142),f2(a1))) % 177.41/177.19 [5441]P5(x54412,x54411)+E(f327(x54411,f486(x54411)),f327(x54411,f530(x54411)))+P1(f327(f327(x54411,f486(x54411)),f530(x54411))) % 177.41/177.19 [5453]E(f327(f101(a1),f403(x54531,x54532)),x54531)+P1(f327(x54532,f327(a106,x54531)))+~P1(f327(x54532,f2(a915))) % 177.41/177.19 [5466]~P60(x54661)+~P1(f327(x54662,f735(x54662,x54661)))+P1(f327(f58(x54661),x54662)) % 177.41/177.19 [5467]~P60(x54671)+~P1(f327(x54672,f744(x54672,x54671)))+P1(f327(f58(x54671),x54672)) % 177.41/177.19 [5502]~P119(x55021)+~E(f82(x55021,x55022),f327(f79(x55021),f78(x55021)))+P1(f327(f327(f235(x55021),x55022),f2(x55021))) % 177.41/177.19 [5577]~E(x55772,f2(a1))+E(f217(x55771,x55772),f327(f327(f252(a1,a1),f2(a1)),f78(a1)))+P1(f327(f327(f235(a1),x55772),f2(a1))) % 177.41/177.19 [5578]~E(x55781,f2(a1))+E(f217(x55781,x55782),f327(f327(f252(a1,a1),f2(a1)),f78(a1)))+P1(f327(f327(f235(a1),x55782),f2(a1))) % 177.41/177.19 [5631]E(f327(f101(a1),f403(x56311,x56312)),x56311)+P1(f327(x56312,f327(a106,x56311)))+P1(f327(f327(f235(a1),x56311),f2(a1))) % 177.41/177.19 [5700]~P119(x57001)+E(f82(x57001,x57002),f327(f79(x57001),f78(x57001)))+~P1(f327(f327(f235(x57001),x57002),f2(x57001))) % 177.41/177.19 [5701]~P84(x57011)+E(f327(f75(x57011),x57012),f327(f79(x57011),x57012))+~P1(f327(f327(f234(x57011),x57012),f2(x57011))) % 177.41/177.19 [5702]~P84(x57021)+E(f327(f75(x57021),x57022),f327(f79(x57021),x57022))+~P1(f327(f327(f235(x57021),x57022),f2(x57021))) % 177.41/177.19 [5703]~P73(x57031)+E(f327(f75(x57031),x57032),f327(f79(x57031),x57032))+~P1(f327(f327(f235(x57031),x57032),f2(x57031))) % 177.41/177.19 [5803]~P1(f327(x58031,f403(x58032,x58031)))+P1(f327(x58031,f327(a106,x58032)))+~P1(f327(x58031,f2(a915))) % 177.41/177.19 [5810]E(x58101,f2(a915))+E(f327(a113,f362(x58102,x58101)),x58101)+~P1(f327(f327(f235(a915),x58101),f327(a113,x58102))) % 177.41/177.19 [5814]P5(x58141,x58142)+~E(f327(x58142,f486(x58142)),f327(x58142,f530(x58142)))+~P1(f327(f327(x58142,f486(x58142)),f530(x58142))) % 177.41/177.19 [5832]~P108(x58321)+P11(x58321,x58322)+P1(f327(f327(f234(a915),f704(x58322,x58321)),f705(x58322,x58321))) % 177.41/177.19 [5833]~P108(x58331)+P11(x58331,x58332)+P1(f327(f327(f234(a915),f712(x58332,x58331)),f716(x58332,x58331))) % 177.41/177.19 [5919]~P84(x59191)+~E(x59192,f2(x59191))+P1(f327(f327(f234(x59191),f327(f75(x59191),x59192)),f2(x59191))) % 177.41/177.19 [6007]~P1(f327(x60071,f403(x60072,x60071)))+P1(f327(x60071,f327(a106,x60072)))+P1(f327(f327(f235(a1),x60072),f2(a1))) % 177.41/177.19 [6032]~P1(f327(x60321,f327(a106,x60322)))+P1(f327(x60321,f2(a915)))+~P1(f327(f327(f235(a1),x60322),f2(a1))) % 177.41/177.19 [6385]~P119(x63851)+~P1(f327(f327(f235(x63851),x63852),f2(x63851)))+P1(f327(f327(f235(x63851),f82(x63851,x63852)),f2(x63851))) % 177.41/177.19 [6501]~P119(x65011)+P1(f327(f327(f234(x65011),f327(f104(x65011),x65012)),f2(x65011)))+~P1(f327(f327(f234(a1),x65012),f2(a1))) % 177.41/177.19 [6502]~P119(x65021)+P1(f327(f327(f235(x65021),f327(f104(x65021),x65022)),f2(x65021)))+~P1(f327(f327(f235(a1),x65022),f2(a1))) % 177.41/177.19 [6511]~P84(x65112)+E(x65111,f2(x65112))+~P1(f327(f327(f234(x65112),f327(f75(x65112),x65111)),f2(x65112))) % 177.41/177.19 [6586]~P142(x65861)+~P1(f327(f327(f329(x65861),x65862),f111(x65861)))+P1(f327(f327(f329(x65861),f327(f79(x65861),x65862)),f111(x65861))) % 177.41/177.19 [6618]~P119(x66181)+~P1(f327(f327(f235(x66181),f82(x66181,x66182)),f2(x66181)))+P1(f327(f327(f235(x66181),x66182),f2(x66181))) % 177.41/177.19 [6791]~P119(x67912)+~P1(f327(f327(f234(x67912),f327(f104(x67912),x67911)),f2(x67912)))+P1(f327(f327(f234(a1),x67911),f2(a1))) % 177.41/177.19 [6792]~P119(x67922)+~P1(f327(f327(f235(x67922),f327(f104(x67922),x67921)),f2(x67922)))+P1(f327(f327(f235(a1),x67921),f2(a1))) % 177.41/177.19 [7300]~P76(x73001)+~P1(f327(f327(f234(x73001),x73002),f2(x73001)))+P1(f327(f327(f234(x73001),f327(f327(f80(x73001),x73002),x73002)),f2(x73001))) % 177.41/177.19 [7301]~P119(x73011)+~P1(f327(f327(f235(x73011),x73012),f2(x73011)))+P1(f327(f327(f235(x73011),f327(f327(f80(x73011),x73012),x73012)),f2(x73011))) % 177.41/177.19 [7302]~P76(x73021)+~P1(f327(f327(f235(x73021),x73022),f2(x73021)))+P1(f327(f327(f235(x73021),f327(f327(f80(x73021),x73022),x73022)),f2(x73021))) % 177.41/177.19 [7870]~P76(x78701)+~P1(f327(f327(f234(x78701),f327(f327(f80(x78701),x78702),x78702)),f2(x78701)))+P1(f327(f327(f234(x78701),x78702),f2(x78701))) % 177.41/177.19 [7871]~P119(x78711)+~P1(f327(f327(f235(x78711),f327(f327(f80(x78711),x78712),x78712)),f2(x78711)))+P1(f327(f327(f235(x78711),x78712),f2(x78711))) % 177.41/177.19 [7872]~P76(x78721)+~P1(f327(f327(f235(x78721),f327(f327(f80(x78721),x78722),x78722)),f2(x78721)))+P1(f327(f327(f235(x78721),x78722),f2(x78721))) % 177.41/177.19 [4896]~E(x48962,f2(a915))+~E(x48961,f2(a915))+E(f327(f327(f80(a915),x48961),x48962),f2(a915)) % 177.41/177.19 [4897]~E(x48972,f78(a915))+~E(x48971,f78(a915))+E(f327(f327(f81(a915),x48971),x48972),f78(a915)) % 177.41/177.19 [4898]~E(x48982,f78(a1))+~E(x48981,f78(a1))+E(f327(f327(f81(a1),x48981),x48982),f78(a1)) % 177.41/177.19 [4953]~P58(x49532)+E(x49531,f2(x49532))+E(f327(f327(f37(x49532),x49531),x49531),f78(x49532)) % 177.41/177.19 [4954]~P122(x49542)+E(x49541,f2(x49542))+E(f327(f327(f291(x49542),x49541),x49541),f78(x49542)) % 177.41/177.19 [4955]~P123(x49552)+E(x49551,f2(x49552))+E(f327(f327(f291(x49552),x49551),x49551),f78(x49552)) % 177.41/177.19 [4973]~P76(x49731)+~E(x49732,f2(x49731))+E(f327(f327(f80(x49731),x49732),x49732),f2(x49731)) % 177.41/177.19 [4976]~P141(x49761)+~E(x49762,f78(x49761))+E(f327(f327(f81(x49761),x49762),x49762),f78(x49761)) % 177.41/177.19 [4977]~P123(x49771)+~E(x49772,f2(x49771))+E(f327(f327(f291(x49771),x49772),x49772),f2(x49771)) % 177.41/177.19 [5022]~E(x50222,f2(a915))+~E(x50221,f2(a915))+E(f327(f79(a1),f327(f101(a1),x50221)),f327(f101(a1),x50222)) % 177.41/177.19 [5041]E(x50411,f78(a915))+E(x50412,f2(a915))+~E(f327(f327(f81(a915),x50412),x50411),x50412) % 177.41/177.19 [5053]E(x50531,f2(a915))+E(x50532,f2(a915))+~E(f327(f327(f81(a915),x50532),x50531),f2(a915)) % 177.41/177.19 [5080]~E(x50802,f2(a915))+~E(x50801,f327(a113,f2(a915)))+E(f327(f327(f80(a915),x50801),x50802),f327(a113,f2(a915))) % 177.41/177.19 [5081]~E(x50811,f2(a915))+~E(x50812,f327(a113,f2(a915)))+E(f327(f327(f80(a915),x50811),x50812),f327(a113,f2(a915))) % 177.41/177.19 [5088]E(x50881,f78(a1))+E(x50882,f327(f105(a1),a98))+~E(f327(f327(f81(a1),x50881),x50882),f78(a1)) % 177.41/177.19 [5089]E(x50891,f78(a1))+E(x50892,f327(f105(a1),a98))+~E(f327(f327(f81(a1),x50892),x50891),f78(a1)) % 177.41/177.19 [5090]E(x50901,f78(a1))+E(x50901,f327(f105(a1),a98))+~E(f327(f327(f81(a1),x50902),x50901),f78(a1)) % 177.41/177.19 [5092]E(x50921,f78(a1))+E(x50921,f327(f105(a1),a98))+~E(f327(f327(f81(a1),x50921),x50922),f78(a1)) % 177.41/177.19 [5113]~P76(x51132)+E(x51131,f2(x51132))+~E(f327(f327(f80(x51132),x51131),x51131),f2(x51132)) % 177.41/177.19 [5119]~E(x51191,f327(f105(a1),a98))+~E(x51192,f327(f105(a1),a98))+E(f327(f327(f81(a1),x51191),x51192),f78(a1)) % 177.41/177.19 [5130]E(x51301,f2(a915))+E(x51302,f2(a915))+~E(f327(f327(f80(a915),x51302),x51301),f327(a113,f2(a915))) % 177.41/177.19 [5140]~P61(x51401)+~P93(x51401)+E(f327(f327(f291(x51401),x51402),f327(f105(x51401),a83)),f2(x51401)) % 177.41/177.19 [5146]~P141(x51461)+~E(x51462,f327(f79(x51461),f78(x51461)))+E(f327(f327(f81(x51461),x51462),x51462),f78(x51461)) % 177.41/177.19 [5151]~P4(x51512)+~P4(x51511)+P4(f327(f327(f80(a1),x51511),x51512)) % 177.41/177.19 [5152]~P4(x51522)+~P4(x51521)+P4(f327(f327(f81(a1),x51521),x51522)) % 177.41/177.19 [5153]~P4(x51532)+~P4(x51531)+P4(f327(f327(f37(a1),x51531),x51532)) % 177.41/177.19 [5155]~E(x51552,f2(a1))+E(x51551,f2(a1))+E(f47(x51551,x51552),f327(f327(f252(a1,a1),f2(a1)),x51551)) % 177.41/177.19 [5178]~E(x51782,f327(a113,f2(a915)))+~E(x51781,f327(a113,f2(a915)))+E(f327(f327(f81(a915),x51781),x51782),f327(a113,f2(a915))) % 177.41/177.19 [5195]E(x51951,f2(a915))+E(x51952,f327(a113,f2(a915)))+~E(f327(f327(f244(a915),x51952),x51951),f327(a113,f2(a915))) % 177.41/177.19 [5196]E(x51961,f2(a915))+E(x51961,f327(a113,f2(a915)))+~E(f327(f327(f80(a915),x51962),x51961),f327(a113,f2(a915))) % 177.41/177.19 [5197]E(x51971,f2(a915))+E(x51971,f327(a113,f2(a915)))+~E(f327(f327(f80(a915),x51971),x51972),f327(a113,f2(a915))) % 177.41/177.19 [5206]~P61(x52061)+~P93(x52061)+E(f327(f327(f291(x52061),x52062),f327(f105(x52061),a98)),f327(f79(x52061),x52062)) % 177.41/177.19 [5226]E(x52261,f327(a106,x52262))+~E(x52261,f2(a915))+P1(f327(f327(f234(a1),f2(a1)),x52262)) % 177.41/177.19 [5227]E(f327(a106,x52271),x52272)+~E(x52272,f2(a915))+P1(f327(f327(f234(a1),f2(a1)),x52271)) % 177.41/177.19 [5243]E(x52431,f327(a113,f2(a915)))+E(x52432,f327(a113,f2(a915)))+~E(f327(f327(f80(a915),x52431),x52432),f327(a113,f2(a915))) % 177.41/177.19 [5254]~E(x52541,f327(a106,x52542))+E(x52541,f2(a915))+P1(f327(f327(f234(a1),f2(a1)),x52542)) % 177.41/177.19 [5255]~E(f327(a106,x52552),x52551)+E(x52551,f2(a915))+P1(f327(f327(f234(a1),f2(a1)),x52552)) % 177.41/177.19 [5277]~P108(x52771)+E(f327(f63(x52771,f189(x52771)),x52772),f14(x52771,x52772))+~P1(f327(f35(x52771),x52772)) % 177.41/177.19 [5278]~P108(x52781)+E(f327(f63(x52781,f238(x52781)),x52782),f15(x52781,x52782))+~P1(f327(f35(x52781),x52782)) % 177.41/177.19 [5279]~P96(x52791)+E(f327(f63(x52791,f102(x52791)),x52792),f13(x52791,x52792))+~P1(f327(f35(x52791),x52792)) % 177.41/177.19 [5280]~P96(x52801)+E(f327(f63(x52801,f103(x52801)),x52802),f10(x52801,x52802))+~P1(f327(f35(x52801),x52802)) % 177.41/177.19 [5357]E(x53571,x53572)+~E(f327(f327(f23(a915),x53572),x53571),f2(a915))+~E(f327(f327(f23(a915),x53571),x53572),f2(a915)) % 177.41/177.19 [5374]P4(x53741)+~P38(x53742)+~P1(f327(f327(f329(a1),x53741),x53742)) % 177.41/177.19 [5404]~P119(x54041)+~E(f82(x54041,x54042),f78(x54041))+P1(f327(f327(f235(x54041),f2(x54041)),x54042)) % 177.41/177.19 [5415]~P93(x54151)+E(f327(f101(x54151),f327(f105(a915),x54152)),f327(f105(x54151),x54152))+P1(f327(a195,f327(f105(a1),x54152))) % 177.41/177.19 [5420]~P42(x54201,x54202)+P43(a910)+P1(f327(f35(f921(x54201,x54201)),x54202)) % 177.41/177.19 [5494]~P108(x54941)+E(f327(f63(x54941,f189(x54941)),x54942),f11(x54941,f189(x54941),x54942))+~P1(f327(f35(x54941),x54942)) % 177.41/177.19 [5495]~P108(x54951)+E(f327(f63(x54951,f238(x54951)),x54952),f12(x54951,f238(x54951),x54952))+~P1(f327(f35(x54951),x54952)) % 177.41/177.19 [5509]E(x55091,x55092)+P1(f327(f327(f235(a915),x55092),x55091))+P1(f327(f327(f235(a915),x55091),x55092)) % 177.41/177.19 [5510]E(x55101,x55102)+P1(f327(f327(f235(a1),x55102),x55101))+P1(f327(f327(f235(a1),x55101),x55102)) % 177.41/177.19 [5564]~P93(x55641)+E(f327(f101(x55641),f327(f105(a915),x55642)),f2(x55641))+~P1(f327(a195,f327(f105(a1),x55642))) % 177.41/177.19 [5567]~E(x55672,f327(a106,x55671))+E(x55671,f327(f101(a1),x55672))+~P1(f327(f327(f234(a1),f2(a1)),x55671)) % 177.41/177.19 [5568]~E(f327(a106,x55681),x55682)+E(x55681,f327(f101(a1),x55682))+~P1(f327(f327(f234(a1),f2(a1)),x55681)) % 177.41/177.19 [5569]~E(x55691,f327(a106,x55692))+E(f327(f101(a1),x55691),x55692)+~P1(f327(f327(f234(a1),f2(a1)),x55692)) % 177.41/177.19 [5579]E(x55791,f327(a106,x55792))+~E(x55792,f327(f101(a1),x55791))+~P1(f327(f327(f234(a1),f2(a1)),x55792)) % 177.41/177.19 [5580]E(f327(a106,x55801),x55802)+~E(x55801,f327(f101(a1),x55802))+~P1(f327(f327(f234(a1),f2(a1)),x55801)) % 177.41/177.19 [5611]~P112(x56112)+E(x56111,f2(x56112))+~P1(f327(f327(f287(x56112),f2(x56112)),x56111)) % 177.41/177.19 [5622]~P84(x56222)+E(x56221,f2(x56222))+P1(f327(f327(f235(x56222),f2(x56222)),f327(f75(x56222),x56221))) % 177.41/177.19 [5687]~P119(x56871)+E(f82(x56871,x56872),f78(x56871))+~P1(f327(f327(f235(x56871),f2(x56871)),x56872)) % 177.41/177.19 [5693]~P93(x56931)+E(f327(f101(x56931),f327(f105(a915),x56932)),f2(x56931))+P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x56932))) % 177.41/177.19 [5704]~P84(x57041)+E(f327(f75(x57041),x57042),x57042)+~P1(f327(f327(f234(x57041),f2(x57041)),x57042)) % 177.41/177.19 [5705]~P84(x57051)+E(f327(f75(x57051),x57052),x57052)+~P1(f327(f327(f235(x57051),f2(x57051)),x57052)) % 177.41/177.19 [5714]E(x57141,f2(a915))+~E(f140(a915,f327(f302(a915,x57142),x57141)),f114(a915))+P1(f327(f327(f234(a915),x57141),x57142)) % 177.41/177.19 [5724]~P68(x57241)+E(f327(f327(f6(x57241,x57241),f5(x57241)),f327(f173(x57241),x57242)),f327(f166(x57241),x57242))+~P1(f327(f138(x57241),x57242)) % 177.41/177.19 [5727]~P142(x57271)+E(f327(f101(x57271),f327(a106,x57272)),f327(f104(x57271),x57272))+~P1(f327(f327(f234(a1),f2(a1)),x57272)) % 177.41/177.19 [5754]E(x57541,x57542)+P1(f327(f327(f235(a915),x57541),x57542))+~P1(f327(f327(f234(a915),x57541),x57542)) % 177.41/177.19 [5755]E(x57551,x57552)+P1(f327(f327(f235(a1),x57551),x57552))+~P1(f327(f327(f234(a1),x57551),x57552)) % 177.41/177.19 [5758]E(x57581,f78(a1))+~E(f327(f327(f81(a1),x57582),x57581),f78(a1))+~P1(f327(f327(f235(a1),f2(a1)),x57582)) % 177.41/177.19 [5759]E(x57591,f78(a1))+~E(f327(f327(f81(a1),x57591),x57592),f78(a1))+~P1(f327(f327(f235(a1),f2(a1)),x57591)) % 177.41/177.19 [5800]~P38(x58002)+P1(f327(f327(f234(a1),f2(a1)),x58001))+~P1(f327(f327(f329(a1),x58001),x58002)) % 177.41/177.19 [5819]~P55(x58191,x58192)+P35(x58191,x58192)+~P1(f327(f35(f921(x58191,x58191)),x58192)) % 177.41/177.19 [5821]~P55(x58211,x58212)+P42(x58211,x58212)+~P1(f327(f35(f921(x58211,x58211)),x58212)) % 177.41/177.19 [5863]E(x58631,f190(f922(x58632,a910)))+~P1(f327(f35(x58632),x58631))+P1(f327(f327(f235(a915),f2(a915)),f327(f36(x58632),x58631))) % 177.41/177.19 [5890]~P1(f327(x58901,x58902))+P1(f327(x58901,f2(a915)))+P1(f327(f327(f235(a915),f449(x58902,x58901)),x58902)) % 177.41/177.19 [5913]E(x59131,f2(a915))+~E(f327(f166(a915),x59132),f2(a915))+~P1(f327(f327(f329(a915),x59131),f327(f173(a915),x59132))) % 177.41/177.19 [5981]E(x59811,x59812)+~P1(f327(f327(f234(a915),x59812),x59811))+~P1(f327(f327(f234(a915),x59811),x59812)) % 177.41/177.19 [5982]E(x59821,x59822)+~P1(f327(f327(f234(a1),x59822),x59821))+~P1(f327(f327(f234(a1),x59821),x59822)) % 177.41/177.19 [5984]E(f327(f36(x59841),x59842),f2(a915))+~P1(f327(f35(x59841),x59842))+P1(f327(f327(f329(x59841),f487(x59842,x59841)),x59842)) % 177.41/177.19 [5993]E(f51(x59931,x59932),f47(x59931,x59932))+P1(f327(f327(f234(a1),f2(a1)),x59931))+~P1(f327(f327(f235(a1),f2(a1)),x59932)) % 177.41/177.19 [6019]~P1(f327(x60191,f391(x60191)))+P1(f327(x60191,f327(a106,x60192)))+~P1(f327(f327(f234(a1),f2(a1)),x60192)) % 177.41/177.19 [6022]P1(f327(f327(f234(a915),x60221),f883(x60222)))+~P1(f327(f35(a915),x60222))+~P1(f327(f327(f329(a915),x60221),x60222)) % 177.41/177.19 [6023]P1(f327(f327(f235(a915),x60231),f885(x60232)))+~P1(f327(f35(a915),x60232))+~P1(f327(f327(f329(a915),x60231),x60232)) % 177.41/177.19 [6054]E(x60541,x60542)+~P1(f327(f327(f235(a915),x60541),f327(a113,x60542)))+P1(f327(f327(f235(a915),x60541),x60542)) % 177.41/177.19 [6090]E(x60901,f327(a113,x60902))+~P1(f327(f327(f234(a915),x60901),f327(a113,x60902)))+P1(f327(f327(f234(a915),x60901),x60902)) % 177.41/177.19 [6106]P1(f327(x61061,f404(x61061)))+~P1(f327(x61061,f327(a106,x61062)))+~P1(f327(f327(f234(a1),f2(a1)),x61062)) % 177.41/177.19 [6122]~P1(f327(x61221,x61222))+~P1(f327(f327(f234(a1),f2(a1)),x61222))+P1(f327(x61221,f327(f101(a1),f386(x61221)))) % 177.41/177.19 [6133]~P84(x61332)+~E(x61331,f2(x61332))+~P1(f327(f327(f235(x61332),f2(x61332)),f327(f75(x61332),x61331))) % 177.41/177.19 [6158]~P55(x61581,x61582)+P35(x61581,f327(f286(x61581,x61581),x61582))+~P1(f327(f35(f921(x61581,x61581)),x61582)) % 177.41/177.19 [6167]~P93(x61671)+E(f327(f101(x61671),f327(f105(a915),x61672)),f327(f105(x61671),x61672))+~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x61672))) % 177.41/177.19 [6170]E(f327(a113,x61701),x61702)+~P1(f327(f327(f235(a915),x61701),x61702))+P1(f327(f327(f235(a915),f327(a113,x61701)),x61702)) % 177.41/177.19 [6186]E(f327(f327(f37(a1),x61861),x61862),f2(a1))+~P1(f327(f327(f234(a1),x61861),f2(a1)))+~P1(f327(f327(f235(a1),x61862),x61861)) % 177.41/177.19 [6197]E(f46(a1,x61971,x61972),x61971)+~P1(f327(f327(f234(a1),x61971),f2(a1)))+~P1(f327(f327(f235(a1),x61972),x61971)) % 177.41/177.19 [6211]E(f48(x62111,x62112),f47(x62111,x62112))+~P1(f327(f327(f234(a1),f2(a1)),x62111))+~P1(f327(f327(f234(a1),f2(a1)),x62112)) % 177.41/177.19 [6221]E(f327(f327(f37(a1),x62211),x62212),f2(a1))+~P1(f327(f327(f234(a1),f2(a1)),x62211))+~P1(f327(f327(f235(a1),x62211),x62212)) % 177.41/177.19 [6235]E(f46(a915,f327(f105(a915),x62351),f327(f105(a915),x62352)),f327(f105(a915),x62351))+P1(f327(a195,f327(f105(a1),x62351)))+~P1(f327(a195,f327(f105(a1),x62352))) % 177.41/177.19 [6237]E(f46(a1,x62371,x62372),x62371)+~P1(f327(f327(f234(a1),f2(a1)),x62371))+~P1(f327(f327(f235(a1),x62371),x62372)) % 177.41/177.19 [6238]E(x62381,x62382)+~P1(f327(f327(f235(a915),x62381),f327(a113,x62382)))+~P1(f327(f327(f234(a915),x62382),x62381)) % 177.41/177.19 [6252]~P76(x62521)+~P1(f327(f327(f234(x62521),x62522),f2(x62521)))+P1(f327(f327(f234(x62521),x62522),f327(f79(x62521),x62522))) % 177.41/177.19 [6253]~P119(x62531)+~P1(f327(f327(f235(x62531),x62532),f2(x62531)))+P1(f327(f327(f235(x62531),x62532),f327(f79(x62531),x62532))) % 177.41/177.19 [6263]~P3(x62631)+E(f327(f327(f64(x62631,x62631,f103(x62631)),f242(x62631)),x62632),f39(x62631,x62632))+~P1(f327(f35(x62631),x62632)) % 177.41/177.19 [6264]~P3(x62641)+E(f327(f327(f64(x62641,x62641,f102(x62641)),f190(x62641)),x62642),f38(x62641,x62642))+~P1(f327(f35(x62641),x62642)) % 177.41/177.19 [6281]~P119(x62811)+~P1(f327(f327(f234(a1),f2(a1)),x62812))+P1(f327(f327(f234(x62811),f2(x62811)),f327(f104(x62811),x62812))) % 177.41/177.19 [6282]~P126(x62821)+~P1(f327(f327(f235(a915),f2(a915)),x62822))+P1(f327(f327(f235(x62821),f2(x62821)),f327(f101(x62821),x62822))) % 177.41/177.19 [6283]~P119(x62831)+~P1(f327(f327(f235(a1),f2(a1)),x62832))+P1(f327(f327(f235(x62831),f2(x62831)),f327(f104(x62831),x62832))) % 177.41/177.19 [6286]~P4(x62862)+~P4(x62861)+E(f327(f310(a915,a1,f101(a1)),f303(a915,f327(a106,x62861),f327(a106,x62862))),f303(a1,x62861,x62862)) % 177.41/177.19 [6292]P1(f327(x62921,x62922))+~P1(f327(f327(f234(a1),f2(a1)),x62922))+~P1(f327(x62921,f327(f101(a1),f387(x62921)))) % 177.41/177.19 [6323]E(f327(f327(f80(a915),f327(f105(a915),x63231)),f327(f105(a915),x63232)),f327(f105(a915),x63231))+P1(f327(f327(f235(a1),x63231),a83))+~P1(f327(f327(f235(a1),x63232),a83)) % 177.41/177.19 [6327]~P119(x63271)+P1(f327(f327(f235(x63271),f2(x63271)),f82(x63271,x63272)))+~P1(f327(f327(f235(x63271),f2(x63271)),x63272)) % 177.41/177.19 [6340]~P78(x63401)+~P1(f327(f327(f234(x63401),x63402),f2(x63401)))+P1(f327(f327(f234(x63401),f2(x63401)),f327(f79(x63401),x63402))) % 177.41/177.19 [6341]~P78(x63411)+~P1(f327(f327(f235(x63411),x63412),f2(x63411)))+P1(f327(f327(f235(x63411),f2(x63411)),f327(f79(x63411),x63412))) % 177.41/177.19 [6344]E(x63441,f242(f922(x63442,a910)))+~E(f327(f36(x63442),x63441),f327(f36(x63442),f242(f922(x63442,a910))))+~P1(f327(f35(x63442),f242(f922(x63442,a910)))) % 177.41/177.19 [6370]~P1(f327(f327(f235(a915),f2(a915)),x63702))+~P1(f327(f327(f287(a915),x63701),x63702))+P1(f327(f327(f234(a915),x63701),x63702)) % 177.41/177.19 [6377]~P76(x63771)+P1(f327(f327(f234(x63771),x63772),f2(x63771)))+~P1(f327(f327(f234(x63771),x63772),f327(f79(x63771),x63772))) % 177.41/177.19 [6378]~P119(x63781)+P1(f327(f327(f235(x63781),x63782),f2(x63781)))+~P1(f327(f327(f235(x63781),x63782),f327(f79(x63781),x63782))) % 177.41/177.19 [6387]~P93(x63871)+P1(f327(f327(f329(x63871),f327(f105(x63871),x63872)),f187(x63871)))+~P1(f327(f327(f234(a1),a83),x63872)) % 177.41/177.19 [6416]E(x64161,f2(a915))+~P1(f327(f327(f235(a915),x64161),f327(a113,x64162)))+P1(f327(f327(f235(a915),f362(x64162,x64161)),x64162)) % 177.41/177.19 [6439]~P119(x64391)+~P1(f327(f327(f235(x64391),f2(x64391)),f82(x64391,x64392)))+P1(f327(f327(f235(x64391),f2(x64391)),x64392)) % 177.41/177.19 [6441]~E(f327(f105(a915),x64412),f327(f105(a915),x64411))+P1(f327(f327(f234(a1),f327(f105(a1),x64411)),f2(a1)))+~P1(f327(a195,f327(f105(a1),x64412))) % 177.41/177.19 [6470]E(f327(f251(a1,a1),f51(x64701,x64702)),f327(f327(f37(a1),x64701),x64702))+~P1(f327(f327(f235(a1),x64701),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x64702)) % 177.41/177.19 [6509]E(f327(f256(a1,a1),f51(x65091,x65092)),f46(a1,x65091,x65092))+~P1(f327(f327(f235(a1),x65091),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x65092)) % 177.41/177.19 [6512]~P119(x65122)+~P1(f327(f327(f234(x65122),f2(x65122)),f327(f104(x65122),x65121)))+P1(f327(f327(f234(a1),f2(a1)),x65121)) % 177.41/177.19 [6513]~P126(x65132)+~P1(f327(f327(f235(x65132),f2(x65132)),f327(f101(x65132),x65131)))+P1(f327(f327(f235(a915),f2(a915)),x65131)) % 177.41/177.19 [6514]~P119(x65142)+~P1(f327(f327(f235(x65142),f2(x65142)),f327(f104(x65142),x65141)))+P1(f327(f327(f235(a1),f2(a1)),x65141)) % 177.41/177.19 [6517]E(f327(f251(a1,a1),f48(x65171,x65172)),f327(f327(f37(a1),x65171),x65172))+~P1(f327(f327(f234(a1),f2(a1)),x65172))+~P1(f327(f327(f235(a1),f2(a1)),x65171)) % 177.41/177.19 [6531]E(f327(f256(a1,a1),f48(x65311,x65312)),f46(a1,x65311,x65312))+~P1(f327(f327(f234(a1),f2(a1)),x65312))+~P1(f327(f327(f235(a1),f2(a1)),x65311)) % 177.41/177.19 [6547]~P78(x65471)+P1(f327(f327(f234(x65471),x65472),f2(x65471)))+~P1(f327(f327(f234(x65471),f2(x65471)),f327(f79(x65471),x65472))) % 177.41/177.19 [6548]~P78(x65481)+P1(f327(f327(f235(x65481),x65482),f2(x65481)))+~P1(f327(f327(f235(x65481),f2(x65481)),f327(f79(x65481),x65482))) % 177.41/177.19 [6574]P1(f327(f50(x65741,x65742),f51(x65741,x65742)))+~P1(f327(f327(f235(a1),x65741),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x65742)) % 177.41/177.19 [6598]P1(f327(f50(x65981,x65982),f48(x65981,x65982)))+~P1(f327(f327(f234(a1),f2(a1)),x65981))+~P1(f327(f327(f235(a1),f2(a1)),x65982)) % 177.41/177.19 [6641]~P78(x66411)+P1(f327(f327(f234(x66411),f327(f79(x66411),x66412)),f2(x66411)))+~P1(f327(f327(f234(x66411),f2(x66411)),x66412)) % 177.41/177.19 [6642]~P78(x66421)+P1(f327(f327(f235(x66421),f327(f79(x66421),x66422)),f2(x66421)))+~P1(f327(f327(f235(x66421),f2(x66421)),x66422)) % 177.41/177.19 [6660]E(f327(f327(f23(a915),f327(a106,x66601)),f327(a106,x66602)),f327(a106,f196(x66601,x66602)))+~P1(f327(f327(f234(a1),f2(a1)),x66602))+~P1(f327(f327(f234(a1),f2(a1)),x66601)) % 177.41/177.19 [6678]P1(f327(f327(f234(a1),f2(a1)),f196(x66781,x66782)))+~P1(f327(f327(f234(a1),f2(a1)),x66782))+~P1(f327(f327(f234(a1),f2(a1)),x66781)) % 177.41/177.19 [6715]~P1(f327(x67151,x67152))+P1(f327(x67151,f2(a915)))+P1(f327(x67151,f327(f327(f80(a915),f449(x67152,x67151)),f78(a915)))) % 177.41/177.19 [6798]E(f327(f105(a915),x67981),f327(f105(a915),x67982))+~P1(f327(f327(f234(a1),f327(f105(a1),x67982)),f2(a1)))+~P1(f327(a195,f327(f105(a1),x67981))) % 177.41/177.19 [6810]~E(x68101,f2(a915))+~E(f671(x68102,x68101),f2(a915))+E(f327(f143(a915,a915,f80(a915),x68101),x68102),f2(a915)) % 177.41/177.19 [6834]~P1(f327(f35(x68341),f463(x68342,x68341)))+~P1(f327(f35(f922(x68341,a910)),x68342))+P1(f327(f35(x68341),f38(f922(x68341,a910),x68342))) % 177.41/177.19 [6840]E(x68401,x68402)+P1(f327(f327(f235(a1),x68401),x68402))+~P1(f327(f327(f235(a1),x68401),f327(f327(f80(a1),x68402),f78(a1)))) % 177.41/177.19 [6841]P1(f327(f327(f234(a915),f327(a106,x68411)),f327(a106,x68412)))+~P1(f327(f327(f234(a1),f2(a1)),x68412))+~P1(f327(f327(f234(a1),x68411),x68412)) % 177.41/177.19 [6842]P1(f327(f327(f234(a915),f327(a106,x68421)),f327(a106,x68422)))+~P1(f327(f327(f235(a1),f2(a1)),x68421))+~P1(f327(f327(f234(a1),x68421),x68422)) % 177.41/177.19 [6844]P1(f327(f327(f235(a915),f327(a106,x68441)),f327(a106,x68442)))+~P1(f327(f327(f234(a1),f2(a1)),x68441))+~P1(f327(f327(f235(a1),x68441),x68442)) % 177.41/177.19 [6845]P1(f327(f327(f235(a915),f327(a106,x68451)),f327(a106,x68452)))+~P1(f327(f327(f235(a1),f2(a1)),x68452))+~P1(f327(f327(f235(a1),x68451),x68452)) % 177.41/177.19 [6856]E(f46(a915,f327(a106,x68561),f327(a106,x68562)),f327(a106,f46(a1,x68561,x68562)))+~P1(f327(f327(f234(a1),f2(a1)),x68562))+~P1(f327(f327(f234(a1),f2(a1)),x68561)) % 177.41/177.19 [6880]~P78(x68801)+~P1(f327(f327(f234(x68801),f327(f79(x68801),x68802)),f2(x68801)))+P1(f327(f327(f234(x68801),f2(x68801)),x68802)) % 177.41/177.19 [6881]~P78(x68811)+~P1(f327(f327(f235(x68811),f327(f79(x68811),x68812)),f2(x68811)))+P1(f327(f327(f235(x68811),f2(x68811)),x68812)) % 177.41/177.19 [6895]~P1(f327(f327(f235(a1),a83),x68952))+~P1(f327(f327(f235(a1),x68951),x68952))+P1(f327(f327(f235(a915),f327(f105(a915),x68951)),f327(f105(a915),x68952))) % 177.41/177.19 [6987]~P1(f327(f327(f234(a1),f2(a1)),x69871))+P1(f327(f327(f235(a915),f327(a106,x69871)),x69872))+~P1(f327(f327(f235(a1),x69871),f327(f101(a1),x69872))) % 177.41/177.19 [6992]P1(f327(x69921,x69922))+~P1(f327(x69921,f327(a20,f812(x69921,x69922))))+~P1(f327(f327(f329(a915),x69922),f242(f922(a915,a910)))) % 177.41/177.19 [7003]E(x70031,f2(a1))+E(f46(a1,x70032,x70031),f2(a1))+E(f327(f327(f23(a1),f327(f79(a1),f327(f327(f37(a1),x70032),x70031))),f78(a1)),f327(f327(f37(a1),x70032),f327(f79(a1),x70031))) % 177.41/177.19 [7017]~P1(f327(f327(f234(a1),f2(a1)),x70171))+~P1(f327(f327(f235(a915),f327(a106,x70171)),x70172))+P1(f327(f327(f235(a1),x70171),f327(f101(a1),x70172))) % 177.41/177.19 [7053]~P1(f327(f327(f234(a915),f327(a106,x70531)),f327(a106,x70532)))+~P1(f327(f327(f234(a1),f2(a1)),x70532))+P1(f327(f327(f234(a1),x70531),x70532)) % 177.41/177.19 [7054]~P1(f327(f327(f234(a915),f327(a106,x70541)),f327(a106,x70542)))+~P1(f327(f327(f235(a1),f2(a1)),x70541))+P1(f327(f327(f234(a1),x70541),x70542)) % 177.41/177.19 [7084]P1(f327(f327(f234(a1),x70841),x70842))+~P1(f327(f327(f234(a915),f327(f105(a915),x70841)),f327(f105(a915),x70842)))+P1(f327(f327(f234(a1),x70841),a83)) % 177.41/177.19 [7110]P1(f327(f327(f234(a1),f2(a1)),f46(a1,x71101,x71102)))+~P1(f327(f327(f234(a1),f2(a1)),x71102))+~P1(f327(f327(f234(a1),f2(a1)),x71101)) % 177.41/177.19 [7208]P1(f327(f327(f235(a1),a83),x72081))+~P1(f327(f327(f235(a1),x72082),x72081))+~P1(f327(f327(f235(a915),f327(f105(a915),x72082)),f327(f105(a915),x72081))) % 177.41/177.19 [7262]E(f327(f327(f252(a1,a1),f327(f327(f37(a1),x72621),x72622)),f46(a1,x72621,x72622)),f51(x72621,x72622))+~P1(f327(f327(f235(a1),x72621),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x72622)) % 177.41/177.19 [7282]E(f327(f327(f252(a1,a1),f327(f327(f37(a1),x72821),x72822)),f46(a1,x72821,x72822)),f48(x72821,x72822))+~P1(f327(f327(f234(a1),f2(a1)),x72822))+~P1(f327(f327(f234(a1),f2(a1)),x72821)) % 177.41/177.19 [7336]~P95(x73362)+E(x73361,f114(x73362))+E(f327(f143(x73362,x73362,f81(x73362),f327(f142(x73362),x73361)),f327(f172(x73362),x73361)),f327(f63(x73362,f81(x73362)),f327(f173(x73362),x73361))) % 177.41/177.19 [7453]~E(x74531,f2(a915))+E(f327(f143(a915,a915,f80(a915),x74531),x74532),f2(a915))+P1(f327(f327(f329(a915),f671(x74532,x74531)),f327(f173(a915),x74532))) % 177.41/177.19 [7506]~P1(f327(f327(f234(a1),x75061),f2(a1)))+P1(f327(f327(f234(a1),f327(f327(f37(a1),x75061),x75062)),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x75062)) % 177.41/177.19 [7507]~P1(f327(f327(f235(a1),x75072),f2(a1)))+P1(f327(f327(f234(a1),f327(f327(f37(a1),x75071),x75072)),f2(a1)))+~P1(f327(f327(f234(a1),f2(a1)),x75071)) % 177.41/177.19 [7508]~P1(f327(f327(f235(a1),x75082),f2(a1)))+P1(f327(f327(f235(a1),f327(f327(f37(a1),x75081),x75082)),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x75081)) % 177.41/177.19 [7510]~P1(f327(f327(f235(a1),x75101),f2(a1)))+P1(f327(f327(f235(a1),f327(f327(f37(a1),x75101),x75102)),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x75102)) % 177.41/177.19 [7516]P1(f327(f327(f329(f922(x75161,a910)),f463(x75162,x75161)),x75162))+~P1(f327(f35(f922(x75161,a910)),x75162))+P1(f327(f35(x75161),f38(f922(x75161,a910),x75162))) % 177.41/177.19 [7604]P23(x76041,x76041,x76042,f242(f922(x76041,a910)))+~E(f327(f310(x76041,x76041,x76042),f242(f922(x76041,a910))),f242(f922(x76041,a910)))+~P1(f327(f35(x76041),f242(f922(x76041,a910)))) % 177.41/177.19 [7724]~P23(x77241,x77241,x77242,f242(f922(x77241,a910)))+E(f327(f310(x77241,x77241,x77242),f242(f922(x77241,a910))),f242(f922(x77241,a910)))+~P1(f327(f35(x77241),f242(f922(x77241,a910)))) % 177.41/177.19 [7864]E(f327(f327(f37(a1),x78641),x78642),f327(f105(a1),a98))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),x78641),x78642)),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x78641)) % 177.41/177.19 [7920]~P1(f327(f327(f235(a1),x79202),f2(a1)))+~P1(f327(f327(f235(a1),f327(f327(f37(a1),x79201),x79202)),f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x79201)) % 177.41/177.19 [7925]E(f327(f327(f80(a1),x79251),x79252),f46(a1,x79251,x79252))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),x79251),x79252)),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x79251)) % 177.41/177.19 [7928]P1(f327(f327(f235(a1),x79281),f2(a1)))+~P1(f327(f327(f235(a1),f327(f327(f37(a1),x79281),x79282)),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x79282)) % 177.41/177.19 [8621]~P108(x86211)+P11(x86211,x86212)+~P1(f327(f327(f234(x86211),f327(f327(f165(x86211),x86212),f704(x86212,x86211))),f327(f327(f165(x86211),x86212),f705(x86212,x86211)))) % 177.41/177.19 [8622]~P108(x86221)+P11(x86221,x86222)+~P1(f327(f327(f234(x86221),f327(f327(f165(x86221),x86222),f712(x86222,x86221))),f327(f327(f165(x86221),x86222),f716(x86222,x86221)))) % 177.41/177.19 [5856]E(x58561,f2(a1))+~E(f46(a1,x58562,x58561),f2(a1))+E(f327(f327(f37(a1),x58562),f327(f79(a1),x58561)),f327(f79(a1),f327(f327(f37(a1),x58562),x58561))) % 177.41/177.19 [5874]~P38(x58742)+~P38(x58741)+P38(f327(f327(f102(f922(a1,a910)),x58741),x58742)) % 177.41/177.19 [5875]~P38(x58752)+~P38(x58751)+P38(f327(f327(f103(f922(a1,a910)),x58751),x58752)) % 177.41/177.19 [5893]~P61(x58931)+~P93(x58931)+E(f327(f79(x58931),f327(f327(f291(x58931),f78(x58931)),x58932)),f327(f327(f291(x58931),f327(f105(x58931),a98)),x58932)) % 177.41/177.19 [6011]E(x60111,f2(a1))+~E(f46(a1,x60112,x60111),f2(a1))+E(f327(f327(f37(a1),f327(f79(a1),x60112)),x60111),f327(f79(a1),f327(f327(f37(a1),x60112),x60111))) % 177.41/177.19 [6152]~P108(x61521)+P11(x61521,x61522)+P1(f327(f327(f235(a915),f705(x61522,x61521)),f327(f191(f916(x61521)),x61522))) % 177.41/177.19 [6153]~P108(x61531)+P11(x61531,x61532)+P1(f327(f327(f235(a915),f716(x61532,x61531)),f327(f191(f916(x61531)),x61532))) % 177.41/177.19 [6317]~P93(x63171)+~E(f327(f105(x63171),x63172),f2(x63171))+P26(x63171,f327(f105(x63171),f327(f327(f80(a1),x63172),f327(f79(a1),a83)))) % 177.41/177.19 [6318]~P93(x63181)+~E(f327(f105(x63181),x63182),f2(x63181))+P26(x63181,f327(f105(x63181),f327(f327(f80(a1),a83),f327(f79(a1),x63182)))) % 177.41/177.19 [6320]E(f327(a52,f48(f327(f79(a1),x63201),f327(f79(a1),x63202))),f47(x63201,x63202))+P1(f327(f327(f234(a1),f2(a1)),x63201))+P1(f327(f327(f235(a1),f2(a1)),x63202)) % 177.41/177.19 [6447]~E(x64472,f2(a915))+~E(x64471,f2(a915))+P1(f327(f327(f234(a1),f327(f101(a1),x64471)),f327(f79(a1),f327(f101(a1),x64472)))) % 177.41/177.19 [6476]E(f327(f327(f80(a915),f327(f105(a915),x64761)),f327(f105(a915),x64762)),f327(f105(a915),f327(f327(f80(a1),x64761),x64762)))+P1(f327(f327(f235(a1),x64761),a83))+P1(f327(f327(f235(a1),x64762),a83)) % 177.41/177.19 [6607]~P76(x66071)+~P1(f327(f327(f234(x66071),f2(x66071)),x66072))+P1(f327(f327(f234(x66071),f327(f79(x66071),x66072)),x66072)) % 177.41/177.19 [6608]~P76(x66081)+~P1(f327(f327(f235(x66081),f2(x66081)),x66082))+P1(f327(f327(f235(x66081),f327(f79(x66081),x66082)),x66082)) % 177.41/177.19 [6784]E(f327(f327(f23(a915),f327(a106,x67841)),f327(a106,x67842)),f327(a106,f327(f327(f23(a1),x67841),x67842)))+~P1(f327(f327(f234(a1),f2(a1)),x67842))+~P1(f327(f327(f234(a1),x67842),x67841)) % 177.41/177.19 [6818]E(f327(a106,f46(a1,f327(f105(a1),x68181),f327(f105(a1),x68182))),f46(a915,f327(f105(a915),x68181),f327(f105(a915),x68182)))+P1(f327(a195,f327(f105(a1),x68181)))+P1(f327(a195,f327(f105(a1),x68182))) % 177.41/177.19 [6835]~P76(x68351)+P1(f327(f327(f234(x68351),f2(x68351)),x68352))+~P1(f327(f327(f234(x68351),f327(f79(x68351),x68352)),x68352)) % 177.41/177.19 [6836]~P76(x68361)+P1(f327(f327(f235(x68361),f2(x68361)),x68362))+~P1(f327(f327(f235(x68361),f327(f79(x68361),x68362)),x68362)) % 177.41/177.19 [6848]~P76(x68481)+~P1(f327(f327(f234(x68481),f2(x68481)),x68482))+P1(f327(f327(f234(x68481),f2(x68481)),f327(f327(f80(x68481),x68482),x68482))) % 177.41/177.19 [6850]~P76(x68501)+~P1(f327(f327(f235(x68501),f2(x68501)),x68502))+P1(f327(f327(f235(x68501),f2(x68501)),f327(f327(f80(x68501),x68502),x68502))) % 177.41/177.19 [6862]E(f327(f327(f80(a915),f327(a106,x68621)),f327(a106,x68622)),f327(a106,f327(f327(f80(a1),x68621),x68622)))+~P1(f327(f327(f234(a1),f2(a1)),x68622))+~P1(f327(f327(f234(a1),f2(a1)),x68621)) % 177.41/177.19 [6874]E(x68741,f2(a915))+P1(f327(f327(f235(a915),f2(a915)),x68742))+~P1(f327(f327(f235(a915),f2(a915)),f327(f327(f244(a915),x68742),x68741))) % 177.41/177.19 [6907]~P93(x69071)+E(f327(f105(x69071),x69072),f2(x69071))+~P26(x69071,f327(f105(x69071),f327(f327(f80(a1),a83),f327(f79(a1),x69072)))) % 177.41/177.19 [6908]~P93(x69081)+E(f327(f105(x69081),x69082),f2(x69081))+~P26(x69081,f327(f105(x69081),f327(f327(f80(a1),x69082),f327(f79(a1),a83)))) % 177.41/177.19 [6965]~P1(f327(f35(x69651),x69652))+~P1(f327(f35(x69651),f242(f922(x69651,a910))))+P1(f327(f35(x69651),f327(f79(f922(x69651,a910)),x69652))) % 177.41/177.19 [6988]~P1(f327(f327(f235(a1),f2(a1)),x69882))+~P1(f327(f327(f234(a1),x69882),x69881))+P1(f327(f327(f235(a1),f2(a1)),f327(f327(f37(a1),x69881),x69882))) % 177.41/177.19 [6989]~P1(f327(f327(f234(a1),x69891),f2(a1)))+~P1(f327(f327(f235(a1),x69892),f2(a1)))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f37(a1),x69891),x69892))) % 177.41/177.19 [7027]~P1(f327(f327(f234(a1),f2(a1)),x70272))+~P1(f327(f327(f234(a1),f2(a1)),x70271))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),x70271),x70272))) % 177.41/177.19 [7028]~P1(f327(f327(f234(a1),f2(a1)),x70282))+~P1(f327(f327(f234(a1),f2(a1)),x70281))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f81(a1),x70281),x70282))) % 177.41/177.19 [7029]~P1(f327(f327(f234(a1),f2(a1)),x70292))+~P1(f327(f327(f234(a1),f2(a1)),x70291))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f37(a1),x70291),x70292))) % 177.41/177.19 [7030]~P1(f327(f327(f234(a1),f2(a1)),x70301))+~P1(f327(f327(f235(a1),f2(a1)),x70302))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f37(a1),x70301),x70302))) % 177.41/177.19 [7031]~P1(f327(f327(f235(a915),f2(a915)),x70312))+~P1(f327(f327(f235(a915),f2(a915)),x70311))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f81(a915),x70311),x70312))) % 177.41/177.19 [7097]E(x70971,f2(a1))+E(f46(a1,x70972,x70971),f2(a1))+E(f327(f327(f23(a1),f327(f79(a1),f327(f327(f37(a1),x70972),x70971))),f78(a1)),f327(f327(f37(a1),f327(f79(a1),x70972)),x70971)) % 177.41/177.19 [7153]P1(f327(f327(f235(a915),f2(a915)),x71531))+P1(f327(f327(f235(a915),f2(a915)),x71532))+~P1(f327(f327(f235(a915),f2(a915)),f327(f327(f80(a915),x71532),x71531))) % 177.41/177.19 [7157]~P76(x71571)+P1(f327(f327(f234(x71571),f2(x71571)),x71572))+~P1(f327(f327(f234(x71571),f2(x71571)),f327(f327(f80(x71571),x71572),x71572))) % 177.41/177.19 [7158]~P76(x71581)+P1(f327(f327(f235(x71581),f2(x71581)),x71582))+~P1(f327(f327(f235(x71581),f2(x71581)),f327(f327(f80(x71581),x71582),x71582))) % 177.41/177.19 [7209]~P1(f327(f35(x72091),x72092))+P1(f327(f35(x72091),f242(f922(x72091,a910))))+~P1(f327(f35(x72091),f327(f79(f922(x72091,a910)),x72092))) % 177.41/177.19 [7274]P1(f327(f327(f234(a1),x72741),f2(a1)))+~P1(f327(f327(f235(a1),x72742),f2(a1)))+~P1(f327(f327(f234(a1),f2(a1)),f327(f327(f37(a1),x72741),x72742))) % 177.41/177.19 [7280]~P1(f327(f327(f235(a1),f2(a1)),x72801))+P1(f327(f327(f234(a1),x72801),x72802))+~P1(f327(f327(f235(a1),f2(a1)),f327(f327(f37(a1),x72802),x72801))) % 177.41/177.19 [7281]~P1(f327(f327(f234(a1),f2(a1)),x72812))+P1(f327(f327(f234(a1),x72811),x72812))+~P1(f327(f327(f235(a1),f2(a1)),f327(f327(f37(a1),x72812),x72811))) % 177.41/177.19 [7311]P1(f327(f327(f234(a1),f2(a1)),x73111))+~P1(f327(f327(f235(a1),f2(a1)),x73112))+~P1(f327(f327(f234(a1),f2(a1)),f327(f327(f37(a1),x73111),x73112))) % 177.41/177.19 [7312]P1(f327(f327(f235(a1),f2(a1)),x73121))+~P1(f327(f327(f234(a1),f2(a1)),x73122))+~P1(f327(f327(f235(a1),f2(a1)),f327(f327(f37(a1),x73122),x73121))) % 177.41/177.19 [7755]~P1(f327(f35(x77552),f242(f922(x77552,a910))))+~P1(f327(f35(x77551),f242(f922(x77551,a910))))+P1(f327(f35(f920(x77551,x77552)),f242(f922(f920(x77551,x77552),a910)))) % 177.41/177.19 [7756]~P1(f327(f35(x77562),f242(f922(x77562,a910))))+~P1(f327(f35(x77561),f242(f922(x77561,a910))))+P1(f327(f35(f921(x77561,x77562)),f242(f922(f921(x77561,x77562),a910)))) % 177.41/177.19 [7828]~P1(f327(f327(f235(a915),f327(a113,f2(a915))),x78281))+~P1(f327(f327(f235(a915),f327(a113,f2(a915))),x78282))+P1(f327(f327(f235(a915),x78281),f327(f327(f81(a915),x78282),x78281))) % 177.41/177.19 [7829]~P1(f327(f327(f235(a915),f327(a113,f2(a915))),x78291))+~P1(f327(f327(f235(a915),f327(a113,f2(a915))),x78292))+P1(f327(f327(f235(a915),x78291),f327(f327(f81(a915),x78291),x78292))) % 177.41/177.19 [7863]E(f327(f36(x78631),f242(f922(x78631,a910))),f327(a113,f2(a915)))+P1(f327(f35(x78632),f242(f922(x78632,a910))))+~P1(f327(f35(f922(x78632,x78631)),f242(f922(f922(x78632,x78631),a910)))) % 177.41/177.19 [7988]~P1(f327(f327(f234(a915),f327(a113,f2(a915))),x79881))+~P1(f327(f327(f234(a915),f327(a113,f2(a915))),x79882))+P1(f327(f327(f234(a915),f327(a113,f2(a915))),f327(f327(f81(a915),x79881),x79882))) % 177.41/177.19 [7989]~P1(f327(f327(f235(a915),f327(a113,f2(a915))),x79892))+~P1(f327(f327(f235(a915),f327(a113,f2(a915))),x79891))+P1(f327(f327(f235(a915),f327(a113,f2(a915))),f327(f327(f81(a915),x79891),x79892))) % 177.41/177.19 [8668]E(x86681,f114(x86682))+~P1(f327(f138(x86682),x86681))+E(f178(x86682,f327(f327(f8(a910,a910,x86682),a322),f327(f327(f7(x86682,x86682,a910),a324),f145(x86682,x86681))),x86681),f115(x86682,x86681)) % 177.41/177.19 [8763]~P38(x87632)+~P38(x87631)+E(f327(f310(a915,a1,f101(a1)),f327(f327(f102(f922(a915,a910)),f327(f310(a1,a915,a106),x87631)),f327(f310(a1,a915,a106),x87632))),f327(f327(f102(f922(a1,a910)),x87631),x87632)) % 177.41/177.19 [8764]~P38(x87642)+~P38(x87641)+E(f327(f310(a915,a1,f101(a1)),f327(f327(f103(f922(a915,a910)),f327(f310(a1,a915,a106),x87641)),f327(f310(a1,a915,a106),x87642))),f327(f327(f103(f922(a1,a910)),x87641),x87642)) % 177.41/177.19 [9431]~P93(x94311)+~E(f327(f105(x94311),x94312),f78(x94311))+P26(x94311,f327(f105(x94311),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f79(a1),x94312)))) % 177.41/177.19 [9673]~P93(x96731)+E(f327(f105(x96731),x96732),f78(x96731))+~P26(x96731,f327(f105(x96731),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f79(a1),x96732)))) % 177.41/177.19 [10435]E(x104351,f2(a1))+E(x104352,f2(a1))+E(f327(f258(a1,a1,a1,a1,f31(a1),f327(f81(a1),f82(a1,x104352))),f327(f327(f327(f97(f921(a1,a1)),f327(f327(a324,f82(a1,x104351)),f82(a1,x104352))),f54(x104351,x104352)),f327(f327(f257(a1,a1,f921(a1,a1)),f327(f327(f18(a1,f922(a1,f921(a1,a1)),f922(a1,f921(a1,a1))),f327(f327(f8(f922(a1,f922(f921(a1,a1),f921(a1,a1))),f922(f922(a1,f921(a1,a1)),f922(a1,f921(a1,a1))),a1),f18(a1,f921(a1,a1),f921(a1,a1))),f327(f327(f8(f921(a1,a1),f922(a1,f922(f921(a1,a1),f921(a1,a1))),a1),f327(f7(a1,f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),f327(f327(f8(a910,f922(f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),a1),f97(f921(a1,a1))),f327(f327(f7(a1,a1,a910),a324),f2(a1))))),f327(f327(f7(a1,a1,f921(a1,a1)),f327(f327(f8(a1,f922(a1,f921(a1,a1)),a1),f252(a1,a1)),f79(a1))),f2(a1))))),f327(f327(f7(a1,f922(a1,a1),f922(a1,f921(a1,a1))),f327(f327(f8(f922(a1,f921(a1,a1)),f922(f922(a1,a1),f922(a1,f921(a1,a1))),a1),f8(a1,f921(a1,a1),a1)),f327(f327(f8(a1,f922(a1,f921(a1,a1)),a1),f252(a1,a1)),f327(f327(f7(a1,a1,a1),f327(f327(f8(a1,f922(a1,a1),a1),f23(a1)),f79(a1))),f78(a1))))),f327(f23(a1),f327(f75(a1),x104352))))),f54(x104351,x104352)))),f47(x104351,x104352)) % 177.41/177.19 [10436]E(x104361,f2(a1))+E(x104362,f2(a1))+E(f327(f258(a1,a1,a1,a1,f31(a1),f327(f81(a1),f82(a1,x104362))),f327(f327(f327(f97(f921(a1,a1)),f327(f327(a326,f327(f327(a325,f327(f327(f235(a1),f2(a1)),x104362)),f327(f327(f234(a1),f2(a1)),x104361))),f327(f327(a325,f327(f327(f235(a1),x104362),f2(a1))),f327(f327(f235(a1),x104361),f2(a1))))),f54(x104361,x104362)),f327(f327(f257(a1,a1,f921(a1,a1)),f327(f327(f18(a1,f922(a1,f921(a1,a1)),f922(a1,f921(a1,a1))),f327(f327(f8(f922(a1,f922(f921(a1,a1),f921(a1,a1))),f922(f922(a1,f921(a1,a1)),f922(a1,f921(a1,a1))),a1),f18(a1,f921(a1,a1),f921(a1,a1))),f327(f327(f8(f921(a1,a1),f922(a1,f922(f921(a1,a1),f921(a1,a1))),a1),f327(f7(a1,f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),f327(f327(f8(a910,f922(f921(a1,a1),f922(f921(a1,a1),f921(a1,a1))),a1),f97(f921(a1,a1))),f327(f327(f7(a1,a1,a910),a324),f2(a1))))),f327(f327(f7(a1,a1,f921(a1,a1)),f327(f327(f8(a1,f922(a1,f921(a1,a1)),a1),f252(a1,a1)),f79(a1))),f2(a1))))),f327(f327(f7(a1,f922(a1,a1),f922(a1,f921(a1,a1))),f327(f327(f8(f922(a1,f921(a1,a1)),f922(f922(a1,a1),f922(a1,f921(a1,a1))),a1),f8(a1,f921(a1,a1),a1)),f327(f327(f8(a1,f922(a1,f921(a1,a1)),a1),f252(a1,a1)),f327(f327(f7(a1,a1,a1),f327(f327(f8(a1,f922(a1,a1),a1),f23(a1)),f79(a1))),f78(a1))))),f327(f23(a1),f327(f75(a1),x104362))))),f54(x104361,x104362)))),f47(x104361,x104362)) % 177.41/177.19 [5882]~P119(x58821)+~P93(x58821)+E(f327(f75(x58821),f327(f327(f244(x58821),f327(f105(x58821),a98)),x58822)),f78(x58821)) % 177.41/177.19 [6388]~P142(x63881)+~P1(f327(f327(f235(a1),x63882),f2(a1)))+E(f327(f79(x63881),f327(f101(x63881),f327(a106,f327(f79(a1),x63882)))),f327(f104(x63881),x63882)) % 177.41/177.19 [6591]P1(f327(f327(f234(a100),x65911),f78(a100)))+E(f327(f327(f80(a100),f78(a100)),f272(x65911,f327(f327(f37(a100),x65912),x65911))),f272(x65911,x65912))+P1(f327(f327(f235(a100),x65912),x65911)) % 177.41/177.19 [7197]~P92(x71971)+~P1(f327(f327(f329(x71971),x71972),f111(x71971)))+~E(f327(f327(f80(x71971),f327(f327(f80(x71971),f78(x71971)),x71972)),x71972),f2(x71971)) % 177.41/177.19 [7313]~P1(f327(f327(f234(a1),x73132),f2(a1)))+~P1(f327(f327(f235(a1),x73131),f2(a1)))+E(f327(f251(a1,a1),f327(a52,f48(f327(f79(a1),x73131),f327(f79(a1),x73132)))),f327(f327(f37(a1),x73131),x73132)) % 177.41/177.19 [7330]~P1(f327(f327(f234(a1),x73302),f2(a1)))+~P1(f327(f327(f235(a1),x73301),f2(a1)))+E(f327(f256(a1,a1),f327(a52,f48(f327(f79(a1),x73301),f327(f79(a1),x73302)))),f46(a1,x73301,x73302)) % 177.41/177.19 [7338]~P1(f327(f327(f235(a1),x73382),f2(a1)))+E(f327(f251(a1,a1),f327(a52,f51(f327(f79(a1),x73381),f327(f79(a1),x73382)))),f327(f327(f37(a1),x73381),x73382))+~P1(f327(f327(f235(a1),f2(a1)),x73381)) % 177.41/177.19 [7356]~P1(f327(f327(f235(a1),x73562),f2(a1)))+E(f327(f256(a1,a1),f327(a52,f51(f327(f79(a1),x73561),f327(f79(a1),x73562)))),f46(a1,x73561,x73562))+~P1(f327(f327(f235(a1),f2(a1)),x73561)) % 177.41/177.19 [7409]E(f327(f327(f37(a1),f327(f327(f244(a1),x74091),x74092)),x74091),f327(f327(f244(a1),x74091),f327(f327(f23(a915),x74092),f327(a113,f2(a915)))))+~P1(f327(f327(f235(a915),f2(a915)),x74092))+~P1(f327(f327(f235(a1),f2(a1)),x74091)) % 177.41/177.19 [7513]~P1(f327(f327(f235(a915),f2(a915)),x75131))+~P1(f327(f327(f235(a915),f2(a915)),x75132))+P1(f327(f327(f235(a915),f327(f327(f23(a915),x75131),x75132)),x75131)) % 177.41/177.19 [7514]~P1(f327(f327(f235(a915),f2(a915)),x75141))+~P1(f327(f327(f235(a915),f78(a915)),x75142))+P1(f327(f327(f235(a915),f327(f327(f37(a915),x75141),x75142)),x75141)) % 177.41/177.19 [7515]~P1(f327(f327(f235(a1),f2(a1)),x75151))+~P1(f327(f327(f235(a1),f78(a1)),x75152))+P1(f327(f327(f235(a1),f327(f327(f37(a1),x75151),x75152)),x75151)) % 177.41/177.19 [7650]E(x76501,f2(a915))+~E(x76502,f2(a1))+~P1(f327(f327(f235(a1),f2(a1)),f327(f327(f244(a1),f327(f75(a1),x76502)),x76501))) % 177.41/177.19 [8067]~E(x80672,f114(f916(x80671)))+E(f327(f191(f916(f916(x80671))),f180(x80671,x80672)),f2(a915))+~P11(a915,f327(f169(a915),f327(f327(f155(f916(x80671),a915),f191(f916(x80671))),x80672))) % 177.41/177.19 [8320]P1(f327(x83201,x83202))+~P1(f327(x83201,f327(a108,f568(x83201,x83202))))+~P1(f327(f327(f329(f922(f921(a915,a915),a910)),x83202),a99)) % 177.41/177.19 [8336]E(x83361,f114(f916(x83362)))+E(f327(f191(f916(x83362)),f327(f327(f165(f916(x83362)),x83361),f2(a915))),f327(f191(f916(f916(x83362))),f180(x83362,x83361)))+~P11(a915,f327(f169(a915),f327(f327(f155(f916(x83362),a915),f191(f916(x83362))),x83361))) % 177.41/177.19 [8476]~P36(x84761,x84762)+~P37(x84761,x84762)+P36(x84761,f327(f327(f23(f922(f921(x84761,x84761),a910)),x84762),f307(x84761,f190(f922(f921(x84761,x84761),a910))))) % 177.41/177.19 [9048]~P1(f327(f35(x90481),f327(f262(x90481),x90482)))+~P1(f327(f35(x90481),f242(f922(x90481,a910))))+P1(f327(f35(x90481),f327(f262(x90481),f327(f327(f8(a910,a910,x90481),a322),x90482)))) % 177.41/177.19 [9114]E(f327(f327(f252(a915,a915),f327(a113,f327(f327(f37(a915),f327(f327(f23(a915),x91141),x91142)),x91142))),f46(a915,f327(f327(f23(a915),x91141),x91142),x91142)),f85(f921(a915,a915),f49(x91141,x91142)))+~P1(f327(f327(f235(a915),f2(a915)),x91142))+~P1(f327(f327(f234(a915),x91142),x91141)) % 177.41/177.19 [9397]~P1(f327(f35(x93971),f327(f262(x93971),x93972)))+P1(f327(f35(x93971),f242(f922(x93971,a910))))+~P1(f327(f35(x93971),f327(f262(x93971),f327(f327(f8(a910,a910,x93971),a322),x93972)))) % 177.41/177.19 [10115]P25(x101151,x101152)+~P35(x101151,f327(f251(f922(f921(x101151,x101151),a910),f922(f921(x101151,x101151),a910)),x101152))+~P1(f327(f327(f234(f922(f921(x101151,x101151),a910)),f327(f327(f289(x101151,x101151,x101151),f327(f251(f922(f921(x101151,x101151),a910),f922(f921(x101151,x101151),a910)),x101152)),f327(f256(f922(f921(x101151,x101151),a910),f922(f921(x101151,x101151),a910)),x101152))),f327(f251(f922(f921(x101151,x101151),a910),f922(f921(x101151,x101151),a910)),x101152))) % 177.41/177.19 [10212]~E(f297(a915,f287(a915),f327(f327(f18(a915,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),a915),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),a915),f327(f8(a910,f922(a910,a910),a915),a325)),f287(a915)))),f327(f327(f8(f922(a915,a910),f922(a915,a910),a915),f327(f8(a910,a910,a915),a322)),f327(f7(a915,a915,a910),f287(a915)))),x102122,x102121),f190(f922(a915,a910)))+~P1(f327(f327(f287(a915),x102122),x102121))+P1(f327(f327(f287(a915),x102121),x102122)) % 177.41/177.19 [10213]~E(f300(a915,f287(a915),f327(f327(f18(a915,f922(a915,a910),f922(a915,a910)),f327(f327(f8(f922(a915,f922(a910,a910)),f922(f922(a915,a910),f922(a915,a910)),a915),f18(a915,a910,a910)),f327(f327(f8(f922(a915,a910),f922(a915,f922(a910,a910)),a915),f327(f8(a910,f922(a910,a910),a915),a325)),f287(a915)))),f327(f327(f8(f922(a915,a910),f922(a915,a910),a915),f327(f8(a910,a910,a915),a322)),f327(f7(a915,a915,a910),f287(a915)))),x102132,x102131),f190(f922(a915,a910)))+~P1(f327(f327(f287(a915),x102132),x102131))+P1(f327(f327(f287(a915),x102131),x102132)) % 177.41/177.19 [7439]~P1(f327(f327(f235(a915),f2(a915)),x74392))+P1(f327(f327(f235(a915),x74391),x74392))+E(f327(a113,f327(f327(f37(a915),f327(f327(f23(a915),x74391),x74392)),x74392)),f327(f327(f37(a915),x74391),x74392)) % 177.41/177.19 [7576]~P1(f327(f327(f235(a915),f2(a915)),x75762))+~P1(f327(f327(f234(a915),x75762),x75761))+E(f327(a113,f327(f327(f37(a915),f327(f327(f23(a915),x75761),x75762)),x75762)),f327(f327(f37(a915),x75761),x75762)) % 177.41/177.19 [8539]~P93(x85391)+~P92(x85391)+~P26(x85391,f327(f105(x85391),f327(f327(f23(a1),f327(f327(f80(a1),x85392),x85392)),a98))) % 177.41/177.19 [9305]E(x93051,f2(a915))+E(f327(f327(f257(a915,a915,f921(a915,a915)),f327(f327(f8(a915,f922(a915,f921(a915,a915)),a915),f252(a915,a915)),a113)),f85(f921(a915,a915),f49(f327(f327(f23(a915),x93052),x93051),x93051))),f85(f921(a915,a915),f49(x93052,x93051)))+P1(f327(f327(f235(a915),x93052),x93051)) % 177.41/177.19 [9483]~P36(x94831,x94832)+~P49(x94831,x94832)+P1(f327(f327(f234(f922(f921(x94831,x94831),a910)),f327(f327(f289(x94831,x94831,x94831),f327(f286(x94831,x94831),x94832)),x94832)),x94832)) % 177.41/177.19 [9738]P1(f327(x97382,f634(x97382,x97381)))+P1(f327(x97381,f634(x97382,x97381)))+E(f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x97381)),f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x97382))) % 177.41/177.19 [9742]~P1(f327(x97422,f634(x97422,x97421)))+~P1(f327(x97421,f634(x97422,x97421)))+E(f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x97421)),f327(f262(a1),f327(f327(f18(a1,a910,a910),f327(f327(f8(a910,f922(a910,a910),a1),a325),f327(f234(a1),f2(a1)))),x97422))) % 177.41/177.19 [7786]~P62(x77861)+~P93(x77861)+E(f327(f327(f291(x77861),x77862),f327(f105(x77861),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))),x77862) % 177.41/177.19 [9430]~P93(x94301)+~E(f327(f105(x94301),x94302),f78(x94301))+P26(x94301,f327(f105(x94301),f327(f327(f80(a1),x94302),f327(f79(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.19 [9614]~P141(x96141)+~E(x96142,f78(x96141))+E(f327(f327(f244(x96141),x96142),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f78(x96141)) % 177.41/177.19 [9615]~P141(x96151)+~E(x96152,f2(x96151))+E(f327(f327(f244(x96151),x96152),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f2(x96151)) % 177.41/177.19 [9630]~P141(x96301)+~E(x96302,f327(f79(x96301),f78(x96301)))+E(f327(f327(f244(x96301),x96302),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f78(x96301)) % 177.41/177.19 [9674]~P93(x96741)+E(f327(f105(x96741),x96742),f78(x96741))+~P26(x96741,f327(f105(x96741),f327(f327(f80(a1),x96742),f327(f79(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.19 [10058]~P119(x100582)+E(x100581,f2(x100582))+P1(f327(f327(f235(x100582),f2(x100582)),f327(f327(f244(x100582),x100581),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.19 [10114]~P119(x101142)+~E(x101141,f2(x101142))+~P1(f327(f327(f235(x101142),f2(x101142)),f327(f327(f244(x101142),x101141),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.19 [10150]P1(f327(f327(f234(a1),x101501),f2(a1)))+P1(f327(f327(f235(a1),x101502),x101501))+E(f327(f44(x101501),f48(x101502,f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101501))),f48(x101502,x101501)) % 177.41/177.19 [10151]~P1(f327(f327(f235(a1),f2(a1)),x101511))+P1(f327(f327(f235(a1),x101512),x101511))+E(f327(f44(x101511),f48(x101512,f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101511))),f48(x101512,x101511)) % 177.41/177.19 [10152]P1(f327(f327(f234(a1),x101521),f2(a1)))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),x101522),x101521)))+E(f327(f44(x101521),f51(x101522,f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101521))),f51(x101522,x101521)) % 177.41/177.19 [10153]~P1(f327(f327(f235(a1),f2(a1)),x101531))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),x101532),x101531)))+E(f327(f44(x101531),f51(x101532,f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101531))),f51(x101532,x101531)) % 177.41/177.19 [10154]~P146(x101541)+~P1(f327(f327(f234(a1),f2(a1)),x101542))+E(f327(f101(x101541),f327(a106,f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x101542))),f327(f327(f80(x101541),f327(f101(x101541),f327(a106,x101542))),f327(f101(x101541),f327(a106,x101542)))) % 177.41/177.19 [5213]~P147(x52131,x52132,x52133)+~E(x52133,f2(a1))+P1(f327(x52131,x52132)) % 177.41/177.19 [5336]~P108(x53361)+~P11(x53361,x53363)+P11(x53361,f171(x53361,x53362,x53363)) % 177.41/177.19 [5337]~P108(x53371)+~P11(x53371,x53373)+P11(x53371,f178(x53371,x53372,x53373)) % 177.41/177.19 [4906]~P74(x49062)+~E(x49063,f327(f79(x49062),x49061))+E(x49061,f327(f79(x49062),x49063)) % 177.41/177.19 [4908]~P74(x49081)+~E(f327(f79(x49081),x49083),x49082)+E(f327(f79(x49081),x49082),x49083) % 177.41/177.19 [4987]~P74(x49873)+E(x49871,x49872)+~E(f327(f79(x49873),x49871),f327(f79(x49873),x49872)) % 177.41/177.19 [4988]~P86(x49883)+E(x49881,x49882)+~E(f327(f79(x49883),x49881),f327(f79(x49883),x49882)) % 177.41/177.19 [4989]~P108(x49893)+E(x49891,x49892)+~E(f327(f282(x49893),x49891),f327(f282(x49893),x49892)) % 177.41/177.19 [4990]~P103(x49903)+E(x49901,x49902)+~E(f327(f101(x49903),x49901),f327(f101(x49903),x49902)) % 177.41/177.19 [4991]~P92(x49913)+E(x49911,x49912)+~E(f327(f104(x49913),x49911),f327(f104(x49913),x49912)) % 177.41/177.19 [4992]~P108(x49923)+E(x49921,x49922)+~E(f327(f304(x49923),x49921),f327(f304(x49923),x49922)) % 177.41/177.19 [4993]~P108(x49933)+E(x49931,x49932)+~E(f327(f283(x49933),x49931),f327(f283(x49933),x49932)) % 177.41/177.19 [4994]~P108(x49943)+E(x49941,x49942)+~E(f327(f301(x49943),x49941),f327(f301(x49943),x49942)) % 177.41/177.19 [5096]~P60(x50961)+~P1(f327(x50962,x50963))+P1(f327(f57(x50961),x50962)) % 177.41/177.19 [5132]~P60(x51323)+P1(f327(x51321,x51322))+~P1(f327(f58(x51323),x51321)) % 177.41/177.19 [5233]~P148(x52331,x52333,x52332)+~E(x52332,f2(a1))+P1(f327(x52331,f2(a1))) % 177.41/177.19 [5272]~E(x52721,f2(a915))+E(f336(x52721,x52722,x52723),f190(f922(x52723,a910)))+~E(f327(f36(x52723),x52722),f327(a113,x52721)) % 177.41/177.19 [5419]~E(x54192,f2(a915))+E(f327(f251(a915,a915),x54191),f2(a915))+~P1(f327(f49(x54193,x54192),x54191)) % 177.41/177.19 [5463]P1(f327(x54631,x54632))+~E(x54633,f327(f101(a1),x54632))+~P1(f327(x54631,f327(a106,x54633))) % 177.41/177.19 [5946]~E(x59463,f2(a915))+~P1(f327(x59461,x59462))+P1(f327(x59461,f46(a915,x59462,x59463))) % 177.41/177.19 [6181]~P104(x61812)+~P104(x61811)+E(f132(x61811,x61812,f133(x61811,x61813),f133(x61812,x61813)),f133(f921(x61811,x61812),x61813)) % 177.41/177.19 [6369]~E(x63693,f2(a915))+P1(f327(x63691,x63692))+~P1(f327(x63691,f46(a915,x63692,x63693))) % 177.41/177.19 [6860]E(x68601,f190(f922(x68602,a910)))+~P1(f327(f35(x68602),x68601))+P1(f327(f62(x68602,x68603,x68601),f630(x68603,x68601,x68602))) % 177.41/177.19 [7052]E(x70521,f2(a915))+~P1(f327(x70522,f465(x70521,x70523,x70522)))+P1(f327(x70522,f46(a915,x70523,x70521))) % 177.41/177.19 [7163]~P3(x71631)+~P1(f327(f327(f234(x71631),x71632),f339(x71633,x71632,x71631)))+P1(f327(f327(f234(x71631),x71632),f39(x71631,x71633))) % 177.41/177.19 [7165]~P1(f327(x71651,x71652))+~P1(f327(x71651,f465(x71653,x71652,x71651)))+P1(f327(x71651,f46(a915,x71652,x71653))) % 177.41/177.19 [7268]E(x72681,f114(x72682))+E(f327(f327(f152(x72682),f685(x72683,x72681,x72682)),f688(x72683,x72681,x72682)),x72681)+~P1(f327(f327(f329(f916(x72682)),x72681),f162(x72682,x72683))) % 177.41/177.19 [7299]~P142(x72991)+~P1(f327(f327(f329(x72991),x72992),f111(x72991)))+P1(f327(f327(f329(x72991),f327(f327(f244(x72991),x72992),x72993)),f111(x72991))) % 177.41/177.19 [7622]P35(x76221,x76222)+~P1(f327(f327(f329(x76221),x76223),f608(x76222,x76221)))+P1(f327(f327(f329(x76221),f631(x76222,x76221,x76223)),f608(x76222,x76221))) % 177.41/177.19 [7890]E(x78901,f114(x78902))+~P1(f327(f327(f329(f916(x78902)),x78901),f162(x78902,x78903)))+P1(f327(f327(f329(f916(x78902)),f688(x78903,x78901,x78902)),f162(x78902,x78903))) % 177.41/177.19 [7942]E(x79421,f2(a915))+E(f327(f327(f80(a915),f327(f327(f81(a915),x79421),f466(x79421,x79422,x79423))),f465(x79421,x79422,x79423)),x79422)+P1(f327(x79423,f46(a915,x79422,x79421))) % 177.41/177.19 [7983]~P1(f327(x79833,x79832))+E(f327(f327(f80(a915),f327(f327(f81(a915),x79831),f466(x79831,x79832,x79833))),f465(x79831,x79832,x79833)),x79832)+P1(f327(x79833,f46(a915,x79832,x79831))) % 177.41/177.19 [8123]P1(f327(f327(f235(a1),x81231),f459(x81232,x81233,x81231)))+P1(f327(f327(x81233,f327(f327(f37(a1),x81232),x81231)),f46(a1,x81232,x81231)))+~P1(f327(f327(f235(a1),x81231),f2(a1))) % 177.41/177.19 [8391]P1(f327(f327(x83912,f327(f327(f37(a1),x83911),x83913)),f46(a1,x83911,x83913)))+~P1(f327(f327(f235(a1),x83913),f2(a1)))+P1(f327(f327(f234(a1),f459(x83911,x83912,x83913)),f2(a1))) % 177.41/177.19 [8573]E(f327(f327(f80(a1),f327(f327(f81(a1),x85731),f462(x85732,x85733,x85731))),f459(x85732,x85733,x85731)),x85732)+P1(f327(f327(x85733,f327(f327(f37(a1),x85732),x85731)),f46(a1,x85732,x85731)))+~P1(f327(f327(f235(a1),x85731),f2(a1))) % 177.41/177.19 [8811]~P1(f327(f327(x88111,f462(x88112,x88111,x88113)),f459(x88112,x88111,x88113)))+P1(f327(f327(x88111,f327(f327(f37(a1),x88112),x88113)),f46(a1,x88112,x88113)))+~P1(f327(f327(f235(a1),x88113),f2(a1))) % 177.41/177.19 [9061]~P108(x90611)+~P11(x90611,x90613)+P11(x90611,f150(x90611,x90611,f5(x90611),x90612,x90613)) % 177.41/177.19 [9560]~P127(x95602)+E(x95601,f2(x95602))+~P1(f327(f327(f234(x95602),f327(f327(f80(x95602),f327(f327(f81(x95602),x95603),x95603)),f327(f327(f81(x95602),x95601),x95601))),f2(x95602))) % 177.41/177.19 [9561]~P127(x95612)+E(x95611,f2(x95612))+~P1(f327(f327(f234(x95612),f327(f327(f80(x95612),f327(f327(f81(x95612),x95611),x95611)),f327(f327(f81(x95612),x95613),x95613))),f2(x95612))) % 177.41/177.19 [10368]~P119(x103681)+~P1(f327(f327(f235(x103681),x103682),f2(x103681)))+P1(f327(f327(f235(x103681),f327(f327(f244(x103681),x103682),f327(a113,f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x103683)))),f2(x103681))) % 177.41/177.19 [10377]~P119(x103772)+E(x103771,f2(x103772))+~P1(f327(f327(f234(x103772),f327(f327(f80(x103772),f327(f327(f244(x103772),x103773),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x103772),x103771),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f2(x103772))) % 177.41/177.19 [10378]~P119(x103782)+E(x103781,f2(x103782))+~P1(f327(f327(f234(x103782),f327(f327(f80(x103782),f327(f327(f244(x103782),x103781),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x103782),x103783),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f2(x103782))) % 177.41/177.19 [4942]~E(x49422,x49423)+~P67(x49421)+E(f327(f327(f23(x49421),x49422),x49423),f2(x49421)) % 177.41/177.19 [4943]~E(x49432,x49433)+~P74(x49431)+E(f327(f327(f23(x49431),x49432),x49433),f2(x49431)) % 177.41/177.19 [4956]~P144(x49561)+~E(x49563,f2(x49561))+E(f327(f327(f80(x49561),x49562),x49563),x49562) % 177.41/177.19 [4974]~P143(x49741)+~E(x49743,f2(x49741))+E(f327(f327(f81(x49741),x49742),x49743),f2(x49741)) % 177.41/177.19 [4975]~P143(x49751)+~E(x49752,f2(x49751))+E(f327(f327(f81(x49751),x49752),x49753),f2(x49751)) % 177.41/177.19 [4996]~E(x49963,f114(x49961))+~E(x49962,f114(x49961))+E(f327(f327(f135(x49961),x49962),x49963),f114(x49961)) % 177.41/177.19 [5086]~P144(x50862)+E(x50861,f2(x50862))+~E(f327(f327(f80(x50862),x50863),x50861),x50863) % 177.41/177.19 [5087]~P74(x50871)+~E(x50872,f327(f79(x50871),x50873))+E(f327(f327(f80(x50871),x50872),x50873),f2(x50871)) % 177.41/177.19 [5094]E(x50941,f114(x50942))+E(x50943,f2(a915))+~E(f327(f327(f176(x50942),x50943),x50941),f114(x50942)) % 177.41/177.19 [5100]~P67(x51003)+E(x51001,x51002)+~E(f327(f327(f23(x51003),x51001),x51002),f2(x51003)) % 177.41/177.19 [5101]~P74(x51013)+E(x51011,x51012)+~E(f327(f327(f23(x51013),x51011),x51012),f2(x51013)) % 177.41/177.19 [5114]~P141(x51142)+E(x51141,f2(x51142))+~E(f327(f327(f244(x51142),x51141),x51143),f2(x51142)) % 177.41/177.19 [5115]~P98(x51152)+E(x51151,f190(x51152))+~E(f327(f327(f102(x51152),x51153),x51151),f190(x51152)) % 177.41/177.19 [5116]~P98(x51162)+E(x51161,f190(x51162))+~E(f327(f327(f102(x51162),x51161),x51163),f190(x51162)) % 177.41/177.19 [5117]~P97(x51172)+E(x51171,f242(x51172))+~E(f327(f327(f103(x51172),x51173),x51171),f242(x51172)) % 177.41/177.19 [5118]~P97(x51182)+E(x51181,f242(x51182))+~E(f327(f327(f103(x51182),x51181),x51183),f242(x51182)) % 177.41/177.19 [5187]~P74(x51872)+E(x51871,f327(f79(x51872),x51873))+~E(f327(f327(f80(x51872),x51871),x51873),f2(x51872)) % 177.41/177.19 [5188]~P74(x51881)+E(f327(f79(x51881),x51882),x51883)+~E(f327(f327(f80(x51881),x51882),x51883),f2(x51881)) % 177.41/177.19 [5190]~E(x51902,x51903)+~P107(x51901)+P1(f327(f327(f234(x51901),x51902),x51903)) % 177.41/177.19 [5192]~E(x51922,x51923)+~P110(x51921)+P1(f327(f327(f234(x51921),x51922),x51923)) % 177.41/177.19 [5289]~P120(x52891)+~E(x52892,f327(f79(x52891),x52893))+E(f327(f327(f81(x52891),x52892),x52892),f327(f327(f81(x52891),x52893),x52893)) % 177.41/177.19 [5297]~P108(x52971)+~P11(x52971,x52973)+P11(x52971,f327(f327(f176(x52971),x52972),x52973)) % 177.41/177.19 [5298]~P108(x52981)+~P11(x52981,x52983)+P11(x52981,f327(f327(f139(x52981),x52982),x52983)) % 177.41/177.19 [5334]E(x53341,x53342)+E(x53343,f2(a915))+~E(f327(f327(f81(a915),x53343),x53341),f327(f327(f81(a915),x53343),x53342)) % 177.41/177.19 [5335]E(x53351,x53352)+E(x53353,f2(a915))+~E(f327(f327(f81(a915),x53351),x53353),f327(f327(f81(a915),x53352),x53353)) % 177.41/177.19 [5412]~E(x54122,x54123)+~P110(x54121)+E(f303(x54121,x54122,x54123),f327(f327(f309(x54121),x54122),f190(f922(x54121,a910)))) % 177.41/177.19 [5460]~E(x54601,x54602)+~P108(x54603)+~P1(f327(f327(f235(x54603),x54601),x54602)) % 177.41/177.19 [5461]~E(x54611,x54612)+~P110(x54613)+~P1(f327(f327(f235(x54613),x54611),x54612)) % 177.41/177.19 [5474]~P110(x54741)+E(f327(f302(x54741,x54742),x54743),f190(f922(x54741,a910)))+P1(f327(f327(f235(x54741),x54742),x54743)) % 177.41/177.19 [5522]~P110(x55221)+E(f305(x55221,x55222,x55223),f190(f922(x55221,a910)))+P1(f327(f327(f235(x55221),x55222),x55223)) % 177.41/177.19 [5523]~P110(x55231)+E(f303(x55231,x55232,x55233),f190(f922(x55231,a910)))+P1(f327(f327(f234(x55231),x55232),x55233)) % 177.41/177.19 [5524]~P110(x55241)+E(f190(f922(x55241,a910)),f305(x55241,x55242,x55243))+P1(f327(f327(f235(x55241),x55242),x55243)) % 177.41/177.19 [5525]~P110(x55251)+E(f190(f922(x55251,a910)),f303(x55251,x55252,x55253))+P1(f327(f327(f234(x55251),x55252),x55253)) % 177.41/177.19 [5533]~P108(x55331)+~E(f327(f327(f238(x55331),x55332),x55333),x55332)+P1(f327(f327(f234(x55331),x55332),x55333)) % 177.41/177.19 [5534]~P108(x55341)+~E(f327(f327(f189(x55341),x55342),x55343),x55343)+P1(f327(f327(f234(x55341),x55342),x55343)) % 177.41/177.19 [5535]~P101(x55351)+~E(f327(f327(f102(x55351),x55352),x55353),x55353)+P1(f327(f327(f234(x55351),x55352),x55353)) % 177.41/177.19 [5536]~P102(x55361)+~E(f327(f327(f103(x55361),x55362),x55363),x55362)+P1(f327(f327(f234(x55361),x55362),x55363)) % 177.41/177.19 [5555]~P108(x55551)+P11(x55551,x55552)+~P11(x55551,f327(f327(f152(x55551),x55553),x55552)) % 177.41/177.19 [5556]~P108(x55561)+P11(x55561,x55562)+~P11(x55561,f327(f327(f135(x55561),x55563),x55562)) % 177.41/177.19 [5557]~P108(x55571)+P11(x55571,x55572)+~P11(x55571,f327(f327(f135(x55571),x55572),x55573)) % 177.41/177.19 [5562]~P58(x55621)+~E(f46(x55621,x55623,x55622),f2(x55621))+P1(f327(f327(f287(x55621),x55622),x55623)) % 177.41/177.19 [5624]~P108(x56241)+P1(f327(f327(f234(x56241),x56243),x56242))+P1(f327(f327(f234(x56241),x56242),x56243)) % 177.41/177.19 [5629]~P108(x56291)+P1(f327(f327(f235(x56291),x56293),x56292))+P1(f327(f327(f234(x56291),x56292),x56293)) % 177.41/177.19 [5667]~P108(x56671)+E(f327(f327(f238(x56671),x56672),x56673),x56673)+~P1(f327(f327(f234(x56671),x56673),x56672)) % 177.41/177.19 [5669]~P108(x56691)+E(f327(f327(f238(x56691),x56692),x56693),x56692)+~P1(f327(f327(f234(x56691),x56692),x56693)) % 177.41/177.19 [5670]~P108(x56701)+E(f327(f327(f189(x56701),x56702),x56703),x56702)+~P1(f327(f327(f234(x56701),x56703),x56702)) % 177.41/177.19 [5672]~P108(x56721)+E(f327(f327(f189(x56721),x56722),x56723),x56723)+~P1(f327(f327(f234(x56721),x56722),x56723)) % 177.41/177.19 [5673]~P101(x56731)+E(f327(f327(f102(x56731),x56732),x56733),x56732)+~P1(f327(f327(f234(x56731),x56733),x56732)) % 177.41/177.19 [5675]~P101(x56751)+E(f327(f327(f102(x56751),x56752),x56753),x56753)+~P1(f327(f327(f234(x56751),x56752),x56753)) % 177.41/177.19 [5676]~P102(x56761)+E(f327(f327(f103(x56761),x56762),x56763),x56763)+~P1(f327(f327(f234(x56761),x56763),x56762)) % 177.41/177.19 [5678]~P102(x56781)+E(f327(f327(f103(x56781),x56782),x56783),x56782)+~P1(f327(f327(f234(x56781),x56782),x56783)) % 177.41/177.19 [5685]~P122(x56852)+E(x56851,f2(x56852))+E(f327(f327(f291(x56852),f327(f79(x56852),x56853)),f327(f79(x56852),x56851)),f327(f327(f291(x56852),x56853),x56851)) % 177.41/177.19 [5692]~P58(x56921)+E(f46(x56921,x56922,x56923),f2(x56921))+~P1(f327(f327(f287(x56921),x56923),x56922)) % 177.41/177.19 [5738]~P110(x57381)+E(f327(f302(x57381,x57382),x57383),f190(f922(x57381,a910)))+~P1(f327(f327(f234(x57381),x57383),x57382)) % 177.41/177.19 [5771]~P110(x57711)+E(f306(x57711,x57712,x57713),f190(f922(x57711,a910)))+~P1(f327(f327(f234(x57711),x57713),x57712)) % 177.41/177.19 [5772]~P110(x57721)+E(f305(x57721,x57722,x57723),f190(f922(x57721,a910)))+~P1(f327(f327(f234(x57721),x57723),x57722)) % 177.41/177.19 [5773]~P110(x57731)+E(f303(x57731,x57732,x57733),f190(f922(x57731,a910)))+~P1(f327(f327(f235(x57731),x57733),x57732)) % 177.41/177.19 [5825]~E(f327(f327(f23(a915),x58251),x58253),x58252)+E(x58251,f327(f327(f80(a915),x58252),x58253))+~P1(f327(f327(f234(a915),x58253),x58251)) % 177.41/177.19 [5826]~E(x58261,f327(f327(f80(a915),x58263),x58262))+E(f327(f327(f23(a915),x58261),x58262),x58263)+~P1(f327(f327(f234(a915),x58262),x58261)) % 177.41/177.19 [5871]~P1(f327(x58711,x58713))+P1(f327(x58711,f388(x58711,x58712)))+~P1(f327(f327(f235(a915),x58713),x58712)) % 177.41/177.19 [5872]~P1(f327(x58721,x58723))+P1(f327(x58721,f407(x58721,x58722)))+~P1(f327(f327(f234(a915),x58723),x58722)) % 177.41/177.19 [5880]~P110(x58801)+~E(f327(f302(x58801,x58802),x58803),f190(f922(x58801,a910)))+~P1(f327(f327(f235(x58801),x58802),x58803)) % 177.41/177.19 [5885]~P107(x58851)+~P1(f327(f327(f235(x58851),x58852),x58853))+P1(f327(f327(f234(x58851),x58852),x58853)) % 177.41/177.19 [5887]~P110(x58871)+~P1(f327(f327(f235(x58871),x58872),x58873))+P1(f327(f327(f234(x58871),x58872),x58873)) % 177.41/177.19 [5996]~P110(x59961)+~E(f305(x59961,x59962,x59963),f190(f922(x59961,a910)))+~P1(f327(f327(f235(x59961),x59962),x59963)) % 177.41/177.19 [5997]~P110(x59971)+~E(f303(x59971,x59972,x59973),f190(f922(x59971,a910)))+~P1(f327(f327(f234(x59971),x59972),x59973)) % 177.41/177.19 [5998]~P110(x59981)+~E(f190(f922(x59981,a910)),f305(x59981,x59982,x59983))+~P1(f327(f327(f235(x59981),x59982),x59983)) % 177.41/177.19 [5999]~P110(x59991)+~E(f190(f922(x59991,a910)),f303(x59991,x59992,x59993))+~P1(f327(f327(f234(x59991),x59992),x59993)) % 177.41/177.19 [6009]P1(f327(x60091,x60092))+~P1(f327(x60091,f389(x60091,x60093)))+~P1(f327(f327(f235(a915),x60092),x60093)) % 177.41/177.19 [6010]P1(f327(x60101,x60102))+~P1(f327(x60101,f408(x60101,x60103)))+~P1(f327(f327(f234(a915),x60102),x60103)) % 177.41/177.19 [6018]~E(x60181,f327(a113,x60183))+P1(f327(f327(f235(a915),x60181),f327(a113,x60182)))+~P1(f327(f327(f235(a915),x60183),x60182)) % 177.41/177.19 [6037]E(x60371,x60372)+~E(f327(f327(f81(a915),x60373),x60371),f327(f327(f81(a915),x60373),x60372))+~P1(f327(f327(f235(a915),f2(a915)),x60373)) % 177.41/177.19 [6097]E(f327(x60971,f363(x60971,x60972,x60973)),f78(a915))+~E(f327(f327(f6(x60973,a915),x60971),x60972),f78(a915))+~P1(f327(f35(x60973),x60972)) % 177.41/177.19 [6114]~P3(x61141)+P1(f327(f327(f234(x61141),x61142),f38(x61141,x61143)))+~P1(f327(f327(f329(x61141),x61142),x61143)) % 177.41/177.19 [6137]~P107(x61371)+~P1(f327(f327(f235(x61371),x61373),x61372))+~P1(f327(f327(f234(x61371),x61372),x61373)) % 177.41/177.19 [6141]~P107(x61411)+~P1(f327(f327(f235(x61411),x61413),x61412))+~P1(f327(f327(f235(x61411),x61412),x61413)) % 177.41/177.19 [6144]~P108(x61441)+~P1(f327(f327(f235(x61441),x61443),x61442))+~P1(f327(f327(f234(x61441),x61442),x61443)) % 177.41/177.19 [6145]~P108(x61451)+~P1(f327(f327(f235(x61451),x61453),x61452))+~P1(f327(f327(f235(x61451),x61452),x61453)) % 177.41/177.19 [6146]~P110(x61461)+~P1(f327(f327(f235(x61461),x61463),x61462))+~P1(f327(f327(f235(x61461),x61462),x61463)) % 177.41/177.19 [6166]~E(x61662,x61663)+~E(x61661,x61662)+E(f290(a915,f287(a915),x61661,x61662),f327(f327(f309(a915),x61663),f190(f922(a915,a910)))) % 177.41/177.19 [6173]~E(f327(x61732,f364(x61732,x61733,x61731)),f2(a915))+E(f327(f327(f6(x61731,a915),x61732),x61733),f2(a915))+~P1(f327(f35(x61731),x61733)) % 177.41/177.19 [6174]~E(f327(x61742,f886(x61742,x61743,x61741)),f78(a915))+E(f327(f327(f9(x61741,a915),x61742),x61743),f78(a915))+~P1(f327(f35(x61741),x61743)) % 177.41/177.19 [6190]~P109(x61901)+~P1(f327(f327(f235(x61901),x61903),x61902))+P1(f327(f327(f329(x61901),x61902),f327(f304(x61901),x61903))) % 177.41/177.19 [6191]~P109(x61911)+~P1(f327(f327(f234(x61911),x61913),x61912))+P1(f327(f327(f329(x61911),x61912),f327(f283(x61911),x61913))) % 177.41/177.19 [6192]~P109(x61921)+~P1(f327(f327(f235(x61921),x61922),x61923))+P1(f327(f327(f329(x61921),x61922),f327(f282(x61921),x61923))) % 177.41/177.19 [6193]~P109(x61931)+~P1(f327(f327(f234(x61931),x61932),x61933))+P1(f327(f327(f329(x61931),x61932),f327(f301(x61931),x61933))) % 177.41/177.19 [6194]~P114(x61941)+~P1(f327(f327(f287(x61941),x61942),x61943))+P1(f327(f327(f287(x61941),x61942),f327(f79(x61941),x61943))) % 177.41/177.19 [6206]E(f327(x62061,f365(x62061,x62062,x62063)),f327(a113,f2(a915)))+~E(f327(f327(f6(x62063,a915),x62061),x62062),f327(a113,f2(a915)))+~P1(f327(f35(x62063),x62062)) % 177.41/177.19 [6293]~P3(x62931)+~P1(f327(f327(f329(x62931),x62933),x62932))+P1(f327(f327(f234(x62931),f39(x62931,x62932)),x62933)) % 177.41/177.19 [6314]~P1(f327(f327(f234(a915),x63141),x63143))+P1(f327(f327(f234(a915),x63141),x63142))+~P1(f327(f327(f234(a915),x63143),x63142)) % 177.41/177.19 [6315]~P1(f327(f327(f234(a1),x63151),x63153))+P1(f327(f327(f234(a1),x63151),x63152))+~P1(f327(f327(f234(a1),x63153),x63152)) % 177.41/177.19 [6335]~P109(x63351)+~P1(f327(f327(f329(x63351),x63353),f327(f283(x63351),x63352)))+P1(f327(f327(f234(x63351),x63352),x63353)) % 177.41/177.19 [6336]~P109(x63361)+~P1(f327(f327(f329(x63361),x63362),f327(f301(x63361),x63363)))+P1(f327(f327(f234(x63361),x63362),x63363)) % 177.41/177.19 [6337]~P109(x63371)+~P1(f327(f327(f329(x63371),x63373),f327(f304(x63371),x63372)))+P1(f327(f327(f235(x63371),x63372),x63373)) % 177.41/177.19 [6338]~P109(x63381)+~P1(f327(f327(f329(x63381),x63382),f327(f282(x63381),x63383)))+P1(f327(f327(f235(x63381),x63382),x63383)) % 177.41/177.19 [6339]~P114(x63391)+~P1(f327(f327(f287(x63391),x63392),f327(f79(x63391),x63393)))+P1(f327(f327(f287(x63391),x63392),x63393)) % 177.41/177.19 [6413]~P1(f327(x64131,x64132))+P1(f327(x64131,f773(x64131)))+~P1(f327(f327(f329(x64133),x64132),f242(f922(x64133,a910)))) % 177.41/177.19 [6557]~P63(x65571)+P1(f327(f327(f235(x65571),f2(x65571)),f454(x65573,x65572,x65571)))+P1(f327(f327(f234(x65571),x65572),x65573)) % 177.41/177.19 [6558]~P64(x65581)+P1(f327(f327(f235(x65581),f2(x65581)),f763(x65583,x65582,x65581)))+P1(f327(f327(f234(x65581),x65582),x65583)) % 177.41/177.19 [6624]~P78(x66241)+~P1(f327(f327(f234(x66241),x66243),f327(f79(x66241),x66242)))+P1(f327(f327(f234(x66241),x66242),f327(f79(x66241),x66243))) % 177.41/177.19 [6626]~P78(x66261)+~P1(f327(f327(f235(x66261),x66263),f327(f79(x66261),x66262)))+P1(f327(f327(f235(x66261),x66262),f327(f79(x66261),x66263))) % 177.41/177.19 [6638]~P1(f327(f327(f235(a915),x66381),x66383))+~P1(f327(f327(f235(a915),x66383),x66382))+P1(f327(f327(f235(a915),f327(a113,x66381)),x66382)) % 177.41/177.19 [6666]~P126(x66661)+P1(f327(f327(f234(x66661),f327(f101(x66661),x66662)),f327(f101(x66661),x66663)))+~P1(f327(f327(f234(a915),x66662),x66663)) % 177.41/177.19 [6667]~P119(x66671)+P1(f327(f327(f234(x66671),f327(f104(x66671),x66672)),f327(f104(x66671),x66673)))+~P1(f327(f327(f234(a1),x66672),x66673)) % 177.41/177.19 [6669]~P119(x66691)+P1(f327(f327(f235(x66691),f327(f104(x66691),x66692)),f327(f104(x66691),x66693)))+~P1(f327(f327(f235(a1),x66692),x66693)) % 177.41/177.19 [6670]~P126(x66701)+P1(f327(f327(f235(x66701),f327(f101(x66701),x66702)),f327(f101(x66701),x66703)))+~P1(f327(f327(f235(a915),x66702),x66703)) % 177.41/177.19 [6676]~P108(x66761)+E(f327(f327(f102(f922(x66761,a910)),f327(f282(x66761),x66762)),f327(f302(x66761,x66762),x66763)),f327(f282(x66761),x66763))+~P1(f327(f327(f234(x66761),x66762),x66763)) % 177.41/177.19 [6706]~P78(x67061)+~P1(f327(f327(f234(x67061),x67063),x67062))+P1(f327(f327(f234(x67061),f327(f79(x67061),x67062)),f327(f79(x67061),x67063))) % 177.41/177.19 [6708]~P86(x67081)+~P1(f327(f327(f234(x67081),x67083),x67082))+P1(f327(f327(f234(x67081),f327(f79(x67081),x67082)),f327(f79(x67081),x67083))) % 177.41/177.19 [6709]~P78(x67091)+~P1(f327(f327(f235(x67091),x67093),x67092))+P1(f327(f327(f235(x67091),f327(f79(x67091),x67092)),f327(f79(x67091),x67093))) % 177.41/177.19 [6744]~P108(x67441)+E(f327(f327(f102(f922(x67441,a910)),f327(f282(x67441),x67442)),f303(x67441,x67442,x67443)),f327(f301(x67441),x67443))+~P1(f327(f327(f234(x67441),x67442),x67443)) % 177.41/177.19 [6745]~P108(x67451)+E(f327(f327(f102(f922(x67451,a910)),f327(f301(x67451),x67452)),f306(x67451,x67452,x67453)),f327(f282(x67451),x67453))+~P1(f327(f327(f235(x67451),x67452),x67453)) % 177.41/177.19 [6746]~P108(x67461)+E(f327(f327(f102(f922(x67461,a910)),f327(f301(x67461),x67462)),f305(x67461,x67462,x67463)),f327(f301(x67461),x67463))+~P1(f327(f327(f234(x67461),x67462),x67463)) % 177.41/177.19 [6779]~P108(x67791)+E(f327(f327(f102(f922(x67791,a910)),f327(f302(x67791,x67792),x67793)),f327(f283(x67791),x67793)),f327(f283(x67791),x67792))+~P1(f327(f327(f234(x67791),x67792),x67793)) % 177.41/177.19 [6935]~P108(x69351)+E(f327(f327(f102(f922(x69351,a910)),f306(x69351,x69352,x69353)),f327(f283(x69351),x69353)),f327(f304(x69351),x69352))+~P1(f327(f327(f235(x69351),x69352),x69353)) % 177.41/177.19 [6936]~P108(x69361)+E(f327(f327(f102(f922(x69361,a910)),f305(x69361,x69362,x69363)),f327(f304(x69361),x69363)),f327(f304(x69361),x69362))+~P1(f327(f327(f234(x69361),x69362),x69363)) % 177.41/177.19 [6937]~P108(x69371)+E(f327(f327(f102(f922(x69371,a910)),f303(x69371,x69372,x69373)),f327(f304(x69371),x69373)),f327(f283(x69371),x69372))+~P1(f327(f327(f234(x69371),x69372),x69373)) % 177.41/177.19 [6956]P1(f327(x69561,x69562))+~P1(f327(f327(f234(a915),x69562),x69563))+P1(f327(f327(f329(a915),f408(x69561,x69563)),f303(a915,f2(a915),x69563))) % 177.41/177.19 [6990]E(x69901,x69902)+~E(f327(f327(f165(x69903),x69901),f632(x69903,x69902,x69901)),f327(f327(f165(x69903),x69902),f632(x69903,x69902,x69901)))+~E(f327(f191(f916(x69903)),x69901),f327(f191(f916(x69903)),x69902)) % 177.41/177.19 [6995]~E(x69953,f327(f327(f37(a915),x69951),x69952))+~P1(f327(f327(f235(a915),f2(a915)),x69952))+P1(f327(f327(f235(a915),x69951),f327(f327(f81(a915),x69952),f327(a113,x69953)))) % 177.41/177.19 [7011]~P1(f327(x70111,x70113))+~P1(f327(f327(f234(a915),x70113),x70112))+P1(f327(f327(f329(a915),f407(x70111,x70112)),f303(a915,f2(a915),x70112))) % 177.41/177.19 [7050]~P1(f327(x70501,x70503))+P1(f327(x70501,f416(x70501,x70502)))+~P1(f327(f327(f329(a915),x70503),f303(a915,f2(a915),x70502))) % 177.41/177.19 [7069]~P126(x70693)+~P1(f327(f327(f234(x70693),f327(f101(x70693),x70691)),f327(f101(x70693),x70692)))+P1(f327(f327(f234(a915),x70691),x70692)) % 177.41/177.19 [7070]~P119(x70703)+~P1(f327(f327(f234(x70703),f327(f104(x70703),x70701)),f327(f104(x70703),x70702)))+P1(f327(f327(f234(a1),x70701),x70702)) % 177.41/177.19 [7072]~P126(x70723)+~P1(f327(f327(f235(x70723),f327(f101(x70723),x70721)),f327(f101(x70723),x70722)))+P1(f327(f327(f235(a915),x70721),x70722)) % 177.41/177.19 [7073]~P119(x70733)+~P1(f327(f327(f235(x70733),f327(f104(x70733),x70731)),f327(f104(x70733),x70732)))+P1(f327(f327(f235(a1),x70731),x70732)) % 177.41/177.19 [7090]~P126(x70901)+~P1(f327(f327(f235(x70901),f78(x70901)),x70902))+P1(f327(f327(f235(x70901),f78(x70901)),f327(f327(f244(x70901),x70902),f327(a113,x70903)))) % 177.41/177.19 [7093]~P78(x70931)+~P1(f327(f327(f234(x70931),f327(f79(x70931),x70933)),f327(f79(x70931),x70932)))+P1(f327(f327(f234(x70931),x70932),x70933)) % 177.41/177.19 [7094]~P86(x70941)+~P1(f327(f327(f234(x70941),f327(f79(x70941),x70943)),f327(f79(x70941),x70942)))+P1(f327(f327(f234(x70941),x70942),x70943)) % 177.41/177.19 [7095]~P78(x70951)+~P1(f327(f327(f235(x70951),f327(f79(x70951),x70953)),f327(f79(x70951),x70952)))+P1(f327(f327(f235(x70951),x70952),x70953)) % 177.41/177.19 [7119]P1(f327(x71191,x71192))+~P1(f327(x71191,f410(x71191,x71193)))+~P1(f327(f327(f329(a915),x71192),f303(a915,f2(a915),x71193))) % 177.41/177.19 [7139]~P63(x71391)+P1(f327(f327(f235(x71391),f454(x71393,x71392,x71391)),f78(x71391)))+P1(f327(f327(f234(x71391),x71392),x71393)) % 177.41/177.19 [7160]~E(f46(a915,x71603,x71602),f46(a915,x71601,x71602))+E(f327(f327(f80(a915),x71601),f327(f327(f81(a915),x71602),f488(x71601,x71602,x71603))),x71603)+~P1(f327(f327(f234(a915),x71601),x71603)) % 177.41/177.19 [7216]E(f327(f327(f6(x72161,a915),x72162),x72163),f2(a915))+~P1(f327(f35(x72161),x72163))+P1(f327(f327(f329(x72161),f364(x72162,x72163,x72161)),x72163)) % 177.41/177.19 [7217]E(f327(f327(f9(x72171,a915),x72172),x72173),f78(a915))+~P1(f327(f35(x72171),x72173))+P1(f327(f327(f329(x72171),f886(x72172,x72173,x72171)),x72173)) % 177.41/177.19 [7239]~P108(x72391)+~P1(f327(f327(f234(x72391),x72392),x72393))+P1(f327(f327(f234(f922(x72391,a910)),f327(f282(x72391),x72392)),f327(f282(x72391),x72393))) % 177.41/177.19 [7240]~P108(x72401)+~P1(f327(f327(f234(x72401),x72403),x72402))+P1(f327(f327(f234(f922(x72401,a910)),f327(f304(x72401),x72402)),f327(f304(x72401),x72403))) % 177.41/177.19 [7241]~P110(x72411)+~P1(f327(f327(f234(x72411),x72413),x72412))+P1(f327(f327(f234(f922(x72411,a910)),f327(f283(x72411),x72412)),f327(f283(x72411),x72413))) % 177.41/177.19 [7242]~P110(x72421)+~P1(f327(f327(f234(x72421),x72422),x72423))+P1(f327(f327(f234(f922(x72421,a910)),f327(f301(x72421),x72422)),f327(f301(x72421),x72423))) % 177.41/177.19 [7243]~P108(x72431)+~P1(f327(f327(f235(x72431),x72432),x72433))+P1(f327(f327(f235(f922(x72431,a910)),f327(f282(x72431),x72432)),f327(f282(x72431),x72433))) % 177.41/177.19 [7254]~P3(x72541)+P1(f327(f327(f234(x72541),x72542),f39(x72541,x72543)))+P1(f327(f327(f329(x72541),f339(x72543,x72542,x72541)),x72543)) % 177.41/177.19 [7260]~P78(x72601)+P1(f327(f327(f234(x72601),f327(f327(f23(x72601),x72602),x72603)),f2(x72601)))+~P1(f327(f327(f234(x72601),x72602),x72603)) % 177.41/177.19 [7261]~P78(x72611)+P1(f327(f327(f235(x72611),f327(f327(f23(x72611),x72612),x72613)),f2(x72611)))+~P1(f327(f327(f235(x72611),x72612),x72613)) % 177.41/177.19 [7303]P1(f327(x73031,x73032))+P1(f327(f327(f234(a915),f410(x73031,x73033)),x73033))+~P1(f327(f327(f329(a915),x73032),f303(a915,f2(a915),x73033))) % 177.41/177.19 [7345]~E(f327(f327(f6(x73451,a915),x73452),x73453),f78(a915))+~P1(f327(f35(x73451),x73453))+P1(f327(f327(f329(x73451),f363(x73452,x73453,x73451)),x73453)) % 177.41/177.19 [7346]~P1(f327(x73461,x73463))+P1(f327(f327(f234(a915),f416(x73461,x73462)),x73462))+~P1(f327(f327(f329(a915),x73463),f303(a915,f2(a915),x73462))) % 177.41/177.19 [7386]~P3(x73861)+P1(f327(f327(f329(x73861),f467(x73863,x73862,x73861)),x73862))+P1(f327(f327(f234(x73861),f38(x73861,x73862)),x73863)) % 177.41/177.19 [7420]~E(f327(f327(f6(x74201,a915),x74202),x74203),f327(a113,f2(a915)))+~P1(f327(f35(x74201),x74203))+P1(f327(f327(f329(x74201),f365(x74202,x74203,x74201)),x74203)) % 177.41/177.19 [7431]E(x74311,f2(a915))+P1(f327(x74312,f46(a915,x74313,x74311)))+P1(f327(f327(f235(a915),f465(x74311,x74313,x74312)),x74311)) % 177.41/177.19 [7542]~P1(f327(x75421,x75422))+P1(f327(x75421,f46(a915,x75422,x75423)))+P1(f327(f327(f235(a915),f465(x75423,x75422,x75421)),x75423)) % 177.41/177.19 [7654]E(x76541,f114(x76542))+~P1(f327(f327(f329(f916(x76542)),x76541),f162(x76542,x76543)))+P1(f327(f327(f329(x76542),f685(x76543,x76541,x76542)),x76543)) % 177.41/177.19 [7676]~P108(x76761)+E(f327(f327(f102(f922(x76761,a910)),f327(f327(f309(x76761),x76762),f190(f922(x76761,a910)))),f306(x76761,x76762,x76763)),f327(f302(x76761,x76762),x76763))+~P1(f327(f327(f235(x76761),x76762),x76763)) % 177.41/177.19 [7698]~P108(x76981)+E(f327(f327(f102(f922(x76981,a910)),f327(f327(f309(x76981),x76982),f190(f922(x76981,a910)))),f305(x76981,x76982,x76983)),f303(x76981,x76982,x76983))+~P1(f327(f327(f234(x76981),x76982),x76983)) % 177.41/177.19 [7808]~P108(x78081)+P1(f327(f327(f234(x78081),x78082),x78083))+~P1(f327(f327(f234(f922(x78081,a910)),f327(f304(x78081),x78083)),f327(f304(x78081),x78082))) % 177.41/177.19 [7809]~P110(x78091)+P1(f327(f327(f234(x78091),x78092),x78093))+~P1(f327(f327(f234(f922(x78091,a910)),f327(f283(x78091),x78093)),f327(f283(x78091),x78092))) % 177.41/177.19 [7810]~P108(x78101)+P1(f327(f327(f234(x78101),x78102),x78103))+~P1(f327(f327(f234(f922(x78101,a910)),f327(f282(x78101),x78102)),f327(f282(x78101),x78103))) % 177.41/177.19 [7811]~P110(x78111)+P1(f327(f327(f234(x78111),x78112),x78113))+~P1(f327(f327(f234(f922(x78111,a910)),f327(f301(x78111),x78112)),f327(f301(x78111),x78113))) % 177.41/177.19 [7812]~P108(x78121)+P1(f327(f327(f235(x78121),x78122),x78123))+~P1(f327(f327(f235(f922(x78121,a910)),f327(f282(x78121),x78122)),f327(f282(x78121),x78123))) % 177.41/177.19 [7835]~P78(x78351)+~P1(f327(f327(f234(x78351),f327(f327(f23(x78351),x78352),x78353)),f2(x78351)))+P1(f327(f327(f234(x78351),x78352),x78353)) % 177.41/177.19 [7836]~P78(x78361)+~P1(f327(f327(f235(x78361),f327(f327(f23(x78361),x78362),x78363)),f2(x78361)))+P1(f327(f327(f235(x78361),x78362),x78363)) % 177.41/177.19 [7990]E(x79901,f2(a915))+~E(f327(f143(a915,a915,f80(a915),x79902),x79903),f2(a915))+~P1(f327(f327(f329(a915),x79901),f327(f173(a915),x79903))) % 177.41/177.19 [7994]~P3(x79941)+~P1(f327(f327(f234(x79941),f467(x79943,x79942,x79941)),x79943))+P1(f327(f327(f234(x79941),f38(x79941,x79942)),x79943)) % 177.41/177.19 [8148]P1(f327(f327(f234(a1),f2(a1)),f460(x81481,x81482,x81483)))+P1(f327(f327(x81482,f327(f327(f37(a1),x81481),x81483)),f46(a1,x81481,x81483)))+~P1(f327(f327(f235(a1),f2(a1)),x81483)) % 177.41/177.19 [8236]E(x82361,x82362)+~E(f327(f191(f916(x82363)),x82361),f327(f191(f916(x82363)),x82362))+~P1(f327(f327(f257(x82363,x82363,a910),a324),f658(x82363,x82361,x82362))) % 177.41/177.19 [8307]~P35(x83072,x83073)+E(x83071,f190(f922(x83072,a910)))+~P1(f327(f327(f234(f922(x83072,a910)),x83071),f327(f285(x83072,x83072,x83073),x83071))) % 177.41/177.19 [8338]~P64(x83381)+~P1(f327(f327(f234(x83381),x83382),f327(f327(f80(x83381),x83383),f763(x83383,x83382,x83381))))+P1(f327(f327(f234(x83381),x83382),x83383)) % 177.41/177.19 [8373]P50(x83731,x83732,x83733)+P1(f327(f327(f329(x83731),f570(x83733,x83732,x83731)),x83732))+P1(f327(f327(f329(f921(x83731,x83731)),f571(x83733,x83732,x83731)),x83733)) % 177.41/177.19 [8394]P1(f327(f327(x83942,f327(f327(f37(a1),x83941),x83943)),f46(a1,x83941,x83943)))+~P1(f327(f327(f235(a1),f2(a1)),x83943))+P1(f327(f327(f235(a1),f460(x83941,x83942,x83943)),x83943)) % 177.41/177.19 [8418]E(f327(f310(a915,a915,f327(f327(f7(a915,a915,a915),f23(a915)),x84181)),f327(f302(a915,x84182),x84183)),f190(f922(a915,a910)))+P1(f327(f327(f235(a915),x84181),x84183))+P1(f327(f327(f235(a915),x84182),x84183)) % 177.41/177.19 [8528]E(f327(f310(a915,a915,f327(f327(f7(a915,a915,a915),f23(a915)),x85281)),f327(f302(a915,x85282),x85283)),f327(f327(f309(a915),f2(a915)),f190(f922(a915,a910))))+P1(f327(f327(f235(a915),x85281),x85283))+~P1(f327(f327(f235(a915),x85282),x85283)) % 177.41/177.19 [8542]~P108(x85421)+E(f150(x85421,x85421,f5(x85421),x85422,x85423),x85423)+~P1(f327(f327(f329(x85421),x85422),f327(f173(x85421),x85423))) % 177.41/177.19 [8555]P23(x85551,x85551,x85552,x85553)+~P1(f327(f35(x85551),x85553))+~P1(f327(f327(f234(f922(x85551,a910)),x85553),f327(f310(x85551,x85551,x85552),x85553))) % 177.41/177.19 [8581]E(f327(f327(f80(a1),f327(f327(f81(a1),x85811),f461(x85812,x85813,x85811))),f460(x85812,x85813,x85811)),x85812)+P1(f327(f327(x85813,f327(f327(f37(a1),x85812),x85811)),f46(a1,x85812,x85811)))+~P1(f327(f327(f235(a1),f2(a1)),x85811)) % 177.41/177.19 [8818]~P1(f327(f327(x88181,f461(x88182,x88181,x88183)),f460(x88182,x88181,x88183)))+P1(f327(f327(x88181,f327(f327(f37(a1),x88182),x88183)),f46(a1,x88182,x88183)))+~P1(f327(f327(f235(a1),f2(a1)),x88183)) % 177.41/177.19 [9705]~P1(f327(f35(x97051),x97052))+~P1(f327(f327(f329(x97051),x97053),x97052))+P1(f327(f327(f235(a915),f327(f36(x97051),f327(f327(f23(f922(x97051,a910)),x97052),f327(f327(f309(x97051),x97053),f190(f922(x97051,a910)))))),f327(f36(x97051),x97052))) % 177.41/177.19 [10312]P50(x103121,x103122,x103123)+~P1(f327(f327(f257(x103121,x103121,a910),f327(f327(f7(x103121,f922(x103121,a910),f922(x103121,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x103121,a910),f922(x103121,a910)),x103121),f8(a910,a910,x103121)),f327(f327(f8(a910,f922(a910,a910),x103121),a325),f327(f327(f7(x103121,f922(x103121,a910),a910),f329(x103121)),x103122)))),f327(f327(f7(x103121,f922(x103121,a910),a910),f329(x103121)),x103122))),f571(x103123,x103122,x103121)))+P1(f327(f327(f329(x103121),f570(x103123,x103122,x103121)),x103122)) % 177.41/177.19 [5646]~P122(x56462)+E(x56461,f2(x56462))+E(f327(f327(f291(x56462),x56463),f327(f79(x56462),x56461)),f327(f79(x56462),f327(f327(f291(x56462),x56463),x56461))) % 177.41/177.19 [5787]~E(x57873,f190(f922(x57871,a910)))+~E(x57872,f190(f922(x57871,a910)))+E(f327(f327(f102(f922(x57871,a910)),x57872),x57873),f190(f922(x57871,a910))) % 177.41/177.19 [5845]~E(x58453,f2(a915))+~P1(f327(x58451,f2(a915)))+P1(f327(x58451,f327(f327(f37(a915),x58452),x58453))) % 177.41/177.19 [5988]~P64(x59882)+E(x59881,f2(x59882))+E(f327(f327(f291(x59882),f327(f75(x59882),x59883)),f327(f75(x59882),x59881)),f327(f75(x59882),f327(f327(f291(x59882),x59883),x59881))) % 177.41/177.19 [6107]~P58(x61071)+E(f327(f327(f81(x61071),x61072),f327(f327(f37(x61071),x61073),x61072)),x61073)+~P1(f327(f327(f287(x61071),x61072),x61073)) % 177.41/177.19 [6162]~P1(f327(f35(x61621),x61623))+E(f327(f36(x61621),f327(f327(f309(x61621),x61622),x61623)),f327(a113,f327(f36(x61621),x61623)))+P1(f327(f327(f329(x61621),x61622),x61623)) % 177.41/177.19 [6241]~E(x62412,f2(a915))+P1(f327(x62411,f2(a915)))+~P1(f327(x62411,f327(f327(f37(a915),x62413),x62412))) % 177.41/177.19 [6258]~P1(f327(f35(x62581),x62583))+E(f327(f36(x62581),f327(f327(f309(x62581),x62582),x62583)),f327(f36(x62581),x62583))+~P1(f327(f327(f329(x62581),x62582),x62583)) % 177.41/177.19 [6295]~P1(f327(f35(x62951),x62953))+E(f327(f36(x62951),f327(f327(f309(x62951),x62952),x62953)),f327(f327(f80(a915),f78(a915)),f327(f36(x62951),x62953)))+P1(f327(f327(f329(x62951),x62952),x62953)) % 177.41/177.19 [6302]~P59(x63021)+E(f327(f327(f37(x63021),x63022),f327(f79(x63021),x63023)),f327(f79(x63021),f327(f327(f37(x63021),x63022),x63023)))+~P1(f327(f327(f287(x63021),x63023),x63022)) % 177.41/177.19 [6414]E(f327(f327(f80(a915),x64141),f366(x64141,x64142,x64143)),x64142)+~P1(f327(x64143,f2(a915)))+P1(f327(x64143,f327(f327(f23(a915),x64142),x64141))) % 177.41/177.19 [6415]E(f327(f327(f80(a915),x64151),f367(x64151,x64152,x64153)),x64152)+~P1(f327(x64153,f2(a915)))+P1(f327(x64153,f327(f327(f23(a915),x64152),x64151))) % 177.41/177.19 [6438]~P59(x64381)+E(f327(f327(f37(x64381),f327(f79(x64381),x64382)),x64383),f327(f79(x64381),f327(f327(f37(x64381),x64382),x64383)))+~P1(f327(f327(f287(x64381),x64383),x64382)) % 177.41/177.19 [6462]~P3(x64621)+~P1(f327(f35(x64621),x64623))+E(f327(f327(f64(x64621,x64621,f102(x64621)),x64622),x64623),f327(f327(f102(x64621),x64622),f38(x64621,x64623))) % 177.41/177.19 [6463]~P3(x64631)+~P1(f327(f35(x64631),x64633))+E(f327(f327(f64(x64631,x64631,f103(x64631)),x64632),x64633),f327(f327(f103(x64631),x64632),f39(x64631,x64633))) % 177.41/177.19 [6469]~P93(x64691)+~E(f327(f105(x64691),x64692),f327(f105(x64691),x64693))+P26(x64691,f327(f105(x64691),f327(f327(f80(a1),x64692),f327(f79(a1),x64693)))) % 177.41/177.19 [6478]~P142(x64781)+E(f327(f327(f23(x64781),f327(f101(x64781),x64782)),f327(f101(x64781),x64783)),f327(f101(x64781),f327(f327(f23(a915),x64782),x64783)))+~P1(f327(f327(f234(a915),x64783),x64782)) % 177.41/177.19 [6485]~P114(x64851)+~P1(f327(f327(f287(x64851),x64852),x64853))+P1(f327(f327(f287(x64851),f327(f79(x64851),x64852)),x64853)) % 177.41/177.19 [6568]E(f327(f327(f80(a915),x65681),f366(x65681,x65682,x65683)),x65682)+P1(f327(f327(f235(a915),x65682),x65681))+P1(f327(x65683,f327(f327(f23(a915),x65682),x65681))) % 177.41/177.19 [6569]E(f327(f327(f80(a915),x65691),f367(x65691,x65692,x65693)),x65692)+P1(f327(f327(f235(a915),x65692),x65691))+P1(f327(x65693,f327(f327(f23(a915),x65692),x65691))) % 177.41/177.19 [6583]~P119(x65831)+E(f327(f327(f81(x65831),f327(f75(x65831),x65832)),x65833),f327(f75(x65831),f327(f327(f81(x65831),x65832),x65833)))+~P1(f327(f327(f234(x65831),f2(x65831)),x65833)) % 177.41/177.19 [6584]~P63(x65841)+E(f327(f327(f291(x65841),f327(f75(x65841),x65842)),x65843),f327(f75(x65841),f327(f327(f291(x65841),x65842),x65843)))+~P1(f327(f327(f235(x65841),f2(x65841)),x65843)) % 177.41/177.19 [6592]~P108(x65921)+~P1(f327(f35(x65921),x65923))+E(f327(f327(f64(x65921,x65921,f189(x65921)),x65922),x65923),f14(x65921,f327(f327(f309(x65921),x65922),x65923))) % 177.41/177.19 [6593]~P108(x65931)+~P1(f327(f35(x65931),x65933))+E(f327(f327(f64(x65931,x65931,f238(x65931)),x65932),x65933),f15(x65931,f327(f327(f309(x65931),x65932),x65933))) % 177.41/177.19 [6594]~P96(x65941)+~P1(f327(f35(x65941),x65943))+E(f327(f327(f64(x65941,x65941,f102(x65941)),x65942),x65943),f13(x65941,f327(f327(f309(x65941),x65942),x65943))) % 177.41/177.19 [6595]~P96(x65951)+~P1(f327(f35(x65951),x65953))+E(f327(f327(f64(x65951,x65951,f103(x65951)),x65952),x65953),f10(x65951,f327(f327(f309(x65951),x65952),x65953))) % 177.41/177.19 [6640]E(x66401,f114(x66402))+~E(f180(x66402,x66403),f114(f916(x66402)))+~P1(f327(f327(f329(f916(x66402)),x66401),f327(f173(f916(x66402)),x66403))) % 177.41/177.19 [6684]~P1(f327(f138(x66841),x66843))+P1(f327(f327(f329(x66841),x66842),f327(f173(x66841),x66843)))+P1(f327(f138(x66841),f327(f327(f152(x66841),x66842),x66843))) % 177.41/177.19 [6695]~P95(x66951)+~P1(f327(f35(x66951),x66953))+E(f327(f63(x66951,f81(x66951)),f327(f327(f309(x66951),x66952),x66953)),f327(f327(f64(x66951,x66951,f81(x66951)),x66952),x66953)) % 177.41/177.19 [6717]~P108(x67171)+~P1(f327(f35(x67171),x67173))+E(f11(x67171,f189(x67171),f327(f327(f309(x67171),x67172),x67173)),f327(f327(f64(x67171,x67171,f189(x67171)),x67172),x67173)) % 177.41/177.19 [6718]~P108(x67181)+~P1(f327(f35(x67181),x67183))+E(f12(x67181,f238(x67181),f327(f327(f309(x67181),x67182),x67183)),f327(f327(f64(x67181,x67181,f238(x67181)),x67182),x67183)) % 177.41/177.19 [6720]P1(f327(x67201,f2(a915)))+~P1(f327(f327(f235(a915),x67202),x67203))+~P1(f327(x67201,f327(f327(f23(a915),x67202),x67203))) % 177.41/177.19 [6741]~P84(x67411)+P1(f327(f327(f234(x67411),x67412),x67413))+~P1(f327(f327(f234(x67411),f327(f75(x67411),x67412)),x67413)) % 177.41/177.19 [6742]~P119(x67421)+P1(f327(f327(f235(x67421),x67422),x67423))+~P1(f327(f327(f235(x67421),f327(f75(x67421),x67422)),x67423)) % 177.41/177.19 [6743]~P114(x67431)+P1(f327(f327(f287(x67431),x67432),x67433))+~P1(f327(f327(f287(x67431),f327(f79(x67431),x67432)),x67433)) % 177.41/177.19 [6760]E(x67601,f114(x67602))+E(f327(f142(x67602),f327(f327(f139(x67602),x67603),x67601)),f327(f327(f165(x67602),x67601),x67603))+~P1(f327(f327(f235(a915),x67603),f327(f191(f916(x67602)),x67601))) % 177.41/177.19 [6812]~P1(f327(x68121,x68123))+P1(f327(x68121,f392(x68121,x68122)))+~P1(f327(f327(f329(a915),x68123),f327(f302(a915,f2(a915)),x68122))) % 177.41/177.19 [6832]P1(f327(x68321,x68322))+~P1(f327(f327(f235(a915),x68322),x68323))+P1(f327(f327(f329(a915),f389(x68321,x68323)),f327(f302(a915,f2(a915)),x68323))) % 177.41/177.19 [6847]~P126(x68471)+~P1(f327(f327(f234(x68471),f78(x68471)),x68472))+P1(f327(f327(f234(x68471),f78(x68471)),f327(f327(f244(x68471),x68472),x68473))) % 177.41/177.19 [6849]~P126(x68491)+~P1(f327(f327(f234(x68491),f2(x68491)),x68492))+P1(f327(f327(f234(x68491),f2(x68491)),f327(f327(f244(x68491),x68492),x68493))) % 177.41/177.19 [6851]~P126(x68511)+~P1(f327(f327(f235(x68511),f2(x68511)),x68512))+P1(f327(f327(f235(x68511),f2(x68511)),f327(f327(f244(x68511),x68512),x68513))) % 177.41/177.19 [6876]~P1(f327(x68761,x68763))+~P1(f327(f327(f235(a915),x68763),x68762))+P1(f327(f327(f329(a915),f388(x68761,x68762)),f327(f302(a915,f2(a915)),x68762))) % 177.41/177.19 [6884]P1(f327(f35(x68841),x68842))+~P1(f327(f35(x68841),x68843))+~P1(f327(f327(f234(f922(x68841,a910)),x68842),x68843)) % 177.41/177.19 [6891]P1(f327(x68911,x68912))+~P1(f327(x68911,f390(x68911,x68913)))+~P1(f327(f327(f329(a915),x68912),f327(f302(a915,f2(a915)),x68913))) % 177.41/177.19 [6904]E(x69041,f2(a915))+P1(f327(x69042,f393(x69041,x69043,x69042)))+~P1(f327(x69042,f327(f327(f37(a915),x69043),x69041))) % 177.41/177.19 [6912]~P127(x69122)+E(x69121,f2(x69122))+~E(f327(f327(f80(x69122),f327(f327(f81(x69122),x69123),x69123)),f327(f327(f81(x69122),x69121),x69121)),f2(x69122)) % 177.41/177.19 [6913]~P127(x69132)+E(x69131,f2(x69132))+~E(f327(f327(f80(x69132),f327(f327(f81(x69132),x69131),x69131)),f327(f327(f81(x69132),x69133),x69133)),f2(x69132)) % 177.41/177.19 [6957]E(x69571,f2(a915))+~P1(f327(x69572,f394(x69571,x69573,x69572)))+P1(f327(x69572,f327(f327(f37(a915),x69573),x69571))) % 177.41/177.19 [6962]~P108(x69621)+~P11(x69621,x69623)+P11(x69621,f327(f327(f149(x69621,x69621,f5(x69621)),x69622),x69623)) % 177.41/177.19 [7004]P1(f327(x70041,f393(x70042,x70043,x70041)))+P1(f327(x70041,f2(a915)))+~P1(f327(x70041,f327(f327(f37(a915),x70043),x70042))) % 177.41/177.19 [7010]~P93(x70101)+E(f327(f105(x70101),x70102),f327(f105(x70101),x70103))+~P26(x70101,f327(f105(x70101),f327(f327(f80(a1),x70102),f327(f79(a1),x70103)))) % 177.41/177.19 [7076]E(x70761,f2(a1))+E(x70762,f2(a1))+~P1(f327(f50(x70762,x70762),f327(f327(f252(a1,a1),x70763),x70761))) % 177.41/177.19 [7077]E(x70771,f78(a1))+E(x70772,f2(a1))+~P1(f327(f50(x70772,x70772),f327(f327(f252(a1,a1),x70771),x70773))) % 177.41/177.19 [7092]P1(f327(x70921,x70922))+P1(f327(f327(f235(a915),f390(x70921,x70923)),x70923))+~P1(f327(f327(f329(a915),x70922),f327(f302(a915,f2(a915)),x70923))) % 177.41/177.19 [7115]~P1(f327(x71151,f366(x71153,x71152,x71151)))+~P1(f327(x71151,f2(a915)))+P1(f327(x71151,f327(f327(f23(a915),x71152),x71153))) % 177.41/177.19 [7116]~P1(f327(x71161,f367(x71163,x71162,x71161)))+~P1(f327(x71161,f2(a915)))+P1(f327(x71161,f327(f327(f23(a915),x71162),x71163))) % 177.41/177.19 [7117]~P1(f327(x71171,f394(x71173,x71172,x71171)))+~P1(f327(x71171,f2(a915)))+P1(f327(x71171,f327(f327(f37(a915),x71172),x71173))) % 177.41/177.19 [7135]~P1(f327(x71351,x71353))+P1(f327(f327(f235(a915),f392(x71351,x71352)),x71352))+~P1(f327(f327(f329(a915),x71353),f327(f302(a915,f2(a915)),x71352))) % 177.41/177.19 [7136]E(f327(f327(f23(a915),f327(f327(f23(a915),x71361),x71362)),f327(f327(f23(a915),x71363),x71362)),f327(f327(f23(a915),x71361),x71363))+~P1(f327(f327(f234(a915),x71362),x71361))+~P1(f327(f327(f234(a915),x71362),x71363)) % 177.41/177.19 [7173]~P78(x71731)+~P1(f327(f327(f234(x71731),f327(f79(x71731),x71733)),x71732))+P1(f327(f327(f234(x71731),f327(f79(x71731),x71732)),x71733)) % 177.41/177.19 [7175]~P84(x71751)+~P1(f327(f327(f234(x71751),f327(f75(x71751),x71752)),x71753))+P1(f327(f327(f234(x71751),f327(f79(x71751),x71752)),x71753)) % 177.41/177.19 [7177]~P78(x71771)+~P1(f327(f327(f235(x71771),f327(f79(x71771),x71773)),x71772))+P1(f327(f327(f235(x71771),f327(f79(x71771),x71772)),x71773)) % 177.41/177.19 [7178]~P119(x71781)+~P1(f327(f327(f235(x71781),f327(f75(x71781),x71782)),x71783))+P1(f327(f327(f235(x71781),f327(f79(x71781),x71782)),x71783)) % 177.41/177.19 [7211]~P1(f327(x72113,f366(x72112,x72111,x72113)))+P1(f327(f327(f235(a915),x72111),x72112))+P1(f327(x72113,f327(f327(f23(a915),x72111),x72112))) % 177.41/177.19 [7212]~P1(f327(x72123,f367(x72122,x72121,x72123)))+P1(f327(f327(f235(a915),x72121),x72122))+P1(f327(x72123,f327(f327(f23(a915),x72121),x72122))) % 177.41/177.19 [7264]~E(f475(x72643,x72642,x72641),f476(x72643,x72642,x72641))+E(f327(f327(f103(f922(x72641,a910)),x72642),f38(f922(x72641,a910),x72643)),f190(f922(x72641,a910)))+P1(f327(f327(f329(f922(x72641,a910)),x72642),x72643)) % 177.41/177.19 [7272]~P1(f327(f35(x72721),x72723))+P1(f327(f35(x72721),f39(f922(x72721,a910),x72722)))+~P1(f327(f327(f329(f922(x72721,a910)),x72723),x72722)) % 177.41/177.19 [7332]~P108(x73321)+E(f327(f327(f102(f922(x73321,a910)),f327(f302(x73321,x73322),x73323)),f327(f327(f309(x73321),x73323),f190(f922(x73321,a910)))),f303(x73321,x73322,x73323))+~P1(f327(f327(f234(x73321),x73322),x73323)) % 177.41/177.19 [7335]E(x73351,f2(a915))+P1(f327(f327(f235(a915),f400(x73351,x73353,x73352)),x73351))+P1(f327(x73352,f327(f327(f37(a915),x73353),x73351))) % 177.41/177.19 [7364]P1(f327(f327(f235(a915),f327(f191(f916(x73641)),x73642)),f775(x73643,x73641)))+~P1(f327(f35(f916(x73641)),x73643))+~P1(f327(f327(f329(f916(x73641)),x73642),x73643)) % 177.41/177.19 [7370]E(x73701,x73702)+~P1(f327(f327(f234(f922(x73703,a910)),x73701),x73702))+P1(f327(f327(f235(f922(x73703,a910)),x73701),x73702)) % 177.41/177.19 [7383]E(x73831,x73832)+~E(f327(f191(f916(x73833)),x73831),f327(f191(f916(x73833)),x73832))+P1(f327(f327(f235(a915),f632(x73833,x73831,x73832)),f327(f191(f916(x73833)),x73832))) % 177.41/177.19 [7432]P6(x74321,x74322,x74323)+~E(f327(f264(x74321,x74321),x74323),x74322)+~E(f327(f327(f289(x74321,x74321,x74321),f327(f286(x74321,x74321),x74323)),x74323),x74323) % 177.41/177.19 [7512]~P1(f327(x75121,f2(a915)))+P1(f327(f327(f235(a915),f400(x75123,x75122,x75121)),x75123))+P1(f327(x75121,f327(f327(f37(a915),x75122),x75123))) % 177.41/177.19 [7521]~P108(x75211)+E(f327(f327(f102(f922(x75211,a910)),f306(x75211,x75212,x75213)),f327(f327(f309(x75211),x75213),f190(f922(x75211,a910)))),f305(x75211,x75212,x75213))+~P1(f327(f327(f235(x75211),x75212),x75213)) % 177.41/177.19 [7611]~P1(f327(f35(x76111),x76113))+P1(f327(f327(f234(a915),f327(f36(x76111),x76112)),f327(f36(x76111),x76113)))+~P1(f327(f327(f234(f922(x76111,a910)),x76112),x76113)) % 177.41/177.19 [7612]~P1(f327(f35(x76121),x76123))+P1(f327(f327(f235(a915),f327(f36(x76121),x76122)),f327(f36(x76121),x76123)))+~P1(f327(f327(f235(f922(x76121,a910)),x76122),x76123)) % 177.41/177.19 [7743]E(x77431,x77432)+~P1(f327(f327(f234(f922(x77433,a910)),x77432),x77431))+~P1(f327(f327(f234(f922(x77433,a910)),x77431),x77432)) % 177.41/177.19 [7746]~P108(x77461)+P11(x77461,x77462)+~P11(x77461,f327(f327(f149(x77461,x77461,f5(x77461)),x77463),x77462)) % 177.41/177.19 [7817]~P1(f327(f327(f235(a915),x78173),x78172))+~P1(f327(f327(f235(a915),x78173),x78171))+P1(f327(f327(f235(a915),f327(f327(f23(a915),x78171),x78172)),f327(f327(f23(a915),x78171),x78173))) % 177.41/177.19 [7818]~P1(f327(f327(f234(a915),x78182),x78181))+~P1(f327(f327(f235(a915),x78181),x78183))+P1(f327(f327(f235(a915),f327(f327(f23(a915),x78181),x78182)),f327(f327(f23(a915),x78183),x78182))) % 177.41/177.19 [7833]~P1(f327(f327(f235(a1),x78332),f2(a1)))+~P1(f327(f327(f234(a1),x78333),x78331))+P1(f327(f327(f234(a1),f327(f327(f37(a1),x78331),x78332)),f327(f327(f37(a1),x78333),x78332))) % 177.41/177.19 [7850]~P1(f327(f327(f235(a915),f2(a915)),x78503))+~P1(f327(f327(f234(a915),x78503),x78502))+P1(f327(f327(f234(a915),f327(f327(f37(a915),x78501),x78502)),f327(f327(f37(a915),x78501),x78503))) % 177.41/177.19 [7851]~P1(f327(f327(f235(a1),f2(a1)),x78512))+~P1(f327(f327(f234(a1),x78511),x78513))+P1(f327(f327(f234(a1),f327(f327(f37(a1),x78511),x78512)),f327(f327(f37(a1),x78513),x78512))) % 177.41/177.19 [7855]~P1(f327(f327(f235(a915),f2(a915)),x78552))+~P1(f327(f327(f235(a915),x78551),x78553))+P1(f327(f327(f235(a915),f327(f327(f81(a915),x78551),x78552)),f327(f327(f81(a915),x78553),x78552))) % 177.41/177.19 [7856]~P1(f327(f327(f235(a915),f2(a915)),x78561))+~P1(f327(f327(f235(a915),x78562),x78563))+P1(f327(f327(f235(a915),f327(f327(f81(a915),x78561),x78562)),f327(f327(f81(a915),x78561),x78563))) % 177.41/177.19 [7857]~P1(f327(f327(f235(a1),f2(a1)),x78571))+~P1(f327(f327(f235(a1),x78572),x78573))+P1(f327(f327(f235(a1),f327(f327(f81(a1),x78571),x78572)),f327(f327(f81(a1),x78571),x78573))) % 177.41/177.19 [7905]E(x79051,f2(a915))+E(f327(f327(f80(a915),f327(f327(f81(a915),x79051),f394(x79051,x79052,x79053))),f400(x79051,x79052,x79053)),x79052)+P1(f327(x79053,f327(f327(f37(a915),x79052),x79051))) % 177.41/177.19 [7964]E(f327(f327(f80(a915),f327(f327(f81(a915),x79641),f394(x79641,x79642,x79643))),f400(x79641,x79642,x79643)),x79642)+~P1(f327(x79643,f2(a915)))+P1(f327(x79643,f327(f327(f37(a915),x79642),x79641))) % 177.41/177.19 [7981]~P1(f327(f35(x79811),x79813))+P1(f327(f327(f329(x79811),f372(x79812,x79813,x79811)),x79813))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f9(x79811,a915),x79812),x79813))) % 177.41/177.19 [7982]~P1(f327(f35(x79821),x79823))+P1(f327(f327(f329(x79821),f477(x79822,x79823,x79821)),x79823))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f9(x79821,a915),x79822),x79823))) % 177.41/177.19 [8082]E(x80821,f2(a915))+P1(f327(f327(f287(a915),x80822),x80823))+~P1(f327(f327(f287(a915),f327(f327(f81(a915),x80821),x80822)),f327(f327(f81(a915),x80821),x80823))) % 177.41/177.19 [8272]E(x82721,f190(f922(x82722,a910)))+E(x82721,f327(f327(f309(x82722),x82723),f190(f922(x82722,a910))))+~P1(f327(f327(f234(f922(x82722,a910)),x82721),f327(f327(f309(x82722),x82723),f190(f922(x82722,a910))))) % 177.41/177.19 [8308]~P1(f327(f327(f235(a915),f78(a915)),x83083))+P1(f327(f327(f234(a915),x83081),x83082))+~P1(f327(f327(f287(a915),f327(f327(f244(a915),x83083),x83081)),f327(f327(f244(a915),x83083),x83082))) % 177.41/177.19 [8310]~P1(f327(f327(f235(a915),f2(a915)),x83103))+P1(f327(f327(f234(a915),x83101),x83102))+~P1(f327(f327(f234(a915),f327(f327(f81(a915),x83103),x83101)),f327(f327(f81(a915),x83103),x83102))) % 177.41/177.19 [8311]~P1(f327(f327(f235(a915),f2(a915)),x83113))+P1(f327(f327(f234(a915),x83111),x83112))+~P1(f327(f327(f234(a915),f327(f327(f81(a915),x83111),x83113)),f327(f327(f81(a915),x83112),x83113))) % 177.41/177.19 [8313]~P1(f327(f327(f235(a915),f2(a915)),x83133))+P1(f327(f327(f235(a915),x83131),x83132))+~P1(f327(f327(f235(a915),f327(f327(f244(a915),x83133),x83131)),f327(f327(f244(a915),x83133),x83132))) % 177.41/177.19 [8315]~P1(f327(f327(f235(a915),f2(a915)),x83153))+P1(f327(f327(f287(a915),x83151),x83152))+~P1(f327(f327(f287(a915),f327(f327(f81(a915),x83153),x83151)),f327(f327(f81(a915),x83153),x83152))) % 177.41/177.19 [8354]~E(f327(f327(f103(f922(x83541,a910)),f476(x83543,x83542,x83541)),f475(x83543,x83542,x83541)),f190(f922(x83541,a910)))+E(f327(f327(f103(f922(x83541,a910)),x83542),f38(f922(x83541,a910),x83543)),f190(f922(x83541,a910)))+P1(f327(f327(f329(f922(x83541,a910)),x83542),x83543)) % 177.41/177.19 [8368]E(x83681,f114(x83682))+~E(f327(f143(f916(x83682),f916(x83682),f135(x83682),f114(x83682)),x83683),f114(x83682))+~P1(f327(f327(f329(f916(x83682)),x83681),f327(f173(f916(x83682)),x83683))) % 177.41/177.19 [8423]E(x84231,f190(f922(f922(x84232,a910),a910)))+P1(f327(f327(f329(f922(x84232,a910)),f473(x84233,x84231,x84232)),x84231))+P1(f327(f327(f234(f922(x84232,a910)),f39(f922(x84232,a910),x84231)),x84233)) % 177.41/177.19 [8429]~P68(x84291)+~P75(x84291)+E(f327(f327(f6(a1,x84291),f327(f327(f8(a915,x84291,a1),x84292),a106)),f327(f310(a915,a1,f101(a1)),x84293)),f327(f327(f6(a915,x84291),x84292),x84293)) % 177.41/177.19 [8430]~P68(x84301)+~P75(x84301)+E(f327(f327(f9(a1,x84301),f327(f327(f8(a915,x84301,a1),x84302),a106)),f327(f310(a915,a1,f101(a1)),x84303)),f327(f327(f9(a915,x84301),x84302),x84303)) % 177.41/177.19 [8472]~P1(f327(f35(x84721),x84723))+~P1(f327(f327(f235(a915),f2(a915)),f327(x84722,f372(x84722,x84723,x84721))))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f9(x84721,a915),x84722),x84723))) % 177.41/177.19 [8473]~P1(f327(f35(x84731),x84733))+~P1(f327(f327(f235(a915),f2(a915)),f327(x84732,f477(x84732,x84733,x84731))))+P1(f327(f327(f235(a915),f2(a915)),f327(f327(f9(x84731,a915),x84732),x84733))) % 177.41/177.19 [8509]~P62(x85092)+E(x85091,f78(x85092))+E(f327(f327(f291(x85092),f327(f327(f23(x85092),f327(f327(f244(x85092),x85091),x85093)),f78(x85092))),f327(f327(f23(x85092),x85091),f78(x85092))),f327(f327(f6(a915,x85092),f327(f244(x85092),x85091)),f327(f302(a915,f2(a915)),x85093))) % 177.41/177.19 [8566]E(x85661,f2(a915))+~P1(f327(x85663,f327(f327(f37(a915),x85662),x85661)))+P1(f327(f327(f235(a915),x85662),f327(f327(f81(a915),x85661),f327(a113,f393(x85661,x85662,x85663))))) % 177.41/177.19 [8585]P1(f327(x85851,f2(a915)))+~P1(f327(x85851,f327(f327(f37(a915),x85852),x85853)))+P1(f327(f327(f235(a915),x85852),f327(f327(f81(a915),x85853),f327(a113,f393(x85853,x85852,x85851))))) % 177.41/177.19 [8623]E(x86231,f2(a915))+~P1(f327(x86233,f327(f327(f37(a915),x86232),x86231)))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x86231),f393(x86231,x86232,x86233))),x86232)) % 177.41/177.19 [8654]P1(f327(x86541,f2(a915)))+~P1(f327(x86541,f327(f327(f37(a915),x86543),x86542)))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x86542),f393(x86542,x86543,x86541))),x86543)) % 177.41/177.19 [8662]~P108(x86621)+E(f327(f327(f149(x86621,x86621,f5(x86621)),x86622),x86623),f150(x86621,x86621,f5(x86621),x86622,x86623))+P1(f327(f327(f329(x86621),x86622),f327(f173(x86621),x86623))) % 177.41/177.19 [8697]~E(f327(x86973,f576(x86972,x86973,x86971)),f327(x86973,f580(x86972,x86973,x86971)))+~P57(x86971,f327(x86973,f577(x86972,x86973,x86971)))+P57(x86971,f327(f327(f40(x86972,f922(x86971,f922(x86971,a910))),f242(f922(x86972,a910))),x86973)) % 177.41/177.19 [8706]E(x87061,f190(f922(f922(x87062,a910),a910)))+~P1(f327(f327(f234(f922(x87062,a910)),f473(x87063,x87061,x87062)),x87063))+P1(f327(f327(f234(f922(x87062,a910)),f39(f922(x87062,a910),x87061)),x87063)) % 177.41/177.19 [8766]~P64(x87661)+~P1(f327(f327(f235(x87661),x87662),x87663))+P1(f327(f327(f235(x87661),x87662),f327(f327(f291(x87661),f327(f327(f80(x87661),x87662),x87663)),f327(f327(f80(x87661),f78(x87661)),f78(x87661))))) % 177.41/177.19 [8824]~P1(f327(f327(x88241,f515(x88241,x88243,x88242)),f521(x88241,x88243,x88242)))+P1(f327(f327(x88241,x88242),x88243))+~P1(f327(f315(f921(a1,a1),a53),f327(f327(f252(a1,a1),x88242),x88243))) % 177.41/177.19 [8825]~P1(f327(f327(x88251,f522(x88251,x88253,x88252)),f523(x88251,x88253,x88252)))+P1(f327(f327(x88251,x88252),x88253))+~P1(f327(f315(f921(a1,a1),a59),f327(f327(f252(a1,a1),x88252),x88253))) % 177.41/177.19 [8826]~P1(f327(f327(x88261,f525(x88261,x88263,x88262)),f526(x88261,x88263,x88262)))+P1(f327(f327(x88261,x88262),x88263))+~P1(f327(f315(f921(a1,a1),a223),f327(f327(f252(a1,a1),x88262),x88263))) % 177.41/177.19 [8827]~P1(f327(f327(x88271,f528(x88271,x88273,x88272)),f529(x88271,x88273,x88272)))+P1(f327(f327(x88271,x88272),x88273))+~P1(f327(f315(f921(a915,a915),a221),f327(f327(f252(a915,a915),x88272),x88273))) % 177.41/177.19 [8828]~P1(f327(f327(x88281,f673(x88281,x88283,x88282)),f675(x88281,x88283,x88282)))+P1(f327(f327(x88281,x88282),x88283))+~P1(f327(f315(f921(a1,a1),a183),f327(f327(f252(a1,a1),x88282),x88283))) % 177.41/177.19 [8829]~P1(f327(f327(x88291,f767(x88291,x88293,x88292)),f769(x88291,x88293,x88292)))+P1(f327(f327(x88291,x88292),x88293))+~P1(f327(f315(f921(a1,a1),a134),f327(f327(f252(a1,a1),x88292),x88293))) % 177.41/177.19 [9104]P1(f327(f327(x91041,x91042),x91043))+P1(f327(f315(f921(a915,a915),a221),f327(f327(f252(a915,a915),f528(x91041,x91043,x91042)),f529(x91041,x91043,x91042))))+~P1(f327(f315(f921(a915,a915),a221),f327(f327(f252(a915,a915),x91042),x91043))) % 177.41/177.19 [9105]P1(f327(f327(x91051,x91052),x91053))+P1(f327(f315(f921(a1,a1),a53),f327(f327(f252(a1,a1),f515(x91051,x91053,x91052)),f521(x91051,x91053,x91052))))+~P1(f327(f315(f921(a1,a1),a53),f327(f327(f252(a1,a1),x91052),x91053))) % 177.41/177.19 [9106]P1(f327(f327(x91061,x91062),x91063))+P1(f327(f315(f921(a1,a1),a59),f327(f327(f252(a1,a1),f522(x91061,x91063,x91062)),f523(x91061,x91063,x91062))))+~P1(f327(f315(f921(a1,a1),a59),f327(f327(f252(a1,a1),x91062),x91063))) % 177.41/177.19 [9107]P1(f327(f327(x91071,x91072),x91073))+P1(f327(f315(f921(a1,a1),a223),f327(f327(f252(a1,a1),f525(x91071,x91073,x91072)),f526(x91071,x91073,x91072))))+~P1(f327(f315(f921(a1,a1),a223),f327(f327(f252(a1,a1),x91072),x91073))) % 177.41/177.19 [9108]P1(f327(f327(x91081,x91082),x91083))+P1(f327(f315(f921(a1,a1),a183),f327(f327(f252(a1,a1),f673(x91081,x91083,x91082)),f675(x91081,x91083,x91082))))+~P1(f327(f315(f921(a1,a1),a183),f327(f327(f252(a1,a1),x91082),x91083))) % 177.41/177.19 [9109]P1(f327(f327(x91091,x91092),x91093))+P1(f327(f315(f921(a1,a1),a134),f327(f327(f252(a1,a1),f767(x91091,x91093,x91092)),f769(x91091,x91093,x91092))))+~P1(f327(f315(f921(a1,a1),a134),f327(f327(f252(a1,a1),x91092),x91093))) % 177.41/177.19 [9443]~P1(f327(f35(x94431),x94433))+P1(f327(f327(f329(f921(f922(x94431,a910),f922(x94431,a910))),f327(f327(f252(f922(x94431,a910),f922(x94431,a910)),x94432),x94433)),f314(x94431)))+~P1(f327(f327(f235(f922(x94431,a910)),x94432),x94433)) % 177.41/177.19 [9516]~P57(x95161,f327(x95163,f577(x95162,x95163,x95161)))+P57(x95161,f327(f327(f40(x95162,f922(x95161,f922(x95161,a910))),f242(f922(x95162,a910))),x95163))+~E(f327(f327(f103(f922(x95161,a910)),f249(x95161,x95161,f327(x95163,f576(x95162,x95163,x95161)))),f250(x95161,x95161,f327(x95163,f580(x95162,x95163,x95161)))),f190(f922(x95161,a910))) % 177.41/177.19 [9719]P50(x97191,x97192,x97193)+P1(f327(f327(f329(f921(x97191,x97191)),f571(x97193,x97192,x97191)),x97193))+~P1(f327(f327(f329(f921(x97191,x97191)),f327(f327(f252(x97191,x97191),f570(x97193,x97192,x97191)),f570(x97193,x97192,x97191))),x97193)) % 177.41/177.19 [10315]P50(x103151,x103152,x103153)+~P1(f327(f327(f257(x103151,x103151,a910),f327(f327(f7(x103151,f922(x103151,a910),f922(x103151,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x103151,a910),f922(x103151,a910)),x103151),f8(a910,a910,x103151)),f327(f327(f8(a910,f922(a910,a910),x103151),a325),f327(f327(f7(x103151,f922(x103151,a910),a910),f329(x103151)),x103152)))),f327(f327(f7(x103151,f922(x103151,a910),a910),f329(x103151)),x103152))),f571(x103153,x103152,x103151)))+~P1(f327(f327(f329(f921(x103151,x103151)),f327(f327(f252(x103151,x103151),f570(x103153,x103152,x103151)),f570(x103153,x103152,x103151))),x103153)) % 177.41/177.19 [5827]~P58(x58272)+E(x58271,f2(x58272))+E(f327(f327(f37(x58272),f327(f327(f81(x58272),x58273),x58271)),x58271),x58273) % 177.41/177.19 [5828]~P58(x58282)+E(x58281,f2(x58282))+E(f327(f327(f37(x58282),f327(f327(f81(x58282),x58281),x58283)),x58281),x58283) % 177.41/177.19 [6479]~P58(x64791)+E(f327(f327(f81(x64791),f327(f327(f37(x64791),x64792),x64793)),x64793),x64792)+~P1(f327(f327(f287(x64791),x64793),x64792)) % 177.41/177.19 [6639]~P68(x66391)+~E(f327(x66392,f2(a915)),f2(x66391))+E(f327(f327(f6(a915,x66391),x66392),f327(f302(a915,f327(a113,f2(a915))),x66393)),f327(f327(f6(a915,x66391),x66392),f327(f302(a915,f2(a915)),x66393))) % 177.41/177.19 [6772]~P58(x67722)+E(x67721,f2(x67722))+E(f327(f327(f37(x67722),f327(f327(f80(x67722),x67723),x67721)),x67721),f327(f327(f80(x67722),f327(f327(f37(x67722),x67723),x67721)),f78(x67722))) % 177.41/177.19 [6773]~P58(x67732)+E(x67731,f2(x67732))+E(f327(f327(f37(x67732),f327(f327(f80(x67732),x67731),x67733)),x67731),f327(f327(f80(x67732),f327(f327(f37(x67732),x67733),x67731)),f78(x67732))) % 177.41/177.19 [6993]~P1(f327(x69933,f2(a1)))+P1(f327(f327(f234(a915),x69931),x69932))+P1(f327(x69933,f327(f101(a1),f327(f327(f23(a915),x69932),x69931)))) % 177.41/177.19 [7098]P1(f327(f327(f235(a915),x70982),x70981))+P1(f327(f327(f234(a915),x70981),x70982))+P1(f327(x70983,f327(f101(a1),f327(f327(f23(a915),x70982),x70981)))) % 177.41/177.19 [7171]E(f327(f327(f80(a915),f327(f105(a915),x71711)),f327(f327(f80(a915),f327(f105(a915),x71712)),x71713)),f327(f327(f80(a915),f327(f105(a915),x71711)),x71713))+P1(f327(a195,f327(f105(a1),x71711)))+~P1(f327(a195,f327(f105(a1),x71712))) % 177.41/177.19 [7251]~E(x72512,f327(f327(f37(a915),x72513),x72511))+~P1(f327(f327(f235(a915),f2(a915)),x72511))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x72511),x72512)),x72513)) % 177.41/177.19 [7368]~P1(f327(f35(x73681),x73683))+~P1(f327(f35(x73681),x73682))+P1(f327(f35(x73681),f327(f327(f102(f922(x73681,a910)),x73682),x73683))) % 177.41/177.19 [7417]~P36(x74171,x74173)+~P36(x74171,x74172)+P36(x74171,f327(f327(f103(f922(f921(x74171,x74171),a910)),x74172),x74173)) % 177.41/177.19 [7418]~P49(x74181,x74183)+~P49(x74181,x74182)+P49(x74181,f327(f327(f102(f922(f921(x74181,x74181),a910)),x74182),x74183)) % 177.41/177.19 [7419]~P49(x74191,x74193)+~P49(x74191,x74192)+P49(x74191,f327(f327(f103(f922(f921(x74191,x74191),a910)),x74192),x74193)) % 177.41/177.19 [7660]~P108(x76601)+~P1(f327(f35(x76601),x76602))+E(f140(x76601,f327(f327(f23(f922(x76601,a910)),x76602),f327(f327(f309(x76601),x76603),f190(f922(x76601,a910))))),f171(x76601,x76603,f140(x76601,x76602))) % 177.41/177.19 [7722]P1(f327(x77221,f2(a1)))+~P1(f327(f327(f235(a915),x77222),x77223))+~P1(f327(x77221,f327(f101(a1),f327(f327(f23(a915),x77222),x77223)))) % 177.41/177.19 [7740]~P1(f327(f35(x77401),x77402))+E(f327(f36(x77401),f327(f327(f23(f922(x77401,a910)),x77402),f327(f327(f309(x77401),x77403),f190(f922(x77401,a910))))),f327(f36(x77401),x77402))+P1(f327(f327(f329(x77401),x77403),x77402)) % 177.41/177.19 [7873]~P126(x78731)+~P1(f327(f327(f235(x78731),f78(x78731)),x78732))+P1(f327(f327(f235(x78731),f78(x78731)),f327(f327(f81(x78731),x78732),f327(f327(f244(x78731),x78732),x78733)))) % 177.41/177.19 [7915]~P1(f327(f35(x79151),x79153))+E(f327(f327(f23(a915),f327(f36(x79151),x79152)),f327(f36(x79151),x79153)),f327(f36(x79151),f327(f327(f23(f922(x79151,a910)),x79152),x79153)))+~P1(f327(f327(f234(f922(x79151,a910)),x79153),x79152)) % 177.41/177.19 [7972]~P1(f327(f327(f234(a915),x79722),x79723))+~P1(f327(f327(f234(a915),x79721),f327(f327(f23(a915),x79723),x79722)))+P1(f327(f327(f234(a915),f327(f327(f80(a915),x79721),x79722)),x79723)) % 177.41/177.19 [8025]P1(f327(f35(x80251),x80252))+~P1(f327(f35(x80251),x80253))+~P1(f327(f35(x80251),f327(f327(f23(f922(x80251,a910)),x80252),x80253))) % 177.41/177.19 [8031]~P1(f327(f35(x80311),x80312))+E(f327(f36(x80311),f327(f327(f23(f922(x80311,a910)),x80312),f327(f327(f309(x80311),x80313),f190(f922(x80311,a910))))),f327(f327(f23(a915),f327(f36(x80311),x80312)),f78(a915)))+~P1(f327(f327(f329(x80311),x80313),x80312)) % 177.41/177.19 [8107]P57(x81071,x81072)+~P57(x81071,x81073)+~P1(f327(f327(f234(f922(x81071,f922(x81071,a910))),x81072),x81073)) % 177.41/177.19 [8147]~P1(f327(f327(f234(a915),x81473),x81472))+P1(f327(f327(f234(a915),x81471),f327(f327(f23(a915),x81472),x81473)))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),x81471),x81473)),x81472)) % 177.41/177.19 [8165]P35(x81651,x81652)+~P35(x81651,x81653)+~P1(f327(f327(f234(f922(f921(x81651,x81651),a910)),x81652),x81653)) % 177.41/177.19 [8166]P55(x81661,x81662)+~P55(x81661,x81663)+~P1(f327(f327(f234(f922(f921(x81661,x81661),a910)),x81662),x81663)) % 177.41/177.19 [8167]P37(x81671,x81672)+~P37(x81671,x81673)+~P1(f327(f327(f234(f922(f921(x81671,x81671),a910)),x81672),x81673)) % 177.41/177.19 [8401]~P126(x84011)+~P1(f327(f327(f235(x84011),f78(x84011)),x84012))+P1(f327(f327(f235(x84011),f327(f327(f244(x84011),x84012),x84013)),f327(f327(f81(x84011),x84012),f327(f327(f244(x84011),x84012),x84013)))) % 177.41/177.19 [8491]~P1(f327(x84911,f2(a1)))+~P1(f327(x84911,f327(f327(f23(a1),f327(f101(a1),x84912)),f327(f101(a1),x84913))))+P1(f327(x84911,f327(f101(a1),f327(f327(f23(a915),x84912),x84913)))) % 177.41/177.19 [8506]~P1(f327(f327(f234(a915),x85063),x85062))+P1(f327(x85061,f327(f327(f23(a1),f327(f101(a1),x85062)),f327(f101(a1),x85063))))+~P1(f327(x85061,f327(f101(a1),f327(f327(f23(a915),x85062),x85063)))) % 177.41/177.19 [8525]P1(f327(f327(f235(a915),x85251),x85252))+~P1(f327(x85253,f327(f327(f23(a1),f327(f101(a1),x85251)),f327(f101(a1),x85252))))+P1(f327(x85253,f327(f101(a1),f327(f327(f23(a915),x85251),x85252)))) % 177.41/177.19 [8578]~P127(x85782)+E(x85781,f2(x85782))+P1(f327(f327(f235(x85782),f2(x85782)),f327(f327(f80(x85782),f327(f327(f81(x85782),x85783),x85783)),f327(f327(f81(x85782),x85781),x85781)))) % 177.41/177.19 [8579]~P127(x85792)+E(x85791,f2(x85792))+P1(f327(f327(f235(x85792),f2(x85792)),f327(f327(f80(x85792),f327(f327(f81(x85792),x85791),x85791)),f327(f327(f81(x85792),x85793),x85793)))) % 177.41/177.19 [8679]~P1(f327(f327(f235(a915),f2(a915)),x86791))+~P1(f327(f327(f235(a1),x86792),x86793))+P1(f327(f327(f235(a1),f327(f327(f81(a1),f327(f101(a1),x86791)),x86792)),f327(f327(f81(a1),f327(f101(a1),x86791)),x86793))) % 177.41/177.19 [8735]E(f327(f327(f103(f922(x87351,a910)),x87352),f38(f922(x87351,a910),x87353)),f190(f922(x87351,a910)))+P1(f327(f327(f329(f922(x87351,a910)),x87352),x87353))+P1(f327(f327(f329(f922(x87351,a910)),f476(x87353,x87352,x87351)),f327(f327(f309(f922(x87351,a910)),x87352),x87353))) % 177.41/177.19 [8736]E(f327(f327(f103(f922(x87361,a910)),x87362),f38(f922(x87361,a910),x87363)),f190(f922(x87361,a910)))+P1(f327(f327(f329(f922(x87361,a910)),x87362),x87363))+P1(f327(f327(f329(f922(x87361,a910)),f475(x87363,x87362,x87361)),f327(f327(f309(f922(x87361,a910)),x87362),x87363))) % 177.41/177.19 [8765]E(x87651,x87652)+~E(f327(f191(f916(x87653)),x87651),f327(f191(f916(x87653)),x87652))+P1(f327(f327(f329(f921(x87653,x87653)),f658(x87653,x87651,x87652)),f327(f173(f921(x87653,x87653)),f327(f327(f182(x87653,x87653),x87652),x87651)))) % 177.41/177.19 [9015]E(f307(x90151,x90152),f307(x90151,x90153))+~P1(f327(f327(f234(f922(f921(x90151,x90151),a910)),x90153),f307(x90151,x90152)))+~P1(f327(f327(f234(f922(f921(x90151,x90151),a910)),x90152),x90153)) % 177.41/177.19 [9082]~P50(x90821,f242(f922(x90821,a910)),x90823)+P1(f327(f327(f234(f922(f921(f916(x90821),f916(x90821)),a910)),f158(x90821,x90822)),f159(x90821,x90823)))+~P1(f327(f327(f234(f922(f921(x90821,x90821),a910)),x90822),x90823)) % 177.41/177.19 [9281]P35(x92811,x92812)+~P1(f327(f327(f329(x92811),x92813),f608(x92812,x92811)))+P1(f327(f327(f329(f921(x92811,x92811)),f327(f327(f252(x92811,x92811),f631(x92812,x92811,x92813)),x92813)),x92812)) % 177.41/177.19 [9316]~P1(f327(f35(x93161),x93162))+P1(f327(f35(f922(x93161,a910)),f327(f327(f61(x93161),x93162),x93163)))+~P1(f327(f327(f234(f922(f921(x93161,x93161),a910)),x93163),f327(f327(f254(x93161,x93161),x93162),f327(f16(f922(x93161,a910),x93161),x93162)))) % 177.41/177.19 [9352]P50(x93521,x93522,x93523)+P1(f327(f327(f329(x93521),f560(x93523,x93522,x93521)),x93522))+~P1(f327(f327(f234(f922(f921(x93521,x93521),a910)),x93523),f327(f327(f254(x93521,x93521),x93522),f327(f16(f922(x93521,a910),x93521),x93522)))) % 177.41/177.19 [9353]P50(x93531,x93532,x93533)+P1(f327(f327(f329(x93531),f569(x93532,x93533,x93531)),x93532))+~P1(f327(f327(f234(f922(f921(x93531,x93531),a910)),x93533),f327(f327(f254(x93531,x93531),x93532),f327(f16(f922(x93531,a910),x93531),x93532)))) % 177.41/177.19 [9387]~P64(x93871)+~P1(f327(f327(f235(x93871),x93872),x93873))+P1(f327(f327(f235(x93871),f327(f327(f291(x93871),f327(f327(f80(x93871),x93872),x93873)),f327(f327(f80(x93871),f78(x93871)),f78(x93871)))),x93873)) % 177.41/177.19 [9416]~P63(x94161)+P1(f327(f327(f234(x94161),x94162),x94163))+~P1(f327(f327(f234(x94161),f327(f327(f81(x94161),f454(x94163,x94162,x94161)),x94162)),x94163)) % 177.41/177.19 [9551]E(f327(f191(f916(f916(x95511))),f327(f137(f916(x95511),f327(f327(f8(a915,a910,f916(x95511)),f327(f235(a915),x95512)),f191(f916(x95511)))),f180(x95511,x95513))),f327(f191(f916(x95511)),f327(f327(f165(f916(x95511)),x95513),x95512)))+~P11(a915,f327(f169(a915),f327(f327(f155(f916(x95511),a915),f191(f916(x95511))),x95513)))+~P1(f327(f327(f235(a915),x95512),f327(f191(f916(f916(x95511))),x95513))) % 177.41/177.19 [9665]~P35(x96651,x96652)+P25(x96651,f327(f327(f252(f922(f921(x96651,x96651),a910),f922(f921(x96651,x96651),a910)),x96652),x96653))+~P1(f327(f327(f234(f922(f921(x96651,x96651),a910)),f327(f327(f289(x96651,x96651,x96651),x96652),x96653)),x96652)) % 177.41/177.19 [9671]E(f327(f327(f155(f916(x96711),x96711),f327(f327(f7(f916(x96711),a915,x96711),f165(x96711)),x96712)),f327(f137(f916(x96711),f327(f327(f8(a915,a910,f916(x96711)),f327(f235(a915),x96712)),f191(f916(x96711)))),f180(x96711,x96713))),f327(f327(f165(f916(x96711)),x96713),x96712))+~P11(a915,f327(f169(a915),f327(f327(f155(f916(x96711),a915),f191(f916(x96711))),x96713)))+~P1(f327(f327(f235(a915),x96712),f327(f191(f916(f916(x96711))),x96713))) % 177.41/177.19 [9807]P50(x98071,x98072,x98073)+~P1(f327(f327(f329(f921(x98071,x98071)),f327(f327(f252(x98071,x98071),f560(x98073,x98072,x98071)),f560(x98073,x98072,x98071))),x98073))+~P1(f327(f327(f234(f922(f921(x98071,x98071),a910)),x98073),f327(f327(f254(x98071,x98071),x98072),f327(f16(f922(x98071,a910),x98071),x98072)))) % 177.41/177.19 [9808]P50(x98081,x98082,x98083)+~P1(f327(f327(f329(f921(x98081,x98081)),f327(f327(f252(x98081,x98081),f569(x98082,x98083,x98081)),f569(x98082,x98083,x98081))),x98083))+~P1(f327(f327(f234(f922(f921(x98081,x98081),a910)),x98083),f327(f327(f254(x98081,x98081),x98082),f327(f16(f922(x98081,a910),x98081),x98082)))) % 177.41/177.19 [9977]~P142(x99771)+~P125(x99771)+E(f327(f327(f291(x99771),f327(f104(x99771),f327(f327(f72(f921(a1,a1),a1,x99772,f251(a1,a1)),f214(x99772)),x99773))),f327(f104(x99771),f327(f327(f72(f921(a1,a1),a1,x99772,f256(a1,a1)),f214(x99772)),x99773))),f224(x99772,x99771,x99773)) % 177.41/177.19 [10182]~E(x101823,f2(a915))+~E(f327(f191(f916(x101821)),f327(f327(f165(f916(x101821)),x101822),f707(x101823,x101821,x101822))),x101823)+E(f327(f327(f155(a915,f916(x101821)),f327(f327(f7(a915,f916(a915),f916(x101821)),f327(f327(f8(f922(a915,x101821),f922(f916(a915),f916(x101821)),a915),f155(a915,x101821)),f327(f7(a915,a915,x101821),f327(f327(f8(f916(x101821),f922(a915,x101821),a915),f165(x101821)),f327(f165(f916(x101821)),x101822))))),f140(a915,f327(f302(a915,f2(a915)),f327(f191(f916(f916(x101821))),x101822))))),f140(a915,f327(f302(a915,f2(a915)),x101823))),f180(x101821,x101822)) % 177.41/177.19 [10183]E(x101831,f114(f916(x101832)))+~E(f327(f191(f916(x101832)),f327(f327(f165(f916(x101832)),x101831),f707(x101833,x101832,x101831))),x101833)+E(f327(f327(f155(a915,f916(x101832)),f327(f327(f7(a915,f916(a915),f916(x101832)),f327(f327(f8(f922(a915,x101832),f922(f916(a915),f916(x101832)),a915),f155(a915,x101832)),f327(f7(a915,a915,x101832),f327(f327(f8(f916(x101832),f922(a915,x101832),a915),f165(x101832)),f327(f165(f916(x101832)),x101831))))),f140(a915,f327(f302(a915,f2(a915)),f327(f191(f916(f916(x101832))),x101831))))),f140(a915,f327(f302(a915,f2(a915)),x101833))),f180(x101832,x101831)) % 177.41/177.19 [10184]~E(x101843,f2(a915))+E(f327(f327(f155(a915,f916(x101841)),f327(f327(f7(a915,f916(a915),f916(x101841)),f327(f327(f8(f922(a915,x101841),f922(f916(a915),f916(x101841)),a915),f155(a915,x101841)),f327(f7(a915,a915,x101841),f327(f327(f8(f916(x101841),f922(a915,x101841),a915),f165(x101841)),f327(f165(f916(x101841)),x101842))))),f140(a915,f327(f302(a915,f2(a915)),f327(f191(f916(f916(x101841))),x101842))))),f140(a915,f327(f302(a915,f2(a915)),x101843))),f180(x101841,x101842))+P1(f327(f327(f235(a915),f707(x101843,x101841,x101842)),f327(f191(f916(f916(x101841))),x101842))) % 177.41/177.19 [10185]E(x101851,f114(f916(x101852)))+E(f327(f327(f155(a915,f916(x101852)),f327(f327(f7(a915,f916(a915),f916(x101852)),f327(f327(f8(f922(a915,x101852),f922(f916(a915),f916(x101852)),a915),f155(a915,x101852)),f327(f7(a915,a915,x101852),f327(f327(f8(f916(x101852),f922(a915,x101852),a915),f165(x101852)),f327(f165(f916(x101852)),x101851))))),f140(a915,f327(f302(a915,f2(a915)),f327(f191(f916(f916(x101852))),x101851))))),f140(a915,f327(f302(a915,f2(a915)),x101853))),f180(x101852,x101851))+P1(f327(f327(f235(a915),f707(x101853,x101852,x101851)),f327(f191(f916(f916(x101852))),x101851))) % 177.41/177.19 [7912]E(f327(f327(f80(a915),f327(f105(a915),x79121)),f327(f327(f80(a915),f327(f105(a915),x79122)),x79123)),f327(f327(f80(a915),f327(f105(a915),f327(f327(f80(a1),x79121),x79122))),x79123))+P1(f327(a195,f327(f105(a1),x79121)))+P1(f327(a195,f327(f105(a1),x79122))) % 177.41/177.19 [8671]~P1(f327(f35(x86711),x86712))+~P1(f327(f327(f329(x86711),x86713),x86712))+E(f327(a113,f327(f36(x86711),f327(f327(f23(f922(x86711,a910)),x86712),f327(f327(f309(x86711),x86713),f190(f922(x86711,a910)))))),f327(f36(x86711),x86712)) % 177.41/177.19 [8687]~P1(f327(f35(x86871),x86872))+~P1(f327(f327(f329(x86871),x86873),x86872))+E(f327(f327(f80(a915),f78(a915)),f327(f36(x86871),f327(f327(f23(f922(x86871,a910)),x86872),f327(f327(f309(x86871),x86873),f190(f922(x86871,a910)))))),f327(f36(x86871),x86872)) % 177.41/177.19 [8774]~P108(x87741)+~P1(f327(f35(x87741),x87743))+E(f327(f327(f149(x87741,x87741,f5(x87741)),x87742),f140(x87741,f327(f327(f23(f922(x87741,a910)),x87743),f327(f327(f309(x87741),x87742),f190(f922(x87741,a910)))))),f140(x87741,f327(f327(f309(x87741),x87742),x87743))) % 177.41/177.19 [8940]~P1(f327(f35(x89401),x89403))+~P1(f327(f35(x89401),x89402))+E(f327(f327(f80(a915),f327(f36(x89401),f327(f327(f102(f922(x89401,a910)),x89402),x89403))),f327(f36(x89401),f327(f327(f103(f922(x89401,a910)),x89402),x89403))),f327(f327(f80(a915),f327(f36(x89401),x89402)),f327(f36(x89401),x89403))) % 177.41/177.19 [10131]~P23(x101311,f922(f922(x101311,a910),a910),f327(f327(f7(x101311,f922(f921(x101311,x101311),a910),f922(f922(x101311,a910),a910)),f327(f327(f8(f922(x101311,a910),f922(f922(f921(x101311,x101311),a910),f922(f922(x101311,a910),a910)),x101311),f61(x101311)),f327(f327(f7(x101311,f922(x101311,a910),f922(x101311,a910)),f309(x101311)),f190(f922(x101311,a910))))),x101313),x101312)+~P1(f327(f35(x101311),x101312))+E(f327(f36(f922(x101311,a910)),f327(f327(f61(x101311),x101312),x101313)),f327(f36(x101311),x101312)) % 177.41/177.19 [8179]~P93(x81791)+P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x81793)))+E(f327(f327(f244(x81791),x81792),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),x81793),x81793)),a98))),f78(x81791)) % 177.41/177.19 [9650]~P93(x96501)+~P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),x96503)))+E(f327(f327(f244(x96501),x96502),f327(f105(a915),f327(f327(f23(a1),f327(f327(f80(a1),x96503),x96503)),a98))),f327(f327(f86(x96501,x96501),f327(f327(f244(x96501),x96502),f327(f105(a915),x96503))),f327(f327(f18(x96501,x96501,x96501),f327(f327(f8(x96501,f922(x96501,x96501),x96501),f81(x96501)),f327(f81(x96501),x96502))),f5(x96501)))) % 177.41/177.19 [10040]~P1(f327(f138(x100401),x100403))+~P1(f327(f327(f329(x100401),x100402),f327(f173(x100401),x100403)))+E(f327(f327(f139(x100401),f327(f191(f916(x100401)),f178(x100401,f327(f327(f8(a910,a910,x100401),a322),f327(f327(f7(x100401,x100401,a910),a324),x100402)),f327(f169(x100401),x100403)))),f327(f169(x100401),x100403)),f327(f327(f152(x100401),x100402),f327(f169(x100401),f178(x100401,f327(f327(f8(a910,a910,x100401),a322),f327(f327(f7(x100401,x100401,a910),a324),x100402)),x100403)))) % 177.41/177.19 [10101]P1(f327(f327(f234(f922(f921(x101011,x101011),a910)),f307(x101011,x101012)),x101013))+~P1(f327(f327(f234(f922(f921(x101011,x101011),a910)),f307(x101011,f190(f922(f921(x101011,x101011),a910)))),x101013))+~P1(f327(f327(f234(f922(f921(x101011,x101011),a910)),f327(f327(f289(x101011,x101011,x101011),f327(f327(f103(f922(f921(x101011,x101011),a910)),f307(x101011,x101012)),x101013)),x101012)),x101013)) % 177.41/177.19 [9957]~P1(f327(f35(x99571),f327(f262(x99571),x99573)))+~P1(f327(f35(x99571),f327(f262(x99571),x99572)))+P1(f327(f35(x99571),f327(f262(x99571),f327(f327(f18(x99571,a910,a910),f327(f327(f8(a910,f922(a910,a910),x99571),a326),x99572)),x99573)))) % 177.41/177.19 [10249]P1(f327(f327(f234(f922(f921(x102491,x102491),a910)),f327(f327(f289(x102491,x102491,x102491),x102492),f307(x102491,x102492))),x102493))+~P1(f327(f327(f234(f922(f921(x102491,x102491),a910)),x102492),x102493))+~P1(f327(f327(f234(f922(f921(x102491,x102491),a910)),f327(f327(f289(x102491,x102491,x102491),f327(f327(f103(f922(f921(x102491,x102491),a910)),f327(f327(f289(x102491,x102491,x102491),x102492),f307(x102491,x102492))),x102493)),x102492)),x102493)) % 177.41/177.19 [10199]~P119(x101992)+E(x101991,f2(x101992))+~E(f327(f327(f80(x101992),f327(f327(f244(x101992),x101993),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x101992),x101991),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f2(x101992)) % 177.41/177.19 [10200]~P119(x102002)+E(x102001,f2(x102002))+~E(f327(f327(f80(x102002),f327(f327(f244(x102002),x102001),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x102002),x102003),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f2(x102002)) % 177.41/177.19 [10205]~P1(f327(f138(x102051),x102053))+~P1(f327(f327(f329(x102051),x102052),f327(f173(x102051),x102053)))+E(f327(f169(x102051),f327(f172(x102051),f327(f327(f139(x102051),f327(f191(f916(x102051)),f178(x102051,f327(f327(f8(a910,a910,x102051),a322),f327(f327(f7(x102051,x102051,a910),a324),x102052)),x102053))),x102053))),f178(x102051,f327(f327(f8(a910,a910,x102051),a322),f327(f327(f7(x102051,x102051,a910),a324),x102052)),f327(f169(x102051),x102053))) % 177.41/177.19 [10297]~P119(x102972)+E(x102971,f2(x102972))+P1(f327(f327(f235(x102972),f2(x102972)),f327(f327(f80(x102972),f327(f327(f244(x102972),x102973),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x102972),x102971),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))))) % 177.41/177.19 [10298]~P119(x102982)+E(x102981,f2(x102982))+P1(f327(f327(f235(x102982),f2(x102982)),f327(f327(f80(x102982),f327(f327(f244(x102982),x102981),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x102982),x102983),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))))) % 177.41/177.19 [10353]~P119(x103531)+P1(f327(f327(f234(x103531),f2(x103531)),x103532))+~P1(f327(f327(f234(x103531),f2(x103531)),f327(f327(f244(x103531),x103532),f327(a113,f327(f327(f81(a915),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),x103533))))) % 177.41/177.19 [5659]~P22(x56591,x56594,x56593)+P22(x56591,x56592,x56593)+~P22(x56591,x56592,x56594) % 177.41/177.19 [5124]~E(x51242,f90(x51243,x51241))+P1(f327(x51241,x51242))+~P1(f327(x51241,x51244)) % 177.41/177.19 [5368]E(f68(x53683,x53682,x53684),x53682)+E(x53681,f734(x53682,x53683,x53684))+~P1(f327(x53684,x53681)) % 177.41/177.19 [6696]E(f68(x66961,x66962,x66963),f85(x66961,x66963))+~E(f771(x66962,x66961,x66963,x66964),x66964)+~P1(f327(x66963,x66964)) % 177.41/177.19 [6905]~P35(x69052,x69054)+~P35(x69051,x69053)+P35(f921(x69051,x69052),f320(x69051,x69052,x69053,x69054)) % 177.41/177.19 [6906]~P36(x69062,x69064)+~P36(x69061,x69063)+P36(f921(x69061,x69062),f320(x69061,x69062,x69063,x69064)) % 177.41/177.19 [5308]~P5(x53084,x53081)+~E(f327(x53081,x53082),f327(x53081,x53083))+P1(f327(f327(x53081,x53082),x53083)) % 177.41/177.19 [5471]~P5(x54714,x54711)+E(f327(x54711,x54712),f327(x54711,x54713))+~P1(f327(f327(x54711,x54712),x54713)) % 177.41/177.19 [5472]~P13(x54724,x54721)+E(f327(x54721,x54722),f327(x54721,x54723))+~P1(f327(f327(x54721,x54722),x54723)) % 177.41/177.19 [5565]~P16(x55653,x55654,x55651)+E(f327(x55651,x55652),f327(f63(x55653,x55654),x55652))+~P1(f327(f35(x55653),x55652)) % 177.41/177.19 [5566]~P7(x55663,x55664,x55661)+E(f327(x55661,x55662),f327(f63(x55663,x55664),x55662))+~P1(f327(f35(x55663),x55662)) % 177.41/177.19 [5694]~P5(x56944,x56941)+~P1(f327(f327(x56941,x56943),x56942))+P1(f327(f327(x56941,x56942),x56943)) % 177.41/177.19 [5695]~P48(x56954,x56951)+~P1(f327(f327(x56951,x56953),x56952))+P1(f327(f327(x56951,x56952),x56953)) % 177.41/177.19 [5696]~P13(x56964,x56961)+~P1(f327(f327(x56961,x56963),x56962))+P1(f327(f327(x56961,x56962),x56963)) % 177.41/177.19 [5697]~P13(x56973,x56971)+P1(f327(f327(x56971,x56972),x56972))+~P1(f327(f327(x56971,x56974),x56972)) % 177.41/177.19 [5698]~P13(x56983,x56981)+P1(f327(f327(x56981,x56982),x56982))+~P1(f327(f327(x56981,x56982),x56984)) % 177.41/177.19 [5768]E(x57681,x57682)+~E(f327(f251(x57683,x57684),x57681),f327(f251(x57683,x57684),x57682))+~E(f327(f256(x57683,x57684),x57681),f327(f256(x57683,x57684),x57682)) % 177.41/177.19 [5796]E(x57961,x57962)+~P1(f327(f49(x57963,x57964),x57962))+~P1(f327(f49(x57963,x57964),x57961)) % 177.41/177.19 [5987]~P68(x59872)+E(f233(x59871,x59872,x59873,x59874),f2(x59872))+P1(f327(f35(x59871),x59874)) % 177.41/177.19 [6035]~P5(x60353,x60352)+~P1(f327(x60351,x60354))+P1(f327(x60351,f815(x60351,x60352,x60353))) % 177.41/177.19 [6132]~P1(f327(f315(x61321,x61322),x61324))+P1(f327(f315(x61321,x61322),x61323))+~P1(f327(f327(x61322,x61323),x61324)) % 177.41/177.19 [6940]~P27(x69401,x69403,x69404)+P1(f327(x69401,x69402))+~P1(f327(f327(f329(a1),x69402),f303(a1,x69403,x69404))) % 177.41/177.19 [7132]~P5(x71321,x71323)+~P1(f327(x71322,x71324))+P1(f327(f327(f329(x71321),f815(x71322,x71323,x71321)),f270(x71321,x71323))) % 177.41/177.19 [8020]E(x80201,f2(a915))+~P1(f327(x80202,x80203))+P1(f327(x80202,f765(x80202,x80203,x80201,x80204))) % 177.41/177.19 [8102]~P108(x81022)+~P1(f327(f138(x81021),x81024))+P1(f327(f138(x81021),f151(x81021,x81022,x81023,x81024))) % 177.41/177.19 [8146]E(f68(x81461,x81462,x81463),f85(x81461,x81463))+~P1(f327(x81463,x81464))+P1(f327(x81463,f771(x81462,x81461,x81463,x81464))) % 177.41/177.19 [8328]~P1(f327(f35(x83282),x83284))+~P1(f327(f35(x83281),x83283))+P1(f327(f35(f920(x83281,x83282)),f313(x83281,x83282,x83283,x83284))) % 177.41/177.19 [8329]~P1(f327(f138(x83292),x83294))+~P1(f327(f138(x83291),x83293))+P1(f327(f138(f921(x83291,x83292)),f60(x83291,x83292,x83293,x83294))) % 177.41/177.19 [8332]P1(f327(f327(f329(f916(x83321)),f327(f327(f135(x83321),x83322),x83323)),f162(x83321,x83324)))+~P1(f327(f327(f329(f916(x83321)),x83323),f162(x83321,x83324)))+~P1(f327(f327(f329(f916(x83321)),x83322),f162(x83321,x83324))) % 177.41/177.19 [8609]E(x86091,f2(a915))+P1(f327(x86092,x86093))+~P1(f327(x86092,f766(x86092,x86093,x86091,x86094))) % 177.41/177.19 [8646]~P108(x86463)+~P1(f327(f138(x86461),f151(x86461,x86463,x86464,x86462)))+P1(f327(f138(x86461),x86462)) % 177.41/177.19 [8929]~P1(f327(f327(f329(f921(x89291,x89291)),f327(f327(f252(x89291,x89291),x89292),x89294)),f307(x89291,x89293)))+P1(f327(f327(f329(x89291),x89292),f316(x89291,x89293)))+~P1(f327(f327(f329(x89291),x89294),f316(x89291,x89293))) % 177.41/177.19 [5292]~P68(x52922)+E(f327(f327(f6(x52921,x52922),x52923),x52924),f2(x52922))+P1(f327(f35(x52921),x52924)) % 177.41/177.19 [5295]~P75(x52952)+E(f327(f327(f9(x52951,x52952),x52953),x52954),f78(x52952))+P1(f327(f35(x52951),x52954)) % 177.41/177.19 [5435]~P69(x54353)+E(x54351,x54352)+~E(f327(f327(f80(x54353),x54354),x54351),f327(f327(f80(x54353),x54354),x54352)) % 177.41/177.19 [5436]~P70(x54363)+E(x54361,x54362)+~E(f327(f327(f80(x54363),x54364),x54361),f327(f327(f80(x54363),x54364),x54362)) % 177.41/177.19 [5438]~P69(x54383)+E(x54381,x54382)+~E(f327(f327(f80(x54383),x54381),x54384),f327(f327(f80(x54383),x54382),x54384)) % 177.41/177.19 [5532]~P121(x55321)+~E(x55323,f327(f327(f81(x55321),x55322),x55324))+P1(f327(f327(f287(x55321),x55322),x55323)) % 177.41/177.19 [5560]~P3(x55603)+E(x55601,f190(f922(x55602,a910)))+E(f327(f327(f40(x55602,x55603),x55601),f327(f16(x55603,x55602),x55604)),x55604) % 177.41/177.19 [5561]~P3(x55613)+E(x55611,f190(f922(x55612,a910)))+E(f327(f327(f41(x55612,x55613),x55611),f327(f16(x55613,x55612),x55614)),x55614) % 177.41/177.19 [5782]~P110(x57823)+E(x57821,x57822)+~E(f303(x57823,x57824,x57821),f327(f327(f309(x57823),x57822),f190(f922(x57823,a910)))) % 177.41/177.19 [5783]~P110(x57833)+E(x57831,x57832)+~E(f303(x57833,x57831,x57832),f327(f327(f309(x57833),x57834),f190(f922(x57833,a910)))) % 177.41/177.19 [5843]~P33(x58433,x58431,x58434)+P33(x58433,x58431,f327(f327(f152(x58433),x58432),x58434))+P1(f327(x58431,x58432)) % 177.41/177.19 [5945]~P29(x59451,x59452,x59454)+~P1(f327(x59452,x59453))+P29(x59451,x59452,f327(f327(f152(x59451),x59453),x59454)) % 177.41/177.19 [6087]P1(f327(x60871,x60872))+~P1(f327(f248(x60873,x60871),x60874))+~P1(f327(f327(f329(x60873),x60872),x60874)) % 177.41/177.19 [6096]~P29(x60961,x60962,x60964)+~P29(x60961,x60962,x60963)+P29(x60961,x60962,f327(f327(f135(x60961),x60963),x60964)) % 177.41/177.19 [6111]P31(x61111,x61112,x61113)+~P31(x61111,x61112,f327(f327(f152(x61111),x61114),x61113))+P1(f327(x61112,x61114)) % 177.41/177.19 [6112]P33(x61121,x61122,x61123)+~P33(x61121,x61122,f327(f327(f152(x61121),x61124),x61123))+P1(f327(x61122,x61124)) % 177.41/177.19 [6187]P31(x61871,x61872,x61873)+P31(x61871,x61872,x61874)+~P31(x61871,x61872,f327(f327(f135(x61871),x61874),x61873)) % 177.41/177.19 [6207]~P68(x62071)+E(f327(f327(f6(a915,x62071),x62072),f327(f302(a915,x62073),f327(a113,x62074))),f2(x62071))+~P1(f327(f327(f235(a915),x62074),x62073)) % 177.41/177.19 [6212]~P59(x62121)+~E(f46(x62121,x62122,x62123),f46(x62121,x62124,x62123))+E(f46(x62121,f327(f79(x62121),x62122),x62123),f46(x62121,f327(f79(x62121),x62124),x62123)) % 177.41/177.19 [6284]P1(f327(x62841,x62842))+~E(f327(f137(x62843,x62841),x62844),x62844)+~P1(f327(f327(f329(x62843),x62842),f327(f173(x62843),x62844))) % 177.41/177.19 [6304]~E(f327(f327(f80(a915),x63043),x63042),f327(f327(f80(a915),x63041),x63044))+~P1(f327(f327(f235(a915),x63043),x63044))+P1(f327(f327(f235(a915),x63041),x63042)) % 177.41/177.19 [6310]P31(x63101,x63102,x63103)+~P1(f327(x63102,x63104))+~P1(f327(f327(f329(x63101),x63104),f327(f173(x63101),x63103))) % 177.41/177.19 [6313]~P58(x63131)+E(f46(x63131,f46(x63131,x63132,x63133),x63134),f46(x63131,x63132,x63134))+~P1(f327(f327(f287(x63131),x63134),x63133)) % 177.41/177.19 [6351]~P29(x63513,x63511,x63514)+P1(f327(x63511,x63512))+~P1(f327(f327(f329(x63513),x63512),f327(f173(x63513),x63514))) % 177.41/177.19 [6353]~E(f327(f137(x63531,x63532),x63533),f114(x63531))+~P1(f327(x63532,x63534))+~P1(f327(f327(f329(x63531),x63534),f327(f173(x63531),x63533))) % 177.41/177.19 [6354]~E(f178(x63543,x63541,x63544),x63544)+P1(f327(x63541,x63542))+~P1(f327(f327(f329(x63543),x63542),f327(f173(x63543),x63544))) % 177.41/177.19 [6381]~E(x63814,f190(f922(x63812,a910)))+~E(x63813,f190(f922(x63811,a910)))+E(f313(x63811,x63812,x63813,x63814),f190(f922(f920(x63811,x63812),a910))) % 177.41/177.19 [6529]P1(f327(x65291,x65292))+~P1(f327(f161(x65293,x65291),x65294))+~P1(f327(f327(f329(x65293),x65292),f327(f173(x65293),x65294))) % 177.41/177.19 [6665]~P28(x66651,x66653,x66654)+P1(f327(x66651,x66652))+~P1(f327(f327(f329(a915),x66652),f327(f302(a915,x66653),x66654))) % 177.41/177.19 [6802]~P68(x68021)+E(f327(f327(f6(a915,x68021),x68022),f303(a915,x68023,f327(a113,x68024))),f2(x68021))+~P1(f327(f327(f235(a915),f327(a113,x68024)),x68023)) % 177.41/177.19 [6943]~P108(x69431)+E(f327(f327(f23(f922(x69431,a910)),f327(f302(x69431,x69432),x69433)),f327(f302(x69431,x69432),x69434)),f327(f302(x69431,x69434),x69433))+~P1(f327(f327(f234(x69431),x69432),x69434)) % 177.41/177.19 [7014]~E(x70143,x70144)+E(x70141,f2(a915))+P1(f327(f327(f329(x70142),x70143),f327(f173(x70142),f170(x70142,x70141,x70144)))) % 177.41/177.19 [7297]~P1(f327(f327(f329(f916(x72971)),x72974),f162(x72971,x72973)))+P1(f327(f327(f329(x72971),x72972),x72973))+~P1(f327(f327(f329(x72971),x72972),f327(f173(x72971),x72974))) % 177.41/177.19 [7304]~P35(x73041,x73042)+P1(f327(f327(f329(x73041),f609(x73042,x73041,x73043)),x73043))+~P1(f327(f327(f329(x73041),x73044),x73043)) % 177.41/177.19 [7361]~P68(x73611)+E(f327(f327(f327(f65(x73611,x73612,f80(x73611)),x73613),f2(x73611)),x73614),f327(f327(f6(x73612,x73611),x73613),x73614))+~P1(f327(f35(x73612),x73614)) % 177.41/177.19 [7363]~P75(x73631)+E(f327(f327(f327(f65(x73631,x73632,f81(x73631)),x73633),f78(x73631)),x73634),f327(f327(f9(x73632,x73631),x73633),x73634))+~P1(f327(f35(x73632),x73634)) % 177.41/177.19 [7392]P23(x73921,x73922,x73923,x73924)+~E(f327(f36(x73922),f327(f310(x73921,x73922,x73923),x73924)),f327(f36(x73921),x73924))+~P1(f327(f35(x73921),x73924)) % 177.41/177.19 [7582]~P68(x75821)+E(f327(f327(f80(x75821),f327(x75822,x75823)),f327(f327(f6(a915,x75821),x75822),f305(a915,x75823,x75824))),f327(f327(f6(a915,x75821),x75822),f303(a915,x75823,x75824)))+~P1(f327(f327(f234(a915),x75823),x75824)) % 177.41/177.19 [7592]~P68(x75921)+~P23(x75922,x75921,x75923,x75924)+E(f327(f327(f6(x75921,x75921),f31(x75921)),f327(f310(x75922,x75921,x75923),x75924)),f327(f327(f6(x75922,x75921),x75923),x75924)) % 177.41/177.19 [7593]~P75(x75931)+~P23(x75932,x75931,x75933,x75934)+E(f327(f327(f9(x75931,x75931),f31(x75931)),f327(f310(x75932,x75931,x75933),x75934)),f327(f327(f9(x75932,x75931),x75933),x75934)) % 177.41/177.19 [7642]E(f327(f36(f920(x76421,x76422)),f313(x76421,x76422,x76423,x76424)),f327(f327(f80(a915),f327(f36(x76421),x76423)),f327(f36(x76422),x76424)))+~P1(f327(f35(x76422),x76424))+~P1(f327(f35(x76421),x76423)) % 177.41/177.19 [7723]E(x77231,x77232)+P1(f327(f327(f329(x77233),x77231),f327(f173(x77233),f171(x77233,x77232,x77234))))+~P1(f327(f327(f329(x77233),x77231),f327(f173(x77233),x77234))) % 177.41/177.19 [7951]~P68(x79511)+E(f327(f327(f80(x79511),f327(f327(f6(a915,x79511),x79512),f327(f302(a915,x79513),x79514))),f327(x79512,x79514)),f327(f327(f6(a915,x79511),x79512),f327(f302(a915,x79513),f327(a113,x79514))))+P1(f327(f327(f235(a915),x79514),x79513)) % 177.41/177.19 [8000]~P23(x80001,x80002,x80003,f242(f922(x80001,a910)))+~P1(f327(f35(x80002),x80004))+P1(f327(f35(x80001),f327(f311(x80001,x80002,x80003),x80004))) % 177.41/177.19 [8117]P1(f327(f327(f329(f916(x81171)),f327(f327(f152(x81171),x81172),x81173)),f162(x81171,x81174)))+~P1(f327(f327(f329(f916(x81171)),x81173),f162(x81171,x81174)))+~P1(f327(f327(f329(x81171),x81172),x81174)) % 177.41/177.19 [8203]~E(f327(f310(x82033,x82031,x82034),f242(f922(x82033,a910))),f242(f922(x82031,a910)))+P1(f327(f35(x82031),x82032))+~P1(f327(f35(x82033),f327(f311(x82033,x82031,x82034),x82032))) % 177.41/177.19 [8298]~P23(x82981,x82983,x82984,x82982)+P1(f327(f35(x82981),x82982))+~P1(f327(f35(x82983),f327(f310(x82981,x82983,x82984),x82982))) % 177.41/177.19 [8322]~E(x83222,x83223)+P1(f327(f327(f329(f921(x83221,x83221)),f327(f327(f252(x83221,x83221),x83222),x83223)),f263(x83221,x83224)))+~P1(f327(f327(f329(x83221),x83222),x83224)) % 177.41/177.19 [8355]~P68(x83551)+E(f327(f327(f80(x83551),f327(f327(f6(a915,x83551),x83552),f303(a915,x83553,x83554))),f327(x83552,f327(a113,x83554))),f327(f327(f6(a915,x83551),x83552),f303(a915,x83553,f327(a113,x83554))))+P1(f327(f327(f235(a915),f327(a113,x83554)),x83553)) % 177.41/177.19 [8415]P1(f327(x84151,x84152))+~P1(f327(x84151,f327(f327(f165(x84153),x84154),f657(x84151,x84154,x84153))))+~P1(f327(f327(f329(x84153),x84152),f327(f173(x84153),x84154))) % 177.41/177.19 [8554]~P1(f327(f327(f329(x85541),x85542),f316(x85541,x85544)))+P1(f327(f327(f329(f916(x85541)),f327(f327(f152(x85541),x85542),x85543)),f316(f916(x85541),f158(x85541,x85544))))+~P1(f327(f327(f329(f916(x85541)),x85543),f316(f916(x85541),f158(x85541,x85544)))) % 177.41/177.19 [8569]~P23(x85692,x85693,x85694,f474(x85694,x85693,x85692,x85691))+P23(x85692,x85693,x85694,f39(f922(x85692,a910),x85691))+E(x85691,f190(f922(f922(x85692,a910),a910))) % 177.41/177.19 [8838]E(x88381,x88382)+~P1(f327(f327(f329(f921(x88383,x88383)),f327(f327(f252(x88383,x88383),x88381),x88382)),f307(x88383,x88384)))+P1(f327(f327(f329(x88383),x88381),f327(f264(x88383,x88383),x88384))) % 177.41/177.19 [9120]E(x91201,f2(a915))+P1(f327(x91202,x91203))+P1(f327(f327(f329(x91204),f766(x91202,x91203,x91201,x91204)),f327(f173(x91204),f170(x91204,x91201,x91203)))) % 177.41/177.19 [9132]E(x91321,f2(a915))+~P1(f327(x91323,x91324))+P1(f327(f327(f329(x91322),f765(x91323,x91324,x91321,x91322)),f327(f173(x91322),f170(x91322,x91321,x91324)))) % 177.41/177.19 [9134]~P24(x91341,x91342,x91343,f242(f922(x91341,a910)),f242(f922(x91342,a910)))+~P1(f327(f35(x91342),x91344))+P1(f327(f35(x91341),f327(f311(x91341,x91342,x91343),x91344))) % 177.41/177.19 [9137]P23(x91372,x91373,x91374,f39(f922(x91372,a910),x91371))+E(x91371,f190(f922(f922(x91372,a910),a910)))+P1(f327(f327(f329(f922(x91372,a910)),f474(x91374,x91373,x91372,x91371)),x91371)) % 177.41/177.19 [9252]~P24(x92523,x92521,x92524,f242(f922(x92523,a910)),f242(f922(x92521,a910)))+P1(f327(f35(x92521),x92522))+~P1(f327(f35(x92523),f327(f311(x92523,x92521,x92524),x92522))) % 177.41/177.19 [9269]P1(f327(f35(x92691),x92692))+~P1(f327(f35(x92694),f327(f310(x92691,x92694,x92693),x92692)))+P1(f327(f327(f329(x92691),f497(x92693,x92694,x92692,x92691)),x92692)) % 177.41/177.19 [9363]~P3(x93632)+E(f327(f327(f64(x93631,x93632,f327(f327(f8(x93632,f922(x93632,x93632),x93631),f102(x93632)),x93633)),f190(x93632)),x93634),f327(f327(f40(x93631,x93632),x93634),x93633))+~P1(f327(f35(x93631),x93634)) % 177.41/177.19 [9364]~P3(x93642)+E(f327(f327(f64(x93641,x93642,f327(f327(f8(x93642,f922(x93642,x93642),x93641),f103(x93642)),x93643)),f242(x93642)),x93644),f327(f327(f41(x93641,x93642),x93644),x93643))+~P1(f327(f35(x93641),x93644)) % 177.41/177.19 [9446]P1(f327(x94461,x94462))+~P1(f327(x94461,f327(f327(f165(x94463),x94464),f694(x94462,x94461,x94464,x94463))))+~P1(f327(f327(f329(x94463),x94462),f327(f173(x94463),x94464))) % 177.41/177.19 [9467]E(x94671,x94672)+~P1(f327(f327(f329(f921(x94673,x94673)),f327(f327(f252(x94673,x94673),x94671),x94672)),f307(x94673,x94674)))+P1(f327(f327(f329(f921(x94673,x94673)),f327(f327(f252(x94673,x94673),x94671),x94672)),f327(f327(f289(x94673,x94673,x94673),x94674),f307(x94673,x94674)))) % 177.41/177.19 [9517]~E(f327(f191(f916(x95171)),x95172),f327(f191(f916(x95171)),x95173))+~P1(f327(f327(f329(f921(f916(x95171),f916(x95171))),f327(f327(f252(f916(x95171),f916(x95171)),x95172),x95173)),f148(x95171,x95174)))+P1(f327(f327(f329(f921(f916(x95171),f916(x95171))),f327(f327(f252(f916(x95171),f916(x95171)),x95172),x95173)),f146(x95171,x95174))) % 177.41/177.19 [9755]P29(x97551,f327(f327(f18(x97551,a910,a910),f327(f327(f8(a910,f922(a910,a910),x97551),a326),f327(f327(f8(a910,a910,x97551),a322),x97552))),f327(a324,x97553)),x97554)+~P1(f327(x97552,x97553))+~P33(x97551,x97552,f327(f327(f152(x97551),x97553),x97554)) % 177.41/177.19 [9921]~P29(x99211,f327(f327(f18(x99211,a910,a910),f327(f327(f8(a910,f922(a910,a910),x99211),a326),f327(f327(f8(a910,a910,x99211),a322),x99212))),f327(a324,x99213)),x99214)+~P1(f327(x99212,x99213))+P33(x99211,x99212,f327(f327(f152(x99211),x99213),x99214)) % 177.41/177.19 [9925]~P33(x99251,x99252,x99254)+~P29(x99251,f327(f327(f18(x99251,a910,a910),f327(f327(f8(a910,f922(a910,a910),x99251),a326),f327(f327(f8(a910,a910,x99251),a322),x99252))),f327(a324,x99253)),x99254)+P33(x99251,x99252,f327(f327(f152(x99251),x99253),x99254)) % 177.41/177.19 [9958]~P67(x99581)+E(f327(f327(f6(a915,x99581),f327(f327(f18(a915,x99581,x99581),f327(f327(f8(x99581,f922(x99581,x99581),a915),f23(x99581)),x99582)),f327(f327(f8(a915,x99581,a915),x99582),f327(f327(f7(a915,a915,a915),f80(a915)),f78(a915))))),f303(a915,x99583,x99584)),f2(x99581))+P1(f327(f327(f234(a915),x99583),x99584)) % 177.41/177.19 [10198]~P35(x101982,x101984)+~P23(x101982,x101981,x101983,f242(f922(x101982,a910)))+P35(x101981,f327(f310(f921(x101982,x101982),f921(x101981,x101981),f258(x101982,x101981,x101982,x101981,x101983,x101983)),x101984)) % 177.41/177.19 [10388]~E(f327(f191(f916(x103881)),x103883),f327(f191(f916(x103881)),x103882))+P1(f327(f327(f329(f921(f916(x103881),f916(x103881))),f327(f327(f252(f916(x103881),f916(x103881)),x103882),x103883)),f159(x103881,x103884)))+~P1(f327(f327(f257(x103881,x103881,a910),f327(f327(f7(x103881,f922(f921(x103881,x103881),a910),f922(x103881,a910)),f327(f327(f8(f922(x103881,f922(f922(f921(x103881,x103881),a910),a910)),f922(f922(f921(x103881,x103881),a910),f922(x103881,a910)),x103881),f7(x103881,f922(f921(x103881,x103881),a910),a910)),f327(f327(f8(f922(x103881,f921(x103881,x103881)),f922(x103881,f922(f922(f921(x103881,x103881),a910),a910)),x103881),f327(f8(f921(x103881,x103881),f922(f922(f921(x103881,x103881),a910),a910),x103881),f329(f921(x103881,x103881)))),f252(x103881,x103881)))),x103884)),f659(x103884,x103883,x103882,x103881))) % 177.41/177.19 [6265]~P58(x62651)+~E(x62652,f2(x62651))+E(f327(f327(f37(x62651),f327(f327(f81(x62651),x62652),x62653)),f327(f327(f81(x62651),x62652),x62654)),f2(x62651)) % 177.41/177.19 [6307]E(x63071,f114(x63072))+E(x63073,f327(f327(f23(a915),f327(f191(f916(x63072)),x63071)),f78(a915)))+E(f145(x63072,f327(f327(f160(x63072,x63071),x63073),x63074)),f145(x63072,x63071)) % 177.41/177.19 [6342]E(x63421,x63422)+P1(f327(x63423,x63422))+~P1(f327(f327(f327(f309(x63424),x63421),x63423),x63422)) % 177.41/177.19 [6358]~P68(x63581)+~P1(f327(f138(x63582),x63584))+E(f327(f166(x63581),f327(f327(f155(x63582,x63581),x63583),x63584)),f327(f327(f6(x63582,x63581),x63583),f327(f173(x63582),x63584))) % 177.41/177.19 [6374]~P75(x63742)+~P1(f327(f35(x63741),x63744))+E(f327(f327(f9(x63741,x63742),f327(f16(x63742,x63741),x63743)),x63744),f327(f327(f244(x63742),x63743),f327(f36(x63741),x63744))) % 177.41/177.19 [6427]~P58(x64272)+E(x64271,f2(x64272))+E(f327(f327(f37(x64272),f327(f327(f81(x64272),x64273),x64271)),f327(f327(f81(x64272),x64274),x64271)),f327(f327(f37(x64272),x64273),x64274)) % 177.41/177.19 [6429]~P61(x64292)+E(x64291,f2(x64292))+E(f327(f327(f291(x64292),f327(f327(f81(x64292),x64293),x64291)),f327(f327(f81(x64292),x64294),x64291)),f327(f327(f291(x64292),x64293),x64294)) % 177.41/177.19 [6430]~P61(x64302)+E(x64301,f2(x64302))+E(f327(f327(f291(x64302),f327(f327(f81(x64302),x64301),x64303)),f327(f327(f81(x64302),x64301),x64304)),f327(f327(f291(x64302),x64303),x64304)) % 177.41/177.19 [6431]~P58(x64312)+E(x64311,f2(x64312))+E(f327(f327(f37(x64312),f327(f327(f81(x64312),x64311),x64313)),f327(f327(f81(x64312),x64311),x64314)),f327(f327(f37(x64312),x64313),x64314)) % 177.41/177.19 [6498]P1(f327(x64981,x64982))+~E(x64983,f327(f327(f80(a915),x64984),x64982))+~P1(f327(x64981,f327(f327(f23(a915),x64983),x64984))) % 177.41/177.19 [6582]~P1(f327(x65822,x65823))+~P1(f327(f161(x65821,x65822),x65824))+P1(f327(f161(x65821,x65822),f327(f327(f152(x65821),x65823),x65824))) % 177.41/177.19 [6622]E(x66221,f114(x66222))+~E(x66223,f327(f327(f23(a915),f327(f191(f916(x66222)),x66221)),f78(a915)))+E(f145(x66222,f327(f327(f160(x66222,x66221),x66223),x66224)),x66224) % 177.41/177.19 [6646]~P108(x66461)+~P1(f327(f327(f234(x66461),x66462),x66464))+P1(f327(f327(f234(x66461),x66462),f327(f327(f189(x66461),x66463),x66464))) % 177.41/177.19 [6648]~P108(x66481)+~P1(f327(f327(f234(x66481),x66482),x66483))+P1(f327(f327(f234(x66481),x66482),f327(f327(f189(x66481),x66483),x66484))) % 177.41/177.19 [6649]~P101(x66491)+~P1(f327(f327(f234(x66491),x66492),x66494))+P1(f327(f327(f234(x66491),x66492),f327(f327(f102(x66491),x66493),x66494))) % 177.41/177.19 [6650]~P101(x66501)+~P1(f327(f327(f234(x66501),x66502),x66503))+P1(f327(f327(f234(x66501),x66502),f327(f327(f102(x66501),x66503),x66504))) % 177.41/177.19 [6652]~P108(x66521)+~P1(f327(f327(f235(x66521),x66522),x66524))+P1(f327(f327(f235(x66521),x66522),f327(f327(f189(x66521),x66523),x66524))) % 177.41/177.19 [6654]~P108(x66541)+~P1(f327(f327(f235(x66541),x66542),x66543))+P1(f327(f327(f235(x66541),x66542),f327(f327(f189(x66541),x66543),x66544))) % 177.41/177.19 [6655]~P101(x66551)+~P1(f327(f327(f235(x66551),x66552),x66554))+P1(f327(f327(f235(x66551),x66552),f327(f327(f102(x66551),x66553),x66554))) % 177.41/177.19 [6656]~P101(x66561)+~P1(f327(f327(f235(x66561),x66562),x66563))+P1(f327(f327(f235(x66561),x66562),f327(f327(f102(x66561),x66563),x66564))) % 177.41/177.19 [6657]~P112(x66571)+~P1(f327(f327(f287(x66571),x66572),x66574))+P1(f327(f327(f287(x66571),x66572),f327(f327(f81(x66571),x66573),x66574))) % 177.41/177.19 [6658]~P112(x66581)+~P1(f327(f327(f287(x66581),x66582),x66583))+P1(f327(f327(f287(x66581),x66582),f327(f327(f81(x66581),x66583),x66584))) % 177.41/177.19 [6747]~E(f327(f327(f165(x67471),x67472),x67473),x67474)+E(f327(f327(f160(x67471,x67472),x67473),x67474),x67472)+~P1(f327(f327(f235(a915),x67473),f327(f191(f916(x67471)),x67472))) % 177.41/177.19 [6786]P1(f327(x67861,x67862))+~P1(f327(x67863,x67862))+~P1(f327(f327(f234(f922(x67864,a910)),x67863),x67861)) % 177.41/177.19 [6819]~E(f327(f327(f160(x68191,x68192),x68193),x68194),x68192)+E(f327(f327(f165(x68191),x68192),x68193),x68194)+~P1(f327(f327(f235(a915),x68193),f327(f191(f916(x68191)),x68192))) % 177.41/177.19 [6833]~P1(f327(f161(x68331,x68332),x68334))+~P1(f327(f161(x68331,x68332),x68333))+P1(f327(f161(x68331,x68332),f327(f327(f135(x68331),x68333),x68334))) % 177.41/177.19 [6939]E(x69391,f190(f922(x69392,a910)))+E(x69393,f190(f922(x69394,a910)))+~E(f327(f327(f254(x69394,x69392),x69393),f327(f16(f922(x69392,a910),x69394),x69391)),f190(f922(f921(x69394,x69392),a910))) % 177.41/177.19 [6959]E(x69591,x69592)+P1(f327(f327(f329(x69593),x69591),x69594))+~P1(f327(f327(f329(x69593),x69591),f327(f327(f309(x69593),x69592),x69594))) % 177.41/177.19 [6976]~P108(x69761)+P1(f327(f327(f234(x69761),x69762),x69763))+~P1(f327(f327(f234(x69761),x69762),f327(f327(f238(x69761),x69764),x69763))) % 177.41/177.19 [6978]~P108(x69781)+P1(f327(f327(f234(x69781),x69782),x69783))+~P1(f327(f327(f234(x69781),x69782),f327(f327(f238(x69781),x69783),x69784))) % 177.41/177.19 [6980]~P102(x69801)+P1(f327(f327(f234(x69801),x69802),x69803))+~P1(f327(f327(f234(x69801),x69802),f327(f327(f103(x69801),x69804),x69803))) % 177.41/177.19 [6982]~P102(x69821)+P1(f327(f327(f234(x69821),x69822),x69823))+~P1(f327(f327(f234(x69821),x69822),f327(f327(f103(x69821),x69823),x69824))) % 177.41/177.19 [6983]~P108(x69831)+P1(f327(f327(f235(x69831),x69832),x69833))+~P1(f327(f327(f235(x69831),x69832),f327(f327(f238(x69831),x69834),x69833))) % 177.41/177.19 [6984]~P108(x69841)+P1(f327(f327(f235(x69841),x69842),x69843))+~P1(f327(f327(f235(x69841),x69842),f327(f327(f238(x69841),x69843),x69844))) % 177.41/177.19 [7005]~E(f327(f327(f165(x70051),x70053),x70054),x70052)+P1(f327(f327(f329(x70051),x70052),f327(f173(x70051),x70053)))+~P1(f327(f327(f235(a915),x70054),f327(f191(f916(x70051)),x70053))) % 177.41/177.19 [7015]~P108(x70151)+~P11(x70151,f327(f327(f152(x70151),x70152),f327(f327(f152(x70151),x70153),x70154)))+P1(f327(f327(f234(x70151),x70152),x70153)) % 177.41/177.19 [7161]~P29(x71612,x71611,x71613)+P1(f327(x71611,f327(f327(f165(x71612),x71613),x71614)))+~P1(f327(f327(f235(a915),x71614),f327(f191(f916(x71612)),x71613))) % 177.41/177.19 [7179]E(x71791,f2(a1))+E(f327(f327(f37(a1),x71792),x71791),x71793)+~P1(f327(f50(x71792,x71791),f327(f327(f252(a1,a1),x71793),x71794))) % 177.41/177.19 [7200]E(f46(a1,x72002,x72001),x72003)+E(x72001,f2(a1))+~P1(f327(f50(x72002,x72001),f327(f327(f252(a1,a1),x72004),x72003))) % 177.41/177.19 [7321]P1(f327(f327(f329(x73211),x73212),x73213))+~P1(f327(f327(f329(x73211),x73212),x73214))+~P1(f327(f327(f235(f922(x73211,a910)),x73214),x73213)) % 177.41/177.19 [7322]P1(f327(f327(f329(x73221),x73222),x73223))+~P1(f327(f327(f329(x73221),x73222),x73224))+~P1(f327(f327(f234(f922(x73221,a910)),x73224),x73223)) % 177.41/177.19 [7333]~P120(x73331)+~E(x73333,f2(x73331))+P1(f327(f327(f287(x73331),f327(f327(f81(x73331),x73332),x73333)),f327(f327(f81(x73331),x73334),x73333))) % 177.41/177.19 [7334]~P120(x73341)+~E(x73342,f2(x73341))+P1(f327(f327(f287(x73341),f327(f327(f81(x73341),x73342),x73343)),f327(f327(f81(x73341),x73342),x73344))) % 177.41/177.19 [7436]P31(x74361,x74362,x74363)+~P1(f327(x74362,f327(f327(f165(x74361),x74363),x74364)))+~P1(f327(f327(f235(a915),x74364),f327(f191(f916(x74361)),x74363))) % 177.41/177.19 [7550]~P109(x75502)+~P1(f327(f327(f235(f922(x75501,x75502)),x75503),x75504))+P1(f327(f327(f234(f922(x75501,x75502)),x75503),x75504)) % 177.41/177.19 [7631]~P22(x76311,x76312,x76314)+P22(x76311,x76312,f327(f327(f309(f913(x76311)),x76313),x76314))+~P22(x76311,x76312,f327(f327(f309(f913(x76311)),x76313),f190(f922(f913(x76311),a910)))) % 177.41/177.19 [7673]~P1(f327(f327(f329(x76731),x76732),x76734))+P1(f327(f327(f329(x76731),x76732),f38(f922(x76731,a910),x76733)))+~P1(f327(f327(f329(f922(x76731,a910)),x76734),x76733)) % 177.41/177.19 [7701]~P82(x77011)+~P1(f327(f327(f234(x77011),x77013),x77014))+P1(f327(f327(f234(x77011),f327(f327(f80(x77011),x77012),x77013)),f327(f327(f80(x77011),x77012),x77014))) % 177.41/177.19 [7702]~P83(x77021)+~P1(f327(f327(f234(x77021),x77023),x77024))+P1(f327(f327(f234(x77021),f327(f327(f80(x77021),x77022),x77023)),f327(f327(f80(x77021),x77022),x77024))) % 177.41/177.19 [7703]~P82(x77031)+~P1(f327(f327(f234(x77031),x77032),x77034))+P1(f327(f327(f234(x77031),f327(f327(f80(x77031),x77032),x77033)),f327(f327(f80(x77031),x77034),x77033))) % 177.41/177.19 [7704]~P83(x77041)+~P1(f327(f327(f234(x77041),x77042),x77044))+P1(f327(f327(f234(x77041),f327(f327(f80(x77041),x77042),x77043)),f327(f327(f80(x77041),x77044),x77043))) % 177.41/177.19 [7705]~P82(x77051)+~P1(f327(f327(f235(x77051),x77053),x77054))+P1(f327(f327(f235(x77051),f327(f327(f80(x77051),x77052),x77053)),f327(f327(f80(x77051),x77052),x77054))) % 177.41/177.19 [7706]~P85(x77061)+~P1(f327(f327(f235(x77061),x77063),x77064))+P1(f327(f327(f235(x77061),f327(f327(f80(x77061),x77062),x77063)),f327(f327(f80(x77061),x77062),x77064))) % 177.41/177.19 [7707]~P82(x77071)+~P1(f327(f327(f235(x77071),x77072),x77074))+P1(f327(f327(f235(x77071),f327(f327(f80(x77071),x77072),x77073)),f327(f327(f80(x77071),x77074),x77073))) % 177.41/177.19 [7708]~P85(x77081)+~P1(f327(f327(f235(x77081),x77082),x77084))+P1(f327(f327(f235(x77081),f327(f327(f80(x77081),x77082),x77083)),f327(f327(f80(x77081),x77084),x77083))) % 177.41/177.19 [7709]~P120(x77091)+~P1(f327(f327(f287(x77091),x77093),x77094))+P1(f327(f327(f287(x77091),f327(f327(f81(x77091),x77092),x77093)),f327(f327(f81(x77091),x77092),x77094))) % 177.41/177.19 [7710]~P120(x77101)+~P1(f327(f327(f287(x77101),x77102),x77104))+P1(f327(f327(f287(x77101),f327(f327(f81(x77101),x77102),x77103)),f327(f327(f81(x77101),x77104),x77103))) % 177.41/177.19 [7717]~P106(x77171)+~P94(x77171)+E(f327(f327(f23(x77171),f327(f327(f81(x77171),x77172),f327(f105(x77171),x77173))),f327(f327(f81(x77171),x77174),f327(f105(x77171),x77173))),f327(f327(f81(x77171),f327(f327(f23(x77171),x77172),x77174)),f327(f105(x77171),x77173))) % 177.41/177.19 [7718]~P140(x77181)+~P94(x77181)+E(f327(f327(f80(x77181),f327(f327(f81(x77181),x77182),f327(f105(x77181),x77183))),f327(f327(f81(x77181),x77184),f327(f105(x77181),x77183))),f327(f327(f81(x77181),f327(f327(f80(x77181),x77182),x77184)),f327(f105(x77181),x77183))) % 177.41/177.19 [7754]~P68(x77541)+E(f327(f327(f80(x77541),f327(x77542,x77543)),f327(f327(f6(a915,x77541),x77542),f303(a915,f327(a113,x77543),x77544))),f327(f327(f6(a915,x77541),x77542),f303(a915,x77543,x77544)))+~P1(f327(f327(f234(a915),x77543),x77544)) % 177.41/177.19 [7766]~P23(x77662,x77661,x77663,f327(f173(x77662),x77664))+~P1(f327(f138(x77662),x77664))+P1(f327(f138(x77661),f327(f327(f155(x77662,x77661),x77663),x77664))) % 177.41/177.19 [7815]~P1(f327(f327(f234(a915),x78152),x78154))+~P1(f327(f327(f234(a915),x78151),x78153))+P1(f327(f327(f234(a915),f327(f327(f80(a915),x78151),x78152)),f327(f327(f80(a915),x78153),x78154))) % 177.41/177.19 [7816]~P1(f327(f327(f234(a915),x78162),x78164))+~P1(f327(f327(f234(a915),x78161),x78163))+P1(f327(f327(f234(a915),f327(f327(f81(a915),x78161),x78162)),f327(f327(f81(a915),x78163),x78164))) % 177.41/177.19 [7819]~P1(f327(f327(f235(a915),x78192),x78194))+~P1(f327(f327(f235(a915),x78191),x78193))+P1(f327(f327(f235(a915),f327(f327(f80(a915),x78191),x78192)),f327(f327(f80(a915),x78193),x78194))) % 177.41/177.19 [7820]~P1(f327(f327(f234(a1),x78202),x78204))+~P1(f327(f327(f235(a1),x78201),x78203))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x78201),x78202)),f327(f327(f80(a1),x78203),x78204))) % 177.41/177.19 [7868]P1(f327(f327(f329(x78681),x78682),x78683))+~P1(f327(f327(f329(x78681),x78682),f39(f922(x78681,a910),x78684)))+~P1(f327(f327(f329(f922(x78681,a910)),x78683),x78684)) % 177.41/177.19 [7884]~P1(f327(x78841,f655(x78841,x78843,x78842)))+P1(f327(x78841,f327(f327(f165(x78842),x78843),x78844)))+~P1(f327(f327(f235(a915),x78844),f327(f191(f916(x78842)),x78843))) % 177.41/177.19 [7889]P1(f327(x78891,x78892))+~P1(f327(f327(f329(x78894),x78892),f327(f173(x78894),x78893)))+P1(f327(f327(f235(a915),f657(x78891,x78893,x78894)),f327(f191(f916(x78894)),x78893))) % 177.41/177.19 [7936]~P109(x79361)+~P1(f327(f327(f235(f922(x79362,x79361)),x79364),x79363))+~P1(f327(f327(f234(f922(x79362,x79361)),x79363),x79364)) % 177.41/177.19 [7979]~P1(f327(x79794,x79792))+~P1(f327(f327(f329(x79791),x79792),x79793))+P1(f327(f327(f329(x79791),x79792),f327(f327(f103(f922(x79791,a910)),x79793),f327(f262(x79791),x79794)))) % 177.41/177.19 [8124]~P1(f327(f327(f329(x81241),x81243),x81244))+~P1(f327(f327(f235(f922(x81241,a910)),x81242),x81244))+P1(f327(f327(f235(f922(x81241,a910)),x81242),f327(f327(f309(x81241),x81243),x81244))) % 177.41/177.19 [8126]E(f327(f327(f103(f922(x81261,a910)),x81262),x81263),f190(f922(x81261,a910)))+~E(f327(f327(f103(f922(x81261,a910)),f38(f922(x81261,a910),x81264)),x81263),f190(f922(x81261,a910)))+~P1(f327(f327(f329(f922(x81261,a910)),x81262),x81264)) % 177.41/177.19 [8199]P1(f327(f327(f329(x81991),x81992),x81993))+~P1(f327(f327(f234(f922(x81991,a910)),x81993),f327(f327(f309(x81991),x81992),x81994)))+P1(f327(f327(f234(f922(x81991,a910)),x81993),x81994)) % 177.41/177.19 [8216]P1(f327(f327(f329(x82162),f655(x82161,x82163,x82162)),f327(f173(x82162),x82163)))+P1(f327(x82161,f327(f327(f165(x82162),x82163),x82164)))+~P1(f327(f327(f235(a915),x82164),f327(f191(f916(x82162)),x82163))) % 177.41/177.19 [8224]~P1(f327(f327(f234(f922(x82241,a910)),x82242),x82244))+P1(f327(f327(f234(f922(x82241,a910)),x82242),x82243))+~P1(f327(f327(f234(f922(x82241,a910)),x82244),x82243)) % 177.41/177.19 [8225]~P1(f327(f327(f235(f922(x82251,a910)),x82252),x82254))+~P1(f327(f327(f234(f922(x82251,a910)),x82254),x82253))+P1(f327(f327(f235(f922(x82251,a910)),x82252),x82253)) % 177.41/177.19 [8226]~P1(f327(f327(f234(f922(x82261,a910)),x82262),x82264))+~P1(f327(f327(f235(f922(x82261,a910)),x82264),x82263))+P1(f327(f327(f235(f922(x82261,a910)),x82262),x82263)) % 177.41/177.19 [8227]~P1(f327(f327(f235(f922(x82271,a910)),x82272),x82274))+P1(f327(f327(f235(f922(x82271,a910)),x82272),x82273))+~P1(f327(f327(f235(f922(x82271,a910)),x82274),x82273)) % 177.41/177.19 [8271]~P1(f327(f327(f329(x82711),x82714),x82713))+~P1(f327(f327(f235(f922(x82711,a910)),x82712),f327(f327(f309(x82711),x82714),x82713)))+P1(f327(f327(f235(f922(x82711,a910)),x82712),x82713)) % 177.41/177.19 [8282]~P82(x82821)+P1(f327(f327(f234(x82821),x82822),x82823))+~P1(f327(f327(f234(x82821),f327(f327(f80(x82821),x82824),x82822)),f327(f327(f80(x82821),x82824),x82823))) % 177.41/177.19 [8284]~P82(x82841)+P1(f327(f327(f234(x82841),x82842),x82843))+~P1(f327(f327(f234(x82841),f327(f327(f80(x82841),x82842),x82844)),f327(f327(f80(x82841),x82843),x82844))) % 177.41/177.19 [8286]~P82(x82861)+P1(f327(f327(f235(x82861),x82862),x82863))+~P1(f327(f327(f235(x82861),f327(f327(f80(x82861),x82864),x82862)),f327(f327(f80(x82861),x82864),x82863))) % 177.41/177.19 [8288]~P82(x82881)+P1(f327(f327(f235(x82881),x82882),x82883))+~P1(f327(f327(f235(x82881),f327(f327(f80(x82881),x82882),x82884)),f327(f327(f80(x82881),x82883),x82884))) % 177.41/177.19 [8339]P1(f327(x83391,x83392))+~E(f327(f327(f139(x83393),f327(f191(f916(x83393)),f178(x83393,x83391,x83394))),x83394),f114(x83393))+~P1(f327(f327(f329(x83393),x83392),f327(f173(x83393),x83394))) % 177.41/177.19 [8457]P1(f327(x84571,x84572))+~P1(f327(f327(f329(x84573),x84572),f327(f173(x84573),x84574)))+P1(f327(f327(f235(a915),f327(f191(f916(x84573)),f327(f137(x84573,x84571),x84574))),f327(f191(f916(x84573)),x84574))) % 177.41/177.19 [8945]~P1(f327(x89451,f748(x89451,x89453,x89452,x89454)))+P1(f327(x89451,f327(f327(f165(x89452),x89453),x89454)))+~P1(f327(f327(f235(a915),x89454),f327(f191(f916(x89452)),x89453))) % 177.41/177.19 [8969]~P23(x89694,x89693,x89691,f242(f922(x89694,a910)))+E(f327(x89691,f878(x89692,x89691,x89693,x89694)),x89692)+~P1(f327(f327(f329(x89693),x89692),f327(f310(x89694,x89693,x89691),f242(f922(x89694,a910))))) % 177.41/177.19 [9037]E(f178(x90371,x90372,x90373),f327(f327(f176(x90371),x90374),x90373))+P1(f327(f327(f235(a915),f718(x90372,x90373,x90371,x90374)),x90374))+P1(f327(f327(f235(a915),x90374),f327(f191(f916(x90371)),x90373))) % 177.41/177.19 [9040]E(f178(x90401,x90402,x90403),f327(f327(f176(x90401),x90404),x90403))+P1(f327(f327(f235(a915),f718(x90402,x90403,x90401,x90404)),x90404))+P1(f327(x90402,f327(f327(f165(x90401),x90403),x90404))) % 177.41/177.19 [9075]P1(f327(x90751,x90752))+~P1(f327(f327(f329(x90754),x90752),f327(f173(x90754),x90753)))+P1(f327(f327(f235(a915),f694(x90752,x90751,x90753,x90754)),f327(f191(f916(x90754)),x90753))) % 177.41/177.19 [9077]E(f178(x90771,x90772,x90773),f327(f327(f176(x90771),x90774),x90773))+P1(f327(f327(f235(a915),x90774),f327(f191(f916(x90771)),x90773)))+P1(f327(f327(f235(a915),f718(x90772,x90773,x90771,x90774)),f327(f191(f916(x90771)),x90773))) % 177.41/177.19 [9084]E(f178(x90841,x90842,x90843),f327(f327(f176(x90841),x90844),x90843))+P1(f327(x90842,f327(f327(f165(x90841),x90843),x90844)))+P1(f327(f327(f235(a915),f718(x90842,x90843,x90841,x90844)),f327(f191(f916(x90841)),x90843))) % 177.41/177.19 [9111]~P126(x91114)+P1(f327(f327(f329(x91111),f641(x91112,x91113,x91111,x91114)),x91113))+P1(f327(f327(f235(x91114),f2(x91114)),f327(f327(f9(x91111,x91114),x91112),x91113))) % 177.41/177.19 [9112]~P126(x91124)+P1(f327(f327(f329(x91121),f642(x91122,x91123,x91121,x91124)),x91123))+P1(f327(f327(f234(x91124),f2(x91124)),f327(f327(f9(x91121,x91124),x91122),x91123))) % 177.41/177.19 [9139]~P1(f327(f35(x91391),x91394))+P1(f327(f327(f329(x91391),f555(x91392,x91393,x91394,x91391)),x91394))+P1(f327(f35(f921(x91391,x91393)),f327(f327(f254(x91391,x91393),x91394),x91392))) % 177.41/177.19 [9171]P1(f327(f327(f329(x91712),f748(x91711,x91713,x91712,x91714)),f327(f173(x91712),x91713)))+P1(f327(x91711,f327(f327(f165(x91712),x91713),x91714)))+~P1(f327(f327(f235(a915),x91714),f327(f191(f916(x91712)),x91713))) % 177.41/177.19 [9300]P1(f327(f327(f234(a915),x93004),f327(f191(f916(x93002)),f178(x93002,x93003,x93001))))+P1(f327(f327(f235(a915),f719(x93001,x93002,x93003,x93004)),x93004))+~P1(f327(f327(f234(a915),x93004),f327(f191(f916(x93002)),x93001))) % 177.41/177.19 [9450]E(f178(x94501,x94502,x94503),f327(f327(f176(x94501),x94504),x94503))+~P1(f327(x94502,f327(f327(f165(x94501),x94503),f718(x94502,x94503,x94501,x94504))))+P1(f327(f327(f235(a915),x94504),f327(f191(f916(x94501)),x94503))) % 177.41/177.19 [9457]E(f178(x94571,x94572,x94573),f327(f327(f176(x94571),x94574),x94573))+~P1(f327(x94572,f327(f327(f165(x94571),x94573),f718(x94572,x94573,x94571,x94574))))+P1(f327(x94572,f327(f327(f165(x94571),x94573),x94574))) % 177.41/177.19 [9461]~P1(f327(f35(x94611),x94613))+~P1(f327(f35(x94612),f327(x94614,f555(x94614,x94612,x94613,x94611))))+P1(f327(f35(f921(x94611,x94612)),f327(f327(f254(x94611,x94612),x94613),x94614))) % 177.41/177.19 [9469]~P126(x94691)+~P1(f327(f327(f234(x94691),f2(x94691)),f327(x94693,f642(x94693,x94694,x94692,x94691))))+P1(f327(f327(f234(x94691),f2(x94691)),f327(f327(f9(x94692,x94691),x94693),x94694))) % 177.41/177.19 [9470]~P126(x94701)+~P1(f327(f327(f235(x94701),f2(x94701)),f327(x94703,f641(x94703,x94704,x94702,x94701))))+P1(f327(f327(f235(x94701),f2(x94701)),f327(f327(f9(x94702,x94701),x94703),x94704))) % 177.41/177.19 [9478]~E(f327(f191(f916(x94784)),x94782),f327(f191(f916(x94784)),x94783))+P1(f327(f327(f329(f921(f916(x94784),f916(x94784))),f327(f327(f252(f916(x94784),f916(x94784)),x94783),x94782)),f159(x94784,x94781)))+P1(f327(f327(f235(a915),f643(x94781,x94782,x94783,x94784)),f327(f191(f916(x94784)),x94783))) % 177.41/177.19 [9530]~P1(f327(x95303,f327(f327(f165(x95302),x95304),f719(x95304,x95302,x95303,x95301))))+P1(f327(f327(f234(a915),x95301),f327(f191(f916(x95302)),f178(x95302,x95303,x95304))))+~P1(f327(f327(f234(a915),x95301),f327(f191(f916(x95302)),x95304))) % 177.41/177.19 [9611]E(f327(f327(f176(x96111),f656(x96112,x96113,x96114,x96111)),x96113),f327(f327(f176(x96111),f656(x96112,x96113,x96114,x96111)),x96114))+~P1(f327(f327(f329(f921(f916(x96111),f916(x96111))),f327(f327(f252(f916(x96111),f916(x96111)),x96114),x96113)),f148(x96111,x96112)))+P1(f327(f327(f235(a915),f327(f191(f916(x96111)),x96114)),f327(f191(f916(x96111)),x96113))) % 177.41/177.19 [9667]~P1(f327(f327(f235(a915),f2(a915)),x96673))+~P1(f327(f327(f235(a915),x96674),x96671))+P1(f327(f327(f235(a915),f327(f327(f80(a915),f327(f327(f81(a915),x96671),f46(a915,x96672,x96673))),x96674)),f327(f327(f81(a915),x96671),x96673))) % 177.41/177.19 [9860]~P109(x98602)+~P1(f327(f327(f234(x98602),f327(x98603,f445(x98604,x98603,x98601,x98602))),f327(x98604,f445(x98604,x98603,x98601,x98602))))+P1(f327(f327(f234(f922(x98601,x98602)),x98603),x98604)) % 177.41/177.19 [9963]~P67(x99631)+E(f327(f327(f6(a915,x99631),f327(f327(f18(a915,x99631,x99631),f327(f327(f8(x99631,f922(x99631,x99631),a915),f23(x99631)),x99632)),f327(f327(f8(a915,x99631,a915),x99632),f327(f327(f7(a915,a915,a915),f80(a915)),f78(a915))))),f303(a915,x99633,x99634)),f327(f327(f23(x99631),f327(x99632,x99633)),f327(x99632,f327(f327(f80(a915),x99634),f78(a915)))))+~P1(f327(f327(f234(a915),x99633),x99634)) % 177.41/177.19 [10039]~P35(x100393,f327(f327(f289(x100393,x100393,x100393),x100392),f307(x100393,x100392)))+~P1(f327(f327(f329(f921(x100393,x100393)),f327(f327(f252(x100393,x100393),f327(x100391,f327(a113,f832(x100392,x100391,x100393)))),f327(x100391,f832(x100392,x100391,x100393)))),f307(x100393,x100392)))+E(f327(x100391,f327(f327(f80(a915),f831(x100392,x100391,x100393)),x100394)),f327(x100391,f831(x100392,x100391,x100393))) % 177.41/177.19 [6924]~P58(x69241)+E(f327(f327(f37(x69241),f327(f327(f81(x69241),x69242),x69243)),x69244),f327(f327(f81(x69241),x69242),f327(f327(f37(x69241),x69243),x69244)))+~P1(f327(f327(f287(x69241),x69244),x69243)) % 177.41/177.19 [7009]E(f327(f327(f135(x70091),x70092),x70093),x70094)+~E(x70093,f327(f327(f139(x70091),f327(f191(f916(x70091)),x70092)),x70094))+~E(f327(f327(f176(x70091),f327(f191(f916(x70091)),x70092)),x70094),x70092) % 177.41/177.19 [7065]~P62(x70652)+E(x70651,f2(x70652))+E(f327(f327(f291(x70652),f327(f327(f244(x70652),x70653),x70654)),f327(f327(f244(x70652),x70651),x70654)),f327(f327(f244(x70652),f327(f327(f291(x70652),x70653),x70651)),x70654)) % 177.41/177.19 [7210]~P58(x72101)+E(f327(f327(f37(x72101),f327(f327(f81(x72101),x72102),x72103)),x72104),f327(f327(f81(x72101),f327(f327(f37(x72101),x72102),x72104)),x72103))+~P1(f327(f327(f287(x72101),x72104),x72102)) % 177.41/177.19 [7219]~P108(x72191)+~P1(f327(f327(f234(x72191),x72193),x72194))+P1(f327(f327(f234(x72191),f327(f327(f238(x72191),x72192),x72193)),x72194)) % 177.41/177.19 [7221]~P108(x72211)+~P1(f327(f327(f234(x72211),x72212),x72214))+P1(f327(f327(f234(x72211),f327(f327(f238(x72211),x72212),x72213)),x72214)) % 177.41/177.19 [7222]~P102(x72221)+~P1(f327(f327(f234(x72221),x72223),x72224))+P1(f327(f327(f234(x72221),f327(f327(f103(x72221),x72222),x72223)),x72224)) % 177.41/177.19 [7223]~P102(x72231)+~P1(f327(f327(f234(x72231),x72232),x72234))+P1(f327(f327(f234(x72231),f327(f327(f103(x72231),x72232),x72233)),x72234)) % 177.41/177.19 [7225]~P108(x72251)+~P1(f327(f327(f235(x72251),x72253),x72254))+P1(f327(f327(f235(x72251),f327(f327(f238(x72251),x72252),x72253)),x72254)) % 177.41/177.19 [7227]~P108(x72271)+~P1(f327(f327(f235(x72271),x72272),x72274))+P1(f327(f327(f235(x72271),f327(f327(f238(x72271),x72272),x72273)),x72274)) % 177.41/177.19 [7228]~P102(x72281)+~P1(f327(f327(f235(x72281),x72283),x72284))+P1(f327(f327(f235(x72281),f327(f327(f103(x72281),x72282),x72283)),x72284)) % 177.41/177.19 [7229]~P102(x72291)+~P1(f327(f327(f235(x72291),x72292),x72294))+P1(f327(f327(f235(x72291),f327(f327(f103(x72291),x72292),x72293)),x72294)) % 177.41/177.19 [7252]~P1(f327(x72523,x72524))+~P1(f327(x72522,x72524))+P1(f327(f327(f327(f103(f922(x72521,a910)),x72522),x72523),x72524)) % 177.41/177.19 [7378]P22(x73781,x73782,x73783)+~P22(x73781,x73784,x73783)+~P1(f327(f327(f234(f922(f913(x73781),a910)),x73784),x73782)) % 177.41/177.19 [7379]P22(x73791,x73792,x73793)+~P22(x73791,x73792,x73794)+~P1(f327(f327(f234(f922(f913(x73791),a910)),x73793),x73794)) % 177.41/177.19 [7744]~P68(x77441)+E(f327(f327(f80(x77441),f327(x77442,x77443)),f327(f327(f6(a915,x77441),x77442),f327(f302(a915,f327(a113,x77443)),x77444))),f327(f327(f6(a915,x77441),x77442),f327(f302(a915,x77443),x77444)))+~P1(f327(f327(f235(a915),x77443),x77444)) % 177.41/177.19 [7762]E(x77621,x77622)+P1(f327(f327(f173(x77623),x77624),x77622))+~P1(f327(f327(f173(x77623),f327(f327(f152(x77623),x77621),x77624)),x77622)) % 177.41/177.19 [7774]~P108(x77741)+P1(f327(f327(f234(x77741),x77742),x77743))+~P1(f327(f327(f234(x77741),f327(f327(f189(x77741),x77744),x77742)),x77743)) % 177.41/177.19 [7776]~P108(x77761)+P1(f327(f327(f234(x77761),x77762),x77763))+~P1(f327(f327(f234(x77761),f327(f327(f189(x77761),x77762),x77764)),x77763)) % 177.41/177.19 [7778]~P101(x77781)+P1(f327(f327(f234(x77781),x77782),x77783))+~P1(f327(f327(f234(x77781),f327(f327(f102(x77781),x77784),x77782)),x77783)) % 177.41/177.19 [7780]~P101(x77801)+P1(f327(f327(f234(x77801),x77802),x77803))+~P1(f327(f327(f234(x77801),f327(f327(f102(x77801),x77802),x77804)),x77803)) % 177.41/177.19 [7781]~P108(x77811)+P1(f327(f327(f235(x77811),x77812),x77813))+~P1(f327(f327(f235(x77811),f327(f327(f189(x77811),x77814),x77812)),x77813)) % 177.41/177.19 [7782]~P108(x77821)+P1(f327(f327(f235(x77821),x77822),x77823))+~P1(f327(f327(f235(x77821),f327(f327(f189(x77821),x77822),x77824)),x77823)) % 177.41/177.19 [7783]~P112(x77831)+P1(f327(f327(f287(x77831),x77832),x77833))+~P1(f327(f327(f287(x77831),f327(f327(f81(x77831),x77834),x77832)),x77833)) % 177.41/177.19 [7784]~P112(x77841)+P1(f327(f327(f287(x77841),x77842),x77843))+~P1(f327(f327(f287(x77841),f327(f327(f81(x77841),x77842),x77844)),x77843)) % 177.41/177.19 [7860]~P1(f327(f327(f329(x78601),x78602),x78604))+P1(f327(f327(f329(x78601),x78602),x78603))+P1(f327(f327(f329(x78601),x78602),f327(f327(f23(f922(x78601,a910)),x78604),x78603))) % 177.41/177.19 [7943]P1(f327(x79431,x79432))+P1(f327(x79433,x79432))+~P1(f327(f327(f327(f102(f922(x79434,a910)),x79433),x79431),x79432)) % 177.41/177.19 [7954]~P1(f327(f327(f329(x79541),x79542),x79544))+~P1(f327(f327(f329(x79541),x79542),x79543))+P1(f327(f327(f329(x79541),x79542),f327(f327(f103(f922(x79541,a910)),x79543),x79544))) % 177.41/177.19 [8001]~P108(x80011)+~P1(f327(f35(x80011),x80014))+E(f327(f327(f64(x80011,x80011,f238(x80011)),x80012),f327(f327(f309(x80011),x80013),x80014)),f327(f327(f238(x80011),x80013),f327(f327(f64(x80011,x80011,f238(x80011)),x80012),x80014))) % 177.41/177.19 [8002]~P108(x80021)+~P1(f327(f35(x80021),x80024))+E(f327(f327(f64(x80021,x80021,f189(x80021)),x80022),f327(f327(f309(x80021),x80023),x80024)),f327(f327(f189(x80021),x80023),f327(f327(f64(x80021,x80021,f189(x80021)),x80022),x80024))) % 177.41/177.19 [8003]~P101(x80031)+~P1(f327(f35(x80031),x80034))+E(f327(f327(f64(x80031,x80031,f102(x80031)),x80032),f327(f327(f309(x80031),x80033),x80034)),f327(f327(f102(x80031),x80033),f327(f327(f64(x80031,x80031,f102(x80031)),x80032),x80034))) % 177.41/177.19 [8004]~P102(x80041)+~P1(f327(f35(x80041),x80044))+E(f327(f327(f64(x80041,x80041,f103(x80041)),x80042),f327(f327(f309(x80041),x80043),x80044)),f327(f327(f103(x80041),x80043),f327(f327(f64(x80041,x80041,f103(x80041)),x80042),x80044))) % 177.41/177.19 [8006]~P106(x80061)+~P94(x80061)+E(f327(f327(f23(x80061),f327(f327(f81(x80061),f327(f105(x80061),x80062)),x80063)),f327(f327(f81(x80061),f327(f105(x80061),x80062)),x80064)),f327(f327(f81(x80061),f327(f105(x80061),x80062)),f327(f327(f23(x80061),x80063),x80064))) % 177.41/177.19 [8007]~P140(x80071)+~P94(x80071)+E(f327(f327(f80(x80071),f327(f327(f81(x80071),f327(f105(x80071),x80072)),x80073)),f327(f327(f81(x80071),f327(f105(x80071),x80072)),x80074)),f327(f327(f81(x80071),f327(f105(x80071),x80072)),f327(f327(f80(x80071),x80073),x80074))) % 177.41/177.19 [8122]E(x81221,x81222)+P1(f327(f327(f329(x81223),x81221),f327(f173(x81223),x81224)))+~P1(f327(f327(f329(x81223),x81221),f327(f173(x81223),f327(f327(f152(x81223),x81222),x81224)))) % 177.41/177.19 [8293]P52(x82931,x82932,x82933)+~P52(x82931,x82932,x82934)+~P1(f327(f327(f234(f922(f921(x82931,x82932),a910)),x82933),x82934)) % 177.41/177.19 [8341]P1(f327(f327(f329(x83411),x83412),x83413))+P1(f327(f327(f329(x83411),x83412),x83414))+~P1(f327(f327(f329(x83411),x83412),f327(f327(f102(f922(x83411,a910)),x83414),x83413))) % 177.41/177.19 [8351]~P50(x83511,x83514,x83513)+~P1(f327(f327(f329(x83511),x83512),x83514))+P1(f327(f327(f329(f921(x83511,x83511)),f327(f327(f252(x83511,x83511),x83512),x83512)),x83513)) % 177.41/177.19 [8363]~P1(f327(f35(x83632),x83634))+~P1(f327(f35(x83631),x83633))+P1(f327(f35(f921(x83631,x83632)),f327(f327(f254(x83631,x83632),x83633),f327(f16(f922(x83632,a910),x83631),x83634)))) % 177.41/177.19 [8364]~P1(f327(f327(f329(x83641),x83642),x83644))+~P1(f327(f327(f234(f922(x83641,a910)),x83643),x83644))+P1(f327(f327(f234(f922(x83641,a910)),f327(f327(f309(x83641),x83642),x83643)),x83644)) % 177.41/177.19 [8371]~P75(x83712)+~P146(x83712)+E(f327(f327(f9(x83711,x83712),f327(f327(f8(a915,x83712,x83711),f101(x83712)),x83713)),x83714),f327(f101(x83712),f327(f327(f9(x83711,a915),x83713),x83714))) % 177.41/177.19 [8372]~P75(x83722)+~P142(x83722)+E(f327(f327(f9(x83721,x83722),f327(f327(f8(a1,x83722,x83721),f104(x83722)),x83723)),x83724),f327(f104(x83722),f327(f327(f9(x83721,a1),x83723),x83724))) % 177.41/177.19 [8396]E(f327(f327(f23(f922(x83961,a910)),x83962),f327(f327(f23(f922(x83961,a910)),x83963),x83964)),x83964)+~P1(f327(f327(f234(f922(x83961,a910)),x83962),x83963))+~P1(f327(f327(f234(f922(x83961,a910)),x83964),x83962)) % 177.41/177.19 [8492]~P1(f327(f35(x84921),x84924))+E(f327(f327(f23(a915),f327(f327(f6(x84921,a915),x84922),x84923)),f327(f327(f6(x84921,a915),x84922),x84924)),f327(f327(f6(x84921,a915),x84922),f327(f327(f23(f922(x84921,a910)),x84923),x84924)))+~P1(f327(f327(f234(f922(x84921,a910)),x84924),x84923)) % 177.41/177.19 [8643]~P6(x86431,x86434,x86433)+~P1(f327(f327(f329(x86431),x86432),x86434))+P1(f327(f327(f329(x86431),x86432),f327(f285(x86431,x86431,x86433),f327(f327(f309(x86431),x86432),f190(f922(x86431,a910)))))) % 177.41/177.19 [8704]~P1(f327(f327(f234(f922(x87041,a910)),x87042),x87043))+~P1(f327(f327(f234(f922(x87041,a910)),x87042),x87044))+P1(f327(f327(f234(f922(x87041,a910)),x87042),f327(f327(f103(f922(x87041,a910)),x87043),x87044))) % 177.41/177.19 [8806]E(x88061,f190(f922(x88062,a910)))+P1(f327(f35(x88063),x88064))+~P1(f327(f35(f921(x88063,x88062)),f327(f327(f254(x88063,x88062),x88064),f327(f16(f922(x88062,a910),x88063),x88061)))) % 177.41/177.19 [8807]E(x88071,f190(f922(x88072,a910)))+P1(f327(f35(x88073),x88074))+~P1(f327(f35(f921(x88072,x88073)),f327(f327(f254(x88072,x88073),x88071),f327(f16(f922(x88073,a910),x88072),x88074)))) % 177.41/177.19 [8880]P1(f327(f327(f329(x88801),x88802),f316(x88801,x88803)))+~P1(f327(f327(f329(x88801),x88804),f316(x88801,x88803)))+~P1(f327(f327(f329(f921(x88801,x88801)),f327(f327(f252(x88801,x88801),x88802),x88804)),x88803)) % 177.41/177.19 [8937]~P35(x89371,x89374)+P1(f327(f327(f329(f921(x89371,x89371)),f327(f327(f252(x89371,x89371),x89373),x89372)),f307(x89371,x89374)))+P35(x89371,f327(f327(f309(f921(x89371,x89371)),f327(f327(f252(x89371,x89371),x89372),x89373)),x89374)) % 177.41/177.19 [8938]~P55(x89381,x89384)+P1(f327(f327(f329(f921(x89381,x89381)),f327(f327(f252(x89381,x89381),x89383),x89382)),f307(x89381,x89384)))+P55(x89381,f327(f327(f309(f921(x89381,x89381)),f327(f327(f252(x89381,x89381),x89382),x89383)),x89384)) % 177.41/177.19 [9020]~E(x90202,x90203)+~P1(f327(f327(f329(x90201),x90202),f327(f173(x90201),x90204)))+P1(f327(f327(f329(f921(x90201,x90201)),f327(f327(f252(x90201,x90201),x90202),x90203)),f327(f173(f921(x90201,x90201)),f327(f327(f182(x90201,x90201),x90204),x90204)))) % 177.41/177.19 [9110]~E(x91103,x91104)+P1(f327(f327(f257(x91101,x91101,a910),a324),x91102))+~P1(f327(f327(f329(f921(x91101,x91101)),x91102),f327(f173(f921(x91101,x91101)),f327(f327(f182(x91101,x91101),x91103),x91104)))) % 177.41/177.19 [9156]P1(f327(f327(f329(f921(f916(x91561),f916(x91561))),f327(f327(f252(f916(x91561),f916(x91561)),x91562),x91563)),f148(x91561,x91564)))+~E(f327(f327(f176(x91561),f327(f191(f916(x91561)),x91562)),x91563),x91562)+~P1(f327(f327(f235(a915),f327(f191(f916(x91561)),x91562)),f327(f191(f916(x91561)),x91563))) % 177.41/177.19 [9159]~P49(x91591,x91594)+~P1(f327(f327(f329(f921(x91591,x91591)),f327(f327(f252(x91591,x91591),x91593),x91592)),x91594))+P1(f327(f327(f329(f921(x91591,x91591)),f327(f327(f252(x91591,x91591),x91592),x91593)),x91594)) % 177.41/177.19 [9250]~P1(f327(f35(x92501),x92504))+P1(f327(f327(f329(x92501),f893(x92502,x92503,x92504,x92501)),x92504))+P1(f327(f35(x92503),f327(f327(f40(x92501,f922(x92503,a910)),x92504),x92502))) % 177.41/177.19 [9251]~P1(f327(f35(x92511),x92514))+P1(f327(f327(f329(x92511),f496(x92512,x92513,x92514,x92511)),x92514))+P1(f327(f35(x92513),f327(f327(f40(x92511,f922(x92513,a910)),x92514),x92512))) % 177.41/177.19 [9336]P1(f327(f327(f329(f921(x93361,x93361)),x93362),f327(f327(f289(x93361,x93361,x93361),x93363),f307(x93361,x93363))))+~P1(f327(f327(f235(a915),f2(a915)),x93364))+~P1(f327(f327(f329(f921(x93361,x93361)),x93362),f327(f327(f184(f921(x93361,x93361),a910),x93364),x93363))) % 177.41/177.19 [9344]~P35(x93441,x93442)+~P1(f327(f327(f329(f921(x93441,x93441)),f327(f327(f252(x93441,x93441),x93444),x93443)),x93442))+~P1(f327(f327(f329(f921(x93441,x93441)),f327(f327(f252(x93441,x93441),x93443),x93444)),x93442)) % 177.41/177.19 [9468]~P1(f327(f35(x94681),x94684))+E(f327(f327(f6(x94681,a915),f327(f327(f8(f922(x94682,a910),a915,x94681),f36(x94682)),x94683)),x94684),f327(f36(f921(x94681,x94682)),f327(f327(f254(x94681,x94682),x94684),x94683)))+P1(f327(f327(f329(x94681),f556(x94683,x94682,x94684,x94681)),x94684)) % 177.41/177.19 [9472]~P1(f327(f138(x94721),x94722))+P1(f327(f138(x94721),f327(f327(f160(x94721,x94722),x94723),x94724)))+P1(f327(f327(f329(x94721),x94724),f327(f327(f23(f922(x94721,a910)),f327(f173(x94721),x94722)),f327(f327(f309(x94721),f327(f327(f165(x94721),x94722),x94723)),f190(f922(x94721,a910)))))) % 177.41/177.19 [9489]~P1(f327(f35(x94892),x94893))+~P1(f327(f35(x94891),f327(x94894,f893(x94894,x94891,x94893,x94892))))+P1(f327(f35(x94891),f327(f327(f40(x94892,f922(x94891,a910)),x94893),x94894))) % 177.41/177.19 [9490]~P1(f327(f35(x94902),x94903))+~P1(f327(f35(x94901),f327(x94904,f496(x94904,x94901,x94903,x94902))))+P1(f327(f35(x94901),f327(f327(f40(x94902,f922(x94901,a910)),x94903),x94904))) % 177.41/177.19 [9568]~P1(f327(f327(f329(f921(x95681,x95681)),x95682),f327(f327(f289(x95681,x95681,x95681),x95684),f307(x95681,x95684))))+P1(f327(f327(f329(f921(x95681,x95681)),x95682),f327(f327(f289(x95681,x95681,x95681),x95683),f307(x95681,x95683))))+~P1(f327(f327(f234(f922(f921(x95681,x95681),a910)),x95684),x95683)) % 177.41/177.19 [9578]E(f327(f327(f176(x95781),f656(x95784,x95783,x95782,x95781)),x95783),f327(f327(f176(x95781),f656(x95784,x95783,x95782,x95781)),x95782))+~P1(f327(f327(f329(f921(f916(x95781),f916(x95781))),f327(f327(f252(f916(x95781),f916(x95781)),x95782),x95783)),f148(x95781,x95784)))+E(f327(f327(f176(x95781),f327(f191(f916(x95781)),x95782)),x95783),x95782) % 177.41/177.19 [9594]~P1(f327(f35(x95941),x95944))+E(f327(f327(f6(x95941,a915),f327(f327(f8(f922(x95942,a910),a915,x95941),f36(x95942)),x95943)),x95944),f327(f36(f921(x95941,x95942)),f327(f327(f254(x95941,x95942),x95944),x95943)))+~P1(f327(f35(x95942),f327(x95943,f556(x95943,x95942,x95944,x95941)))) % 177.41/177.19 [9598]~E(f327(f191(f916(x95981)),x95983),f327(f191(f916(x95981)),x95982))+P1(f327(f327(f329(f921(f916(x95981),f916(x95981))),f327(f327(f252(f916(x95981),f916(x95981)),x95982),x95983)),f159(x95981,x95984)))+P1(f327(f327(f329(f921(x95981,x95981)),f659(x95984,x95983,x95982,x95981)),f327(f173(f921(x95981,x95981)),f327(f327(f182(x95981,x95981),x95982),x95983)))) % 177.41/177.19 [9679]~P1(f327(f327(f329(f921(f916(x96791),f916(x96791))),f327(f327(f252(f916(x96791),f916(x96791)),x96792),x96793)),f148(x96791,x96794)))+E(f327(f327(f176(x96791),f327(f191(f916(x96791)),x96792)),x96793),x96792)+P1(f327(f327(f235(a915),f656(x96794,x96793,x96792,x96791)),f327(f327(f238(a915),f327(f191(f916(x96791)),x96792)),f327(f191(f916(x96791)),x96793)))) % 177.41/177.19 [9703]~P1(f327(f327(f329(f921(f916(x97031),f916(x97031))),f327(f327(f252(f916(x97031),f916(x97031)),x97032),x97033)),f148(x97031,x97034)))+P1(f327(f327(f235(a915),f327(f191(f916(x97031)),x97032)),f327(f191(f916(x97031)),x97033)))+P1(f327(f327(f235(a915),f656(x97034,x97033,x97032,x97031)),f327(f327(f238(a915),f327(f191(f916(x97031)),x97032)),f327(f191(f916(x97031)),x97033)))) % 177.41/177.19 [10107]~P1(f327(f327(f329(f921(f916(x101071),f916(x101071))),f327(f327(f252(f916(x101071),f916(x101071)),x101072),x101073)),f148(x101071,x101074)))+E(f327(f327(f176(x101071),f327(f191(f916(x101071)),x101072)),x101073),x101072)+P1(f327(f327(f329(f921(x101071,x101071)),f327(f327(f252(x101071,x101071),f327(f327(f165(x101071),x101072),f656(x101074,x101073,x101072,x101071))),f327(f327(f165(x101071),x101073),f656(x101074,x101073,x101072,x101071)))),x101074)) % 177.41/177.19 [10108]~P1(f327(f327(f329(f921(f916(x101081),f916(x101081))),f327(f327(f252(f916(x101081),f916(x101081)),x101082),x101083)),f148(x101081,x101084)))+P1(f327(f327(f235(a915),f327(f191(f916(x101081)),x101082)),f327(f191(f916(x101081)),x101083)))+P1(f327(f327(f329(f921(x101081,x101081)),f327(f327(f252(x101081,x101081),f327(f327(f165(x101081),x101082),f656(x101084,x101083,x101082,x101081))),f327(f327(f165(x101081),x101083),f656(x101084,x101083,x101082,x101081)))),x101084)) % 177.41/177.19 [10175]~E(f327(f191(f916(x101751)),x101752),f327(f191(f916(x101751)),x101753))+P1(f327(f327(f329(f921(f916(x101751),f916(x101751))),f327(f327(f252(f916(x101751),f916(x101751)),x101752),x101753)),f159(x101751,x101754)))+~P1(f327(f327(f329(f921(x101751,x101751)),f327(f327(f252(x101751,x101751),f327(f327(f165(x101751),x101752),f643(x101754,x101753,x101752,x101751))),f327(f327(f165(x101751),x101753),f643(x101754,x101753,x101752,x101751)))),x101754)) % 177.41/177.19 [10326]~P68(x103261)+~P1(f327(f35(x103262),x103264))+E(f327(f166(x103261),f327(f327(f155(x103262,x103261),x103263),f90(f916(x103262),f327(f327(f18(f916(x103262),a910,a910),f327(f327(f8(a910,f922(a910,a910),f916(x103262)),a325),f327(f327(f7(f916(x103262),f922(x103262,a910),a910),f327(f327(f8(f922(x103262,a910),f922(f922(x103262,a910),a910),f916(x103262)),a324),f173(x103262))),x103264))),f138(x103262))))),f233(x103262,x103261,x103263,x103264)) % 177.41/177.19 [7594]~P61(x75942)+E(x75941,f2(x75942))+E(f327(f327(f291(x75942),f327(f327(f80(x75942),x75943),f327(f327(f81(x75942),x75944),x75941))),x75941),f327(f327(f80(x75942),x75944),f327(f327(f291(x75942),x75943),x75941))) % 177.41/177.19 [7595]~P58(x75952)+E(x75951,f2(x75952))+E(f327(f327(f37(x75952),f327(f327(f80(x75952),x75953),f327(f327(f81(x75952),x75954),x75951))),x75951),f327(f327(f80(x75952),x75954),f327(f327(f37(x75952),x75953),x75951))) % 177.41/177.19 [7596]~P58(x75962)+E(x75961,f2(x75962))+E(f327(f327(f37(x75962),f327(f327(f80(x75962),x75963),f327(f327(f81(x75962),x75961),x75964))),x75961),f327(f327(f80(x75962),x75964),f327(f327(f37(x75962),x75963),x75961))) % 177.41/177.19 [7823]~P62(x78232)+E(x78231,f2(x78232))+E(f327(f327(f291(x78232),f327(f327(f23(x78232),x78233),f327(f327(f81(x78232),x78231),x78234))),x78231),f327(f327(f23(x78232),f327(f327(f291(x78232),x78233),x78231)),x78234)) % 177.41/177.19 [7824]~P61(x78242)+E(x78241,f2(x78242))+E(f327(f327(f291(x78242),f327(f327(f80(x78242),x78243),f327(f327(f81(x78242),x78244),x78241))),x78241),f327(f327(f80(x78242),f327(f327(f291(x78242),x78243),x78241)),x78244)) % 177.41/177.19 [7825]~P62(x78252)+E(x78251,f2(x78252))+E(f327(f327(f291(x78252),f327(f327(f80(x78252),x78253),f327(f327(f81(x78252),x78251),x78254))),x78251),f327(f327(f80(x78252),f327(f327(f291(x78252),x78253),x78251)),x78254)) % 177.41/177.19 [8523]~P1(f327(f161(x85231,x85233),x85234))+~P1(f327(f161(x85231,x85232),x85234))+P1(f327(f161(x85231,f327(f327(f103(f922(x85231,a910)),x85232),x85233)),x85234)) % 177.41/177.19 [8895]~E(f327(f327(f289(x88951,x88951,x88951),x88952),x88954),f190(f922(f921(x88951,x88951),a910)))+~E(f327(f327(f289(x88951,x88951,x88951),x88952),x88953),f190(f922(f921(x88951,x88951),a910)))+E(f327(f327(f289(x88951,x88951,x88951),x88952),f327(f327(f102(f922(f921(x88951,x88951),a910)),x88953),x88954)),f190(f922(f921(x88951,x88951),a910))) % 177.41/177.19 [9021]~P1(f327(f327(f234(f922(x90211,a910)),x90213),x90214))+~P1(f327(f327(f234(f922(x90211,a910)),x90212),x90214))+P1(f327(f327(f234(f922(x90211,a910)),f327(f327(f102(f922(x90211,a910)),x90212),x90213)),x90214)) % 177.41/177.19 [9398]~P1(f327(f35(x93981),x93984))+~P1(f327(f35(x93981),x93983))+E(f327(f327(f23(a915),f327(f327(f80(a915),f327(f327(f6(x93981,a915),x93982),x93983)),f327(f327(f6(x93981,a915),x93982),x93984))),f327(f327(f6(x93981,a915),x93982),f327(f327(f103(f922(x93981,a910)),x93983),x93984))),f327(f327(f6(x93981,a915),x93982),f327(f327(f102(f922(x93981,a910)),x93983),x93984))) % 177.41/177.19 [9486]~P1(f327(f327(f329(x94861),x94863),x94862))+~P1(f327(f327(f234(f922(x94861,a910)),x94862),f327(f327(f309(x94861),x94863),x94864)))+P1(f327(f327(f234(f922(x94861,a910)),f327(f327(f23(f922(x94861,a910)),x94862),f327(f327(f309(x94861),x94863),f190(f922(x94861,a910))))),x94864)) % 177.41/177.19 [9654]~P1(f327(f327(f329(x96541),x96543),x96542))+P1(f327(f327(f234(f922(x96541,a910)),x96542),f327(f327(f309(x96541),x96543),x96544)))+~P1(f327(f327(f234(f922(x96541,a910)),f327(f327(f23(f922(x96541,a910)),x96542),f327(f327(f309(x96541),x96543),f190(f922(x96541,a910))))),x96544)) % 177.41/177.19 [9744]~P1(f327(f327(f234(a915),x97441),x97443))+~P1(f327(f327(f235(a915),x97442),x97444))+P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),f327(f327(f252(a915,a915),x97441),x97442)),f327(f327(f252(a915,a915),x97443),x97444))),a32)) % 177.41/177.19 [9745]~P1(f327(f327(f234(a915),x97452),x97454))+~P1(f327(f327(f234(a915),x97451),x97453))+P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),f327(f327(f252(a915,a915),x97451),x97452)),f327(f327(f252(a915,a915),x97453),x97454))),a70)) % 177.41/177.19 [10037]~P1(f327(f327(f329(f916(x100371)),x100374),f162(x100371,x100373)))+~P1(f327(f327(f329(f916(x100371)),x100374),f162(x100371,x100372)))+P1(f327(f161(x100371,f327(f327(f103(f922(x100371,a910)),f327(f327(f7(x100371,f922(x100371,a910),a910),f329(x100371)),x100372)),f327(f327(f7(x100371,f922(x100371,a910),a910),f329(x100371)),x100373))),x100374)) % 177.41/177.19 [10141]~P23(x101411,f922(f922(x101411,a910),a910),f327(f327(f7(x101411,f922(f921(x101411,x101411),a910),f922(f922(x101411,a910),a910)),f327(f327(f8(f922(x101411,a910),f922(f922(f921(x101411,x101411),a910),f922(f922(x101411,a910),a910)),x101411),f61(x101411)),f327(f327(f7(x101411,f922(x101411,a910),f922(x101411,a910)),f309(x101411)),f190(f922(x101411,a910))))),x101413),x101412)+~P1(f327(f327(f329(x101411),x101414),x101412))+E(f327(f327(f23(f922(f922(x101411,a910),a910)),f327(f327(f61(x101411),x101412),x101413)),f327(f327(f61(x101411),f327(f327(f309(x101411),x101414),f190(f922(x101411,a910)))),x101413)),f327(f327(f61(x101411),f327(f327(f23(f922(x101411,a910)),x101412),f327(f327(f309(x101411),x101414),f190(f922(x101411,a910))))),x101413)) % 177.41/177.19 [10279]~P50(x102791,x102792,x102794)+~P1(f327(f327(f329(f921(x102791,x102791)),x102793),x102794))+P1(f327(f327(f257(x102791,x102791,a910),f327(f327(f7(x102791,f922(x102791,a910),f922(x102791,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x102791,a910),f922(x102791,a910)),x102791),f8(a910,a910,x102791)),f327(f327(f8(a910,f922(a910,a910),x102791),a325),f327(f327(f7(x102791,f922(x102791,a910),a910),f329(x102791)),x102792)))),f327(f327(f7(x102791,f922(x102791,a910),a910),f329(x102791)),x102792))),x102793)) % 177.41/177.19 [10294]P1(f327(f35(x102941),x102942))+~P1(f327(f35(x102943),f327(f310(x102941,x102943,x102944),x102942)))+~P1(f327(f35(x102941),f327(f262(x102941),f327(f327(f18(x102941,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102941),a325),f327(f327(f7(x102941,f922(x102941,a910),a910),f329(x102941)),x102942))),f327(f327(f7(x102941,x102943,a910),f327(f327(f8(x102943,f922(x102943,a910),x102941),a324),x102944)),f327(x102944,f497(x102944,x102943,x102942,x102941))))))) % 177.41/177.19 [8277]~P62(x82772)+E(x82771,f2(x82772))+E(f327(f327(f291(x82772),f327(f327(f23(x82772),f327(f327(f81(x82772),x82771),x82773)),x82774)),x82771),f327(f327(f23(x82772),x82773),f327(f327(f291(x82772),x82774),x82771))) % 177.41/177.19 [8278]~P62(x82782)+E(x82781,f2(x82782))+E(f327(f327(f291(x82782),f327(f327(f80(x82782),f327(f327(f81(x82782),x82781),x82783)),x82784)),x82781),f327(f327(f80(x82782),x82783),f327(f327(f291(x82782),x82784),x82781))) % 177.41/177.19 [9185]~E(f327(f327(f289(x91851,x91851,x91851),x91853),x91854),f190(f922(f921(x91851,x91851),a910)))+~E(f327(f327(f289(x91851,x91851,x91851),x91852),x91854),f190(f922(f921(x91851,x91851),a910)))+E(f327(f327(f289(x91851,x91851,x91851),f327(f327(f102(f922(f921(x91851,x91851),a910)),x91852),x91853)),x91854),f190(f922(f921(x91851,x91851),a910))) % 177.41/177.19 [9953]~P1(f327(f161(x99531,x99533),x99534))+~P1(f327(f161(x99531,x99532),x99534))+P1(f327(f161(x99531,f327(f327(f18(x99531,a910,a910),f327(f327(f8(a910,f922(a910,a910),x99531),a325),x99532)),x99533)),x99534)) % 177.41/177.19 [10215]P1(f327(x102151,f494(x102152,x102153,x102151,x102154)))+~P1(f327(f35(x102154),f327(f262(x102154),x102151)))+P1(f327(f35(x102153),f327(f262(x102153),f327(f327(f8(f922(x102154,a910),a910,x102153),f87(x102154)),f327(f327(f8(f922(x102154,a910),f922(x102154,a910),x102153),f327(f18(x102154,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102154),a325),x102151))),x102152))))) % 177.41/177.19 [10233]~P1(f327(f35(x102332),f327(f262(x102332),x102333)))+~P1(f327(f35(x102331),f327(f262(x102331),f327(f327(f7(x102331,x102332,a910),x102334),f494(x102334,x102331,x102333,x102332)))))+P1(f327(f35(x102331),f327(f262(x102331),f327(f327(f8(f922(x102332,a910),a910,x102331),f87(x102332)),f327(f327(f8(f922(x102332,a910),f922(x102332,a910),x102331),f327(f18(x102332,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102332),a325),x102333))),x102334))))) % 177.41/177.19 [10305]~P1(f327(f35(x103051),x103054))+P1(f327(f327(f329(x103051),f790(x103052,x103053,x103054,x103051)),x103054))+P1(f327(f35(x103053),f327(f262(x103053),f327(f327(f8(f922(x103051,a910),a910,x103053),f87(x103051)),f327(f327(f8(f922(x103051,a910),f922(x103051,a910),x103053),f327(f18(x103051,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103051),a325),f327(f327(f7(x103051,f922(x103051,a910),a910),f329(x103051)),x103054)))),x103052))))) % 177.41/177.19 [10311]~P1(f327(f35(x103112),x103113))+~P1(f327(f35(x103111),f327(f262(x103111),f327(f327(f7(x103111,x103112,a910),x103114),f790(x103114,x103111,x103113,x103112)))))+P1(f327(f35(x103111),f327(f262(x103111),f327(f327(f8(f922(x103112,a910),a910,x103111),f87(x103112)),f327(f327(f8(f922(x103112,a910),f922(x103112,a910),x103111),f327(f18(x103112,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103112),a325),f327(f327(f7(x103112,f922(x103112,a910),a910),f329(x103112)),x103113)))),x103114))))) % 177.41/177.19 [5201]~E(x52012,x52014)+E(f170(x52011,x52012,x52013),f170(x52011,x52014,x52015))+~E(x52012,f2(a915)) % 177.41/177.19 [5452]E(x54521,x54522)+~E(f170(x54524,x54523,x54521),f170(x54524,x54525,x54522))+E(x54523,f2(a915)) % 177.41/177.19 [6726]E(x67261,x67262)+~E(f327(x67263,x67261),f327(x67263,x67262))+~P23(x67264,x67265,x67263,f242(f922(x67264,a910))) % 177.41/177.19 [7626]E(x76261,x76262)+~P23(x76263,x76264,x76265,f242(f922(x76263,a910)))+~E(f327(f310(x76263,x76264,x76265),x76261),f327(f310(x76263,x76264,x76265),x76262)) % 177.41/177.19 [7877]P23(x78772,x78773,f500(x78774,x78773,x78772,x78771),x78771)+~E(f327(f310(x78773,x78772,x78775),x78774),x78771)+E(x78771,f190(f922(x78772,a910))) % 177.41/177.19 [8407]~P1(f327(f327(x84073,x84072),x84075))+~P1(f327(f327(x84073,x84074),x84072))+P1(f327(f327(f329(x84071),x84072),f290(x84071,x84073,x84074,x84075))) % 177.41/177.19 [8408]~P1(f327(f327(x84083,x84082),x84085))+~P1(f327(f327(x84083,x84084),x84082))+P1(f327(f327(f329(x84081),x84082),f299(x84081,x84083,x84084,x84085))) % 177.41/177.19 [8712]~P23(x87121,x87122,x87123,x87124)+P24(x87121,x87122,x87123,x87124,x87125)+~E(f327(f310(x87121,x87122,x87123),x87124),x87125) % 177.41/177.19 [8845]~P24(x88451,x88453,x88454,x88452,x88455)+~P1(f327(f35(x88453),x88455))+P1(f327(f35(x88451),x88452)) % 177.41/177.19 [8846]~P24(x88463,x88461,x88464,x88465,x88462)+~P1(f327(f35(x88463),x88465))+P1(f327(f35(x88461),x88462)) % 177.41/177.19 [8978]~P23(x89781,x89783,x89785,f242(f922(x89781,a910)))+~P23(x89783,x89782,x89784,f242(f922(x89783,a910)))+P23(x89781,x89782,f327(f72(x89783,x89782,x89781,x89784),x89785),f242(f922(x89781,a910))) % 177.41/177.19 [9545]P1(f327(f327(f329(f921(x95451,x95451)),f327(f327(f252(x95451,x95451),x95452),x95453)),f307(x95451,x95454)))+~P1(f327(f327(f329(f921(x95451,x95451)),f327(f327(f252(x95451,x95451),x95452),x95455)),f307(x95451,x95454)))+~P1(f327(f327(f329(f921(x95451,x95451)),f327(f327(f252(x95451,x95451),x95455),x95453)),f307(x95451,x95454))) % 177.41/177.19 [9585]~P108(x95852)+~P1(f327(f138(x95851),x95855))+P1(f327(f138(x95851),f150(x95851,x95852,x95853,x95854,x95855))) % 177.41/177.19 [5527]~E(x55272,f114(x55271))+E(f327(f327(f135(x55271),x55272),x55273),f327(f327(f152(x55271),x55274),x55275))+~E(x55273,f327(f327(f152(x55271),x55274),x55275)) % 177.41/177.19 [5528]~E(x55282,f114(x55281))+E(f327(f327(f135(x55281),x55282),x55283),f327(f327(f152(x55281),x55284),x55285))+~E(f327(f327(f152(x55281),x55284),x55285),x55283) % 177.41/177.19 [6682]~E(f327(f191(f916(x66821)),x66825),f327(f191(f916(x66822)),x66824))+E(f327(f327(f155(f921(x66821,x66822),x66822),f256(x66821,x66822)),x66823),x66824)+~E(f327(f327(f182(x66821,x66822),x66825),x66824),x66823) % 177.41/177.19 [6683]~E(f327(f191(f916(x66831)),x66834),f327(f191(f916(x66832)),x66835))+E(f327(f327(f155(f921(x66831,x66832),x66831),f251(x66831,x66832)),x66833),x66834)+~E(f327(f327(f182(x66831,x66832),x66834),x66835),x66833) % 177.41/177.19 [7162]~P108(x71621)+~P11(x71621,f327(f327(f155(x71622,x71621),x71623),x71625))+P11(x71621,f327(f327(f155(x71622,x71621),x71623),f327(f137(x71622,x71624),x71625))) % 177.41/177.19 [7205]~P1(f327(x72053,x72055))+~P1(f327(f327(x72052,x72054),x72055))+P1(f327(f327(f93(x72051,x72052,x72053),x72054),x72055)) % 177.41/177.19 [7305]~P108(x73051)+P11(x73051,f327(f327(f155(x73052,x73051),x73053),f171(x73052,x73054,x73055)))+~P11(x73051,f327(f327(f155(x73052,x73051),x73053),x73055)) % 177.41/177.19 [7328]~P52(x73283,x73282,x73285)+~P52(x73281,x73283,x73284)+P52(x73281,x73282,f327(f327(f289(x73281,x73283,x73282),x73284),x73285)) % 177.41/177.19 [7425]E(x74251,x74252)+~P23(x74253,x74254,x74255,f242(f922(x74253,a910)))+~E(f327(f327(f155(x74253,x74254),x74255),x74251),f327(f327(f155(x74253,x74254),x74255),x74252)) % 177.41/177.19 [7580]~P1(f327(f327(f234(a915),x75801),f327(x75803,x75805)))+P1(f327(f327(f234(a915),x75801),f156(x75802,x75803,x75804)))+~P1(f327(f327(f329(x75802),x75805),f327(f173(x75802),x75804))) % 177.41/177.19 [7581]~P1(f327(f327(f235(a915),x75811),f327(x75813,x75815)))+P1(f327(f327(f235(a915),x75811),f156(x75812,x75813,x75814)))+~P1(f327(f327(f329(x75812),x75815),f327(f173(x75812),x75814))) % 177.41/177.19 [7973]P1(f327(x79731,x79732))+~P1(f327(x79731,x79733))+~P1(f327(f327(f329(x79734),x79732),f327(f173(x79734),f170(x79734,x79735,x79733)))) % 177.41/177.19 [7974]P1(f327(x79741,x79742))+~P1(f327(x79741,x79743))+~P1(f327(f327(f329(x79744),x79743),f327(f173(x79744),f170(x79744,x79745,x79742)))) % 177.41/177.19 [7978]~P110(x79781)+P1(f327(f327(f234(f922(x79781,a910)),f303(x79781,x79782,x79783)),f303(x79781,x79784,x79785)))+P1(f327(f327(f234(x79781),x79782),x79783)) % 177.41/177.19 [7999]~P3(x79991)+P1(f327(f327(f234(x79991),f327(f327(f41(x79992,x79991),x79993),x79994)),f327(x79994,x79995)))+~P1(f327(f327(f329(x79992),x79995),x79993)) % 177.41/177.19 [8068]~P23(x80681,x80682,x80684,x80683)+E(f327(f77(x80681,x80682,x80683,x80684),f327(x80684,x80685)),x80685)+~P1(f327(f327(f329(x80681),x80685),x80683)) % 177.41/177.19 [8069]~P23(x80691,x80692,x80694,x80693)+E(f327(f92(x80691,x80692,x80693,x80694),f327(x80694,x80695)),x80695)+~P1(f327(f327(f329(x80691),x80695),x80693)) % 177.41/177.19 [8266]~P1(f327(x82661,x82665))+P1(f327(x82661,f861(x82661,x82662,x82663,x82664)))+~P1(f327(f327(f329(x82664),x82665),x82663)) % 177.41/177.19 [8267]~P1(f327(x82671,x82675))+P1(f327(x82671,f861(x82671,x82672,x82673,x82674)))+~P1(f327(f327(f329(x82674),x82675),x82672)) % 177.41/177.19 [8361]P1(f327(f35(x83611),x83612))+~P1(f327(f35(x83613),x83614))+~P1(f327(f327(f234(f922(x83611,a910)),x83612),f327(f310(x83613,x83611,x83615),x83614))) % 177.41/177.19 [8527]E(x85271,x85272)+~P23(x85273,x85274,x85275,f327(f327(f102(f922(x85273,a910)),f327(f173(x85273),x85271)),f327(f173(x85273),x85272)))+~E(f327(f327(f155(x85273,x85274),x85275),x85271),f327(f327(f155(x85273,x85274),x85275),x85272)) % 177.41/177.19 [8580]~P110(x85801)+~P1(f327(f327(f235(f922(x85801,a910)),f303(x85801,x85804,x85805)),f303(x85801,x85802,x85803)))+P1(f327(f327(f234(x85801),x85802),x85803)) % 177.41/177.19 [8642]~P23(x86421,x86424,x86425,f242(f922(x86421,a910)))+~P1(f327(f327(f329(x86424),f327(x86425,x86422)),f327(f310(x86421,x86424,x86425),x86423)))+P1(f327(f327(f329(x86421),x86422),x86423)) % 177.41/177.19 [8718]P1(f327(x87181,x87182))+~P1(f327(x87181,f876(x87181,x87183,x87184,x87185)))+~P1(f327(f327(f329(x87185),x87182),x87184)) % 177.41/177.19 [8719]P1(f327(x87191,x87192))+~P1(f327(x87191,f876(x87191,x87193,x87194,x87195)))+~P1(f327(f327(f329(x87195),x87192),x87193)) % 177.41/177.19 [9018]~P23(x90182,x90183,x90181,x90184)+E(f327(x90181,f327(f77(x90182,x90183,x90184,x90181),x90185)),x90185)+~P1(f327(f327(f329(x90183),x90185),f327(f310(x90182,x90183,x90181),x90184))) % 177.41/177.19 [9125]E(x91251,f114(x91252))+E(f327(f327(f152(x91252),x91253),f676(x91254,x91253,x91255,x91251,x91252)),x91251)+~E(f327(f327(f135(x91252),x91251),x91255),f327(f327(f152(x91252),x91253),x91254)) % 177.41/177.19 [9126]E(x91261,f114(x91262))+E(f327(f327(f152(x91262),x91263),f677(x91264,x91261,x91265,x91263,x91262)),x91261)+~E(f327(f327(f135(x91262),x91261),x91264),f327(f327(f152(x91262),x91263),x91265)) % 177.41/177.19 [9144]E(f327(f327(f152(x91442),x91443),f676(x91444,x91443,x91441,x91445,x91442)),x91445)+~E(f327(f327(f135(x91442),x91445),x91441),f327(f327(f152(x91442),x91443),x91444))+E(x91441,f327(f327(f152(x91442),x91443),x91444)) % 177.41/177.19 [9145]E(f327(f327(f152(x91451),x91452),f677(x91454,x91455,x91453,x91452,x91451)),x91455)+~E(f327(f327(f135(x91451),x91455),x91454),f327(f327(f152(x91451),x91452),x91453))+E(f327(f327(f152(x91451),x91452),x91453),x91454) % 177.41/177.19 [9221]~E(f327(f310(x92213,x92212,x92214),f242(f922(x92213,a910))),f242(f922(x92212,a910)))+~E(f327(f310(x92211,x92213,x92215),f242(f922(x92211,a910))),f242(f922(x92213,a910)))+E(f327(f310(x92211,x92212,f327(f72(x92213,x92212,x92211,x92214),x92215)),f242(f922(x92211,a910))),f242(f922(x92212,a910))) % 177.41/177.19 [9591]E(x95911,f114(x95912))+~E(f327(f327(f135(x95912),x95911),x95913),f327(f327(f152(x95912),x95915),x95914))+E(f327(f327(f135(x95912),f677(x95913,x95911,x95914,x95915,x95912)),x95913),x95914) % 177.41/177.19 [9592]E(x95921,f114(x95922))+~E(f327(f327(f135(x95922),x95921),x95925),f327(f327(f152(x95922),x95924),x95923))+E(f327(f327(f135(x95922),f676(x95923,x95924,x95925,x95921,x95922)),x95925),x95923) % 177.41/177.19 [9599]E(f327(f327(f135(x95992),f676(x95994,x95993,x95991,x95995,x95992)),x95991),x95994)+~E(f327(f327(f135(x95992),x95995),x95991),f327(f327(f152(x95992),x95993),x95994))+E(x95991,f327(f327(f152(x95992),x95993),x95994)) % 177.41/177.19 [9600]~E(f327(f327(f135(x96001),x96005),x96004),f327(f327(f152(x96001),x96002),x96003))+E(f327(f327(f135(x96001),f677(x96004,x96005,x96003,x96002,x96001)),x96004),x96003)+E(f327(f327(f152(x96001),x96002),x96003),x96004) % 177.41/177.19 [9601]E(f327(f327(f135(x96011),x96015),f679(x96013,x96012,x96014,x96015,x96011)),x96012)+E(f327(f327(f135(x96011),x96012),f678(x96013,x96012,x96014,x96015,x96011)),x96015)+~E(f327(f327(f135(x96011),x96015),x96014),f327(f327(f135(x96011),x96012),x96013)) % 177.41/177.19 [9637]~P108(x96371)+P11(x96371,f327(f327(f155(x96372,x96371),x96373),f150(x96372,x96371,x96373,x96374,x96375)))+~P11(x96371,f327(f327(f155(x96372,x96371),x96373),x96375)) % 177.41/177.19 [9651]~P56(x96515,x96511,x96514,x96513)+P1(f327(f327(x96511,x96512),f539(x96513,x96514,x96511,x96515,x96512)))+~P1(f327(f327(f329(x96515),x96512),x96514)) % 177.41/177.19 [9652]~P56(x96525,x96521,x96524,x96523)+P1(f327(f327(x96521,x96522),f795(x96523,x96524,x96521,x96525,x96522)))+~P1(f327(f327(f329(x96525),x96522),x96524)) % 177.41/177.19 [9756]~P1(f327(f327(f329(f921(x97561,x97561)),f327(f327(f252(x97561,x97561),x97565),x97563)),f307(x97561,x97564)))+P1(f327(f327(f329(f921(x97561,x97561)),f327(f327(f252(x97561,x97561),x97562),x97563)),f327(f327(f289(x97561,x97561,x97561),x97564),f307(x97561,x97564))))+~P1(f327(f327(f329(f921(x97561,x97561)),f327(f327(f252(x97561,x97561),x97562),x97565)),f327(f327(f289(x97561,x97561,x97561),x97564),f307(x97561,x97564)))) % 177.41/177.19 [9757]~P1(f327(f327(f329(f921(x97571,x97571)),f327(f327(f252(x97571,x97571),x97572),x97575)),f307(x97571,x97574)))+P1(f327(f327(f329(f921(x97571,x97571)),f327(f327(f252(x97571,x97571),x97572),x97573)),f327(f327(f289(x97571,x97571,x97571),x97574),f307(x97571,x97574))))+~P1(f327(f327(f329(f921(x97571,x97571)),f327(f327(f252(x97571,x97571),x97575),x97573)),f327(f327(f289(x97571,x97571,x97571),x97574),f307(x97571,x97574)))) % 177.41/177.19 [9759]P1(f327(f327(f329(f921(f916(x97591),f916(x97591))),f327(f327(f252(f916(x97591),f916(x97591)),x97592),x97593)),f159(x97591,f307(x97591,x97594))))+~P1(f327(f327(f329(f921(f916(x97591),f916(x97591))),f327(f327(f252(f916(x97591),f916(x97591)),x97592),x97595)),f159(x97591,f307(x97591,x97594))))+~P1(f327(f327(f329(f921(f916(x97591),f916(x97591))),f327(f327(f252(f916(x97591),f916(x97591)),x97595),x97593)),f159(x97591,f307(x97591,x97594)))) % 177.41/177.19 [9763]E(f327(f327(f135(x97631),x97632),f678(x97633,x97632,x97634,x97635,x97631)),x97635)+E(f327(f327(f135(x97631),f679(x97633,x97632,x97634,x97635,x97631)),x97633),x97634)+~E(f327(f327(f135(x97631),x97632),x97633),f327(f327(f135(x97631),x97635),x97634)) % 177.41/177.19 [9764]E(f327(f327(f135(x97641),x97642),f679(x97643,x97644,x97645,x97642,x97641)),x97644)+E(f327(f327(f135(x97641),f678(x97643,x97644,x97645,x97642,x97641)),x97645),x97643)+~E(f327(f327(f135(x97641),x97642),x97645),f327(f327(f135(x97641),x97644),x97643)) % 177.41/177.19 [9818]P1(f327(f327(f329(f921(x98181,x98181)),f327(f327(f252(x98181,x98181),x98182),x98183)),f327(f327(f289(x98181,x98181,x98181),x98184),f307(x98181,x98184))))+~P1(f327(f327(f329(f921(x98181,x98181)),f327(f327(f252(x98181,x98181),x98182),x98185)),f327(f327(f289(x98181,x98181,x98181),x98184),f307(x98181,x98184))))+~P1(f327(f327(f329(f921(x98181,x98181)),f327(f327(f252(x98181,x98181),x98185),x98183)),f327(f327(f289(x98181,x98181,x98181),x98184),f307(x98181,x98184)))) % 177.41/177.19 [9845]P32(x98451,x98452,x98453,x98454,x98455)+~E(f327(f191(f916(x98451)),x98454),f327(f191(f916(x98452)),x98455))+~P1(f327(f327(f257(x98451,x98452,a910),x98453),f695(x98455,x98454,x98453,x98452,x98451))) % 177.41/177.19 [9846]P32(x98461,x98462,x98463,x98464,x98465)+~E(f327(f191(f916(x98461)),x98464),f327(f191(f916(x98462)),x98465))+~P1(f327(f327(f257(x98461,x98462,a910),x98463),f696(x98463,x98465,x98464,x98462,x98461))) % 177.41/177.19 [9851]E(f327(f327(f135(x98511),f678(x98512,x98513,x98514,x98515,x98511)),x98514),x98512)+~E(f327(f327(f135(x98511),x98513),x98512),f327(f327(f135(x98511),x98515),x98514))+E(f327(f327(f135(x98511),f679(x98512,x98513,x98514,x98515,x98511)),x98512),x98514) % 177.41/177.19 [9866]~P108(x98662)+E(f327(f327(f149(x98661,x98662,x98663),x98664),x98665),f327(f327(f152(x98661),x98664),x98665))+P1(f327(f327(f329(x98661),f740(x98664,x98663,x98665,x98661,x98662)),f327(f173(x98661),x98665))) % 177.41/177.19 [9870]~P56(x98701,x98704,x98703,x98702)+~P1(f327(f327(f329(x98701),x98705),x98703))+P1(f327(f327(f329(x98701),f539(x98702,x98703,x98704,x98701,x98705)),x98702)) % 177.41/177.19 [9871]~P56(x98711,x98714,x98713,x98712)+~P1(f327(f327(f329(x98711),x98715),x98713))+P1(f327(f327(f329(x98711),f795(x98712,x98713,x98714,x98711,x98715)),x98712)) % 177.41/177.19 [9986]~P1(f327(f327(f329(f921(f922(x99861,a910),f922(x99861,a910))),f327(f327(f252(f922(x99861,a910),f922(x99861,a910)),x99864),x99863)),f319(x99861,x99862)))+~P1(f327(f327(f329(x99861),x99865),x99864))+P1(f327(f327(f329(x99861),f597(x99862,x99863,x99864,x99861,x99865)),x99863)) % 177.41/177.19 [9997]~P108(x99972)+E(f327(f327(f149(x99971,x99972,x99973),x99974),x99975),f327(f327(f152(x99971),x99974),x99975))+~P1(f327(f327(f234(x99972),f327(x99973,x99974)),f327(x99973,f740(x99974,x99973,x99975,x99971,x99972)))) % 177.41/177.19 [10046]~P23(x100463,x100464,x100465,f242(f922(x100463,a910)))+P1(f327(x100461,x100462))+~P1(f327(x100461,f327(f92(x100463,x100464,f242(f922(x100463,a910)),x100465),f808(x100462,x100461,x100465,x100464,x100463)))) % 177.41/177.19 [10193]P32(x101931,x101932,x101933,x101934,x101935)+~E(f327(f191(f916(x101931)),x101934),f327(f191(f916(x101932)),x101935))+~P1(f327(f327(x101933,f327(f327(f165(x101931),x101934),f697(x101935,x101934,x101933,x101932,x101931))),f327(f327(f165(x101932),x101935),f697(x101935,x101934,x101933,x101932,x101931)))) % 177.41/177.19 [10194]P32(x101941,x101942,x101943,x101944,x101945)+~E(f327(f191(f916(x101941)),x101944),f327(f191(f916(x101942)),x101945))+~P1(f327(f327(x101943,f327(f327(f165(x101941),x101944),f732(x101943,x101945,x101942,x101944,x101941))),f327(f327(f165(x101942),x101945),f732(x101943,x101945,x101942,x101944,x101941)))) % 177.41/177.19 [6756]~P15(x67562,x67565,x67561)+~P1(f327(f35(x67562),x67564))+E(f327(x67561,f327(f327(f309(x67562),x67563),x67564)),f327(f327(f64(x67562,x67562,x67565),x67563),x67564)) % 177.41/177.19 [6757]~E(x67573,x67574)+~E(x67572,x67575)+E(f327(f327(f309(x67571),x67572),f327(f327(f309(x67571),x67573),f190(f922(x67571,a910)))),f327(f327(f309(x67571),x67574),f327(f327(f309(x67571),x67575),f190(f922(x67571,a910))))) % 177.41/177.19 [6767]P1(f327(x67672,x67675))+E(f178(x67671,x67672,f327(f327(f135(x67671),x67673),x67674)),f178(x67671,x67672,x67673))+~P1(f327(f327(f329(x67671),x67675),f327(f173(x67671),x67673))) % 177.41/177.19 [6805]E(f327(x68051,x68052),f190(f922(x68053,a910)))+~E(f327(f327(f40(x68054,f922(x68053,a910)),x68055),x68051),f190(f922(x68053,a910)))+~P1(f327(f327(f329(x68054),x68052),x68055)) % 177.41/177.19 [6806]E(f327(x68061,x68062),f242(f922(x68063,a910)))+~E(f327(f327(f41(x68064,f922(x68063,a910)),x68065),x68061),f242(f922(x68063,a910)))+~P1(f327(f327(f329(x68064),x68062),x68065)) % 177.41/177.19 [7315]~E(x73152,x73154)+~P144(x73151)+E(f327(f327(f80(x73151),f327(f327(f81(x73151),x73152),x73153)),f327(f327(f81(x73151),x73154),x73155)),f327(f327(f80(x73151),f327(f327(f81(x73151),x73152),x73155)),f327(f327(f81(x73151),x73154),x73153))) % 177.41/177.19 [7377]~P3(x73771)+~P1(f327(f327(f329(x73774),x73773),x73775))+P1(f327(f327(f234(x73771),f327(x73772,x73773)),f327(f327(f40(x73774,x73771),x73775),x73772))) % 177.41/177.19 [7430]~P109(x74301)+P1(f327(f327(f234(x74301),f327(x74302,x74303)),f327(x74304,x74303)))+~P1(f327(f327(f234(f922(x74305,x74301)),x74302),x74304)) % 177.41/177.19 [7551]E(x75511,x75512)+E(x75513,x75511)+~E(f327(f327(f309(x75514),x75511),f327(f327(f309(x75514),x75515),f190(f922(x75514,a910)))),f327(f327(f309(x75514),x75512),f327(f327(f309(x75514),x75513),f190(f922(x75514,a910))))) % 177.41/177.19 [7552]E(x75521,x75522)+E(x75523,x75521)+~E(f327(f327(f309(x75524),x75523),f327(f327(f309(x75524),x75522),f190(f922(x75524,a910)))),f327(f327(f309(x75524),x75525),f327(f327(f309(x75524),x75521),f190(f922(x75524,a910))))) % 177.41/177.19 [7553]E(x75531,x75532)+E(x75531,x75533)+~E(f327(f327(f309(x75534),x75533),f327(f327(f309(x75534),x75532),f190(f922(x75534,a910)))),f327(f327(f309(x75534),x75535),f327(f327(f309(x75534),x75531),f190(f922(x75534,a910))))) % 177.41/177.19 [7554]E(x75541,x75542)+E(x75541,x75543)+~E(f327(f327(f309(x75544),x75541),f327(f327(f309(x75544),x75545),f190(f922(x75544,a910)))),f327(f327(f309(x75544),x75542),f327(f327(f309(x75544),x75543),f190(f922(x75544,a910))))) % 177.41/177.19 [8078]P23(x80781,x80782,x80783,x80784)+~P23(x80781,x80782,x80783,x80785)+~P1(f327(f327(f234(f922(x80781,a910)),x80784),x80785)) % 177.41/177.19 [8108]~E(f327(x81083,x81085),x81084)+~P23(x81081,x81082,x81083,f242(f922(x81081,a910)))+E(f327(f92(x81081,x81082,f242(f922(x81081,a910)),x81083),x81084),x81085) % 177.41/177.19 [8254]E(x82541,x82542)+~E(f327(f310(x82543,x82544,x82545),x82541),f327(f310(x82543,x82544,x82545),x82542))+~P23(x82543,x82544,x82545,f327(f327(f102(f922(x82543,a910)),x82541),x82542)) % 177.41/177.19 [8331]P1(f327(x83312,x83314))+E(f327(f327(f139(x83311),f327(f191(f916(x83311)),f178(x83311,x83312,x83313))),x83313),f327(f327(f152(x83311),x83314),x83315))+~E(f327(f327(f135(x83311),f178(x83311,x83312,x83313)),f327(f327(f152(x83311),x83314),x83315)),x83313) % 177.41/177.19 [8359]~P23(x83591,x83592,x83593,x83595)+~P23(x83591,x83592,x83593,x83594)+P23(x83591,x83592,x83593,f327(f327(f103(f922(x83591,a910)),x83594),x83595)) % 177.41/177.19 [8466]~P68(x84661)+E(f327(f327(f80(x84661),f327(x84662,x84663)),f327(f166(x84661),f327(f327(f155(x84664,x84661),x84662),f171(x84664,x84663,x84665)))),f327(f166(x84661),f327(f327(f155(x84664,x84661),x84662),x84665)))+~P1(f327(f327(f329(x84664),x84663),f327(f173(x84664),x84665))) % 177.41/177.19 [8553]~P108(x85531)+~P11(x85531,f327(f327(f155(x85532,x85531),x85533),x85535))+P11(x85531,f327(f327(f155(x85532,x85531),x85533),f327(f327(f149(x85532,x85531,x85533),x85534),x85535))) % 177.41/177.19 [8638]~P3(x86381)+P1(f327(f327(f234(x86381),f327(f327(f40(x86382,x86381),x86383),x86384)),f327(f327(f40(x86382,x86381),x86385),x86384)))+~P1(f327(f327(f234(f922(x86382,a910)),x86383),x86385)) % 177.41/177.19 [8639]~P3(x86391)+P1(f327(f327(f234(x86391),f327(f327(f41(x86392,x86391),x86393),x86394)),f327(f327(f41(x86392,x86391),x86395),x86394)))+~P1(f327(f327(f234(f922(x86392,a910)),x86395),x86393)) % 177.41/177.19 [8672]~P108(x86723)+P1(f327(f138(x86721),x86722))+~P1(f327(f138(x86721),f327(f327(f149(x86721,x86723,x86724),x86725),x86722))) % 177.41/177.19 [8817]~P108(x88171)+~P1(f327(f327(f329(x88172),x88173),f327(f173(x88172),x88174)))+~P1(f327(f138(x88172),f327(f327(f149(x88172,x88171,x88175),x88173),x88174))) % 177.41/177.19 [8907]~P108(x89071)+P11(x89071,f327(f327(f155(x89072,x89071),x89073),x89074))+~P11(x89071,f327(f327(f155(x89072,x89071),x89073),f327(f327(f149(x89072,x89071,x89073),x89075),x89074))) % 177.41/177.19 [8953]~P23(x89532,x89531,x89534,x89533)+E(f327(f310(x89531,x89532,f92(x89532,x89531,x89533,x89534)),f327(f310(x89532,x89531,x89534),x89535)),x89535)+~P1(f327(f327(f234(f922(x89532,a910)),x89535),x89533)) % 177.41/177.19 [9006]~P108(x90062)+E(f327(f327(f149(x90061,x90062,x90063),x90064),x90065),f150(x90061,x90062,x90063,x90064,x90065))+P1(f327(f327(f329(x90062),f327(x90063,x90064)),f327(f310(x90061,x90062,x90063),f327(f173(x90061),x90065)))) % 177.41/177.19 [9087]~P108(x90872)+E(f150(x90871,x90872,x90873,x90874,x90875),x90875)+~P1(f327(f327(f329(x90872),f327(x90873,x90874)),f327(f310(x90871,x90872,x90873),f327(f173(x90871),x90875)))) % 177.41/177.19 [9103]~P23(x91032,x91031,x91033,x91035)+P1(f327(f327(f235(f922(x91031,a910)),f327(f310(x91032,x91031,x91033),x91034)),f327(f310(x91032,x91031,x91033),x91035)))+~P1(f327(f327(f235(f922(x91032,a910)),x91034),x91035)) % 177.41/177.19 [9262]~P23(x92621,x92622,x92623,f242(f922(x92621,a910)))+~P1(f327(f327(f234(f922(x92622,a910)),x92624),f327(f310(x92621,x92622,x92623),x92625)))+P1(f327(f327(f234(f922(x92621,a910)),f327(f311(x92621,x92622,x92623),x92624)),x92625)) % 177.41/177.19 [9285]~E(f327(f310(x92853,x92851,x92854),f242(f922(x92853,a910))),f242(f922(x92851,a910)))+P1(f327(f327(f234(f922(x92851,a910)),x92852),f327(f310(x92853,x92851,x92854),x92855)))+~P1(f327(f327(f234(f922(x92853,a910)),f327(f311(x92853,x92851,x92854),x92852)),x92855)) % 177.41/177.19 [9391]~P23(x93911,x93914,x93915,f242(f922(x93911,a910)))+~P1(f327(f327(f234(f922(x93914,a910)),f327(f310(x93911,x93914,x93915),x93912)),f327(f310(x93911,x93914,x93915),x93913)))+P1(f327(f327(f234(f922(x93911,a910)),x93912),x93913)) % 177.41/177.19 [9513]~P81(x95131)+~E(f327(x95133,f715(x95133,x95134,x95135,x95132,x95131)),f2(x95131))+E(f327(f166(x95131),f327(f327(f155(x95132,x95131),x95133),f327(f137(x95132,x95134),x95135))),f327(f166(x95131),f327(f327(f155(x95132,x95131),x95133),x95135))) % 177.41/177.19 [9540]~P24(x95401,x95402,x95403,f242(f922(x95401,a910)),f242(f922(x95402,a910)))+~P1(f327(f327(f234(f922(x95402,a910)),x95404),f327(f310(x95401,x95402,x95403),x95405)))+P1(f327(f327(f234(f922(x95401,a910)),f327(f311(x95401,x95402,x95403),x95404)),x95405)) % 177.41/177.19 [9569]~P24(x95693,x95691,x95694,f242(f922(x95693,a910)),f242(f922(x95691,a910)))+P1(f327(f327(f234(f922(x95691,a910)),x95692),f327(f310(x95693,x95691,x95694),x95695)))+~P1(f327(f327(f234(f922(x95693,a910)),f327(f311(x95693,x95691,x95694),x95692)),x95695)) % 177.41/177.19 [9696]~P14(x96961,x96962,x96963)+~P1(f327(f35(x96961),x96965))+P1(f327(f66(x96961,x96962,x96963,x96964,x96965),f327(f327(f64(x96961,x96962,x96963),x96964),x96965))) % 177.41/177.19 [9776]~P24(x97762,x97761,x97764,f242(f922(x97762,a910)),f242(f922(x97761,a910)))+~P24(x97761,x97763,x97765,f242(f922(x97761,a910)),f242(f922(x97763,a910)))+E(f327(f72(x97761,x97762,x97763,f92(x97762,x97761,f242(f922(x97762,a910)),x97764)),f92(x97761,x97763,f242(f922(x97761,a910)),x97765)),f92(x97762,x97763,f242(f922(x97762,a910)),f327(f72(x97761,x97763,x97762,x97765),x97764))) % 177.41/177.19 [9777]P1(f327(x97771,f635(x97772,x97771,x97773,x97774,x97775)))+~P1(f327(f327(f234(f922(x97775,a910)),x97774),x97773))+P1(f327(f327(f234(f922(x97775,a910)),f327(f327(f103(f922(x97775,a910)),x97774),f327(f262(x97775),x97771))),f327(f327(f103(f922(x97775,a910)),x97773),f327(f262(x97775),x97772)))) % 177.41/177.19 [9791]~P81(x97911)+~P1(f327(x97914,f715(x97913,x97914,x97915,x97912,x97911)))+E(f327(f166(x97911),f327(f327(f155(x97912,x97911),x97913),f327(f137(x97912,x97914),x97915))),f327(f166(x97911),f327(f327(f155(x97912,x97911),x97913),x97915))) % 177.41/177.19 [9868]~P3(x98685)+P1(f327(f327(f329(x98681),f355(x98682,x98683,x98681,x98684,x98685)),x98683))+P1(f327(f327(f234(x98685),x98684),f327(f327(f41(x98681,x98685),x98683),x98682))) % 177.41/177.19 [9872]~P81(x98721)+E(f327(f166(x98721),f327(f327(f155(x98722,x98721),x98723),f327(f137(x98722,x98724),x98725))),f327(f166(x98721),f327(f327(f155(x98722,x98721),x98723),x98725)))+P1(f327(f327(f329(x98722),f715(x98723,x98724,x98725,x98722,x98721)),f327(f173(x98722),x98725))) % 177.41/177.19 [9882]~P1(f327(x98825,f635(x98825,x98823,x98824,x98822,x98821)))+~P1(f327(f327(f234(f922(x98821,a910)),x98822),x98824))+P1(f327(f327(f234(f922(x98821,a910)),f327(f327(f103(f922(x98821,a910)),x98822),f327(f262(x98821),x98823))),f327(f327(f103(f922(x98821,a910)),x98824),f327(f262(x98821),x98825)))) % 177.41/177.19 [9898]~P23(x98985,x98983,x98984,f242(f922(x98985,a910)))+P1(f327(x98981,x98982))+P1(f327(f327(f329(x98983),f808(x98982,x98981,x98984,x98983,x98985)),f327(f310(x98985,x98983,x98984),f242(f922(x98985,a910))))) % 177.41/177.19 [9922]P32(x99221,x99222,x99223,x99224,x99225)+~E(f327(f191(f916(x99222)),x99225),f327(f191(f916(x99221)),x99224))+P1(f327(f327(f235(a915),f697(x99225,x99224,x99223,x99222,x99221)),f327(f191(f916(x99221)),x99224))) % 177.41/177.19 [9923]P32(x99231,x99232,x99233,x99234,x99235)+~E(f327(f191(f916(x99232)),x99235),f327(f191(f916(x99231)),x99234))+P1(f327(f327(f235(a915),f732(x99233,x99235,x99232,x99234,x99231)),f327(f191(f916(x99231)),x99234))) % 177.41/177.19 [9954]P1(f327(f327(f329(x99541),f635(x99542,x99543,x99544,x99545,x99541)),x99545))+~P1(f327(f327(f234(f922(x99541,a910)),x99545),x99544))+P1(f327(f327(f234(f922(x99541,a910)),f327(f327(f103(f922(x99541,a910)),x99545),f327(f262(x99541),x99543))),f327(f327(f103(f922(x99541,a910)),x99544),f327(f262(x99541),x99542)))) % 177.41/177.19 [9998]~P3(x99981)+~P1(f327(f327(f234(x99981),x99982),f327(x99985,f355(x99985,x99984,x99983,x99982,x99981))))+P1(f327(f327(f234(x99981),x99982),f327(f327(f41(x99983,x99981),x99984),x99985))) % 177.41/177.19 [10035]~P75(x100351)+~P1(f327(f35(x100352),x100355))+E(f327(f327(f327(f65(x100351,x100352,f81(x100351)),f327(f327(f18(x100352,x100351,x100351),f327(f327(f8(x100351,f922(x100351,x100351),x100352),f81(x100351)),x100353)),x100354)),f78(x100351)),x100355),f327(f327(f81(x100351),f327(f327(f327(f65(x100351,x100352,f81(x100351)),x100353),f78(x100351)),x100355)),f327(f327(f327(f65(x100351,x100352,f81(x100351)),x100354),f78(x100351)),x100355))) % 177.41/177.19 [10090]~P1(f327(f327(f329(f921(f922(x100901,a910),f922(x100901,a910))),f327(f327(f252(f922(x100901,a910),f922(x100901,a910)),x100905),x100904)),f319(x100901,x100903)))+~P1(f327(f327(f329(x100901),x100902),x100905))+P1(f327(f327(f329(f921(x100901,x100901)),f327(f327(f252(x100901,x100901),x100902),f597(x100903,x100904,x100905,x100901,x100902))),x100903)) % 177.41/177.19 [10230]~P1(f327(f327(f329(f921(f916(x102301),f916(x102301))),f327(f327(f252(f916(x102301),f916(x102301)),f327(f327(f135(x102301),x102305),x102302)),f327(f327(f135(x102301),x102305),x102303))),f148(x102301,x102304)))+P1(f327(f327(f329(f921(f916(x102301),f916(x102301))),f327(f327(f252(f916(x102301),f916(x102301)),x102302),x102303)),f148(x102301,x102304)))+P1(f327(f327(f329(f921(x102301,x102301)),f327(f327(f252(x102301,x102301),f684(x102304,x102303,x102302,x102305,x102301)),f684(x102304,x102303,x102302,x102305,x102301))),x102304)) % 177.41/177.19 [7433]~E(x74333,x74335)+E(f327(f327(f165(x74331),f327(f327(f160(x74331,x74332),x74333),x74334)),x74335),x74334)+~P1(f327(f327(f235(a915),x74333),f327(f191(f916(x74331)),x74332))) % 177.41/177.19 [7548]~E(f327(f327(f135(x75481),x75482),x75484),f327(f327(f135(x75481),x75483),x75485))+E(f327(f327(f176(x75481),f327(f191(f916(x75481)),x75482)),x75483),x75482)+P1(f327(f327(f234(a915),f327(f191(f916(x75481)),x75483)),f327(f191(f916(x75481)),x75482))) % 177.41/177.19 [8039]~E(f327(f327(f135(x80391),x80392),x80394),f327(f327(f135(x80391),x80393),x80395))+E(f327(f327(f176(x80391),f327(f191(f916(x80391)),x80392)),x80393),x80392)+~P1(f327(f327(f234(a915),f327(f191(f916(x80391)),x80392)),f327(f191(f916(x80391)),x80393))) % 177.41/177.19 [8063]~P1(f327(f35(x80631),f327(x80634,x80635)))+~P1(f327(f327(f329(x80632),x80635),x80633))+P1(f327(f35(x80631),f327(f327(f41(x80632,f922(x80631,a910)),x80633),x80634))) % 177.41/177.19 [8238]~P50(x82381,x82383,x82385)+~P50(x82381,x82382,x82384)+P50(x82381,f327(f327(f102(f922(x82381,a910)),x82382),x82383),f327(f327(f102(f922(f921(x82381,x82381),a910)),x82384),x82385)) % 177.41/177.19 [8239]~P50(x82391,x82393,x82395)+~P50(x82391,x82392,x82394)+P50(x82391,f327(f327(f103(f922(x82391,a910)),x82392),x82393),f327(f327(f103(f922(f921(x82391,x82391),a910)),x82394),x82395)) % 177.41/177.19 [8593]E(f327(f327(f252(x85931,x85932),f327(f327(f165(x85931),x85933),x85934)),f327(f327(f165(x85932),x85935),x85934)),f327(f327(f165(f921(x85931,x85932)),f327(f327(f182(x85931,x85932),x85933),x85935)),x85934))+~P1(f327(f327(f235(a915),x85934),f327(f191(f916(x85931)),x85933)))+~P1(f327(f327(f235(a915),x85934),f327(f191(f916(x85932)),x85935))) % 177.41/177.19 [8746]~P50(x87461,x87463,x87464)+P1(f327(f327(f329(x87461),x87462),x87463))+~P1(f327(f327(f329(f921(x87461,x87461)),f327(f327(f252(x87461,x87461),x87465),x87462)),x87464)) % 177.41/177.19 [8747]~P50(x87471,x87473,x87474)+P1(f327(f327(f329(x87471),x87472),x87473))+~P1(f327(f327(f329(f921(x87471,x87471)),f327(f327(f252(x87471,x87471),x87472),x87475)),x87474)) % 177.41/177.19 [8748]~P6(x87481,x87483,x87484)+P1(f327(f327(f329(x87481),x87482),x87483))+~P1(f327(f327(f329(f921(x87481,x87481)),f327(f327(f252(x87481,x87481),x87485),x87482)),x87484)) % 177.41/177.19 [8749]~P6(x87491,x87493,x87494)+P1(f327(f327(f329(x87491),x87492),x87493))+~P1(f327(f327(f329(f921(x87491,x87491)),f327(f327(f252(x87491,x87491),x87492),x87495)),x87494)) % 177.41/177.19 [9030]~P6(x90301,x90305,x90302)+E(f327(f285(x90301,x90301,x90302),f327(f327(f309(x90301),x90303),f190(f922(x90301,a910)))),f327(f285(x90301,x90301,x90302),f327(f327(f309(x90301),x90304),f190(f922(x90301,a910)))))+~P1(f327(f327(f329(f921(x90301,x90301)),f327(f327(f252(x90301,x90301),x90303),x90304)),x90302)) % 177.41/177.19 [9218]P1(f327(x92181,x92182))+~P1(f327(f327(f329(x92183),x92182),x92185))+P1(f327(f327(f329(x92183),f876(x92181,x92184,x92185,x92183)),f327(f327(f102(f922(x92183,a910)),x92185),x92184))) % 177.41/177.19 [9219]P1(f327(x92191,x92192))+~P1(f327(f327(f329(x92193),x92192),x92194))+P1(f327(f327(f329(x92193),f876(x92191,x92194,x92195,x92193)),f327(f327(f102(f922(x92193,a910)),x92195),x92194))) % 177.41/177.19 [9227]~P1(f327(x92272,x92275))+~P1(f327(f327(f329(x92271),x92275),x92274))+P1(f327(f327(f329(x92271),f861(x92272,x92273,x92274,x92271)),f327(f327(f102(f922(x92271,a910)),x92274),x92273))) % 177.41/177.19 [9228]~P1(f327(x92282,x92285))+~P1(f327(f327(f329(x92281),x92285),x92283))+P1(f327(f327(f329(x92281),f861(x92282,x92283,x92284,x92281)),f327(f327(f102(f922(x92281,a910)),x92284),x92283))) % 177.41/177.19 [9243]~P1(f327(f327(f234(f922(x92431,a910)),x92435),x92433))+~P1(f327(f327(f234(f922(x92431,a910)),x92432),x92434))+P1(f327(f327(f234(f922(x92431,a910)),f327(f327(f23(f922(x92431,a910)),x92432),x92433)),f327(f327(f23(f922(x92431,a910)),x92434),x92435))) % 177.41/177.19 [9244]~P1(f327(f327(f234(f922(x92441,a910)),x92443),x92445))+~P1(f327(f327(f234(f922(x92441,a910)),x92442),x92444))+P1(f327(f327(f234(f922(x92441,a910)),f327(f327(f102(f922(x92441,a910)),x92442),x92443)),f327(f327(f102(f922(x92441,a910)),x92444),x92445))) % 177.41/177.19 [9245]~P1(f327(f327(f234(f922(x92451,a910)),x92453),x92455))+~P1(f327(f327(f234(f922(x92451,a910)),x92452),x92454))+P1(f327(f327(f234(f922(x92451,a910)),f327(f327(f103(f922(x92451,a910)),x92452),x92453)),f327(f327(f103(f922(x92451,a910)),x92454),x92455))) % 177.41/177.19 [9339]P1(f327(f327(f329(f921(x93391,x93391)),f327(f327(f252(x93391,x93391),x93392),x93393)),f321(x93391,x93394,x93395)))+~P1(f327(f327(f234(a915),f327(x93394,x93392)),f327(x93394,x93393)))+~P1(f327(f327(f329(f921(x93391,x93391)),f327(f327(f252(x93391,x93391),x93392),x93393)),x93395)) % 177.41/177.19 [9523]P1(f327(f327(f329(f921(x95231,x95231)),f327(f327(f252(x95231,x95231),x95232),x95233)),f307(x95231,x95234)))+~P1(f327(f327(f329(f921(x95231,x95231)),f327(f327(f252(x95231,x95231),x95232),x95235)),f307(x95231,x95234)))+~P1(f327(f327(f329(f921(x95231,x95231)),f327(f327(f252(x95231,x95231),x95235),x95233)),x95234)) % 177.41/177.19 [9524]P1(f327(f327(f329(f921(x95241,x95241)),f327(f327(f252(x95241,x95241),x95242),x95243)),f307(x95241,x95244)))+~P1(f327(f327(f329(f921(x95241,x95241)),f327(f327(f252(x95241,x95241),x95245),x95243)),f307(x95241,x95244)))+~P1(f327(f327(f329(f921(x95241,x95241)),f327(f327(f252(x95241,x95241),x95242),x95245)),x95244)) % 177.41/177.19 [9624]E(x96241,x96242)+E(f327(a113,f612(x96243,x96244,x96241,x96242,x96245)),x96244)+~P1(f327(f327(f329(f921(x96245,x96245)),f327(f327(f252(x96245,x96245),x96242),x96241)),f327(f327(f184(f921(x96245,x96245),a910),x96244),x96243))) % 177.41/177.19 [9625]E(x96251,x96252)+E(f327(a113,f615(x96253,x96254,x96251,x96252,x96255)),x96254)+~P1(f327(f327(f329(f921(x96255,x96255)),f327(f327(f252(x96255,x96255),x96252),x96251)),f327(f327(f184(f921(x96255,x96255),a910),x96254),x96253))) % 177.41/177.19 [9626]E(x96261,f2(a915))+E(f327(a113,f612(x96262,x96261,x96263,x96264,x96265)),x96261)+~P1(f327(f327(f329(f921(x96265,x96265)),f327(f327(f252(x96265,x96265),x96264),x96263)),f327(f327(f184(f921(x96265,x96265),a910),x96261),x96262))) % 177.41/177.19 [9627]E(x96271,f2(a915))+E(f327(a113,f615(x96272,x96271,x96273,x96274,x96275)),x96271)+~P1(f327(f327(f329(f921(x96275,x96275)),f327(f327(f252(x96275,x96275),x96274),x96273)),f327(f327(f184(f921(x96275,x96275),a910),x96271),x96272))) % 177.41/177.19 [9648]P1(f327(f327(f329(f921(x96481,x96481)),f327(f327(f252(x96481,x96481),x96482),x96483)),f327(f327(f289(x96481,x96481,x96481),x96484),f307(x96481,x96484))))+~P1(f327(f327(f329(f921(x96481,x96481)),f327(f327(f252(x96481,x96481),x96482),x96485)),x96484))+~P1(f327(f327(f329(f921(x96481,x96481)),f327(f327(f252(x96481,x96481),x96485),x96483)),x96484)) % 177.41/177.19 [9655]~P1(f327(f327(f329(f921(x96551,x96551)),f327(f327(f252(x96551,x96551),x96552),x96555)),f307(x96551,x96554)))+P1(f327(f327(f329(f921(x96551,x96551)),f327(f327(f252(x96551,x96551),x96552),x96553)),f327(f327(f289(x96551,x96551,x96551),x96554),f307(x96551,x96554))))+~P1(f327(f327(f329(f921(x96551,x96551)),f327(f327(f252(x96551,x96551),x96555),x96553)),x96554)) % 177.41/177.19 [9690]~P6(x96901,x96905,x96902)+~P1(f327(f327(f329(f921(x96901,x96901)),f327(f327(f252(x96901,x96901),x96903),x96904)),x96902))+P1(f327(f327(f234(f922(x96901,a910)),f327(f285(x96901,x96901,x96902),f327(f327(f309(x96901),x96903),f190(f922(x96901,a910))))),f327(f285(x96901,x96901,x96902),f327(f327(f309(x96901),x96904),f190(f922(x96901,a910)))))) % 177.41/177.19 [9749]P1(f327(f327(f329(f921(x97491,x97491)),f327(f327(f252(x97491,x97491),x97492),x97493)),f327(f327(f289(x97491,x97491,x97491),x97494),f307(x97491,x97494))))+~P1(f327(f327(f329(f921(x97491,x97491)),f327(f327(f252(x97491,x97491),x97492),x97495)),f327(f327(f289(x97491,x97491,x97491),x97494),f307(x97491,x97494))))+~P1(f327(f327(f329(f921(x97491,x97491)),f327(f327(f252(x97491,x97491),x97495),x97493)),x97494)) % 177.41/177.19 [9750]P1(f327(f327(f329(f921(x97501,x97501)),f327(f327(f252(x97501,x97501),x97502),x97503)),f327(f327(f289(x97501,x97501,x97501),x97504),f307(x97501,x97504))))+~P1(f327(f327(f329(f921(x97501,x97501)),f327(f327(f252(x97501,x97501),x97505),x97503)),f327(f327(f289(x97501,x97501,x97501),x97504),f307(x97501,x97504))))+~P1(f327(f327(f329(f921(x97501,x97501)),f327(f327(f252(x97501,x97501),x97502),x97505)),x97504)) % 177.41/177.19 [9800]~P1(f327(f66(x98001,x98001,x98004,x98002,x98003),x98005))+P1(f327(f327(f329(x98001),x98002),x98003))+P1(f327(f62(x98001,x98004,f327(f327(f309(x98001),x98002),x98003)),x98005)) % 177.41/177.19 [9838]~E(f327(f310(x98383,x98382,x98385),x98384),x98381)+E(x98381,f190(f922(x98382,a910)))+P1(f327(f327(f234(f922(x98383,a910)),f327(f310(x98382,x98383,f500(x98384,x98383,x98382,x98381)),x98381)),x98384)) % 177.41/177.19 [9885]~P3(x98855)+P1(f327(f327(f329(x98851),f345(x98852,x98853,x98854,x98851,x98855)),x98854))+P1(f327(f327(f234(x98855),f327(f327(f40(x98851,x98855),x98854),x98853)),x98852)) % 177.41/177.19 [9941]P32(x99411,x99412,x99413,x99414,x99415)+~E(f327(f191(f916(x99411)),x99414),f327(f191(f916(x99412)),x99415))+P1(f327(f327(f329(f921(x99411,x99412)),f695(x99415,x99414,x99413,x99412,x99411)),f327(f173(f921(x99411,x99412)),f327(f327(f182(x99411,x99412),x99414),x99415)))) % 177.41/177.19 [9942]P32(x99421,x99422,x99423,x99424,x99425)+~E(f327(f191(f916(x99421)),x99424),f327(f191(f916(x99422)),x99425))+P1(f327(f327(f329(f921(x99421,x99422)),f696(x99423,x99425,x99424,x99422,x99421)),f327(f173(f921(x99421,x99422)),f327(f327(f182(x99421,x99422),x99424),x99425)))) % 177.41/177.19 [10069]E(x100691,x100692)+P1(f327(f327(f329(f921(x100693,x100693)),f327(f327(f252(x100693,x100693),x100691),f613(x100694,x100695,x100692,x100691,x100693))),x100694))+~P1(f327(f327(f329(f921(x100693,x100693)),f327(f327(f252(x100693,x100693),x100691),x100692)),f327(f327(f184(f921(x100693,x100693),a910),x100695),x100694))) % 177.41/177.19 [10070]E(x100701,f2(a915))+P1(f327(f327(f329(f921(x100702,x100702)),f327(f327(f252(x100702,x100702),x100703),f613(x100704,x100701,x100705,x100703,x100702))),x100704))+~P1(f327(f327(f329(f921(x100702,x100702)),f327(f327(f252(x100702,x100702),x100703),x100705)),f327(f327(f184(f921(x100702,x100702),a910),x100701),x100704))) % 177.41/177.19 [10110]~P3(x101101)+~P1(f327(f327(f234(x101101),f327(x101104,f345(x101105,x101104,x101103,x101102,x101101))),x101105))+P1(f327(f327(f234(x101101),f327(f327(f40(x101102,x101101),x101103),x101104)),x101105)) % 177.41/177.19 [10162]E(x101621,x101622)+P1(f327(f327(f329(f921(x101623,x101623)),f327(f327(f252(x101623,x101623),f616(x101624,x101625,x101621,x101622,x101623)),x101621)),x101624))+~P1(f327(f327(f329(f921(x101623,x101623)),f327(f327(f252(x101623,x101623),x101622),x101621)),f327(f327(f184(f921(x101623,x101623),a910),x101625),x101624))) % 177.41/177.19 [10163]E(x101631,f2(a915))+P1(f327(f327(f329(f921(x101632,x101632)),f327(f327(f252(x101632,x101632),f616(x101633,x101631,x101634,x101635,x101632)),x101634)),x101633))+~P1(f327(f327(f329(f921(x101632,x101632)),f327(f327(f252(x101632,x101632),x101635),x101634)),f327(f327(f184(f921(x101632,x101632),a910),x101631),x101633))) % 177.41/177.19 [10167]E(x101671,x101672)+P1(f327(f327(f329(f921(x101673,x101673)),f327(f327(f252(x101673,x101673),x101671),f616(x101674,x101675,x101672,x101671,x101673))),f327(f327(f184(f921(x101673,x101673),a910),f615(x101674,x101675,x101672,x101671,x101673)),x101674)))+~P1(f327(f327(f329(f921(x101673,x101673)),f327(f327(f252(x101673,x101673),x101671),x101672)),f327(f327(f184(f921(x101673,x101673),a910),x101675),x101674))) % 177.41/177.19 [10168]E(x101681,f2(a915))+P1(f327(f327(f329(f921(x101682,x101682)),f327(f327(f252(x101682,x101682),x101683),f616(x101684,x101681,x101685,x101683,x101682))),f327(f327(f184(f921(x101682,x101682),a910),f615(x101684,x101681,x101685,x101683,x101682)),x101684)))+~P1(f327(f327(f329(f921(x101682,x101682)),f327(f327(f252(x101682,x101682),x101683),x101685)),f327(f327(f184(f921(x101682,x101682),a910),x101681),x101684))) % 177.41/177.19 [10221]E(x102211,x102212)+P1(f327(f327(f329(f921(x102213,x102213)),f327(f327(f252(x102213,x102213),f613(x102214,x102215,x102211,x102212,x102213)),x102211)),f327(f327(f184(f921(x102213,x102213),a910),f612(x102214,x102215,x102211,x102212,x102213)),x102214)))+~P1(f327(f327(f329(f921(x102213,x102213)),f327(f327(f252(x102213,x102213),x102212),x102211)),f327(f327(f184(f921(x102213,x102213),a910),x102215),x102214))) % 177.41/177.19 [10222]E(x102221,f2(a915))+P1(f327(f327(f329(f921(x102222,x102222)),f327(f327(f252(x102222,x102222),f613(x102223,x102221,x102224,x102225,x102222)),x102224)),f327(f327(f184(f921(x102222,x102222),a910),f612(x102223,x102221,x102224,x102225,x102222)),x102223)))+~P1(f327(f327(f329(f921(x102222,x102222)),f327(f327(f252(x102222,x102222),x102225),x102224)),f327(f327(f184(f921(x102222,x102222),a910),x102221),x102223))) % 177.41/177.19 [10257]~P68(x102572)+~P1(f327(f35(x102571),x102575))+E(f327(f327(f6(x102571,x102572),f327(f327(f7(x102571,x102572,x102572),f327(f327(f18(x102571,x102572,f922(x102572,x102572)),f327(f327(f8(a910,f922(x102572,f922(x102572,x102572)),x102571),f97(x102572)),f327(f327(f7(x102571,f922(x102571,a910),a910),f329(x102571)),x102573))),x102574)),f2(x102572))),x102575),f327(f327(f6(x102571,x102572),x102574),f327(f327(f103(f922(x102571,a910)),x102575),x102573))) % 177.41/177.19 [8814]~P68(x88141)+~P1(f327(f35(x88144),x88145))+E(f327(f327(f80(x88141),f327(x88142,x88143)),f327(f327(f6(x88144,x88141),x88142),f327(f327(f23(f922(x88144,a910)),x88145),f327(f327(f309(x88144),x88143),f190(f922(x88144,a910)))))),f327(f327(f6(x88144,x88141),x88142),f327(f327(f309(x88144),x88143),x88145))) % 177.41/177.19 [8815]~P75(x88151)+~P1(f327(f35(x88154),x88155))+E(f327(f327(f81(x88151),f327(x88152,x88153)),f327(f327(f9(x88154,x88151),x88152),f327(f327(f23(f922(x88154,a910)),x88155),f327(f327(f309(x88154),x88153),f190(f922(x88154,a910)))))),f327(f327(f9(x88154,x88151),x88152),f327(f327(f309(x88154),x88153),x88155))) % 177.41/177.19 [9151]~P108(x91512)+~P11(x91512,f327(f169(x91512),f327(f327(f155(x91511,x91512),x91514),x91515)))+E(f327(f137(x91511,f327(f327(f8(x91512,a910,x91511),f327(f235(x91512),x91513)),x91514)),x91515),f178(x91511,f327(f327(f8(x91512,a910,x91511),f327(f235(x91512),x91513)),x91514),x91515)) % 177.41/177.19 [9175]~P68(x91751)+E(f327(f327(f80(x91751),f327(f327(f6(a915,x91751),x91752),f303(a915,x91753,x91754))),f327(f327(f6(a915,x91751),x91752),f303(a915,f327(f327(f80(a915),x91754),f78(a915)),f327(f327(f80(a915),x91754),x91755)))),f327(f327(f6(a915,x91751),x91752),f303(a915,x91753,f327(f327(f80(a915),x91754),x91755))))+~P1(f327(f327(f234(a915),x91753),f327(f327(f80(a915),x91754),f78(a915)))) % 177.41/177.19 [9176]~P1(f327(f327(f329(x91761),x91764),x91765))+~P1(f327(f327(f234(f922(x91761,a910)),f327(f173(x91761),x91762)),x91765))+P1(f327(f327(f234(f922(x91761,a910)),f327(f173(x91761),f327(f327(f160(x91761,x91762),x91763),x91764))),x91765)) % 177.41/177.19 [9399]~P3(x93992)+~P1(f327(f35(x93991),x93995))+E(f327(f327(f64(x93991,x93992,f327(f327(f8(x93992,f922(x93992,x93992),x93991),f102(x93992)),x93993)),x93994),x93995),f327(f327(f102(x93992),x93994),f327(f327(f40(x93991,x93992),x93995),x93993))) % 177.41/177.19 [9400]~P3(x94002)+~P1(f327(f35(x94001),x94005))+E(f327(f327(f64(x94001,x94002,f327(f327(f8(x94002,f922(x94002,x94002),x94001),f103(x94002)),x94003)),x94004),x94005),f327(f327(f103(x94002),x94004),f327(f327(f41(x94001,x94002),x94005),x94003))) % 177.41/177.19 [9448]E(f327(x94481,x94482),f327(x94481,x94483))+P1(f327(f327(f235(a915),f327(x94481,x94482)),f327(x94481,x94483)))+~P1(f327(f327(f329(f921(x94484,x94484)),f327(f327(f252(x94484,x94484),x94482),x94483)),f154(x94484,f327(f327(f152(f922(x94484,a915)),x94481),x94485)))) % 177.41/177.19 [9481]~E(f327(x94814,x94812),f327(x94814,x94813))+~P1(f327(f327(f329(f921(x94811,x94811)),f327(f327(f252(x94811,x94811),x94812),x94813)),f154(x94811,x94815)))+P1(f327(f327(f329(f921(x94811,x94811)),f327(f327(f252(x94811,x94811),x94812),x94813)),f154(x94811,f327(f327(f152(f922(x94811,a915)),x94814),x94815)))) % 177.41/177.19 [9501]~P23(x95011,x95012,x95013,x95015)+P23(x95011,x95012,x95013,f327(f327(f309(x95011),x95014),x95015))+P1(f327(f327(f329(x95012),f327(x95013,x95014)),f327(f310(x95011,x95012,x95013),f327(f327(f23(f922(x95011,a910)),x95015),f327(f327(f309(x95011),x95014),f190(f922(x95011,a910))))))) % 177.41/177.19 [9504]P1(f327(x95042,x95045))+~P1(f327(f327(f329(x95041),x95045),f327(f173(x95041),x95043)))+E(f327(f327(f139(x95041),f327(f191(f916(x95041)),f178(x95041,x95042,f327(f327(f135(x95041),x95043),x95044)))),f327(f327(f135(x95041),x95043),x95044)),f327(f327(f135(x95041),f327(f327(f139(x95041),f327(f191(f916(x95041)),f178(x95041,x95042,x95043))),x95043)),x95044)) % 177.41/177.19 [9509]~P1(f327(f327(f329(f921(x95091,x95091)),f327(f327(f252(x95091,x95091),x95092),x95093)),f154(x95091,x95095)))+~P1(f327(f327(f234(a915),f327(x95094,x95092)),f327(x95094,x95093)))+P1(f327(f327(f329(f921(x95091,x95091)),f327(f327(f252(x95091,x95091),x95092),x95093)),f154(x95091,f327(f327(f152(f922(x95091,a915)),x95094),x95095)))) % 177.41/177.19 [9576]P1(f327(f327(f329(f921(x95764,x95764)),f327(f327(f252(x95764,x95764),x95762),x95763)),f154(x95764,x95765)))+P1(f327(f327(f235(a915),f327(x95761,x95762)),f327(x95761,x95763)))+~P1(f327(f327(f329(f921(x95764,x95764)),f327(f327(f252(x95764,x95764),x95762),x95763)),f154(x95764,f327(f327(f152(f922(x95764,a915)),x95761),x95765)))) % 177.41/177.19 [9721]~P1(f327(f327(f329(f921(f916(x97211),f916(x97211))),f327(f327(f252(f916(x97211),f916(x97211)),x97212),x97214)),f159(x97211,x97215)))+~P1(f327(f327(f235(a915),x97213),f327(f191(f916(x97211)),x97212)))+P1(f327(f327(f329(f921(x97211,x97211)),f327(f327(f252(x97211,x97211),f327(f327(f165(x97211),x97212),x97213)),f327(f327(f165(x97211),x97214),x97213))),x97215)) % 177.41/177.19 [9964]E(x99641,f2(a1))+~P1(f327(f50(x99643,x99641),f327(f327(f252(a1,a1),x99644),x99645)))+P1(f327(f50(f327(f327(f81(a1),x99642),x99643),x99641),f327(f327(f252(a1,a1),f327(f327(f80(a1),f327(f327(f81(a1),x99642),x99644)),f327(f327(f37(a1),f327(f327(f81(a1),x99642),x99645)),x99641))),f46(a1,f327(f327(f81(a1),x99642),x99645),x99641)))) % 177.41/177.19 [9965]~P1(f327(f327(f235(a915),f2(a915)),x99653))+~P1(f327(f49(x99652,x99653),f327(f327(f252(a915,a915),x99654),x99655)))+P1(f327(f49(f327(f327(f81(a915),x99651),x99652),x99653),f327(f327(f252(a915,a915),f327(f327(f80(a915),f327(f327(f81(a915),x99651),x99654)),f327(f327(f37(a915),f327(f327(f81(a915),x99651),x99655)),x99653))),f46(a915,f327(f327(f81(a915),x99651),x99655),x99653)))) % 177.41/177.19 [10280]~P68(x102802)+~P1(f327(f35(x102801),x102804))+E(f327(f327(f6(x102801,x102802),x102803),f327(f262(x102801),f327(f327(f18(x102801,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102801),a325),f327(f327(f7(x102801,f922(x102801,a910),a910),f329(x102801)),x102804))),f327(f327(f7(x102801,f922(x102801,a910),a910),f329(x102801)),x102805)))),f327(f327(f6(x102801,x102802),f327(f327(f7(x102801,x102802,x102802),f327(f327(f18(x102801,x102802,f922(x102802,x102802)),f327(f327(f8(a910,f922(x102802,f922(x102802,x102802)),x102801),f97(x102802)),f327(f327(f7(x102801,f922(x102801,a910),a910),f329(x102801)),x102805))),x102803)),f2(x102802))),x102804)) % 177.41/177.19 [8445]~E(f327(f327(f135(x84451),x84452),x84455),f327(f327(f135(x84451),x84453),x84454))+E(f327(f327(f135(x84451),f327(f327(f139(x84451),f327(f191(f916(x84451)),x84452)),x84453)),x84454),x84455)+P1(f327(f327(f234(a915),f327(f191(f916(x84451)),x84453)),f327(f191(f916(x84451)),x84452))) % 177.41/177.19 [8641]~E(f327(f327(f135(x86412),x86413),x86411),f327(f327(f135(x86412),x86414),x86415))+E(x86411,f327(f327(f135(x86412),f327(f327(f139(x86412),f327(f191(f916(x86412)),x86413)),x86414)),x86415))+~P1(f327(f327(f234(a915),f327(f191(f916(x86412)),x86413)),f327(f191(f916(x86412)),x86414))) % 177.41/177.19 [8729]~E(f327(f327(f80(a915),f327(f327(f81(a915),x87293),x87294)),x87291),f327(f327(f80(a915),f327(f327(f81(a915),x87292),x87294)),x87295))+~P1(f327(f327(f234(a915),x87293),x87292))+E(x87291,f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x87292),x87293)),x87294)),x87295)) % 177.41/177.19 [8730]~E(f327(f327(f80(a915),f327(f327(f81(a915),x87301),x87303)),x87304),f327(f327(f80(a915),f327(f327(f81(a915),x87302),x87303)),x87305))+~P1(f327(f327(f234(a915),x87302),x87301))+E(f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x87301),x87302)),x87303)),x87304),x87305) % 177.41/177.19 [8898]E(f327(f327(f80(a915),f327(f327(f81(a915),x88981),x88982)),x88983),f327(f327(f80(a915),f327(f327(f81(a915),x88984),x88982)),x88985))+~P1(f327(f327(f234(a915),x88984),x88981))+~E(x88985,f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x88981),x88984)),x88982)),x88983)) % 177.41/177.19 [8899]E(f327(f327(f80(a915),f327(f327(f81(a915),x88991),x88992)),x88993),f327(f327(f80(a915),f327(f327(f81(a915),x88994),x88992)),x88995))+~P1(f327(f327(f234(a915),x88994),x88991))+~E(f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x88991),x88994)),x88992)),x88993),x88995) % 177.41/177.19 [9775]~P61(x97752)+~P1(f327(f35(x97751),x97755))+E(f327(f327(f9(x97751,x97752),f327(f327(f18(x97751,x97752,x97752),f327(f327(f8(x97752,f922(x97752,x97752),x97751),f291(x97752)),x97753)),x97754)),x97755),f327(f327(f291(x97752),f327(f327(f9(x97751,x97752),x97753),x97755)),f327(f327(f9(x97751,x97752),x97754),x97755))) % 177.41/177.19 [9905]~E(f619(x99055,x99054,x99053,x99052,x99051),f620(x99055,x99054,x99053,x99052,x99051))+P1(f327(f327(f329(f921(x99051,x99051)),f327(f327(f252(x99051,x99051),x99052),x99053)),f307(x99051,x99054)))+~P1(f327(f327(f329(f921(x99051,x99051)),f327(f327(f252(x99051,x99051),x99052),x99053)),f307(x99051,f327(f327(f102(f922(f921(x99051,x99051),a910)),x99054),x99055)))) % 177.41/177.19 [9906]~E(f621(x99065,x99064,x99063,x99062,x99061),f622(x99065,x99064,x99063,x99062,x99061))+P1(f327(f327(f329(f921(x99061,x99061)),f327(f327(f252(x99061,x99061),x99062),x99063)),f307(x99061,x99064)))+~P1(f327(f327(f329(f921(x99061,x99061)),f327(f327(f252(x99061,x99061),x99062),x99063)),f307(x99061,f327(f327(f102(f922(f921(x99061,x99061),a910)),x99064),x99065)))) % 177.41/177.19 [10100]P1(f327(f327(f329(f921(x101001,x101001)),f327(f327(f252(x101001,x101001),x101002),f622(x101005,x101004,x101003,x101002,x101001))),f307(x101001,x101004)))+P1(f327(f327(f329(f921(x101001,x101001)),f327(f327(f252(x101001,x101001),x101002),x101003)),f307(x101001,x101004)))+~P1(f327(f327(f329(f921(x101001,x101001)),f327(f327(f252(x101001,x101001),x101002),x101003)),f307(x101001,f327(f327(f102(f922(f921(x101001,x101001),a910)),x101004),x101005)))) % 177.41/177.19 [10189]P1(f327(f327(f329(f921(x101891,x101891)),f327(f327(f252(x101891,x101891),f620(x101895,x101894,x101893,x101892,x101891)),x101893)),f307(x101891,x101894)))+P1(f327(f327(f329(f921(x101891,x101891)),f327(f327(f252(x101891,x101891),x101892),x101893)),f307(x101891,x101894)))+~P1(f327(f327(f329(f921(x101891,x101891)),f327(f327(f252(x101891,x101891),x101892),x101893)),f307(x101891,f327(f327(f102(f922(f921(x101891,x101891),a910)),x101894),x101895)))) % 177.41/177.19 [10228]P1(f327(f327(f329(f921(x102281,x102281)),f327(f327(f252(x102281,x102281),x102282),x102283)),f307(x102281,x102284)))+P1(f327(f327(f329(f921(x102281,x102281)),f327(f327(f252(x102281,x102281),f619(x102285,x102284,x102283,x102282,x102281)),f620(x102285,x102284,x102283,x102282,x102281))),x102285))+~P1(f327(f327(f329(f921(x102281,x102281)),f327(f327(f252(x102281,x102281),x102282),x102283)),f307(x102281,f327(f327(f102(f922(f921(x102281,x102281),a910)),x102284),x102285)))) % 177.41/177.19 [10229]P1(f327(f327(f329(f921(x102291,x102291)),f327(f327(f252(x102291,x102291),x102292),x102293)),f307(x102291,x102294)))+P1(f327(f327(f329(f921(x102291,x102291)),f327(f327(f252(x102291,x102291),f622(x102295,x102294,x102293,x102292,x102291)),f621(x102295,x102294,x102293,x102292,x102291))),x102295))+~P1(f327(f327(f329(f921(x102291,x102291)),f327(f327(f252(x102291,x102291),x102292),x102293)),f307(x102291,f327(f327(f102(f922(f921(x102291,x102291),a910)),x102294),x102295)))) % 177.41/177.19 [10375]~P1(f327(f327(f329(f921(f916(x103751),f916(x103751))),f327(f327(f252(f916(x103751),f916(x103751)),x103754),x103755)),f159(x103751,x103752)))+~P1(f327(f327(f329(f921(x103751,x103751)),x103753),f327(f173(f921(x103751,x103751)),f327(f327(f182(x103751,x103751),x103754),x103755))))+P1(f327(f327(f257(x103751,x103751,a910),f327(f327(f7(x103751,f922(f921(x103751,x103751),a910),f922(x103751,a910)),f327(f327(f8(f922(x103751,f922(f922(f921(x103751,x103751),a910),a910)),f922(f922(f921(x103751,x103751),a910),f922(x103751,a910)),x103751),f7(x103751,f922(f921(x103751,x103751),a910),a910)),f327(f327(f8(f922(x103751,f921(x103751,x103751)),f922(x103751,f922(f922(f921(x103751,x103751),a910),a910)),x103751),f327(f8(f921(x103751,x103751),f922(f922(f921(x103751,x103751),a910),a910),x103751),f329(f921(x103751,x103751)))),f252(x103751,x103751)))),x103752)),x103753)) % 177.41/177.19 [9804]~P1(f327(f327(f234(a915),x98043),x98042))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),f327(f327(f81(a915),x98043),x98044)),x98041)),f327(f327(f80(a915),f327(f327(f81(a915),x98042),x98044)),x98045)))+P1(f327(f327(f234(a915),x98041),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x98042),x98043)),x98044)),x98045))) % 177.41/177.19 [9805]~P1(f327(f327(f234(a915),x98053),x98052))+~P1(f327(f327(f235(a915),f327(f327(f80(a915),f327(f327(f81(a915),x98053),x98054)),x98051)),f327(f327(f80(a915),f327(f327(f81(a915),x98052),x98054)),x98055)))+P1(f327(f327(f235(a915),x98051),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x98052),x98053)),x98054)),x98055))) % 177.41/177.19 [9822]~P1(f327(f327(f234(a915),x98221),x98224))+P1(f327(f327(f234(a915),f327(f327(f80(a915),f327(f327(f81(a915),x98221),x98222)),x98223)),f327(f327(f80(a915),f327(f327(f81(a915),x98224),x98222)),x98225)))+~P1(f327(f327(f234(a915),x98223),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x98224),x98221)),x98222)),x98225))) % 177.41/177.19 [9823]~P1(f327(f327(f234(a915),x98231),x98234))+P1(f327(f327(f235(a915),f327(f327(f80(a915),f327(f327(f81(a915),x98231),x98232)),x98233)),f327(f327(f80(a915),f327(f327(f81(a915),x98234),x98232)),x98235)))+~P1(f327(f327(f235(a915),x98233),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x98234),x98231)),x98232)),x98235))) % 177.41/177.19 [9939]~P1(f327(f327(f234(a915),x99392),x99391))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),f327(f327(f81(a915),x99391),x99393)),x99394)),f327(f327(f80(a915),f327(f327(f81(a915),x99392),x99393)),x99395)))+P1(f327(f327(f234(a915),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x99391),x99392)),x99393)),x99394)),x99395)) % 177.41/177.19 [9940]~P1(f327(f327(f234(a915),x99402),x99401))+~P1(f327(f327(f235(a915),f327(f327(f80(a915),f327(f327(f81(a915),x99401),x99403)),x99404)),f327(f327(f80(a915),f327(f327(f81(a915),x99402),x99403)),x99405)))+P1(f327(f327(f235(a915),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x99401),x99402)),x99403)),x99404)),x99405)) % 177.41/177.19 [9983]~P1(f327(f327(f234(a915),x99834),x99831))+P1(f327(f327(f234(a915),f327(f327(f80(a915),f327(f327(f81(a915),x99831),x99832)),x99833)),f327(f327(f80(a915),f327(f327(f81(a915),x99834),x99832)),x99835)))+~P1(f327(f327(f234(a915),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x99831),x99834)),x99832)),x99833)),x99835)) % 177.41/177.19 [9984]~P1(f327(f327(f234(a915),x99844),x99841))+P1(f327(f327(f235(a915),f327(f327(f80(a915),f327(f327(f81(a915),x99841),x99842)),x99843)),f327(f327(f80(a915),f327(f327(f81(a915),x99844),x99842)),x99845)))+~P1(f327(f327(f235(a915),f327(f327(f80(a915),f327(f327(f81(a915),f327(f327(f23(a915),x99841),x99844)),x99842)),x99843)),x99845)) % 177.41/177.19 [10216]~P9(x102161,x102162,x102165,x102163)+~P1(f327(f327(f329(f921(x102161,x102161)),x102164),x102165))+P1(f327(f327(f257(x102161,x102161,a910),f327(f327(f7(x102161,f922(x102161,x102162),f922(x102161,a910)),f327(f327(f8(f922(x102162,a910),f922(f922(x102161,x102162),f922(x102161,a910)),x102161),f8(x102162,a910,x102161)),f327(f327(f8(x102162,f922(x102162,a910),x102161),a324),x102163))),x102163)),x102164)) % 177.41/177.19 [8605]~P17(x86056,x86051,x86052,x86054)+E(f327(f72(x86051,x86051,x86051,f327(x86052,x86053)),f327(x86054,x86055)),f327(f72(x86051,x86051,x86051,f327(x86054,x86055)),f327(x86052,x86053)))+~P1(f327(f35(x86056),x86055)) % 177.41/177.19 [9042]~P23(x90421,x90423,x90425,x90426)+~P23(x90423,x90422,x90424,f327(f310(x90421,x90423,x90425),x90426))+P23(x90421,x90422,f327(f72(x90423,x90422,x90421,x90424),x90425),x90426) % 177.41/177.19 [9608]~P1(f327(f327(x96084,x96082),x96086))+~P1(f327(f327(x96083,x96085),x96082))+P1(f327(f327(f329(x96081),x96082),f297(x96081,x96083,x96084,x96085,x96086))) % 177.41/177.19 [9609]~P1(f327(f327(x96093,x96092),x96096))+~P1(f327(f327(x96094,x96095),x96092))+P1(f327(f327(f329(x96091),x96092),f300(x96091,x96093,x96094,x96095,x96096))) % 177.41/177.19 [9722]E(x97221,x97222)+E(x97223,x97224)+~P1(f327(f327(f329(f921(f916(x97225),f916(x97225))),f327(f327(f252(f916(x97225),f916(x97225)),f327(f327(f152(x97225),x97223),x97221)),f327(f327(f152(x97225),x97224),x97222))),f158(x97225,x97226))) % 177.41/177.19 [9731]~E(x97312,x97314)+P1(f327(f327(f329(f921(f916(x97311),f916(x97311))),f327(f327(f252(f916(x97311),f916(x97311)),f327(f327(f152(x97311),x97312),x97313)),f327(f327(f152(x97311),x97314),x97315))),f146(x97311,x97316)))+~P1(f327(f327(f329(f921(f916(x97311),f916(x97311))),f327(f327(f252(f916(x97311),f916(x97311)),x97313),x97315)),f146(x97311,x97316))) % 177.41/177.19 [9732]~E(x97322,x97324)+P1(f327(f327(f329(f921(f916(x97321),f916(x97321))),f327(f327(f252(f916(x97321),f916(x97321)),f327(f327(f152(x97321),x97322),x97323)),f327(f327(f152(x97321),x97324),x97325))),f148(x97321,x97326)))+~P1(f327(f327(f329(f921(f916(x97321),f916(x97321))),f327(f327(f252(f916(x97321),f916(x97321)),x97323),x97325)),f148(x97321,x97326))) % 177.41/177.19 [9733]~E(x97332,x97334)+P1(f327(f327(f329(f921(f916(x97331),f916(x97331))),f327(f327(f252(f916(x97331),f916(x97331)),f327(f327(f152(x97331),x97332),x97333)),f327(f327(f152(x97331),x97334),x97335))),f158(x97331,x97336)))+~P1(f327(f327(f329(f921(f916(x97331),f916(x97331))),f327(f327(f252(f916(x97331),f916(x97331)),x97333),x97335)),f158(x97331,x97336))) % 177.41/177.19 [9734]~E(x97342,x97344)+P1(f327(f327(f329(f921(f916(x97341),f916(x97341))),f327(f327(f252(f916(x97341),f916(x97341)),f327(f327(f135(x97341),x97342),x97343)),f327(f327(f135(x97341),x97344),x97345))),f158(x97341,x97346)))+~P1(f327(f327(f329(f921(f916(x97341),f916(x97341))),f327(f327(f252(f916(x97341),f916(x97341)),x97343),x97345)),f158(x97341,x97346))) % 177.41/177.19 [9735]~E(x97353,x97355)+P1(f327(f327(f329(f921(f916(x97351),f916(x97351))),f327(f327(f252(f916(x97351),f916(x97351)),f327(f327(f135(x97351),x97352),x97353)),f327(f327(f135(x97351),x97354),x97355))),f158(x97351,x97356)))+~P1(f327(f327(f329(f921(f916(x97351),f916(x97351))),f327(f327(f252(f916(x97351),f916(x97351)),x97352),x97354)),f158(x97351,x97356))) % 177.41/177.19 [9792]E(x97921,x97922)+P1(f327(f327(f329(f921(f916(x97923),f916(x97923))),f327(f327(f252(f916(x97923),f916(x97923)),x97921),x97922)),f158(x97923,x97924)))+~P1(f327(f327(f329(f921(f916(x97923),f916(x97923))),f327(f327(f252(f916(x97923),f916(x97923)),f327(f327(f152(x97923),x97925),x97921)),f327(f327(f152(x97923),x97926),x97922))),f158(x97923,x97924))) % 177.41/177.19 [9943]~E(x99433,x99435)+P1(f327(f327(f329(f921(f916(x99431),f916(x99431))),f327(f327(f252(f916(x99431),f916(x99431)),f327(f327(f135(x99431),x99432),f327(f327(f152(x99431),x99433),f114(x99431)))),f327(f327(f135(x99431),x99434),f327(f327(f152(x99431),x99435),f114(x99431))))),f158(x99431,x99436)))+~P1(f327(f327(f329(f921(f916(x99431),f916(x99431))),f327(f327(f252(f916(x99431),f916(x99431)),x99432),x99434)),f158(x99431,x99436))) % 177.41/177.19 [9987]E(x99871,x99872)+E(x99873,x99874)+~P1(f327(f327(f329(f921(f916(x99875),f916(x99875))),f327(f327(f252(f916(x99875),f916(x99875)),f327(f327(f135(x99875),x99873),f327(f327(f152(x99875),x99871),f114(x99875)))),f327(f327(f135(x99875),x99874),f327(f327(f152(x99875),x99872),f114(x99875))))),f158(x99875,x99876))) % 177.41/177.19 [10014]E(x100141,x100142)+~P1(f327(f327(f329(f921(f916(x100143),f916(x100143))),f327(f327(f252(f916(x100143),f916(x100143)),f327(f327(f135(x100143),x100141),f327(f327(f152(x100143),x100145),f114(x100143)))),f327(f327(f135(x100143),x100142),f327(f327(f152(x100143),x100146),f114(x100143))))),f158(x100143,x100144)))+P1(f327(f327(f329(f921(f916(x100143),f916(x100143))),f327(f327(f252(f916(x100143),f916(x100143)),x100141),x100142)),f158(x100143,x100144))) % 177.41/177.19 [10052]~P1(f327(f327(f329(f921(f922(x100521,a910),f922(x100521,a910))),f327(f327(f252(f922(x100521,a910),f922(x100521,a910)),x100522),x100524)),f319(x100521,x100526)))+~P1(f327(f327(f329(f921(f922(x100521,a910),f922(x100521,a910))),f327(f327(f252(f922(x100521,a910),f922(x100521,a910)),x100523),x100525)),f319(x100521,x100526)))+P1(f327(f327(f329(f921(f922(x100521,a910),f922(x100521,a910))),f327(f327(f252(f922(x100521,a910),f922(x100521,a910)),f327(f327(f102(f922(x100521,a910)),x100522),x100523)),f327(f327(f102(f922(x100521,a910)),x100524),x100525))),f319(x100521,x100526))) % 177.41/177.19 [5835]~E(f327(f327(f135(x58351),x58356),x58353),x58355)+E(f327(f327(f135(x58351),x58352),x58353),f327(f327(f152(x58351),x58354),x58355))+~E(x58352,f327(f327(f152(x58351),x58354),x58356)) % 177.41/177.19 [5836]~E(f327(f327(f135(x58361),x58366),x58363),x58365)+E(f327(f327(f135(x58361),x58362),x58363),f327(f327(f135(x58361),x58364),x58365))+~E(x58362,f327(f327(f135(x58361),x58364),x58366)) % 177.41/177.19 [5838]E(f327(f327(f135(x58381),x58382),x58383),f327(f327(f152(x58381),x58384),x58385))+~E(f327(f327(f152(x58381),x58384),x58386),x58382)+~E(x58385,f327(f327(f135(x58381),x58386),x58383)) % 177.41/177.19 [5840]~E(f327(f327(f135(x58401),x58402),x58406),x58404)+E(f327(f327(f135(x58401),x58402),x58403),f327(f327(f135(x58401),x58404),x58405))+~E(x58403,f327(f327(f135(x58401),x58406),x58405)) % 177.41/177.19 [6991]E(f327(x69911,x69912),f327(x69913,x69912))+~E(f327(f327(f155(x69914,x69915),x69911),x69916),f327(f327(f155(x69914,x69915),x69913),x69916))+~P1(f327(f327(f329(x69914),x69912),f327(f173(x69914),x69916))) % 177.41/177.19 [7380]~P17(x73804,x73805,x73806,x73801)+E(f327(f327(x73801,x73802),x73803),f327(f327(f64(x73804,x73805,x73806),x73803),x73802))+~P1(f327(f35(x73804),x73802)) % 177.41/177.19 [7451]~E(x74512,f327(x74514,x74516))+~P1(f327(f327(f329(x74513),x74516),x74515))+P1(f327(f327(f329(x74511),x74512),f327(f310(x74513,x74511,x74514),x74515))) % 177.41/177.19 [7452]~E(f327(x74524,x74522),x74526)+~P1(f327(f327(f329(x74523),x74526),x74525))+P1(f327(f327(f329(x74521),x74522),f327(f311(x74521,x74523,x74524),x74525))) % 177.41/177.19 [7898]~P30(x78981,x78982,x78984,x78986)+P30(x78981,x78982,f327(f327(f152(x78981),x78983),x78984),f327(f327(f152(x78981),x78985),x78986))+~P1(f327(f327(x78982,x78983),x78985)) % 177.41/177.19 [8908]~P54(x89084,x89085,x89081,x89082,x89086)+E(f327(x89081,f327(x89082,x89083)),x89083)+~P1(f327(f327(f329(x89085),x89083),x89086)) % 177.41/177.19 [9408]~P24(x94082,x94081,x94085,x94084,x94083)+E(f327(f92(x94081,x94082,x94083,f92(x94082,x94081,x94084,x94085)),x94086),f327(x94085,x94086))+~P1(f327(f327(f329(x94082),x94086),x94084)) % 177.41/177.19 [9419]~P23(x94191,x94192,x94193,x94196)+P23(x94191,x94192,f74(x94191,x94192,x94193,x94194,x94195),x94196)+P1(f327(f327(f329(x94192),x94195),f327(f310(x94191,x94192,x94193),x94196))) % 177.41/177.19 [9724]E(x97241,x97242)+E(f327(f191(f916(x97243)),x97244),f327(f191(f916(x97243)),x97245))+~P1(f327(f327(f329(f921(f916(x97243),f916(x97243))),f327(f327(f252(f916(x97243),f916(x97243)),f327(f327(f152(x97243),x97241),x97244)),f327(f327(f152(x97243),x97242),x97245))),f146(x97243,x97246))) % 177.41/177.19 [9787]~P14(x97871,x97872,x97873)+E(f327(f327(f64(x97871,x97872,x97873),x97874),x97875),x97876)+~P1(f327(f66(x97871,x97872,x97873,x97874,x97875),x97876)) % 177.41/177.19 [9795]E(f327(f191(f916(x97951)),x97952),f327(f191(f916(x97951)),x97953))+P1(f327(f327(f329(f921(f916(x97951),f916(x97951))),f327(f327(f252(f916(x97951),f916(x97951)),x97952),x97953)),f146(x97951,x97954)))+~P1(f327(f327(f329(f921(f916(x97951),f916(x97951))),f327(f327(f252(f916(x97951),f916(x97951)),f327(f327(f152(x97951),x97955),x97952)),f327(f327(f152(x97951),x97956),x97953))),f146(x97951,x97954))) % 177.41/177.19 [9816]~P1(f327(f327(f329(f921(x98161,x98161)),f327(f327(f252(x98161,x98161),x98162),x98164)),f307(x98161,x98166)))+P1(f327(f327(f329(f921(f916(x98161),f916(x98161))),f327(f327(f252(f916(x98161),f916(x98161)),f327(f327(f152(x98161),x98162),x98163)),f327(f327(f152(x98161),x98164),x98165))),f307(f916(x98161),f158(x98161,x98166))))+~P1(f327(f327(f329(f921(f916(x98161),f916(x98161))),f327(f327(f252(f916(x98161),f916(x98161)),x98163),x98165)),f307(f916(x98161),f158(x98161,x98166)))) % 177.41/177.19 [9993]~P1(f327(x99932,x99936))+~E(f327(f137(x99931,x99932),x99933),f327(f327(f152(x99931),x99934),x99935))+~P1(f327(f327(f329(x99931),x99936),f327(f173(x99931),f741(x99935,x99934,x99933,x99932,x99931)))) % 177.41/177.19 [9994]~P1(f327(x99944,x99946))+~E(f327(f327(f152(x99941),x99942),x99943),f327(f137(x99941,x99944),x99945))+~P1(f327(f327(f329(x99941),x99946),f327(f173(x99941),f739(x99945,x99944,x99943,x99942,x99941)))) % 177.41/177.19 [10316]~P68(x103162)+E(f327(f327(f6(x103161,x103162),f327(f327(f8(f922(x103163,a910),x103162,x103161),f327(f6(x103163,x103162),x103164)),f327(f327(f8(f922(x103163,a910),f922(x103163,a910),x103161),f262(x103163)),f327(f327(f8(f922(x103163,a910),f922(x103163,a910),x103161),f327(f18(x103163,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103163),a325),f327(f327(f7(x103163,f922(x103163,a910),a910),f329(x103163)),x103165)))),f327(f7(x103163,x103161,a910),f327(f327(f8(x103161,f922(x103161,a910),x103163),a324),x103166)))))),f327(f310(x103163,x103161,x103166),x103165)),f327(f327(f6(x103163,x103162),x103164),x103165))+~P1(f327(f35(x103163),x103165)) % 177.41/177.19 [7049]~P108(x70493)+P1(f327(x70492,x70495))+E(f327(f137(x70491,x70492),f327(f327(f149(x70491,x70493,x70494),x70495),x70496)),f327(f137(x70491,x70492),x70496)) % 177.41/177.19 [7051]P1(f327(x70511,x70512))+~E(f167(x70513,x70511,x70514),f327(f327(f252(f916(x70513),f916(x70513)),x70515),x70516))+~P1(f327(f327(f329(x70513),x70512),f327(f173(x70513),x70515))) % 177.41/177.19 [7096]~P1(f327(x70962,x70966))+~E(f167(x70961,x70962,x70963),f327(f327(f252(f916(x70961),f916(x70961)),x70964),x70965))+~P1(f327(f327(f329(x70961),x70966),f327(f173(x70961),x70965))) % 177.41/177.19 [7761]~P12(x77611,x77612,x77613)+~P1(f327(f35(x77611),x77616))+E(f327(f327(f64(x77611,x77612,x77613),x77614),f327(f327(f309(x77611),x77615),x77616)),f327(f327(f64(x77611,x77612,x77613),f327(f327(x77613,x77615),x77614)),x77616)) % 177.41/177.19 [7814]~P108(x78142)+~P1(f327(f327(f234(x78142),f327(x78143,x78144)),f327(x78143,x78145)))+E(f327(f327(f149(x78141,x78142,x78143),x78144),f327(f327(f152(x78141),x78145),x78146)),f327(f327(f152(x78141),x78144),f327(f327(f152(x78141),x78145),x78146))) % 177.41/177.19 [7926]E(x79261,x79262)+~E(f327(f327(f254(x79263,x79264),x79261),f327(f16(f922(x79264,a910),x79263),x79265)),f327(f327(f254(x79263,x79264),x79262),f327(f16(f922(x79264,a910),x79263),x79265)))+~P1(f327(f327(f329(x79264),x79266),x79265)) % 177.41/177.19 [7991]~P12(x79911,x79912,x79913)+~P1(f327(f35(x79911),x79916))+E(f327(f327(f64(x79911,x79912,x79913),x79914),f327(f327(f309(x79911),x79915),x79916)),f327(f327(x79913,x79915),f327(f327(f64(x79911,x79912,x79913),x79914),x79916))) % 177.41/177.19 [8109]~P14(x81091,x81092,x81093)+~P1(f327(f35(x81091),x81096))+E(f327(f327(f64(x81091,x81092,x81093),f327(f327(x81093,x81094),x81095)),x81096),f327(f327(x81093,x81094),f327(f327(f64(x81091,x81092,x81093),x81095),x81096))) % 177.41/177.19 [8177]~P18(x81772,x81775,x81776,x81771)+~P1(f327(f35(x81772),x81774))+E(f327(x81771,f327(f327(f309(x81772),x81773),x81774)),f327(f72(x81775,x81775,x81775,f327(x81771,x81774)),f327(x81776,x81773))) % 177.41/177.19 [8209]~P108(x82092)+P1(f327(f327(f234(x82092),f327(x82093,x82094)),f327(x82093,x82095)))+E(f327(f327(f149(x82091,x82092,x82093),x82094),f327(f327(f152(x82091),x82095),x82096)),f327(f327(f152(x82091),x82095),f327(f327(f149(x82091,x82092,x82093),x82094),x82096))) % 177.41/177.19 [8352]~E(f327(f191(f916(x83521)),x83525),f327(f191(f916(x83522)),x83526))+~E(f327(f191(f916(x83521)),x83523),f327(f191(f916(x83522)),x83524))+E(f327(f327(f135(f921(x83521,x83522)),f327(f327(f182(x83521,x83522),x83523),x83524)),f327(f327(f182(x83521,x83522),x83525),x83526)),f327(f327(f182(x83521,x83522),f327(f327(f135(x83521),x83523),x83525)),f327(f327(f135(x83522),x83524),x83526))) % 177.41/177.19 [8463]~E(x84632,f327(f310(x84633,x84631,x84634),x84636))+P1(f327(f327(f234(f922(x84631,a910)),x84632),f327(f310(x84633,x84631,x84634),x84635)))+~P1(f327(f327(f234(f922(x84633,a910)),x84636),x84635)) % 177.41/177.19 [8564]~P108(x85645)+E(f327(x85641,x85642),f327(x85641,x85643))+E(f327(f327(f149(x85644,x85645,x85641),x85642),f327(f327(f149(x85644,x85645,x85641),x85643),x85646)),f327(f327(f149(x85644,x85645,x85641),x85643),f327(f327(f149(x85644,x85645,x85641),x85642),x85646))) % 177.41/177.19 [8738]~P1(f327(f327(f329(x87382),x87384),f327(x87386,x87383)))+~P1(f327(f327(f329(x87381),x87383),x87385))+P1(f327(f327(f329(f921(x87381,x87382)),f327(f327(f252(x87381,x87382),x87383),x87384)),f327(f327(f254(x87381,x87382),x87385),x87386))) % 177.41/177.19 [9216]~P68(x92162)+~P23(x92164,x92161,x92165,x92166)+E(f327(f327(f6(x92161,x92162),x92163),f327(f310(x92164,x92161,x92165),x92166)),f327(f327(f6(x92164,x92162),f327(f72(x92161,x92162,x92164,x92163),x92165)),x92166)) % 177.41/177.19 [9217]~P75(x92172)+~P23(x92174,x92171,x92175,x92176)+E(f327(f327(f9(x92171,x92172),x92173),f327(f310(x92174,x92171,x92175),x92176)),f327(f327(f9(x92174,x92172),f327(f72(x92171,x92172,x92174,x92173),x92175)),x92176)) % 177.41/177.19 [9264]~P32(x92642,x92645,x92641,x92643,x92646)+P1(f327(f327(x92641,f327(f327(f165(x92642),x92643),x92644)),f327(f327(f165(x92645),x92646),x92644)))+~P1(f327(f327(f235(a915),x92644),f327(f191(f916(x92645)),x92646))) % 177.41/177.19 [9265]~P32(x92652,x92655,x92651,x92653,x92656)+P1(f327(f327(x92651,f327(f327(f165(x92652),x92653),x92654)),f327(f327(f165(x92655),x92656),x92654)))+~P1(f327(f327(f235(a915),x92654),f327(f191(f916(x92652)),x92653))) % 177.41/177.19 [9276]~E(f327(f310(x92761,x92762,x92763),x92764),x92766)+E(f327(f310(x92761,x92762,x92763),f327(f310(x92762,x92761,f92(x92761,x92762,x92764,x92763)),x92765)),x92765)+~P1(f327(f327(f234(f922(x92762,a910)),x92765),x92766)) % 177.41/177.19 [9476]~P17(x94763,x94761,x94766,x94762)+~P1(f327(f35(x94763),x94764))+E(f327(f72(x94761,x94761,x94761,f327(x94762,f327(f327(f23(f922(x94763,a910)),x94764),f327(f327(f309(x94763),x94765),f190(f922(x94763,a910)))))),f327(x94766,x94765)),f327(x94762,f327(f327(f309(x94763),x94765),x94764))) % 177.41/177.19 [10081]~E(f327(f310(x100812,x100814,x100816),f242(f922(x100812,a910))),f242(f922(x100814,a910)))+~E(f327(f310(x100811,x100813,x100815),f242(f922(x100811,a910))),f242(f922(x100813,a910)))+E(f327(f310(f921(x100811,x100812),f921(x100813,x100814),f258(x100811,x100813,x100812,x100814,x100815,x100816)),f242(f922(f921(x100811,x100812),a910))),f242(f922(f921(x100813,x100814),a910))) % 177.41/177.19 [10139]~P23(x101393,x101394,x101395,f327(x101396,f484(x101396,x101395,x101394,x101393,x101392,x101391)))+P23(x101393,x101394,x101395,f327(f327(f41(x101392,f922(x101393,a910)),x101391),x101396))+E(x101391,f190(f922(x101392,a910))) % 177.41/177.19 [10197]P23(x101976,x101975,x101974,f327(f327(f41(x101972,f922(x101976,a910)),x101971),x101973))+E(x101971,f190(f922(x101972,a910)))+P1(f327(f327(f329(x101972),f484(x101973,x101974,x101975,x101976,x101972,x101971)),x101971)) % 177.41/177.19 [10202]P1(f327(f327(f329(x102021),f592(x102022,x102023,x102024,x102025,x102026,x102021)),x102026))+P1(f327(f327(f234(f922(f921(x102021,x102024),a910)),f327(f327(f254(x102021,x102024),x102026),x102023)),f327(f327(f254(x102021,x102024),x102025),x102022)))+~P1(f327(f327(f234(f922(x102021,a910)),x102026),x102025)) % 177.41/177.19 [10242]P22(x102426,x102425,f327(f327(f309(f913(x102426)),f327(f327(f327(f91(x102426),x102421),x102423),x102422)),f190(f922(f913(x102426),a910))))+~P22(x102426,x102425,f327(f327(f309(f913(x102426)),f327(f327(f327(f91(x102426),x102424),x102423),x102422)),f190(f922(f913(x102426),a910))))+P1(f327(f327(x102421,f887(x102421,x102422,x102423,x102424,x102425,x102426)),f897(x102421,x102422,x102423,x102424,x102425,x102426))) % 177.41/177.19 [10243]P22(x102436,x102435,f327(f327(f309(f913(x102436)),f327(f327(f327(f91(x102436),x102434),x102433),x102432)),f190(f922(f913(x102436),a910))))+~P22(x102436,x102435,f327(f327(f309(f913(x102436)),f327(f327(f327(f91(x102436),x102434),x102433),x102431)),f190(f922(f913(x102436),a910))))+P1(f327(f327(x102431,f360(x102432,x102431,x102433,x102434,x102435,x102436)),f371(x102432,x102431,x102433,x102434,x102435,x102436))) % 177.41/177.19 [10285]~P22(x102851,x102852,f327(f327(f309(f913(x102851)),f327(f327(f327(f91(x102851),x102853),x102854),x102856)),f190(f922(f913(x102851),a910))))+P22(x102851,x102852,f327(f327(f309(f913(x102851)),f327(f327(f327(f91(x102851),x102853),x102854),x102855)),f190(f922(f913(x102851),a910))))+~P1(f327(f327(x102855,f360(x102855,x102856,x102854,x102853,x102852,x102851)),f371(x102855,x102856,x102854,x102853,x102852,x102851))) % 177.41/177.19 [10286]~P22(x102861,x102862,f327(f327(f309(f913(x102861)),f327(f327(f327(f91(x102861),x102866),x102864),x102865)),f190(f922(f913(x102861),a910))))+P22(x102861,x102862,f327(f327(f309(f913(x102861)),f327(f327(f327(f91(x102861),x102863),x102864),x102865)),f190(f922(f913(x102861),a910))))+~P1(f327(f327(x102866,f887(x102863,x102865,x102864,x102866,x102862,x102861)),f897(x102863,x102865,x102864,x102866,x102862,x102861))) % 177.41/177.19 [10330]~P1(f327(f327(f234(f922(x103302,a910)),f327(x103304,f592(x103306,x103304,x103302,x103305,x103303,x103301))),f327(x103306,f592(x103306,x103304,x103302,x103305,x103303,x103301))))+~P1(f327(f327(f234(f922(x103301,a910)),x103303),x103305))+P1(f327(f327(f234(f922(f921(x103301,x103302),a910)),f327(f327(f254(x103301,x103302),x103303),x103304)),f327(f327(f254(x103301,x103302),x103305),x103306))) % 177.41/177.19 [7948]~P1(f327(x79481,x79485))+~P1(f327(x79486,x79484))+P1(f327(x79481,f327(f256(x79482,x79483),f327(f327(f252(x79482,x79483),x79484),x79485)))) % 177.41/177.19 [7949]~P1(f327(x79491,x79494))+~P1(f327(x79496,x79495))+P1(f327(x79491,f327(f251(x79492,x79493),f327(f327(f252(x79492,x79493),x79494),x79495)))) % 177.41/177.19 [7996]~P1(f327(f327(x79964,x79966),x79965))+~P1(f327(f327(f329(x79961),x79966),x79963))+P1(f327(f327(f327(f40(x79961,f922(x79962,a910)),x79963),x79964),x79965)) % 177.41/177.19 [8302]~P1(f327(f327(f329(x83021),x83022),f327(x83025,x83026)))+~P1(f327(f327(f329(x83023),x83026),x83024))+P1(f327(f327(f329(x83021),x83022),f327(f327(f40(x83023,f922(x83021,a910)),x83024),x83025))) % 177.41/177.19 [8346]P1(f327(f327(x83461,x83462),x83463))+~P1(f327(f327(x83464,x83462),x83463))+~P1(f327(f327(f234(f922(x83465,f922(x83466,a910))),x83464),x83461)) % 177.41/177.19 [8486]P1(f327(f327(x84861,x84862),x84863))+~P1(f327(f327(f329(x84864),x84862),x84865))+~P1(f327(f327(f327(f41(x84864,f922(x84866,a910)),x84865),x84861),x84863)) % 177.41/177.19 [8620]P1(f327(f327(f329(x86201),x86202),f327(x86203,x86204)))+~P1(f327(f327(f329(x86205),x86204),x86206))+~P1(f327(f327(f329(x86201),x86202),f327(f327(f41(x86205,f922(x86201,a910)),x86206),x86203))) % 177.41/177.19 [8887]~P9(x88874,x88875,x88876,x88871)+E(f327(x88871,x88872),f327(x88871,x88873))+~P1(f327(f327(f329(f921(x88874,x88874)),f327(f327(f252(x88874,x88874),x88872),x88873)),x88876)) % 177.41/177.19 [8922]P1(f327(f327(f234(f922(x89221,a910)),x89222),f327(x89223,x89224)))+~P1(f327(f327(f329(x89225),x89224),x89226))+~P1(f327(f327(f234(f922(x89221,a910)),x89222),f327(f327(f41(x89225,f922(x89221,a910)),x89226),x89223))) % 177.41/177.19 [8955]~P52(x89553,x89554,f327(f286(x89554,x89553),x89555))+E(x89551,f190(f922(x89552,a910)))+E(f327(f327(f41(x89552,f922(x89553,a910)),x89551),f327(f327(f8(f922(x89554,a910),f922(x89553,a910),x89552),f285(x89554,x89553,x89555)),x89556)),f327(f285(x89554,x89553,x89555),f327(f327(f41(x89552,f922(x89554,a910)),x89551),x89556))) % 177.41/177.19 [9033]P1(f327(f327(f329(x90331),x90332),f327(f285(x90333,x90331,x90334),x90335)))+~P1(f327(f327(f329(x90333),x90336),x90335))+~P1(f327(f327(f329(f921(x90333,x90331)),f327(f327(f252(x90333,x90331),x90336),x90332)),x90334)) % 177.41/177.19 [9341]P1(f327(f327(f234(f922(x93411,a910)),f327(f285(x93412,x93411,x93413),x93414)),f327(f285(x93412,x93411,x93415),x93416)))+~P1(f327(f327(f234(f922(x93412,a910)),x93414),x93416))+~P1(f327(f327(f234(f922(f921(x93412,x93411),a910)),x93413),x93415)) % 177.41/177.19 [9525]~P1(f327(f327(f329(x95252),x95256),x95254))+~P1(f327(f327(f234(f922(x95251,a910)),x95253),x95255))+P1(f327(f327(f234(f922(f921(x95251,x95252),a910)),f327(f327(f254(x95251,x95252),x95253),f327(f16(f922(x95252,a910),x95251),x95254))),f327(f327(f254(x95251,x95252),x95255),f327(f16(f922(x95252,a910),x95251),x95254)))) % 177.41/177.19 [9537]~P32(x95371,x95372,x95373,x95375,x95376)+P1(f327(f327(f257(x95371,x95372,a910),x95373),x95374))+~P1(f327(f327(f329(f921(x95371,x95372)),x95374),f327(f173(f921(x95371,x95372)),f327(f327(f182(x95371,x95372),x95375),x95376)))) % 177.41/177.19 [9677]~E(x96773,x96775)+P1(f327(f327(f329(f921(f916(x96771),f916(x96771))),f327(f327(f252(f916(x96771),f916(x96771)),f327(f327(f152(x96771),x96772),x96773)),f327(f327(f152(x96771),x96774),x96775))),f158(x96771,x96776)))+~P1(f327(f327(f329(f921(x96771,x96771)),f327(f327(f252(x96771,x96771),x96772),x96774)),x96776)) % 177.41/177.19 [9683]~E(f327(f191(f916(x96831)),x96833),f327(f191(f916(x96831)),x96835))+P1(f327(f327(f329(f921(f916(x96831),f916(x96831))),f327(f327(f252(f916(x96831),f916(x96831)),f327(f327(f152(x96831),x96832),x96833)),f327(f327(f152(x96831),x96834),x96835))),f146(x96831,x96836)))+~P1(f327(f327(f329(f921(x96831,x96831)),f327(f327(f252(x96831,x96831),x96832),x96834)),x96836)) % 177.41/177.19 [9716]P1(f327(f327(f329(f921(x97161,x97161)),f327(f327(f252(x97161,x97161),x97162),x97163)),f327(f327(f184(f921(x97161,x97161),a910),f327(a113,x97164)),x97165)))+~P1(f327(f327(f329(f921(x97161,x97161)),f327(f327(f252(x97161,x97161),x97166),x97163)),x97165))+~P1(f327(f327(f329(f921(x97161,x97161)),f327(f327(f252(x97161,x97161),x97162),x97166)),f327(f327(f184(f921(x97161,x97161),a910),x97164),x97165))) % 177.41/177.19 [9717]P1(f327(f327(f329(f921(x97171,x97171)),f327(f327(f252(x97171,x97171),x97172),x97173)),f327(f327(f184(f921(x97171,x97171),a910),f327(a113,x97174)),x97175)))+~P1(f327(f327(f329(f921(x97171,x97171)),f327(f327(f252(x97171,x97171),x97172),x97176)),x97175))+~P1(f327(f327(f329(f921(x97171,x97171)),f327(f327(f252(x97171,x97171),x97176),x97173)),f327(f327(f184(f921(x97171,x97171),a910),x97174),x97175))) % 177.41/177.19 [9720]~P1(f327(f327(f329(x97204),x97205),x97206))+P1(f327(f327(f234(f922(x97201,a910)),x97202),x97203))+~P1(f327(f327(f234(f922(f921(x97201,x97204),a910)),f327(f327(f254(x97201,x97204),x97202),f327(f16(f922(x97204,a910),x97201),x97206))),f327(f327(f254(x97201,x97204),x97203),f327(f16(f922(x97204,a910),x97201),x97206)))) % 177.41/177.19 [9765]E(x97651,x97652)+~P1(f327(f327(f329(f921(f916(x97653),f916(x97653))),f327(f327(f252(f916(x97653),f916(x97653)),f327(f327(f152(x97653),x97651),x97655)),f327(f327(f152(x97653),x97652),x97656))),f146(x97653,x97654)))+P1(f327(f327(f329(f921(x97653,x97653)),f327(f327(f252(x97653,x97653),x97651),x97652)),x97654)) % 177.41/177.19 [9766]E(x97661,x97662)+~P1(f327(f327(f329(f921(f916(x97663),f916(x97663))),f327(f327(f252(f916(x97663),f916(x97663)),f327(f327(f152(x97663),x97661),x97665)),f327(f327(f152(x97663),x97662),x97666))),f148(x97663,x97664)))+P1(f327(f327(f329(f921(x97663,x97663)),f327(f327(f252(x97663,x97663),x97661),x97662)),x97664)) % 177.41/177.19 [9767]E(x97671,x97672)+~P1(f327(f327(f329(f921(f916(x97673),f916(x97673))),f327(f327(f252(f916(x97673),f916(x97673)),f327(f327(f152(x97673),x97671),x97675)),f327(f327(f152(x97673),x97672),x97676))),f158(x97673,x97674)))+P1(f327(f327(f329(f921(x97673,x97673)),f327(f327(f252(x97673,x97673),x97671),x97672)),x97674)) % 177.41/177.19 [9803]P1(f327(f327(f329(f921(f916(x98031),f916(x98031))),f327(f327(f252(f916(x98031),f916(x98031)),f327(f327(f152(x98031),x98032),x98033)),f327(f327(f152(x98031),x98034),x98035))),f159(x98031,x98036)))+~P1(f327(f327(f329(f921(f916(x98031),f916(x98031))),f327(f327(f252(f916(x98031),f916(x98031)),x98033),x98035)),f159(x98031,x98036)))+~P1(f327(f327(f329(f921(x98031,x98031)),f327(f327(f252(x98031,x98031),x98032),x98034)),x98036)) % 177.41/177.19 [9820]P1(f327(x98201,x98202))+~P1(f327(x98201,f902(x98201,x98203,x98204,x98205,x98206)))+~P1(f327(f327(f329(x98206),x98202),f327(f327(f40(x98205,f922(x98206,a910)),x98204),x98203))) % 177.41/177.19 [9825]~P1(f327(f327(f329(f921(f916(x98251),f916(x98251))),f327(f327(f252(f916(x98251),f916(x98251)),f327(f327(f152(x98251),x98252),x98255)),f327(f327(f152(x98251),x98253),x98256))),f146(x98251,x98254)))+P1(f327(f327(f329(f921(f916(x98251),f916(x98251))),f327(f327(f252(f916(x98251),f916(x98251)),x98255),x98256)),f146(x98251,x98254)))+P1(f327(f327(f329(f921(x98251,x98251)),f327(f327(f252(x98251,x98251),x98252),x98253)),x98254)) % 177.41/177.19 [9826]~P1(f327(f327(f329(f921(f916(x98261),f916(x98261))),f327(f327(f252(f916(x98261),f916(x98261)),f327(f327(f152(x98261),x98262),x98265)),f327(f327(f152(x98261),x98263),x98266))),f148(x98261,x98264)))+P1(f327(f327(f329(f921(f916(x98261),f916(x98261))),f327(f327(f252(f916(x98261),f916(x98261)),x98265),x98266)),f148(x98261,x98264)))+P1(f327(f327(f329(f921(x98261,x98261)),f327(f327(f252(x98261,x98261),x98262),x98263)),x98264)) % 177.41/177.19 [9827]~P1(f327(f327(f329(f921(f916(x98271),f916(x98271))),f327(f327(f252(f916(x98271),f916(x98271)),f327(f327(f152(x98271),x98272),x98275)),f327(f327(f152(x98271),x98273),x98276))),f158(x98271,x98274)))+P1(f327(f327(f329(f921(f916(x98271),f916(x98271))),f327(f327(f252(f916(x98271),f916(x98271)),x98275),x98276)),f158(x98271,x98274)))+P1(f327(f327(f329(f921(x98271,x98271)),f327(f327(f252(x98271,x98271),x98272),x98273)),x98274)) % 177.41/177.19 [9916]P1(f327(x99161,x99162))+P1(f327(f327(f329(x99163),f903(x99161,x99164,x99165,x99163,x99166)),x99165))+~P1(f327(f327(f329(x99166),x99162),f327(f327(f40(x99163,f922(x99166,a910)),x99165),x99164))) % 177.41/177.19 [9927]~E(x99272,x99274)+P1(f327(f327(f329(f921(f916(x99271),f916(x99271))),f327(f327(f252(f916(x99271),f916(x99271)),f327(f327(f135(x99271),x99272),f327(f327(f152(x99271),x99273),f114(x99271)))),f327(f327(f135(x99271),x99274),f327(f327(f152(x99271),x99275),f114(x99271))))),f158(x99271,x99276)))+~P1(f327(f327(f329(f921(x99271,x99271)),f327(f327(f252(x99271,x99271),x99273),x99275)),x99276)) % 177.41/177.19 [10002]E(x100021,x100022)+~P1(f327(f327(f329(f921(f916(x100023),f916(x100023))),f327(f327(f252(f916(x100023),f916(x100023)),f327(f327(f135(x100023),x100025),f327(f327(f152(x100023),x100021),f114(x100023)))),f327(f327(f135(x100023),x100026),f327(f327(f152(x100023),x100022),f114(x100023))))),f158(x100023,x100024)))+P1(f327(f327(f329(f921(x100023,x100023)),f327(f327(f252(x100023,x100023),x100021),x100022)),x100024)) % 177.41/177.19 [10033]~P1(f327(f327(f329(f921(f916(x100331),f916(x100331))),f327(f327(f252(f916(x100331),f916(x100331)),f327(f327(f135(x100331),x100335),f327(f327(f152(x100331),x100332),f114(x100331)))),f327(f327(f135(x100331),x100336),f327(f327(f152(x100331),x100333),f114(x100331))))),f158(x100331,x100334)))+P1(f327(f327(f329(f921(f916(x100331),f916(x100331))),f327(f327(f252(f916(x100331),f916(x100331)),x100335),x100336)),f158(x100331,x100334)))+P1(f327(f327(f329(f921(x100331,x100331)),f327(f327(f252(x100331,x100331),x100332),x100333)),x100334)) % 177.41/177.19 [10053]P1(f327(x100531,x100532))+P1(f327(f327(f329(x100533),f902(x100531,x100534,x100535,x100536,x100533)),f327(x100534,f903(x100531,x100534,x100535,x100536,x100533))))+~P1(f327(f327(f329(x100533),x100532),f327(f327(f40(x100536,f922(x100533,a910)),x100535),x100534))) % 177.41/177.19 [10206]P1(f327(f327(f329(x102061),f834(x102062,x102063,x102064,x102065,x102066,x102061)),x102065))+~P1(f327(f327(f234(f922(x102061,a910)),x102066),x102065))+P1(f327(f327(f234(f922(x102064,a910)),f327(f327(f41(x102061,f922(x102064,a910)),x102065),x102063)),f327(f327(f41(x102061,f922(x102064,a910)),x102065),x102062))) % 177.41/177.19 [10331]~P1(f327(f327(f234(f922(x103311,a910)),f327(x103314,f834(x103315,x103314,x103311,x103313,x103316,x103312))),f327(x103315,f834(x103315,x103314,x103311,x103313,x103316,x103312))))+~P1(f327(f327(f234(f922(x103312,a910)),x103316),x103313))+P1(f327(f327(f234(f922(x103311,a910)),f327(f327(f41(x103312,f922(x103311,a910)),x103313),x103314)),f327(f327(f41(x103312,f922(x103311,a910)),x103313),x103315))) % 177.41/177.19 [9053]~P14(x90533,x90534,x90531)+~P1(f327(f35(x90533),x90536))+E(f327(f327(x90531,x90532),f327(f327(f64(x90533,x90534,x90531),x90535),f327(f327(f23(f922(x90533,a910)),x90536),f327(f327(f309(x90533),x90532),f190(f922(x90533,a910)))))),f327(f327(f64(x90533,x90534,x90531),x90535),f327(f327(f309(x90533),x90532),x90536))) % 177.41/177.19 [9350]~P1(f327(f327(f329(x93505),x93503),x93506))+P1(f327(f327(f234(f922(x93501,a910)),f327(x93502,x93503)),x93504))+~P1(f327(f327(f234(f922(x93501,a910)),f327(f327(f40(x93505,f922(x93501,a910)),x93506),x93502)),x93504)) % 177.41/177.19 [9976]~P6(x99761,x99765,x99764)+P1(f327(f327(f329(f921(x99761,x99761)),f327(f327(f252(x99761,x99761),x99762),x99763)),x99764))+~P1(f327(f327(f329(x99761),x99766),f327(f327(f103(f922(x99761,a910)),f327(f285(x99761,x99761,x99764),f327(f327(f309(x99761),x99762),f190(f922(x99761,a910))))),f327(f285(x99761,x99761,x99764),f327(f327(f309(x99761),x99763),f190(f922(x99761,a910))))))) % 177.41/177.19 [8775]~P106(x87752)+~E(f327(f327(f80(x87752),f327(f327(f81(x87752),x87754),x87755)),x87751),f327(f327(f80(x87752),f327(f327(f81(x87752),x87753),x87755)),x87756))+E(x87751,f327(f327(f80(x87752),f327(f327(f81(x87752),f327(f327(f23(x87752),x87753),x87754)),x87755)),x87756)) % 177.41/177.19 [8776]~P106(x87761)+~E(f327(f327(f80(x87761),f327(f327(f81(x87761),x87762),x87764)),x87765),f327(f327(f80(x87761),f327(f327(f81(x87761),x87763),x87764)),x87766))+E(f327(f327(f80(x87761),f327(f327(f81(x87761),f327(f327(f23(x87761),x87762),x87763)),x87764)),x87765),x87766) % 177.41/177.19 [8958]~P106(x89581)+E(f327(f327(f80(x89581),f327(f327(f81(x89581),x89582),x89583)),x89584),f327(f327(f80(x89581),f327(f327(f81(x89581),x89585),x89583)),x89586))+~E(x89586,f327(f327(f80(x89581),f327(f327(f81(x89581),f327(f327(f23(x89581),x89582),x89585)),x89583)),x89584)) % 177.41/177.19 [8959]~P106(x89591)+E(f327(f327(f80(x89591),f327(f327(f81(x89591),x89592),x89593)),x89594),f327(f327(f80(x89591),f327(f327(f81(x89591),x89595),x89593)),x89596))+~E(f327(f327(f80(x89591),f327(f327(f81(x89591),f327(f327(f23(x89591),x89592),x89595)),x89593)),x89594),x89596) % 177.41/177.19 [9287]~P1(f327(f327(x92874,x92875),x92876))+~P1(f327(f327(x92873,x92875),x92876))+P1(f327(f327(f327(f327(f103(f922(x92871,f922(x92872,a910))),x92873),x92874),x92875),x92876)) % 177.41/177.19 [9546]P1(f327(f327(x95461,x95462),x95463))+P1(f327(f327(x95464,x95462),x95463))+~P1(f327(f327(f327(f327(f102(f922(x95465,f922(x95466,a910))),x95464),x95461),x95462),x95463)) % 177.41/177.19 [9840]~P111(x98401)+~P1(f327(f327(f234(x98401),f327(f327(f80(x98401),f327(f327(f81(x98401),x98404),x98405)),x98402)),f327(f327(f80(x98401),f327(f327(f81(x98401),x98403),x98405)),x98406)))+P1(f327(f327(f234(x98401),x98402),f327(f327(f80(x98401),f327(f327(f81(x98401),f327(f327(f23(x98401),x98403),x98404)),x98405)),x98406))) % 177.41/177.19 [9841]~P111(x98411)+~P1(f327(f327(f235(x98411),f327(f327(f80(x98411),f327(f327(f81(x98411),x98414),x98415)),x98412)),f327(f327(f80(x98411),f327(f327(f81(x98411),x98413),x98415)),x98416)))+P1(f327(f327(f235(x98411),x98412),f327(f327(f80(x98411),f327(f327(f81(x98411),f327(f327(f23(x98411),x98413),x98414)),x98415)),x98416))) % 177.41/177.19 [9864]~P111(x98641)+P1(f327(f327(f234(x98641),f327(f327(f80(x98641),f327(f327(f81(x98641),x98642),x98643)),x98644)),f327(f327(f80(x98641),f327(f327(f81(x98641),x98645),x98643)),x98646)))+~P1(f327(f327(f234(x98641),x98644),f327(f327(f80(x98641),f327(f327(f81(x98641),f327(f327(f23(x98641),x98645),x98642)),x98643)),x98646))) % 177.41/177.19 [9865]~P111(x98651)+P1(f327(f327(f235(x98651),f327(f327(f80(x98651),f327(f327(f81(x98651),x98652),x98653)),x98654)),f327(f327(f80(x98651),f327(f327(f81(x98651),x98655),x98653)),x98656)))+~P1(f327(f327(f235(x98651),x98654),f327(f327(f80(x98651),f327(f327(f81(x98651),f327(f327(f23(x98651),x98655),x98652)),x98653)),x98656))) % 177.41/177.19 [9968]~P111(x99681)+~P1(f327(f327(f234(x99681),f327(f327(f80(x99681),f327(f327(f81(x99681),x99682),x99684)),x99685)),f327(f327(f80(x99681),f327(f327(f81(x99681),x99683),x99684)),x99686)))+P1(f327(f327(f234(x99681),f327(f327(f80(x99681),f327(f327(f81(x99681),f327(f327(f23(x99681),x99682),x99683)),x99684)),x99685)),x99686)) % 177.41/177.19 [9969]~P111(x99691)+~P1(f327(f327(f235(x99691),f327(f327(f80(x99691),f327(f327(f81(x99691),x99692),x99694)),x99695)),f327(f327(f80(x99691),f327(f327(f81(x99691),x99693),x99694)),x99696)))+P1(f327(f327(f235(x99691),f327(f327(f80(x99691),f327(f327(f81(x99691),f327(f327(f23(x99691),x99692),x99693)),x99694)),x99695)),x99696)) % 177.41/177.19 [10016]~P111(x100161)+P1(f327(f327(f234(x100161),f327(f327(f80(x100161),f327(f327(f81(x100161),x100162),x100163)),x100164)),f327(f327(f80(x100161),f327(f327(f81(x100161),x100165),x100163)),x100166)))+~P1(f327(f327(f234(x100161),f327(f327(f80(x100161),f327(f327(f81(x100161),f327(f327(f23(x100161),x100162),x100165)),x100163)),x100164)),x100166)) % 177.41/177.19 [10017]~P111(x100171)+P1(f327(f327(f235(x100171),f327(f327(f80(x100171),f327(f327(f81(x100171),x100172),x100173)),x100174)),f327(f327(f80(x100171),f327(f327(f81(x100171),x100175),x100173)),x100176)))+~P1(f327(f327(f235(x100171),f327(f327(f80(x100171),f327(f327(f81(x100171),f327(f327(f23(x100171),x100172),x100175)),x100173)),x100174)),x100176)) % 177.41/177.19 [10190]~P68(x101902)+~P1(f327(f35(x101901),x101906))+E(f327(f327(f6(x101901,x101902),f327(f327(f18(x101901,x101902,x101902),f327(f327(f18(x101901,x101902,f922(x101902,x101902)),f327(f327(f8(a910,f922(x101902,f922(x101902,x101902)),x101901),f97(x101902)),x101903)),x101904)),x101905)),x101906),f327(f327(f80(x101902),f327(f327(f6(x101901,x101902),x101904),f327(f327(f103(f922(x101901,a910)),x101906),f327(f262(x101901),x101903)))),f327(f327(f6(x101901,x101902),x101905),f327(f327(f103(f922(x101901,a910)),x101906),f327(f79(f922(x101901,a910)),f327(f262(x101901),x101903)))))) % 177.41/177.19 [10253]P1(f327(f327(f329(x102532),x102534),x102536))+P1(f327(f327(f329(x102532),x102535),x102536))+E(f327(f311(x102531,x102532,f327(f327(f7(x102531,x102532,x102532),f327(f327(f7(x102531,x102532,f922(x102532,x102532)),f327(f327(f8(a910,f922(x102532,f922(x102532,x102532)),x102531),f97(x102532)),f327(f327(f7(x102531,f922(x102531,a910),a910),f329(x102531)),x102533))),x102534)),x102535)),x102536),f190(f922(x102531,a910))) % 177.41/177.19 [10254]P1(f327(f327(f329(x102542),x102545),x102546))+~P1(f327(f327(f329(x102542),x102544),x102546))+E(f327(f311(x102541,x102542,f327(f327(f7(x102541,x102542,x102542),f327(f327(f7(x102541,x102542,f922(x102542,x102542)),f327(f327(f8(a910,f922(x102542,f922(x102542,x102542)),x102541),f97(x102542)),f327(f327(f7(x102541,f922(x102541,a910),a910),f329(x102541)),x102543))),x102544)),x102545)),x102546),x102543) % 177.41/177.19 [10255]P1(f327(f327(f329(x102552),x102554),x102556))+~P1(f327(f327(f329(x102552),x102555),x102556))+E(f327(f311(x102551,x102552,f327(f327(f7(x102551,x102552,x102552),f327(f327(f7(x102551,x102552,f922(x102552,x102552)),f327(f327(f8(a910,f922(x102552,f922(x102552,x102552)),x102551),f97(x102552)),f327(f327(f7(x102551,f922(x102551,a910),a910),f329(x102551)),x102553))),x102554)),x102555)),x102556),f327(f79(f922(x102551,a910)),x102553)) % 177.41/177.19 [10256]~P1(f327(f327(f329(x102562),x102564),x102566))+~P1(f327(f327(f329(x102562),x102565),x102566))+E(f327(f311(x102561,x102562,f327(f327(f7(x102561,x102562,x102562),f327(f327(f7(x102561,x102562,f922(x102562,x102562)),f327(f327(f8(a910,f922(x102562,f922(x102562,x102562)),x102561),f97(x102562)),f327(f327(f7(x102561,f922(x102561,a910),a910),f329(x102561)),x102563))),x102564)),x102565)),x102566),f242(f922(x102561,a910))) % 177.41/177.19 [8808]E(x88081,x88082)+~P54(x88084,x88085,x88083,x88086,x88087)+~E(f327(x88083,x88081),f327(x88083,x88082)) % 177.41/177.19 [8837]~P8(x88376,x88375,x88377,x88374,x88371)+E(f327(f327(x88371,x88372),x88373),x88374)+P1(f327(f35(x88375),x88373)) % 177.41/177.19 [9706]P40(x97061,x97062,x97063,x97064,x97065,f327(f327(x97063,x97066),x97067))+~E(f327(f327(x97063,x97066),x97067),x97064)+~E(x97065,f190(f922(x97061,a910))) % 177.41/177.19 [9886]~P1(f327(x98866,x98863))+~P1(f327(f327(f329(f921(x98862,x98862)),f327(f327(f252(x98862,x98862),x98864),x98865)),f327(x98867,x98863)))+P1(f327(f327(f329(f921(f921(x98861,x98862),f921(x98861,x98862))),f327(f327(f252(f921(x98861,x98862),f921(x98861,x98862)),f327(f327(f252(x98861,x98862),x98863),x98864)),f327(f327(f252(x98861,x98862),x98863),x98865))),f280(x98861,x98862,x98866,x98867))) % 177.41/177.19 [10319]~P40(x103192,x103197,x103193,x103196,x103191,f327(f327(x103193,x103195),x103194))+E(f327(f327(x103193,f510(x103194,x103195,x103191,x103196,x103193,x103197,x103192)),f524(x103194,x103195,x103191,x103196,x103193,x103197,x103192)),f327(f327(x103193,x103195),x103194))+E(x103191,f190(f922(x103192,a910))) % 177.41/177.19 [10320]~P40(x103207,x103206,x103201,x103204,x103205,f327(f327(x103201,x103202),x103203))+E(f327(f327(x103201,f510(x103203,x103202,x103205,x103204,x103201,x103206,x103207)),f524(x103203,x103202,x103205,x103204,x103201,x103206,x103207)),f327(f327(x103201,x103202),x103203))+E(f327(f327(x103201,x103202),x103203),x103204) % 177.41/177.19 [9383]~P32(x93831,x93832,x93833,x93835,x93837)+P32(x93831,x93832,x93833,f327(f327(f152(x93831),x93834),x93835),f327(f327(f152(x93832),x93836),x93837))+~P1(f327(f327(x93833,x93834),x93836)) % 177.41/177.19 [9401]P32(x94011,x94012,x94013,x94014,x94015)+~P32(x94011,x94012,x94013,f327(f327(f135(x94011),x94016),x94014),f327(f327(f135(x94012),x94017),x94015))+~E(f327(f191(f916(x94011)),x94016),f327(f191(f916(x94012)),x94017)) % 177.41/177.19 [9402]P32(x94021,x94022,x94023,x94024,x94025)+~P32(x94021,x94022,x94023,f327(f327(f135(x94021),x94024),x94026),f327(f327(f135(x94022),x94025),x94027))+~E(f327(f191(f916(x94021)),x94024),f327(f191(f916(x94022)),x94025)) % 177.41/177.19 [9612]~P32(x96121,x96122,x96123,x96125,x96127)+~P32(x96121,x96122,x96123,x96124,x96126)+P32(x96121,x96122,x96123,f327(f327(f135(x96121),x96124),x96125),f327(f327(f135(x96122),x96126),x96127)) % 177.41/177.19 [9961]~P1(f327(f66(x99611,x99614,x99615,x99616,x99613),x99617))+P1(f327(f66(x99611,x99614,x99615,x99616,f327(f327(f309(x99611),x99612),x99613)),f327(f327(x99615,x99612),x99617)))+P1(f327(f327(f329(x99611),x99612),x99613)) % 177.41/177.19 [10347]~P40(x103472,x103477,x103476,x103475,x103471,f327(f327(x103476,x103474),x103473))+E(x103471,f190(f922(x103472,a910)))+P1(f327(f327(f329(x103472),f510(x103473,x103474,x103471,x103475,x103476,x103477,x103472)),x103471)) % 177.41/177.19 [10348]~P40(x103485,x103487,x103481,x103484,x103486,f327(f327(x103481,x103482),x103483))+E(f327(f327(x103481,x103482),x103483),x103484)+P1(f327(f327(f329(x103485),f510(x103483,x103482,x103486,x103484,x103481,x103487,x103485)),x103486)) % 177.41/177.19 [10437]E(f327(f327(f252(x104371,x104372),x104373),x104374),f327(f327(f252(x104371,x104372),x104375),x104376))+P1(f327(f327(f329(f921(f921(x104371,x104372),f921(x104371,x104372))),f327(f327(f252(f921(x104371,x104372),f921(x104371,x104372)),f327(f327(f252(x104371,x104372),f841(x104377,x104374,x104373,x104376,x104375,x104372,x104371)),f842(x104377,x104374,x104373,x104376,x104375,x104372,x104371))),f327(f327(f252(x104371,x104372),x104373),x104374))),f307(f921(x104371,x104372),x104377)))+~P1(f327(f327(f329(f921(f921(x104371,x104372),f921(x104371,x104372))),f327(f327(f252(f921(x104371,x104372),f921(x104371,x104372)),f327(f327(f252(x104371,x104372),x104375),x104376)),f327(f327(f252(x104371,x104372),x104373),x104374))),f307(f921(x104371,x104372),x104377))) % 177.41/177.19 [9078]~P19(x90784,x90785,x90786,x90787,x90781)+~P1(f327(f35(x90785),x90783))+E(f327(f327(x90781,x90782),x90783),f327(f327(f327(f65(x90784,x90785,x90786),x90782),x90787),x90783)) % 177.41/177.19 [9079]~P8(x90794,x90795,x90796,x90797,x90791)+~P1(f327(f35(x90795),x90793))+E(f327(f327(x90791,x90792),x90793),f327(f327(f327(f65(x90794,x90795,x90796),x90792),x90797),x90793)) % 177.41/177.19 [9670]~P22(x96701,x96702,f327(f327(f309(f913(x96701)),f327(f327(f327(f91(x96701),x96703),x96704),x96707)),f190(f922(f913(x96701),a910))))+P22(x96701,x96702,f327(f327(f309(f913(x96701)),f327(f327(f327(f91(x96701),x96703),f30(x96704,x96705)),x96706)),f190(f922(f913(x96701),a910))))+~P22(x96701,x96702,f327(f327(f309(f913(x96701)),f327(f327(f327(f91(x96701),x96707),x96705),x96706)),f190(f922(f913(x96701),a910)))) % 177.41/177.19 [9859]~P21(x98593,x98594,x98595,x98597,x98596,x98591)+~P1(f327(f35(x98594),x98592))+E(f327(x98591,x98592),f327(f327(f327(f65(x98593,x98594,x98595),x98596),x98597),x98592)) % 177.41/177.19 [10011]P40(x100111,x100112,x100113,x100114,x100115,f327(f327(x100113,x100116),x100117))+~P40(x100111,x100112,x100113,x100114,f327(f327(f23(f922(x100111,a910)),x100115),f327(f327(f309(x100111),x100116),f190(f922(x100111,a910)))),x100117)+~P1(f327(f327(f329(x100111),x100116),x100115)) % 177.41/177.19 [10287]~P22(x102871,x102872,f327(f327(f309(f913(x102871)),f327(f327(f327(f91(x102871),f93(x102871,x102873,x102874)),x102875),x102877)),f190(f922(f913(x102871),a910))))+P22(x102871,x102872,f327(f327(f309(f913(x102871)),f327(f327(f327(f91(x102871),x102873),f27(x102874,x102875,x102876)),x102877)),f190(f922(f913(x102871),a910))))+~P22(x102871,x102872,f327(f327(f309(f913(x102871)),f327(f327(f327(f91(x102871),f93(x102871,x102873,f327(f72(a910,a910,a911,a322),x102874))),x102876),x102877)),f190(f922(f913(x102871),a910)))) % 177.41/177.19 [10371]P1(f327(f327(x103717,f785(x103714,x103715,x103711,x103716,x103713,x103712,x103717)),f786(x103714,x103715,x103711,x103716,x103713,x103712,x103717)))+~P1(f327(f327(x103717,f327(f256(x103712,x103713),x103716)),f327(f251(x103712,x103713),x103716)))+P1(f327(x103711,f327(f327(f257(x103712,x103713,x103714),x103715),x103716))) % 177.41/177.19 [10381]~P40(x103812,x103813,x103814,x103815,x103811,f327(f327(x103814,x103817),x103816))+P40(x103812,x103813,x103814,x103815,f327(f327(f23(f922(x103812,a910)),x103811),f327(f327(f309(x103812),f510(x103816,x103817,x103811,x103815,x103814,x103813,x103812)),f190(f922(x103812,a910)))),f524(x103816,x103817,x103811,x103815,x103814,x103813,x103812))+E(x103811,f190(f922(x103812,a910))) % 177.41/177.19 [10382]~P40(x103825,x103826,x103821,x103824,x103827,f327(f327(x103821,x103822),x103823))+P40(x103825,x103826,x103821,x103824,f327(f327(f23(f922(x103825,a910)),x103827),f327(f327(f309(x103825),f510(x103823,x103822,x103827,x103824,x103821,x103826,x103825)),f190(f922(x103825,a910)))),f524(x103823,x103822,x103827,x103824,x103821,x103826,x103825))+E(f327(f327(x103821,x103822),x103823),x103824) % 177.41/177.19 [10404]~P1(f327(x104041,f327(f327(x104045,f786(x104044,x104045,x104041,x104046,x104043,x104042,x104047)),f785(x104044,x104045,x104041,x104046,x104043,x104042,x104047))))+~P1(f327(f327(x104047,f327(f256(x104042,x104043),x104046)),f327(f251(x104042,x104043),x104046)))+P1(f327(x104041,f327(f327(f257(x104042,x104043,x104044),x104045),x104046))) % 177.41/177.19 [9691]P1(f327(f327(f234(f922(f921(x96911,x96912),a910)),f327(f327(f289(x96911,x96913,x96912),x96914),x96915)),f327(f327(f289(x96911,x96913,x96912),x96916),x96917)))+~P1(f327(f327(f234(f922(f921(x96913,x96912),a910)),x96915),x96917))+~P1(f327(f327(f234(f922(f921(x96911,x96913),a910)),x96914),x96916)) % 177.41/177.19 [10431]E(f327(f327(f252(x104311,x104312),x104313),x104314),f327(f327(f252(x104311,x104312),x104315),x104316))+~P1(f327(f327(f329(f921(f921(x104311,x104312),f921(x104311,x104312))),f327(f327(f252(f921(x104311,x104312),f921(x104311,x104312)),f327(f327(f252(x104311,x104312),x104313),x104314)),f327(f327(f252(x104311,x104312),x104315),x104316))),f307(f921(x104311,x104312),x104317)))+P1(f327(f327(f329(f921(f921(x104311,x104312),f921(x104311,x104312))),f327(f327(f252(f921(x104311,x104312),f921(x104311,x104312)),f327(f327(f252(x104311,x104312),x104313),x104314)),f327(f327(f252(x104311,x104312),f841(x104317,x104316,x104315,x104314,x104313,x104312,x104311)),f842(x104317,x104316,x104315,x104314,x104313,x104312,x104311)))),x104317)) % 177.41/177.19 [10022]~P1(f327(f327(f329(x100221),x100226),x100225))+P1(f327(f66(x100221,x100222,x100223,x100224,x100225),f327(f327(x100223,x100226),x100227)))+~P1(f327(f66(x100221,x100222,x100223,x100224,f327(f327(f23(f922(x100221,a910)),x100225),f327(f327(f309(x100221),x100226),f190(f922(x100221,a910))))),x100227)) % 177.41/177.19 [10444]~P139(x104441)+~P23(f921(x104442,x104443),x104441,f327(f257(x104442,x104443,x104441),f327(f327(f7(x104442,f922(x104443,x104441),f922(x104443,x104441)),f327(f327(f8(f922(x104441,x104441),f922(f922(x104443,x104441),f922(x104443,x104441)),x104442),f8(x104441,x104441,x104443)),f327(f327(f8(x104441,f922(x104441,x104441),x104442),f81(x104441)),x104444))),x104445)),f327(f327(f254(x104442,x104443),x104446),f327(f16(f922(x104443,a910),x104442),x104447)))+E(f327(f327(f6(x104441,x104441),f31(x104441)),f327(f262(x104441),f327(f327(f8(f922(x104442,a910),a910,x104441),f87(x104442)),f327(f327(f8(f922(x104442,f922(x104443,a910)),f922(x104442,a910),x104441),f327(f8(f922(x104443,a910),a910,x104442),f87(x104443))),f327(f327(f7(x104441,f922(x104442,f922(x104443,a910)),f922(x104442,f922(x104443,a910))),f327(f327(f8(f922(x104442,f922(f922(x104443,a910),f922(x104443,a910))),f922(f922(x104442,f922(x104443,a910)),f922(x104442,f922(x104443,a910))),x104441),f18(x104442,f922(x104443,a910),f922(x104443,a910))),f327(f327(f8(f922(x104442,f922(x104443,f922(a910,a910))),f922(x104442,f922(f922(x104443,a910),f922(x104443,a910))),x104441),f327(f8(f922(x104443,f922(a910,a910)),f922(f922(x104443,a910),f922(x104443,a910)),x104442),f18(x104443,a910,a910))),f327(f327(f8(f922(x104442,f922(x104443,a910)),f922(x104442,f922(x104443,f922(a910,a910))),x104441),f327(f8(f922(x104443,a910),f922(x104443,f922(a910,a910)),x104442),f327(f8(a910,f922(a910,a910),x104443),a325))),f327(f327(f7(x104441,f922(x104442,f922(x104443,x104441)),f922(x104442,f922(x104443,a910))),f327(f327(f8(f922(f922(x104443,x104441),f922(x104443,a910)),f922(f922(x104442,f922(x104443,x104441)),f922(x104442,f922(x104443,a910))),x104441),f8(f922(x104443,x104441),f922(x104443,a910),x104442)),f327(f327(f8(f922(x104441,a910),f922(f922(x104443,x104441),f922(x104443,a910)),x104441),f8(x104441,a910,x104443)),a324))),f327(f327(f7(x104442,f922(x104443,x104441),f922(x104443,x104441)),f327(f327(f8(f922(x104441,x104441),f922(f922(x104443,x104441),f922(x104443,x104441)),x104442),f8(x104441,x104441,x104443)),f327(f327(f8(x104441,f922(x104441,x104441),x104442),f81(x104441)),x104444))),x104445)))))),f327(f327(f7(x104442,f922(x104443,a910),f922(x104443,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x104443,a910),f922(x104443,a910)),x104442),f8(a910,a910,x104443)),f327(f327(f8(a910,f922(a910,a910),x104442),a325),f327(f327(f7(x104442,f922(x104442,a910),a910),f329(x104442)),x104446)))),f327(f327(f7(x104443,f922(x104443,a910),a910),f329(x104443)),x104447))))))),f327(f327(f81(x104441),f327(f327(f6(x104442,x104441),x104444),x104446)),f327(f327(f6(x104443,x104441),x104445),x104447))) % 177.41/177.19 [9695]~P24(x96951,x96953,x96955,x96956,x96958)+~P24(x96953,x96952,x96954,x96958,x96957)+P24(x96951,x96952,f327(f72(x96953,x96952,x96951,x96954),x96955),x96956,x96957) % 177.41/177.19 [9725]P24(x97251,x97252,x97253,x97254,x97255)+~P24(x97256,x97251,x97257,x97258,x97254)+~P24(x97256,x97252,f327(f72(x97251,x97252,x97256,x97253),x97257),x97258,x97255) % 177.41/177.19 [9857]~P1(f327(f327(x98574,x98576),x98578))+~P1(f327(f327(x98575,x98578),x98577))+P1(f327(f327(f253(x98571,x98572,x98573,x98574,x98575),x98576),x98577)) % 177.41/177.19 [9453]~P17(x94538,x94531,x94533,x94535)+~P1(f327(f35(x94538),x94536))+E(f327(f72(x94531,x94531,x94532,f327(x94533,x94534)),f327(f72(x94531,x94531,x94532,f327(x94535,x94536)),x94537)),f327(f72(x94531,x94531,x94532,f327(x94535,x94536)),f327(f72(x94531,x94531,x94532,f327(x94533,x94534)),x94537))) % 177.41/177.19 [9847]~P20(x98477,x98472,x98475,x98478,x98476,x98471)+~P1(f327(f35(x98472),x98474))+E(f327(x98471,f327(f327(f309(x98472),x98473),x98474)),f327(f327(x98475,f327(x98476,x98473)),f327(x98471,x98474))) % 177.41/177.19 [9966]~P23(x99662,x99664,x99666,x99668)+~P23(x99661,x99663,x99665,x99667)+P23(f921(x99661,x99662),f921(x99663,x99664),f258(x99661,x99663,x99662,x99664,x99665,x99666),f327(f327(f254(x99661,x99662),x99667),f327(f16(f922(x99662,a910),x99661),x99668))) % 177.41/177.19 [9638]P1(f327(f327(f329(f921(x96381,x96382)),f327(f327(f252(x96381,x96382),x96383),x96384)),f327(f327(f289(x96381,x96385,x96382),x96386),x96387)))+~P1(f327(f327(f329(f921(x96381,x96385)),f327(f327(f252(x96381,x96385),x96383),x96388)),x96386))+~P1(f327(f327(f329(f921(x96385,x96382)),f327(f327(f252(x96385,x96382),x96388),x96384)),x96387)) % 177.41/177.19 [9828]~P1(f327(f327(f234(f922(f921(x98283,x98282),a910)),x98285),f327(f327(f254(x98283,x98282),x98288),f327(f16(f922(x98282,a910),x98283),x98287))))+~P1(f327(f327(f234(f922(f921(x98281,x98283),a910)),x98284),f327(f327(f254(x98281,x98283),x98286),f327(f16(f922(x98283,a910),x98281),x98288))))+P1(f327(f327(f234(f922(f921(x98281,x98282),a910)),f327(f327(f289(x98281,x98283,x98282),x98284),x98285)),f327(f327(f254(x98281,x98282),x98286),f327(f16(f922(x98282,a910),x98281),x98287)))) % 177.41/177.19 [9881]~E(x98813,x98815)+P1(f327(f327(f329(f921(f921(x98811,x98812),f921(x98811,x98812))),f327(f327(f252(f921(x98811,x98812),f921(x98811,x98812)),f327(f327(f252(x98811,x98812),x98813),x98814)),f327(f327(f252(x98811,x98812),x98815),x98816))),f320(x98811,x98812,x98817,x98818)))+~P1(f327(f327(f329(f921(x98812,x98812)),f327(f327(f252(x98812,x98812),x98814),x98816)),x98818)) % 177.41/177.19 [9985]E(x99851,x99852)+~P1(f327(f327(f329(f921(f921(x99853,x99855),f921(x99853,x99855))),f327(f327(f252(f921(x99853,x99855),f921(x99853,x99855)),f327(f327(f252(x99853,x99855),x99851),x99856)),f327(f327(f252(x99853,x99855),x99852),x99857))),f320(x99853,x99855,x99854,x99858)))+P1(f327(f327(f329(f921(x99853,x99853)),f327(f327(f252(x99853,x99853),x99851),x99852)),x99854)) % 177.41/177.19 [10001]~P1(f327(f327(f329(f921(f921(x100011,x100015),f921(x100011,x100015))),f327(f327(f252(f921(x100011,x100015),f921(x100011,x100015)),f327(f327(f252(x100011,x100015),x100012),x100016)),f327(f327(f252(x100011,x100015),x100013),x100017))),f320(x100011,x100015,x100014,x100018)))+P1(f327(f327(f329(f921(x100011,x100011)),f327(f327(f252(x100011,x100011),x100012),x100013)),x100014))+P1(f327(f327(f329(f921(x100015,x100015)),f327(f327(f252(x100015,x100015),x100016),x100017)),x100018)) % 177.41/177.19 [9917]~P21(x99177,x99175,x99171,x99178,x99172,x99174)+~P1(f327(f35(x99175),x99176))+E(f327(f327(x99171,f327(x99172,x99173)),f327(x99174,f327(f327(f23(f922(x99175,a910)),x99176),f327(f327(f309(x99175),x99173),f190(f922(x99175,a910)))))),f327(x99174,f327(f327(f309(x99175),x99173),x99176))) % 177.41/177.19 [9407]~P1(f327(f327(f327(x94075,x94078),x94076),x94077))+~P1(f327(f327(f329(x94071),x94078),x94074))+P1(f327(f327(f327(f327(f40(x94071,f922(x94072,f922(x94073,a910))),x94074),x94075),x94076),x94077)) % 177.41/177.19 [9623]P1(f327(f327(f327(x96231,x96232),x96233),x96234))+~P1(f327(f327(f329(x96235),x96232),x96236))+~P1(f327(f327(f327(f327(f41(x96235,f922(x96237,f922(x96238,a910))),x96236),x96231),x96233),x96234)) % 177.41/177.19 [9821]~P19(x98213,x98212,x98214,x98218,x98211)+~P1(f327(f35(x98212),x98217))+E(f327(f327(x98211,f327(f327(f18(x98212,x98213,x98213),f327(f327(f8(x98213,f922(x98213,x98213),x98212),x98214),x98215)),x98216)),x98217),f327(f327(x98214,f327(f327(x98211,x98215),x98217)),f327(f327(x98211,x98216),x98217))) % 177.41/177.19 [10087]~E(f327(f310(x100872,x100874,x100876),x100878),x1008710)+~E(f327(f310(x100871,x100873,x100875),x100877),x100879)+E(f327(f310(f921(x100871,x100872),f921(x100873,x100874),f258(x100871,x100873,x100872,x100874,x100875,x100876)),f327(f327(f254(x100871,x100872),x100877),f327(f16(f922(x100872,a910),x100871),x100878))),f327(f327(f254(x100873,x100874),x100879),f327(f16(f922(x100874,a910),x100873),x1008710))) % 177.41/177.19 [5046]~P41(x50461,x50462)+~P47(x50461,x50462)+~P48(x50461,x50462)+P5(x50461,x50462) % 177.41/177.19 [5002]~P108(x50022)+~P11(x50022,x50021)+P11(x50022,f115(x50022,x50021))+E(x50021,f114(x50022)) % 177.41/177.19 [5003]~P108(x50032)+~P11(x50032,x50031)+P11(x50032,f703(x50031,x50032))+E(x50031,f114(x50032)) % 177.41/177.19 [5245]~P3(x52452)+E(f10(x52452,x52451),f39(x52452,x52451))+E(x52451,f190(f922(x52452,a910)))+~P1(f327(f35(x52452),x52451)) % 177.41/177.19 [5246]~P3(x52462)+E(f13(x52462,x52461),f38(x52462,x52461))+E(x52461,f190(f922(x52462,a910)))+~P1(f327(f35(x52462),x52461)) % 177.41/177.19 [5401]~P108(x54012)+~P11(x54012,x54011)+E(x54011,f114(x54012))+E(f327(f327(f152(x54012),f722(x54011,x54012)),f703(x54011,x54012)),x54011) % 177.41/177.19 [6218]~P96(x62182)+E(x62181,f190(f922(x62182,a910)))+P1(f327(f327(f234(x62182),f10(x62182,x62181)),f13(x62182,x62181)))+~P1(f327(f35(x62182),x62181)) % 177.41/177.19 [6232]~P38(x62322)+~P38(x62321)+E(x62321,x62322)+~E(f327(f310(a1,a915,a106),x62321),f327(f310(a1,a915,a106),x62322)) % 177.41/177.19 [9266]~P119(x92661)+~P1(f327(f327(f329(x92661),x92662),f111(x92661)))+P1(f327(f327(f235(x92661),f327(f327(f80(x92661),f327(f327(f80(x92661),f78(x92661)),x92662)),x92662)),f2(x92661)))+~P1(f327(f327(f235(x92661),x92662),f2(x92661))) % 177.41/177.19 [9506]~P119(x95061)+~P1(f327(f327(f329(x95061),x95062),f111(x95061)))+~P1(f327(f327(f235(x95061),f327(f327(f80(x95061),f327(f327(f80(x95061),f78(x95061)),x95062)),x95062)),f2(x95061)))+P1(f327(f327(f235(x95061),x95062),f2(x95061))) % 177.41/177.19 [5061]~P139(x50612)+~P116(x50612)+E(x50611,f2(a915))+E(f327(f327(f244(x50612),f2(x50612)),x50611),f2(x50612)) % 177.41/177.19 [5064]~P139(x50641)+~P116(x50641)+~E(x50642,f2(a915))+E(f327(f327(f244(x50641),f2(x50641)),x50642),f78(x50641)) % 177.41/177.19 [5231]~P141(x52312)+E(x52311,f78(x52312))+E(x52311,f327(f79(x52312),f78(x52312)))+~E(f327(f327(f81(x52312),x52311),x52311),f78(x52312)) % 177.41/177.19 [5482]~P89(x54822)+E(x54821,f2(x54822))+E(f82(x54822,x54821),f327(f79(x54822),f78(x54822)))+P1(f327(f327(f235(x54822),f2(x54822)),x54821)) % 177.41/177.19 [5725]~P89(x57252)+E(f82(x57252,x57251),f78(x57252))+E(x57251,f2(x57252))+~P1(f327(f327(f235(x57252),f2(x57252)),x57251)) % 177.41/177.19 [5734]E(x57341,x57342)+~E(f327(f105(a915),x57341),f327(f105(a915),x57342))+P1(f327(a195,f327(f105(a1),x57342)))+P1(f327(a195,f327(f105(a1),x57341))) % 177.41/177.19 [5785]~P92(x57851)+~E(x57852,f2(x57851))+E(f327(f327(f80(x57851),x57852),x57852),f2(x57851))+~P1(f327(f327(f329(x57851),x57852),f111(x57851))) % 177.41/177.19 [5824]E(x58241,f2(a1))+~E(f327(f327(f37(a1),x58242),x58241),f2(a1))+P1(f327(f327(f235(a1),x58241),x58242))+P1(f327(f327(f235(a1),x58242),x58241)) % 177.41/177.19 [5854]E(x58541,f2(a1))+~E(f327(f327(f37(a1),x58542),x58541),f2(a1))+P1(f327(f327(f234(a1),x58542),f2(a1)))+P1(f327(f327(f235(a1),x58542),x58541)) % 177.41/177.19 [5888]E(x58881,f2(a1))+~E(f327(f327(f37(a1),x58882),x58881),f2(a1))+P1(f327(f327(f234(a1),f2(a1)),x58882))+P1(f327(f327(f235(a1),x58881),x58882)) % 177.41/177.19 [5923]~P92(x59232)+E(x59231,f2(x59232))+~E(f327(f327(f80(x59232),x59231),x59231),f2(x59232))+~P1(f327(f327(f329(x59232),x59231),f111(x59232))) % 177.41/177.19 [5985]E(f327(f105(a915),x59851),f327(f105(a915),x59852))+~E(f327(f105(a1),x59852),f2(a1))+P1(f327(a195,f327(f105(a1),x59852)))+~P1(f327(a195,f327(f105(a1),x59851))) % 177.41/177.19 [6014]~E(f327(f105(a915),x60142),f327(f105(a915),x60141))+E(f327(f105(a1),x60141),f2(a1))+P1(f327(a195,f327(f105(a1),x60141)))+~P1(f327(a195,f327(f105(a1),x60142))) % 177.41/177.19 [6024]~P108(x60242)+E(x60241,f190(f922(x60242,a910)))+~P1(f327(f35(x60242),x60241))+P1(f327(f327(f329(x60242),f14(x60242,x60241)),x60241)) % 177.41/177.19 [6025]~P108(x60252)+E(x60251,f190(f922(x60252,a910)))+~P1(f327(f35(x60252),x60251))+P1(f327(f327(f329(x60252),f15(x60252,x60251)),x60251)) % 177.41/177.19 [6195]~P119(x61951)+~P93(x61951)+P1(f327(f327(f234(x61951),f2(x61951)),f327(f105(x61951),x61952)))+~P1(f327(f327(f234(a1),a83),x61952)) % 177.41/177.19 [6196]~P119(x61961)+~P93(x61961)+P1(f327(f327(f235(x61961),f2(x61961)),f327(f105(x61961),x61962)))+~P1(f327(f327(f235(a1),a83),x61962)) % 177.41/177.19 [6217]~P119(x62171)+~P93(x62171)+E(f327(f75(x62171),f327(f105(x62171),x62172)),f327(f105(x62171),x62172))+P1(f327(f327(f235(x62171),f327(f105(x62171),x62172)),f2(x62171))) % 177.41/177.19 [6256]E(x62561,x62562)+~E(f327(a106,x62561),f327(a106,x62562))+~P1(f327(f327(f234(a1),f2(a1)),x62562))+~P1(f327(f327(f234(a1),f2(a1)),x62561)) % 177.41/177.19 [6454]~P93(x64542)+~P119(x64542)+~P1(f327(f327(f234(x64542),f2(x64542)),f327(f105(x64542),x64541)))+P1(f327(f327(f234(a1),a83),x64541)) % 177.41/177.19 [6455]~P93(x64552)+~P119(x64552)+~P1(f327(f327(f235(x64552),f2(x64552)),f327(f105(x64552),x64551)))+P1(f327(f327(f235(a1),a83),x64551)) % 177.41/177.19 [6460]~P119(x64601)+~P93(x64601)+P1(f327(f327(f234(x64601),f327(f105(x64601),x64602)),f2(x64601)))+~P1(f327(f327(f234(a1),x64602),a83)) % 177.41/177.19 [6461]~P119(x64611)+~P93(x64611)+P1(f327(f327(f235(x64611),f327(f105(x64611),x64612)),f2(x64611)))+~P1(f327(f327(f235(a1),x64612),a83)) % 177.41/177.19 [6777]~P93(x67772)+~P119(x67772)+~P1(f327(f327(f234(x67772),f327(f105(x67772),x67771)),f2(x67772)))+P1(f327(f327(f234(a1),x67771),a83)) % 177.41/177.19 [6778]~P93(x67782)+~P119(x67782)+~P1(f327(f327(f235(x67782),f327(f105(x67782),x67781)),f2(x67782)))+P1(f327(f327(f235(a1),x67781),a83)) % 177.41/177.19 [6870]~P119(x68701)+~P93(x68701)+E(f327(f75(x68701),f327(f105(x68701),x68702)),f327(f79(x68701),f327(f105(x68701),x68702)))+~P1(f327(f327(f235(x68701),f327(f105(x68701),x68702)),f2(x68701))) % 177.41/177.19 [6888]E(f327(f105(a915),x68881),f327(f105(a915),x68882))+~E(f327(f105(a1),x68882),f2(a1))+~P1(f327(f327(f234(a1),f327(f105(a1),x68881)),f2(a1)))+~P1(f327(a195,f327(f105(a1),x68881))) % 177.41/177.19 [7768]~P108(x77682)+E(x77681,f190(f922(x77682,a910)))+~P1(f327(f35(x77682),x77681))+P1(f327(f327(f234(x77682),f12(x77682,f238(x77682),x77681)),f11(x77682,f189(x77682),x77681))) % 177.41/177.19 [8085]~P38(x80852)+~P4(x80851)+P1(f327(f327(f329(a1),x80851),x80852))+~P1(f327(f327(f329(a915),f327(a106,x80851)),f327(f310(a1,a915,a106),x80852))) % 177.41/177.19 [6020]~P142(x60202)+E(x60201,f2(a1))+E(f327(f79(x60202),f327(f104(x60202),f327(f79(a1),x60201))),f327(f104(x60202),x60201))+~P1(f327(f327(f235(a1),x60201),f2(a1))) % 177.41/177.19 [6098]~P92(x60981)+~P93(x60981)+~P26(x60981,f327(f105(x60981),x60982))+P26(x60981,f327(f105(x60981),f327(f327(f80(a1),x60982),x60982))) % 177.41/177.19 [6443]~P76(x64432)+E(x64431,f190(f922(x64432,a910)))+E(f15(x64432,f327(f310(x64432,x64432,f79(x64432)),x64431)),f327(f79(x64432),f14(x64432,x64431)))+~P1(f327(f35(x64432),x64431)) % 177.41/177.19 [6444]~P76(x64442)+E(x64441,f190(f922(x64442,a910)))+E(f14(x64442,f327(f310(x64442,x64442,f79(x64442)),x64441)),f327(f79(x64442),f15(x64442,x64441)))+~P1(f327(f35(x64442),x64441)) % 177.41/177.19 [6477]~P92(x64771)+~P93(x64771)+P26(x64771,f327(f105(x64771),x64772))+~P26(x64771,f327(f105(x64771),f327(f327(f80(a1),x64772),x64772))) % 177.41/177.19 [6570]E(x65701,f2(a1))+E(f327(a52,f51(f327(f79(a1),x65701),f327(f79(a1),x65702))),f47(x65701,x65702))+P1(f327(f327(f234(a1),f2(a1)),x65702))+~P1(f327(f327(f234(a1),f2(a1)),x65701)) % 177.41/177.19 [8865]~P38(x88652)+~P38(x88651)+P1(f327(f327(f235(f922(a915,a910)),f327(f310(a1,a915,a106),x88651)),f327(f310(a1,a915,a106),x88652)))+~P1(f327(f327(f235(f922(a1,a910)),x88651),x88652)) % 177.41/177.19 [9098]~E(f725(x90982,x90981),f726(x90982,x90981))+~P1(f327(f138(x90981),f727(x90982,x90981)))+~P1(f327(f138(f916(x90981)),x90982))+P1(f327(f138(x90981),f327(f143(f916(x90981),f916(x90981),f135(x90981),f114(x90981)),x90982))) % 177.41/177.19 [9186]~P38(x91862)+~P38(x91861)+~P1(f327(f327(f234(f922(a915,a910)),f327(f310(a1,a915,a106),x91861)),f327(f310(a1,a915,a106),x91862)))+P1(f327(f327(f234(f922(a1,a910)),x91861),x91862)) % 177.41/177.19 [9187]~P38(x91872)+~P38(x91871)+~P1(f327(f327(f235(f922(a915,a910)),f327(f310(a1,a915,a106),x91871)),f327(f310(a1,a915,a106),x91872)))+P1(f327(f327(f235(f922(a1,a910)),x91871),x91872)) % 177.41/177.19 [9193]~E(f725(x91932,x91931),f726(x91932,x91931))+~P1(f327(f138(f916(x91931)),x91932))+P1(f327(f138(x91931),f327(f143(f916(x91931),f916(x91931),f135(x91931),f114(x91931)),x91932)))+P1(f327(f327(f329(f916(x91931)),f727(x91932,x91931)),f327(f173(f916(x91931)),x91932))) % 177.41/177.19 [9234]~P1(f327(f138(x92341),f727(x92342,x92341)))+~P1(f327(f138(f916(x92341)),x92342))+P1(f327(f138(x92341),f327(f143(f916(x92341),f916(x92341),f135(x92341),f114(x92341)),x92342)))+P1(f327(f327(f329(f916(x92341)),f726(x92342,x92341)),f327(f173(f916(x92341)),x92342))) % 177.41/177.19 [9235]~P1(f327(f138(x92351),f727(x92352,x92351)))+~P1(f327(f138(f916(x92351)),x92352))+P1(f327(f138(x92351),f327(f143(f916(x92351),f916(x92351),f135(x92351),f114(x92351)),x92352)))+P1(f327(f327(f329(f916(x92351)),f725(x92352,x92351)),f327(f173(f916(x92351)),x92352))) % 177.41/177.19 [9312]~P1(f327(f138(f916(x93121)),x93122))+P1(f327(f138(x93121),f327(f143(f916(x93121),f916(x93121),f135(x93121),f114(x93121)),x93122)))+P1(f327(f327(f329(f916(x93121)),f726(x93122,x93121)),f327(f173(f916(x93121)),x93122)))+P1(f327(f327(f329(f916(x93121)),f727(x93122,x93121)),f327(f173(f916(x93121)),x93122))) % 177.41/177.19 [9313]~P1(f327(f138(f916(x93131)),x93132))+P1(f327(f138(x93131),f327(f143(f916(x93131),f916(x93131),f135(x93131),f114(x93131)),x93132)))+P1(f327(f327(f329(f916(x93131)),f725(x93132,x93131)),f327(f173(f916(x93131)),x93132)))+P1(f327(f327(f329(f916(x93131)),f727(x93132,x93131)),f327(f173(f916(x93131)),x93132))) % 177.41/177.19 [9327]~E(f327(f327(f103(f922(x93271,a910)),f327(f173(x93271),f726(x93272,x93271))),f327(f173(x93271),f725(x93272,x93271))),f190(f922(x93271,a910)))+~P1(f327(f138(x93271),f727(x93272,x93271)))+~P1(f327(f138(f916(x93271)),x93272))+P1(f327(f138(x93271),f327(f143(f916(x93271),f916(x93271),f135(x93271),f114(x93271)),x93272))) % 177.41/177.19 [9389]~E(f327(f327(f103(f922(x93891,a910)),f327(f173(x93891),f726(x93892,x93891))),f327(f173(x93891),f725(x93892,x93891))),f190(f922(x93891,a910)))+~P1(f327(f138(f916(x93891)),x93892))+P1(f327(f138(x93891),f327(f143(f916(x93891),f916(x93891),f135(x93891),f114(x93891)),x93892)))+P1(f327(f327(f329(f916(x93891)),f727(x93892,x93891)),f327(f173(f916(x93891)),x93892))) % 177.41/177.19 [9663]E(x96631,f2(a1))+E(x96632,f2(a1))+E(f327(f327(f86(a1,f921(a1,a1)),f327(f327(a219,x96632),x96631)),f327(f327(f18(a1,a1,f921(a1,a1)),f327(f327(f8(a1,f922(a1,f921(a1,a1)),a1),f252(a1,a1)),f327(f37(a1),x96632))),f327(f37(a1),x96631))),f217(x96632,x96631))+P1(f327(f327(f235(a1),x96631),f2(a1))) % 177.41/177.19 [8411]~P93(x84112)+~P119(x84112)+~P1(f327(f327(f234(x84112),f327(f105(x84112),x84111)),f78(x84112)))+P1(f327(f327(f234(a1),x84111),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))) % 177.41/177.19 [8412]~P93(x84122)+~P119(x84122)+~P1(f327(f327(f235(x84122),f327(f105(x84122),x84121)),f78(x84122)))+P1(f327(f327(f235(a1),x84121),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))) % 177.41/177.19 [8681]~P119(x86811)+~P93(x86811)+P1(f327(f327(f234(x86811),f327(f105(x86811),x86812)),f78(x86811)))+~P1(f327(f327(f234(a1),x86812),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))) % 177.41/177.19 [8682]~P119(x86821)+~P93(x86821)+P1(f327(f327(f235(x86821),f327(f105(x86821),x86822)),f78(x86821)))+~P1(f327(f327(f235(a1),x86822),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))) % 177.41/177.19 [8893]~P93(x88932)+~P119(x88932)+~P1(f327(f327(f234(x88932),f78(x88932)),f327(f105(x88932),x88931)))+P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),x88931)) % 177.41/177.19 [8894]~P93(x88942)+~P119(x88942)+~P1(f327(f327(f235(x88942),f78(x88942)),f327(f105(x88942),x88941)))+P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),x88941)) % 177.41/177.19 [9272]~P119(x92721)+~P93(x92721)+P1(f327(f327(f234(x92721),f78(x92721)),f327(f105(x92721),x92722)))+~P1(f327(f327(f234(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),x92722)) % 177.41/177.19 [9273]~P119(x92731)+~P93(x92731)+P1(f327(f327(f235(x92731),f78(x92731)),f327(f105(x92731),x92732)))+~P1(f327(f327(f235(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),x92732)) % 177.41/177.19 [9794]~P141(x97942)+E(x97941,f78(x97942))+E(x97941,f327(f79(x97942),f78(x97942)))+~E(f327(f327(f244(x97942),x97941),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f78(x97942)) % 177.41/177.19 [10063]~P63(x100631)+~P93(x100631)+~P1(f327(f327(f235(x100631),f2(x100631)),x100632))+P1(f327(f327(f235(x100631),f2(x100631)),f327(f327(f291(x100631),x100632),f327(f105(x100631),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.19 [10116]~P63(x101161)+~P93(x101161)+P1(f327(f327(f235(x101161),f2(x101161)),x101162))+~P1(f327(f327(f235(x101161),f2(x101161)),f327(f327(f291(x101161),x101162),f327(f105(x101161),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.19 [10411]~P142(x104112)+E(x104111,f2(a1))+P1(f327(f327(f235(a1),x104111),f2(a1)))+E(f327(f327(f257(a1,a1,x104112),f327(f327(f7(a1,f922(a1,f922(x104112,x104112)),f922(a1,x104112)),f327(f327(f8(f922(f922(x104112,x104112),x104112),f922(f922(a1,f922(x104112,x104112)),f922(a1,x104112)),a1),f8(f922(x104112,x104112),x104112,a1)),f327(f327(f8(x104112,f922(f922(x104112,x104112),x104112),a1),f86(x104112,x104112)),f104(x104112)))),f327(f327(f7(a1,f922(x104112,x104112),f922(x104112,x104112)),f327(f327(f8(f922(x104112,f922(x104112,x104112)),f922(f922(x104112,x104112),f922(x104112,x104112)),a1),f18(x104112,x104112,x104112)),f327(f327(f7(a1,f922(x104112,x104112),f922(x104112,f922(x104112,x104112))),f327(f327(f8(f922(x104112,f922(x104112,x104112)),f922(f922(x104112,x104112),f922(x104112,f922(x104112,x104112))),a1),f8(x104112,f922(x104112,x104112),x104112)),f327(f327(f8(a910,f922(x104112,f922(x104112,x104112)),a1),f97(x104112)),f327(f327(f7(a1,a1,a910),a324),f2(a1))))),f327(f327(f18(x104112,x104112,x104112),f80(x104112)),f5(x104112))))),f327(f327(f7(x104112,x104112,x104112),f327(f327(f8(x104112,f922(x104112,x104112),x104112),f80(x104112)),f327(f327(f18(x104112,x104112,x104112),f80(x104112)),f5(x104112)))),f78(x104112))))),f47(x104111,f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f104(x104112),x104111)) % 177.41/177.19 [5491]~P36(x54911,x54913)+~P49(x54911,x54913)+~P50(x54911,x54912,x54913)+P6(x54911,x54912,x54913) % 177.41/177.19 [5030]~P92(x50303)+~P93(x50303)+E(x50301,x50302)+~E(f327(f105(x50303),x50301),f327(f105(x50303),x50302)) % 177.41/177.19 [5501]~P47(x55011,x55012)+~P48(x55011,x55012)+P13(x55011,x55012)+~P1(f327(f327(x55012,x55013),x55013)) % 177.41/177.19 [6000]P13(x60002,x60001)+E(f327(x60001,f802(x60001)),f327(x60001,f803(x60001)))+P1(f327(f327(x60001,f802(x60001)),f803(x60001)))+~P1(f327(f327(x60001,x60003),x60003)) % 177.41/177.19 [6205]~P1(f327(x62051,x62052))+~P1(f327(x62051,x62053))+~P1(f327(f327(f234(a915),x62053),f449(x62052,x62051)))+P1(f327(x62051,f2(a915))) % 177.41/177.19 [6276]P13(x62761,x62762)+P1(f327(f327(x62762,f802(x62762)),f802(x62762)))+P1(f327(f327(x62762,f802(x62762)),f803(x62762)))+~P1(f327(f327(x62762,x62763),x62763)) % 177.41/177.19 [6277]P13(x62771,x62772)+P1(f327(f327(x62772,f802(x62772)),f803(x62772)))+P1(f327(f327(x62772,f803(x62772)),f803(x62772)))+~P1(f327(f327(x62772,x62773),x62773)) % 177.41/177.19 [6632]P148(x66322,x66323,x66321)+E(x66321,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f850(x66321,x66323,x66322)))+P1(f327(f327(f235(a1),x66321),f2(a1))) % 177.41/177.19 [6633]P147(x66332,x66333,x66331)+E(x66331,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f858(x66331,x66333,x66332)))+P1(f327(f327(f235(a1),x66331),f2(a1))) % 177.41/177.19 [6758]P147(x67581,x67582,x67583)+~P1(f327(x67581,x67582))+P1(f327(f327(f234(a1),f2(a1)),f858(x67583,x67582,x67581)))+P1(f327(f327(f235(a1),x67583),f2(a1))) % 177.41/177.19 [6783]P148(x67831,x67832,x67833)+P1(f327(f327(f234(a1),f2(a1)),f850(x67833,x67832,x67831)))+~P1(f327(x67831,f2(a1)))+P1(f327(f327(f235(a1),x67833),f2(a1))) % 177.41/177.19 [6813]P148(x68132,x68133,x68131)+E(x68131,f2(a1))+~P1(f327(x68132,f851(x68131,x68133,x68132)))+P1(f327(f327(f235(a1),x68131),f2(a1))) % 177.41/177.19 [6814]P147(x68142,x68143,x68141)+E(x68141,f2(a1))+~P1(f327(x68142,f858(x68141,x68143,x68142)))+P1(f327(f327(f235(a1),x68141),f2(a1))) % 177.41/177.19 [6915]~P108(x69151)+~P3(x69151)+~P1(f327(f327(f235(x69151),x69152),f38(x69151,x69153)))+P1(f327(f327(f235(x69151),x69152),f464(x69153,x69152,x69151))) % 177.41/177.19 [6925]P147(x69251,x69252,x69253)+~P1(f327(x69251,x69252))+~P1(f327(x69251,f858(x69253,x69252,x69251)))+P1(f327(f327(f235(a1),x69253),f2(a1))) % 177.41/177.19 [6955]P148(x69551,x69552,x69553)+~P1(f327(x69551,f851(x69553,x69552,x69551)))+~P1(f327(x69551,f2(a1)))+P1(f327(f327(f235(a1),x69553),f2(a1))) % 177.41/177.19 [7206]P148(x72062,x72063,x72061)+E(x72061,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f850(x72061,x72063,x72062)))+P1(f327(f327(f235(a1),x72061),f849(x72061,x72063,x72062))) % 177.41/177.19 [7207]P147(x72072,x72073,x72071)+E(x72071,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f858(x72071,x72073,x72072)))+P1(f327(f327(f235(a1),x72071),f857(x72071,x72073,x72072))) % 177.41/177.19 [7327]P147(x73271,x73272,x73273)+~P1(f327(x73271,x73272))+P1(f327(f327(f234(a1),f2(a1)),f858(x73273,x73272,x73271)))+P1(f327(f327(f235(a1),x73273),f857(x73273,x73272,x73271))) % 177.41/177.19 [7348]P148(x73481,x73482,x73483)+P1(f327(f327(f234(a1),f2(a1)),f850(x73483,x73482,x73481)))+P1(f327(f327(f235(a1),x73483),f849(x73483,x73482,x73481)))+~P1(f327(x73481,f2(a1))) % 177.41/177.19 [7381]P148(x73812,x73813,x73811)+E(x73811,f2(a1))+~P1(f327(x73812,f851(x73811,x73813,x73812)))+P1(f327(f327(f235(a1),x73811),f849(x73811,x73813,x73812))) % 177.41/177.19 [7382]P147(x73822,x73823,x73821)+E(x73821,f2(a1))+~P1(f327(x73822,f858(x73821,x73823,x73822)))+P1(f327(f327(f235(a1),x73821),f857(x73821,x73823,x73822))) % 177.41/177.19 [7426]P148(x74262,x74263,x74261)+E(x74261,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f850(x74261,x74263,x74262)))+~P1(f327(x74262,f856(x74261,x74263,x74262))) % 177.41/177.19 [7427]P147(x74272,x74273,x74271)+E(x74271,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f858(x74271,x74273,x74272)))+~P1(f327(x74272,f857(x74271,x74273,x74272))) % 177.41/177.19 [7523]P147(x75231,x75232,x75233)+~P1(f327(x75231,x75232))+~P1(f327(x75231,f858(x75233,x75232,x75231)))+P1(f327(f327(f235(a1),x75233),f857(x75233,x75232,x75231))) % 177.41/177.19 [7538]P148(x75381,x75382,x75383)+~P1(f327(x75381,f851(x75383,x75382,x75381)))+P1(f327(f327(f235(a1),x75383),f849(x75383,x75382,x75381)))+~P1(f327(x75381,f2(a1))) % 177.41/177.19 [7541]P147(x75411,x75412,x75413)+~P1(f327(x75411,x75412))+P1(f327(f327(f234(a1),f2(a1)),f858(x75413,x75412,x75411)))+~P1(f327(x75411,f857(x75413,x75412,x75411))) % 177.41/177.19 [7557]P148(x75571,x75572,x75573)+P1(f327(f327(f234(a1),f2(a1)),f850(x75573,x75572,x75571)))+~P1(f327(x75571,f856(x75573,x75572,x75571)))+~P1(f327(x75571,f2(a1))) % 177.41/177.19 [7578]P148(x75782,x75783,x75781)+E(x75781,f2(a1))+~P1(f327(x75782,f851(x75781,x75783,x75782)))+~P1(f327(x75782,f856(x75781,x75783,x75782))) % 177.41/177.19 [7579]P147(x75792,x75793,x75791)+E(x75791,f2(a1))+~P1(f327(x75792,f858(x75791,x75793,x75792)))+~P1(f327(x75792,f857(x75791,x75793,x75792))) % 177.41/177.19 [7665]P147(x76651,x76652,x76653)+~P1(f327(x76651,x76652))+~P1(f327(x76651,f858(x76653,x76652,x76651)))+~P1(f327(x76651,f857(x76653,x76652,x76651))) % 177.41/177.19 [7682]P148(x76821,x76822,x76823)+~P1(f327(x76821,f851(x76823,x76822,x76821)))+~P1(f327(x76821,f856(x76823,x76822,x76821)))+~P1(f327(x76821,f2(a1))) % 177.41/177.19 [7727]P148(x77272,x77273,x77271)+E(x77271,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f850(x77271,x77273,x77272)))+P1(f327(f327(f234(a1),f849(x77271,x77273,x77272)),f2(a1))) % 177.41/177.19 [7728]P147(x77282,x77283,x77281)+E(x77281,f2(a1))+P1(f327(f327(f234(a1),f2(a1)),f858(x77281,x77283,x77282)))+P1(f327(f327(f234(a1),f857(x77281,x77283,x77282)),f2(a1))) % 177.41/177.19 [7729]~P142(x77291)+~P1(f327(f327(f329(x77291),x77293),f111(x77291)))+~P1(f327(f327(f329(x77291),x77292),f111(x77291)))+P1(f327(f327(f329(x77291),f327(f327(f23(x77291),x77292),x77293)),f111(x77291))) % 177.41/177.19 [7730]~P142(x77301)+~P1(f327(f327(f329(x77301),x77303),f111(x77301)))+~P1(f327(f327(f329(x77301),x77302),f111(x77301)))+P1(f327(f327(f329(x77301),f327(f327(f80(x77301),x77302),x77303)),f111(x77301))) % 177.41/177.19 [7731]~P146(x77311)+~P1(f327(f327(f329(x77311),x77313),f187(x77311)))+~P1(f327(f327(f329(x77311),x77312),f187(x77311)))+P1(f327(f327(f329(x77311),f327(f327(f80(x77311),x77312),x77313)),f187(x77311))) % 177.41/177.19 [7732]~P142(x77321)+~P1(f327(f327(f329(x77321),x77323),f111(x77321)))+~P1(f327(f327(f329(x77321),x77322),f111(x77321)))+P1(f327(f327(f329(x77321),f327(f327(f81(x77321),x77322),x77323)),f111(x77321))) % 177.41/177.19 [7733]~P146(x77331)+~P1(f327(f327(f329(x77331),x77333),f187(x77331)))+~P1(f327(f327(f329(x77331),x77332),f187(x77331)))+P1(f327(f327(f329(x77331),f327(f327(f81(x77331),x77332),x77333)),f187(x77331))) % 177.41/177.19 [7734]~P88(x77341)+~P1(f327(f327(f234(x77341),x77343),f2(x77341)))+~P1(f327(f327(f234(x77341),x77342),f2(x77341)))+P1(f327(f327(f234(x77341),f327(f327(f80(x77341),x77342),x77343)),f2(x77341))) % 177.41/177.19 [7735]~P88(x77351)+~P1(f327(f327(f234(x77351),x77353),f2(x77351)))+~P1(f327(f327(f235(x77351),x77352),f2(x77351)))+P1(f327(f327(f235(x77351),f327(f327(f80(x77351),x77352),x77353)),f2(x77351))) % 177.41/177.19 [7736]~P88(x77361)+~P1(f327(f327(f234(x77361),x77362),f2(x77361)))+~P1(f327(f327(f235(x77361),x77363),f2(x77361)))+P1(f327(f327(f235(x77361),f327(f327(f80(x77361),x77362),x77363)),f2(x77361))) % 177.41/177.19 [7737]~P88(x77371)+~P1(f327(f327(f235(x77371),x77373),f2(x77371)))+~P1(f327(f327(f235(x77371),x77372),f2(x77371)))+P1(f327(f327(f235(x77371),f327(f327(f80(x77371),x77372),x77373)),f2(x77371))) % 177.41/177.19 [7764]P148(x77643,x77642,x77641)+E(x77641,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x77641),f851(x77641,x77642,x77643))),f850(x77641,x77642,x77643)),x77642)+P1(f327(f327(f235(a1),x77641),f2(a1))) % 177.41/177.19 [7765]P147(x77653,x77652,x77651)+E(x77651,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x77651),f859(x77651,x77652,x77653))),f858(x77651,x77652,x77653)),x77652)+P1(f327(f327(f235(a1),x77651),f2(a1))) % 177.41/177.19 [7848]P147(x78481,x78482,x78483)+~P1(f327(x78481,x78482))+P1(f327(f327(f234(a1),f2(a1)),f858(x78483,x78482,x78481)))+P1(f327(f327(f234(a1),f857(x78483,x78482,x78481)),f2(a1))) % 177.41/177.19 [7878]P148(x78781,x78782,x78783)+P1(f327(f327(f234(a1),f2(a1)),f850(x78783,x78782,x78781)))+~P1(f327(x78781,f2(a1)))+P1(f327(f327(f234(a1),f849(x78783,x78782,x78781)),f2(a1))) % 177.41/177.19 [7887]P147(x78873,x78872,x78871)+~P1(f327(x78873,x78872))+E(f327(f327(f80(a1),f327(f327(f81(a1),x78871),f859(x78871,x78872,x78873))),f858(x78871,x78872,x78873)),x78872)+P1(f327(f327(f235(a1),x78871),f2(a1))) % 177.41/177.19 [7893]P148(x78932,x78933,x78931)+E(x78931,f2(a1))+~P1(f327(x78932,f851(x78931,x78933,x78932)))+P1(f327(f327(f234(a1),f849(x78931,x78933,x78932)),f2(a1))) % 177.41/177.19 [7894]P147(x78942,x78943,x78941)+E(x78941,f2(a1))+~P1(f327(x78942,f858(x78941,x78943,x78942)))+P1(f327(f327(f234(a1),f857(x78941,x78943,x78942)),f2(a1))) % 177.41/177.19 [7899]P148(x78993,x78992,x78991)+E(f327(f327(f80(a1),f327(f327(f81(a1),x78991),f851(x78991,x78992,x78993))),f850(x78991,x78992,x78993)),x78992)+~P1(f327(x78993,f2(a1)))+P1(f327(f327(f235(a1),x78991),f2(a1))) % 177.41/177.19 [7955]P147(x79551,x79552,x79553)+~P1(f327(x79551,x79552))+~P1(f327(x79551,f858(x79553,x79552,x79551)))+P1(f327(f327(f234(a1),f857(x79553,x79552,x79551)),f2(a1))) % 177.41/177.19 [7959]P148(x79591,x79592,x79593)+~P1(f327(x79591,f851(x79593,x79592,x79591)))+~P1(f327(x79591,f2(a1)))+P1(f327(f327(f234(a1),f849(x79593,x79592,x79591)),f2(a1))) % 177.41/177.19 [8026]~P127(x80261)+~P1(f327(f327(f234(x80261),f327(f327(f81(x80261),x80263),x80262)),f2(x80261)))+P1(f327(f327(f234(x80261),x80262),f2(x80261)))+P1(f327(f327(f234(x80261),x80263),f2(x80261))) % 177.41/177.19 [8027]~P63(x80271)+~P1(f327(f327(f234(x80271),f327(f327(f291(x80271),x80273),x80272)),f2(x80271)))+P1(f327(f327(f234(x80271),x80272),f2(x80271)))+P1(f327(f327(f234(x80271),x80273),f2(x80271))) % 177.41/177.19 [8028]~P63(x80281)+~P1(f327(f327(f235(x80281),f327(f327(f291(x80281),x80283),x80282)),f2(x80281)))+P1(f327(f327(f235(x80281),x80282),f2(x80281)))+P1(f327(f327(f235(x80281),x80283),f2(x80281))) % 177.41/177.19 [8141]P148(x81413,x81412,x81411)+E(x81411,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x81411),f851(x81411,x81412,x81413))),f850(x81411,x81412,x81413)),x81412)+P1(f327(f327(f235(a1),x81411),f849(x81411,x81412,x81413))) % 177.41/177.19 [8142]P147(x81423,x81422,x81421)+E(x81421,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x81421),f859(x81421,x81422,x81423))),f858(x81421,x81422,x81423)),x81422)+P1(f327(f327(f235(a1),x81421),f857(x81421,x81422,x81423))) % 177.41/177.19 [8154]P148(x81543,x81542,x81541)+E(x81541,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x81541),f856(x81541,x81542,x81543))),f849(x81541,x81542,x81543)),x81542)+P1(f327(f327(f234(a1),f2(a1)),f850(x81541,x81542,x81543))) % 177.41/177.19 [8155]P147(x81553,x81552,x81551)+E(x81551,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x81551),f860(x81551,x81552,x81553))),f857(x81551,x81552,x81553)),x81552)+P1(f327(f327(f234(a1),f2(a1)),f858(x81551,x81552,x81553))) % 177.41/177.19 [8197]P147(x81973,x81972,x81971)+~P1(f327(x81973,x81972))+E(f327(f327(f80(a1),f327(f327(f81(a1),x81971),f859(x81971,x81972,x81973))),f858(x81971,x81972,x81973)),x81972)+P1(f327(f327(f235(a1),x81971),f857(x81971,x81972,x81973))) % 177.41/177.19 [8206]P148(x82063,x82062,x82061)+E(f327(f327(f80(a1),f327(f327(f81(a1),x82061),f851(x82061,x82062,x82063))),f850(x82061,x82062,x82063)),x82062)+P1(f327(f327(f235(a1),x82061),f849(x82061,x82062,x82063)))+~P1(f327(x82063,f2(a1))) % 177.41/177.19 [8212]P147(x82123,x82122,x82121)+~P1(f327(x82123,x82122))+E(f327(f327(f80(a1),f327(f327(f81(a1),x82121),f860(x82121,x82122,x82123))),f857(x82121,x82122,x82123)),x82122)+P1(f327(f327(f234(a1),f2(a1)),f858(x82121,x82122,x82123))) % 177.41/177.19 [8218]P148(x82183,x82182,x82181)+E(f327(f327(f80(a1),f327(f327(f81(a1),x82181),f856(x82181,x82182,x82183))),f849(x82181,x82182,x82183)),x82182)+P1(f327(f327(f234(a1),f2(a1)),f850(x82181,x82182,x82183)))+~P1(f327(x82183,f2(a1))) % 177.41/177.19 [8229]P148(x82293,x82292,x82291)+E(x82291,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x82291),f851(x82291,x82292,x82293))),f850(x82291,x82292,x82293)),x82292)+~P1(f327(x82293,f856(x82291,x82292,x82293))) % 177.41/177.19 [8230]P147(x82303,x82302,x82301)+E(x82301,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x82301),f859(x82301,x82302,x82303))),f858(x82301,x82302,x82303)),x82302)+~P1(f327(x82303,f857(x82301,x82302,x82303))) % 177.41/177.19 [8231]P148(x82313,x82312,x82311)+E(x82311,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x82311),f856(x82311,x82312,x82313))),f849(x82311,x82312,x82313)),x82312)+~P1(f327(x82313,f851(x82311,x82312,x82313))) % 177.41/177.19 [8232]P147(x82323,x82322,x82321)+E(x82321,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x82321),f860(x82321,x82322,x82323))),f857(x82321,x82322,x82323)),x82322)+~P1(f327(x82323,f858(x82321,x82322,x82323))) % 177.41/177.19 [8291]P147(x82913,x82912,x82911)+~P1(f327(x82913,x82912))+E(f327(f327(f80(a1),f327(f327(f81(a1),x82911),f859(x82911,x82912,x82913))),f858(x82911,x82912,x82913)),x82912)+~P1(f327(x82913,f857(x82911,x82912,x82913))) % 177.41/177.19 [8292]P147(x82923,x82922,x82921)+~P1(f327(x82923,x82922))+E(f327(f327(f80(a1),f327(f327(f81(a1),x82921),f860(x82921,x82922,x82923))),f857(x82921,x82922,x82923)),x82922)+~P1(f327(x82923,f858(x82921,x82922,x82923))) % 177.41/177.19 [8305]P148(x83053,x83052,x83051)+E(f327(f327(f80(a1),f327(f327(f81(a1),x83051),f851(x83051,x83052,x83053))),f850(x83051,x83052,x83053)),x83052)+~P1(f327(x83053,f856(x83051,x83052,x83053)))+~P1(f327(x83053,f2(a1))) % 177.41/177.19 [8306]P148(x83063,x83062,x83061)+E(f327(f327(f80(a1),f327(f327(f81(a1),x83061),f856(x83061,x83062,x83063))),f849(x83061,x83062,x83063)),x83062)+~P1(f327(x83063,f851(x83061,x83062,x83063)))+~P1(f327(x83063,f2(a1))) % 177.41/177.19 [8404]P148(x84043,x84042,x84041)+E(x84041,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x84041),f851(x84041,x84042,x84043))),f850(x84041,x84042,x84043)),x84042)+P1(f327(f327(f234(a1),f849(x84041,x84042,x84043)),f2(a1))) % 177.41/177.19 [8405]P147(x84053,x84052,x84051)+E(x84051,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x84051),f859(x84051,x84052,x84053))),f858(x84051,x84052,x84053)),x84052)+P1(f327(f327(f234(a1),f857(x84051,x84052,x84053)),f2(a1))) % 177.41/177.19 [8444]P147(x84443,x84442,x84441)+~P1(f327(x84443,x84442))+E(f327(f327(f80(a1),f327(f327(f81(a1),x84441),f859(x84441,x84442,x84443))),f858(x84441,x84442,x84443)),x84442)+P1(f327(f327(f234(a1),f857(x84441,x84442,x84443)),f2(a1))) % 177.41/177.19 [8449]P148(x84493,x84492,x84491)+E(f327(f327(f80(a1),f327(f327(f81(a1),x84491),f851(x84491,x84492,x84493))),f850(x84491,x84492,x84493)),x84492)+~P1(f327(x84493,f2(a1)))+P1(f327(f327(f234(a1),f849(x84491,x84492,x84493)),f2(a1))) % 177.41/177.19 [8583]P148(x85833,x85832,x85831)+E(x85831,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x85831),f856(x85831,x85832,x85833))),f849(x85831,x85832,x85833)),x85832)+E(f327(f327(f80(a1),f327(f327(f81(a1),x85831),f851(x85831,x85832,x85833))),f850(x85831,x85832,x85833)),x85832) % 177.41/177.19 [8584]P147(x85843,x85842,x85841)+E(x85841,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x85841),f860(x85841,x85842,x85843))),f857(x85841,x85842,x85843)),x85842)+E(f327(f327(f80(a1),f327(f327(f81(a1),x85841),f859(x85841,x85842,x85843))),f858(x85841,x85842,x85843)),x85842) % 177.41/177.19 [8604]P147(x86043,x86042,x86041)+~P1(f327(x86043,x86042))+E(f327(f327(f80(a1),f327(f327(f81(a1),x86041),f860(x86041,x86042,x86043))),f857(x86041,x86042,x86043)),x86042)+E(f327(f327(f80(a1),f327(f327(f81(a1),x86041),f859(x86041,x86042,x86043))),f858(x86041,x86042,x86043)),x86042) % 177.41/177.19 [8615]P148(x86153,x86152,x86151)+E(f327(f327(f80(a1),f327(f327(f81(a1),x86151),f856(x86151,x86152,x86153))),f849(x86151,x86152,x86153)),x86152)+E(f327(f327(f80(a1),f327(f327(f81(a1),x86151),f851(x86151,x86152,x86153))),f850(x86151,x86152,x86153)),x86152)+~P1(f327(x86153,f2(a1))) % 177.41/177.19 [9280]~P127(x92801)+~E(x92803,f2(x92801))+~E(x92802,f2(x92801))+P1(f327(f327(f234(x92801),f327(f327(f80(x92801),f327(f327(f81(x92801),x92802),x92802)),f327(f327(f81(x92801),x92803),x92803))),f2(x92801))) % 177.41/177.19 [10350]~P119(x103501)+~E(x103503,f2(x103501))+~E(x103502,f2(x103501))+P1(f327(f327(f234(x103501),f327(f327(f80(x103501),f327(f327(f244(x103501),x103502),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x103501),x103503),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))),f2(x103501))) % 177.41/177.19 [4978]~E(x49783,x49781)+~P122(x49782)+E(x49781,f2(x49782))+E(f327(f327(f291(x49782),x49783),x49781),f78(x49782)) % 177.41/177.19 [5031]~P98(x50311)+~E(x50313,f190(x50311))+~E(x50312,f190(x50311))+E(f327(f327(f102(x50311),x50312),x50313),f190(x50311)) % 177.41/177.19 [5032]~P97(x50321)+~E(x50323,f242(x50321))+~E(x50322,f242(x50321))+E(f327(f327(f103(x50321),x50322),x50323),f242(x50321)) % 177.41/177.19 [5125]~P122(x51253)+E(x51251,x51252)+E(x51252,f2(x51253))+~E(f327(f327(f291(x51253),x51251),x51252),f78(x51253)) % 177.41/177.19 [5143]~P134(x51432)+E(x51431,f2(x51432))+E(x51433,f2(x51432))+~E(f327(f327(f81(x51432),x51433),x51431),f2(x51432)) % 177.41/177.19 [5144]~P143(x51442)+E(x51441,f2(x51442))+E(x51443,f2(x51442))+~E(f327(f327(f81(x51442),x51443),x51441),f2(x51442)) % 177.41/177.19 [5520]~P120(x55203)+E(x55201,x55202)+E(x55201,f327(f79(x55203),x55202))+~E(f327(f327(f81(x55203),x55201),x55201),f327(f327(f81(x55203),x55202),x55202)) % 177.41/177.19 [5559]~P86(x55591)+E(f327(f79(x55591),x55592),x55593)+~E(f327(f327(f102(x55591),x55592),x55593),f242(x55591))+~E(f327(f327(f103(x55591),x55592),x55593),f190(x55591)) % 177.41/177.19 [5640]~P119(x56403)+E(x56401,x56402)+P1(f327(f327(f235(x56403),x56402),x56401))+P1(f327(f327(f235(x56403),x56401),x56402)) % 177.41/177.19 [5641]~P108(x56413)+E(x56411,x56412)+P1(f327(f327(f235(x56413),x56412),x56411))+P1(f327(f327(f235(x56413),x56411),x56412)) % 177.41/177.19 [5642]~E(x56422,x56423)+~P108(x56421)+P1(f327(f327(f235(x56421),x56422),x56423))+P1(f327(f327(f234(x56421),x56422),x56423)) % 177.41/177.19 [5904]~P110(x59043)+E(x59041,x59042)+~P1(f327(f327(f234(x59043),x59042),x59041))+P1(f327(f327(f235(x59043),x59042),x59041)) % 177.41/177.19 [5906]~P108(x59063)+E(x59061,x59062)+~P1(f327(f327(f234(x59063),x59061),x59062))+P1(f327(f327(f235(x59063),x59061),x59062)) % 177.41/177.19 [5912]~P110(x59123)+E(x59121,x59122)+~P1(f327(f327(f234(x59123),x59121),x59122))+P1(f327(f327(f235(x59123),x59121),x59122)) % 177.41/177.19 [6017]P147(x60171,x60172,x60173)+~P1(f327(x60171,x60172))+P1(f327(f327(f235(a1),x60173),f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x60173)) % 177.41/177.19 [6071]P148(x60711,x60712,x60713)+~P1(f327(x60711,f2(a1)))+P1(f327(f327(f235(a1),x60713),f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x60713)) % 177.41/177.19 [6076]~P96(x60761)+E(f327(f327(f102(x60761),x60762),f10(x60761,x60763)),x60762)+~P1(f327(f35(x60761),x60763))+~P1(f327(f327(f329(x60761),x60762),x60763)) % 177.41/177.19 [6077]~P96(x60771)+E(f327(f327(f103(x60771),x60772),f13(x60771,x60773)),x60772)+~P1(f327(f35(x60771),x60773))+~P1(f327(f327(f329(x60771),x60772),x60773)) % 177.41/177.19 [6115]~P108(x61151)+E(f327(f327(f238(x61151),x61152),f15(x61151,x61153)),f15(x61151,x61153))+~P1(f327(f35(x61151),x61153))+~P1(f327(f327(f329(x61151),x61152),x61153)) % 177.41/177.19 [6116]~P108(x61161)+E(f327(f327(f189(x61161),x61162),f14(x61161,x61163)),f14(x61161,x61163))+~P1(f327(f35(x61161),x61163))+~P1(f327(f327(f329(x61161),x61162),x61163)) % 177.41/177.19 [6117]~P96(x61171)+E(f327(f327(f102(x61171),x61172),f13(x61171,x61173)),f13(x61171,x61173))+~P1(f327(f35(x61171),x61173))+~P1(f327(f327(f329(x61171),x61172),x61173)) % 177.41/177.19 [6118]~P96(x61181)+E(f327(f327(f103(x61181),x61182),f10(x61181,x61183)),f10(x61181,x61183))+~P1(f327(f35(x61181),x61183))+~P1(f327(f327(f329(x61181),x61182),x61183)) % 177.41/177.19 [6157]E(x61571,x61572)+~P110(x61573)+~P1(f327(f327(f234(x61573),x61572),x61571))+~P1(f327(f327(f234(x61573),x61571),x61572)) % 177.41/177.19 [6305]~P107(x63051)+P1(f327(f327(f235(x63051),x63053),x63052))+~P1(f327(f327(f234(x63051),x63053),x63052))+P1(f327(f327(f234(x63051),x63052),x63053)) % 177.41/177.19 [6332]~P108(x63321)+~P1(f327(f35(x63321),x63323))+P1(f327(f327(f234(x63321),x63322),f14(x63321,x63323)))+~P1(f327(f327(f329(x63321),x63322),x63323)) % 177.41/177.19 [6379]~P108(x63791)+E(f327(f327(f238(x63791),x63792),f11(x63791,f189(x63791),x63793)),x63792)+~P1(f327(f35(x63791),x63793))+~P1(f327(f327(f329(x63791),x63792),x63793)) % 177.41/177.19 [6380]~P108(x63801)+E(f327(f327(f189(x63801),x63802),f12(x63801,f238(x63801),x63803)),x63802)+~P1(f327(f35(x63801),x63803))+~P1(f327(f327(f329(x63801),x63802),x63803)) % 177.41/177.19 [6522]E(x65221,x65222)+~E(f327(f327(f23(a915),x65221),x65223),f327(f327(f23(a915),x65222),x65223))+~P1(f327(f327(f234(a915),x65223),x65221))+~P1(f327(f327(f234(a915),x65223),x65222)) % 177.41/177.19 [6549]~P108(x65491)+~P1(f327(f35(x65491),x65492))+~P1(f327(f327(f329(x65491),x65493),x65492))+P1(f327(f327(f234(x65491),f15(x65491,x65492)),x65493)) % 177.41/177.19 [6611]P148(x66112,x66113,x66111)+E(x66111,f2(a1))+P1(f327(f327(f235(a1),x66111),f849(x66111,x66113,x66112)))+P1(f327(f327(f235(a1),f2(a1)),x66111)) % 177.41/177.19 [6612]P147(x66122,x66123,x66121)+E(x66121,f2(a1))+P1(f327(f327(f235(a1),x66121),f857(x66121,x66123,x66122)))+P1(f327(f327(f235(a1),f2(a1)),x66121)) % 177.41/177.19 [6613]~P108(x66131)+E(f327(f327(f238(x66131),x66132),f12(x66131,f238(x66131),x66133)),f12(x66131,f238(x66131),x66133))+~P1(f327(f35(x66131),x66133))+~P1(f327(f327(f329(x66131),x66132),x66133)) % 177.41/177.19 [6614]~P108(x66141)+E(f327(f327(f189(x66141),x66142),f11(x66141,f189(x66141),x66143)),f11(x66141,f189(x66141),x66143))+~P1(f327(f35(x66141),x66143))+~P1(f327(f327(f329(x66141),x66142),x66143)) % 177.41/177.19 [6619]~P1(f327(x66191,x66192))+P1(f327(x66191,f502(x66192,x66191,x66193)))+P1(f327(x66191,f2(a915)))+~P1(f327(f327(f235(a915),x66192),x66193)) % 177.41/177.19 [6677]~P1(f327(x66771,x66772))+~P1(f327(f35(x66773),x66772))+P1(f327(x66771,f418(x66771,x66772,x66773)))+P1(f327(x66771,f190(f922(x66773,a910)))) % 177.41/177.19 [6690]~P119(x66901)+~P93(x66901)+P1(f327(f327(f234(x66901),f327(f105(x66901),x66902)),f327(f105(x66901),x66903)))+~P1(f327(f327(f234(a1),x66902),x66903)) % 177.41/177.19 [6691]~P119(x66911)+~P93(x66911)+P1(f327(f327(f235(x66911),f327(f105(x66911),x66912)),f327(f105(x66911),x66913)))+~P1(f327(f327(f235(a1),x66912),x66913)) % 177.41/177.19 [6694]~P1(f327(x66941,x66943))+~P1(f327(f35(x66942),x66943))+P1(f327(f35(x66942),f418(x66941,x66943,x66942)))+P1(f327(x66941,f190(f922(x66942,a910)))) % 177.41/177.19 [6728]P147(x67281,x67282,x67283)+~P1(f327(x67281,x67282))+P1(f327(f327(f235(a1),x67283),f857(x67283,x67282,x67281)))+P1(f327(f327(f235(a1),f2(a1)),x67283)) % 177.41/177.19 [6764]P148(x67641,x67642,x67643)+P1(f327(f327(f235(a1),x67643),f849(x67643,x67642,x67641)))+~P1(f327(x67641,f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x67643)) % 177.41/177.19 [6794]~P109(x67941)+~P94(x67941)+E(f327(f327(f238(x67941),f327(f105(x67941),x67942)),f327(f105(x67941),x67943)),f327(f105(x67941),x67943))+P1(f327(f327(f234(x67941),f327(f105(x67941),x67942)),f327(f105(x67941),x67943))) % 177.41/177.19 [6795]~P109(x67951)+~P94(x67951)+E(f327(f327(f189(x67951),f327(f105(x67951),x67952)),f327(f105(x67951),x67953)),f327(f105(x67951),x67952))+P1(f327(f327(f234(x67951),f327(f105(x67951),x67952)),f327(f105(x67951),x67953))) % 177.41/177.19 [6853]P148(x68532,x68533,x68531)+E(x68531,f2(a1))+~P1(f327(x68532,f856(x68531,x68533,x68532)))+P1(f327(f327(f235(a1),f2(a1)),x68531)) % 177.41/177.19 [6854]P147(x68542,x68543,x68541)+E(x68541,f2(a1))+~P1(f327(x68542,f857(x68541,x68543,x68542)))+P1(f327(f327(f235(a1),f2(a1)),x68541)) % 177.41/177.19 [6858]P1(f327(x68581,x68582))+~P1(f327(f35(x68583),x68582))+P1(f327(x68581,f409(x68581,x68582,x68583)))+~P1(f327(x68581,f190(f922(x68583,a910)))) % 177.41/177.19 [6879]P1(f327(x68791,x68792))+P1(f327(f35(x68793),f409(x68791,x68792,x68793)))+~P1(f327(f35(x68793),x68792))+~P1(f327(x68791,f190(f922(x68793,a910)))) % 177.41/177.19 [6944]P147(x69441,x69442,x69443)+~P1(f327(x69441,x69442))+~P1(f327(x69441,f857(x69443,x69442,x69441)))+P1(f327(f327(f235(a1),f2(a1)),x69443)) % 177.41/177.19 [6974]P148(x69741,x69742,x69743)+~P1(f327(x69741,f856(x69743,x69742,x69741)))+~P1(f327(x69741,f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x69743)) % 177.41/177.19 [7082]~P93(x70823)+~P119(x70823)+~P1(f327(f327(f234(x70823),f327(f105(x70823),x70821)),f327(f105(x70823),x70822)))+P1(f327(f327(f234(a1),x70821),x70822)) % 177.41/177.19 [7083]~P93(x70833)+~P119(x70833)+~P1(f327(f327(f235(x70833),f327(f105(x70833),x70831)),f327(f105(x70833),x70832)))+P1(f327(f327(f235(a1),x70831),x70832)) % 177.41/177.19 [7111]~P108(x71111)+~P11(x71111,x71113)+P11(x71111,f327(f327(f152(x71111),x71112),x71113))+~P1(f327(f327(f234(x71111),x71112),f706(x71113,x71112,x71111))) % 177.41/177.19 [7112]~P108(x71121)+~P11(x71121,x71123)+P11(x71121,f327(f327(f152(x71121),x71122),x71123))+~P1(f327(f327(f234(x71121),x71122),f708(x71123,x71122,x71121))) % 177.41/177.19 [7113]~P108(x71131)+~P11(x71131,x71133)+P11(x71131,f327(f327(f152(x71131),x71132),x71133))+~P1(f327(f327(f234(x71131),x71132),f747(x71132,x71133,x71131))) % 177.41/177.19 [7198]P148(x71982,x71983,x71981)+E(x71981,f2(a1))+P1(f327(f327(f235(a1),x71981),f2(a1)))+P1(f327(f327(f235(a1),f850(x71981,x71983,x71982)),x71981)) % 177.41/177.19 [7199]P147(x71992,x71993,x71991)+E(x71991,f2(a1))+P1(f327(f327(f235(a1),x71991),f2(a1)))+P1(f327(f327(f235(a1),f858(x71991,x71993,x71992)),x71991)) % 177.41/177.19 [7237]P148(x72372,x72373,x72371)+E(x72371,f2(a1))+P1(f327(f327(f234(a1),f849(x72371,x72373,x72372)),f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x72371)) % 177.41/177.19 [7238]P147(x72382,x72383,x72381)+E(x72381,f2(a1))+P1(f327(f327(f234(a1),f857(x72381,x72383,x72382)),f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x72381)) % 177.41/177.19 [7263]~P108(x72631)+~P11(x72631,x72633)+E(f327(f327(f149(x72631,x72631,f5(x72631)),x72632),f171(x72631,x72632,x72633)),x72633)+~P1(f327(f327(f329(x72631),x72632),f327(f173(x72631),x72633))) % 177.41/177.19 [7310]P147(x73101,x73102,x73103)+~P1(f327(x73101,x73102))+P1(f327(f327(f235(a1),x73103),f2(a1)))+P1(f327(f327(f235(a1),f858(x73103,x73102,x73101)),x73103)) % 177.41/177.19 [7316]~P109(x73161)+~P94(x73161)+E(f327(f327(f238(x73161),f327(f105(x73161),x73162)),f327(f105(x73161),x73163)),f327(f105(x73161),x73162))+~P1(f327(f327(f234(x73161),f327(f105(x73161),x73162)),f327(f105(x73161),x73163))) % 177.41/177.19 [7317]~P109(x73171)+~P94(x73171)+E(f327(f327(f189(x73171),f327(f105(x73171),x73172)),f327(f105(x73171),x73173)),f327(f105(x73171),x73173))+~P1(f327(f327(f234(x73171),f327(f105(x73171),x73172)),f327(f105(x73171),x73173))) % 177.41/177.19 [7331]P148(x73311,x73312,x73313)+~P1(f327(x73311,f2(a1)))+P1(f327(f327(f235(a1),x73313),f2(a1)))+P1(f327(f327(f235(a1),f850(x73313,x73312,x73311)),x73313)) % 177.41/177.19 [7341]P147(x73411,x73412,x73413)+~P1(f327(x73411,x73412))+P1(f327(f327(f234(a1),f857(x73413,x73412,x73411)),f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x73413)) % 177.41/177.19 [7365]P148(x73651,x73652,x73653)+~P1(f327(x73651,f2(a1)))+P1(f327(f327(f234(a1),f849(x73653,x73652,x73651)),f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x73653)) % 177.41/177.19 [7393]~P1(f327(x73931,x73932))+P1(f327(x73931,f2(a915)))+~P1(f327(f327(f235(a915),x73932),x73933))+P1(f327(f327(f235(a915),f502(x73932,x73931,x73933)),x73933)) % 177.41/177.19 [7410]~P108(x74101)+~P11(x74101,x74103)+P11(x74101,f327(f327(f152(x74101),x74102),x74103))+P1(f327(f327(f329(x74101),f706(x74103,x74102,x74101)),f327(f173(x74101),x74103))) % 177.41/177.19 [7411]~P108(x74111)+~P11(x74111,x74113)+P11(x74111,f327(f327(f152(x74111),x74112),x74113))+P1(f327(f327(f329(x74111),f708(x74113,x74112,x74111)),f327(f173(x74111),x74113))) % 177.41/177.19 [7412]~P108(x74121)+~P11(x74121,x74123)+P11(x74121,f327(f327(f152(x74121),x74122),x74123))+P1(f327(f327(f329(x74121),f747(x74122,x74123,x74121)),f327(f173(x74121),x74123))) % 177.41/177.19 [7527]~P108(x75271)+~P3(x75271)+~P1(f327(f327(f235(x75271),x75273),f38(x75271,x75272)))+P1(f327(f327(f329(x75271),f464(x75272,x75273,x75271)),x75272)) % 177.41/177.19 [7680]~P108(x76801)+~P3(x76801)+~P1(f327(f327(f235(x76801),f39(x76801,x76803)),x76802))+P1(f327(f327(f329(x76801),f351(x76802,x76803,x76801)),x76803)) % 177.41/177.19 [7681]~P108(x76811)+~P3(x76811)+~P1(f327(f327(f235(x76811),f39(x76811,x76813)),x76812))+P1(f327(f327(f235(x76811),f351(x76812,x76813,x76811)),x76812)) % 177.41/177.19 [7693]P148(x76932,x76933,x76931)+E(x76931,f2(a1))+P1(f327(f327(f235(a1),x76931),f849(x76931,x76933,x76932)))+P1(f327(f327(f235(a1),f850(x76931,x76933,x76932)),x76931)) % 177.41/177.19 [7694]P147(x76942,x76943,x76941)+E(x76941,f2(a1))+P1(f327(f327(f235(a1),x76941),f857(x76941,x76943,x76942)))+P1(f327(f327(f235(a1),f858(x76941,x76943,x76942)),x76941)) % 177.41/177.19 [7787]P148(x77873,x77872,x77871)+E(x77871,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x77871),f856(x77871,x77872,x77873))),f849(x77871,x77872,x77873)),x77872)+P1(f327(f327(f235(a1),f2(a1)),x77871)) % 177.41/177.19 [7788]P147(x77883,x77882,x77881)+E(x77881,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x77881),f860(x77881,x77882,x77883))),f857(x77881,x77882,x77883)),x77882)+P1(f327(f327(f235(a1),f2(a1)),x77881)) % 177.41/177.19 [7790]~P127(x77901)+~P1(f327(f327(f234(x77901),x77903),f2(x77901)))+P1(f327(f327(f234(x77901),f327(f327(f81(x77901),x77902),x77903)),f2(x77901)))+~P1(f327(f327(f234(x77901),f2(x77901)),x77902)) % 177.41/177.19 [7791]~P127(x77911)+~P1(f327(f327(f234(x77911),x77912),f2(x77911)))+P1(f327(f327(f234(x77911),f327(f327(f81(x77911),x77912),x77913)),f2(x77911)))+~P1(f327(f327(f234(x77911),f2(x77911)),x77913)) % 177.41/177.19 [7793]~P135(x77931)+~P1(f327(f327(f234(x77931),x77933),f2(x77931)))+P1(f327(f327(f234(x77931),f327(f327(f81(x77931),x77932),x77933)),f2(x77931)))+~P1(f327(f327(f234(x77931),f2(x77931)),x77932)) % 177.41/177.19 [7795]~P135(x77951)+~P1(f327(f327(f234(x77951),x77952),f2(x77951)))+P1(f327(f327(f234(x77951),f327(f327(f81(x77951),x77952),x77953)),f2(x77951)))+~P1(f327(f327(f234(x77951),f2(x77951)),x77953)) % 177.41/177.19 [7796]~P63(x77961)+~P1(f327(f327(f234(x77961),x77963),f2(x77961)))+P1(f327(f327(f234(x77961),f327(f327(f291(x77961),x77962),x77963)),f2(x77961)))+~P1(f327(f327(f234(x77961),f2(x77961)),x77962)) % 177.41/177.19 [7797]~P63(x77971)+~P1(f327(f327(f234(x77971),x77972),f2(x77971)))+P1(f327(f327(f234(x77971),f327(f327(f291(x77971),x77972),x77973)),f2(x77971)))+~P1(f327(f327(f234(x77971),f2(x77971)),x77973)) % 177.41/177.19 [7798]~P64(x77981)+~P1(f327(f327(f234(x77981),x77982),f2(x77981)))+P1(f327(f327(f234(x77981),f327(f327(f291(x77981),x77982),x77983)),f2(x77981)))+~P1(f327(f327(f235(x77981),f2(x77981)),x77983)) % 177.41/177.19 [7799]~P64(x77991)+~P1(f327(f327(f235(x77991),x77993),f2(x77991)))+P1(f327(f327(f234(x77991),f327(f327(f291(x77991),x77992),x77993)),f2(x77991)))+~P1(f327(f327(f234(x77991),f2(x77991)),x77992)) % 177.41/177.19 [7801]~P130(x78011)+~P1(f327(f327(f235(x78011),x78013),f2(x78011)))+P1(f327(f327(f235(x78011),f327(f327(f81(x78011),x78012),x78013)),f2(x78011)))+~P1(f327(f327(f235(x78011),f2(x78011)),x78012)) % 177.41/177.19 [7802]~P130(x78021)+~P1(f327(f327(f235(x78021),x78022),f2(x78021)))+P1(f327(f327(f235(x78021),f327(f327(f81(x78021),x78022),x78023)),f2(x78021)))+~P1(f327(f327(f235(x78021),f2(x78021)),x78023)) % 177.41/177.19 [7803]~P63(x78031)+~P1(f327(f327(f235(x78031),x78033),f2(x78031)))+P1(f327(f327(f235(x78031),f327(f327(f291(x78031),x78032),x78033)),f2(x78031)))+~P1(f327(f327(f235(x78031),f2(x78031)),x78032)) % 177.41/177.19 [7804]~P63(x78041)+~P1(f327(f327(f235(x78041),x78042),f2(x78041)))+P1(f327(f327(f235(x78041),f327(f327(f291(x78041),x78042),x78043)),f2(x78041)))+~P1(f327(f327(f235(x78041),f2(x78041)),x78043)) % 177.41/177.19 [7805]~P64(x78051)+~P1(f327(f327(f235(x78051),x78053),f2(x78051)))+P1(f327(f327(f235(x78051),f327(f327(f291(x78051),x78052),x78053)),f2(x78051)))+~P1(f327(f327(f235(x78051),f2(x78051)),x78052)) % 177.41/177.19 [7806]~P64(x78061)+~P1(f327(f327(f235(x78061),x78062),f2(x78061)))+P1(f327(f327(f235(x78061),f327(f327(f291(x78061),x78062),x78063)),f2(x78061)))+~P1(f327(f327(f235(x78061),f2(x78061)),x78063)) % 177.41/177.19 [7821]P147(x78211,x78212,x78213)+~P1(f327(x78211,x78212))+P1(f327(f327(f235(a1),x78213),f857(x78213,x78212,x78211)))+P1(f327(f327(f235(a1),f858(x78213,x78212,x78211)),x78213)) % 177.41/177.19 [7834]P148(x78341,x78342,x78343)+P1(f327(f327(f235(a1),x78343),f849(x78343,x78342,x78341)))+~P1(f327(x78341,f2(a1)))+P1(f327(f327(f235(a1),f850(x78343,x78342,x78341)),x78343)) % 177.41/177.19 [7885]P148(x78852,x78853,x78851)+E(x78851,f2(a1))+~P1(f327(x78852,f856(x78851,x78853,x78852)))+P1(f327(f327(f235(a1),f850(x78851,x78853,x78852)),x78851)) % 177.41/177.19 [7886]P147(x78862,x78863,x78861)+E(x78861,f2(a1))+~P1(f327(x78862,f857(x78861,x78863,x78862)))+P1(f327(f327(f235(a1),f858(x78861,x78863,x78862)),x78861)) % 177.41/177.19 [7896]P147(x78963,x78962,x78961)+~P1(f327(x78963,x78962))+E(f327(f327(f80(a1),f327(f327(f81(a1),x78961),f860(x78961,x78962,x78963))),f857(x78961,x78962,x78963)),x78962)+P1(f327(f327(f235(a1),f2(a1)),x78961)) % 177.41/177.19 [7911]P148(x79113,x79112,x79111)+E(f327(f327(f80(a1),f327(f327(f81(a1),x79111),f856(x79111,x79112,x79113))),f849(x79111,x79112,x79113)),x79112)+~P1(f327(x79113,f2(a1)))+P1(f327(f327(f235(a1),f2(a1)),x79111)) % 177.41/177.19 [7939]~P1(f327(x79391,x79393))+~P1(f327(f35(x79392),x79393))+P1(f327(f327(f329(x79392),f419(x79391,x79393,x79392)),f418(x79391,x79393,x79392)))+P1(f327(x79391,f190(f922(x79392,a910)))) % 177.41/177.19 [7950]P147(x79501,x79502,x79503)+~P1(f327(x79501,x79502))+~P1(f327(x79501,f857(x79503,x79502,x79501)))+P1(f327(f327(f235(a1),f858(x79503,x79502,x79501)),x79503)) % 177.41/177.19 [7956]P148(x79561,x79562,x79563)+~P1(f327(x79561,f856(x79563,x79562,x79561)))+~P1(f327(x79561,f2(a1)))+P1(f327(f327(f235(a1),f850(x79563,x79562,x79561)),x79563)) % 177.41/177.19 [8057]~P127(x80571)+~P1(f327(f327(f234(x80571),f327(f327(f81(x80571),x80573),x80572)),f2(x80571)))+P1(f327(f327(f234(x80571),x80572),f2(x80571)))+P1(f327(f327(f234(x80571),f2(x80571)),x80572)) % 177.41/177.19 [8058]~P127(x80581)+~P1(f327(f327(f234(x80581),f327(f327(f81(x80581),x80582),x80583)),f2(x80581)))+P1(f327(f327(f234(x80581),x80582),f2(x80581)))+P1(f327(f327(f234(x80581),f2(x80581)),x80582)) % 177.41/177.19 [8059]~P63(x80591)+~P1(f327(f327(f234(x80591),f327(f327(f291(x80591),x80593),x80592)),f2(x80591)))+P1(f327(f327(f234(x80591),x80592),f2(x80591)))+P1(f327(f327(f234(x80591),f2(x80591)),x80592)) % 177.41/177.19 [8060]~P63(x80601)+~P1(f327(f327(f234(x80601),f327(f327(f291(x80601),x80602),x80603)),f2(x80601)))+P1(f327(f327(f234(x80601),x80602),f2(x80601)))+P1(f327(f327(f234(x80601),f2(x80601)),x80602)) % 177.41/177.19 [8061]~P63(x80611)+~P1(f327(f327(f235(x80611),f327(f327(f291(x80611),x80613),x80612)),f2(x80611)))+P1(f327(f327(f235(x80611),x80612),f2(x80611)))+P1(f327(f327(f235(x80611),f2(x80611)),x80612)) % 177.41/177.19 [8062]~P63(x80621)+~P1(f327(f327(f235(x80621),f327(f327(f291(x80621),x80622),x80623)),f2(x80621)))+P1(f327(f327(f235(x80621),x80622),f2(x80621)))+P1(f327(f327(f235(x80621),f2(x80621)),x80622)) % 177.41/177.19 [8086]~P127(x80861)+~P1(f327(f327(f234(x80861),f327(f327(f81(x80861),x80862),x80863)),f2(x80861)))+P1(f327(f327(f234(x80861),f2(x80861)),x80862))+P1(f327(f327(f234(x80861),f2(x80861)),x80863)) % 177.41/177.19 [8087]~P63(x80871)+~P1(f327(f327(f234(x80871),f327(f327(f291(x80871),x80872),x80873)),f2(x80871)))+P1(f327(f327(f234(x80871),f2(x80871)),x80872))+P1(f327(f327(f234(x80871),f2(x80871)),x80873)) % 177.41/177.19 [8088]~P63(x80881)+~P1(f327(f327(f235(x80881),f327(f327(f291(x80881),x80882),x80883)),f2(x80881)))+P1(f327(f327(f235(x80881),f2(x80881)),x80882))+P1(f327(f327(f235(x80881),f2(x80881)),x80883)) % 177.41/177.19 [8110]P148(x81102,x81103,x81101)+E(x81101,f2(a1))+P1(f327(f327(f234(a1),f849(x81101,x81103,x81102)),f2(a1)))+P1(f327(f327(f235(a1),f850(x81101,x81103,x81102)),x81101)) % 177.41/177.19 [8111]P147(x81112,x81113,x81111)+E(x81111,f2(a1))+P1(f327(f327(f234(a1),f857(x81111,x81113,x81112)),f2(a1)))+P1(f327(f327(f235(a1),f858(x81111,x81113,x81112)),x81111)) % 177.41/177.19 [8118]~P126(x81181)+~P1(f327(f327(f235(x81181),x81182),f78(x81181)))+P1(f327(f327(f235(x81181),f327(f327(f244(x81181),x81182),f327(a113,x81183))),f78(x81181)))+~P1(f327(f327(f235(x81181),f2(x81181)),x81182)) % 177.41/177.19 [8171]~P108(x81711)+~E(x81713,f114(x81711))+~P11(x81711,f327(f169(x81711),x81713))+E(f327(f143(x81711,x81711,f327(f7(x81711,x81711,x81711),f189(x81711)),x81712),f327(f169(x81711),x81713)),x81712) % 177.41/177.19 [8174]P147(x81741,x81742,x81743)+~P1(f327(x81741,x81742))+P1(f327(f327(f234(a1),f857(x81743,x81742,x81741)),f2(a1)))+P1(f327(f327(f235(a1),f858(x81743,x81742,x81741)),x81743)) % 177.41/177.19 [8181]P148(x81811,x81812,x81813)+~P1(f327(x81811,f2(a1)))+P1(f327(f327(f234(a1),f849(x81813,x81812,x81811)),f2(a1)))+P1(f327(f327(f235(a1),f850(x81813,x81812,x81811)),x81813)) % 177.41/177.19 [8399]P148(x83993,x83992,x83991)+E(x83991,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x83991),f856(x83991,x83992,x83993))),f849(x83991,x83992,x83993)),x83992)+P1(f327(f327(f235(a1),f850(x83991,x83992,x83993)),x83991)) % 177.41/177.19 [8400]P147(x84003,x84002,x84001)+E(x84001,f2(a1))+E(f327(f327(f80(a1),f327(f327(f81(a1),x84001),f860(x84001,x84002,x84003))),f857(x84001,x84002,x84003)),x84002)+P1(f327(f327(f235(a1),f858(x84001,x84002,x84003)),x84001)) % 177.41/177.19 [8435]P147(x84353,x84352,x84351)+~P1(f327(x84353,x84352))+E(f327(f327(f80(a1),f327(f327(f81(a1),x84351),f860(x84351,x84352,x84353))),f857(x84351,x84352,x84353)),x84352)+P1(f327(f327(f235(a1),f858(x84351,x84352,x84353)),x84351)) % 177.41/177.19 [8436]~P68(x84361)+~P75(x84361)+~P38(x84363)+E(f327(f327(f6(a915,x84361),f327(f327(f8(a1,x84361,a915),x84362),f101(a1))),f327(f310(a1,a915,a106),x84363)),f327(f327(f6(a1,x84361),x84362),x84363)) % 177.41/177.19 [8437]~P68(x84371)+~P75(x84371)+~P38(x84373)+E(f327(f327(f9(a915,x84371),f327(f327(f8(a1,x84371,a915),x84372),f101(a1))),f327(f310(a1,a915,a106),x84373)),f327(f327(f9(a1,x84371),x84372),x84373)) % 177.41/177.19 [8446]P148(x84463,x84462,x84461)+E(f327(f327(f80(a1),f327(f327(f81(a1),x84461),f856(x84461,x84462,x84463))),f849(x84461,x84462,x84463)),x84462)+~P1(f327(x84463,f2(a1)))+P1(f327(f327(f235(a1),f850(x84461,x84462,x84463)),x84461)) % 177.41/177.19 [8468]~E(x84682,f2(a915))+~E(f327(f251(a915,a915),x84683),f2(a915))+~E(x84681,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),x84683)),x84682)),f327(f256(a915,a915),x84683)))+P1(f327(f49(x84681,x84682),x84683)) % 177.41/177.19 [8524]P1(f327(x85241,x85242))+~P1(f327(f327(f329(x85243),f402(x85241,x85242,x85243)),f409(x85241,x85242,x85243)))+~P1(f327(f35(x85243),x85242))+~P1(f327(x85241,f190(f922(x85243,a910)))) % 177.41/177.19 [9152]P1(f327(x91521,x91522))+~P1(f327(f35(x91523),x91522))+~P1(f327(x91521,f327(f327(f309(x91523),f402(x91521,x91522,x91523)),f409(x91521,x91522,x91523))))+~P1(f327(x91521,f190(f922(x91523,a910)))) % 177.41/177.19 [9382]P1(f327(f327(f234(a1),x93821),f2(a1)))+~P1(f327(f327(f235(a1),f327(f327(f80(a1),f327(f327(f81(a1),x93823),x93821)),x93822)),f2(a1)))+~P1(f327(f327(f234(a1),f2(a1)),x93822))+~P1(f327(f327(f235(a1),f2(a1)),x93823)) % 177.41/177.19 [5974]~P108(x59742)+E(x59741,f190(f922(x59742,a910)))+~P1(f327(f35(x59742),x59741))+E(f14(x59742,f327(f327(f309(x59742),x59743),x59741)),f327(f327(f189(x59742),x59743),f14(x59742,x59741))) % 177.41/177.19 [5975]~P108(x59752)+E(x59751,f190(f922(x59752,a910)))+~P1(f327(f35(x59752),x59751))+E(f15(x59752,f327(f327(f309(x59752),x59753),x59751)),f327(f327(f238(x59752),x59753),f15(x59752,x59751))) % 177.41/177.19 [5976]~P96(x59762)+E(x59761,f190(f922(x59762,a910)))+~P1(f327(f35(x59762),x59761))+E(f13(x59762,f327(f327(f309(x59762),x59763),x59761)),f327(f327(f102(x59762),x59763),f13(x59762,x59761))) % 177.41/177.19 [5977]~P96(x59772)+E(x59771,f190(f922(x59772,a910)))+~P1(f327(f35(x59772),x59771))+E(f10(x59772,f327(f327(f309(x59772),x59773),x59771)),f327(f327(f103(x59772),x59773),f10(x59772,x59771))) % 177.41/177.19 [6301]~P127(x63011)+~E(x63013,f2(x63011))+~E(x63012,f2(x63011))+E(f327(f327(f80(x63011),f327(f327(f81(x63011),x63012),x63012)),f327(f327(f81(x63011),x63013),x63013)),f2(x63011)) % 177.41/177.19 [6372]~P95(x63722)+E(x63721,f190(f922(x63722,a910)))+~P1(f327(f35(x63722),x63721))+E(f327(f63(x63722,f81(x63722)),f327(f327(f309(x63722),x63723),x63721)),f327(f327(f81(x63722),x63723),f327(f63(x63722,f81(x63722)),x63721))) % 177.41/177.19 [6499]~P108(x64992)+E(x64991,f190(f922(x64992,a910)))+~P1(f327(f35(x64992),x64991))+E(f11(x64992,f189(x64992),f327(f327(f309(x64992),x64993),x64991)),f327(f327(f189(x64992),x64993),f11(x64992,f189(x64992),x64991))) % 177.41/177.19 [6500]~P108(x65002)+E(x65001,f190(f922(x65002,a910)))+~P1(f327(f35(x65002),x65001))+E(f12(x65002,f238(x65002),f327(f327(f309(x65002),x65003),x65001)),f327(f327(f238(x65002),x65003),f12(x65002,f238(x65002),x65001))) % 177.41/177.19 [7008]~P72(x70081)+~P1(f327(f35(x70081),x70083))+E(f327(f63(x70081,f81(x70081)),f327(f327(f309(x70081),x70082),x70083)),f327(f327(f64(x70081,x70081,f81(x70081)),x70082),x70083))+P1(f327(f327(f329(x70081),x70082),x70083)) % 177.41/177.19 [7089]~E(f327(f327(f80(a1),x70892),f327(f327(f81(a1),x70893),x70891)),x70893)+~P1(f327(f327(f235(a1),f2(a1)),x70893))+P1(f327(f327(f234(a1),f78(a1)),x70891))+~P1(f327(f327(f235(a1),x70892),x70893)) % 177.41/177.19 [7118]~E(f327(f327(f80(a1),x71182),f327(f327(f81(a1),x71183),x71181)),x71183)+P1(f327(f327(f234(a1),x71181),f78(a1)))+~P1(f327(f327(f234(a1),f2(a1)),x71182))+~P1(f327(f327(f235(a1),f2(a1)),x71183)) % 177.41/177.19 [7134]E(x71341,f2(a915))+~P1(f327(f49(x71343,x71341),x71342))+~P1(f327(f327(f235(a915),f2(a915)),x71341))+P1(f327(f327(f235(a915),f327(f256(a915,a915),x71342)),x71341)) % 177.41/177.19 [7166]~P138(x71661)+~P1(f327(f327(f234(x71661),x71662),f2(x71661)))+~P1(f327(f327(f234(x71661),x71663),f2(x71661)))+E(f327(f327(f81(x71661),f327(f75(x71661),x71662)),f327(f75(x71661),x71663)),f327(f75(x71661),f327(f327(f81(x71661),x71662),x71663))) % 177.41/177.19 [7214]~P138(x72141)+~P1(f327(f327(f234(x72141),x72142),f2(x72141)))+E(f327(f327(f81(x72141),f327(f75(x72141),x72142)),f327(f75(x72141),x72143)),f327(f75(x72141),f327(f327(f81(x72141),x72142),x72143)))+~P1(f327(f327(f234(x72141),f2(x72141)),x72143)) % 177.41/177.19 [7215]~P138(x72151)+~P1(f327(f327(f234(x72151),x72153),f2(x72151)))+E(f327(f327(f81(x72151),f327(f75(x72151),x72152)),f327(f75(x72151),x72153)),f327(f75(x72151),f327(f327(f81(x72151),x72152),x72153)))+~P1(f327(f327(f234(x72151),f2(x72151)),x72152)) % 177.41/177.19 [7271]~P138(x72711)+E(f327(f327(f81(x72711),f327(f75(x72711),x72712)),f327(f75(x72711),x72713)),f327(f75(x72711),f327(f327(f81(x72711),x72712),x72713)))+~P1(f327(f327(f234(x72711),f2(x72711)),x72712))+~P1(f327(f327(f234(x72711),f2(x72711)),x72713)) % 177.41/177.19 [7288]~P111(x72881)+~P1(f327(f327(f234(x72881),x72883),f2(x72881)))+~P1(f327(f327(f234(x72881),x72882),f2(x72881)))+P1(f327(f327(f234(x72881),f2(x72881)),f327(f327(f81(x72881),x72882),x72883))) % 177.41/177.19 [7289]~P127(x72891)+~P1(f327(f327(f234(x72891),x72893),f2(x72891)))+~P1(f327(f327(f234(x72891),x72892),f2(x72891)))+P1(f327(f327(f234(x72891),f2(x72891)),f327(f327(f81(x72891),x72892),x72893))) % 177.41/177.19 [7290]~P63(x72901)+~P1(f327(f327(f234(x72901),x72903),f2(x72901)))+~P1(f327(f327(f234(x72901),x72902),f2(x72901)))+P1(f327(f327(f234(x72901),f2(x72901)),f327(f327(f291(x72901),x72902),x72903))) % 177.41/177.19 [7291]~P64(x72911)+~P1(f327(f327(f235(x72911),x72913),f2(x72911)))+~P1(f327(f327(f234(x72911),x72912),f2(x72911)))+P1(f327(f327(f234(x72911),f2(x72911)),f327(f327(f291(x72911),x72912),x72913))) % 177.41/177.19 [7292]~P127(x72921)+~P1(f327(f327(f235(x72921),x72923),f2(x72921)))+~P1(f327(f327(f235(x72921),x72922),f2(x72921)))+P1(f327(f327(f235(x72921),f2(x72921)),f327(f327(f81(x72921),x72922),x72923))) % 177.41/177.19 [7293]~P63(x72931)+~P1(f327(f327(f235(x72931),x72933),f2(x72931)))+~P1(f327(f327(f235(x72931),x72932),f2(x72931)))+P1(f327(f327(f235(x72931),f2(x72931)),f327(f327(f291(x72931),x72932),x72933))) % 177.41/177.19 [7294]~P64(x72941)+~P1(f327(f327(f235(x72941),x72943),f2(x72941)))+~P1(f327(f327(f235(x72941),x72942),f2(x72941)))+P1(f327(f327(f235(x72941),f2(x72941)),f327(f327(f291(x72941),x72942),x72943))) % 177.41/177.19 [7295]~P126(x72951)+~P1(f327(f327(f235(a915),f2(a915)),x72953))+~P1(f327(f327(f235(x72951),f78(x72951)),x72952))+P1(f327(f327(f235(x72951),f78(x72951)),f327(f327(f244(x72951),x72952),x72953))) % 177.41/177.19 [7395]~P111(x73951)+~P1(f327(f327(f234(x73951),f2(x73951)),x73953))+~P1(f327(f327(f234(x73951),f2(x73951)),x73952))+P1(f327(f327(f234(x73951),f2(x73951)),f327(f327(f81(x73951),x73952),x73953))) % 177.41/177.19 [7396]~P127(x73961)+~P1(f327(f327(f234(x73961),f2(x73961)),x73963))+~P1(f327(f327(f234(x73961),f2(x73961)),x73962))+P1(f327(f327(f234(x73961),f2(x73961)),f327(f327(f81(x73961),x73962),x73963))) % 177.41/177.19 [7397]~P135(x73971)+~P1(f327(f327(f234(x73971),f2(x73971)),x73973))+~P1(f327(f327(f234(x73971),f2(x73971)),x73972))+P1(f327(f327(f234(x73971),f2(x73971)),f327(f327(f81(x73971),x73972),x73973))) % 177.41/177.19 [7398]~P63(x73981)+~P1(f327(f327(f234(x73981),f2(x73981)),x73983))+~P1(f327(f327(f234(x73981),f2(x73981)),x73982))+P1(f327(f327(f234(x73981),f2(x73981)),f327(f327(f291(x73981),x73982),x73983))) % 177.41/177.19 [7399]~P64(x73991)+~P1(f327(f327(f235(x73991),f2(x73991)),x73993))+~P1(f327(f327(f234(x73991),f2(x73991)),x73992))+P1(f327(f327(f234(x73991),f2(x73991)),f327(f327(f291(x73991),x73992),x73993))) % 177.41/177.19 [7400]~P126(x74001)+~P1(f327(f327(f235(x74001),f78(x74001)),x74003))+~P1(f327(f327(f235(x74001),f78(x74001)),x74002))+P1(f327(f327(f235(x74001),f78(x74001)),f327(f327(f81(x74001),x74002),x74003))) % 177.41/177.19 [7403]~P88(x74031)+~P1(f327(f327(f235(x74031),f2(x74031)),x74033))+~P1(f327(f327(f235(x74031),f2(x74031)),x74032))+P1(f327(f327(f235(x74031),f2(x74031)),f327(f327(f80(x74031),x74032),x74033))) % 177.41/177.19 [7404]~P130(x74041)+~P1(f327(f327(f235(x74041),f2(x74041)),x74043))+~P1(f327(f327(f235(x74041),f2(x74041)),x74042))+P1(f327(f327(f235(x74041),f2(x74041)),f327(f327(f81(x74041),x74042),x74043))) % 177.41/177.19 [7405]~P63(x74051)+~P1(f327(f327(f235(x74051),f2(x74051)),x74053))+~P1(f327(f327(f235(x74051),f2(x74051)),x74052))+P1(f327(f327(f235(x74051),f2(x74051)),f327(f327(f291(x74051),x74052),x74053))) % 177.41/177.19 [7406]~P64(x74061)+~P1(f327(f327(f235(x74061),f2(x74061)),x74063))+~P1(f327(f327(f235(x74061),f2(x74061)),x74062))+P1(f327(f327(f235(x74061),f2(x74061)),f327(f327(f291(x74061),x74062),x74063))) % 177.41/177.19 [7485]~P108(x74851)+~P1(f327(f35(x74851),x74853))+E(f14(x74851,f327(f327(f309(x74851),x74852),x74853)),x74852)+~E(f327(f327(f23(f922(x74851,a910)),x74853),f327(f327(f309(x74851),x74852),f190(f922(x74851,a910)))),f190(f922(x74851,a910))) % 177.41/177.19 [7486]~P108(x74861)+~P1(f327(f35(x74861),x74863))+E(f15(x74861,f327(f327(f309(x74861),x74862),x74863)),x74862)+~E(f327(f327(f23(f922(x74861,a910)),x74863),f327(f327(f309(x74861),x74862),f190(f922(x74861,a910)))),f190(f922(x74861,a910))) % 177.41/177.19 [7487]~P96(x74871)+~P1(f327(f35(x74871),x74873))+E(f13(x74871,f327(f327(f309(x74871),x74872),x74873)),x74872)+~E(f327(f327(f23(f922(x74871,a910)),x74873),f327(f327(f309(x74871),x74872),f190(f922(x74871,a910)))),f190(f922(x74871,a910))) % 177.41/177.19 [7488]~P96(x74881)+~P1(f327(f35(x74881),x74883))+E(f10(x74881,f327(f327(f309(x74881),x74882),x74883)),x74882)+~E(f327(f327(f23(f922(x74881,a910)),x74883),f327(f327(f309(x74881),x74882),f190(f922(x74881,a910)))),f190(f922(x74881,a910))) % 177.41/177.19 [7490]~P127(x74901)+P1(f327(f327(f234(x74901),x74902),f2(x74901)))+P1(f327(f327(f234(x74901),f2(x74901)),x74903))+~P1(f327(f327(f234(x74901),f2(x74901)),f327(f327(f81(x74901),x74903),x74902))) % 177.41/177.19 [7491]~P127(x74911)+P1(f327(f327(f234(x74911),x74912),f2(x74911)))+P1(f327(f327(f234(x74911),f2(x74911)),x74913))+~P1(f327(f327(f234(x74911),f2(x74911)),f327(f327(f81(x74911),x74912),x74913))) % 177.41/177.19 [7492]~P63(x74921)+P1(f327(f327(f234(x74921),x74922),f2(x74921)))+P1(f327(f327(f234(x74921),f2(x74921)),x74923))+~P1(f327(f327(f234(x74921),f2(x74921)),f327(f327(f291(x74921),x74923),x74922))) % 177.41/177.19 [7493]~P63(x74931)+P1(f327(f327(f234(x74931),x74932),f2(x74931)))+P1(f327(f327(f234(x74931),f2(x74931)),x74933))+~P1(f327(f327(f234(x74931),f2(x74931)),f327(f327(f291(x74931),x74932),x74933))) % 177.41/177.19 [7494]~P127(x74941)+P1(f327(f327(f234(x74941),x74942),f2(x74941)))+P1(f327(f327(f234(x74941),f2(x74941)),x74942))+~P1(f327(f327(f234(x74941),f2(x74941)),f327(f327(f81(x74941),x74943),x74942))) % 177.41/177.19 [7495]~P127(x74951)+P1(f327(f327(f234(x74951),x74952),f2(x74951)))+P1(f327(f327(f234(x74951),f2(x74951)),x74952))+~P1(f327(f327(f234(x74951),f2(x74951)),f327(f327(f81(x74951),x74952),x74953))) % 177.41/177.19 [7496]~P63(x74961)+P1(f327(f327(f234(x74961),x74962),f2(x74961)))+P1(f327(f327(f234(x74961),f2(x74961)),x74962))+~P1(f327(f327(f234(x74961),f2(x74961)),f327(f327(f291(x74961),x74963),x74962))) % 177.41/177.19 [7497]~P63(x74971)+P1(f327(f327(f234(x74971),x74972),f2(x74971)))+P1(f327(f327(f234(x74971),f2(x74971)),x74972))+~P1(f327(f327(f234(x74971),f2(x74971)),f327(f327(f291(x74971),x74972),x74973))) % 177.41/177.19 [7498]~P63(x74981)+P1(f327(f327(f235(x74981),x74982),f2(x74981)))+P1(f327(f327(f235(x74981),f2(x74981)),x74983))+~P1(f327(f327(f235(x74981),f2(x74981)),f327(f327(f291(x74981),x74983),x74982))) % 177.41/177.19 [7499]~P63(x74991)+P1(f327(f327(f235(x74991),x74992),f2(x74991)))+P1(f327(f327(f235(x74991),f2(x74991)),x74993))+~P1(f327(f327(f235(x74991),f2(x74991)),f327(f327(f291(x74991),x74992),x74993))) % 177.41/177.19 [7500]~P63(x75001)+P1(f327(f327(f235(x75001),x75002),f2(x75001)))+P1(f327(f327(f235(x75001),f2(x75001)),x75002))+~P1(f327(f327(f235(x75001),f2(x75001)),f327(f327(f291(x75001),x75003),x75002))) % 177.41/177.19 [7501]~P63(x75011)+P1(f327(f327(f235(x75011),x75012),f2(x75011)))+P1(f327(f327(f235(x75011),f2(x75011)),x75012))+~P1(f327(f327(f235(x75011),f2(x75011)),f327(f327(f291(x75011),x75012),x75013))) % 177.41/177.19 [7586]~E(f327(f327(f103(f922(x75861,a910)),f327(f173(x75861),x75862)),f327(f173(x75861),x75863)),f190(f922(x75861,a910)))+~P1(f327(f138(x75861),x75863))+~P1(f327(f138(x75861),x75862))+P1(f327(f138(x75861),f327(f327(f135(x75861),x75862),x75863))) % 177.41/177.19 [7587]~P108(x75871)+~P1(f327(f35(x75871),x75873))+E(f11(x75871,f189(x75871),f327(f327(f309(x75871),x75872),x75873)),x75872)+~E(f327(f327(f23(f922(x75871,a910)),x75873),f327(f327(f309(x75871),x75872),f190(f922(x75871,a910)))),f190(f922(x75871,a910))) % 177.41/177.19 [7588]~P108(x75881)+~P1(f327(f35(x75881),x75883))+E(f12(x75881,f238(x75881),f327(f327(f309(x75881),x75882),x75883)),x75882)+~E(f327(f327(f23(f922(x75881,a910)),x75883),f327(f327(f309(x75881),x75882),f190(f922(x75881,a910)))),f190(f922(x75881,a910))) % 177.41/177.19 [7602]~P84(x76021)+~P1(f327(f327(f234(x76021),x76022),x76023))+~P1(f327(f327(f234(x76021),f327(f79(x76021),x76022)),x76023))+P1(f327(f327(f234(x76021),f327(f75(x76021),x76022)),x76023)) % 177.41/177.19 [7603]~P119(x76031)+~P1(f327(f327(f235(x76031),x76032),x76033))+~P1(f327(f327(f235(x76031),f327(f79(x76031),x76032)),x76033))+P1(f327(f327(f235(x76031),f327(f75(x76031),x76032)),x76033)) % 177.41/177.19 [7670]~P130(x76701)+P1(f327(f327(f235(x76701),f2(x76701)),x76702))+~P1(f327(f327(f235(x76701),f2(x76701)),x76703))+~P1(f327(f327(f235(x76701),f2(x76701)),f327(f327(f81(x76701),x76703),x76702))) % 177.41/177.19 [7671]~P130(x76711)+P1(f327(f327(f235(x76711),f2(x76711)),x76712))+~P1(f327(f327(f235(x76711),f2(x76711)),x76713))+~P1(f327(f327(f235(x76711),f2(x76711)),f327(f327(f81(x76711),x76712),x76713))) % 177.41/177.19 [7970]E(x79701,x79702)+~P1(f327(f35(x79703),x79701))+~P1(f327(f327(f234(a915),f327(f36(x79703),x79701)),f327(f36(x79703),x79702)))+~P1(f327(f327(f234(f922(x79703,a910)),x79702),x79701)) % 177.41/177.19 [8115]~P1(f327(f327(f235(a1),x81151),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x81152))+~P1(f327(f327(f234(a1),x81152),x81153))+P1(f327(f327(f234(a1),f327(f327(f37(a1),x81151),x81152)),f327(f327(f37(a1),x81151),x81153))) % 177.41/177.19 [8125]~P1(f327(f327(f234(a1),f2(a1)),x81251))+~P1(f327(f327(f235(a1),f2(a1)),x81253))+~P1(f327(f327(f234(a1),x81253),x81252))+P1(f327(f327(f234(a1),f327(f327(f37(a1),x81251),x81252)),f327(f327(f37(a1),x81251),x81253))) % 177.41/177.19 [8259]E(f327(x82591,f471(x82592,x82591,x82593)),x82592)+~P1(f327(f327(f234(a1),x82592),f327(x82591,x82593)))+P1(f327(f327(f235(a915),f472(x82592,x82591,x82593)),x82593))+~P1(f327(f327(f234(a1),f327(x82591,f2(a915))),x82592)) % 177.41/177.19 [8260]E(f327(x82601,f482(x82602,x82601,x82603)),x82602)+~P1(f327(f327(f234(a1),x82602),f327(x82601,x82603)))+P1(f327(f327(f235(a915),f483(x82602,x82601,x82603)),x82603))+~P1(f327(f327(f234(a1),f327(x82601,f2(a915))),x82602)) % 177.41/177.19 [8362]~P1(f327(f35(x83621),x83623))+~P1(f327(f327(f235(a915),f327(f36(x83621),x83622)),f327(f36(x83621),x83623)))+~P1(f327(f327(f234(f922(x83621,a910)),x83622),x83623))+P1(f327(f327(f235(f922(x83621,a910)),x83622),x83623)) % 177.41/177.19 [8389]E(f327(f327(f80(a1),f425(x83893,x83891,x83892)),f426(x83893,x83891,x83892)),x83891)+E(f327(f327(f23(a1),x83891),x83892),x83891)+~P1(f327(f327(f235(a1),f2(a1)),x83892))+~P1(f327(f327(f329(a1),f327(f327(f23(a1),x83891),f78(a1))),x83893)) % 177.41/177.19 [8390]E(f327(f327(f23(a1),f432(x83903,x83901,x83902)),f433(x83903,x83901,x83902)),x83901)+E(f327(f327(f80(a1),x83901),x83902),x83901)+~P1(f327(f327(f235(a1),f2(a1)),x83902))+~P1(f327(f327(f329(a1),f327(f327(f80(a1),x83901),f78(a1))),x83903)) % 177.41/177.19 [8441]~P1(f327(f327(f234(a915),x84413),x84411))+P1(f327(f327(f234(a915),x84411),x84412))+~P1(f327(f327(f234(a915),x84413),x84412))+~P1(f327(f327(f234(a915),f327(f327(f23(a915),x84411),x84413)),f327(f327(f23(a915),x84412),x84413))) % 177.41/177.19 [8442]~P1(f327(f327(f234(a915),x84423),x84421))+P1(f327(f327(f235(a915),x84421),x84422))+~P1(f327(f327(f234(a915),x84423),x84422))+~P1(f327(f327(f235(a915),f327(f327(f23(a915),x84421),x84423)),f327(f327(f23(a915),x84422),x84423))) % 177.41/177.19 [8461]~P108(x84612)+E(x84611,f114(x84612))+~P11(x84612,f327(f169(x84612),x84611))+E(f327(f143(x84612,x84612,f327(f7(x84612,x84612,x84612),f189(x84612)),x84613),f327(f169(x84612),x84611)),f327(f327(f189(x84612),f327(f327(f165(x84612),x84611),f2(a915))),x84613)) % 177.41/177.19 [8529]E(f327(f327(f23(a1),x85291),x85292),x85291)+~P1(f327(f327(f235(a1),f2(a1)),x85292))+P1(f327(f327(f329(a1),f425(x85293,x85291,x85292)),x85293))+~P1(f327(f327(f329(a1),f327(f327(f23(a1),x85291),f78(a1))),x85293)) % 177.41/177.19 [8530]E(f327(f327(f80(a1),x85301),x85302),x85301)+~P1(f327(f327(f235(a1),f2(a1)),x85302))+P1(f327(f327(f329(a1),f432(x85303,x85301,x85302)),x85303))+~P1(f327(f327(f329(a1),f327(f327(f80(a1),x85301),f78(a1))),x85303)) % 177.41/177.19 [8602]~P1(f327(f327(f234(a1),x86021),f327(x86022,x86023)))+P1(f327(f327(f235(a915),f472(x86021,x86022,x86023)),x86023))+P1(f327(f327(f234(a915),f471(x86021,x86022,x86023)),x86023))+~P1(f327(f327(f234(a1),f327(x86022,f2(a915))),x86021)) % 177.41/177.19 [8603]~P1(f327(f327(f234(a1),x86031),f327(x86032,x86033)))+P1(f327(f327(f235(a915),f483(x86031,x86032,x86033)),x86033))+P1(f327(f327(f234(a915),f482(x86031,x86032,x86033)),x86033))+~P1(f327(f327(f234(a1),f327(x86032,f2(a915))),x86031)) % 177.41/177.19 [8675]E(f327(f327(f23(a1),x86751),x86752),x86751)+~P1(f327(f327(f235(a1),f2(a1)),x86752))+P1(f327(f327(f329(a1),f426(x86753,x86751,x86752)),f303(a1,f78(a1),x86752)))+~P1(f327(f327(f329(a1),f327(f327(f23(a1),x86751),f78(a1))),x86753)) % 177.41/177.19 [8676]E(f327(f327(f80(a1),x86761),x86762),x86761)+~P1(f327(f327(f235(a1),f2(a1)),x86762))+P1(f327(f327(f329(a1),f433(x86763,x86761,x86762)),f303(a1,f78(a1),x86762)))+~P1(f327(f327(f329(a1),f327(f327(f80(a1),x86761),f78(a1))),x86763)) % 177.41/177.19 [8809]~P126(x88091)+~P1(f327(f327(f235(x88091),x88092),f78(x88091)))+~P1(f327(f327(f235(x88091),f2(x88091)),x88092))+P1(f327(f327(f235(x88091),f327(f327(f81(x88091),x88092),f327(f327(f244(x88091),x88092),x88093))),f327(f327(f244(x88091),x88092),x88093))) % 177.41/177.19 [8902]~P1(f327(x89021,x89022))+P1(f327(x89021,f2(a915)))+~P1(f327(f327(f235(a915),x89022),x89023))+~P1(f327(x89021,f46(a915,f327(a113,f502(x89022,x89021,x89023)),x89023))) % 177.41/177.19 [9054]E(f529(x90541,x90542,x90543),f2(a915))+P1(f327(f327(x90541,x90543),x90542))+P1(f327(f327(x90541,f529(x90541,x90542,x90543)),f46(a915,f528(x90541,x90542,x90543),f529(x90541,x90542,x90543))))+~P1(f327(f315(f921(a915,a915),a221),f327(f327(f252(a915,a915),x90543),x90542))) % 177.41/177.19 [9092]~P23(x90921,x90921,x90922,x90923)+E(f327(f310(x90921,x90921,x90922),x90923),x90923)+~P1(f327(f35(x90921),x90923))+~P1(f327(f327(f234(f922(x90921,a910)),f327(f310(x90921,x90921,x90922),x90923)),x90923)) % 177.41/177.19 [9309]P1(f327(f327(x93091,x93092),x93093))+P1(f327(f327(f235(a1),f767(x93091,x93093,x93092)),f769(x93091,x93093,x93092)))+P1(f327(f327(x93091,f767(x93091,x93093,x93092)),f327(f327(f80(a1),f769(x93091,x93093,x93092)),f78(a1))))+~P1(f327(f315(f921(a1,a1),a134),f327(f327(f252(a1,a1),x93092),x93093))) % 177.41/177.19 [9326]P1(f327(f327(x93261,x93262),x93263))+~P1(f327(f327(f235(a1),f526(x93261,x93263,x93262)),f2(a1)))+P1(f327(f327(x93261,f327(f79(a1),f525(x93261,x93263,x93262))),f327(f79(a1),f526(x93261,x93263,x93262))))+~P1(f327(f315(f921(a1,a1),a223),f327(f327(f252(a1,a1),x93262),x93263))) % 177.41/177.19 [9512]P1(f327(f327(x95121,x95122),x95123))+P1(f327(f327(x95121,f327(f327(f80(a1),f673(x95121,x95123,x95122)),f78(a1))),f675(x95121,x95123,x95122)))+~P1(f327(f327(f234(a1),f673(x95121,x95123,x95122)),f675(x95121,x95123,x95122)))+~P1(f327(f315(f921(a1,a1),a183),f327(f327(f252(a1,a1),x95122),x95123))) % 177.41/177.19 [9948]~P60(x99482)+~P60(x99481)+~P1(f327(f57(f921(x99481,x99482)),x99483))+P1(f327(f57(x99481),f327(f327(f8(f922(x99482,a910),a910,x99481),f57(x99482)),f327(f327(f8(f922(x99482,f921(x99481,x99482)),f922(x99482,a910),x99481),f327(f8(f921(x99481,x99482),a910,x99482),x99483)),f252(x99481,x99482))))) % 177.41/177.19 [9949]~P60(x99492)+~P60(x99491)+~P1(f327(f58(f921(x99491,x99492)),x99493))+P1(f327(f58(x99491),f327(f327(f8(f922(x99492,a910),a910,x99491),f58(x99492)),f327(f327(f8(f922(x99492,f921(x99491,x99492)),f922(x99492,a910),x99491),f327(f8(f921(x99491,x99492),a910,x99492),x99493)),f252(x99491,x99492))))) % 177.41/177.19 [10044]~P60(x100442)+~P60(x100441)+P1(f327(f57(f921(x100441,x100442)),x100443))+~P1(f327(f57(x100441),f327(f327(f8(f922(x100442,a910),a910,x100441),f57(x100442)),f327(f327(f8(f922(x100442,f921(x100441,x100442)),f922(x100442,a910),x100441),f327(f8(f921(x100441,x100442),a910,x100442),x100443)),f252(x100441,x100442))))) % 177.41/177.19 [10045]~P60(x100452)+~P60(x100451)+P1(f327(f58(f921(x100451,x100452)),x100453))+~P1(f327(f58(x100451),f327(f327(f8(f922(x100452,a910),a910,x100451),f58(x100452)),f327(f327(f8(f922(x100452,f921(x100451,x100452)),f922(x100452,a910),x100451),f327(f8(f921(x100451,x100452),a910,x100452),x100453)),f252(x100451,x100452))))) % 177.41/177.19 [10219]E(f327(x102191,f471(x102192,x102191,x102193)),x102192)+~P1(f327(f327(f234(a1),x102192),f327(x102191,x102193)))+~P1(f327(f327(f234(a1),f327(f75(a1),f327(f327(f23(a1),f327(x102191,f327(f327(f80(a915),f472(x102192,x102191,x102193)),f78(a915)))),f327(x102191,f472(x102192,x102191,x102193))))),f78(a1)))+~P1(f327(f327(f234(a1),f327(x102191,f2(a915))),x102192)) % 177.41/177.19 [10220]E(f327(x102201,f482(x102202,x102201,x102203)),x102202)+~P1(f327(f327(f234(a1),x102202),f327(x102201,x102203)))+~P1(f327(f327(f234(a1),f327(f75(a1),f327(f327(f23(a1),f327(x102201,f327(f327(f80(a915),f483(x102202,x102201,x102203)),f78(a915)))),f327(x102201,f483(x102202,x102201,x102203))))),f78(a1)))+~P1(f327(f327(f234(a1),f327(x102201,f2(a915))),x102202)) % 177.41/177.19 [10223]~P1(f327(f327(f234(a1),x102231),f327(x102232,x102233)))+~P1(f327(f327(f234(a1),f327(f75(a1),f327(f327(f23(a1),f327(x102232,f327(f327(f80(a915),f472(x102231,x102232,x102233)),f78(a915)))),f327(x102232,f472(x102231,x102232,x102233))))),f78(a1)))+P1(f327(f327(f234(a915),f471(x102231,x102232,x102233)),x102233))+~P1(f327(f327(f234(a1),f327(x102232,f2(a915))),x102231)) % 177.41/177.19 [10224]~P1(f327(f327(f234(a1),x102241),f327(x102242,x102243)))+~P1(f327(f327(f234(a1),f327(f75(a1),f327(f327(f23(a1),f327(x102242,f327(f327(f80(a915),f483(x102241,x102242,x102243)),f78(a915)))),f327(x102242,f483(x102241,x102242,x102243))))),f78(a1)))+P1(f327(f327(f234(a915),f482(x102241,x102242,x102243)),x102243))+~P1(f327(f327(f234(a1),f327(x102242,f2(a915))),x102241)) % 177.41/177.19 [10283]E(x102831,x102832)+~E(f327(f143(f916(x102833),f916(x102833),f135(x102833),f114(x102833)),x102831),f327(f143(f916(x102833),f916(x102833),f135(x102833),f114(x102833)),x102832))+~E(f327(f191(f916(f916(x102833))),x102831),f327(f191(f916(f916(x102833))),x102832))+~P1(f327(f327(f257(f916(x102833),f916(x102833),a910),f327(f327(f7(f916(x102833),f922(f916(x102833),a915),f922(f916(x102833),a910)),f327(f327(f8(f922(a915,a910),f922(f922(f916(x102833),a915),f922(f916(x102833),a910)),f916(x102833)),f8(a915,a910,f916(x102833))),f327(f327(f8(a915,f922(a915,a910),f916(x102833)),a324),f191(f916(x102833))))),f191(f916(x102833)))),f699(x102831,x102832,x102833))) % 177.41/177.19 [10284]E(x102841,x102842)+~E(f327(f143(f916(x102843),f916(x102843),f135(x102843),f114(x102843)),x102841),f327(f143(f916(x102843),f916(x102843),f135(x102843),f114(x102843)),x102842))+~E(f327(f191(f916(f916(x102843))),x102841),f327(f191(f916(f916(x102843))),x102842))+~P1(f327(f327(f257(f916(x102843),f916(x102843),a910),f327(f327(f7(f916(x102843),f922(f916(x102843),a915),f922(f916(x102843),a910)),f327(f327(f8(f922(a915,a910),f922(f922(f916(x102843),a915),f922(f916(x102843),a910)),f916(x102843)),f8(a915,a910,f916(x102843))),f327(f327(f8(a915,f922(a915,a910),f916(x102843)),a324),f191(f916(x102843))))),f191(f916(x102843)))),f700(x102842,x102841,x102843))) % 177.41/177.19 [6996]~E(f78(a915),f2(a915))+~P1(f327(f35(x69961),x69963))+~P1(f327(f35(x69961),x69962))+E(f327(f327(f80(a915),f327(f36(x69961),x69962)),f327(f36(x69961),x69963)),f327(f36(x69961),f327(f327(f102(f922(x69961,a910)),x69962),x69963))) % 177.41/177.19 [7413]~P108(x74131)+~P1(f327(f35(x74131),x74132))+~P1(f327(f327(f329(x74131),x74133),x74132))+P1(f327(f327(f234(x74131),f327(f63(x74131,f238(x74131)),x74132)),x74133)) % 177.41/177.19 [7414]~P102(x74141)+~P1(f327(f35(x74141),x74142))+~P1(f327(f327(f329(x74141),x74143),x74142))+P1(f327(f327(f234(x74141),f327(f63(x74141,f103(x74141)),x74142)),x74143)) % 177.41/177.19 [7664]~P1(f327(f35(x76641),x76643))+~P1(f327(f35(x76641),x76642))+~E(f327(f327(f103(f922(x76641,a910)),x76642),x76643),f190(f922(x76641,a910)))+E(f327(f327(f80(a915),f327(f36(x76641),x76642)),f327(f36(x76641),x76643)),f327(f36(x76641),f327(f327(f102(f922(x76641,a910)),x76642),x76643))) % 177.41/177.19 [8447]~P35(x84471,x84473)+~P35(x84471,x84472)+~E(f327(f327(f103(f922(x84471,a910)),f327(f264(x84471,x84471),x84472)),f327(f284(x84471,x84471),x84473)),f190(f922(x84471,a910)))+P35(x84471,f327(f327(f102(f922(f921(x84471,x84471),a910)),x84472),x84473)) % 177.41/177.19 [8541]E(x85411,f327(f327(f37(a915),x85412),x85413))+~P1(f327(f327(f235(a915),f2(a915)),x85413))+~P1(f327(f327(f235(a915),x85412),f327(f327(f81(a915),x85413),f327(a113,x85411))))+~P1(f327(f327(f234(a915),f327(f327(f81(a915),x85413),x85411)),x85412)) % 177.41/177.19 [8673]~P1(f327(f35(x86731),x86732))+~P1(f327(f35(x86731),x86733))+E(f327(f327(f80(a915),f327(f36(x86731),x86732)),f327(f36(x86731),x86733)),f327(f36(x86731),f327(f327(f102(f922(x86731,a910)),x86732),x86733)))+P1(f327(f327(f329(x86731),f373(x86733,x86732,x86731)),f327(f327(f103(f922(x86731,a910)),x86732),x86733))) % 177.41/177.19 [9066]~P127(x90662)+~E(x90661,f2(x90662))+~E(x90663,f2(x90662))+~P1(f327(f327(f235(x90662),f2(x90662)),f327(f327(f80(x90662),f327(f327(f81(x90662),x90663),x90663)),f327(f327(f81(x90662),x90661),x90661)))) % 177.41/177.19 [9593]~P35(x95931,x95933)+~P35(x95931,x95932)+P35(x95931,f327(f327(f102(f922(f921(x95931,x95931),a910)),x95932),x95933))+~P1(f327(f327(f234(f922(f921(x95931,x95931),a910)),f327(f327(f289(x95931,x95931,x95931),x95932),x95933)),x95932)) % 177.41/177.19 [9723]~P1(f327(x97231,x97233))+~P1(f327(f35(x97232),x97233))+P1(f327(x97231,f190(f922(x97232,a910))))+~P1(f327(x97231,f327(f327(f23(f922(x97232,a910)),f418(x97231,x97233,x97232)),f327(f327(f309(x97232),f419(x97231,x97233,x97232)),f190(f922(x97232,a910)))))) % 177.41/177.19 [8849]~P1(f327(f327(f235(a1),f2(a1)),x88493))+P1(f327(f327(f234(a1),f2(a1)),x88491))+~P1(f327(f327(f235(a1),x88492),x88493))+~P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),f327(f327(f81(a1),x88493),x88491)),x88492))) % 177.41/177.19 [8873]~P108(x88731)+~P1(f327(f35(x88731),x88732))+E(f327(f327(f23(f922(x88731,a910)),x88732),f327(f327(f309(x88731),x88733),f190(f922(x88731,a910)))),f190(f922(x88731,a910)))+E(f327(f327(f189(x88731),x88733),f14(x88731,f327(f327(f23(f922(x88731,a910)),x88732),f327(f327(f309(x88731),x88733),f190(f922(x88731,a910)))))),f14(x88731,f327(f327(f309(x88731),x88733),x88732))) % 177.41/177.19 [8874]~P108(x88741)+~P1(f327(f35(x88741),x88742))+E(f327(f327(f23(f922(x88741,a910)),x88742),f327(f327(f309(x88741),x88743),f190(f922(x88741,a910)))),f190(f922(x88741,a910)))+E(f327(f327(f238(x88741),x88743),f15(x88741,f327(f327(f23(f922(x88741,a910)),x88742),f327(f327(f309(x88741),x88743),f190(f922(x88741,a910)))))),f15(x88741,f327(f327(f309(x88741),x88743),x88742))) % 177.41/177.19 [8875]~P96(x88751)+~P1(f327(f35(x88751),x88752))+E(f327(f327(f23(f922(x88751,a910)),x88752),f327(f327(f309(x88751),x88753),f190(f922(x88751,a910)))),f190(f922(x88751,a910)))+E(f327(f327(f102(x88751),x88753),f13(x88751,f327(f327(f23(f922(x88751,a910)),x88752),f327(f327(f309(x88751),x88753),f190(f922(x88751,a910)))))),f13(x88751,f327(f327(f309(x88751),x88753),x88752))) % 177.41/177.19 [8876]~P96(x88761)+~P1(f327(f35(x88761),x88762))+E(f327(f327(f23(f922(x88761,a910)),x88762),f327(f327(f309(x88761),x88763),f190(f922(x88761,a910)))),f190(f922(x88761,a910)))+E(f327(f327(f103(x88761),x88763),f10(x88761,f327(f327(f23(f922(x88761,a910)),x88762),f327(f327(f309(x88761),x88763),f190(f922(x88761,a910)))))),f10(x88761,f327(f327(f309(x88761),x88763),x88762))) % 177.41/177.19 [8948]~P108(x89481)+~P1(f327(f35(x89481),x89482))+E(f327(f327(f23(f922(x89481,a910)),x89482),f327(f327(f309(x89481),x89483),f190(f922(x89481,a910)))),f190(f922(x89481,a910)))+E(f327(f327(f189(x89481),x89483),f11(x89481,f189(x89481),f327(f327(f23(f922(x89481,a910)),x89482),f327(f327(f309(x89481),x89483),f190(f922(x89481,a910)))))),f11(x89481,f189(x89481),f327(f327(f309(x89481),x89483),x89482))) % 177.41/177.19 [8949]~P108(x89491)+~P1(f327(f35(x89491),x89492))+E(f327(f327(f23(f922(x89491,a910)),x89492),f327(f327(f309(x89491),x89493),f190(f922(x89491,a910)))),f190(f922(x89491,a910)))+E(f327(f327(f238(x89491),x89493),f12(x89491,f238(x89491),f327(f327(f23(f922(x89491,a910)),x89492),f327(f327(f309(x89491),x89493),f190(f922(x89491,a910)))))),f12(x89491,f238(x89491),f327(f327(f309(x89491),x89493),x89492))) % 177.41/177.19 [9531]E(x95311,x95312)+~E(f327(f143(f916(x95313),f916(x95313),f135(x95313),f114(x95313)),x95311),f327(f143(f916(x95313),f916(x95313),f135(x95313),f114(x95313)),x95312))+~E(f327(f191(f916(f916(x95313))),x95311),f327(f191(f916(f916(x95313))),x95312))+P1(f327(f327(f329(f921(f916(x95313),f916(x95313))),f699(x95311,x95312,x95313)),f327(f173(f921(f916(x95313),f916(x95313))),f327(f327(f182(f916(x95313),f916(x95313)),x95312),x95311)))) % 177.41/177.19 [9532]E(x95321,x95322)+~E(f327(f143(f916(x95323),f916(x95323),f135(x95323),f114(x95323)),x95321),f327(f143(f916(x95323),f916(x95323),f135(x95323),f114(x95323)),x95322))+~E(f327(f191(f916(f916(x95323))),x95321),f327(f191(f916(f916(x95323))),x95322))+P1(f327(f327(f329(f921(f916(x95323),f916(x95323))),f700(x95322,x95321,x95323)),f327(f173(f921(f916(x95323),f916(x95323))),f327(f327(f182(f916(x95323),f916(x95323)),x95321),x95322)))) % 177.41/177.19 [10391]~P77(x103912)+E(x103911,f190(f922(x103912,a910)))+~P1(f327(f35(x103912),x103911))+E(f14(x103912,f327(f262(x103912),f327(f327(f8(f922(x103912,a910),a910,x103912),f87(x103912)),f327(f327(f7(x103912,f922(x103912,a910),f922(x103912,a910)),f327(f327(f8(f922(x103912,f922(a910,a910)),f922(f922(x103912,a910),f922(x103912,a910)),x103912),f18(x103912,a910,a910)),f327(f327(f8(f922(x103912,a910),f922(x103912,f922(a910,a910)),x103912),f327(f8(a910,f922(a910,a910),x103912),a325)),f327(f327(f7(x103912,f922(x103912,x103912),f922(x103912,a910)),f327(f327(f8(f922(x103912,a910),f922(f922(x103912,x103912),f922(x103912,a910)),x103912),f8(x103912,a910,x103912)),a324)),f327(f80(x103912),x103913))))),f327(f327(f7(x103912,f922(x103912,a910),a910),f329(x103912)),x103911))))),f327(f327(f80(x103912),x103913),f14(x103912,x103911))) % 177.41/177.19 [10392]~P77(x103922)+E(x103921,f190(f922(x103922,a910)))+~P1(f327(f35(x103922),x103921))+E(f15(x103922,f327(f262(x103922),f327(f327(f8(f922(x103922,a910),a910,x103922),f87(x103922)),f327(f327(f7(x103922,f922(x103922,a910),f922(x103922,a910)),f327(f327(f8(f922(x103922,f922(a910,a910)),f922(f922(x103922,a910),f922(x103922,a910)),x103922),f18(x103922,a910,a910)),f327(f327(f8(f922(x103922,a910),f922(x103922,f922(a910,a910)),x103922),f327(f8(a910,f922(a910,a910),x103922),a325)),f327(f327(f7(x103922,f922(x103922,x103922),f922(x103922,a910)),f327(f327(f8(f922(x103922,a910),f922(f922(x103922,x103922),f922(x103922,a910)),x103922),f8(x103922,a910,x103922)),a324)),f327(f80(x103922),x103923))))),f327(f327(f7(x103922,f922(x103922,a910),a910),f329(x103922)),x103921))))),f327(f327(f80(x103922),x103923),f15(x103922,x103921))) % 177.41/177.19 [10393]~P100(x103932)+E(x103931,f190(f922(x103932,a910)))+~P1(f327(f35(x103932),x103931))+E(f10(x103932,f327(f262(x103932),f327(f327(f8(f922(x103932,a910),a910,x103932),f87(x103932)),f327(f327(f7(x103932,f922(x103932,a910),f922(x103932,a910)),f327(f327(f8(f922(x103932,f922(a910,a910)),f922(f922(x103932,a910),f922(x103932,a910)),x103932),f18(x103932,a910,a910)),f327(f327(f8(f922(x103932,a910),f922(x103932,f922(a910,a910)),x103932),f327(f8(a910,f922(a910,a910),x103932),a325)),f327(f327(f7(x103932,f922(x103932,x103932),f922(x103932,a910)),f327(f327(f8(f922(x103932,a910),f922(f922(x103932,x103932),f922(x103932,a910)),x103932),f8(x103932,a910,x103932)),a324)),f327(f102(x103932),x103933))))),f327(f327(f7(x103932,f922(x103932,a910),a910),f329(x103932)),x103931))))),f327(f327(f102(x103932),x103933),f10(x103932,x103931))) % 177.41/177.19 [10394]~P100(x103942)+E(x103941,f190(f922(x103942,a910)))+~P1(f327(f35(x103942),x103941))+E(f13(x103942,f327(f262(x103942),f327(f327(f8(f922(x103942,a910),a910,x103942),f87(x103942)),f327(f327(f7(x103942,f922(x103942,a910),f922(x103942,a910)),f327(f327(f8(f922(x103942,f922(a910,a910)),f922(f922(x103942,a910),f922(x103942,a910)),x103942),f18(x103942,a910,a910)),f327(f327(f8(f922(x103942,a910),f922(x103942,f922(a910,a910)),x103942),f327(f8(a910,f922(a910,a910),x103942),a325)),f327(f327(f7(x103942,f922(x103942,x103942),f922(x103942,a910)),f327(f327(f8(f922(x103942,a910),f922(f922(x103942,x103942),f922(x103942,a910)),x103942),f8(x103942,a910,x103942)),a324)),f327(f103(x103942),x103943))))),f327(f327(f7(x103942,f922(x103942,a910),a910),f329(x103942)),x103941))))),f327(f327(f103(x103942),x103943),f13(x103942,x103941))) % 177.41/177.19 [10395]~P108(x103952)+E(x103951,f190(f922(x103952,a910)))+~P1(f327(f35(x103952),x103951))+E(f11(x103952,f189(x103952),f327(f262(x103952),f327(f327(f8(f922(x103952,a910),a910,x103952),f87(x103952)),f327(f327(f7(x103952,f922(x103952,a910),f922(x103952,a910)),f327(f327(f8(f922(x103952,f922(a910,a910)),f922(f922(x103952,a910),f922(x103952,a910)),x103952),f18(x103952,a910,a910)),f327(f327(f8(f922(x103952,a910),f922(x103952,f922(a910,a910)),x103952),f327(f8(a910,f922(a910,a910),x103952),a325)),f327(f327(f7(x103952,f922(x103952,x103952),f922(x103952,a910)),f327(f327(f8(f922(x103952,a910),f922(f922(x103952,x103952),f922(x103952,a910)),x103952),f8(x103952,a910,x103952)),a324)),f327(f238(x103952),x103953))))),f327(f327(f7(x103952,f922(x103952,a910),a910),f329(x103952)),x103951))))),f327(f327(f238(x103952),x103953),f11(x103952,f189(x103952),x103951))) % 177.41/177.19 [10396]~P108(x103962)+E(x103961,f190(f922(x103962,a910)))+~P1(f327(f35(x103962),x103961))+E(f12(x103962,f238(x103962),f327(f262(x103962),f327(f327(f8(f922(x103962,a910),a910,x103962),f87(x103962)),f327(f327(f7(x103962,f922(x103962,a910),f922(x103962,a910)),f327(f327(f8(f922(x103962,f922(a910,a910)),f922(f922(x103962,a910),f922(x103962,a910)),x103962),f18(x103962,a910,a910)),f327(f327(f8(f922(x103962,a910),f922(x103962,f922(a910,a910)),x103962),f327(f8(a910,f922(a910,a910),x103962),a325)),f327(f327(f7(x103962,f922(x103962,x103962),f922(x103962,a910)),f327(f327(f8(f922(x103962,a910),f922(f922(x103962,x103962),f922(x103962,a910)),x103962),f8(x103962,a910,x103962)),a324)),f327(f189(x103962),x103963))))),f327(f327(f7(x103962,f922(x103962,a910),a910),f329(x103962)),x103961))))),f327(f327(f189(x103962),x103963),f12(x103962,f238(x103962),x103961))) % 177.41/177.19 [10109]~P119(x101091)+~E(x101093,f2(x101091))+~E(x101092,f2(x101091))+E(f327(f327(f80(x101091),f327(f327(f244(x101091),x101092),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x101091),x101093),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f2(x101091)) % 177.41/177.19 [10264]~P126(x102641)+~P1(f327(f327(f234(x102641),f2(x102641)),x102643))+P1(f327(f327(f234(x102641),x102642),x102643))+~P1(f327(f327(f234(x102641),f327(f327(f244(x102641),x102642),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x102641),x102643),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))))) % 177.41/177.19 [10322]~P119(x103222)+~E(x103221,f2(x103222))+~E(x103223,f2(x103222))+~P1(f327(f327(f235(x103222),f2(x103222)),f327(f327(f80(x103222),f327(f327(f244(x103222),x103223),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))),f327(f327(f244(x103222),x103221),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))))) % 177.41/177.19 [6877]~P5(x68773,x68772)+~P1(f327(x68771,x68774))+~P1(f327(f327(f329(x68773),x68774),f270(x68773,x68772)))+P1(f327(x68771,f816(x68771,x68772,x68773))) % 177.41/177.19 [8784]P24(x87841,x87842,f820(x87843,x87842,x87844,x87841),x87844,x87843)+~E(f327(f36(x87841),x87844),f327(f36(x87842),x87843))+~P1(f327(f35(x87842),x87843))+~P1(f327(f35(x87841),x87844)) % 177.41/177.19 [9494]E(x94941,x94942)+~E(f651(x94941,x94942,x94944,x94943),f652(x94941,x94942,x94944,x94943))+P1(f327(f327(f329(f921(f916(x94943),f916(x94943))),f327(f327(f252(f916(x94943),f916(x94943)),x94942),x94941)),f148(x94943,x94944)))+P1(f327(f327(f329(f921(f916(x94943),f916(x94943))),f327(f327(f252(f916(x94943),f916(x94943)),x94941),x94942)),f148(x94943,x94944))) % 177.41/177.19 [5016]~P61(x50162)+~E(x50164,f2(x50162))+~E(x50161,f2(x50162))+E(x50161,f327(f327(f291(x50162),x50163),x50164)) % 177.41/177.19 [5017]~P61(x50171)+~E(x50173,f2(x50171))+~E(x50174,f2(x50171))+E(f327(f327(f291(x50171),x50172),x50173),x50174) % 177.41/177.19 [5133]~P61(x51332)+E(x51331,f2(x51332))+~E(x51333,f2(x51332))+~E(x51331,f327(f327(f291(x51332),x51334),x51333)) % 177.41/177.19 [5134]~P61(x51342)+E(x51341,f2(x51342))+~E(x51343,f2(x51342))+~E(f327(f327(f291(x51342),x51344),x51343),x51341) % 177.41/177.19 [5315]~P122(x53152)+E(x53151,f2(x53152))+~E(f327(f327(f291(x53152),x53153),x53151),x53154)+E(x53153,f327(f327(f81(x53152),x53154),x53151)) % 177.41/177.19 [5317]~P122(x53172)+E(x53171,f2(x53172))+~E(f327(f327(f81(x53172),x53173),x53171),x53174)+E(x53173,f327(f327(f291(x53172),x53174),x53171)) % 177.41/177.19 [5318]~P61(x53182)+E(x53181,f2(x53182))+~E(f327(f327(f291(x53182),x53183),x53181),x53184)+E(x53183,f327(f327(f81(x53182),x53184),x53181)) % 177.41/177.19 [5319]~P61(x53192)+E(x53191,f2(x53192))+~E(f327(f327(f81(x53192),x53193),x53191),x53194)+E(x53193,f327(f327(f291(x53192),x53194),x53191)) % 177.41/177.19 [5320]~P122(x53202)+E(x53201,f2(x53202))+~E(x53203,f327(f327(f291(x53202),x53204),x53201))+E(f327(f327(f81(x53202),x53203),x53201),x53204) % 177.41/177.19 [5322]~P122(x53222)+E(x53221,f2(x53222))+~E(x53223,f327(f327(f81(x53222),x53224),x53221))+E(f327(f327(f291(x53222),x53223),x53221),x53224) % 177.41/177.19 [5323]~P61(x53232)+E(x53231,f2(x53232))+~E(x53233,f327(f327(f291(x53232),x53234),x53231))+E(f327(f327(f81(x53232),x53233),x53231),x53234) % 177.41/177.19 [5324]~P61(x53242)+E(x53241,f2(x53242))+~E(x53243,f327(f327(f81(x53242),x53244),x53241))+E(f327(f327(f291(x53242),x53243),x53241),x53244) % 177.41/177.19 [5348]~P61(x53482)+~E(x53481,f2(x53482))+~E(f327(f327(f81(x53482),x53481),x53484),x53483)+E(x53481,f327(f327(f291(x53482),x53483),x53484)) % 177.41/177.19 [5349]~P61(x53491)+~E(x53494,f2(x53491))+~E(x53492,f327(f327(f81(x53491),x53494),x53493))+E(f327(f327(f291(x53491),x53492),x53493),x53494) % 177.41/177.19 [5422]~E(x54223,x54224)+~E(x54222,x54223)+~P110(x54221)+E(f303(x54221,x54222,x54223),f327(f327(f309(x54221),x54224),f190(f922(x54221,a910)))) % 177.41/177.19 [5630]~E(f115(x56302,x56301),x56303)+~E(f145(x56302,x56301),x56304)+E(x56301,f114(x56302))+E(f327(f327(f135(x56302),x56303),f327(f327(f152(x56302),x56304),f114(x56302))),x56301) % 177.41/177.19 [6267]~P126(x62673)+E(x62671,x62672)+~E(f327(f327(f244(x62673),x62674),x62671),f327(f327(f244(x62673),x62674),x62672))+~P1(f327(f327(f235(x62673),f78(x62673)),x62674)) % 177.41/177.19 [6268]E(x62681,x62682)+~E(f327(f327(f309(x62683),x62684),x62681),f327(f327(f309(x62683),x62684),x62682))+P1(f327(f327(f329(x62683),x62684),x62682))+P1(f327(f327(f329(x62683),x62684),x62681)) % 177.41/177.19 [6311]E(f327(x63111,x63112),f78(a915))+~E(f327(f327(f9(x63113,a915),x63111),x63114),f78(a915))+~P1(f327(f35(x63113),x63114))+~P1(f327(f327(f329(x63113),x63112),x63114)) % 177.41/177.19 [6312]E(f327(x63121,x63122),f2(a915))+~E(f327(f327(f6(x63123,a915),x63121),x63124),f2(a915))+~P1(f327(f35(x63123),x63124))+~P1(f327(f327(f329(x63123),x63122),x63124)) % 177.41/177.19 [6533]~P110(x65331)+~P1(f327(f327(f234(x65331),x65334),x65333))+P1(f327(f327(f234(x65331),x65332),x65333))+~P1(f327(f327(f234(x65331),x65332),x65334)) % 177.41/177.19 [6534]~P107(x65341)+~P1(f327(f327(f234(x65341),x65342),x65344))+P1(f327(f327(f234(x65341),x65342),x65343))+~P1(f327(f327(f234(x65341),x65344),x65343)) % 177.41/177.19 [6535]~P110(x65351)+~P1(f327(f327(f235(x65351),x65354),x65353))+P1(f327(f327(f235(x65351),x65352),x65353))+~P1(f327(f327(f234(x65351),x65352),x65354)) % 177.41/177.19 [6536]~P110(x65361)+~P1(f327(f327(f235(x65361),x65362),x65364))+P1(f327(f327(f235(x65361),x65362),x65363))+~P1(f327(f327(f234(x65361),x65364),x65363)) % 177.41/177.19 [6537]~P110(x65371)+~P1(f327(f327(f235(x65371),x65374),x65373))+P1(f327(f327(f235(x65371),x65372),x65373))+~P1(f327(f327(f235(x65371),x65372),x65374)) % 177.41/177.19 [6538]~P107(x65381)+~P1(f327(f327(f235(x65381),x65382),x65384))+P1(f327(f327(f235(x65381),x65382),x65383))+~P1(f327(f327(f234(x65381),x65384),x65383)) % 177.41/177.19 [6539]~P107(x65391)+~P1(f327(f327(f235(x65391),x65394),x65393))+P1(f327(f327(f235(x65391),x65392),x65393))+~P1(f327(f327(f234(x65391),x65392),x65394)) % 177.41/177.19 [6540]~P107(x65401)+~P1(f327(f327(f235(x65401),x65402),x65404))+P1(f327(f327(f235(x65401),x65402),x65403))+~P1(f327(f327(f235(x65401),x65404),x65403)) % 177.41/177.19 [6541]~P112(x65411)+~P1(f327(f327(f287(x65411),x65412),x65414))+P1(f327(f327(f287(x65411),x65412),x65413))+~P1(f327(f327(f287(x65411),x65414),x65413)) % 177.41/177.19 [6620]~P33(x66204,x66203,x66202)+E(x66201,f752(x66202,x66203,x66204))+~P1(f327(x66203,x66201))+~P1(f327(f327(f329(x66204),x66201),f327(f173(x66204),x66202))) % 177.41/177.19 [6621]~P33(x66214,x66213,x66212)+E(x66211,f762(x66212,x66213,x66214))+~P1(f327(x66213,x66211))+~P1(f327(f327(f329(x66214),x66211),f327(f173(x66214),x66212))) % 177.41/177.19 [6770]~P3(x67701)+~P1(f327(f327(f234(x67701),x67702),f39(x67701,x67704)))+P1(f327(f327(f234(x67701),x67702),x67703))+~P1(f327(f327(f329(x67701),x67703),x67704)) % 177.41/177.19 [6918]~P108(x69181)+~P11(x69181,f327(f327(f152(x69181),x69182),x69184))+~P1(f327(f327(f329(x69181),x69183),f327(f173(x69181),x69184)))+P1(f327(f327(f234(x69181),x69182),x69183)) % 177.41/177.19 [7006]~P3(x70061)+~P1(f327(f327(f234(x70061),f38(x70061,x70064)),x70063))+P1(f327(f327(f234(x70061),x70062),x70063))+~P1(f327(f327(f329(x70061),x70062),x70064)) % 177.41/177.19 [7148]~P58(x71481)+P1(f327(f327(f287(x71481),x71482),f46(x71481,x71483,x71484)))+~P1(f327(f327(f287(x71481),x71482),x71484))+~P1(f327(f327(f287(x71481),x71482),x71483)) % 177.41/177.19 [7416]~P108(x74161)+E(f327(f327(f102(f922(x74161,a910)),f327(f302(x74161,x74162),x74163)),f327(f302(x74161,x74163),x74164)),f327(f302(x74161,x74162),x74164))+~P1(f327(f327(f234(x74161),x74163),x74164))+~P1(f327(f327(f234(x74161),x74162),x74163)) % 177.41/177.19 [7460]P33(x74601,x74602,x74603)+~E(f764(x74603,x74602,x74601,x74604),x74604)+~P1(f327(x74602,x74604))+~P1(f327(f327(f329(x74601),x74604),f327(f173(x74601),x74603))) % 177.41/177.19 [7461]P33(x74611,x74612,x74613)+~E(f772(x74613,x74612,x74611,x74614),x74614)+~P1(f327(x74612,x74614))+~P1(f327(f327(f329(x74611),x74614),f327(f173(x74611),x74613))) % 177.41/177.19 [7504]~P58(x75041)+~P1(f327(f327(f287(x75041),x75042),f46(x75041,x75043,x75044)))+P1(f327(f327(f287(x75041),x75042),x75043))+~P1(f327(f327(f287(x75041),x75042),x75044)) % 177.41/177.19 [7537]~P108(x75371)+E(f327(f327(f102(f922(x75371,a910)),f327(f302(x75371,x75372),x75373)),f303(x75371,x75373,x75374)),f303(x75371,x75372,x75374))+~P1(f327(f327(f234(x75371),x75373),x75374))+~P1(f327(f327(f234(x75371),x75372),x75373)) % 177.41/177.19 [7597]~P108(x75971)+E(f327(f327(f102(f922(x75971,a910)),f306(x75971,x75972,x75973)),f327(f302(x75971,x75973),x75974)),f306(x75971,x75972,x75974))+~P1(f327(f327(f234(x75971),x75973),x75974))+~P1(f327(f327(f235(x75971),x75972),x75973)) % 177.41/177.19 [7614]~P108(x76141)+E(f327(f327(f102(f922(x76141,a910)),f303(x76141,x76142,x76143)),f306(x76141,x76143,x76144)),f327(f302(x76141,x76142),x76144))+~P1(f327(f327(f234(x76141),x76142),x76143))+~P1(f327(f327(f235(x76141),x76143),x76144)) % 177.41/177.19 [7645]~P108(x76451)+E(f327(f327(f102(f922(x76451,a910)),f306(x76451,x76452,x76453)),f303(x76451,x76453,x76454)),f305(x76451,x76452,x76454))+~P1(f327(f327(f234(x76451),x76453),x76454))+~P1(f327(f327(f235(x76451),x76452),x76453)) % 177.41/177.19 [7646]~P108(x76461)+E(f327(f327(f102(f922(x76461,a910)),f305(x76461,x76462,x76463)),f306(x76461,x76463,x76464)),f306(x76461,x76462,x76464))+~P1(f327(f327(f234(x76461),x76462),x76463))+~P1(f327(f327(f235(x76461),x76463),x76464)) % 177.41/177.19 [7647]~P108(x76471)+E(f327(f327(f102(f922(x76471,a910)),f305(x76471,x76472,x76473)),f305(x76471,x76473,x76474)),f305(x76471,x76472,x76474))+~P1(f327(f327(f234(x76471),x76473),x76474))+~P1(f327(f327(f234(x76471),x76472),x76473)) % 177.41/177.19 [7648]~P108(x76481)+E(f327(f327(f102(f922(x76481,a910)),f303(x76481,x76482,x76483)),f305(x76481,x76483,x76484)),f303(x76481,x76482,x76484))+~P1(f327(f327(f234(x76481),x76483),x76484))+~P1(f327(f327(f234(x76481),x76482),x76483)) % 177.41/177.19 [8431]P23(x84311,x84312,f875(x84313,x84312,x84314,x84311),x84314)+~P1(f327(f35(x84312),x84313))+~P1(f327(f35(x84311),x84314))+~P1(f327(f327(f234(a915),f327(f36(x84311),x84314)),f327(f36(x84312),x84313))) % 177.41/177.19 [8452]P33(x84521,x84522,x84523)+~P1(f327(x84522,x84524))+P1(f327(x84522,f764(x84523,x84522,x84521,x84524)))+~P1(f327(f327(f329(x84521),x84524),f327(f173(x84521),x84523))) % 177.41/177.19 [8453]P33(x84531,x84532,x84533)+~P1(f327(x84532,x84534))+P1(f327(x84532,f772(x84533,x84532,x84531,x84534)))+~P1(f327(f327(f329(x84531),x84534),f327(f173(x84531),x84533))) % 177.41/177.19 [8507]~P75(x85071)+~E(f327(x85073,f501(x85073,x85074,x85072,x85071)),f78(x85071))+E(f327(f327(f327(f65(x85071,x85072,f81(x85071)),x85073),f78(x85071)),x85074),f78(x85071))+~P1(f327(f35(x85072),x85074)) % 177.41/177.19 [8773]~P126(x87731)+~P1(f327(f327(f234(x87731),f2(x87731)),x87733))+P1(f327(f327(f234(x87731),x87732),x87733))+~P1(f327(f327(f234(x87731),f327(f327(f244(x87731),x87732),f327(a113,x87734))),f327(f327(f244(x87731),x87733),f327(a113,x87734)))) % 177.41/177.19 [9093]P33(x90931,x90932,x90933)+~P1(f327(x90932,x90934))+~P1(f327(f327(f329(x90931),x90934),f327(f173(x90931),x90933)))+P1(f327(f327(f329(x90931),f764(x90933,x90932,x90931,x90934)),f327(f173(x90931),x90933))) % 177.41/177.19 [9094]P33(x90941,x90942,x90943)+~P1(f327(x90942,x90944))+~P1(f327(f327(f329(x90941),x90944),f327(f173(x90941),x90943)))+P1(f327(f327(f329(x90941),f772(x90943,x90942,x90941,x90944)),f327(f173(x90941),x90943))) % 177.41/177.19 [9172]~P75(x91721)+E(f327(f327(f327(f65(x91721,x91722,f81(x91721)),x91723),f78(x91721)),x91724),f78(x91721))+~P1(f327(f35(x91722),x91724))+P1(f327(f327(f329(x91722),f501(x91723,x91724,x91722,x91721)),x91724)) % 177.41/177.19 [9664]~P1(f327(f327(f234(a1),x96644),f2(a1)))+P1(f327(f327(f234(a1),f327(f327(f80(a1),f327(f327(f81(a1),x96641),f46(a1,x96642,x96643))),x96644)),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x96643))+~P1(f327(f327(f235(a1),x96641),x96644)) % 177.41/177.19 [10102]~P1(f327(f35(x101021),x101022))+~P1(f327(f327(f329(x101021),x101024),x101022))+~P1(f327(f327(f329(x101021),x101023),x101022))+P1(f327(f327(f235(a915),f327(f36(x101021),f327(f327(f23(f922(x101021,a910)),f327(f327(f23(f922(x101021,a910)),x101022),f327(f327(f309(x101021),x101023),f190(f922(x101021,a910))))),f327(f327(f309(x101021),x101024),f190(f922(x101021,a910)))))),f327(f36(x101021),x101022))) % 177.41/177.19 [7064]~P139(x70643)+~P121(x70643)+P1(f327(x70641,f852(x70642,x70641,x70643)))+~P1(f327(x70641,f327(f327(f81(x70643),x70642),x70644))) % 177.41/177.19 [7122]~P108(x71221)+~P1(f327(f327(f234(x71221),x71222),x71224))+~P1(f327(f327(f234(x71221),x71222),x71223))+P1(f327(f327(f234(x71221),x71222),f327(f327(f238(x71221),x71223),x71224))) % 177.41/177.19 [7125]~P102(x71251)+~P1(f327(f327(f234(x71251),x71252),x71254))+~P1(f327(f327(f234(x71251),x71252),x71253))+P1(f327(f327(f234(x71251),x71252),f327(f327(f103(x71251),x71253),x71254))) % 177.41/177.19 [7126]~P108(x71261)+~P1(f327(f327(f235(x71261),x71262),x71264))+~P1(f327(f327(f235(x71261),x71262),x71263))+P1(f327(f327(f235(x71261),x71262),f327(f327(f238(x71261),x71263),x71264))) % 177.41/177.19 [7146]~P62(x71462)+E(x71461,f2(x71462))+E(f327(f327(f291(x71462),f327(f327(f244(x71462),x71461),x71463)),f327(f327(f244(x71462),x71461),x71464)),f327(f327(f244(x71462),x71461),f327(f327(f23(a915),x71463),x71464)))+~P1(f327(f327(f234(a915),x71464),x71463)) % 177.41/177.19 [7192]~P108(x71921)+~P11(x71921,f327(f327(f152(x71921),x71923),x71924))+P11(x71921,f327(f327(f152(x71921),x71922),f327(f327(f152(x71921),x71923),x71924)))+~P1(f327(f327(f234(x71921),x71922),x71923)) % 177.41/177.19 [7230]~P88(x72301)+~P1(f327(f327(f234(x72301),f2(x72301)),x72304))+~P1(f327(f327(f234(x72301),x72302),x72303))+P1(f327(f327(f234(x72301),x72302),f327(f327(f80(x72301),x72303),x72304))) % 177.41/177.19 [7231]~P88(x72311)+~P1(f327(f327(f234(x72311),f2(x72311)),x72313))+~P1(f327(f327(f234(x72311),x72312),x72314))+P1(f327(f327(f234(x72311),x72312),f327(f327(f80(x72311),x72313),x72314))) % 177.41/177.19 [7232]~P126(x72321)+~P1(f327(f327(f235(x72321),f2(x72321)),x72323))+~P1(f327(f327(f235(x72321),x72322),x72324))+P1(f327(f327(f235(x72321),x72322),f327(f327(f80(x72321),x72323),x72324))) % 177.41/177.19 [7233]~P88(x72331)+~P1(f327(f327(f234(x72331),x72332),x72334))+~P1(f327(f327(f235(x72331),f2(x72331)),x72333))+P1(f327(f327(f235(x72331),x72332),f327(f327(f80(x72331),x72333),x72334))) % 177.41/177.19 [7234]~P88(x72341)+~P1(f327(f327(f234(x72341),f2(x72341)),x72343))+~P1(f327(f327(f235(x72341),x72342),x72344))+P1(f327(f327(f235(x72341),x72342),f327(f327(f80(x72341),x72343),x72344))) % 177.41/177.19 [7275]~P108(x72751)+P1(f327(f327(f234(x72751),x72752),x72753))+P1(f327(f327(f234(x72751),x72752),x72754))+~P1(f327(f327(f234(x72751),x72752),f327(f327(f189(x72751),x72754),x72753))) % 177.41/177.19 [7276]~P108(x72761)+P1(f327(f327(f235(x72761),x72762),x72763))+P1(f327(f327(f235(x72761),x72762),x72764))+~P1(f327(f327(f235(x72761),x72762),f327(f327(f189(x72761),x72764),x72763))) % 177.41/177.19 [7570]~P110(x75702)+~P60(x75701)+~P1(f327(f327(f235(f922(x75701,x75702)),x75703),x75704))+P1(f327(f327(f234(f922(x75701,x75702)),x75703),x75704)) % 177.41/177.19 [7932]~P64(x79321)+~P1(f327(f327(f235(x79321),x79324),f2(x79321)))+~P1(f327(f327(f234(x79321),x79323),f327(f327(f291(x79321),x79322),x79324)))+P1(f327(f327(f234(x79321),x79322),f327(f327(f81(x79321),x79323),x79324))) % 177.41/177.19 [7933]~P64(x79331)+~P1(f327(f327(f235(x79331),x79334),f2(x79331)))+~P1(f327(f327(f234(x79331),x79333),f327(f327(f81(x79331),x79332),x79334)))+P1(f327(f327(f234(x79331),x79332),f327(f327(f291(x79331),x79333),x79334))) % 177.41/177.19 [7934]~P64(x79341)+~P1(f327(f327(f235(x79341),x79344),f2(x79341)))+~P1(f327(f327(f235(x79341),x79343),f327(f327(f291(x79341),x79342),x79344)))+P1(f327(f327(f235(x79341),x79342),f327(f327(f81(x79341),x79343),x79344))) % 177.41/177.19 [7935]~P64(x79351)+~P1(f327(f327(f235(x79351),x79354),f2(x79351)))+~P1(f327(f327(f235(x79351),x79353),f327(f327(f81(x79351),x79352),x79354)))+P1(f327(f327(f235(x79351),x79352),f327(f327(f291(x79351),x79353),x79354))) % 177.41/177.19 [8040]~P111(x80401)+~P1(f327(f327(f234(x80401),x80402),f2(x80401)))+~P1(f327(f327(f234(x80401),x80404),x80403))+P1(f327(f327(f234(x80401),f327(f327(f81(x80401),x80402),x80403)),f327(f327(f81(x80401),x80402),x80404))) % 177.41/177.19 [8041]~P127(x80411)+~P1(f327(f327(f235(x80411),x80412),f2(x80411)))+~P1(f327(f327(f234(x80411),x80414),x80413))+P1(f327(f327(f234(x80411),f327(f327(f81(x80411),x80412),x80413)),f327(f327(f81(x80411),x80412),x80414))) % 177.41/177.19 [8042]~P111(x80421)+~P1(f327(f327(f234(x80421),x80423),f2(x80421)))+~P1(f327(f327(f234(x80421),x80424),x80422))+P1(f327(f327(f234(x80421),f327(f327(f81(x80421),x80422),x80423)),f327(f327(f81(x80421),x80424),x80423))) % 177.41/177.19 [8043]~P63(x80431)+~P1(f327(f327(f234(x80431),x80433),f2(x80431)))+~P1(f327(f327(f234(x80431),x80434),x80432))+P1(f327(f327(f234(x80431),f327(f327(f291(x80431),x80432),x80433)),f327(f327(f291(x80431),x80434),x80433))) % 177.41/177.19 [8047]~P127(x80471)+~P1(f327(f327(f235(x80471),x80473),f2(x80471)))+~P1(f327(f327(f235(x80471),x80474),x80472))+P1(f327(f327(f235(x80471),f327(f327(f81(x80471),x80472),x80473)),f327(f327(f81(x80471),x80474),x80473))) % 177.41/177.19 [8048]~P127(x80481)+~P1(f327(f327(f235(x80481),x80482),f2(x80481)))+~P1(f327(f327(f235(x80481),x80484),x80483))+P1(f327(f327(f235(x80481),f327(f327(f81(x80481),x80482),x80483)),f327(f327(f81(x80481),x80482),x80484))) % 177.41/177.19 [8049]~P64(x80491)+~P1(f327(f327(f235(x80491),x80493),f2(x80491)))+~P1(f327(f327(f235(x80491),x80494),x80492))+P1(f327(f327(f235(x80491),f327(f327(f291(x80491),x80492),x80493)),f327(f327(f291(x80491),x80494),x80493))) % 177.41/177.19 [8050]~P126(x80501)+~P1(f327(f327(f235(x80501),f78(x80501)),x80502))+~P1(f327(f327(f234(a915),x80503),x80504))+P1(f327(f327(f234(x80501),f327(f327(f244(x80501),x80502),x80503)),f327(f327(f244(x80501),x80502),x80504))) % 177.41/177.19 [8051]~P126(x80511)+~P1(f327(f327(f234(x80511),f78(x80511)),x80512))+~P1(f327(f327(f234(a915),x80513),x80514))+P1(f327(f327(f234(x80511),f327(f327(f244(x80511),x80512),x80513)),f327(f327(f244(x80511),x80512),x80514))) % 177.41/177.19 [8053]~P126(x80531)+~P1(f327(f327(f235(x80531),f78(x80531)),x80532))+~P1(f327(f327(f235(a915),x80533),x80534))+P1(f327(f327(f235(x80531),f327(f327(f244(x80531),x80532),x80533)),f327(f327(f244(x80531),x80532),x80534))) % 177.41/177.19 [8080]P1(f327(f327(f235(a915),f2(a915)),f327(x80801,x80802)))+~P1(f327(f35(x80803),x80804))+~P1(f327(f327(f329(x80803),x80802),x80804))+~P1(f327(f327(f235(a915),f2(a915)),f327(f327(f9(x80803,a915),x80801),x80804))) % 177.41/177.19 [8089]~P127(x80891)+~P1(f327(f327(f235(x80891),f2(x80891)),x80892))+~P1(f327(f327(f234(x80891),x80893),x80894))+P1(f327(f327(f234(x80891),f327(f327(f81(x80891),x80892),x80893)),f327(f327(f81(x80891),x80892),x80894))) % 177.41/177.19 [8090]~P137(x80901)+~P1(f327(f327(f234(x80901),x80903),x80904))+~P1(f327(f327(f234(x80901),f2(x80901)),x80902))+P1(f327(f327(f234(x80901),f327(f327(f81(x80901),x80902),x80903)),f327(f327(f81(x80901),x80902),x80904))) % 177.41/177.19 [8091]~P136(x80911)+~P1(f327(f327(f234(x80911),x80913),x80914))+~P1(f327(f327(f234(x80911),f2(x80911)),x80912))+P1(f327(f327(f234(x80911),f327(f327(f81(x80911),x80912),x80913)),f327(f327(f81(x80911),x80912),x80914))) % 177.41/177.19 [8092]~P137(x80921)+~P1(f327(f327(f234(x80921),x80922),x80924))+~P1(f327(f327(f234(x80921),f2(x80921)),x80923))+P1(f327(f327(f234(x80921),f327(f327(f81(x80921),x80922),x80923)),f327(f327(f81(x80921),x80924),x80923))) % 177.41/177.19 [8093]~P126(x80931)+~P1(f327(f327(f234(x80931),x80932),x80934))+~P1(f327(f327(f234(x80931),f2(x80931)),x80932))+P1(f327(f327(f234(x80931),f327(f327(f244(x80931),x80932),x80933)),f327(f327(f244(x80931),x80934),x80933))) % 177.41/177.19 [8094]~P63(x80941)+~P1(f327(f327(f234(x80941),x80942),x80944))+~P1(f327(f327(f234(x80941),f2(x80941)),x80943))+P1(f327(f327(f234(x80941),f327(f327(f291(x80941),x80942),x80943)),f327(f327(f291(x80941),x80944),x80943))) % 177.41/177.19 [8096]~P130(x80961)+~P1(f327(f327(f235(x80961),x80963),x80964))+~P1(f327(f327(f235(x80961),f2(x80961)),x80962))+P1(f327(f327(f235(x80961),f327(f327(f81(x80961),x80962),x80963)),f327(f327(f81(x80961),x80962),x80964))) % 177.41/177.19 [8097]~P124(x80971)+~P1(f327(f327(f235(x80971),x80973),x80974))+~P1(f327(f327(f235(x80971),f2(x80971)),x80972))+P1(f327(f327(f235(x80971),f327(f327(f81(x80971),x80972),x80973)),f327(f327(f81(x80971),x80972),x80974))) % 177.41/177.19 [8098]~P127(x80981)+~P1(f327(f327(f235(x80981),x80982),x80984))+~P1(f327(f327(f235(x80981),f2(x80981)),x80983))+P1(f327(f327(f235(x80981),f327(f327(f81(x80981),x80982),x80983)),f327(f327(f81(x80981),x80984),x80983))) % 177.41/177.19 [8099]~P130(x80991)+~P1(f327(f327(f235(x80991),x80992),x80994))+~P1(f327(f327(f235(x80991),f2(x80991)),x80993))+P1(f327(f327(f235(x80991),f327(f327(f81(x80991),x80992),x80993)),f327(f327(f81(x80991),x80994),x80993))) % 177.41/177.19 [8100]~P127(x81001)+~P1(f327(f327(f235(x81001),x81003),x81004))+~P1(f327(f327(f235(x81001),f2(x81001)),x81002))+P1(f327(f327(f235(x81001),f327(f327(f81(x81001),x81002),x81003)),f327(f327(f81(x81001),x81002),x81004))) % 177.41/177.19 [8101]~P64(x81011)+~P1(f327(f327(f235(x81011),x81012),x81014))+~P1(f327(f327(f235(x81011),f2(x81011)),x81013))+P1(f327(f327(f235(x81011),f327(f327(f291(x81011),x81012),x81013)),f327(f327(f291(x81011),x81014),x81013))) % 177.41/177.19 [8143]~P109(x81432)+P1(f327(f327(f235(f922(x81431,x81432)),x81434),x81433))+~P1(f327(f327(f234(f922(x81431,x81432)),x81434),x81433))+P1(f327(f327(f234(f922(x81431,x81432)),x81433),x81434)) % 177.41/177.19 [8183]P1(f327(f327(f329(x81831),x81832),x81833))+P1(f327(f327(f329(x81831),x81832),x81834))+~P1(f327(f327(f234(f922(x81831,a910)),x81834),x81833))+P1(f327(f327(f235(f922(x81831,a910)),x81834),f327(f327(f309(x81831),x81832),x81833))) % 177.41/177.19 [8294]~P120(x82942)+E(x82941,f2(x82942))+P1(f327(f327(f287(x82942),x82943),x82944))+~P1(f327(f327(f287(x82942),f327(f327(f81(x82942),x82943),x82941)),f327(f327(f81(x82942),x82944),x82941))) % 177.41/177.19 [8295]~P120(x82952)+E(x82951,f2(x82952))+P1(f327(f327(f287(x82952),x82953),x82954))+~P1(f327(f327(f287(x82952),f327(f327(f81(x82952),x82951),x82953)),f327(f327(f81(x82952),x82951),x82954))) % 177.41/177.19 [8344]P1(f327(f327(f329(x83441),x83442),x83443))+P1(f327(f327(f329(x83441),x83442),x83444))+~P1(f327(f327(f235(f922(x83441,a910)),x83444),f327(f327(f309(x83441),x83442),x83443)))+P1(f327(f327(f234(f922(x83441,a910)),x83444),x83443)) % 177.41/177.19 [8409]~P127(x84091)+P1(f327(f327(f235(x84091),x84093),x84092))+P1(f327(f327(f235(x84091),x84092),x84093))+~P1(f327(f327(f235(x84091),f327(f327(f81(x84091),x84094),x84092)),f327(f327(f81(x84091),x84094),x84093))) % 177.41/177.19 [8410]~P127(x84101)+P1(f327(f327(f235(x84101),x84103),x84102))+P1(f327(f327(f235(x84101),x84102),x84103))+~P1(f327(f327(f235(x84101),f327(f327(f81(x84101),x84102),x84104)),f327(f327(f81(x84101),x84103),x84104))) % 177.41/177.19 [8421]~P127(x84211)+P1(f327(f327(f235(x84211),x84214),f2(x84211)))+P1(f327(f327(f235(x84211),x84212),x84213))+~P1(f327(f327(f235(x84211),f327(f327(f81(x84211),x84212),x84214)),f327(f327(f81(x84211),x84213),x84214))) % 177.41/177.19 [8422]~P127(x84221)+P1(f327(f327(f235(x84221),x84224),f2(x84221)))+P1(f327(f327(f235(x84221),x84222),x84223))+~P1(f327(f327(f235(x84221),f327(f327(f81(x84221),x84224),x84222)),f327(f327(f81(x84221),x84224),x84223))) % 177.41/177.19 [8425]~P127(x84251)+P1(f327(f327(f235(x84251),x84252),x84253))+P1(f327(f327(f235(x84251),f2(x84251)),x84254))+~P1(f327(f327(f235(x84251),f327(f327(f81(x84251),x84254),x84253)),f327(f327(f81(x84251),x84254),x84252))) % 177.41/177.19 [8426]~P127(x84261)+P1(f327(f327(f235(x84261),x84262),x84263))+P1(f327(f327(f235(x84261),f2(x84261)),x84264))+~P1(f327(f327(f235(x84261),f327(f327(f81(x84261),x84263),x84264)),f327(f327(f81(x84261),x84262),x84264))) % 177.41/177.19 [8439]~P127(x84391)+P1(f327(f327(f235(x84391),x84392),f2(x84391)))+P1(f327(f327(f235(x84391),f2(x84391)),x84392))+~P1(f327(f327(f235(x84391),f327(f327(f81(x84391),x84393),x84392)),f327(f327(f81(x84391),x84394),x84392))) % 177.41/177.19 [8440]~P127(x84401)+P1(f327(f327(f235(x84401),x84402),f2(x84401)))+P1(f327(f327(f235(x84401),f2(x84401)),x84402))+~P1(f327(f327(f235(x84401),f327(f327(f81(x84401),x84402),x84403)),f327(f327(f81(x84401),x84402),x84404))) % 177.41/177.19 [8469]~P127(x84691)+~P1(f327(f327(f235(x84691),x84694),f2(x84691)))+P1(f327(f327(f234(x84691),x84692),x84693))+~P1(f327(f327(f234(x84691),f327(f327(f81(x84691),x84694),x84693)),f327(f327(f81(x84691),x84694),x84692))) % 177.41/177.19 [8470]~P127(x84701)+~P1(f327(f327(f235(x84701),x84704),f2(x84701)))+P1(f327(f327(f235(x84701),x84702),x84703))+~P1(f327(f327(f235(x84701),f327(f327(f81(x84701),x84704),x84703)),f327(f327(f81(x84701),x84704),x84702))) % 177.41/177.19 [8481]~P126(x84813)+~P1(f327(f327(f235(x84813),f78(x84813)),x84814))+P1(f327(f327(f234(a915),x84811),x84812))+~P1(f327(f327(f234(x84813),f327(f327(f244(x84813),x84814),x84811)),f327(f327(f244(x84813),x84814),x84812))) % 177.41/177.19 [8483]~P126(x84833)+~P1(f327(f327(f235(x84833),f78(x84833)),x84834))+P1(f327(f327(f235(a915),x84831),x84832))+~P1(f327(f327(f235(x84833),f327(f327(f244(x84833),x84834),x84831)),f327(f327(f244(x84833),x84834),x84832))) % 177.41/177.19 [8493]~P127(x84931)+P1(f327(f327(f234(x84931),x84932),x84933))+~P1(f327(f327(f235(x84931),f2(x84931)),x84934))+~P1(f327(f327(f234(x84931),f327(f327(f81(x84931),x84934),x84932)),f327(f327(f81(x84931),x84934),x84933))) % 177.41/177.19 [8494]~P130(x84941)+P1(f327(f327(f234(x84941),x84942),x84943))+~P1(f327(f327(f235(x84941),f2(x84941)),x84944))+~P1(f327(f327(f234(x84941),f327(f327(f81(x84941),x84944),x84942)),f327(f327(f81(x84941),x84944),x84943))) % 177.41/177.19 [8495]~P130(x84951)+P1(f327(f327(f234(x84951),x84952),x84953))+~P1(f327(f327(f235(x84951),f2(x84951)),x84954))+~P1(f327(f327(f234(x84951),f327(f327(f81(x84951),x84952),x84954)),f327(f327(f81(x84951),x84953),x84954))) % 177.41/177.19 [8496]~P127(x84961)+P1(f327(f327(f235(x84961),x84962),x84963))+~P1(f327(f327(f235(x84961),f2(x84961)),x84964))+~P1(f327(f327(f235(x84961),f327(f327(f81(x84961),x84964),x84962)),f327(f327(f81(x84961),x84964),x84963))) % 177.41/177.19 [8497]~P130(x84971)+P1(f327(f327(f235(x84971),x84972),x84973))+~P1(f327(f327(f234(x84971),f2(x84971)),x84974))+~P1(f327(f327(f235(x84971),f327(f327(f81(x84971),x84974),x84972)),f327(f327(f81(x84971),x84974),x84973))) % 177.41/177.19 [8498]~P131(x84981)+P1(f327(f327(f235(x84981),x84982),x84983))+~P1(f327(f327(f234(x84981),f2(x84981)),x84984))+~P1(f327(f327(f235(x84981),f327(f327(f81(x84981),x84984),x84982)),f327(f327(f81(x84981),x84984),x84983))) % 177.41/177.19 [8499]~P126(x84991)+~P1(f327(f327(f234(x84991),f2(x84991)),x84993))+P1(f327(f327(f235(x84991),x84992),x84993))+~P1(f327(f327(f235(x84991),f327(f327(f244(x84991),x84992),x84994)),f327(f327(f244(x84991),x84993),x84994))) % 177.41/177.19 [8500]~P130(x85001)+P1(f327(f327(f235(x85001),x85002),x85003))+~P1(f327(f327(f234(x85001),f2(x85001)),x85004))+~P1(f327(f327(f235(x85001),f327(f327(f81(x85001),x85002),x85004)),f327(f327(f81(x85001),x85003),x85004))) % 177.41/177.19 [8501]~P131(x85011)+P1(f327(f327(f235(x85011),x85012),x85013))+~P1(f327(f327(f234(x85011),f2(x85011)),x85014))+~P1(f327(f327(f235(x85011),f327(f327(f81(x85011),x85012),x85014)),f327(f327(f81(x85011),x85013),x85014))) % 177.41/177.19 [8544]P1(f327(f327(f329(x85441),x85442),x85443))+~P1(f327(f327(f234(f922(x85441,a910)),x85443),x85444))+~P1(f327(f327(f235(f922(x85441,a910)),x85443),x85444))+P1(f327(f327(f235(f922(x85441,a910)),x85443),f327(f327(f309(x85441),x85442),x85444))) % 177.41/177.19 [8576]~P139(x85761)+~P121(x85761)+P1(f327(f327(f287(x85761),x85762),f327(f327(f80(x85761),f852(x85762,x85763,x85761)),f2(x85761))))+~P1(f327(x85763,f327(f327(f81(x85761),x85762),x85764))) % 177.41/177.19 [8923]E(f327(f327(f23(a1),f436(x89231,x89232,x89233,x89234)),f437(x89231,x89232,x89233,x89234)),x89234)+~P1(f327(f327(f235(a1),f2(a1)),x89233))+~P1(f327(f327(f234(a1),x89231),x89234))+P1(f327(f327(f234(a1),x89231),f327(f327(f80(a1),x89234),x89233))) % 177.41/177.19 [8924]E(f327(f327(f23(a1),f451(x89241,x89242,x89243,x89244)),f452(x89241,x89242,x89243,x89244)),x89244)+~P1(f327(f327(f235(a1),f2(a1)),x89243))+~P1(f327(f327(f235(a1),x89241),x89244))+P1(f327(f327(f235(a1),x89241),f327(f327(f80(a1),x89244),x89243))) % 177.41/177.19 [9074]~E(f327(f327(f165(x90741),x90743),f674(x90744,x90743,x90741,x90742)),f327(f327(f165(x90741),x90744),f674(x90744,x90743,x90741,x90742)))+E(f327(f327(f176(x90741),x90742),x90743),f327(f327(f176(x90741),x90742),x90744))+~P1(f327(f327(f234(a915),x90742),f327(f191(f916(x90741)),x90743)))+~P1(f327(f327(f234(a915),x90742),f327(f191(f916(x90741)),x90744))) % 177.41/177.19 [9140]~P1(f327(f327(f235(a1),f2(a1)),x91403))+~P1(f327(f327(f234(a1),x91401),x91404))+P1(f327(f327(f329(a1),f436(x91401,x91402,x91403,x91404)),x91402))+P1(f327(f327(f234(a1),x91401),f327(f327(f80(a1),x91404),x91403))) % 177.41/177.19 [9141]~P1(f327(f327(f235(a1),f2(a1)),x91413))+~P1(f327(f327(f235(a1),x91411),x91414))+P1(f327(f327(f329(a1),f451(x91411,x91412,x91413,x91414)),x91412))+P1(f327(f327(f235(a1),x91411),f327(f327(f80(a1),x91414),x91413))) % 177.41/177.19 [9181]~P108(x91811)+~P1(f327(f35(x91811),x91813))+~P1(f327(f327(f329(x91811),x91814),x91813))+P1(f327(f327(f234(x91811),f327(f327(f64(x91811,x91811,f238(x91811)),x91812),x91813)),f327(f327(f238(x91811),x91814),x91812))) % 177.41/177.19 [9182]~P102(x91821)+~P1(f327(f35(x91821),x91823))+~P1(f327(f327(f329(x91821),x91824),x91823))+P1(f327(f327(f234(x91821),f327(f327(f64(x91821,x91821,f103(x91821)),x91822),x91823)),f327(f327(f103(x91821),x91824),x91822))) % 177.41/177.19 [9226]E(f327(f327(f176(x92261),x92262),x92263),f327(f327(f176(x92261),x92262),x92264))+P1(f327(f327(f235(a915),f674(x92263,x92264,x92261,x92262)),x92262))+~P1(f327(f327(f234(a915),x92262),f327(f191(f916(x92261)),x92263)))+~P1(f327(f327(f234(a915),x92262),f327(f191(f916(x92261)),x92264))) % 177.41/177.19 [9231]~P1(f327(f327(f235(a1),f2(a1)),x92313))+~P1(f327(f327(f234(a1),x92311),x92312))+P1(f327(f327(f329(a1),f437(x92311,x92314,x92313,x92312)),f303(a1,f78(a1),x92313)))+P1(f327(f327(f234(a1),x92311),f327(f327(f80(a1),x92312),x92313))) % 177.41/177.19 [9232]~P1(f327(f327(f235(a1),f2(a1)),x92323))+~P1(f327(f327(f235(a1),x92321),x92322))+P1(f327(f327(f329(a1),f452(x92321,x92324,x92323,x92322)),f303(a1,f78(a1),x92323)))+P1(f327(f327(f235(a1),x92321),f327(f327(f80(a1),x92322),x92323))) % 177.41/177.19 [9552]~P108(x95521)+~P1(f327(f35(x95521),x95524))+P1(f327(f327(f329(x95521),f872(x95522,x95523,x95524,x95521)),x95524))+P1(f327(f327(f234(x95521),f327(f327(f64(x95521,x95521,f189(x95521)),x95522),x95524)),f327(f327(f189(x95521),x95523),x95522))) % 177.41/177.19 [9553]~P101(x95531)+~P1(f327(f35(x95531),x95534))+P1(f327(f327(f329(x95531),f508(x95532,x95533,x95534,x95531)),x95534))+P1(f327(f327(f234(x95531),f327(f327(f64(x95531,x95531,f102(x95531)),x95532),x95534)),f327(f327(f102(x95531),x95533),x95532))) % 177.41/177.19 [9681]~P108(x96811)+~P1(f327(f35(x96811),x96813))+~P1(f327(f327(f234(x96811),f872(x96812,x96814,x96813,x96811)),x96814))+P1(f327(f327(f234(x96811),f327(f327(f64(x96811,x96811,f189(x96811)),x96812),x96813)),f327(f327(f189(x96811),x96814),x96812))) % 177.41/177.19 [9682]~P101(x96821)+~P1(f327(f35(x96821),x96823))+~P1(f327(f327(f234(x96821),f508(x96822,x96824,x96823,x96821)),x96824))+P1(f327(f327(f234(x96821),f327(f327(f64(x96821,x96821,f102(x96821)),x96822),x96823)),f327(f327(f102(x96821),x96824),x96822))) % 177.41/177.19 [9684]~P1(f327(f327(f234(a1),f2(a1)),x96844))+~P1(f327(f327(f235(a1),f2(a1)),x96843))+~P1(f327(f327(f235(a1),x96844),x96841))+P1(f327(f327(f235(a1),f327(f327(f80(a1),f327(f327(f81(a1),x96841),f46(a1,x96842,x96843))),x96844)),f327(f327(f81(a1),x96841),x96843))) % 177.41/177.19 [10073]E(x100731,x100732)+P1(f327(f327(f329(f921(f916(x100733),f916(x100733))),f327(f327(f252(f916(x100733),f916(x100733)),x100732),x100731)),f148(x100733,x100734)))+P1(f327(f327(f329(f921(f916(x100733),f916(x100733))),f327(f327(f252(f916(x100733),f916(x100733)),x100731),x100732)),f148(x100733,x100734)))+~P1(f327(f327(f329(f921(x100733,x100733)),f327(f327(f252(x100733,x100733),f651(x100731,x100732,x100734,x100733)),f652(x100731,x100732,x100734,x100733))),x100734)) % 177.41/177.19 [10074]E(x100741,x100742)+P1(f327(f327(f329(f921(f916(x100743),f916(x100743))),f327(f327(f252(f916(x100743),f916(x100743)),x100742),x100741)),f148(x100743,x100744)))+P1(f327(f327(f329(f921(f916(x100743),f916(x100743))),f327(f327(f252(f916(x100743),f916(x100743)),x100741),x100742)),f148(x100743,x100744)))+~P1(f327(f327(f329(f921(x100743,x100743)),f327(f327(f252(x100743,x100743),f652(x100741,x100742,x100744,x100743)),f651(x100741,x100742,x100744,x100743))),x100744)) % 177.41/177.19 [7636]~P108(x76361)+~P1(f327(f327(f234(x76361),x76363),x76364))+~P1(f327(f327(f234(x76361),x76362),x76364))+P1(f327(f327(f234(x76361),f327(f327(f189(x76361),x76362),x76363)),x76364)) % 177.41/177.19 [7639]~P101(x76391)+~P1(f327(f327(f234(x76391),x76393),x76394))+~P1(f327(f327(f234(x76391),x76392),x76394))+P1(f327(f327(f234(x76391),f327(f327(f102(x76391),x76392),x76393)),x76394)) % 177.41/177.19 [7640]~P108(x76401)+~P1(f327(f327(f235(x76401),x76403),x76404))+~P1(f327(f327(f235(x76401),x76402),x76404))+P1(f327(f327(f235(x76401),f327(f327(f189(x76401),x76402),x76403)),x76404)) % 177.41/177.19 [7957]~E(x79571,x79573)+E(f140(a915,f327(f302(a915,x79571),x79572)),f327(f327(f152(a915),x79573),x79574))+~E(f140(a915,f327(f302(a915,f327(f327(f80(a915),x79571),f78(a915))),x79572)),x79574)+~P1(f327(f327(f235(a915),x79571),x79572)) % 177.41/177.19 [7965]~P108(x79651)+P1(f327(f327(f234(x79651),x79652),x79653))+P1(f327(f327(f234(x79651),x79654),x79653))+~P1(f327(f327(f234(x79651),f327(f327(f238(x79651),x79654),x79652)),x79653)) % 177.41/177.19 [7966]~P108(x79661)+P1(f327(f327(f235(x79661),x79662),x79663))+P1(f327(f327(f235(x79661),x79664),x79663))+~P1(f327(f327(f235(x79661),f327(f327(f238(x79661),x79664),x79662)),x79663)) % 177.41/177.19 [8241]~P63(x82411)+~P1(f327(f327(f235(x82411),f2(x82411)),x82413))+~P1(f327(f327(f234(x82411),x82412),f327(f327(f291(x82411),x82414),x82413)))+P1(f327(f327(f234(x82411),f327(f327(f81(x82411),x82412),x82413)),x82414)) % 177.41/177.19 [8242]~P64(x82421)+~P1(f327(f327(f235(x82421),f2(x82421)),x82423))+~P1(f327(f327(f234(x82421),x82422),f327(f327(f291(x82421),x82424),x82423)))+P1(f327(f327(f234(x82421),f327(f327(f81(x82421),x82422),x82423)),x82424)) % 177.41/177.19 [8243]~P63(x82431)+~P1(f327(f327(f235(x82431),f2(x82431)),x82433))+~P1(f327(f327(f234(x82431),x82432),f327(f327(f81(x82431),x82434),x82433)))+P1(f327(f327(f234(x82431),f327(f327(f291(x82431),x82432),x82433)),x82434)) % 177.41/177.19 [8245]~P64(x82451)+~P1(f327(f327(f235(x82451),f2(x82451)),x82453))+~P1(f327(f327(f234(x82451),x82452),f327(f327(f81(x82451),x82454),x82453)))+P1(f327(f327(f234(x82451),f327(f327(f291(x82451),x82452),x82453)),x82454)) % 177.41/177.19 [8246]~P63(x82461)+~P1(f327(f327(f235(x82461),f2(x82461)),x82463))+~P1(f327(f327(f235(x82461),x82462),f327(f327(f291(x82461),x82464),x82463)))+P1(f327(f327(f235(x82461),f327(f327(f81(x82461),x82462),x82463)),x82464)) % 177.41/177.19 [8247]~P64(x82471)+~P1(f327(f327(f235(x82471),f2(x82471)),x82473))+~P1(f327(f327(f235(x82471),x82472),f327(f327(f291(x82471),x82474),x82473)))+P1(f327(f327(f235(x82471),f327(f327(f81(x82471),x82472),x82473)),x82474)) % 177.41/177.19 [8248]~P63(x82481)+~P1(f327(f327(f235(x82481),f2(x82481)),x82483))+~P1(f327(f327(f235(x82481),x82482),f327(f327(f81(x82481),x82484),x82483)))+P1(f327(f327(f235(x82481),f327(f327(f291(x82481),x82482),x82483)),x82484)) % 177.41/177.19 [8250]~P64(x82501)+~P1(f327(f327(f235(x82501),f2(x82501)),x82503))+~P1(f327(f327(f235(x82501),x82502),f327(f327(f81(x82501),x82504),x82503)))+P1(f327(f327(f235(x82501),f327(f327(f291(x82501),x82502),x82503)),x82504)) % 177.41/177.19 [8379]~P63(x83791)+~P1(f327(f327(f235(x83791),f2(x83791)),x83794))+P1(f327(f327(f234(x83791),x83792),f327(f327(f81(x83791),x83793),x83794)))+~P1(f327(f327(f234(x83791),f327(f327(f291(x83791),x83792),x83794)),x83793)) % 177.41/177.19 [8380]~P63(x83801)+~P1(f327(f327(f235(x83801),f2(x83801)),x83804))+P1(f327(f327(f234(x83801),x83802),f327(f327(f291(x83801),x83803),x83804)))+~P1(f327(f327(f234(x83801),f327(f327(f81(x83801),x83802),x83804)),x83803)) % 177.41/177.19 [8382]~P64(x83821)+~P1(f327(f327(f235(x83821),f2(x83821)),x83824))+P1(f327(f327(f234(x83821),x83822),f327(f327(f81(x83821),x83823),x83824)))+~P1(f327(f327(f234(x83821),f327(f327(f291(x83821),x83822),x83824)),x83823)) % 177.41/177.19 [8383]~P64(x83831)+~P1(f327(f327(f235(x83831),f2(x83831)),x83834))+P1(f327(f327(f234(x83831),x83832),f327(f327(f291(x83831),x83833),x83834)))+~P1(f327(f327(f234(x83831),f327(f327(f81(x83831),x83832),x83834)),x83833)) % 177.41/177.19 [8384]~P63(x83841)+~P1(f327(f327(f235(x83841),f2(x83841)),x83844))+P1(f327(f327(f235(x83841),x83842),f327(f327(f81(x83841),x83843),x83844)))+~P1(f327(f327(f235(x83841),f327(f327(f291(x83841),x83842),x83844)),x83843)) % 177.41/177.19 [8385]~P63(x83851)+~P1(f327(f327(f235(x83851),f2(x83851)),x83854))+P1(f327(f327(f235(x83851),x83852),f327(f327(f291(x83851),x83853),x83854)))+~P1(f327(f327(f235(x83851),f327(f327(f81(x83851),x83852),x83854)),x83853)) % 177.41/177.19 [8387]~P64(x83871)+~P1(f327(f327(f235(x83871),f2(x83871)),x83874))+P1(f327(f327(f235(x83871),x83872),f327(f327(f81(x83871),x83873),x83874)))+~P1(f327(f327(f235(x83871),f327(f327(f291(x83871),x83872),x83874)),x83873)) % 177.41/177.19 [8388]~P64(x83881)+~P1(f327(f327(f235(x83881),f2(x83881)),x83884))+P1(f327(f327(f235(x83881),x83882),f327(f327(f291(x83881),x83883),x83884)))+~P1(f327(f327(f235(x83881),f327(f327(f81(x83881),x83882),x83884)),x83883)) % 177.41/177.19 [8547]~P64(x85471)+~P1(f327(f327(f235(x85471),x85473),f2(x85471)))+~P1(f327(f327(f234(x85471),f327(f327(f291(x85471),x85474),x85473)),x85472))+P1(f327(f327(f234(x85471),f327(f327(f81(x85471),x85472),x85473)),x85474)) % 177.41/177.19 [8548]~P64(x85481)+~P1(f327(f327(f235(x85481),x85483),f2(x85481)))+~P1(f327(f327(f234(x85481),f327(f327(f81(x85481),x85484),x85483)),x85482))+P1(f327(f327(f234(x85481),f327(f327(f291(x85481),x85482),x85483)),x85484)) % 177.41/177.19 [8549]~P64(x85491)+~P1(f327(f327(f235(x85491),x85493),f2(x85491)))+~P1(f327(f327(f235(x85491),f327(f327(f291(x85491),x85494),x85493)),x85492))+P1(f327(f327(f235(x85491),f327(f327(f81(x85491),x85492),x85493)),x85494)) % 177.41/177.19 [8550]~P64(x85501)+~P1(f327(f327(f235(x85501),x85503),f2(x85501)))+~P1(f327(f327(f235(x85501),f327(f327(f81(x85501),x85504),x85503)),x85502))+P1(f327(f327(f235(x85501),f327(f327(f291(x85501),x85502),x85503)),x85504)) % 177.41/177.19 [8562]~P1(f327(x85621,x85624))+~P1(f327(f327(f235(a915),x85622),f327(f327(f81(a915),x85623),f327(a113,x85624))))+P1(f327(x85621,f327(f327(f37(a915),x85622),x85623)))+~P1(f327(f327(f234(a915),f327(f327(f81(a915),x85623),x85624)),x85622)) % 177.41/177.19 [8771]~P108(x87711)+~P1(f327(f35(x87711),x87714))+~P1(f327(f327(f329(x87711),x87712),x87714))+P1(f327(f327(f234(x87711),f327(f327(f189(x87711),x87712),x87713)),f327(f327(f64(x87711,x87711,f189(x87711)),x87713),x87714))) % 177.41/177.19 [8772]~P101(x87721)+~P1(f327(f35(x87721),x87724))+~P1(f327(f327(f329(x87721),x87722),x87724))+P1(f327(f327(f234(x87721),f327(f327(f102(x87721),x87722),x87723)),f327(f327(f64(x87721,x87721,f102(x87721)),x87723),x87724))) % 177.41/177.19 [8925]~P1(f327(f35(x89251),x89252))+E(f327(f36(x89251),f327(f327(f23(f922(x89251,a910)),x89252),f327(f327(f309(x89251),x89253),x89254))),f327(f327(f23(a915),f327(f36(x89251),f327(f327(f23(f922(x89251,a910)),x89252),x89254))),f78(a915)))+P1(f327(f327(f329(x89251),x89253),x89254))+~P1(f327(f327(f329(x89251),x89253),x89252)) % 177.41/177.19 [9002]E(f327(f327(f80(a1),f438(x90021,x90022,x90023,x90024)),f439(x90021,x90022,x90023,x90024)),x90024)+~P1(f327(f327(f235(a1),f2(a1)),x90023))+~P1(f327(f327(f234(a1),x90024),x90021))+P1(f327(f327(f234(a1),f327(f327(f23(a1),x90024),x90023)),x90021)) % 177.41/177.19 [9003]E(f327(f327(f80(a1),f453(x90031,x90032,x90033,x90034)),f444(x90031,x90032,x90033,x90034)),x90034)+~P1(f327(f327(f235(a1),f2(a1)),x90033))+~P1(f327(f327(f235(a1),x90034),x90031))+P1(f327(f327(f235(a1),f327(f327(f23(a1),x90034),x90033)),x90031)) % 177.41/177.19 [9211]~P1(f327(f327(f235(a1),f2(a1)),x92113))+~P1(f327(f327(f234(a1),x92114),x92111))+P1(f327(f327(f329(a1),f438(x92111,x92112,x92113,x92114)),x92112))+P1(f327(f327(f234(a1),f327(f327(f23(a1),x92114),x92113)),x92111)) % 177.41/177.19 [9212]~P1(f327(f327(f235(a1),f2(a1)),x92123))+~P1(f327(f327(f235(a1),x92124),x92121))+P1(f327(f327(f329(a1),f453(x92121,x92122,x92123,x92124)),x92122))+P1(f327(f327(f235(a1),f327(f327(f23(a1),x92124),x92123)),x92121)) % 177.41/177.19 [9298]~P1(f327(f327(f235(a1),f2(a1)),x92982))+~P1(f327(f327(f234(a1),x92981),x92983))+P1(f327(f327(f329(a1),f439(x92983,x92984,x92982,x92981)),f303(a1,f78(a1),x92982)))+P1(f327(f327(f234(a1),f327(f327(f23(a1),x92981),x92982)),x92983)) % 177.41/177.19 [9299]~P1(f327(f327(f235(a1),f2(a1)),x92992))+~P1(f327(f327(f235(a1),x92991),x92993))+P1(f327(f327(f329(a1),f444(x92993,x92994,x92992,x92991)),f303(a1,f78(a1),x92992)))+P1(f327(f327(f235(a1),f327(f327(f23(a1),x92991),x92992)),x92993)) % 177.41/177.19 [9317]~P1(f327(f327(f234(a1),f2(a1)),x93174))+~P1(f327(f327(f235(a1),f2(a1)),x93173))+~P1(f327(f327(f235(a1),x93174),x93171))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),f327(f327(f81(a1),x93171),f46(a1,x93172,x93173))),x93174))) % 177.41/177.19 [9346]E(x93461,x93462)+~P37(x93463,x93464)+~P1(f327(f327(f329(f921(x93463,x93463)),f327(f327(f252(x93463,x93463),x93462),x93461)),x93464))+~P1(f327(f327(f329(f921(x93463,x93463)),f327(f327(f252(x93463,x93463),x93461),x93462)),x93464)) % 177.41/177.19 [9378]~P108(x93781)+~P1(f327(f35(x93781),x93784))+~P1(f327(f327(f234(x93781),x93782),f871(x93783,x93782,x93784,x93781)))+P1(f327(f327(f234(x93781),f327(f327(f238(x93781),x93782),x93783)),f327(f327(f64(x93781,x93781,f238(x93781)),x93783),x93784))) % 177.41/177.19 [9379]~P102(x93791)+~P1(f327(f35(x93791),x93794))+~P1(f327(f327(f234(x93791),x93792),f506(x93793,x93792,x93794,x93791)))+P1(f327(f327(f234(x93791),f327(f327(f103(x93791),x93792),x93793)),f327(f327(f64(x93791,x93791,f103(x93791)),x93793),x93794))) % 177.41/177.19 [9395]~P1(f327(f327(f234(a1),x93954),f2(a1)))+~P1(f327(f327(f235(a1),f2(a1)),x93952))+~P1(f327(f327(f235(a1),x93951),x93954))+P1(f327(f327(f235(a1),f327(f327(f81(a1),x93951),x93952)),f327(f327(f80(a1),f327(f327(f81(a1),x93951),f46(a1,x93953,x93952))),x93954))) % 177.41/177.19 [9420]P1(f327(f35(x94201),x94202))+~P1(f327(f35(x94201),x94203))+~P1(f327(f327(f329(f922(x94201,a910)),x94202),f327(f327(f61(x94201),x94203),x94204)))+~P1(f327(f327(f234(f922(f921(x94201,x94201),a910)),x94204),f327(f327(f254(x94201,x94201),x94203),f327(f16(f922(x94201,a910),x94201),x94203)))) % 177.41/177.19 [9444]~P108(x94441)+~P1(f327(f35(x94441),x94444))+P1(f327(f327(f329(x94441),f871(x94442,x94443,x94444,x94441)),x94444))+P1(f327(f327(f234(x94441),f327(f327(f238(x94441),x94443),x94442)),f327(f327(f64(x94441,x94441,f238(x94441)),x94442),x94444))) % 177.41/177.19 [9445]~P102(x94451)+~P1(f327(f35(x94451),x94454))+P1(f327(f327(f329(x94451),f506(x94452,x94453,x94454,x94451)),x94454))+P1(f327(f327(f234(x94451),f327(f327(f103(x94451),x94453),x94452)),f327(f327(f64(x94451,x94451,f103(x94451)),x94452),x94454))) % 177.41/177.19 [9849]~P1(f327(f35(x98492),x98494))+~P1(f327(f35(x98491),x98493))+~P1(f327(f327(f234(a915),f327(f36(x98492),x98494)),f327(f36(x98491),x98493)))+P1(f327(f327(f234(f922(x98491,a910)),f327(f310(x98492,x98491,f875(x98493,x98491,x98494,x98492)),x98494)),x98493)) % 177.41/177.19 [9493]~P1(f327(f327(f329(x94931),x94932),x94934))+P1(f327(f327(f329(x94931),x94932),x94933))+~P1(f327(f327(f235(f922(x94931,a910)),x94934),f327(f327(f309(x94931),x94932),x94933)))+P1(f327(f327(f235(f922(x94931,a910)),f327(f327(f23(f922(x94931,a910)),x94934),f327(f327(f309(x94931),x94932),f190(f922(x94931,a910))))),x94933)) % 177.41/177.19 [9661]~P1(f327(f327(f329(x96611),x96612),x96614))+P1(f327(f327(f329(x96611),x96612),x96613))+P1(f327(f327(f235(f922(x96611,a910)),x96614),f327(f327(f309(x96611),x96612),x96613)))+~P1(f327(f327(f235(f922(x96611,a910)),f327(f327(f23(f922(x96611,a910)),x96614),f327(f327(f309(x96611),x96612),f190(f922(x96611,a910))))),x96613)) % 177.41/177.19 [9687]P1(f327(f327(f329(x96871),x96872),x96873))+~P1(f327(f327(f234(f922(x96871,a910)),x96874),x96873))+P1(f327(f327(f235(f922(x96871,a910)),x96874),f327(f327(f309(x96871),x96872),x96873)))+~P1(f327(f327(f235(f922(x96871,a910)),f327(f327(f23(f922(x96871,a910)),x96874),f327(f327(f309(x96871),x96872),f190(f922(x96871,a910))))),x96873)) % 177.41/177.19 [9692]~P1(f327(f327(f329(x96921),x96923),x96922))+~P1(f327(f327(f235(f922(x96921,a910)),x96922),x96924))+P1(f327(f327(f235(f922(x96921,a910)),x96922),f327(f327(f309(x96921),x96923),x96924)))+~P1(f327(f327(f235(f922(x96921,a910)),f327(f327(f23(f922(x96921,a910)),x96922),f327(f327(f309(x96921),x96923),f190(f922(x96921,a910))))),x96924)) % 177.41/177.19 [9709]~P1(f327(f327(f234(f922(x97091,a910)),x97092),x97094))+~P1(f327(f327(f235(f922(x97091,a910)),x97092),x97094))+P1(f327(f327(f235(f922(x97091,a910)),x97092),f327(f327(f309(x97091),x97093),x97094)))+~P1(f327(f327(f235(f922(x97091,a910)),f327(f327(f23(f922(x97091,a910)),x97092),f327(f327(f309(x97091),x97093),f190(f922(x97091,a910))))),x97094)) % 177.41/177.19 [9754]~P110(x97542)+~P60(x97541)+~P1(f327(f327(f234(f922(x97541,x97542)),x97543),x97544))+P1(f327(f58(x97541),f327(f327(f18(x97541,x97542,a910),f327(f327(f8(x97542,f922(x97542,a910),x97541),f234(x97542)),x97543)),x97544))) % 177.41/177.19 [9897]~P110(x98972)+~P60(x98971)+P1(f327(f327(f234(f922(x98971,x98972)),x98973),x98974))+~P1(f327(f58(x98971),f327(f327(f18(x98971,x98972,a910),f327(f327(f8(x98972,f922(x98972,a910),x98971),f234(x98972)),x98973)),x98974))) % 177.41/177.19 [10064]E(f327(f327(f165(x100641),f327(f327(f165(f916(x100641)),f180(x100641,x100642)),x100643)),x100644),f327(f327(f165(x100641),f327(f327(f165(f916(x100641)),x100642),x100644)),x100643))+~P1(f327(f327(f235(a915),x100643),f327(f191(f916(f916(x100641))),f180(x100641,x100642))))+~P11(a915,f327(f169(a915),f327(f327(f155(f916(x100641),a915),f191(f916(x100641))),x100642)))+~P1(f327(f327(f235(a915),x100644),f327(f191(f916(f916(x100641))),f327(f137(f916(x100641),f327(f327(f8(a915,a910,f916(x100641)),f327(f235(a915),x100643)),f191(f916(x100641)))),x100642)))) % 177.41/177.19 [10085]~P1(f327(f327(f329(f921(a915,a915)),x100854),x100851))+~P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),x100854),x100852)),a32))+~P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x100851),x100853)),a33))+P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x100851),f327(f327(f309(f921(a915,a915)),x100852),x100853))),a33)) % 177.41/177.19 [10086]~P1(f327(f327(f329(f921(a915,a915)),x100864),x100861))+~P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),x100864),x100862)),a70))+~P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x100861),x100863)),a71))+P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x100861),f327(f327(f309(f921(a915,a915)),x100862),x100863))),a71)) % 177.41/177.19 [9975]~P110(x99752)+~P60(x99751)+~P1(f327(f327(f235(f922(x99751,x99752)),x99753),x99754))+P1(f327(f57(x99751),f327(f327(f8(a910,a910,x99751),a322),f327(f327(f18(x99751,x99752,a910),f327(f327(f8(x99752,f922(x99752,a910),x99751),a324),x99753)),x99754)))) % 177.41/177.19 [10098]~P1(f327(f327(f329(f921(a915,a915)),x100984),x100983))+~P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),x100981),x100984)),a32))+~P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x100982),x100983)),a34))+P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),f327(f327(f309(f921(a915,a915)),x100981),x100982)),x100983)),a34)) % 177.41/177.19 [10099]~P1(f327(f327(f329(f921(a915,a915)),x100994),x100993))+~P1(f327(f327(f329(f921(f921(a915,a915),f921(a915,a915))),f327(f327(f252(f921(a915,a915),f921(a915,a915)),x100991),x100994)),a70))+~P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),x100992),x100993)),a69))+P1(f327(f327(f329(f921(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910))),f327(f327(f252(f922(f921(a915,a915),a910),f922(f921(a915,a915),a910)),f327(f327(f309(f921(a915,a915)),x100991),x100992)),x100993)),a69)) % 177.41/177.19 [6214]~P5(x62144,x62141)+~P1(f327(f327(x62141,x62142),x62145))+P1(f327(f327(x62141,x62142),x62143))+~P1(f327(f327(x62141,x62145),x62143)) % 177.41/177.19 [6215]~P47(x62154,x62151)+~P1(f327(f327(x62151,x62152),x62155))+P1(f327(f327(x62151,x62152),x62153))+~P1(f327(f327(x62151,x62155),x62153)) % 177.41/177.19 [6216]~P13(x62164,x62161)+~P1(f327(f327(x62161,x62162),x62165))+P1(f327(f327(x62161,x62162),x62163))+~P1(f327(f327(x62161,x62165),x62163)) % 177.41/177.19 [8910]~P5(x89104,x89103)+~P1(f327(x89101,x89105))+P1(f327(x89102,f828(x89102,x89101,x89103,x89104)))+P1(f327(x89101,f827(x89102,x89101,x89103,x89104))) % 177.41/177.19 [9148]~P5(x91484,x91483)+~P1(f327(x91482,x91485))+~P1(f327(x91481,f827(x91481,x91482,x91483,x91484)))+P1(f327(x91481,f828(x91481,x91482,x91483,x91484))) % 177.41/177.19 [9330]~P5(x93304,x93303)+~P1(f327(x93301,x93305))+P1(f327(f327(f329(x93304),f828(x93302,x93301,x93303,x93304)),f270(x93304,x93303)))+P1(f327(x93301,f827(x93302,x93301,x93303,x93304))) % 177.41/177.19 [9451]~P5(x94511,x94514)+~P1(f327(x94513,x94515))+~P1(f327(x94512,f827(x94512,x94513,x94514,x94511)))+P1(f327(f327(f329(x94511),f828(x94512,x94513,x94514,x94511)),f270(x94511,x94514))) % 177.41/177.19 [9743]~P36(x97431,x97434)+P1(f327(f327(f329(f921(f916(x97431),f916(x97431))),f327(f327(f252(f916(x97431),f916(x97431)),x97432),x97433)),f148(x97431,x97434)))+~P1(f327(f327(f329(f921(f916(x97431),f916(x97431))),f327(f327(f252(f916(x97431),f916(x97431)),x97432),x97435)),f148(x97431,x97434)))+~P1(f327(f327(f329(f921(f916(x97431),f916(x97431))),f327(f327(f252(f916(x97431),f916(x97431)),x97435),x97433)),f148(x97431,x97434))) % 177.41/177.19 [5451]~P67(x54515)+E(x54511,x54512)+~E(x54513,x54514)+~E(f327(f327(f23(x54515),x54513),x54514),f327(f327(f23(x54515),x54511),x54512)) % 177.41/177.19 [6333]~P15(x63335,x63331,x63333)+E(f327(f327(x63331,x63332),f327(x63333,x63334)),f327(x63333,x63334))+~P1(f327(f35(x63335),x63334))+~P1(f327(f327(f329(x63335),x63332),x63334)) % 177.41/177.19 [6524]~P78(x65241)+~E(f327(f327(f23(x65241),x65244),x65245),f327(f327(f23(x65241),x65242),x65243))+~P1(f327(f327(f234(x65241),x65244),x65245))+P1(f327(f327(f234(x65241),x65242),x65243)) % 177.41/177.19 [6526]~P78(x65261)+~E(f327(f327(f23(x65261),x65264),x65265),f327(f327(f23(x65261),x65262),x65263))+~P1(f327(f327(f235(x65261),x65264),x65265))+P1(f327(f327(f235(x65261),x65262),x65263)) % 177.41/177.19 [7505]~E(x75052,f327(f327(f152(x75051),x75054),x75055))+P1(f327(f327(f329(f916(x75051)),x75052),f162(x75051,x75053)))+~P1(f327(f327(f329(f916(x75051)),x75055),f162(x75051,x75053)))+~P1(f327(f327(f329(x75051),x75054),x75053)) % 177.41/177.19 [7906]~E(f327(f191(f916(x79061)),x79063),f327(f191(f916(x79062)),x79064))+~E(f327(f327(f155(f921(x79061,x79062),x79062),f256(x79061,x79062)),x79065),x79064)+~E(f327(f327(f155(f921(x79061,x79062),x79061),f251(x79061,x79062)),x79065),x79063)+E(f327(f327(f182(x79061,x79062),x79063),x79064),x79065) % 177.41/177.19 [8237]~P110(x82371)+P1(f327(f327(f235(f922(x82371,a910)),f303(x82371,x82372,x82373)),f303(x82371,x82374,x82375)))+~P1(f327(f327(f234(x82371),x82374),x82375))+P1(f327(f327(f234(x82371),x82372),x82373)) % 177.41/177.19 [8337]~P110(x83371)+P1(f327(f327(f234(f922(x83371,a910)),f303(x83371,x83372,x83373)),f303(x83371,x83374,x83375)))+~P1(f327(f327(f234(x83371),x83373),x83375))+~P1(f327(f327(f234(x83371),x83374),x83372)) % 177.41/177.19 [8455]~P108(x84551)+P1(f327(f327(f234(x84551),x84552),x84553))+P1(f327(f327(f234(x84551),x84554),x84553))+~P1(f327(f327(f234(f922(x84551,a910)),f327(f302(x84551,x84553),x84552)),f327(f302(x84551,x84554),x84555))) % 177.41/177.19 [8456]~P108(x84561)+P1(f327(f327(f234(x84561),x84562),x84563))+P1(f327(f327(f234(x84561),x84562),x84564))+~P1(f327(f327(f234(f922(x84561,a910)),f327(f302(x84561,x84563),x84562)),f327(f302(x84561,x84565),x84564))) % 177.41/177.19 [8688]~P110(x86881)+~P1(f327(f327(f234(f922(x86881,a910)),f303(x86881,x86884,x86882)),f303(x86881,x86885,x86883)))+P1(f327(f327(f234(x86881),x86882),x86883))+~P1(f327(f327(f234(x86881),x86884),x86882)) % 177.41/177.19 [8689]~P110(x86891)+~P1(f327(f327(f235(f922(x86891,a910)),f303(x86891,x86894,x86892)),f303(x86891,x86895,x86893)))+P1(f327(f327(f234(x86891),x86892),x86893))+~P1(f327(f327(f234(x86891),x86894),x86892)) % 177.41/177.19 [8690]~P110(x86901)+~P1(f327(f327(f234(f922(x86901,a910)),f303(x86901,x86903,x86904)),f303(x86901,x86902,x86905)))+P1(f327(f327(f234(x86901),x86902),x86903))+~P1(f327(f327(f234(x86901),x86903),x86904)) % 177.41/177.19 [8691]~P110(x86911)+~P1(f327(f327(f235(f922(x86911,a910)),f303(x86911,x86913,x86914)),f303(x86911,x86912,x86915)))+P1(f327(f327(f234(x86911),x86912),x86913))+~P1(f327(f327(f234(x86911),x86913),x86914)) % 177.41/177.19 [6213]~P15(x62132,x62135,x62133)+E(x62131,f190(f922(x62132,a910)))+~P1(f327(f35(x62132),x62131))+E(f327(x62133,f327(f327(f309(x62132),x62134),x62131)),f327(f327(x62135,x62134),f327(x62133,x62131))) % 177.41/177.19 [6994]~E(x69941,x69942)+~E(f327(f327(f103(f922(x69943,a910)),x69944),x69945),f190(f922(x69943,a910)))+~P1(f327(f327(f329(x69943),x69942),x69945))+~P1(f327(f327(f329(x69943),x69941),x69944)) % 177.41/177.19 [7075]~P16(x70752,x70755,x70751)+~P1(f327(f35(x70752),x70754))+E(f327(x70751,f327(f327(f309(x70752),x70753),x70754)),f327(f327(f64(x70752,x70752,x70755),x70753),x70754))+P1(f327(f327(f329(x70752),x70753),x70754)) % 177.41/177.19 [7142]~P68(x71422)+~P1(f327(f35(x71421),x71425))+E(f327(f327(f6(x71421,x71422),x71423),f327(f327(f309(x71421),x71424),x71425)),f327(f327(f80(x71422),f327(x71423,x71424)),f327(f327(f6(x71421,x71422),x71423),x71425)))+P1(f327(f327(f329(x71421),x71424),x71425)) % 177.41/177.19 [7144]~P75(x71442)+~P1(f327(f35(x71441),x71445))+E(f327(f327(f9(x71441,x71442),x71443),f327(f327(f309(x71441),x71444),x71445)),f327(f327(f81(x71442),f327(x71443,x71444)),f327(f327(f9(x71441,x71442),x71443),x71445)))+P1(f327(f327(f329(x71441),x71444),x71445)) % 177.41/177.19 [7649]~P16(x76492,x76495,x76491)+~P1(f327(f35(x76492),x76494))+E(f327(x76491,f327(f327(f309(x76492),x76493),x76494)),x76493)+~E(f327(f327(f23(f922(x76492,a910)),x76494),f327(f327(f309(x76492),x76493),f190(f922(x76492,a910)))),f190(f922(x76492,a910))) % 177.41/177.19 [8005]~P58(x80051)+E(f327(f327(f37(x80051),f327(f327(f81(x80051),x80052),x80053)),f327(f327(f81(x80051),x80054),x80055)),f327(f327(f81(x80051),f327(f327(f37(x80051),x80052),x80054)),f327(f327(f37(x80051),x80053),x80055)))+~P1(f327(f327(f287(x80051),x80055),x80053))+~P1(f327(f327(f287(x80051),x80054),x80052)) % 177.41/177.19 [8009]~P83(x80091)+~P1(f327(f327(f234(x80091),x80093),x80095))+~P1(f327(f327(f234(x80091),x80092),x80094))+P1(f327(f327(f234(x80091),f327(f327(f80(x80091),x80092),x80093)),f327(f327(f80(x80091),x80094),x80095))) % 177.41/177.19 [8010]~P108(x80101)+~P1(f327(f327(f234(x80101),x80103),x80105))+~P1(f327(f327(f234(x80101),x80102),x80104))+P1(f327(f327(f234(x80101),f327(f327(f238(x80101),x80102),x80103)),f327(f327(f238(x80101),x80104),x80105))) % 177.41/177.19 [8011]~P108(x80111)+~P1(f327(f327(f234(x80111),x80113),x80115))+~P1(f327(f327(f234(x80111),x80112),x80114))+P1(f327(f327(f234(x80111),f327(f327(f189(x80111),x80112),x80113)),f327(f327(f189(x80111),x80114),x80115))) % 177.41/177.19 [8012]~P101(x80121)+~P1(f327(f327(f234(x80121),x80123),x80125))+~P1(f327(f327(f234(x80121),x80122),x80124))+P1(f327(f327(f234(x80121),f327(f327(f102(x80121),x80122),x80123)),f327(f327(f102(x80121),x80124),x80125))) % 177.41/177.19 [8013]~P102(x80131)+~P1(f327(f327(f234(x80131),x80133),x80135))+~P1(f327(f327(f234(x80131),x80132),x80134))+P1(f327(f327(f234(x80131),f327(f327(f103(x80131),x80132),x80133)),f327(f327(f103(x80131),x80134),x80135))) % 177.41/177.19 [8014]~P85(x80141)+~P1(f327(f327(f234(x80141),x80143),x80145))+~P1(f327(f327(f235(x80141),x80142),x80144))+P1(f327(f327(f235(x80141),f327(f327(f80(x80141),x80142),x80143)),f327(f327(f80(x80141),x80144),x80145))) % 177.41/177.19 [8015]~P85(x80151)+~P1(f327(f327(f234(x80151),x80152),x80154))+~P1(f327(f327(f235(x80151),x80153),x80155))+P1(f327(f327(f235(x80151),f327(f327(f80(x80151),x80152),x80153)),f327(f327(f80(x80151),x80154),x80155))) % 177.41/177.19 [8016]~P85(x80161)+~P1(f327(f327(f235(x80161),x80163),x80165))+~P1(f327(f327(f235(x80161),x80162),x80164))+P1(f327(f327(f235(x80161),f327(f327(f80(x80161),x80162),x80163)),f327(f327(f80(x80161),x80164),x80165))) % 177.41/177.19 [8017]~P112(x80171)+~P1(f327(f327(f287(x80171),x80173),x80175))+~P1(f327(f327(f287(x80171),x80172),x80174))+P1(f327(f327(f287(x80171),f327(f327(f81(x80171),x80172),x80173)),f327(f327(f81(x80171),x80174),x80175))) % 177.41/177.19 [8153]~P144(x81535)+E(x81531,x81532)+E(x81533,x81534)+~E(f327(f327(f80(x81535),f327(f327(f81(x81535),x81533),x81531)),f327(f327(f81(x81535),x81534),x81532)),f327(f327(f80(x81535),f327(f327(f81(x81535),x81533),x81532)),f327(f327(f81(x81535),x81534),x81531))) % 177.41/177.19 [8357]~P108(x83574)+~P1(f327(f138(x83571),x83573))+P1(f327(f327(f329(x83571),x83572),f327(f173(x83571),x83573)))+P1(f327(f138(x83571),f327(f327(f149(x83571,x83574,x83575),x83572),x83573))) % 177.41/177.19 [8502]~P67(x85021)+E(f327(f327(f23(x85021),f327(f327(f6(a915,x85021),x85022),f327(f302(a915,x85023),x85024))),f327(f327(f6(a915,x85021),x85022),f327(f302(a915,x85023),x85025))),f327(f327(f6(a915,x85021),x85022),f327(f302(a915,x85025),x85024)))+~P1(f327(f327(f234(a915),x85025),x85024))+~P1(f327(f327(f234(a915),x85023),x85025)) % 177.41/177.19 [8503]~P68(x85031)+E(f327(f327(f80(x85031),f327(f327(f6(a915,x85031),x85032),f327(f302(a915,x85033),x85034))),f327(f327(f6(a915,x85031),x85032),f327(f302(a915,x85034),x85035))),f327(f327(f6(a915,x85031),x85032),f327(f302(a915,x85033),x85035)))+~P1(f327(f327(f234(a915),x85034),x85035))+~P1(f327(f327(f234(a915),x85033),x85034)) % 177.41/177.19 [8831]~P62(x88312)+E(x88311,f2(x88312))+E(x88313,f2(x88312))+E(f327(f327(f291(x88312),f327(f327(f23(x88312),f327(f327(f81(x88312),x88314),x88311)),f327(f327(f81(x88312),x88315),x88313))),f327(f327(f81(x88312),x88313),x88311)),f327(f327(f23(x88312),f327(f327(f291(x88312),x88314),x88313)),f327(f327(f291(x88312),x88315),x88311))) % 177.41/177.19 [8832]~P62(x88322)+E(x88321,f2(x88322))+E(x88323,f2(x88322))+E(f327(f327(f291(x88322),f327(f327(f80(x88322),f327(f327(f81(x88322),x88324),x88321)),f327(f327(f81(x88322),x88325),x88323))),f327(f327(f81(x88322),x88323),x88321)),f327(f327(f80(x88322),f327(f327(f291(x88322),x88324),x88323)),f327(f327(f291(x88322),x88325),x88321))) % 177.41/177.19 [8841]~E(x88412,f327(x88413,x88411))+E(x88411,f878(x88412,x88413,x88414,x88415))+~P23(x88415,x88414,x88413,f242(f922(x88415,a910)))+~P1(f327(f327(f329(x88414),x88412),f327(f310(x88415,x88414,x88413),f242(f922(x88415,a910))))) % 177.41/177.19 [9058]~P119(x90581)+~P1(f327(f327(f235(x90581),f327(f75(x90581),x90582)),x90584))+P1(f327(f327(f235(x90581),f327(f327(f81(x90581),f327(f75(x90581),x90582)),f327(f75(x90581),x90583))),f327(f327(f81(x90581),x90584),x90585)))+~P1(f327(f327(f235(x90581),f327(f75(x90581),x90583)),x90585)) % 177.41/177.19 [9173]~P23(x91731,x91733,x91735,x91732)+~P1(f327(f35(x91733),x91734))+P1(f327(f327(f234(a915),f327(f36(x91731),x91732)),f327(f36(x91733),x91734)))+~P1(f327(f327(f234(f922(x91733,a910)),f327(f310(x91731,x91733,x91735),x91732)),x91734)) % 177.41/177.19 [9240]~P68(x92402)+~P23(x92401,x92401,x92404,x92405)+~P1(f327(f35(x92401),x92405))+E(f327(f327(f6(x92401,x92402),f327(f72(x92401,x92402,x92401,x92403),x92404)),x92405),f327(f327(f6(x92401,x92402),x92403),f327(f310(x92401,x92401,x92404),x92405))) % 177.41/177.19 [9241]~P75(x92412)+~P23(x92411,x92411,x92414,x92415)+~P1(f327(f35(x92411),x92415))+E(f327(f327(f9(x92411,x92412),f327(f72(x92411,x92412,x92411,x92413),x92414)),x92415),f327(f327(f9(x92411,x92412),x92413),f327(f310(x92411,x92411,x92414),x92415))) % 177.41/177.19 [9358]~P35(x93581,x93582)+~P1(f327(f327(f329(x93581),x93583),x93584))+~P1(f327(f327(f329(x93581),x93585),x93584))+~P1(f327(f327(f329(f921(x93581,x93581)),f327(f327(f252(x93581,x93581),x93585),f609(x93582,x93581,x93584))),x93582)) % 177.41/177.19 [9394]~P23(x93942,x93943,x93945,x93941)+E(x93941,f190(f922(x93942,a910)))+E(f327(f310(x93943,x93942,f492(x93944,x93943,x93942,x93941)),x93944),x93941)+~P1(f327(f327(f234(f922(x93943,a910)),f327(f310(x93942,x93943,x93945),x93941)),x93944)) % 177.41/177.19 [9878]~P108(x98785)+~P3(x98785)+P1(f327(f327(f329(x98781),f344(x98782,x98783,x98781,x98784,x98785)),x98783))+~P1(f327(f327(f235(x98785),x98784),f327(f327(f40(x98781,x98785),x98783),x98782))) % 177.41/177.19 [9883]~P108(x98831)+~P3(x98831)+P1(f327(f327(f235(x98831),x98832),f327(x98833,f344(x98833,x98834,x98835,x98832,x98831))))+~P1(f327(f327(f235(x98831),x98832),f327(f327(f40(x98835,x98831),x98834),x98833))) % 177.41/177.19 [9902]~P68(x99025)+~P83(x99025)+P1(f327(f327(f329(x99021),f873(x99022,x99023,x99024,x99021,x99025)),x99024))+P1(f327(f327(f234(x99025),f327(f327(f6(x99021,x99025),x99023),x99024)),f327(f327(f6(x99021,x99025),x99022),x99024))) % 177.41/177.19 [9962]~P72(x99621)+~P1(f327(f66(x99621,x99621,f81(x99621),x99622,x99623),x99625))+P1(f327(f327(f329(x99621),x99622),x99623))+P1(f327(f66(x99621,x99621,f81(x99621),x99624,f327(f327(f309(x99621),x99622),x99623)),f327(f327(f81(x99621),x99624),x99625))) % 177.41/177.19 [10176]~P68(x101762)+~P1(f327(f35(x101761),x101765))+E(f327(f327(f6(x101761,x101762),f327(f327(f7(x101761,x101762,x101762),f327(f327(f18(x101761,x101762,f922(x101762,x101762)),f327(f327(f8(a910,f922(x101762,f922(x101762,x101762)),x101761),f97(x101762)),f327(a324,x101763))),x101764)),f2(x101762))),x101765),f2(x101762))+P1(f327(f327(f329(x101761),x101763),x101765)) % 177.41/177.19 [10177]~P75(x101772)+~P1(f327(f35(x101771),x101775))+E(f327(f327(f9(x101771,x101772),f327(f327(f7(x101771,x101772,x101772),f327(f327(f18(x101771,x101772,f922(x101772,x101772)),f327(f327(f8(a910,f922(x101772,f922(x101772,x101772)),x101771),f97(x101772)),f327(a324,x101773))),x101774)),f78(x101772))),x101775),f78(x101772))+P1(f327(f327(f329(x101771),x101773),x101775)) % 177.41/177.19 [10178]~P68(x101782)+~P1(f327(f35(x101781),x101785))+E(f327(f327(f6(x101781,x101782),f327(f327(f7(x101781,x101782,x101782),f327(f327(f18(x101781,x101782,f922(x101782,x101782)),f327(f327(f8(a910,f922(x101782,f922(x101782,x101782)),x101781),f97(x101782)),f327(a324,x101783))),x101784)),f2(x101782))),x101785),f327(x101784,x101783))+~P1(f327(f327(f329(x101781),x101783),x101785)) % 177.41/177.19 [10179]~P75(x101792)+~P1(f327(f35(x101791),x101795))+E(f327(f327(f9(x101791,x101792),f327(f327(f7(x101791,x101792,x101792),f327(f327(f18(x101791,x101792,f922(x101792,x101792)),f327(f327(f8(a910,f922(x101792,f922(x101792,x101792)),x101791),f97(x101792)),f327(a324,x101793))),x101794)),f78(x101792))),x101795),f327(x101794,x101793))+~P1(f327(f327(f329(x101791),x101793),x101795)) % 177.41/177.19 [10191]~P68(x101911)+~P83(x101911)+~P1(f327(f327(f234(x101911),f327(x101913,f873(x101915,x101913,x101914,x101912,x101911))),f327(x101915,f873(x101915,x101913,x101914,x101912,x101911))))+P1(f327(f327(f234(x101911),f327(f327(f6(x101912,x101911),x101913),x101914)),f327(f327(f6(x101912,x101911),x101915),x101914))) % 177.41/177.19 [10237]~P68(x102372)+~P1(f327(f35(x102371),x102375))+E(f327(f327(f6(x102371,x102372),f327(f327(f7(x102371,x102372,x102372),f327(f327(f18(x102371,x102372,f922(x102372,x102372)),f327(f327(f8(a910,f922(x102372,f922(x102372,x102372)),x102371),f97(x102372)),f327(f327(f7(x102371,x102371,a910),a324),x102373))),x102374)),f2(x102372))),x102375),f2(x102372))+P1(f327(f327(f329(x102371),x102373),x102375)) % 177.41/177.19 [10238]~P75(x102382)+~P1(f327(f35(x102381),x102385))+E(f327(f327(f9(x102381,x102382),f327(f327(f7(x102381,x102382,x102382),f327(f327(f18(x102381,x102382,f922(x102382,x102382)),f327(f327(f8(a910,f922(x102382,f922(x102382,x102382)),x102381),f97(x102382)),f327(f327(f7(x102381,x102381,a910),a324),x102383))),x102384)),f78(x102382))),x102385),f78(x102382))+P1(f327(f327(f329(x102381),x102383),x102385)) % 177.41/177.19 [10240]~P68(x102402)+~P1(f327(f35(x102401),x102405))+E(f327(f327(f6(x102401,x102402),f327(f327(f7(x102401,x102402,x102402),f327(f327(f18(x102401,x102402,f922(x102402,x102402)),f327(f327(f8(a910,f922(x102402,f922(x102402,x102402)),x102401),f97(x102402)),f327(f327(f7(x102401,x102401,a910),a324),x102403))),x102404)),f2(x102402))),x102405),f327(x102404,x102403))+~P1(f327(f327(f329(x102401),x102403),x102405)) % 177.41/177.19 [10241]~P75(x102412)+~P1(f327(f35(x102411),x102415))+E(f327(f327(f9(x102411,x102412),f327(f327(f7(x102411,x102412,x102412),f327(f327(f18(x102411,x102412,f922(x102412,x102412)),f327(f327(f8(a910,f922(x102412,f922(x102412,x102412)),x102411),f97(x102412)),f327(f327(f7(x102411,x102411,a910),a324),x102413))),x102414)),f78(x102412))),x102415),f327(x102414,x102413))+~P1(f327(f327(f329(x102411),x102413),x102415)) % 177.41/177.19 [8008]~P67(x80082)+~P1(f327(f35(x80081),x80084))+E(f327(f327(f6(x80081,x80082),x80083),f327(f327(f23(f922(x80081,a910)),x80084),f327(f327(f309(x80081),x80085),f190(f922(x80081,a910))))),f327(f327(f6(x80081,x80082),x80083),x80084))+P1(f327(f327(f329(x80081),x80085),x80084)) % 177.41/177.19 [8510]~P106(x85102)+~P1(f327(f35(x85101),x85104))+E(f327(f327(f6(x85101,x85102),x85103),f327(f327(f23(f922(x85101,a910)),x85104),f327(f327(f309(x85101),x85105),f190(f922(x85101,a910))))),f327(f327(f23(x85102),f327(f327(f6(x85101,x85102),x85103),x85104)),f327(x85103,x85105)))+~P1(f327(f327(f329(x85101),x85105),x85104)) % 177.41/177.19 [8511]~P67(x85112)+~P1(f327(f35(x85111),x85114))+E(f327(f327(f6(x85111,x85112),x85113),f327(f327(f23(f922(x85111,a910)),x85114),f327(f327(f309(x85111),x85115),f190(f922(x85111,a910))))),f327(f327(f23(x85112),f327(f327(f6(x85111,x85112),x85113),x85114)),f327(x85113,x85115)))+~P1(f327(f327(f329(x85111),x85115),x85114)) % 177.41/177.19 [8540]~P67(x85401)+~P1(f327(f35(x85402),x85404))+E(f327(f327(f23(x85401),f327(f327(f6(x85402,x85401),x85403),x85404)),f327(f327(f6(x85402,x85401),x85403),x85405)),f327(f327(f6(x85402,x85401),x85403),f327(f327(f23(f922(x85402,a910)),x85404),x85405)))+~P1(f327(f327(f234(f922(x85402,a910)),x85405),x85404)) % 177.41/177.19 [8559]P1(f327(f35(x85591),f327(x85592,x85593)))+~P1(f327(f35(x85594),x85595))+~P1(f327(f327(f329(x85594),x85593),x85595))+~P1(f327(f35(x85591),f327(f327(f40(x85594,f922(x85591,a910)),x85595),x85592))) % 177.41/177.19 [9014]~P6(x90141,x90145,x90144)+~E(f327(f285(x90141,x90141,x90144),f327(f327(f309(x90141),x90142),f190(f922(x90141,a910)))),f327(f285(x90141,x90141,x90144),f327(f327(f309(x90141),x90143),f190(f922(x90141,a910)))))+~P1(f327(f327(f329(x90141),x90143),x90145))+P1(f327(f327(f329(f921(x90141,x90141)),f327(f327(f252(x90141,x90141),x90142),x90143)),x90144)) % 177.41/177.19 [9315]~P1(f327(x93151,x93155))+P1(f327(x93151,f874(x93151,x93152,x93153,x93154)))+P1(f327(x93151,f870(x93151,x93152,x93153,x93154)))+~P1(f327(f327(f329(x93154),x93155),f327(f327(f102(f922(x93154,a910)),x93153),x93152))) % 177.41/177.19 [9498]~P1(f327(x94981,x94985))+P1(f327(x94981,f870(x94981,x94982,x94983,x94984)))+P1(f327(f327(f329(x94984),f874(x94981,x94982,x94983,x94984)),x94982))+~P1(f327(f327(f329(x94984),x94985),f327(f327(f102(f922(x94984,a910)),x94983),x94982))) % 177.41/177.19 [9499]~P1(f327(x94991,x94995))+P1(f327(x94991,f874(x94991,x94992,x94993,x94994)))+P1(f327(f327(f329(x94994),f870(x94991,x94992,x94993,x94994)),x94993))+~P1(f327(f327(f329(x94994),x94995),f327(f327(f102(f922(x94994,a910)),x94993),x94992))) % 177.41/177.19 [9503]P1(f327(x95031,x95032))+~P1(f327(x95031,f880(x95031,x95033,x95034,x95035)))+~P1(f327(x95031,f879(x95031,x95033,x95034,x95035)))+~P1(f327(f327(f329(x95035),x95032),f327(f327(f102(f922(x95035,a910)),x95034),x95033))) % 177.41/177.19 [9508]~P36(x95081,x95084)+~P1(f327(f327(f329(f921(x95081,x95081)),f327(f327(f252(x95081,x95081),x95082),x95085)),x95084))+P1(f327(f327(f329(f921(x95081,x95081)),f327(f327(f252(x95081,x95081),x95082),x95083)),x95084))+~P1(f327(f327(f329(f921(x95081,x95081)),f327(f327(f252(x95081,x95081),x95085),x95083)),x95084)) % 177.41/177.19 [9547]E(x95471,x95472)+~P1(f327(f327(f329(f921(x95473,x95473)),f327(f327(f252(x95473,x95473),x95471),x95472)),f307(x95473,x95475)))+P1(f327(f327(f329(x95473),x95471),x95474))+~P1(f327(f327(f234(f922(f921(x95473,x95473),a910)),x95475),f327(f327(f254(x95473,x95473),x95474),f327(f16(f922(x95473,a910),x95473),x95474)))) % 177.41/177.19 [9565]P1(f327(x95651,x95652))+~P1(f327(x95651,f879(x95651,x95654,x95655,x95653)))+P1(f327(f327(f329(x95653),f880(x95651,x95654,x95655,x95653)),x95654))+~P1(f327(f327(f329(x95653),x95652),f327(f327(f102(f922(x95653,a910)),x95655),x95654))) % 177.41/177.19 [9566]P1(f327(x95661,x95662))+~P1(f327(x95661,f880(x95661,x95664,x95665,x95663)))+P1(f327(f327(f329(x95663),f879(x95661,x95664,x95665,x95663)),x95665))+~P1(f327(f327(f329(x95663),x95662),f327(f327(f102(f922(x95663,a910)),x95665),x95664))) % 177.41/177.19 [9633]P1(f327(x96331,x96332))+P1(f327(f327(f329(x96333),f880(x96331,x96334,x96335,x96333)),x96334))+P1(f327(f327(f329(x96333),f879(x96331,x96334,x96335,x96333)),x96335))+~P1(f327(f327(f329(x96333),x96332),f327(f327(f102(f922(x96333,a910)),x96335),x96334))) % 177.41/177.19 [9635]~P1(f327(x96352,x96355))+P1(f327(f327(f329(x96351),f874(x96352,x96353,x96354,x96351)),x96353))+P1(f327(f327(f329(x96351),f870(x96352,x96353,x96354,x96351)),x96354))+~P1(f327(f327(f329(x96351),x96355),f327(f327(f102(f922(x96351,a910)),x96354),x96353))) % 177.41/177.19 [9785]~P6(x97851,x97855,x97854)+~P1(f327(f327(f329(x97851),x97853),x97855))+P1(f327(f327(f329(f921(x97851,x97851)),f327(f327(f252(x97851,x97851),x97852),x97853)),x97854))+~P1(f327(f327(f234(f922(x97851,a910)),f327(f285(x97851,x97851,x97854),f327(f327(f309(x97851),x97853),f190(f922(x97851,a910))))),f327(f285(x97851,x97851,x97854),f327(f327(f309(x97851),x97852),f190(f922(x97851,a910)))))) % 177.41/177.19 [9913]~P108(x99135)+~P3(x99135)+P1(f327(f327(f329(x99131),f356(x99132,x99133,x99134,x99131,x99135)),x99134))+~P1(f327(f327(f235(x99135),f327(f327(f41(x99131,x99135),x99134),x99133)),x99132)) % 177.41/177.19 [9945]~P83(x99455)+~P81(x99455)+P1(f327(f327(f329(x99451),f691(x99452,x99453,x99454,x99451,x99455)),f327(f173(x99451),x99454)))+P1(f327(f327(f234(x99455),f327(f166(x99455),f327(f327(f155(x99451,x99455),x99453),x99454))),f327(f166(x99455),f327(f327(f155(x99451,x99455),x99452),x99454)))) % 177.41/177.19 [10054]~P108(x100541)+~P3(x100541)+P1(f327(f327(f235(x100541),f327(x100542,f356(x100543,x100542,x100544,x100545,x100541))),x100543))+~P1(f327(f327(f235(x100541),f327(f327(f41(x100545,x100541),x100544),x100542)),x100543)) % 177.41/177.19 [10195]~P83(x101951)+~P81(x101951)+~P1(f327(f327(f234(x101951),f327(x101953,f691(x101955,x101953,x101954,x101952,x101951))),f327(x101955,f691(x101955,x101953,x101954,x101952,x101951))))+P1(f327(f327(f234(x101951),f327(f166(x101951),f327(f327(f155(x101952,x101951),x101953),x101954))),f327(f166(x101951),f327(f327(f155(x101952,x101951),x101955),x101954)))) % 177.41/177.19 [8854]~P68(x88541)+~P1(f327(f35(x88544),x88545))+~P1(f327(f327(f329(x88544),x88543),x88545))+E(f327(f327(f80(x88541),f327(x88542,x88543)),f327(f327(f6(x88544,x88541),x88542),f327(f327(f23(f922(x88544,a910)),x88545),f327(f327(f309(x88544),x88543),f190(f922(x88544,a910)))))),f327(f327(f6(x88544,x88541),x88542),x88545)) % 177.41/177.19 [8855]~P75(x88551)+~P1(f327(f35(x88554),x88555))+~P1(f327(f327(f329(x88554),x88553),x88555))+E(f327(f327(f81(x88551),f327(x88552,x88553)),f327(f327(f9(x88554,x88551),x88552),f327(f327(f23(f922(x88554,a910)),x88555),f327(f327(f309(x88554),x88553),f190(f922(x88554,a910)))))),f327(f327(f9(x88554,x88551),x88552),x88555)) % 177.41/177.19 [8915]~P16(x89151,x89154,x89155)+~P1(f327(f35(x89151),x89152))+E(f327(f327(f23(f922(x89151,a910)),x89152),f327(f327(f309(x89151),x89153),f190(f922(x89151,a910)))),f190(f922(x89151,a910)))+E(f327(f327(x89154,x89153),f327(x89155,f327(f327(f23(f922(x89151,a910)),x89152),f327(f327(f309(x89151),x89153),f190(f922(x89151,a910)))))),f327(x89155,f327(f327(f309(x89151),x89153),x89152))) % 177.41/177.19 [9293]~P68(x92931)+~P1(f327(f35(x92932),x92935))+~P1(f327(f35(x92932),x92934))+E(f327(f327(f80(x92931),f327(f327(f6(x92932,x92931),x92933),f327(f327(f102(f922(x92932,a910)),x92934),x92935))),f327(f327(f6(x92932,x92931),x92933),f327(f327(f103(f922(x92932,a910)),x92934),x92935))),f327(f327(f80(x92931),f327(f327(f6(x92932,x92931),x92933),x92934)),f327(f327(f6(x92932,x92931),x92933),x92935))) % 177.41/177.19 [9295]~P75(x92951)+~P1(f327(f35(x92952),x92955))+~P1(f327(f35(x92952),x92954))+E(f327(f327(f81(x92951),f327(f327(f9(x92952,x92951),x92953),f327(f327(f102(f922(x92952,a910)),x92954),x92955))),f327(f327(f9(x92952,x92951),x92953),f327(f327(f103(f922(x92952,a910)),x92954),x92955))),f327(f327(f81(x92951),f327(f327(f9(x92952,x92951),x92953),x92954)),f327(f327(f9(x92952,x92951),x92953),x92955))) % 177.41/177.19 [9433]~P67(x94331)+~P1(f327(f35(x94332),x94335))+~P1(f327(f35(x94332),x94334))+E(f327(f327(f23(x94331),f327(f327(f80(x94331),f327(f327(f6(x94332,x94331),x94333),x94334)),f327(f327(f6(x94332,x94331),x94333),x94335))),f327(f327(f6(x94332,x94331),x94333),f327(f327(f103(f922(x94332,a910)),x94334),x94335))),f327(f327(f6(x94332,x94331),x94333),f327(f327(f102(f922(x94332,a910)),x94334),x94335))) % 177.41/177.19 [9645]~P23(x96451,x96452,x96453,x96455)+~P23(x96451,x96452,x96453,x96454)+P23(x96451,x96452,x96453,f327(f327(f102(f922(x96451,a910)),x96454),x96455))+~E(f327(f327(f103(f922(x96452,a910)),f327(f310(x96451,x96452,x96453),f327(f327(f23(f922(x96451,a910)),x96454),x96455))),f327(f310(x96451,x96452,x96453),f327(f327(f23(f922(x96451,a910)),x96455),x96454))),f190(f922(x96452,a910))) % 177.41/177.19 [9760]E(x97601,f2(a1))+~P1(f327(f327(f235(a1),f2(a1)),x97603))+~P1(f327(f50(x97602,x97601),f327(f327(f252(a1,a1),x97604),x97605)))+P1(f327(f50(x97602,f327(f327(f81(a1),x97601),x97603)),f327(f327(f252(a1,a1),f327(f327(f37(a1),x97604),x97603)),f327(f327(f80(a1),f327(f327(f81(a1),x97601),f46(a1,x97604,x97603))),x97605)))) % 177.41/177.19 [9768]~P1(f327(f327(f235(a915),f2(a915)),x97683))+~P1(f327(f327(f235(a915),f2(a915)),x97682))+~P1(f327(f49(x97681,x97682),f327(f327(f252(a915,a915),x97684),x97685)))+P1(f327(f49(x97681,f327(f327(f81(a915),x97682),x97683)),f327(f327(f252(a915,a915),f327(f327(f37(a915),x97684),x97683)),f327(f327(f80(a915),f327(f327(f81(a915),x97682),f46(a915,x97684,x97683))),x97685)))) % 177.41/177.19 [9817]~P75(x98171)+~P1(f327(f35(x98172),x98175))+~P1(f327(f35(x98172),x98174))+E(f327(f327(f81(x98171),f327(f327(f327(f65(x98171,x98172,f81(x98171)),x98173),f78(x98171)),f327(f327(f102(f922(x98172,a910)),x98174),x98175))),f327(f327(f327(f65(x98171,x98172,f81(x98171)),x98173),f78(x98171)),f327(f327(f103(f922(x98172,a910)),x98174),x98175))),f327(f327(f81(x98171),f327(f327(f327(f65(x98171,x98172,f81(x98171)),x98173),f78(x98171)),x98174)),f327(f327(f327(f65(x98171,x98172,f81(x98171)),x98173),f78(x98171)),x98175))) % 177.41/177.19 [9819]~E(f327(f327(f176(x98191),x98195),x98192),f327(f327(f176(x98191),x98195),x98193))+P1(f327(f327(f329(f921(f916(x98191),f916(x98191))),f327(f327(f252(f916(x98191),f916(x98191)),x98192),x98193)),f148(x98191,x98194)))+~P1(f327(f327(f235(a915),x98195),f327(f327(f238(a915),f327(f191(f916(x98191)),x98192)),f327(f191(f916(x98191)),x98193))))+~P1(f327(f327(f329(f921(x98191,x98191)),f327(f327(f252(x98191,x98191),f327(f327(f165(x98191),x98192),x98195)),f327(f327(f165(x98191),x98193),x98195))),x98194)) % 177.41/177.19 [9934]~P83(x99345)+~P146(x99345)+P1(f327(f327(f329(x99341),f383(x99342,x99343,x99344,x99341,x99345)),x99344))+P1(f327(f327(f234(x99345),f327(f327(f6(x99341,x99345),x99343),x99344)),f327(f327(f81(x99345),f327(f101(x99345),f327(f36(x99341),x99344))),x99342))) % 177.41/177.19 [10112]~P83(x101121)+~P146(x101121)+~P1(f327(f327(f234(x101121),f327(x101123,f383(x101125,x101123,x101124,x101122,x101121))),x101125))+P1(f327(f327(f234(x101121),f327(f327(f6(x101122,x101121),x101123),x101124)),f327(f327(f81(x101121),f327(f101(x101121),f327(f36(x101122),x101124))),x101125))) % 177.41/177.19 [8883]E(f327(f327(f135(x88831),x88832),x88833),f327(f327(f135(x88831),x88834),x88835))+~E(f327(f327(f176(x88831),f327(f191(f916(x88831)),x88832)),x88834),x88832)+~E(f327(f327(f135(x88831),f327(f327(f139(x88831),f327(f191(f916(x88831)),x88832)),x88834)),x88835),x88833)+P1(f327(f327(f234(a915),f327(f191(f916(x88831)),x88834)),f327(f191(f916(x88831)),x88832))) % 177.41/177.19 [9013]E(f327(f327(f135(x90131),x90132),x90133),f327(f327(f135(x90131),x90134),x90135))+~E(f327(f327(f176(x90131),f327(f191(f916(x90131)),x90132)),x90134),x90132)+~E(x90133,f327(f327(f135(x90131),f327(f327(f139(x90131),f327(f191(f916(x90131)),x90132)),x90134)),x90135))+~P1(f327(f327(f234(a915),f327(f191(f916(x90131)),x90132)),f327(f191(f916(x90131)),x90134))) % 177.41/177.19 [10260]~P1(f327(x102605,x102604))+~P1(f327(f35(x102602),f327(f262(x102602),x102605)))+P1(f327(f35(x102601),f327(f262(x102601),f327(f327(f7(x102601,x102602,a910),x102603),x102604))))+~P1(f327(f35(x102601),f327(f262(x102601),f327(f327(f8(f922(x102602,a910),a910,x102601),f87(x102602)),f327(f327(f8(f922(x102602,a910),f922(x102602,a910),x102601),f327(f18(x102602,a910,a910),f327(f327(f8(a910,f922(a910,a910),x102602),a325),x102605))),x102603))))) % 177.41/177.19 [10333]~P1(f327(f35(x103332),x103335))+~P1(f327(f327(f329(x103332),x103334),x103335))+P1(f327(f35(x103331),f327(f262(x103331),f327(f327(f7(x103331,x103332,a910),x103333),x103334))))+~P1(f327(f35(x103331),f327(f262(x103331),f327(f327(f8(f922(x103332,a910),a910,x103331),f87(x103332)),f327(f327(f8(f922(x103332,a910),f922(x103332,a910),x103331),f327(f18(x103332,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103332),a325),f327(f327(f7(x103332,f922(x103332,a910),a910),f329(x103332)),x103335)))),x103333))))) % 177.41/177.19 [8669]~P17(x86695,x86691,x86696,x86692)+E(f327(f72(x86691,x86691,x86691,f327(x86692,x86693)),f327(x86692,x86694)),f327(f72(x86691,x86691,x86691,f327(x86692,x86694)),f327(x86692,x86693)))+~P1(f327(f35(x86695),x86694))+~P1(f327(f35(x86695),x86693)) % 177.41/177.19 [8064]~P23(x80641,x80642,x80644,x80643)+~E(f327(x80644,x80646),x80645)+E(f327(f77(x80641,x80642,x80643,x80644),x80645),x80646)+~P1(f327(f327(f329(x80641),x80646),x80643)) % 177.41/177.19 [8065]~P23(x80651,x80652,x80654,x80653)+~E(f327(x80654,x80656),x80655)+E(f327(f92(x80651,x80652,x80653,x80654),x80655),x80656)+~P1(f327(f327(f329(x80651),x80656),x80653)) % 177.41/177.19 [8258]~P18(x82586,x82581,x82584,x82582)+E(f327(f72(x82581,x82581,x82581,f327(x82582,x82583)),f327(x82584,x82585)),f327(x82582,x82583))+~P1(f327(f35(x82586),x82583))+~P1(f327(f327(f329(x82586),x82585),x82583)) % 177.41/177.19 [9386]E(x93861,x93862)+~E(f327(f92(x93863,x93864,x93865,x93866),x93861),f327(f92(x93863,x93864,x93865,x93866),x93862))+~P1(f327(f327(f329(x93864),x93862),f327(f310(x93863,x93864,x93866),x93865)))+~P1(f327(f327(f329(x93864),x93861),f327(f310(x93863,x93864,x93866),x93865))) % 177.41/177.19 [9482]~P17(x94823,x94821,x94826,x94822)+E(f327(f72(x94821,x94821,x94821,f327(x94822,f327(f327(f23(f922(x94823,a910)),x94824),f327(f327(f309(x94823),x94825),f190(f922(x94823,a910)))))),f327(x94826,x94825)),f327(x94822,x94824))+~P1(f327(f35(x94823),x94824))+~P1(f327(f327(f329(x94823),x94825),x94824)) % 177.41/177.19 [7149]~P59(x71491)+~E(f46(x71491,x71493,x71494),f46(x71491,x71496,x71494))+~E(f46(x71491,x71492,x71494),f46(x71491,x71495,x71494))+E(f46(x71491,f327(f327(f23(x71491),x71492),x71493),x71494),f46(x71491,f327(f327(f23(x71491),x71495),x71496),x71494)) % 177.41/177.19 [7150]~P58(x71501)+~E(f46(x71501,x71503,x71504),f46(x71501,x71506,x71504))+~E(f46(x71501,x71502,x71504),f46(x71501,x71505,x71504))+E(f46(x71501,f327(f327(f80(x71501),x71502),x71503),x71504),f46(x71501,f327(f327(f80(x71501),x71505),x71506),x71504)) % 177.41/177.19 [7151]~P58(x71511)+~E(f46(x71511,x71513,x71514),f46(x71511,x71516,x71514))+~E(f46(x71511,x71512,x71514),f46(x71511,x71515,x71514))+E(f46(x71511,f327(f327(f81(x71511),x71512),x71513),x71514),f46(x71511,f327(f327(f81(x71511),x71515),x71516),x71514)) % 177.41/177.19 [7960]~P14(x79601,x79602,x79603)+~P1(f327(f35(x79601),x79606))+E(f327(f327(f64(x79601,x79602,x79603),x79604),f327(f327(f309(x79601),x79605),x79606)),f327(f327(f64(x79601,x79602,x79603),f327(f327(x79603,x79605),x79604)),x79606))+P1(f327(f327(f329(x79601),x79605),x79606)) % 177.41/177.19 [8023]~P3(x80231)+P1(f327(f327(f234(x80231),x80232),f327(x80233,x80234)))+~P1(f327(f327(f329(x80235),x80234),x80236))+~P1(f327(f327(f234(x80231),x80232),f327(f327(f41(x80235,x80231),x80236),x80233))) % 177.41/177.19 [8180]~P14(x81801,x81802,x81803)+~P1(f327(f35(x81801),x81806))+E(f327(f327(f64(x81801,x81802,x81803),x81804),f327(f327(f309(x81801),x81805),x81806)),f327(f327(x81803,x81805),f327(f327(f64(x81801,x81802,x81803),x81804),x81806)))+P1(f327(f327(f329(x81801),x81805),x81806)) % 177.41/177.19 [8276]~P108(x82763)+~P1(f327(x82762,x82765))+~P11(x82763,f327(f327(f155(x82761,x82763),x82764),x82766))+E(f327(f137(x82761,x82762),f327(f327(f149(x82761,x82763,x82764),x82765),x82766)),f327(f327(f149(x82761,x82763,x82764),x82765),f327(f137(x82761,x82762),x82766))) % 177.41/177.19 [8299]E(x82991,x82992)+E(x82993,f2(a1))+~P1(f327(f50(x82994,x82993),f327(f327(f252(a1,a1),x82995),x82992)))+~P1(f327(f50(x82994,x82993),f327(f327(f252(a1,a1),x82996),x82991))) % 177.41/177.19 [8300]E(x83001,x83002)+E(x83003,f2(a1))+~P1(f327(f50(x83004,x83003),f327(f327(f252(a1,a1),x83002),x83005)))+~P1(f327(f50(x83004,x83003),f327(f327(f252(a1,a1),x83001),x83006))) % 177.41/177.19 [8323]~P17(x83232,x83235,x83236,x83231)+~P1(f327(f35(x83232),x83234))+E(f327(x83231,f327(f327(f309(x83232),x83233),x83234)),f327(f72(x83235,x83235,x83235,f327(x83231,x83234)),f327(x83236,x83233)))+P1(f327(f327(f329(x83232),x83233),x83234)) % 177.41/177.19 [8543]~P18(x85435,x85431,x85436,x85432)+E(f327(f72(x85431,x85431,x85431,f327(x85432,x85433)),f327(x85432,x85434)),f327(x85432,x85433))+~P1(f327(f35(x85435),x85433))+~P1(f327(f327(f234(f922(x85435,a910)),x85434),x85433)) % 177.41/177.19 [9689]~P23(x96891,x96892,x96894,x96893)+~P1(f327(f327(f329(x96892),x96895),f327(f310(x96891,x96892,x96894),x96893)))+P1(f327(f327(f329(x96891),f327(f77(x96891,x96892,x96893,x96894),x96895)),x96896))+~P1(f327(f327(f234(f922(x96891,a910)),x96893),x96896)) % 177.41/177.19 [10065]~P68(x100652)+~E(f590(x100651,x100653,x100655,x100656,x100654,x100652),f591(x100651,x100653,x100655,x100656,x100654,x100652))+~P1(f327(f35(x100654),x100656))+E(f327(f327(f6(x100651,x100652),x100653),f327(f310(x100654,x100651,x100655),x100656)),f327(f327(f6(x100654,x100652),f327(f72(x100651,x100652,x100654,x100653),x100655)),x100656)) % 177.41/177.19 [10094]~P68(x100946)+E(f327(x100941,f590(x100942,x100943,x100941,x100944,x100945,x100946)),f327(x100941,f591(x100942,x100943,x100941,x100944,x100945,x100946)))+E(f327(f327(f6(x100942,x100946),x100943),f327(f310(x100945,x100942,x100941),x100944)),f327(f327(f6(x100945,x100946),f327(f72(x100942,x100946,x100945,x100943),x100941)),x100944))+~P1(f327(f35(x100945),x100944)) % 177.41/177.19 [10144]~P68(x101442)+~E(f327(x101443,f327(x101445,f591(x101441,x101443,x101445,x101446,x101444,x101442))),f2(x101442))+~P1(f327(f35(x101444),x101446))+E(f327(f327(f6(x101441,x101442),x101443),f327(f310(x101444,x101441,x101445),x101446)),f327(f327(f6(x101444,x101442),f327(f72(x101441,x101442,x101444,x101443),x101445)),x101446)) % 177.41/177.19 [10203]~P68(x102032)+~P1(f327(f35(x102034),x102036))+E(f327(f327(f6(x102031,x102032),x102033),f327(f310(x102034,x102031,x102035),x102036)),f327(f327(f6(x102034,x102032),f327(f72(x102031,x102032,x102034,x102033),x102035)),x102036))+P1(f327(f327(f329(x102034),f591(x102031,x102033,x102035,x102036,x102034,x102032)),x102036)) % 177.41/177.19 [10204]~P68(x102042)+~P1(f327(f35(x102044),x102046))+E(f327(f327(f6(x102041,x102042),x102043),f327(f310(x102044,x102041,x102045),x102046)),f327(f327(f6(x102044,x102042),f327(f72(x102041,x102042,x102044,x102043),x102045)),x102046))+P1(f327(f327(f329(x102044),f590(x102041,x102043,x102045,x102046,x102044,x102042)),x102046)) % 177.41/177.19 [10332]~P75(x103321)+~P1(f327(f35(x103322),x103326))+E(f327(f327(f327(f65(x103321,x103322,f81(x103321)),f327(f327(f18(x103322,f922(x103323,a910),x103321),f327(f327(f7(x103322,x103321,f922(f922(x103323,a910),x103321)),f327(f327(f8(f922(x103323,x103321),f922(x103321,f922(f922(x103323,a910),x103321)),x103322),f65(x103321,x103323,f81(x103321))),x103324)),f78(x103321))),x103325)),f78(x103321)),x103326),f327(f327(f327(f65(x103321,f921(x103322,x103323),f81(x103321)),f327(f257(x103322,x103323,x103321),x103324)),f78(x103321)),f327(f327(f254(x103322,x103323),x103326),x103325)))+P1(f327(f327(f329(x103322),f559(x103324,x103325,x103323,x103326,x103322,x103321)),x103326)) % 177.41/177.19 [10354]~P75(x103541)+~P1(f327(f35(x103542),x103546))+E(f327(f327(f327(f65(x103541,x103542,f81(x103541)),f327(f327(f18(x103542,f922(x103543,a910),x103541),f327(f327(f7(x103542,x103541,f922(f922(x103543,a910),x103541)),f327(f327(f8(f922(x103543,x103541),f922(x103541,f922(f922(x103543,a910),x103541)),x103542),f65(x103541,x103543,f81(x103541))),x103544)),f78(x103541))),x103545)),f78(x103541)),x103546),f327(f327(f327(f65(x103541,f921(x103542,x103543),f81(x103541)),f327(f257(x103542,x103543,x103541),x103544)),f78(x103541)),f327(f327(f254(x103542,x103543),x103546),x103545)))+~P1(f327(f35(x103543),f327(x103545,f559(x103544,x103545,x103543,x103546,x103542,x103541)))) % 177.41/177.19 [8454]~P18(x84542,x84545,x84546,x84541)+~P1(f327(f35(x84542),x84544))+~P1(f327(f35(x84542),x84543))+E(f327(x84541,f327(f327(f102(f922(x84542,a910)),x84543),x84544)),f327(f72(x84545,x84545,x84545,f327(x84541,x84543)),f327(x84541,x84544))) % 177.41/177.19 [8670]~P3(x86701)+P1(f327(f327(f234(x86701),f327(x86702,x86703)),x86704))+~P1(f327(f327(f329(x86705),x86703),x86706))+~P1(f327(f327(f234(x86701),f327(f327(f40(x86705,x86701),x86706),x86702)),x86704)) % 177.41/177.19 [9101]~P23(x91012,x91011,x91013,x91016)+E(f327(f327(f23(f922(x91011,a910)),f327(f310(x91012,x91011,x91013),x91014)),f327(f310(x91012,x91011,x91013),x91015)),f327(f310(x91012,x91011,x91013),f327(f327(f23(f922(x91012,a910)),x91014),x91015)))+~P1(f327(f327(f234(f922(x91012,a910)),x91015),x91016))+~P1(f327(f327(f234(f922(x91012,a910)),x91014),x91016)) % 177.41/177.19 [9102]~P23(x91022,x91021,x91023,x91026)+E(f327(f327(f103(f922(x91021,a910)),f327(f310(x91022,x91021,x91023),x91024)),f327(f310(x91022,x91021,x91023),x91025)),f327(f310(x91022,x91021,x91023),f327(f327(f103(f922(x91022,a910)),x91024),x91025)))+~P1(f327(f327(f234(f922(x91022,a910)),x91025),x91026))+~P1(f327(f327(f234(f922(x91022,a910)),x91024),x91026)) % 177.41/177.19 [9360]E(x93601,x93602)+~P52(x93603,x93604,x93605)+~P1(f327(f327(f329(f921(x93603,x93604)),f327(f327(f252(x93603,x93604),x93606),x93602)),x93605))+~P1(f327(f327(f329(f921(x93603,x93604)),f327(f327(f252(x93603,x93604),x93606),x93601)),x93605)) % 177.41/177.19 [10140]~P72(x101401)+~E(f327(x101403,f507(x101404,x101406,x101403,x101405,x101402,x101401)),f327(x101406,f507(x101404,x101406,x101403,x101405,x101402,x101401)))+~P1(f327(f35(x101402),x101405))+E(f327(f327(f327(f65(x101401,x101402,f81(x101401)),x101403),x101404),x101405),f327(f327(f327(f65(x101401,x101402,f81(x101401)),x101406),x101404),x101405)) % 177.41/177.19 [10201]~P72(x102011)+~P1(f327(f35(x102012),x102015))+E(f327(f327(f327(f65(x102011,x102012,f81(x102011)),x102013),x102014),x102015),f327(f327(f327(f65(x102011,x102012,f81(x102011)),x102016),x102014),x102015))+P1(f327(f327(f329(x102012),f507(x102014,x102013,x102016,x102015,x102012,x102011)),x102015)) % 177.41/177.19 [8897]~P72(x88971)+~P1(f327(f35(x88972),x88976))+P1(f327(f327(f329(x88972),x88975),x88976))+E(f327(f327(f327(f65(x88971,x88972,f81(x88971)),x88973),x88974),f327(f327(f309(x88972),x88975),x88976)),f327(f327(f81(x88971),f327(x88973,x88975)),f327(f327(f327(f65(x88971,x88972,f81(x88971)),x88973),x88974),x88976))) % 177.41/177.19 [8950]~P6(x89501,x89506,x89503)+~P9(x89501,f922(x89502,a910),x89503,x89505)+~P1(f327(f327(f329(x89501),x89504),x89506))+E(f327(f327(f40(x89501,f922(x89502,a910)),f327(f285(x89501,x89501,x89503),f327(f327(f309(x89501),x89504),f190(f922(x89501,a910))))),x89505),f327(x89505,x89504)) % 177.41/177.19 [9076]~P14(x90763,x90764,x90761)+~P1(f327(f35(x90763),x90766))+~P1(f327(f327(f329(x90763),x90762),x90766))+E(f327(f327(x90761,x90762),f327(f327(f64(x90763,x90764,x90761),x90765),f327(f327(f23(f922(x90763,a910)),x90766),f327(f327(f309(x90763),x90762),f190(f922(x90763,a910)))))),f327(f327(f64(x90763,x90764,x90761),x90765),x90766)) % 177.41/177.19 [9370]~P17(x93703,x93701,x93706,x93702)+~P1(f327(f35(x93703),x93705))+~P1(f327(f35(x93703),x93704))+E(f327(f72(x93701,x93701,x93701,f327(x93702,f327(f327(f102(f922(x93703,a910)),x93704),x93705))),f327(x93702,f327(f327(f103(f922(x93703,a910)),x93704),x93705))),f327(f72(x93701,x93701,x93701,f327(x93702,x93704)),f327(x93702,x93705))) % 177.41/177.19 [9713]~E(x97133,f327(f327(f160(x97131,x97132),x97135),x97136))+P1(f327(f327(f329(f921(f916(x97131),f916(x97131))),f327(f327(f252(f916(x97131),f916(x97131)),x97132),x97133)),f158(x97131,x97134)))+~P1(f327(f327(f235(a915),x97135),f327(f191(f916(x97131)),x97132)))+~P1(f327(f327(f329(f921(x97131,x97131)),f327(f327(f252(x97131,x97131),f327(f327(f165(x97131),x97132),x97135)),x97136)),x97134)) % 177.41/177.19 [10217]~P68(x102172)+~P1(f327(f35(x102171),x102176))+P1(f327(f327(f329(x102171),f557(x102174,x102175,x102173,x102176,x102171,x102172)),x102176))+E(f327(f327(f6(x102171,x102172),f327(f327(f18(x102171,f922(x102173,a910),x102172),f327(f327(f8(f922(x102173,x102172),f922(f922(x102173,a910),x102172),x102171),f6(x102173,x102172)),x102174)),x102175)),x102176),f327(f327(f6(f921(x102171,x102173),x102172),f327(f257(x102171,x102173,x102172),x102174)),f327(f327(f254(x102171,x102173),x102176),x102175))) % 177.41/177.19 [10218]~P75(x102182)+~P1(f327(f35(x102181),x102186))+P1(f327(f327(f329(x102181),f558(x102184,x102185,x102183,x102186,x102181,x102182)),x102186))+E(f327(f327(f9(x102181,x102182),f327(f327(f18(x102181,f922(x102183,a910),x102182),f327(f327(f8(f922(x102183,x102182),f922(f922(x102183,a910),x102182),x102181),f9(x102183,x102182)),x102184)),x102185)),x102186),f327(f327(f9(f921(x102181,x102183),x102182),f327(f257(x102181,x102183,x102182),x102184)),f327(f327(f254(x102181,x102183),x102186),x102185))) % 177.41/177.19 [10258]~P68(x102582)+~P1(f327(f35(x102581),x102586))+~P1(f327(f35(x102583),f327(x102585,f557(x102584,x102585,x102583,x102586,x102581,x102582))))+E(f327(f327(f6(x102581,x102582),f327(f327(f18(x102581,f922(x102583,a910),x102582),f327(f327(f8(f922(x102583,x102582),f922(f922(x102583,a910),x102582),x102581),f6(x102583,x102582)),x102584)),x102585)),x102586),f327(f327(f6(f921(x102581,x102583),x102582),f327(f257(x102581,x102583,x102582),x102584)),f327(f327(f254(x102581,x102583),x102586),x102585))) % 177.41/177.19 [10259]~P75(x102592)+~P1(f327(f35(x102591),x102596))+~P1(f327(f35(x102593),f327(x102595,f558(x102594,x102595,x102593,x102596,x102591,x102592))))+E(f327(f327(f9(x102591,x102592),f327(f327(f18(x102591,f922(x102593,a910),x102592),f327(f327(f8(f922(x102593,x102592),f922(f922(x102593,a910),x102592),x102591),f9(x102593,x102592)),x102594)),x102595)),x102596),f327(f327(f9(f921(x102591,x102593),x102592),f327(f257(x102591,x102593,x102592),x102594)),f327(f327(f254(x102591,x102593),x102596),x102595))) % 177.41/177.19 [10239]~P75(x102392)+~P1(f327(f35(x102391),x102396))+P1(f327(f327(f329(x102391),x102393),x102396))+E(f327(f327(f9(x102391,x102392),f327(f327(f7(x102391,x102392,x102392),f327(f327(f18(x102391,x102392,f922(x102392,x102392)),f327(f327(f8(a910,f922(x102392,f922(x102392,x102392)),x102391),f97(x102392)),f327(f327(f7(x102391,x102391,a910),a324),x102393))),x102394)),x102395)),x102396),f327(f327(f244(x102392),x102395),f327(f36(x102391),x102396))) % 177.41/177.19 [10244]~P75(x102442)+~P1(f327(f35(x102441),x102446))+~P1(f327(f327(f329(x102441),x102443),x102446))+E(f327(f327(f9(x102441,x102442),f327(f327(f7(x102441,x102442,x102442),f327(f327(f18(x102441,x102442,f922(x102442,x102442)),f327(f327(f8(a910,f922(x102442,f922(x102442,x102442)),x102441),f97(x102442)),f327(f327(f7(x102441,x102441,a910),a324),x102443))),x102444)),x102445)),x102446),f327(f327(f81(x102442),f327(x102444,x102443)),f327(f327(f244(x102442),x102445),f327(f327(f23(a915),f327(f36(x102441),x102446)),f78(a915))))) % 177.41/177.19 [10323]~P1(f327(f35(x103231),x103235))+~P1(f327(f35(x103232),x103233))+P1(f327(f327(f329(x103232),f493(x103236,x103234,x103233,x103232,x103235,x103231)),x103233))+E(f327(f327(f6(x103231,a915),f327(f327(f8(f922(x103232,a910),a915,x103231),f36(x103232)),f327(f327(f8(f922(x103232,a910),f922(x103232,a910),x103231),f262(x103232)),f327(f327(f8(f922(x103232,a910),f922(x103232,a910),x103231),f327(f18(x103232,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103232),a325),f327(f327(f7(x103232,f922(x103232,a910),a910),f329(x103232)),x103233)))),x103234)))),x103235),f327(f327(f81(a915),x103236),f327(f36(x103232),x103233))) % 177.41/177.19 [10324]~P1(f327(f35(x103241),x103245))+~P1(f327(f35(x103242),x103243))+P1(f327(f327(f329(x103242),f495(x103246,x103244,x103243,x103242,x103245,x103241)),x103243))+E(f327(f327(f6(x103241,a915),f327(f327(f8(f922(x103242,a910),a915,x103241),f36(x103242)),f327(f327(f8(f922(x103242,a910),f922(x103242,a910),x103241),f262(x103242)),f327(f327(f8(f922(x103242,a910),f922(x103242,a910),x103241),f327(f18(x103242,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103242),a325),f327(f327(f7(x103242,f922(x103242,a910),a910),f329(x103242)),x103243)))),x103244)))),x103245),f327(f327(f6(x103242,a915),x103246),x103243)) % 177.41/177.19 [10367]~P1(f327(f35(x103672),x103673))+~P1(f327(f35(x103671),x103675))+~E(f327(f36(x103671),f327(f262(x103671),f327(f327(f18(x103671,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103671),a325),f327(f327(f7(x103671,f922(x103671,a910),a910),f329(x103671)),x103675))),f327(f327(f7(x103671,x103672,a910),x103674),f493(x103676,x103674,x103673,x103672,x103675,x103671))))),x103676)+E(f327(f327(f6(x103671,a915),f327(f327(f8(f922(x103672,a910),a915,x103671),f36(x103672)),f327(f327(f8(f922(x103672,a910),f922(x103672,a910),x103671),f262(x103672)),f327(f327(f8(f922(x103672,a910),f922(x103672,a910),x103671),f327(f18(x103672,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103672),a325),f327(f327(f7(x103672,f922(x103672,a910),a910),f329(x103672)),x103673)))),x103674)))),x103675),f327(f327(f81(a915),x103676),f327(f36(x103672),x103673))) % 177.41/177.19 [10369]~P1(f327(f35(x103692),x103693))+~P1(f327(f35(x103691),x103695))+~E(f327(f36(x103691),f327(f262(x103691),f327(f327(f18(x103691,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103691),a325),f327(f327(f7(x103691,f922(x103691,a910),a910),f329(x103691)),x103695))),f327(f327(f7(x103691,x103692,a910),x103694),f495(x103696,x103694,x103693,x103692,x103695,x103691))))),f327(x103696,f495(x103696,x103694,x103693,x103692,x103695,x103691)))+E(f327(f327(f6(x103691,a915),f327(f327(f8(f922(x103692,a910),a915,x103691),f36(x103692)),f327(f327(f8(f922(x103692,a910),f922(x103692,a910),x103691),f262(x103692)),f327(f327(f8(f922(x103692,a910),f922(x103692,a910),x103691),f327(f18(x103692,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103692),a325),f327(f327(f7(x103692,f922(x103692,a910),a910),f329(x103692)),x103693)))),x103694)))),x103695),f327(f327(f6(x103692,a915),x103696),x103693)) % 177.41/177.19 [9990]E(x99901,x99902)+~P14(x99903,x99904,x99905)+~P1(f327(f66(x99903,x99904,x99905,x99906,x99907),x99902))+~P1(f327(f66(x99903,x99904,x99905,x99906,x99907),x99901)) % 177.41/177.19 [9789]P1(f327(x97891,x97892))+~P1(f327(f327(f329(x97897),x97892),f327(x97896,x97894)))+~P1(f327(x97891,f901(x97891,x97896,x97895,x97893,x97897)))+~P1(f327(f327(f329(x97893),x97894),x97895)) % 177.41/177.19 [10231]~P14(x102317,x102316,x102311)+E(f327(f327(x102311,x102312),f553(x102312,x102313,x102314,x102315,x102311,x102316,x102317)),x102313)+~P1(f327(f66(x102317,x102316,x102311,x102315,x102314),x102313))+~P1(f327(f327(f329(x102317),x102312),x102314)) % 177.41/177.19 [10301]~P14(x103011,x103012,x103013)+~P1(f327(f66(x103011,x103012,x103013,x103014,x103015),x103017))+P1(f327(f66(x103011,x103012,x103013,x103014,f327(f327(f23(f922(x103011,a910)),x103015),f327(f327(f309(x103011),x103016),f190(f922(x103011,a910))))),f553(x103016,x103017,x103015,x103014,x103013,x103012,x103011)))+~P1(f327(f327(f329(x103011),x103016),x103015)) % 177.41/177.19 [9440]P24(x94401,x94402,x94403,x94404,x94405)+~P24(x94401,x94402,x94403,x94406,x94407)+~E(f327(f310(x94401,x94402,x94403),x94404),x94405)+~P1(f327(f327(f234(f922(x94401,a910)),x94404),x94406)) % 177.41/177.19 [9680]~P24(x96801,x96802,x96803,x96805,x96807)+~P24(x96801,x96802,x96803,x96804,x96806)+P24(x96801,x96802,x96803,f327(f327(f102(f922(x96801,a910)),x96804),x96805),f327(f327(f102(f922(x96802,a910)),x96806),x96807))+~E(f327(f327(f103(f922(x96802,a910)),x96806),x96807),f190(f922(x96802,a910))) % 177.41/177.19 [9685]~P72(x96851)+~P23(x96855,x96852,x96856,x96857)+~P1(f327(f35(x96855),x96857))+E(f327(f327(f327(f65(x96851,x96852,f81(x96851)),x96853),x96854),f327(f310(x96855,x96852,x96856),x96857)),f327(f327(f327(f65(x96851,x96855,f81(x96851)),f327(f72(x96852,x96851,x96855,x96853),x96856)),x96854),x96857)) % 177.41/177.19 [9812]~E(f327(f327(f309(x98121),x98125),x98126),f327(f327(f309(x98121),x98122),x98123))+~P1(f327(f66(x98121,x98121,x98124,x98122,x98123),x98127))+P1(f327(f327(f329(x98121),x98122),x98123))+P1(f327(f62(x98121,x98124,f327(f327(f309(x98121),x98125),x98126)),x98127)) % 177.41/177.19 [9896]P1(f327(x98961,x98962))+~P1(f327(f327(f329(x98963),x98962),f327(x98964,x98967)))+~P1(f327(f327(f329(x98966),x98967),x98965))+P1(f327(f327(f329(x98963),f901(x98961,x98964,x98965,x98966,x98963)),f327(f327(f40(x98966,f922(x98963,a910)),x98965),x98964))) % 177.41/177.19 [9914]~P23(x99142,x99141,x99145,x99144)+~P23(x99141,x99143,x99146,f327(f310(x99142,x99141,x99145),x99144))+E(f327(f327(f72(x99141,x99142,x99143,f77(x99142,x99141,x99144,x99145)),f77(x99141,x99143,f327(f310(x99142,x99141,x99145),x99144),x99146)),x99147),f327(f77(x99142,x99143,x99144,f327(f72(x99141,x99143,x99142,x99146),x99145)),x99147))+~P1(f327(f327(f329(x99143),x99147),f327(f310(x99141,x99143,x99146),f327(f310(x99142,x99141,x99145),x99144)))) % 177.41/177.19 [9915]~P23(x99152,x99151,x99155,x99154)+~P23(x99151,x99153,x99156,f327(f310(x99152,x99151,x99155),x99154))+E(f327(f327(f72(x99151,x99152,x99153,f92(x99152,x99151,x99154,x99155)),f92(x99151,x99153,f327(f310(x99152,x99151,x99155),x99154),x99156)),x99157),f327(f92(x99152,x99153,x99154,f327(f72(x99151,x99153,x99152,x99156),x99155)),x99157))+~P1(f327(f327(f329(x99153),x99157),f327(f310(x99151,x99153,x99156),f327(f310(x99152,x99151,x99155),x99154)))) % 177.41/177.19 [10232]~P14(x102327,x102326,x102321)+E(f327(f327(x102321,x102322),f614(x102323,x102324,x102322,x102325,x102321,x102326,x102327)),x102323)+P1(f327(f327(f329(x102327),x102322),x102324))+~P1(f327(f66(x102327,x102326,x102321,x102325,f327(f327(f309(x102327),x102322),x102324)),x102323)) % 177.41/177.19 [10300]~P14(x103001,x103004,x103005)+P1(f327(f66(x103001,x103004,x103005,x103006,x103003),f614(x103007,x103003,x103002,x103006,x103005,x103004,x103001)))+P1(f327(f327(f329(x103001),x103002),x103003))+~P1(f327(f66(x103001,x103004,x103005,x103006,f327(f327(f309(x103001),x103002),x103003)),x103007)) % 177.41/177.19 [9972]E(x99721,f2(a1))+~P1(f327(f50(x99723,x99721),f327(f327(f252(a1,a1),x99725),x99727)))+~P1(f327(f50(x99722,x99721),f327(f327(f252(a1,a1),x99724),x99726)))+P1(f327(f50(f327(f327(f80(a1),x99722),x99723),x99721),f327(f327(f252(a1,a1),f327(f327(f80(a1),f327(f327(f80(a1),x99724),x99725)),f327(f327(f37(a1),f327(f327(f80(a1),x99726),x99727)),x99721))),f46(a1,f327(f327(f80(a1),x99726),x99727),x99721)))) % 177.41/177.19 [9974]~P1(f327(f327(f235(a915),f2(a915)),x99743))+~P1(f327(f49(x99742,x99743),f327(f327(f252(a915,a915),x99745),x99747)))+~P1(f327(f49(x99741,x99743),f327(f327(f252(a915,a915),x99744),x99746)))+P1(f327(f49(f327(f327(f80(a915),x99741),x99742),x99743),f327(f327(f252(a915,a915),f327(f327(f80(a915),f327(f327(f80(a915),x99744),x99745)),f327(f327(f37(a915),f327(f327(f80(a915),x99746),x99747)),x99743))),f46(a915,f327(f327(f80(a915),x99746),x99747),x99743)))) % 177.41/177.19 [10366]~P68(x103662)+~P1(f327(f35(x103663),x103665))+~P1(f327(f35(x103661),x103667))+E(f327(f327(f6(x103661,x103662),f327(f327(f18(x103661,f922(x103663,a910),x103662),f327(f327(f8(f922(x103663,x103662),f922(f922(x103663,a910),x103662),x103661),f6(x103663,x103662)),x103664)),f327(f327(f8(f922(x103663,a910),f922(x103663,a910),x103661),f262(x103663)),f327(f327(f8(f922(x103663,a910),f922(x103663,a910),x103661),f327(f18(x103663,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103663),a325),f327(f327(f7(x103663,f922(x103663,a910),a910),f329(x103663)),x103665)))),x103666)))),x103667),f327(f327(f6(x103663,x103662),f327(f327(f18(x103663,f922(x103661,a910),x103662),f327(f327(f8(f922(x103661,x103662),f922(f922(x103661,a910),x103662),x103663),f6(x103661,x103662)),f327(f7(x103661,x103663,x103662),x103664))),f327(f327(f8(f922(x103661,a910),f922(x103661,a910),x103663),f262(x103661)),f327(f327(f8(f922(x103661,a910),f922(x103661,a910),x103663),f327(f18(x103661,a910,a910),f327(f327(f8(a910,f922(a910,a910),x103661),a325),f327(f327(f7(x103661,f922(x103661,a910),a910),f329(x103661)),x103667)))),f327(f7(x103661,x103663,a910),x103666))))),x103665)) % 177.41/177.19 [10321]~P19(x103218,x103217,x103216,x103215,x103211)+~E(f327(x103212,f853(x103214,x103212,x103213,x103211,x103215,x103216,x103217)),f327(x103214,f853(x103214,x103212,x103213,x103211,x103215,x103216,x103217)))+E(f327(f327(x103211,x103212),x103213),f327(f327(x103211,x103214),x103213))+~P1(f327(f35(x103217),x103213)) % 177.41/177.19 [9848]~P20(x98487,x98486,x98481,x98488,x98482,x98484)+E(f327(f327(x98481,f327(x98482,x98483)),f327(x98484,x98485)),f327(x98484,x98485))+~P1(f327(f35(x98486),x98485))+~P1(f327(f327(f329(x98486),x98483),x98485)) % 177.41/177.19 [9852]~P10(x98526,x98521,x98522,x98528,x98523,x98524)+~P6(x98526,x98527,x98528)+P9(x98521,x98522,x98523,f327(x98524,x98525))+~P1(f327(f327(f329(x98526),x98525),x98527)) % 177.41/177.19 [10339]~P19(x103398,x103395,x103397,x103396,x103391)+E(f327(f327(x103391,x103392),x103393),f327(f327(x103391,x103394),x103393))+~P1(f327(f35(x103395),x103393))+P1(f327(f327(f329(x103395),f853(x103392,x103394,x103393,x103391,x103396,x103397,x103395)),x103393)) % 177.41/177.19 [10418]~P1(f327(f327(x104181,x104186),x104185))+P1(f327(f327(x104181,f835(x104181,x104184,x104185,x104186,x104183,x104182,x104187,x104188)),f846(x104181,x104184,x104185,x104186,x104183,x104182,x104187,x104188)))+P1(f327(f327(x104181,x104182),x104183))+~P1(f327(f327(f329(f921(f921(x104188,x104187),f921(x104188,x104187))),f327(f327(f252(f921(x104188,x104187),f921(x104188,x104187)),f327(f327(f252(x104188,x104187),x104182),x104183)),f327(f327(f252(x104188,x104187),x104186),x104185))),f307(f921(x104188,x104187),x104184))) % 177.41/177.19 [10419]~P1(f327(f327(x104191,x104196),x104195))+P1(f327(f327(x104191,f836(x104191,x104194,x104193,x104192,x104195,x104196,x104197,x104198)),f837(x104191,x104194,x104193,x104192,x104195,x104196,x104197,x104198)))+P1(f327(f327(x104191,x104192),x104193))+~P1(f327(f327(f329(f921(f921(x104198,x104197),f921(x104198,x104197))),f327(f327(f252(f921(x104198,x104197),f921(x104198,x104197)),f327(f327(f252(x104198,x104197),x104196),x104195)),f327(f327(f252(x104198,x104197),x104192),x104193))),f307(f921(x104198,x104197),x104194))) % 177.41/177.19 [10429]~P1(f327(f327(x104291,f838(x104291,x104296,x104295,x104294,x104293,x104292,x104297,x104298)),f843(x104291,x104296,x104295,x104294,x104293,x104292,x104297,x104298)))+P1(f327(f327(x104291,x104292),x104293))+~P1(f327(f327(x104291,x104294),x104295))+~P1(f327(f327(f329(f921(f921(x104298,x104297),f921(x104298,x104297))),f327(f327(f252(f921(x104298,x104297),f921(x104298,x104297)),f327(f327(f252(x104298,x104297),x104292),x104293)),f327(f327(f252(x104298,x104297),x104294),x104295))),f307(f921(x104298,x104297),x104296))) % 177.41/177.19 [10430]~P1(f327(f327(x104301,f839(x104301,x104306,x104303,x104302,x104305,x104304,x104307,x104308)),f840(x104301,x104306,x104303,x104302,x104305,x104304,x104307,x104308)))+P1(f327(f327(x104301,x104302),x104303))+~P1(f327(f327(x104301,x104304),x104305))+~P1(f327(f327(f329(f921(f921(x104308,x104307),f921(x104308,x104307))),f327(f327(f252(f921(x104308,x104307),f921(x104308,x104307)),f327(f327(f252(x104308,x104307),x104304),x104305)),f327(f327(f252(x104308,x104307),x104302),x104303))),f307(f921(x104308,x104307),x104306))) % 177.41/177.19 [10443]~P1(f327(f327(x104431,x104436),x104437))+P1(f327(f327(x104431,x104432),x104433))+P1(f327(f327(f329(f921(f921(x104434,x104435),f921(x104434,x104435))),f327(f327(f252(f921(x104434,x104435),f921(x104434,x104435)),f327(f327(f252(x104434,x104435),x104436),x104437)),f327(f327(f252(x104434,x104435),f836(x104431,x104438,x104433,x104432,x104437,x104436,x104435,x104434)),f837(x104431,x104438,x104433,x104432,x104437,x104436,x104435,x104434)))),f307(f921(x104434,x104435),x104438)))+~P1(f327(f327(f329(f921(f921(x104434,x104435),f921(x104434,x104435))),f327(f327(f252(f921(x104434,x104435),f921(x104434,x104435)),f327(f327(f252(x104434,x104435),x104436),x104437)),f327(f327(f252(x104434,x104435),x104432),x104433))),f307(f921(x104434,x104435),x104438))) % 177.41/177.19 [10445]~P1(f327(f327(x104451,x104458),x104457))+P1(f327(f327(x104451,x104452),x104453))+P1(f327(f327(f329(f921(f921(x104454,x104455),f921(x104454,x104455))),f327(f327(f252(f921(x104454,x104455),f921(x104454,x104455)),f327(f327(f252(x104454,x104455),f835(x104451,x104456,x104457,x104458,x104453,x104452,x104455,x104454)),f846(x104451,x104456,x104457,x104458,x104453,x104452,x104455,x104454))),f327(f327(f252(x104454,x104455),x104458),x104457))),f307(f921(x104454,x104455),x104456)))+~P1(f327(f327(f329(f921(f921(x104454,x104455),f921(x104454,x104455))),f327(f327(f252(f921(x104454,x104455),f921(x104454,x104455)),f327(f327(f252(x104454,x104455),x104452),x104453)),f327(f327(f252(x104454,x104455),x104458),x104457))),f307(f921(x104454,x104455),x104456))) % 177.41/177.19 [9465]~P17(x94657,x94651,x94658,x94653)+~P1(f327(f35(x94657),x94655))+~P1(f327(f35(x94657),x94654))+E(f327(f72(x94651,x94651,x94652,f327(x94653,x94654)),f327(f72(x94651,x94651,x94652,f327(x94653,x94655)),x94656)),f327(f72(x94651,x94651,x94652,f327(x94653,x94655)),f327(f72(x94651,x94651,x94652,f327(x94653,x94654)),x94656))) % 177.41/177.19 [9474]~P32(x94741,x94742,x94743,x94744,x94747)+P32(x94741,x94742,x94743,f327(f327(f160(x94741,x94744),x94745),x94746),f327(f327(f160(x94742,x94747),x94745),x94748))+~P1(f327(f327(x94743,x94746),x94748))+~P1(f327(f327(f235(a915),x94745),f327(f191(f916(x94741)),x94744))) % 177.41/177.19 [9475]~P32(x94751,x94752,x94753,x94754,x94757)+P32(x94751,x94752,x94753,f327(f327(f160(x94751,x94754),x94755),x94756),f327(f327(f160(x94752,x94757),x94755),x94758))+~P1(f327(f327(x94753,x94756),x94758))+~P1(f327(f327(f235(a915),x94755),f327(f191(f916(x94752)),x94757))) % 177.41/177.19 [9554]~P23(x95542,x95542,x95545,x95546)+~P19(x95543,x95542,x95547,x95548,x95541)+~P1(f327(f35(x95542),x95546))+E(f327(f327(x95541,f327(f72(x95542,x95543,x95542,x95544),x95545)),x95546),f327(f327(x95541,x95544),f327(f310(x95542,x95542,x95545),x95546))) % 177.41/177.19 [9813]P24(x98131,x98132,x98133,x98134,x98135)+~P24(x98132,x98136,x98137,x98135,x98138)+~P24(x98131,x98136,f327(f72(x98132,x98136,x98131,x98137),x98133),x98134,x98138)+~P1(f327(f327(f234(f922(x98132,a910)),f327(f310(x98131,x98132,x98133),x98134)),x98135)) % 177.41/177.19 [9850]~P21(x98507,x98502,x98505,x98508,x98506,x98501)+~P1(f327(f35(x98502),x98504))+E(f327(x98501,f327(f327(f309(x98502),x98503),x98504)),f327(f327(x98505,f327(x98506,x98503)),f327(x98501,x98504)))+P1(f327(f327(f329(x98502),x98503),x98504)) % 177.41/177.19 [9861]~P20(x98616,x98615,x98611,x98617,x98618,x98612)+E(f327(f327(x98611,f327(x98612,x98613)),f327(x98612,x98614)),f327(x98612,x98614))+~P1(f327(f35(x98615),x98614))+~P1(f327(f327(f234(f922(x98615,a910)),x98613),x98614)) % 177.41/177.19 [9452]P1(f327(f327(f329(f921(f916(x94521),f916(x94521))),f327(f327(f252(f916(x94521),f916(x94521)),x94522),x94523)),f158(x94521,x94524)))+~E(x94523,f327(f327(f135(x94521),x94525),f327(f327(f152(x94521),x94526),x94527)))+~E(x94522,f327(f327(f135(x94521),x94525),f327(f327(f152(x94521),x94528),x94527)))+~P1(f327(f327(f329(f921(x94521,x94521)),f327(f327(f252(x94521,x94521),x94528),x94526)),x94524)) % 177.41/177.19 [9855]~P20(x98556,x98552,x98555,x98557,x98558,x98551)+~P1(f327(f35(x98552),x98554))+~P1(f327(f35(x98552),x98553))+E(f327(x98551,f327(f327(f102(f922(x98552,a910)),x98553),x98554)),f327(f327(x98555,f327(x98551,x98553)),f327(x98551,x98554))) % 177.41/177.19 [10408]~P23(x104084,x104082,x104085,x104088)+E(f327(f327(f41(x104081,f922(x104082,a910)),x104083),f327(f327(f8(f922(x104084,a910),f922(x104082,a910),x104081),f310(x104084,x104082,x104085)),x104086)),f327(f310(x104084,x104082,x104085),f327(f327(f41(x104081,f922(x104084,a910)),x104083),x104086)))+~P1(f327(f327(f329(x104081),x104087),x104083))+P1(f327(f327(f329(x104081),f399(x104087,x104086,x104083,x104081,x104088,x104085,x104082,x104084)),x104083)) % 177.41/177.19 [10434]~P23(x104344,x104342,x104345,x104347)+E(f327(f327(f41(x104341,f922(x104342,a910)),x104343),f327(f327(f8(f922(x104344,a910),f922(x104342,a910),x104341),f310(x104344,x104342,x104345)),x104346)),f327(f310(x104344,x104342,x104345),f327(f327(f41(x104341,f922(x104344,a910)),x104343),x104346)))+~P1(f327(f327(f329(x104341),x104348),x104343))+~P1(f327(f327(f234(f922(x104344,a910)),f327(x104346,f399(x104348,x104346,x104343,x104341,x104347,x104345,x104342,x104344))),x104347)) % 177.41/177.19 [10446]~P1(f327(f327(x104461,x104468),x104467))+P1(f327(f327(x104461,x104462),x104463))+~P1(f327(f327(f329(f921(f921(x104464,x104465),f921(x104464,x104465))),f327(f327(f252(f921(x104464,x104465),f921(x104464,x104465)),f327(f327(f252(x104464,x104465),x104462),x104463)),f327(f327(f252(x104464,x104465),x104468),x104467))),f307(f921(x104464,x104465),x104466)))+P1(f327(f327(f329(f921(f921(x104464,x104465),f921(x104464,x104465))),f327(f327(f252(f921(x104464,x104465),f921(x104464,x104465)),f327(f327(f252(x104464,x104465),f838(x104461,x104466,x104467,x104468,x104463,x104462,x104465,x104464)),f843(x104461,x104466,x104467,x104468,x104463,x104462,x104465,x104464))),f327(f327(f252(x104464,x104465),f835(x104461,x104466,x104467,x104468,x104463,x104462,x104465,x104464)),f846(x104461,x104466,x104467,x104468,x104463,x104462,x104465,x104464)))),x104466)) % 177.41/177.19 [10447]~P1(f327(f327(x104471,x104478),x104477))+P1(f327(f327(x104471,x104472),x104473))+~P1(f327(f327(f329(f921(f921(x104474,x104475),f921(x104474,x104475))),f327(f327(f252(f921(x104474,x104475),f921(x104474,x104475)),f327(f327(f252(x104474,x104475),x104478),x104477)),f327(f327(f252(x104474,x104475),x104472),x104473))),f307(f921(x104474,x104475),x104476)))+P1(f327(f327(f329(f921(f921(x104474,x104475),f921(x104474,x104475))),f327(f327(f252(f921(x104474,x104475),f921(x104474,x104475)),f327(f327(f252(x104474,x104475),f836(x104471,x104476,x104473,x104472,x104477,x104478,x104475,x104474)),f837(x104471,x104476,x104473,x104472,x104477,x104478,x104475,x104474))),f327(f327(f252(x104474,x104475),f839(x104471,x104476,x104473,x104472,x104477,x104478,x104475,x104474)),f840(x104471,x104476,x104473,x104472,x104477,x104478,x104475,x104474)))),x104476)) % 177.41/177.19 [9924]~P21(x99247,x99245,x99241,x99248,x99242,x99244)+~P1(f327(f35(x99245),x99246))+~P1(f327(f327(f329(x99245),x99243),x99246))+E(f327(f327(x99241,f327(x99242,x99243)),f327(x99244,f327(f327(f23(f922(x99245,a910)),x99246),f327(f327(f309(x99245),x99243),f190(f922(x99245,a910)))))),f327(x99244,x99246)) % 177.41/177.19 [9932]~P21(x99326,x99323,x99321,x99327,x99328,x99322)+~P1(f327(f35(x99323),x99325))+~P1(f327(f35(x99323),x99324))+E(f327(f327(x99321,f327(x99322,f327(f327(f102(f922(x99323,a910)),x99324),x99325))),f327(x99322,f327(f327(f103(f922(x99323,a910)),x99324),x99325))),f327(f327(x99321,f327(x99322,x99324)),f327(x99322,x99325))) % 177.41/177.19 [10015]P40(x100151,x100152,x100153,x100154,x100155,f327(f327(x100153,x100156),x100157))+~P40(x100151,x100152,x100153,x100154,f327(f327(f23(f922(x100151,a910)),x100155),f327(f327(f309(x100151),x100158),f190(f922(x100151,a910)))),x100159)+~E(f327(f327(x100153,x100156),x100157),f327(f327(x100153,x100158),x100159))+~P1(f327(f327(f329(x100151),x100158),x100155)) % 177.41/177.19 [9956]~P10(x99566,x99567,x99568,x99569,x995610,x99561)+E(f327(f327(x99561,x99562),x99563),f327(f327(x99561,x99564),x99565))+~P1(f327(f327(f329(f921(x99567,x99567)),f327(f327(f252(x99567,x99567),x99563),x99565)),x995610))+~P1(f327(f327(f329(f921(x99566,x99566)),f327(f327(f252(x99566,x99566),x99562),x99564)),x99569)) % 177.41/177.19 [9558]~P96(x95582)+E(x95581,f190(f922(x95582,a910)))+~P1(f327(f35(x95582),x95581))+P1(f327(f327(f329(x95582),f13(x95582,x95581)),x95581))+~P1(f327(f327(f329(x95582),f327(f327(f102(x95582),f890(x95581,x95582)),f891(x95581,x95582))),f327(f327(f309(x95582),f890(x95581,x95582)),f327(f327(f309(x95582),f891(x95581,x95582)),f190(f922(x95582,a910)))))) % 177.41/177.19 [9559]~P96(x95592)+E(x95591,f190(f922(x95592,a910)))+~P1(f327(f35(x95592),x95591))+P1(f327(f327(f329(x95592),f10(x95592,x95591)),x95591))+~P1(f327(f327(f329(x95592),f327(f327(f103(x95592),f354(x95591,x95592)),f357(x95591,x95592))),f327(f327(f309(x95592),f354(x95591,x95592)),f327(f327(f309(x95592),f357(x95591,x95592)),f190(f922(x95592,a910)))))) % 177.41/177.19 [9590]~P72(x95902)+E(x95901,f190(f922(x95902,a910)))+~P1(f327(f35(x95902),x95901))+P1(f327(f327(f329(x95902),f327(f63(x95902,f81(x95902)),x95901)),x95901))+~P1(f327(f327(f329(x95902),f327(f327(f81(x95902),f768(x95901,x95902)),f780(x95901,x95902))),f327(f327(f309(x95902),f768(x95901,x95902)),f327(f327(f309(x95902),f780(x95901,x95902)),f190(f922(x95902,a910)))))) % 177.41/177.19 [9595]~P108(x95952)+E(x95951,f190(f922(x95952,a910)))+~P1(f327(f35(x95952),x95951))+P1(f327(f327(f329(x95952),f11(x95952,f189(x95952),x95951)),x95951))+~P1(f327(f327(f329(x95952),f327(f327(f189(x95952),f789(x95951,x95952)),f799(x95951,x95952))),f327(f327(f309(x95952),f789(x95951,x95952)),f327(f327(f309(x95952),f799(x95951,x95952)),f190(f922(x95952,a910)))))) % 177.41/177.19 [9596]~P108(x95962)+E(x95961,f190(f922(x95962,a910)))+~P1(f327(f35(x95962),x95961))+P1(f327(f327(f329(x95962),f12(x95962,f238(x95962),x95961)),x95961))+~P1(f327(f327(f329(x95962),f327(f327(f238(x95962),f807(x95961,x95962)),f821(x95961,x95962))),f327(f327(f309(x95962),f807(x95961,x95962)),f327(f327(f309(x95962),f821(x95961,x95962)),f190(f922(x95962,a910)))))) % 177.41/177.19 [6713]~P88(x67132)+E(x67131,f2(x67132))+~E(f327(f327(f80(x67132),x67133),x67131),f2(x67132))+~P1(f327(f327(f234(x67132),f2(x67132)),x67133))+~P1(f327(f327(f234(x67132),f2(x67132)),x67131)) % 177.41/177.19 [6714]~P88(x67142)+E(x67141,f2(x67142))+~E(f327(f327(f80(x67142),x67141),x67143),f2(x67142))+~P1(f327(f327(f234(x67142),f2(x67142)),x67143))+~P1(f327(f327(f234(x67142),f2(x67142)),x67141)) % 177.41/177.19 [6910]~P1(f327(f327(f287(a915),x69102),x69101))+~P1(f327(f327(f287(a915),x69101),x69103))+P1(f327(f327(f287(a915),x69102),x69103))+P1(f327(f327(f287(a915),x69101),x69102))+P1(f327(f327(f287(a915),x69103),x69101)) % 177.41/177.19 [7081]~P1(f327(f327(f287(a915),x70811),x70813))+~P1(f327(f327(f287(a915),x70813),x70812))+~P1(f327(f327(f287(a915),x70812),x70811))+P1(f327(f327(f287(a915),x70811),x70812))+P1(f327(f327(f287(a915),x70813),x70811)) % 177.41/177.19 [7250]~P108(x72502)+~P11(x72502,x72501)+E(x72501,f114(x72502))+~P1(f327(f327(f329(x72502),x72503),f327(f173(x72502),f703(x72501,x72502))))+P1(f327(f327(f234(x72502),f722(x72501,x72502)),x72503)) % 177.41/177.19 [7421]~P108(x74211)+E(f15(x74211,x74212),x74213)+~P1(f327(f35(x74211),x74212))+~P1(f327(f327(f234(x74211),x74213),f653(x74213,x74212,x74211)))+~P1(f327(f327(f329(x74211),x74213),x74212)) % 177.41/177.20 [7454]~P108(x74541)+~P11(x74541,x74542)+~P11(x74541,x74543)+P11(x74541,f327(f327(f135(x74541),x74542),x74543))+P1(f327(f327(f329(x74541),f709(x74543,x74542,x74541)),f327(f173(x74541),x74542))) % 177.41/177.20 [7455]~P108(x74551)+~P11(x74551,x74552)+~P11(x74551,x74553)+P11(x74551,f327(f327(f135(x74551),x74552),x74553))+P1(f327(f327(f329(x74551),f710(x74553,x74552,x74551)),f327(f173(x74551),x74553))) % 177.41/177.20 [7517]~P108(x75171)+E(f14(x75171,x75172),x75173)+~P1(f327(f35(x75171),x75172))+P1(f327(f327(f329(x75171),f663(x75173,x75172,x75171)),x75172))+~P1(f327(f327(f329(x75171),x75173),x75172)) % 177.41/177.20 [7518]~P108(x75181)+E(f15(x75181,x75182),x75183)+~P1(f327(f35(x75181),x75182))+P1(f327(f327(f329(x75181),f653(x75183,x75182,x75181)),x75182))+~P1(f327(f327(f329(x75181),x75183),x75182)) % 177.41/177.20 [8084]~P108(x80841)+E(f14(x80841,x80842),x80843)+~P1(f327(f35(x80841),x80842))+~P1(f327(f327(f329(x80841),x80843),x80842))+~P1(f327(f327(f234(x80841),f663(x80843,x80842,x80841)),x80843)) % 177.41/177.20 [8402]~P108(x84021)+~P11(x84021,x84022)+~P11(x84021,x84023)+P11(x84021,f327(f327(f135(x84021),x84022),x84023))+~P1(f327(f327(f234(x84021),f709(x84023,x84022,x84021)),f710(x84023,x84022,x84021))) % 177.41/177.20 [9196]~P108(x91962)+E(x91961,f190(f922(x91962,a910)))+~E(f327(f327(f189(x91962),f327(x91963,f862(x91961,x91963,x91962))),f327(x91963,f864(x91961,x91963,x91962))),f327(x91963,f327(f327(f189(x91962),f862(x91961,x91963,x91962)),f864(x91961,x91963,x91962))))+E(f14(x91962,f327(f310(x91962,x91962,x91963),x91961)),f327(x91963,f14(x91962,x91961)))+~P1(f327(f35(x91962),x91961)) % 177.41/177.20 [9197]~P108(x91972)+E(x91971,f190(f922(x91972,a910)))+~E(f327(f327(f238(x91972),f327(x91973,f865(x91971,x91973,x91972))),f327(x91973,f867(x91971,x91973,x91972))),f327(x91973,f327(f327(f238(x91972),f865(x91971,x91973,x91972)),f867(x91971,x91973,x91972))))+E(f15(x91972,f327(f310(x91972,x91972,x91973),x91971)),f327(x91973,f15(x91972,x91971)))+~P1(f327(f35(x91972),x91971)) % 177.41/177.20 [9198]~P96(x91982)+E(x91981,f190(f922(x91982,a910)))+~E(f327(f327(f102(x91982),f327(x91983,f889(x91981,x91983,x91982))),f327(x91983,f892(x91981,x91983,x91982))),f327(x91983,f327(f327(f102(x91982),f889(x91981,x91983,x91982)),f892(x91981,x91983,x91982))))+E(f13(x91982,f327(f310(x91982,x91982,x91983),x91981)),f327(x91983,f13(x91982,x91981)))+~P1(f327(f35(x91982),x91981)) % 177.41/177.20 [9199]~P96(x91992)+E(x91991,f190(f922(x91992,a910)))+~E(f327(f327(f103(x91992),f327(x91993,f353(x91991,x91993,x91992))),f327(x91993,f358(x91991,x91993,x91992))),f327(x91993,f327(f327(f103(x91992),f353(x91991,x91993,x91992)),f358(x91991,x91993,x91992))))+E(f10(x91992,f327(f310(x91992,x91992,x91993),x91991)),f327(x91993,f10(x91992,x91991)))+~P1(f327(f35(x91992),x91991)) % 177.41/177.20 [9267]~P108(x92672)+E(x92671,f190(f922(x92672,a910)))+~E(f327(f327(f189(x92672),f327(x92673,f829(x92671,x92673,x92672))),f327(x92673,f833(x92671,x92673,x92672))),f327(x92673,f327(f327(f189(x92672),f829(x92671,x92673,x92672)),f833(x92671,x92673,x92672))))+E(f11(x92672,f189(x92672),f327(f310(x92672,x92672,x92673),x92671)),f327(x92673,f11(x92672,f189(x92672),x92671)))+~P1(f327(f35(x92672),x92671)) % 177.41/177.20 [9268]~P108(x92682)+E(x92681,f190(f922(x92682,a910)))+~E(f327(f327(f238(x92682),f327(x92683,f855(x92681,x92683,x92682))),f327(x92683,f863(x92681,x92683,x92682))),f327(x92683,f327(f327(f238(x92682),f855(x92681,x92683,x92682)),f863(x92681,x92683,x92682))))+E(f12(x92682,f238(x92682),f327(f310(x92682,x92682,x92683),x92681)),f327(x92683,f12(x92682,f238(x92682),x92681)))+~P1(f327(f35(x92682),x92681)) % 177.41/177.20 [6730]~P72(x67302)+E(x67301,f190(f922(x67302,a910)))+~P1(f327(f35(x67302),x67301))+E(f327(f63(x67302,f81(x67302)),f327(f327(f309(x67302),x67303),x67301)),f327(f327(f81(x67302),x67303),f327(f63(x67302,f81(x67302)),x67301)))+P1(f327(f327(f329(x67302),x67303),x67301)) % 177.41/177.20 [7256]~P108(x72562)+E(f327(f327(f238(x72562),f15(x72562,x72561)),f15(x72562,x72563)),f15(x72562,x72563))+E(x72561,f190(f922(x72562,a910)))+~P1(f327(f35(x72562),x72563))+~P1(f327(f327(f234(f922(x72562,a910)),x72561),x72563)) % 177.41/177.20 [7257]~P108(x72572)+E(f327(f327(f189(x72572),f14(x72572,x72571)),f14(x72572,x72573)),f14(x72572,x72573))+E(x72571,f190(f922(x72572,a910)))+~P1(f327(f35(x72572),x72573))+~P1(f327(f327(f234(f922(x72572,a910)),x72571),x72573)) % 177.41/177.20 [7258]~P96(x72582)+E(f327(f327(f102(x72582),f13(x72582,x72581)),f13(x72582,x72583)),f13(x72582,x72583))+E(x72581,f190(f922(x72582,a910)))+~P1(f327(f35(x72582),x72583))+~P1(f327(f327(f234(f922(x72582,a910)),x72581),x72583)) % 177.41/177.20 [7259]~P96(x72592)+E(f327(f327(f103(x72592),f10(x72592,x72591)),f10(x72592,x72593)),f10(x72592,x72593))+E(x72591,f190(f922(x72592,a910)))+~P1(f327(f35(x72592),x72593))+~P1(f327(f327(f234(f922(x72592,a910)),x72591),x72593)) % 177.41/177.20 [7564]~P108(x75642)+E(x75641,f190(f922(x75642,a910)))+~P1(f327(f35(x75642),x75643))+P1(f327(f327(f234(x75642),f14(x75642,x75641)),f14(x75642,x75643)))+~P1(f327(f327(f234(f922(x75642,a910)),x75641),x75643)) % 177.41/177.20 [7565]~P108(x75652)+E(x75651,f190(f922(x75652,a910)))+~P1(f327(f35(x75652),x75653))+P1(f327(f327(f234(x75652),f15(x75652,x75653)),f15(x75652,x75651)))+~P1(f327(f327(f234(f922(x75652,a910)),x75651),x75653)) % 177.41/177.20 [7618]~P108(x76181)+E(f14(x76181,x76182),x76183)+~P1(f327(f35(x76181),x76182))+~E(f327(f327(f23(f922(x76181,a910)),x76182),f327(f327(f309(x76181),x76183),f190(f922(x76181,a910)))),f190(f922(x76181,a910)))+~P1(f327(f327(f329(x76181),x76183),x76182)) % 177.41/177.20 [7619]~P108(x76191)+E(f15(x76191,x76192),x76193)+~P1(f327(f35(x76191),x76192))+~E(f327(f327(f23(f922(x76191,a910)),x76192),f327(f327(f309(x76191),x76193),f190(f922(x76191,a910)))),f190(f922(x76191,a910)))+~P1(f327(f327(f329(x76191),x76193),x76192)) % 177.41/177.20 [7620]~P96(x76201)+E(f13(x76201,x76202),x76203)+~P1(f327(f35(x76201),x76202))+~E(f327(f327(f23(f922(x76201,a910)),x76202),f327(f327(f309(x76201),x76203),f190(f922(x76201,a910)))),f190(f922(x76201,a910)))+~P1(f327(f327(f329(x76201),x76203),x76202)) % 177.41/177.20 [7621]~P96(x76211)+E(f10(x76211,x76212),x76213)+~P1(f327(f35(x76211),x76212))+~E(f327(f327(f23(f922(x76211,a910)),x76212),f327(f327(f309(x76211),x76213),f190(f922(x76211,a910)))),f190(f922(x76211,a910)))+~P1(f327(f327(f329(x76211),x76213),x76212)) % 177.41/177.20 [7715]~P108(x77151)+E(f11(x77151,f189(x77151),x77152),x77153)+~P1(f327(f35(x77151),x77152))+~E(f327(f327(f23(f922(x77151,a910)),x77152),f327(f327(f309(x77151),x77153),f190(f922(x77151,a910)))),f190(f922(x77151,a910)))+~P1(f327(f327(f329(x77151),x77153),x77152)) % 177.41/177.20 [7716]~P108(x77161)+E(f12(x77161,f238(x77161),x77162),x77163)+~P1(f327(f35(x77161),x77162))+~E(f327(f327(f23(f922(x77161,a910)),x77162),f327(f327(f309(x77161),x77163),f190(f922(x77161,a910)))),f190(f922(x77161,a910)))+~P1(f327(f327(f329(x77161),x77163),x77162)) % 177.41/177.20 [7751]~P108(x77512)+E(x77511,f190(f922(x77512,a910)))+~P1(f327(f35(x77512),x77511))+~P1(f327(f327(f234(x77512),x77513),f689(x77513,x77511,x77512)))+P1(f327(f327(f234(x77512),x77513),f327(f63(x77512,f238(x77512)),x77511))) % 177.41/177.20 [7752]~P102(x77522)+E(x77521,f190(f922(x77522,a910)))+~P1(f327(f35(x77522),x77521))+~P1(f327(f327(f234(x77522),x77523),f898(x77523,x77521,x77522)))+P1(f327(f327(f234(x77522),x77523),f327(f63(x77522,f103(x77522)),x77521))) % 177.41/177.20 [7753]~P108(x77532)+E(x77531,f190(f922(x77532,a910)))+~P1(f327(f35(x77532),x77531))+~P1(f327(f327(f235(x77532),x77533),f711(x77533,x77531,x77532)))+P1(f327(f327(f235(x77532),x77533),f327(f63(x77532,f238(x77532)),x77531))) % 177.41/177.20 [7840]~P108(x78402)+E(x78401,f190(f922(x78402,a910)))+~P1(f327(f35(x78402),x78401))+P1(f327(f327(f329(x78402),f689(x78403,x78401,x78402)),x78401))+P1(f327(f327(f234(x78402),x78403),f327(f63(x78402,f238(x78402)),x78401))) % 177.41/177.20 [7841]~P108(x78412)+E(x78411,f190(f922(x78412,a910)))+~P1(f327(f35(x78412),x78411))+P1(f327(f327(f329(x78412),f711(x78413,x78411,x78412)),x78411))+P1(f327(f327(f235(x78412),x78413),f327(f63(x78412,f238(x78412)),x78411))) % 177.41/177.20 [7842]~P102(x78422)+E(x78421,f190(f922(x78422,a910)))+~P1(f327(f35(x78422),x78421))+P1(f327(f327(f329(x78422),f898(x78423,x78421,x78422)),x78421))+P1(f327(f327(f234(x78422),x78423),f327(f63(x78422,f103(x78422)),x78421))) % 177.41/177.20 [7962]~P108(x79622)+E(x79621,f190(f922(x79622,a910)))+E(f327(f327(f238(x79622),f12(x79622,f238(x79622),x79621)),f12(x79622,f238(x79622),x79623)),f12(x79622,f238(x79622),x79623))+~P1(f327(f35(x79622),x79623))+~P1(f327(f327(f234(f922(x79622,a910)),x79621),x79623)) % 177.41/177.20 [7963]~P108(x79632)+E(x79631,f190(f922(x79632,a910)))+E(f327(f327(f189(x79632),f11(x79632,f189(x79632),x79631)),f11(x79632,f189(x79632),x79633)),f11(x79632,f189(x79632),x79633))+~P1(f327(f35(x79632),x79633))+~P1(f327(f327(f234(f922(x79632,a910)),x79631),x79633)) % 177.41/177.20 [8161]~E(f478(x81611,x81613,x81612),f479(x81611,x81613,x81612))+~E(f327(f36(x81612),f480(x81611,x81613,x81612)),x81611)+E(f327(f327(f81(a915),x81611),f327(f36(f922(x81612,a910)),x81613)),f327(f36(x81612),f38(f922(x81612,a910),x81613)))+~P1(f327(f35(x81612),f38(f922(x81612,a910),x81613)))+~P1(f327(f35(f922(x81612,a910)),x81613)) % 177.41/177.20 [8342]~P108(x83422)+E(x83421,f190(f922(x83422,a910)))+~P1(f327(f35(x83422),x83423))+P1(f327(f327(f234(x83422),f327(f63(x83422,f238(x83422)),x83423)),f327(f63(x83422,f238(x83422)),x83421)))+~P1(f327(f327(f234(f922(x83422,a910)),x83421),x83423)) % 177.41/177.20 [8640]~E(f478(x86401,x86403,x86402),f479(x86401,x86403,x86402))+E(f327(f327(f81(a915),x86401),f327(f36(f922(x86402,a910)),x86403)),f327(f36(x86402),f38(f922(x86402,a910),x86403)))+P1(f327(f327(f329(f922(x86402,a910)),f480(x86401,x86403,x86402)),x86403))+~P1(f327(f35(x86402),f38(f922(x86402,a910),x86403)))+~P1(f327(f35(f922(x86402,a910)),x86403)) % 177.41/177.20 [8666]~E(f327(f36(x86662),f480(x86661,x86663,x86662)),x86661)+E(f327(f327(f81(a915),x86661),f327(f36(f922(x86662,a910)),x86663)),f327(f36(x86662),f38(f922(x86662,a910),x86663)))+P1(f327(f327(f329(f922(x86662,a910)),f479(x86661,x86663,x86662)),x86663))+~P1(f327(f35(x86662),f38(f922(x86662,a910),x86663)))+~P1(f327(f35(f922(x86662,a910)),x86663)) % 177.41/177.20 [8667]~E(f327(f36(x86672),f480(x86671,x86673,x86672)),x86671)+E(f327(f327(f81(a915),x86671),f327(f36(f922(x86672,a910)),x86673)),f327(f36(x86672),f38(f922(x86672,a910),x86673)))+P1(f327(f327(f329(f922(x86672,a910)),f478(x86671,x86673,x86672)),x86673))+~P1(f327(f35(x86672),f38(f922(x86672,a910),x86673)))+~P1(f327(f35(f922(x86672,a910)),x86673)) % 177.41/177.20 [8692]~E(f327(f36(x86922),f480(x86921,x86923,x86922)),x86921)+~E(f327(f327(f103(f922(x86922,a910)),f479(x86921,x86923,x86922)),f478(x86921,x86923,x86922)),f190(f922(x86922,a910)))+E(f327(f327(f81(a915),x86921),f327(f36(f922(x86922,a910)),x86923)),f327(f36(x86922),f38(f922(x86922,a910),x86923)))+~P1(f327(f35(f922(x86922,a910)),x86923))+~P1(f327(f35(x86922),f38(f922(x86922,a910),x86923))) % 177.41/177.20 [8956]E(f327(f327(f81(a915),x89561),f327(f36(f922(x89562,a910)),x89563)),f327(f36(x89562),f38(f922(x89562,a910),x89563)))+P1(f327(f327(f329(f922(x89562,a910)),f480(x89561,x89563,x89562)),x89563))+P1(f327(f327(f329(f922(x89562,a910)),f479(x89561,x89563,x89562)),x89563))+~P1(f327(f35(f922(x89562,a910)),x89563))+~P1(f327(f35(x89562),f38(f922(x89562,a910),x89563))) % 177.41/177.20 [8957]E(f327(f327(f81(a915),x89571),f327(f36(f922(x89572,a910)),x89573)),f327(f36(x89572),f38(f922(x89572,a910),x89573)))+P1(f327(f327(f329(f922(x89572,a910)),f480(x89571,x89573,x89572)),x89573))+P1(f327(f327(f329(f922(x89572,a910)),f478(x89571,x89573,x89572)),x89573))+~P1(f327(f35(f922(x89572,a910)),x89573))+~P1(f327(f35(x89572),f38(f922(x89572,a910),x89573))) % 177.41/177.20 [8983]~E(f327(f327(f103(f922(x89832,a910)),f479(x89831,x89833,x89832)),f478(x89831,x89833,x89832)),f190(f922(x89832,a910)))+E(f327(f327(f81(a915),x89831),f327(f36(f922(x89832,a910)),x89833)),f327(f36(x89832),f38(f922(x89832,a910),x89833)))+~P1(f327(f35(f922(x89832,a910)),x89833))+P1(f327(f327(f329(f922(x89832,a910)),f480(x89831,x89833,x89832)),x89833))+~P1(f327(f35(x89832),f38(f922(x89832,a910),x89833))) % 177.41/177.20 [9242]~P95(x92422)+E(x92421,f190(f922(x92422,a910)))+~E(f327(f327(f81(x92422),f327(x92423,f868(x92421,x92423,x92422))),f327(x92423,f869(x92421,x92423,x92422))),f327(x92423,f327(f327(f81(x92422),f868(x92421,x92423,x92422)),f869(x92421,x92423,x92422))))+~P1(f327(f35(x92422),x92421))+E(f327(f63(x92422,f81(x92422)),f327(f310(x92422,x92422,x92423),x92421)),f327(x92423,f327(f63(x92422,f81(x92422)),x92421))) % 177.41/177.20 [10174]P1(f327(f327(x101741,x101742),x101743))+P1(f327(f327(f235(a1),f522(x101741,x101743,x101742)),f523(x101741,x101743,x101742)))+P1(f327(f327(f234(a1),f523(x101741,x101743,x101742)),f2(a1)))+P1(f327(f327(x101741,f522(x101741,x101743,x101742)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f523(x101741,x101743,x101742))))+~P1(f327(f315(f921(a1,a1),a59),f327(f327(f252(a1,a1),x101742),x101743))) % 177.41/177.20 [10180]P1(f327(f327(x101801,x101802),x101803))+P1(f327(f327(f234(a1),f521(x101801,x101803,x101802)),f2(a1)))+P1(f327(f327(x101801,f515(x101801,x101803,x101802)),f327(f327(f81(a1),f327(f105(a1),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f521(x101801,x101803,x101802))))+P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),f515(x101801,x101803,x101802)),f521(x101801,x101803,x101802))))+~P1(f327(f315(f921(a1,a1),a53),f327(f327(f252(a1,a1),x101802),x101803))) % 177.41/177.20 [8133]~P119(x81331)+~P1(f327(f327(f234(x81331),x81332),f78(x81331)))+~P1(f327(f327(f234(x81331),f2(x81331)),x81332))+~P1(f327(f327(f234(x81331),f2(x81331)),x81333))+P1(f327(f327(f234(x81331),f327(f327(f81(x81331),x81332),x81333)),x81333)) % 177.41/177.20 [8134]~P119(x81341)+~P1(f327(f327(f234(x81341),x81343),f78(x81341)))+~P1(f327(f327(f234(x81341),f2(x81341)),x81343))+~P1(f327(f327(f234(x81341),f2(x81341)),x81342))+P1(f327(f327(f234(x81341),f327(f327(f81(x81341),x81342),x81343)),x81342)) % 177.41/177.20 [8487]~P108(x84872)+E(x84871,f190(f922(x84872,a910)))+~P1(f327(f35(x84872),x84871))+P1(f327(f327(f329(x84872),f672(x84873,x84871,x84872)),x84871))+~P1(f327(f327(f234(x84872),f327(f63(x84872,f238(x84872)),x84871)),x84873)) % 177.41/177.20 [8488]~P108(x84882)+E(x84881,f190(f922(x84882,a910)))+~P1(f327(f35(x84882),x84881))+P1(f327(f327(f329(x84882),f698(x84883,x84881,x84882)),x84881))+~P1(f327(f327(f235(x84882),f327(f63(x84882,f238(x84882)),x84881)),x84883)) % 177.41/177.20 [8489]~P108(x84892)+E(x84891,f190(f922(x84892,a910)))+~P1(f327(f35(x84892),x84891))+P1(f327(f327(f234(x84892),f672(x84893,x84891,x84892)),x84893))+~P1(f327(f327(f234(x84892),f327(f63(x84892,f238(x84892)),x84891)),x84893)) % 177.41/177.20 [8490]~P108(x84902)+E(x84901,f190(f922(x84902,a910)))+~P1(f327(f35(x84902),x84901))+P1(f327(f327(f235(x84902),f698(x84903,x84901,x84902)),x84903))+~P1(f327(f327(f235(x84902),f327(f63(x84902,f238(x84902)),x84901)),x84903)) % 177.41/177.20 [8575]~P1(f327(x85751,x85753))+P1(f327(x85751,f441(x85751,x85752)))+P1(f327(x85751,f435(x85751,x85752)))+~P1(f327(f327(f235(a1),f2(a1)),x85752))+P1(f327(x85751,f327(f327(f23(a1),f435(x85751,x85752)),f327(f327(f81(a1),f442(x85751,x85752)),x85752)))) % 177.41/177.20 [8793]~P1(f327(x87931,x87933))+P1(f327(x87931,f435(x87931,x87932)))+~P1(f327(f327(f235(a1),f2(a1)),x87932))+P1(f327(f327(f329(a1),f441(x87931,x87932)),f303(a1,f78(a1),x87932)))+P1(f327(x87931,f327(f327(f23(a1),f435(x87931,x87932)),f327(f327(f81(a1),f442(x87931,x87932)),x87932)))) % 177.41/177.20 [9005]~P1(f327(x90051,x90053))+~P1(f327(x90051,f435(x90051,x90052)))+P1(f327(x90051,f441(x90051,x90052)))+~P1(f327(f327(f235(a1),f2(a1)),x90052))+~P1(f327(x90051,f327(f327(f23(a1),f435(x90051,x90052)),f327(f327(f81(a1),f442(x90051,x90052)),x90052)))) % 177.41/177.20 [9133]~P1(f327(x91331,x91333))+~P1(f327(x91331,f435(x91331,x91332)))+~P1(f327(f327(f235(a1),f2(a1)),x91332))+P1(f327(f327(f329(a1),f441(x91331,x91332)),f303(a1,f78(a1),x91332)))+~P1(f327(x91331,f327(f327(f23(a1),f435(x91331,x91332)),f327(f327(f81(a1),f442(x91331,x91332)),x91332)))) % 177.41/177.20 [8911]~P108(x89111)+~P1(f327(f35(x89111),x89112))+E(f327(f327(f23(f922(x89111,a910)),x89112),f327(f327(f309(x89111),x89113),f190(f922(x89111,a910)))),f190(f922(x89111,a910)))+~P1(f327(f327(f329(x89111),x89113),x89112))+E(f327(f327(f189(x89111),x89113),f14(x89111,f327(f327(f23(f922(x89111,a910)),x89112),f327(f327(f309(x89111),x89113),f190(f922(x89111,a910)))))),f14(x89111,x89112)) % 177.41/177.20 [8912]~P108(x89121)+~P1(f327(f35(x89121),x89122))+E(f327(f327(f23(f922(x89121,a910)),x89122),f327(f327(f309(x89121),x89123),f190(f922(x89121,a910)))),f190(f922(x89121,a910)))+~P1(f327(f327(f329(x89121),x89123),x89122))+E(f327(f327(f238(x89121),x89123),f15(x89121,f327(f327(f23(f922(x89121,a910)),x89122),f327(f327(f309(x89121),x89123),f190(f922(x89121,a910)))))),f15(x89121,x89122)) % 177.41/177.20 [8913]~P96(x89131)+~P1(f327(f35(x89131),x89132))+E(f327(f327(f23(f922(x89131,a910)),x89132),f327(f327(f309(x89131),x89133),f190(f922(x89131,a910)))),f190(f922(x89131,a910)))+~P1(f327(f327(f329(x89131),x89133),x89132))+E(f327(f327(f102(x89131),x89133),f13(x89131,f327(f327(f23(f922(x89131,a910)),x89132),f327(f327(f309(x89131),x89133),f190(f922(x89131,a910)))))),f13(x89131,x89132)) % 177.41/177.20 [8914]~P96(x89141)+~P1(f327(f35(x89141),x89142))+E(f327(f327(f23(f922(x89141,a910)),x89142),f327(f327(f309(x89141),x89143),f190(f922(x89141,a910)))),f190(f922(x89141,a910)))+~P1(f327(f327(f329(x89141),x89143),x89142))+E(f327(f327(f103(x89141),x89143),f10(x89141,f327(f327(f23(f922(x89141,a910)),x89142),f327(f327(f309(x89141),x89143),f190(f922(x89141,a910)))))),f10(x89141,x89142)) % 177.41/177.20 [8976]~P108(x89761)+~P1(f327(f35(x89761),x89762))+E(f327(f327(f23(f922(x89761,a910)),x89762),f327(f327(f309(x89761),x89763),f190(f922(x89761,a910)))),f190(f922(x89761,a910)))+~P1(f327(f327(f329(x89761),x89763),x89762))+E(f327(f327(f189(x89761),x89763),f11(x89761,f189(x89761),f327(f327(f23(f922(x89761,a910)),x89762),f327(f327(f309(x89761),x89763),f190(f922(x89761,a910)))))),f11(x89761,f189(x89761),x89762)) % 177.41/177.20 [8977]~P108(x89771)+~P1(f327(f35(x89771),x89772))+E(f327(f327(f23(f922(x89771,a910)),x89772),f327(f327(f309(x89771),x89773),f190(f922(x89771,a910)))),f190(f922(x89771,a910)))+~P1(f327(f327(f329(x89771),x89773),x89772))+E(f327(f327(f238(x89771),x89773),f12(x89771,f238(x89771),f327(f327(f23(f922(x89771,a910)),x89772),f327(f327(f309(x89771),x89773),f190(f922(x89771,a910)))))),f12(x89771,f238(x89771),x89772)) % 177.41/177.20 [8992]~P108(x89921)+~P1(f327(f35(x89921),x89923))+~P1(f327(f35(x89921),x89922))+E(f327(f327(f103(f922(x89921,a910)),x89922),x89923),f190(f922(x89921,a910)))+E(f327(f327(f238(x89921),f15(x89921,f327(f327(f102(f922(x89921,a910)),x89922),x89923))),f15(x89921,f327(f327(f103(f922(x89921,a910)),x89922),x89923))),f327(f327(f238(x89921),f15(x89921,x89922)),f15(x89921,x89923))) % 177.41/177.20 [8993]~P108(x89931)+~P1(f327(f35(x89931),x89933))+~P1(f327(f35(x89931),x89932))+E(f327(f327(f103(f922(x89931,a910)),x89932),x89933),f190(f922(x89931,a910)))+E(f327(f327(f189(x89931),f14(x89931,f327(f327(f102(f922(x89931,a910)),x89932),x89933))),f14(x89931,f327(f327(f103(f922(x89931,a910)),x89932),x89933))),f327(f327(f189(x89931),f14(x89931,x89932)),f14(x89931,x89933))) % 177.41/177.20 [8994]~P96(x89941)+~P1(f327(f35(x89941),x89943))+~P1(f327(f35(x89941),x89942))+E(f327(f327(f103(f922(x89941,a910)),x89942),x89943),f190(f922(x89941,a910)))+E(f327(f327(f102(x89941),f13(x89941,f327(f327(f102(f922(x89941,a910)),x89942),x89943))),f13(x89941,f327(f327(f103(f922(x89941,a910)),x89942),x89943))),f327(f327(f102(x89941),f13(x89941,x89942)),f13(x89941,x89943))) % 177.41/177.20 [8995]~P96(x89951)+~P1(f327(f35(x89951),x89953))+~P1(f327(f35(x89951),x89952))+E(f327(f327(f103(f922(x89951,a910)),x89952),x89953),f190(f922(x89951,a910)))+E(f327(f327(f103(x89951),f10(x89951,f327(f327(f102(f922(x89951,a910)),x89952),x89953))),f10(x89951,f327(f327(f103(f922(x89951,a910)),x89952),x89953))),f327(f327(f103(x89951),f10(x89951,x89952)),f10(x89951,x89953))) % 177.41/177.20 [9214]~P108(x92141)+~P1(f327(f35(x92141),x92143))+~P1(f327(f35(x92141),x92142))+E(f327(f327(f103(f922(x92141,a910)),x92142),x92143),f190(f922(x92141,a910)))+E(f327(f327(f238(x92141),f12(x92141,f238(x92141),f327(f327(f102(f922(x92141,a910)),x92142),x92143))),f12(x92141,f238(x92141),f327(f327(f103(f922(x92141,a910)),x92142),x92143))),f327(f327(f238(x92141),f12(x92141,f238(x92141),x92142)),f12(x92141,f238(x92141),x92143))) % 177.41/177.20 [9215]~P108(x92151)+~P1(f327(f35(x92151),x92153))+~P1(f327(f35(x92151),x92152))+E(f327(f327(f103(f922(x92151,a910)),x92152),x92153),f190(f922(x92151,a910)))+E(f327(f327(f189(x92151),f11(x92151,f189(x92151),f327(f327(f102(f922(x92151,a910)),x92152),x92153))),f11(x92151,f189(x92151),f327(f327(f103(f922(x92151,a910)),x92152),x92153))),f327(f327(f189(x92151),f11(x92151,f189(x92151),x92152)),f11(x92151,f189(x92151),x92153))) % 177.41/177.20 [10012]~P126(x100123)+E(x100121,x100122)+~P1(f327(f327(f234(x100123),f2(x100123)),x100122))+~P1(f327(f327(f234(x100123),f2(x100123)),x100121))+~E(f327(f327(f244(x100123),x100121),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)))),f327(f327(f244(x100123),x100122),f327(f105(a915),f327(f327(f80(a1),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98)),f327(f327(f23(a1),f327(f327(f80(a1),a83),a83)),a98))))) % 177.41/177.20 [6055]~P58(x60552)+E(x60551,f2(x60552))+~E(f327(f327(f37(x60552),x60553),x60551),x60554)+E(x60553,f327(f327(f81(x60552),x60554),x60551))+~P1(f327(f327(f287(x60552),x60551),x60553)) % 177.41/177.20 [6056]~P58(x60562)+E(x60561,f2(x60562))+~E(x60563,f327(f327(f81(x60562),x60564),x60561))+E(f327(f327(f37(x60562),x60563),x60561),x60564)+~P1(f327(f327(f287(x60562),x60561),x60563)) % 177.41/177.20 [6528]E(f363(x65281,x65282,x65283),x65284)+E(f327(x65281,x65284),f2(a915))+~E(f327(f327(f6(x65283,a915),x65281),x65282),f78(a915))+~P1(f327(f35(x65283),x65282))+~P1(f327(f327(f329(x65283),x65284),x65282)) % 177.41/177.20 [6590]E(f365(x65901,x65902,x65903),x65904)+E(f327(x65901,x65904),f2(a915))+~E(f327(f327(f6(x65903,a915),x65901),x65902),f327(a113,f2(a915)))+~P1(f327(f35(x65903),x65902))+~P1(f327(f327(f329(x65903),x65904),x65902)) % 177.41/177.20 [6699]~P108(x66991)+~P3(x66991)+P1(f327(f327(f235(x66991),x66992),f38(x66991,x66993)))+~P1(f327(f327(f235(x66991),x66992),x66994))+~P1(f327(f327(f329(x66991),x66994),x66993)) % 177.41/177.20 [6873]~P108(x68731)+~P3(x68731)+~P1(f327(f327(f235(x68731),x68734),x68733))+P1(f327(f327(f235(x68731),f39(x68731,x68732)),x68733))+~P1(f327(f327(f329(x68731),x68734),x68732)) % 177.41/177.20 [7133]~P126(x71333)+E(x71331,x71332)+~E(f327(f327(f244(x71333),x71331),f327(a113,x71334)),f327(f327(f244(x71333),x71332),f327(a113,x71334)))+~P1(f327(f327(f234(x71333),f2(x71333)),x71332))+~P1(f327(f327(f234(x71333),f2(x71333)),x71331)) % 177.41/177.20 [7347]~E(f370(x73472,x73473,x73471,x73474),x73474)+~E(f327(x73472,x73474),f78(a915))+E(f327(f327(f6(x73471,a915),x73472),x73473),f78(a915))+~P1(f327(f35(x73471),x73473))+~P1(f327(f327(f329(x73471),x73474),x73473)) % 177.41/177.20 [7354]~P112(x73544)+~P134(x73544)+E(f327(x73541,f352(x73541,x73542,x73543,x73544)),f2(x73544))+~E(f327(f327(f9(x73543,x73544),x73541),x73542),f2(x73544))+~P1(f327(f35(x73543),x73542)) % 177.41/177.20 [7444]~E(f368(x74442,x74443,x74441,x74444),x74444)+~E(f327(x74442,x74444),f327(a113,f2(a915)))+E(f327(f327(f6(x74441,a915),x74442),x74443),f327(a113,f2(a915)))+~P1(f327(f35(x74441),x74443))+~P1(f327(f327(f329(x74441),x74444),x74443)) % 177.41/177.20 [8173]~E(f327(x81732,x81734),f78(a915))+~E(f327(x81732,f370(x81732,x81733,x81731,x81734)),f2(a915))+E(f327(f327(f6(x81731,a915),x81732),x81733),f78(a915))+~P1(f327(f35(x81731),x81733))+~P1(f327(f327(f329(x81731),x81734),x81733)) % 177.41/177.20 [8211]~E(f327(x82112,x82114),f327(a113,f2(a915)))+~E(f327(x82112,f368(x82112,x82113,x82111,x82114)),f2(a915))+E(f327(f327(f6(x82111,a915),x82112),x82113),f327(a113,f2(a915)))+~P1(f327(f35(x82111),x82113))+~P1(f327(f327(f329(x82111),x82114),x82113)) % 177.41/177.20 [8297]~P139(x82972)+~P121(x82972)+~P1(f327(x82971,x82974))+~P1(f327(f327(f287(x82972),x82973),f327(f327(f80(x82972),x82974),f2(x82972))))+P1(f327(x82971,f327(f327(f81(x82972),x82973),f854(x82973,x82971,x82972)))) % 177.41/177.20 [8760]~P108(x87601)+~P11(x87601,x87604)+P11(x87601,x87602)+~E(x87602,f327(f327(f152(x87601),x87603),x87604))+~P1(f327(f327(f234(x87601),x87603),f724(x87602,x87601,x87604,x87603))) % 177.41/177.20 [8797]E(x87971,x87972)+E(f327(f327(f23(a1),f427(x87973,x87972,x87974,x87971)),f420(x87973,x87972,x87974,x87971)),x87971)+~E(f327(f327(f80(a1),x87971),x87974),x87972)+~P1(f327(f327(f235(a1),f2(a1)),x87974))+~P1(f327(f327(f329(a1),x87972),x87973)) % 177.41/177.20 [8798]E(x87981,x87982)+E(f327(f327(f80(a1),f428(x87983,x87982,x87984,x87981)),f429(x87983,x87982,x87984,x87981)),x87981)+~E(f327(f327(f23(a1),x87981),x87984),x87982)+~P1(f327(f327(f235(a1),f2(a1)),x87984))+~P1(f327(f327(f329(a1),x87982),x87983)) % 177.41/177.20 [8990]E(f327(x89901,f627(x89902,x89901,x89903,x89904)),x89902)+P1(f327(f327(f234(a915),x89904),f628(x89902,x89901,x89903,x89904)))+~P1(f327(f327(f234(a1),x89902),f327(x89901,x89903)))+~P1(f327(f327(f235(a915),x89904),x89903))+~P1(f327(f327(f234(a1),f327(x89901,x89904)),x89902)) % 177.41/177.20 [8991]~P108(x89911)+~P11(x89911,x89913)+P11(x89911,x89912)+~E(x89912,f327(f327(f152(x89911),x89914),x89913))+P1(f327(f327(f329(x89911),f724(x89912,x89911,x89913,x89914)),f327(f173(x89911),x89913))) % 177.41/177.20 [9009]~P112(x90094)+~P134(x90094)+~E(f327(f327(f9(x90091,x90094),x90092),x90093),f2(x90094))+~P1(f327(f35(x90091),x90093))+P1(f327(f327(f329(x90091),f352(x90092,x90093,x90091,x90094)),x90093)) % 177.41/177.20 [9047]~E(f327(x90472,x90474),f78(a915))+E(f327(f327(f6(x90471,a915),x90472),x90473),f78(a915))+~P1(f327(f35(x90471),x90473))+~P1(f327(f327(f329(x90471),x90474),x90473))+P1(f327(f327(f329(x90471),f370(x90472,x90473,x90471,x90474)),x90473)) % 177.41/177.20 [9059]E(x90591,x90592)+~E(f327(f327(f80(a1),x90592),x90594),x90591)+~P1(f327(f327(f235(a1),f2(a1)),x90594))+~P1(f327(f327(f329(a1),x90591),x90593))+P1(f327(f327(f329(a1),f427(x90593,x90591,x90594,x90592)),x90593)) % 177.41/177.20 [9060]E(x90601,x90602)+~E(f327(f327(f23(a1),x90602),x90604),x90601)+~P1(f327(f327(f235(a1),f2(a1)),x90604))+~P1(f327(f327(f329(a1),x90601),x90603))+P1(f327(f327(f329(a1),f428(x90603,x90601,x90604,x90602)),x90603)) % 177.41/177.20 [9062]~E(f327(x90622,x90624),f327(a113,f2(a915)))+E(f327(f327(f6(x90621,a915),x90622),x90623),f327(a113,f2(a915)))+~P1(f327(f35(x90621),x90623))+~P1(f327(f327(f329(x90621),x90624),x90623))+P1(f327(f327(f329(x90621),f368(x90622,x90623,x90621,x90624)),x90623)) % 177.41/177.20 [9067]P56(x90672,x90673,x90674,x90671)+E(x90671,f190(f922(x90672,a910)))+~P1(f327(f35(x90672),x90674))+~P1(f327(f35(x90672),x90671))+P1(f327(f327(f329(x90672),f793(x90673,x90671,x90674,x90672)),x90674)) % 177.41/177.20 [9068]P56(x90682,x90683,x90684,x90681)+E(x90681,f190(f922(x90682,a910)))+~P1(f327(f35(x90682),x90684))+~P1(f327(f35(x90682),x90681))+P1(f327(f327(f329(x90682),f538(x90681,x90684,x90683,x90682)),x90684)) % 177.41/177.20 [9069]P56(x90692,x90693,x90694,x90691)+E(x90691,f190(f922(x90692,a910)))+~P1(f327(f35(x90692),x90694))+~P1(f327(f35(x90692),x90691))+P1(f327(f327(f329(x90692),f794(x90691,x90694,x90693,x90692)),x90694)) % 177.41/177.20 [9146]E(x91461,x91462)+~E(f327(f327(f80(a1),x91462),x91464),x91461)+~P1(f327(f327(f235(a1),f2(a1)),x91464))+~P1(f327(f327(f329(a1),x91461),x91463))+P1(f327(f327(f329(a1),f420(x91463,x91461,x91464,x91462)),f303(a1,f78(a1),x91464))) % 177.41/177.20 [9147]E(x91471,x91472)+~E(f327(f327(f23(a1),x91472),x91474),x91471)+~P1(f327(f327(f235(a1),f2(a1)),x91474))+~P1(f327(f327(f329(a1),x91471),x91473))+P1(f327(f327(f329(a1),f429(x91473,x91471,x91474,x91472)),f303(a1,f78(a1),x91474))) % 177.41/177.20 [9220]P1(f327(f327(f234(a915),x92201),f627(x92202,x92203,x92204,x92201)))+~P1(f327(f327(f234(a1),x92202),f327(x92203,x92204)))+P1(f327(f327(f234(a915),x92201),f628(x92202,x92203,x92204,x92201)))+~P1(f327(f327(f235(a915),x92201),x92204))+~P1(f327(f327(f234(a1),f327(x92203,x92201)),x92202)) % 177.41/177.20 [9334]E(f327(x93341,f627(x93342,x93341,x93343,x93344)),x93342)+~P1(f327(f327(f234(a1),x93342),f327(x93341,x93343)))+P1(f327(f327(f235(a915),f628(x93342,x93341,x93343,x93344)),x93343))+~P1(f327(f327(f235(a915),x93344),x93343))+~P1(f327(f327(f234(a1),f327(x93341,x93344)),x93342)) % 177.41/177.20 [9462]~P1(f327(f327(f234(a1),x94622),f327(x94623,x94624)))+P1(f327(f327(f234(a915),x94621),f628(x94622,x94623,x94624,x94621)))+P1(f327(f327(f234(a915),f627(x94622,x94623,x94624,x94621)),x94624))+~P1(f327(f327(f235(a915),x94621),x94624))+~P1(f327(f327(f234(a1),f327(x94623,x94621)),x94622)) % 177.41/177.20 [9463]~P1(f327(f327(f234(a1),x94632),f327(x94633,x94634)))+P1(f327(f327(f234(a915),x94631),f627(x94632,x94633,x94634,x94631)))+P1(f327(f327(f235(a915),f628(x94632,x94633,x94634,x94631)),x94634))+~P1(f327(f327(f235(a915),x94631),x94634))+~P1(f327(f327(f234(a1),f327(x94633,x94631)),x94632)) % 177.41/177.20 [9571]~P1(f327(f327(f234(a1),x95711),f327(x95712,x95713)))+P1(f327(f327(f235(a915),f628(x95711,x95712,x95713,x95714)),x95713))+~P1(f327(f327(f235(a915),x95714),x95713))+~P1(f327(f327(f234(a1),f327(x95712,x95714)),x95711))+P1(f327(f327(f234(a915),f627(x95711,x95712,x95713,x95714)),x95713)) % 177.41/177.20 [9657]E(x96571,f190(f922(x96572,a910)))+~P1(f327(f35(x96572),x96574))+~P1(f327(f35(x96572),x96571))+P1(f327(f327(f329(f921(f922(x96572,a910),f922(x96572,a910))),f327(f327(f252(f922(x96572,a910),f922(x96572,a910)),x96574),x96571)),f319(x96572,x96573)))+P1(f327(f327(f329(x96572),f547(x96573,x96571,x96574,x96572)),x96574)) % 177.41/177.20 [9658]E(x96581,f190(f922(x96582,a910)))+~P1(f327(f35(x96582),x96584))+~P1(f327(f35(x96582),x96581))+P1(f327(f327(f329(f921(f922(x96582,a910),f922(x96582,a910))),f327(f327(f252(f922(x96582,a910),f922(x96582,a910)),x96584),x96581)),f319(x96582,x96583)))+P1(f327(f327(f329(x96582),f596(x96583,x96581,x96584,x96582)),x96584)) % 177.41/177.20 [10334]E(f327(x103341,f627(x103342,x103341,x103343,x103344)),x103342)+~P1(f327(f327(f234(a1),x103342),f327(x103341,x103343)))+~P1(f327(f327(f234(a1),f327(f75(a1),f327(f327(f23(a1),f327(x103341,f327(f327(f80(a915),f628(x103342,x103341,x103343,x103344)),f78(a915)))),f327(x103341,f628(x103342,x103341,x103343,x103344))))),f78(a1)))+~P1(f327(f327(f235(a915),x103344),x103343))+~P1(f327(f327(f234(a1),f327(x103341,x103344)),x103342)) % 177.41/177.20 [10335]~P1(f327(f327(f234(a1),x103352),f327(x103353,x103354)))+P1(f327(f327(f234(a915),x103351),f627(x103352,x103353,x103354,x103351)))+~P1(f327(f327(f234(a1),f327(f75(a1),f327(f327(f23(a1),f327(x103353,f327(f327(f80(a915),f628(x103352,x103353,x103354,x103351)),f78(a915)))),f327(x103353,f628(x103352,x103353,x103354,x103351))))),f78(a1)))+~P1(f327(f327(f235(a915),x103351),x103354))+~P1(f327(f327(f234(a1),f327(x103353,x103351)),x103352)) % 177.41/177.20 [10336]~P1(f327(f327(f234(a1),x103361),f327(x103362,x103363)))+~P1(f327(f327(f234(a1),f327(f75(a1),f327(f327(f23(a1),f327(x103362,f327(f327(f80(a915),f628(x103361,x103362,x103363,x103364)),f78(a915)))),f327(x103362,f628(x103361,x103362,x103363,x103364))))),f78(a1)))+~P1(f327(f327(f235(a915),x103364),x103363))+~P1(f327(f327(f234(a1),f327(x103362,x103364)),x103361))+P1(f327(f327(f234(a915),f627(x103361,x103362,x103363,x103364)),x103363)) % 177.41/177.20 [7407]~P63(x74071)+P1(f327(f327(f235(x74071),x74072),f2(x74071)))+~P1(f327(f327(f234(x74071),x74073),f2(x74071)))+P1(f327(f327(f235(x74071),f2(x74071)),x74072))+P1(f327(f327(f234(x74071),x74073),f327(f327(f291(x74071),x74074),x74072))) % 177.41/177.20 [7408]~P63(x74081)+P1(f327(f327(f235(x74081),x74082),f2(x74081)))+~P1(f327(f327(f235(x74081),x74083),f2(x74081)))+P1(f327(f327(f235(x74081),f2(x74081)),x74082))+P1(f327(f327(f235(x74081),x74083),f327(f327(f291(x74081),x74084),x74082))) % 177.41/177.20 [7655]~P63(x76551)+P1(f327(f327(f234(x76551),x76552),f2(x76551)))+P1(f327(f327(f235(x76551),x76553),f2(x76551)))+P1(f327(f327(f235(x76551),f2(x76551)),x76553))+~P1(f327(f327(f234(x76551),x76552),f327(f327(f291(x76551),x76554),x76553))) % 177.41/177.20 [7656]~P63(x76561)+P1(f327(f327(f235(x76561),x76562),f2(x76561)))+P1(f327(f327(f235(x76561),x76563),f2(x76561)))+P1(f327(f327(f235(x76561),f2(x76561)),x76563))+~P1(f327(f327(f235(x76561),x76562),f327(f327(f291(x76561),x76564),x76563))) % 177.41/177.20 [7772]E(x77721,x77722)+~E(f327(f327(f165(x77723),x77724),x77721),f327(f327(f165(x77723),x77724),x77722))+~P1(f327(f138(x77723),x77724))+~P1(f327(f327(f235(a915),x77722),f327(f191(f916(x77723)),x77724)))+~P1(f327(f327(f235(a915),x77721),f327(f191(f916(x77723)),x77724))) % 177.41/177.20 [8135]~P63(x81351)+~P1(f327(f327(f234(x81351),x81353),f2(x81351)))+P1(f327(f327(f235(x81351),f2(x81351)),x81352))+~P1(f327(f327(f234(x81351),x81354),f327(f327(f81(x81351),x81353),x81352)))+P1(f327(f327(f234(x81351),x81353),f327(f327(f291(x81351),x81354),x81352))) % 177.41/177.20 [8136]~P63(x81361)+~P1(f327(f327(f235(x81361),x81363),f2(x81361)))+P1(f327(f327(f235(x81361),f2(x81361)),x81362))+~P1(f327(f327(f235(x81361),x81364),f327(f327(f81(x81361),x81363),x81362)))+P1(f327(f327(f235(x81361),x81363),f327(f327(f291(x81361),x81364),x81362))) % 177.41/177.20 [8137]~P63(x81371)+~P1(f327(f327(f235(x81371),x81372),f2(x81371)))+P1(f327(f327(f235(x81371),f2(x81371)),x81372))+~P1(f327(f327(f234(x81371),x81374),f327(f327(f81(x81371),x81373),x81372)))+P1(f327(f327(f234(x81371),x81373),f327(f327(f291(x81371),x81374),x81372))) % 177.41/177.20 [8138]~P63(x81381)+~P1(f327(f327(f235(x81381),x81382),f2(x81381)))+P1(f327(f327(f235(x81381),f2(x81381)),x81382))+~P1(f327(f327(f234(x81381),x81384),f327(f327(f291(x81381),x81383),x81382)))+P1(f327(f327(f234(x81381),x81383),f327(f327(f81(x81381),x81384),x81382))) % 177.41/177.20 [8139]~P63(x81391)+~P1(f327(f327(f235(x81391),x81392),f2(x81391)))+P1(f327(f327(f235(x81391),f2(x81391)),x81392))+~P1(f327(f327(f235(x81391),x81394),f327(f327(f81(x81391),x81393),x81392)))+P1(f327(f327(f235(x81391),x81393),f327(f327(f291(x81391),x81394),x81392))) % 177.41/177.20 [8140]~P63(x81401)+~P1(f327(f327(f235(x81401),x81402),f2(x81401)))+P1(f327(f327(f235(x81401),f2(x81401)),x81402))+~P1(f327(f327(f235(x81401),x81404),f327(f327(f291(x81401),x81403),x81402)))+P1(f327(f327(f235(x81401),x81403),f327(f327(f81(x81401),x81404),x81402))) % 177.41/177.20 [8265]~P58(x82651)+~P1(f327(f327(f287(x82651),x82653),x82654))+~P1(f327(f327(f287(x82651),x82653),x82652))+~P1(f327(f327(f287(x82651),x82652),x82654))+P1(f327(f327(f287(x82651),f327(f327(f37(x82651),x82652),x82653)),f327(f327(f37(x82651),x82654),x82653))) % 177.41/177.20 [8280]~P108(x82801)+~P11(x82801,x82802)+~P1(f327(f327(f234(a915),x82803),x82804))+P1(f327(f327(f234(x82801),f327(f327(f165(x82801),x82802),x82803)),f327(f327(f165(x82801),x82802),x82804)))+~P1(f327(f327(f235(a915),x82804),f327(f191(f916(x82801)),x82802))) % 177.41/177.20 [8333]~P126(x83331)+~P1(f327(f327(f234(x83331),x83332),f78(x83331)))+~P1(f327(f327(f234(x83331),f2(x83331)),x83332))+~P1(f327(f327(f234(a915),x83334),x83333))+P1(f327(f327(f234(x83331),f327(f327(f244(x83331),x83332),x83333)),f327(f327(f244(x83331),x83332),x83334))) % 177.41/177.20 [8334]~P126(x83341)+~P1(f327(f327(f235(x83341),x83342),f78(x83341)))+~P1(f327(f327(f235(x83341),f2(x83341)),x83342))+~P1(f327(f327(f235(a915),x83344),x83343))+P1(f327(f327(f235(x83341),f327(f327(f244(x83341),x83342),x83343)),f327(f327(f244(x83341),x83342),x83344))) % 177.41/177.20 [8335]~P126(x83351)+~P1(f327(f327(f234(x83351),f2(x83351)),x83352))+~P1(f327(f327(f235(a915),f2(a915)),x83353))+~P1(f327(f327(f235(x83351),x83352),x83354))+P1(f327(f327(f235(x83351),f327(f327(f244(x83351),x83352),x83353)),f327(f327(f244(x83351),x83354),x83353))) % 177.41/177.20 [8353]~P108(x83531)+~P11(x83531,f327(f169(x83531),x83532))+~P1(f327(f327(f234(a915),x83534),x83533))+P1(f327(f327(f234(x83531),f327(f327(f165(x83531),x83532),x83533)),f327(f327(f165(x83531),x83532),x83534)))+~P1(f327(f327(f235(a915),x83533),f327(f191(f916(x83531)),x83532))) % 177.41/177.20 [8582]~P58(x85821)+P1(f327(f327(f287(x85821),x85822),x85823))+~P1(f327(f327(f287(x85821),x85824),x85823))+~P1(f327(f327(f287(x85821),x85824),x85822))+~P1(f327(f327(f287(x85821),f327(f327(f37(x85821),x85822),x85824)),f327(f327(f37(x85821),x85823),x85824))) % 177.41/177.20 [8597]~P63(x85971)+~P1(f327(f327(f234(x85971),x85972),f2(x85971)))+~P1(f327(f327(f234(x85971),x85973),x85974))+~P1(f327(f327(f235(x85971),f2(x85971)),f327(f327(f81(x85971),x85973),x85974)))+P1(f327(f327(f234(x85971),f327(f327(f291(x85971),x85972),x85973)),f327(f327(f291(x85971),x85972),x85974))) % 177.41/177.20 [8598]~P64(x85981)+~P1(f327(f327(f235(x85981),x85982),f2(x85981)))+~P1(f327(f327(f235(x85981),x85983),x85984))+~P1(f327(f327(f235(x85981),f2(x85981)),f327(f327(f81(x85981),x85983),x85984)))+P1(f327(f327(f235(x85981),f327(f327(f291(x85981),x85982),x85983)),f327(f327(f291(x85981),x85982),x85984))) % 177.41/177.20 [8607]~P64(x86071)+~P1(f327(f327(f234(x86071),x86074),x86073))+~P1(f327(f327(f234(x86071),f2(x86071)),x86072))+~P1(f327(f327(f235(x86071),f2(x86071)),f327(f327(f81(x86071),x86073),x86074)))+P1(f327(f327(f234(x86071),f327(f327(f291(x86071),x86072),x86073)),f327(f327(f291(x86071),x86072),x86074))) % 177.41/177.20 [8608]~P64(x86081)+~P1(f327(f327(f235(x86081),x86084),x86083))+~P1(f327(f327(f235(x86081),f2(x86081)),x86082))+~P1(f327(f327(f235(x86081),f2(x86081)),f327(f327(f81(x86081),x86083),x86084)))+P1(f327(f327(f235(x86081),f327(f327(f291(x86081),x86082),x86083)),f327(f327(f291(x86081),x86082),x86084))) % 177.41/177.20 [8708]P1(f327(x87081,x87082))+~P1(f327(f35(x87084),x87082))+P1(f327(x87081,f544(x87081,x87083,x87082,x87084)))+~P1(f327(x87081,f190(f922(x87084,a910))))+~P1(f327(f327(f234(f922(x87084,a910)),x87082),x87083)) % 177.41/177.20 [8717]P1(f327(x87171,x87172))+P1(f327(f35(x87173),f544(x87171,x87174,x87172,x87173)))+~P1(f327(f35(x87173),x87172))+~P1(f327(x87171,f190(f922(x87173,a910))))+~P1(f327(f327(f234(f922(x87173,a910)),x87172),x87174)) % 177.41/177.20 [8985]E(f327(f327(f80(a1),f430(x89851,x89852,x89853,x89854)),f431(x89851,x89852,x89853,x89854)),x89854)+~P1(f327(f327(f235(a1),f2(a1)),x89853))+~P1(f327(f327(f235(a1),x89852),x89854))+~P1(f327(f327(f329(a1),x89852),x89851))+P1(f327(f327(f235(a1),x89852),f327(f327(f23(a1),x89854),x89853))) % 177.41/177.20 [9202]~P1(f327(f327(f235(a1),f2(a1)),x92023))+~P1(f327(f327(f235(a1),x92022),x92024))+~P1(f327(f327(f329(a1),x92022),x92021))+P1(f327(f327(f329(a1),f430(x92021,x92022,x92023,x92024)),x92021))+P1(f327(f327(f235(a1),x92022),f327(f327(f23(a1),x92024),x92023))) % 177.41/177.20 [9213]P1(f327(x92131,x92132))+~P1(f327(f35(x92133),x92132))+P1(f327(f327(f329(x92133),f532(x92131,x92134,x92132,x92133)),x92134))+~P1(f327(x92131,f190(f922(x92133,a910))))+~P1(f327(f327(f234(f922(x92133,a910)),x92132),x92134)) % 177.41/177.20 [9230]E(f327(f327(f80(a1),f421(x92301,x92302,x92303,x92304)),f422(x92301,x92302,x92303,x92304)),x92304)+~P1(f327(f327(f235(a1),f2(a1)),x92303))+~P1(f327(f327(f234(a1),x92302),x92304))+P1(f327(f327(f234(a1),x92302),f327(f327(f23(a1),x92304),x92303)))+~P1(f327(f327(f329(a1),f327(f327(f23(a1),x92302),f78(a1))),x92301)) % 177.41/177.20 [9284]~P1(f327(f327(f235(a1),f2(a1)),x92843))+~P1(f327(f327(f235(a1),x92841),x92842))+~P1(f327(f327(f329(a1),x92841),x92844))+P1(f327(f327(f329(a1),f431(x92844,x92841,x92843,x92842)),f303(a1,f78(a1),x92843)))+P1(f327(f327(f235(a1),x92841),f327(f327(f23(a1),x92842),x92843))) % 177.41/177.20 [9310]~P68(x93102)+~E(f777(x93103,x93104,x93101,x93102),f778(x93103,x93104,x93101,x93102))+~P1(f327(f35(x93101),f779(x93103,x93104,x93101,x93102)))+E(f327(f327(f6(f922(x93101,a910),x93102),f327(f6(x93101,x93102),x93103)),x93104),f327(f327(f6(x93101,x93102),x93103),f38(f922(x93101,a910),x93104)))+~P1(f327(f35(f922(x93101,a910)),x93104)) % 177.41/177.20 [9314]~P68(x93142)+~E(f327(x93143,f781(x93143,x93144,x93141,x93142)),f2(x93142))+~P1(f327(f35(x93141),f779(x93143,x93144,x93141,x93142)))+E(f327(f327(f6(f922(x93141,a910),x93142),f327(f6(x93141,x93142),x93143)),x93144),f327(f327(f6(x93141,x93142),x93143),f38(f922(x93141,a910),x93144)))+~P1(f327(f35(f922(x93141,a910)),x93144)) % 177.41/177.20 [9377]~P1(f327(f327(f235(a1),f2(a1)),x93773))+~P1(f327(f327(f234(a1),x93772),x93774))+P1(f327(f327(f329(a1),f421(x93771,x93772,x93773,x93774)),x93771))+P1(f327(f327(f234(a1),x93772),f327(f327(f23(a1),x93774),x93773)))+~P1(f327(f327(f329(a1),f327(f327(f23(a1),x93772),f78(a1))),x93771)) % 177.41/177.20 [9421]~P1(f327(f327(f235(a1),f2(a1)),x94213))+~P1(f327(f327(f234(a1),x94211),x94212))+P1(f327(f327(f329(a1),f422(x94214,x94211,x94213,x94212)),f303(a1,f78(a1),x94213)))+P1(f327(f327(f234(a1),x94211),f327(f327(f23(a1),x94212),x94213)))+~P1(f327(f327(f329(a1),f327(f327(f23(a1),x94211),f78(a1))),x94214)) % 177.41/177.20 [9442]~P68(x94422)+~E(f777(x94423,x94424,x94421,x94422),f778(x94423,x94424,x94421,x94422))+E(f327(f327(f6(f922(x94421,a910),x94422),f327(f6(x94421,x94422),x94423)),x94424),f327(f327(f6(x94421,x94422),x94423),f38(f922(x94421,a910),x94424)))+P1(f327(f327(f329(f922(x94421,a910)),f779(x94423,x94424,x94421,x94422)),x94424))+~P1(f327(f35(f922(x94421,a910)),x94424)) % 177.41/177.20 [9447]~P68(x94472)+~E(f327(x94473,f781(x94473,x94474,x94471,x94472)),f2(x94472))+E(f327(f327(f6(f922(x94471,a910),x94472),f327(f6(x94471,x94472),x94473)),x94474),f327(f327(f6(x94471,x94472),x94473),f38(f922(x94471,a910),x94474)))+P1(f327(f327(f329(f922(x94471,a910)),f779(x94473,x94474,x94471,x94472)),x94474))+~P1(f327(f35(f922(x94471,a910)),x94474)) % 177.41/177.20 [9548]~P68(x95482)+~P1(f327(f35(x95481),f779(x95483,x95484,x95481,x95482)))+E(f327(f327(f6(f922(x95481,a910),x95482),f327(f6(x95481,x95482),x95483)),x95484),f327(f327(f6(x95481,x95482),x95483),f38(f922(x95481,a910),x95484)))+P1(f327(f327(f329(f922(x95481,a910)),f778(x95483,x95484,x95481,x95482)),x95484))+~P1(f327(f35(f922(x95481,a910)),x95484)) % 177.41/177.20 [9549]~P68(x95492)+~P1(f327(f35(x95491),f779(x95493,x95494,x95491,x95492)))+E(f327(f327(f6(f922(x95491,a910),x95492),f327(f6(x95491,x95492),x95493)),x95494),f327(f327(f6(x95491,x95492),x95493),f38(f922(x95491,a910),x95494)))+P1(f327(f327(f329(f922(x95491,a910)),f777(x95493,x95494,x95491,x95492)),x95494))+~P1(f327(f35(f922(x95491,a910)),x95494)) % 177.41/177.20 [9628]~P68(x96282)+E(f327(f327(f6(f922(x96281,a910),x96282),f327(f6(x96281,x96282),x96283)),x96284),f327(f327(f6(x96281,x96282),x96283),f38(f922(x96281,a910),x96284)))+P1(f327(f327(f329(f922(x96281,a910)),f779(x96283,x96284,x96281,x96282)),x96284))+P1(f327(f327(f329(f922(x96281,a910)),f778(x96283,x96284,x96281,x96282)),x96284))+~P1(f327(f35(f922(x96281,a910)),x96284)) % 177.41/177.20 [9629]~P68(x96292)+E(f327(f327(f6(f922(x96291,a910),x96292),f327(f6(x96291,x96292),x96293)),x96294),f327(f327(f6(x96291,x96292),x96293),f38(f922(x96291,a910),x96294)))+P1(f327(f327(f329(f922(x96291,a910)),f779(x96293,x96294,x96291,x96292)),x96294))+P1(f327(f327(f329(f922(x96291,a910)),f777(x96293,x96294,x96291,x96292)),x96294))+~P1(f327(f35(f922(x96291,a910)),x96294)) % 177.41/177.20 [9646]~P68(x96462)+P1(f327(f327(f329(x96461),f781(x96463,x96464,x96461,x96462)),f778(x96463,x96464,x96461,x96462)))+~P1(f327(f35(x96461),f779(x96463,x96464,x96461,x96462)))+E(f327(f327(f6(f922(x96461,a910),x96462),f327(f6(x96461,x96462),x96463)),x96464),f327(f327(f6(x96461,x96462),x96463),f38(f922(x96461,a910),x96464)))+~P1(f327(f35(f922(x96461,a910)),x96464)) % 177.41/177.20 [9647]~P68(x96472)+P1(f327(f327(f329(x96471),f781(x96473,x96474,x96471,x96472)),f777(x96473,x96474,x96471,x96472)))+~P1(f327(f35(x96471),f779(x96473,x96474,x96471,x96472)))+E(f327(f327(f6(f922(x96471,a910),x96472),f327(f6(x96471,x96472),x96473)),x96474),f327(f327(f6(x96471,x96472),x96473),f38(f922(x96471,a910),x96474)))+~P1(f327(f35(f922(x96471,a910)),x96474)) % 177.41/177.20 [9660]P1(f327(x96601,x96602))+~P1(f327(f327(f329(x96603),f532(x96601,x96604,x96602,x96603)),f544(x96601,x96604,x96602,x96603)))+~P1(f327(f35(x96603),x96602))+~P1(f327(x96601,f190(f922(x96603,a910))))+~P1(f327(f327(f234(f922(x96603,a910)),x96602),x96604)) % 177.41/177.20 [9698]~P68(x96982)+P1(f327(f327(f329(x96981),f781(x96983,x96984,x96981,x96982)),f778(x96983,x96984,x96981,x96982)))+E(f327(f327(f6(f922(x96981,a910),x96982),f327(f6(x96981,x96982),x96983)),x96984),f327(f327(f6(x96981,x96982),x96983),f38(f922(x96981,a910),x96984)))+P1(f327(f327(f329(f922(x96981,a910)),f779(x96983,x96984,x96981,x96982)),x96984))+~P1(f327(f35(f922(x96981,a910)),x96984)) % 177.41/177.20 [9699]~P68(x96992)+P1(f327(f327(f329(x96991),f781(x96993,x96994,x96991,x96992)),f777(x96993,x96994,x96991,x96992)))+E(f327(f327(f6(f922(x96991,a910),x96992),f327(f6(x96991,x96992),x96993)),x96994),f327(f327(f6(x96991,x96992),x96993),f38(f922(x96991,a910),x96994)))+P1(f327(f327(f329(f922(x96991,a910)),f779(x96993,x96994,x96991,x96992)),x96994))+~P1(f327(f35(f922(x96991,a910)),x96994)) % 177.41/177.20 [9875]P1(f327(x98751,x98752))+~P1(f327(f35(x98753),x98752))+~P1(f327(x98751,f327(f327(f309(x98753),f532(x98751,x98754,x98752,x98753)),f544(x98751,x98754,x98752,x98753))))+~P1(f327(x98751,f190(f922(x98753,a910))))+~P1(f327(f327(f234(f922(x98753,a910)),x98752),x98754)) % 177.41/177.20 [7907]~P63(x79071)+P1(f327(f327(f235(x79071),x79072),f2(x79071)))+~P1(f327(f327(f234(x79071),f2(x79071)),x79074))+P1(f327(f327(f235(x79071),f2(x79071)),x79072))+P1(f327(f327(f234(x79071),f327(f327(f291(x79071),x79073),x79072)),x79074)) % 177.41/177.20 [7908]~P63(x79081)+P1(f327(f327(f235(x79081),x79082),f2(x79081)))+P1(f327(f327(f235(x79081),f2(x79081)),x79082))+~P1(f327(f327(f235(x79081),f2(x79081)),x79084))+P1(f327(f327(f235(x79081),f327(f327(f291(x79081),x79083),x79082)),x79084)) % 177.41/177.20 [8186]~P1(f327(f327(f234(a1),x81864),f2(a1)))+~E(x81862,f327(f327(f80(a1),f327(f327(f81(a1),x81861),x81863)),x81864))+P1(f327(f327(f235(a1),f2(a1)),x81861))+~P1(f327(f327(f235(a1),x81861),x81864))+P1(f327(f50(x81862,x81861),f327(f327(f252(a1,a1),x81863),x81864))) % 177.41/177.20 [8220]~P1(f327(x82201,x82204))+P1(f327(x82201,f417(x82202,x82201,x82203)))+~P1(f327(f327(f234(a1),f2(a1)),x82202))+~P1(f327(f327(f235(a1),f2(a1)),x82203))+P1(f327(x82201,f327(f327(f23(a1),x82204),f327(f327(f81(a1),x82202),x82203)))) % 177.41/177.20 [8221]~P1(f327(x82211,x82214))+P1(f327(x82211,f450(x82212,x82211,x82213)))+~P1(f327(f327(f234(a1),f2(a1)),x82212))+~P1(f327(f327(f235(a1),f2(a1)),x82213))+P1(f327(x82211,f327(f327(f80(a1),x82214),f327(f327(f81(a1),x82212),x82213)))) % 177.41/177.20 [8222]~P63(x82221)+P1(f327(f327(f235(x82221),x82222),f2(x82221)))+P1(f327(f327(f235(x82221),f2(x82221)),x82222))+P1(f327(f327(f234(x82221),f2(x82221)),x82223))+~P1(f327(f327(f234(x82221),f327(f327(f291(x82221),x82224),x82222)),x82223)) % 177.41/177.20 [8223]~P63(x82231)+P1(f327(f327(f235(x82231),x82232),f2(x82231)))+P1(f327(f327(f235(x82231),f2(x82231)),x82232))+P1(f327(f327(f235(x82231),f2(x82231)),x82233))+~P1(f327(f327(f235(x82231),f327(f327(f291(x82231),x82234),x82232)),x82233)) % 177.41/177.20 [8275]~E(x82751,f327(f327(f80(a1),f327(f327(f81(a1),x82752),x82753)),x82754))+~P1(f327(f327(f234(a1),f2(a1)),x82754))+~P1(f327(f327(f235(a1),f2(a1)),x82752))+~P1(f327(f327(f235(a1),x82754),x82752))+P1(f327(f50(x82751,x82752),f327(f327(f252(a1,a1),x82753),x82754))) % 177.41/177.20 [8392]~P63(x83921)+P1(f327(f327(f235(x83921),x83922),f2(x83921)))+~P1(f327(f327(f234(x83921),f2(x83921)),x83924))+~P1(f327(f327(f234(x83921),x83923),f327(f327(f81(x83921),x83924),x83922)))+P1(f327(f327(f234(x83921),f327(f327(f291(x83921),x83923),x83922)),x83924)) % 177.41/177.20 [8393]~P63(x83931)+P1(f327(f327(f235(x83931),x83932),f2(x83931)))+~P1(f327(f327(f235(x83931),f2(x83931)),x83934))+~P1(f327(f327(f235(x83931),x83933),f327(f327(f81(x83931),x83934),x83932)))+P1(f327(f327(f235(x83931),f327(f327(f291(x83931),x83933),x83932)),x83934)) % 177.41/177.20 [8477]~P63(x84771)+P1(f327(f327(f235(x84771),x84772),f2(x84771)))+~P1(f327(f327(f234(x84771),x84773),f2(x84771)))+P1(f327(f327(f234(x84771),x84773),f327(f327(f291(x84771),x84774),x84772)))+~P1(f327(f327(f234(x84771),f327(f327(f81(x84771),x84773),x84772)),x84774)) % 177.41/177.20 [8478]~P63(x84781)+P1(f327(f327(f235(x84781),x84782),f2(x84781)))+~P1(f327(f327(f235(x84781),x84783),f2(x84781)))+P1(f327(f327(f235(x84781),x84783),f327(f327(f291(x84781),x84784),x84782)))+~P1(f327(f327(f235(x84781),f327(f327(f81(x84781),x84783),x84782)),x84784)) % 177.41/177.20 [8629]~P63(x86291)+~P1(f327(f327(f235(x86291),x86292),f2(x86291)))+P1(f327(f327(f235(x86291),f2(x86291)),x86292))+~P1(f327(f327(f234(x86291),f327(f327(f291(x86291),x86294),x86292)),x86293))+P1(f327(f327(f234(x86291),f327(f327(f81(x86291),x86293),x86292)),x86294)) % 177.41/177.20 [8630]~P63(x86301)+~P1(f327(f327(f235(x86301),x86302),f2(x86301)))+P1(f327(f327(f235(x86301),f2(x86301)),x86302))+~P1(f327(f327(f234(x86301),f327(f327(f81(x86301),x86304),x86302)),x86303))+P1(f327(f327(f234(x86301),f327(f327(f291(x86301),x86303),x86302)),x86304)) % 177.41/177.20 [8631]~P63(x86311)+~P1(f327(f327(f235(x86311),x86312),f2(x86311)))+P1(f327(f327(f235(x86311),f2(x86311)),x86312))+~P1(f327(f327(f235(x86311),f327(f327(f291(x86311),x86314),x86312)),x86313))+P1(f327(f327(f235(x86311),f327(f327(f81(x86311),x86313),x86312)),x86314)) % 177.41/177.20 [8632]~P63(x86321)+~P1(f327(f327(f235(x86321),x86322),f2(x86321)))+P1(f327(f327(f235(x86321),f2(x86321)),x86322))+~P1(f327(f327(f235(x86321),f327(f327(f81(x86321),x86324),x86322)),x86323))+P1(f327(f327(f235(x86321),f327(f327(f291(x86321),x86323),x86322)),x86324)) % 177.41/177.20 [8648]~P63(x86481)+~P1(f327(f327(f234(x86481),f2(x86481)),x86484))+P1(f327(f327(f235(x86481),f2(x86481)),x86482))+~P1(f327(f327(f234(x86481),f327(f327(f81(x86481),x86484),x86482)),x86483))+P1(f327(f327(f234(x86481),f327(f327(f291(x86481),x86483),x86482)),x86484)) % 177.41/177.20 [8649]~P63(x86491)+~P1(f327(f327(f235(x86491),f2(x86491)),x86494))+P1(f327(f327(f235(x86491),f2(x86491)),x86492))+~P1(f327(f327(f235(x86491),f327(f327(f81(x86491),x86494),x86492)),x86493))+P1(f327(f327(f235(x86491),f327(f327(f291(x86491),x86493),x86492)),x86494)) % 177.41/177.20 [8725]~P63(x87251)+~P1(f327(f327(f235(x87251),x87254),f2(x87251)))+~P1(f327(f327(f234(x87251),x87253),f327(f327(f81(x87251),x87252),x87254)))+P1(f327(f327(f234(x87251),x87252),f327(f327(f291(x87251),x87253),x87254)))+~P1(f327(f327(f234(x87251),f327(f327(f81(x87251),x87252),x87254)),x87253)) % 177.41/177.20 [8726]~P63(x87261)+~P1(f327(f327(f234(x87261),x87262),f2(x87261)))+~P1(f327(f327(f234(x87261),x87263),f327(f327(f81(x87261),x87262),x87264)))+P1(f327(f327(f234(x87261),x87262),f327(f327(f291(x87261),x87263),x87264)))+~P1(f327(f327(f234(x87261),f327(f327(f81(x87261),x87262),x87264)),x87263)) % 177.41/177.20 [8727]~P63(x87271)+~P1(f327(f327(f235(x87271),x87274),f2(x87271)))+~P1(f327(f327(f235(x87271),x87273),f327(f327(f81(x87271),x87272),x87274)))+P1(f327(f327(f235(x87271),x87272),f327(f327(f291(x87271),x87273),x87274)))+~P1(f327(f327(f235(x87271),f327(f327(f81(x87271),x87272),x87274)),x87273)) % 177.41/177.20 [8728]~P63(x87281)+~P1(f327(f327(f235(x87281),x87282),f2(x87281)))+~P1(f327(f327(f235(x87281),x87283),f327(f327(f81(x87281),x87282),x87284)))+P1(f327(f327(f235(x87281),x87282),f327(f327(f291(x87281),x87283),x87284)))+~P1(f327(f327(f235(x87281),f327(f327(f81(x87281),x87282),x87284)),x87283)) % 177.41/177.20 [8850]~P63(x88501)+~P1(f327(f327(f235(x88501),x88503),f2(x88501)))+~P1(f327(f327(f234(x88501),x88502),f327(f327(f81(x88501),x88504),x88503)))+~P1(f327(f327(f234(x88501),f327(f327(f81(x88501),x88504),x88503)),x88502))+P1(f327(f327(f234(x88501),f327(f327(f291(x88501),x88502),x88503)),x88504)) % 177.41/177.20 [8851]~P63(x88511)+~P1(f327(f327(f235(x88511),x88513),f2(x88511)))+~P1(f327(f327(f235(x88511),x88512),f327(f327(f81(x88511),x88514),x88513)))+~P1(f327(f327(f235(x88511),f327(f327(f81(x88511),x88514),x88513)),x88512))+P1(f327(f327(f235(x88511),f327(f327(f291(x88511),x88512),x88513)),x88514)) % 177.41/177.20 [8868]~P63(x88681)+~P1(f327(f327(f234(x88681),f2(x88681)),x88684))+~P1(f327(f327(f234(x88681),x88682),f327(f327(f81(x88681),x88684),x88683)))+~P1(f327(f327(f234(x88681),f327(f327(f81(x88681),x88684),x88683)),x88682))+P1(f327(f327(f234(x88681),f327(f327(f291(x88681),x88682),x88683)),x88684)) % 177.41/177.20 [8869]~P63(x88691)+~P1(f327(f327(f235(x88691),f2(x88691)),x88694))+~P1(f327(f327(f235(x88691),x88692),f327(f327(f81(x88691),x88694),x88693)))+~P1(f327(f327(f235(x88691),f327(f327(f81(x88691),x88694),x88693)),x88692))+P1(f327(f327(f235(x88691),f327(f327(f291(x88691),x88692),x88693)),x88694)) % 177.41/177.20 [9052]E(f327(f327(f23(a1),f440(x90521,x90522,x90523,x90524)),f434(x90521,x90522,x90523,x90524)),x90524)+~P1(f327(f327(f235(a1),f2(a1)),x90523))+~P1(f327(f327(f329(a1),x90522),x90521))+~P1(f327(f327(f235(a1),x90524),x90522))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x90524),x90523)),x90522)) % 177.41/177.20 [9127]~P1(f327(x91271,x91272))+~P1(f327(f327(f234(a1),f2(a1)),x91273))+~P1(f327(f327(f235(a1),f2(a1)),x91274))+~P1(f327(x91271,f327(f327(f23(a1),f417(x91273,x91271,x91274)),x91274)))+P1(f327(x91271,f327(f327(f23(a1),x91272),f327(f327(f81(a1),x91273),x91274)))) % 177.41/177.20 [9128]~P1(f327(x91281,x91282))+~P1(f327(f327(f234(a1),f2(a1)),x91283))+~P1(f327(f327(f235(a1),f2(a1)),x91284))+~P1(f327(x91281,f327(f327(f80(a1),f450(x91283,x91281,x91284)),x91284)))+P1(f327(x91281,f327(f327(f80(a1),x91282),f327(f327(f81(a1),x91283),x91284)))) % 177.41/177.20 [9278]~P1(f327(f327(f235(a1),f2(a1)),x92783))+~P1(f327(f327(f329(a1),x92782),x92781))+~P1(f327(f327(f235(a1),x92784),x92782))+P1(f327(f327(f329(a1),f440(x92781,x92782,x92783,x92784)),x92781))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x92784),x92783)),x92782)) % 177.41/177.20 [9297]E(f327(f327(f23(a1),f423(x92971,x92972,x92973,x92974)),f424(x92971,x92972,x92973,x92974)),x92974)+~P1(f327(f327(f235(a1),f2(a1)),x92973))+~P1(f327(f327(f234(a1),x92974),x92972))+~P1(f327(f327(f329(a1),f327(f327(f80(a1),x92972),f78(a1))),x92971))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x92974),x92973)),x92972)) % 177.41/177.20 [9325]~P1(f327(f327(f235(a1),f2(a1)),x93252))+~P1(f327(f327(f329(a1),x93253),x93254))+~P1(f327(f327(f235(a1),x93251),x93253))+P1(f327(f327(f329(a1),f434(x93254,x93253,x93252,x93251)),f303(a1,f78(a1),x93252)))+P1(f327(f327(f235(a1),f327(f327(f80(a1),x93251),x93252)),x93253)) % 177.41/177.20 [9413]~P1(f327(f327(f235(a1),f2(a1)),x94133))+~P1(f327(f327(f234(a1),x94134),x94132))+P1(f327(f327(f329(a1),f423(x94131,x94132,x94133,x94134)),x94131))+~P1(f327(f327(f329(a1),f327(f327(f80(a1),x94132),f78(a1))),x94131))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x94134),x94133)),x94132)) % 177.41/177.20 [9458]~P1(f327(f327(f235(a1),f2(a1)),x94582))+~P1(f327(f327(f234(a1),x94581),x94583))+P1(f327(f327(f329(a1),f424(x94584,x94583,x94582,x94581)),f303(a1,f78(a1),x94582)))+~P1(f327(f327(f329(a1),f327(f327(f80(a1),x94583),f78(a1))),x94584))+P1(f327(f327(f234(a1),f327(f327(f80(a1),x94581),x94582)),x94583)) % 177.41/177.20 [9753]~P35(x97531,x97533)+~P25(x97531,x97534)+P35(x97531,f327(f327(f102(f922(f921(x97531,x97531),a910)),x97532),x97533))+~P1(f327(f327(f234(f922(f921(x97531,x97531),a910)),x97532),f327(f251(f922(f921(x97531,x97531),a910),f922(f921(x97531,x97531),a910)),x97534)))+~P1(f327(f327(f234(f922(f921(x97531,x97531),a910)),x97533),f327(f256(f922(f921(x97531,x97531),a910),f922(f921(x97531,x97531),a910)),x97534))) % 177.41/177.20 [10143]~P16(x101432,x101434,x101433)+E(x101431,f190(f922(x101432,a910)))+~P1(f327(f35(x101432),x101431))+P1(f327(f327(f329(x101432),f327(x101433,x101431)),x101431))+~P1(f327(f327(f329(x101432),f327(f327(x101434,f907(x101431,x101433,x101434,x101432)),f350(x101431,x101433,x101434,x101432))),f327(f327(f309(x101432),f907(x101431,x101433,x101434,x101432)),f327(f327(f309(x101432),f350(x101431,x101433,x101434,x101432)),f190(f922(x101432,a910)))))) % 177.41/177.20 [10067]~P110(x100672)+~P60(x100671)+~P1(f327(f327(f234(f922(x100671,x100672)),x100673),x100674))+P1(f327(f327(f235(f922(x100671,x100672)),x100673),x100674))+~P1(f327(f57(x100671),f327(f327(f8(a910,a910,x100671),a322),f327(f327(f18(x100671,x100672,a910),f327(f327(f8(x100672,f922(x100672,a910),x100671),a324),x100673)),x100674)))) % 177.41/177.20 [9666]~P52(x96661,x96661,x96664)+P1(f327(f327(f329(f921(x96661,x96661)),f327(f327(f252(x96661,x96661),x96662),x96663)),f307(x96661,x96664)))+P1(f327(f327(f329(f921(x96661,x96661)),f327(f327(f252(x96661,x96661),x96663),x96662)),f307(x96661,x96664)))+~P1(f327(f327(f329(f921(x96661,x96661)),f327(f327(f252(x96661,x96661),x96665),x96662)),f307(x96661,x96664)))+~P1(f327(f327(f329(f921(x96661,x96661)),f327(f327(f252(x96661,x96661),x96665),x96663)),f307(x96661,x96664))) % 177.41/177.20 [5794]E(x57941,f2(a915))+~E(f327(f36(x57942),x57945),x57941)+E(f327(f36(x57942),x57943),f327(a113,x57941))+~E(x57943,f327(f327(f309(x57942),x57944),x57945))+P1(f327(f327(f329(x57942),x57944),x57945)) % 177.41/177.20 [5916]~P62(x59162)+E(x59161,f2(x59162))+E(x59163,f2(x59162))+~E(f327(f327(f291(x59162),x59164),x59163),f327(f327(f291(x59162),x59165),x59161))+E(f327(f327(f81(x59162),x59164),x59161),f327(f327(f81(x59162),x59165),x59163)) % 177.41/177.20 [5917]~P62(x59172)+E(x59171,f2(x59172))+E(x59173,f2(x59172))+~E(f327(f327(f81(x59172),x59174),x59173),f327(f327(f81(x59172),x59175),x59171))+E(f327(f327(f291(x59172),x59174),x59171),f327(f327(f291(x59172),x59175),x59173)) % 177.41/177.20 [5986]~E(f327(f36(x59861),x59865),x59863)+~E(x59865,f190(f922(x59861,a910)))+E(f327(f36(x59861),x59862),f327(a113,x59863))+~E(x59862,f327(f327(f309(x59861),x59864),x59865))+P1(f327(f327(f329(x59861),x59864),x59865)) % 177.41/177.20 [6225]~P112(x62252)+~E(f327(x62253,x62255),f2(x62252))+E(f327(f327(f9(x62251,x62252),x62253),x62254),f2(x62252))+~P1(f327(f35(x62251),x62254))+~P1(f327(f327(f329(x62251),x62255),x62254)) % 177.41/177.20 [6603]~P108(x66033)+E(x66031,x66032)+~E(f327(f302(x66033,x66034),x66031),f327(f302(x66033,x66035),x66032))+~P1(f327(f327(f235(x66033),x66035),x66032))+~P1(f327(f327(f235(x66033),x66034),x66031)) % 177.41/177.20 [6604]~P108(x66043)+E(x66041,x66042)+~E(f327(f302(x66043,x66041),x66044),f327(f302(x66043,x66042),x66045))+~P1(f327(f327(f235(x66043),x66042),x66045))+~P1(f327(f327(f235(x66043),x66041),x66044)) % 177.41/177.20 [7672]~P108(x76721)+~P11(x76721,f327(f327(f135(x76721),x76724),x76725))+~P1(f327(f327(f329(x76721),x76723),f327(f173(x76721),x76725)))+~P1(f327(f327(f329(x76721),x76722),f327(f173(x76721),x76724)))+P1(f327(f327(f234(x76721),x76722),x76723)) % 177.41/177.20 [8762]~P110(x87621)+~P1(f327(f327(f235(f922(x87621,a910)),f303(x87621,x87625,x87622)),f303(x87621,x87624,x87623)))+~P1(f327(f327(f234(x87621),x87625),x87622))+P1(f327(f327(f235(x87621),x87622),x87623))+P1(f327(f327(f235(x87621),x87624),x87625)) % 177.41/177.20 [10186]~P15(x101862,x101865,x101863)+E(x101861,f190(f922(x101862,a910)))+~E(f327(f327(x101865,f327(x101864,f384(x101861,x101864,x101863,x101865,x101862))),f327(x101864,f397(x101861,x101864,x101863,x101865,x101862))),f327(x101864,f327(f327(x101865,f384(x101861,x101864,x101863,x101865,x101862)),f397(x101861,x101864,x101863,x101865,x101862))))+E(f327(x101863,f327(f310(x101862,x101862,x101864),x101861)),f327(x101864,f327(x101863,x101861)))+~P1(f327(f35(x101862),x101861)) % 177.41/177.20 [6600]~P16(x66002,x66005,x66003)+E(x66001,f190(f922(x66002,a910)))+~P1(f327(f35(x66002),x66001))+E(f327(x66003,f327(f327(f309(x66002),x66004),x66001)),f327(f327(x66005,x66004),f327(x66003,x66001)))+P1(f327(f327(f329(x66002),x66004),x66001)) % 177.41/177.20 [7435]~P15(x74352,x74353,x74354)+E(f327(f327(x74353,f327(x74354,x74351)),f327(x74354,x74355)),f327(x74354,x74355))+E(x74351,f190(f922(x74352,a910)))+~P1(f327(f35(x74352),x74355))+~P1(f327(f327(f234(f922(x74352,a910)),x74351),x74355)) % 177.41/177.20 [7807]~P16(x78074,x78075,x78071)+E(f327(x78071,x78072),x78073)+~P1(f327(f35(x78074),x78072))+~E(f327(f327(f23(f922(x78074,a910)),x78072),f327(f327(f309(x78074),x78073),f190(f922(x78074,a910)))),f190(f922(x78074,a910)))+~P1(f327(f327(f329(x78074),x78073),x78072)) % 177.41/177.20 [8683]~P75(x86831)+~P121(x86831)+~P1(f327(f35(x86832),x86835))+P1(f327(f327(f287(x86831),f327(f327(f9(x86832,x86831),x86833),x86834)),f327(f327(f9(x86832,x86831),x86833),x86835)))+~P1(f327(f327(f234(f922(x86832,a910)),x86834),x86835)) % 177.41/177.20 [8732]E(x87321,x87322)+~P6(x87323,x87324,x87325)+E(f327(f327(f103(f922(x87323,a910)),x87321),x87322),f190(f922(x87323,a910)))+~P1(f327(f327(f329(f922(x87323,a910)),x87322),f327(f327(f61(x87323),x87324),x87325)))+~P1(f327(f327(f329(f922(x87323,a910)),x87321),f327(f327(f61(x87323),x87324),x87325))) % 177.41/177.20 [9541]~P68(x95412)+~E(f327(x95413,f455(x95413,x95414,x95415,x95411,x95412)),f2(x95412))+E(f327(f327(f6(x95411,x95412),x95413),x95414),f327(f327(f6(x95411,x95412),x95413),x95415))+~P1(f327(f35(x95411),x95415))+~P1(f327(f327(f234(f922(x95411,a910)),x95414),x95415)) % 177.41/177.20 [9542]~P68(x95422)+~E(f327(x95423,f456(x95423,x95424,x95425,x95421,x95422)),f2(x95422))+E(f327(f327(f6(x95421,x95422),x95423),x95424),f327(f327(f6(x95421,x95422),x95423),x95425))+~P1(f327(f35(x95421),x95425))+~P1(f327(f327(f234(f922(x95421,a910)),x95424),x95425)) % 177.41/177.20 [9543]~P75(x95432)+~E(f327(x95433,f894(x95433,x95434,x95435,x95431,x95432)),f78(x95432))+E(f327(f327(f9(x95431,x95432),x95433),x95434),f327(f327(f9(x95431,x95432),x95433),x95435))+~P1(f327(f35(x95431),x95435))+~P1(f327(f327(f234(f922(x95431,a910)),x95434),x95435)) % 177.41/177.20 [9544]~P75(x95442)+~E(f327(x95443,f895(x95443,x95444,x95445,x95441,x95442)),f78(x95442))+E(f327(f327(f9(x95441,x95442),x95443),x95444),f327(f327(f9(x95441,x95442),x95443),x95445))+~P1(f327(f35(x95441),x95445))+~P1(f327(f327(f234(f922(x95441,a910)),x95444),x95445)) % 177.41/177.20 [10020]~P88(x100201)+~P1(f327(f35(x100202),x100205))+~P1(f327(f327(f234(x100201),f2(x100201)),f327(x100203,f375(x100203,x100204,x100205,x100202,x100201))))+P1(f327(f327(f234(x100201),f327(f327(f6(x100202,x100201),x100203),x100204)),f327(f327(f6(x100202,x100201),x100203),x100205)))+~P1(f327(f327(f234(f922(x100202,a910)),x100204),x100205)) % 177.41/177.20 [7669]E(x76691,f2(a915))+P1(f327(x76692,x76693))+~E(x76694,f327(f327(f80(a915),f327(f327(f81(a915),x76691),x76693)),x76695))+~P1(f327(f327(f235(a915),x76695),x76691))+~P1(f327(x76692,f327(f327(f37(a915),x76694),x76691))) % 177.41/177.20 [7745]E(x77451,f2(a915))+P1(f327(x77452,x77453))+~P1(f327(x77452,f46(a915,x77454,x77451)))+~E(x77454,f327(f327(f80(a915),f327(f327(f81(a915),x77451),x77455)),x77453))+~P1(f327(f327(f235(a915),x77453),x77451)) % 177.41/177.20 [8036]~P62(x80363)+E(f327(x80361,x80362),f2(x80363))+~P1(f327(f35(x80364),x80365))+E(f327(f327(f9(x80364,x80363),x80361),f327(f327(f23(f922(x80364,a910)),x80365),f327(f327(f309(x80364),x80362),f190(f922(x80364,a910))))),f327(f327(f9(x80364,x80363),x80361),x80365))+P1(f327(f327(f329(x80364),x80362),x80365)) % 177.41/177.20 [8432]~P68(x84321)+~P1(f327(f35(x84322),x84325))+~P1(f327(f35(x84322),x84324))+~E(f327(f327(f103(f922(x84322,a910)),x84324),x84325),f190(f922(x84322,a910)))+E(f327(f327(f80(x84321),f327(f327(f6(x84322,x84321),x84323),x84324)),f327(f327(f6(x84322,x84321),x84323),x84325)),f327(f327(f6(x84322,x84321),x84323),f327(f327(f102(f922(x84322,a910)),x84324),x84325))) % 177.41/177.20 [8434]~P75(x84341)+~P1(f327(f35(x84342),x84345))+~P1(f327(f35(x84342),x84344))+~E(f327(f327(f103(f922(x84342,a910)),x84344),x84345),f190(f922(x84342,a910)))+E(f327(f327(f81(x84341),f327(f327(f9(x84342,x84341),x84343),x84344)),f327(f327(f9(x84342,x84341),x84343),x84345)),f327(f327(f9(x84342,x84341),x84343),f327(f327(f102(f922(x84342,a910)),x84344),x84345))) % 177.41/177.20 [8532]~P62(x85323)+E(f327(x85321,x85322),f2(x85323))+~P1(f327(f35(x85324),x85325))+E(f327(f327(f9(x85324,x85323),x85321),f327(f327(f23(f922(x85324,a910)),x85325),f327(f327(f309(x85324),x85322),f190(f922(x85324,a910))))),f327(f327(f291(x85323),f327(f327(f9(x85324,x85323),x85321),x85325)),f327(x85321,x85322)))+~P1(f327(f327(f329(x85324),x85322),x85325)) % 177.41/177.20 [9255]~P6(x92551,x92555,x92554)+~E(f327(f327(f61(x92551),f327(f327(f309(x92551),x92552),f190(f922(x92551,a910)))),x92554),f327(f327(f61(x92551),f327(f327(f309(x92551),x92553),f190(f922(x92551,a910)))),x92554))+~P1(f327(f327(f329(x92551),x92553),x92555))+~P1(f327(f327(f329(x92551),x92552),x92555))+P1(f327(f327(f329(f921(x92551,x92551)),f327(f327(f252(x92551,x92551),x92552),x92553)),x92554)) % 177.41/177.20 [9277]~P6(x92771,x92775,x92773)+E(f327(f327(f61(x92771),f327(f327(f309(x92771),x92772),f190(f922(x92771,a910)))),x92773),f327(f327(f61(x92771),f327(f327(f309(x92771),x92774),f190(f922(x92771,a910)))),x92773))+~P1(f327(f327(f329(x92771),x92774),x92775))+~P1(f327(f327(f329(x92771),x92772),x92775))+~P1(f327(f327(f329(f921(x92771,x92771)),f327(f327(f252(x92771,x92771),x92772),x92774)),x92773)) % 177.41/177.20 [9570]~P75(x95701)+~P1(f327(f35(x95702),x95705))+~P1(f327(f35(x95702),x95704))+~E(f327(f327(f103(f922(x95702,a910)),x95704),x95705),f190(f922(x95702,a910)))+E(f327(f327(f81(x95701),f327(f327(f327(f65(x95701,x95702,f81(x95701)),x95703),f78(x95701)),x95704)),f327(f327(f327(f65(x95701,x95702,f81(x95701)),x95703),f78(x95701)),x95705)),f327(f327(f327(f65(x95701,x95702,f81(x95701)),x95703),f78(x95701)),f327(f327(f102(f922(x95702,a910)),x95704),x95705))) % 177.41/177.20 [9581]~P68(x95811)+~E(f327(x95813,f374(x95813,x95815,x95814,x95812,x95811)),f2(x95811))+~P1(f327(f35(x95812),x95814))+~P1(f327(f35(x95812),x95815))+E(f327(f327(f80(x95811),f327(f327(f6(x95812,x95811),x95813),x95814)),f327(f327(f6(x95812,x95811),x95813),x95815)),f327(f327(f6(x95812,x95811),x95813),f327(f327(f102(f922(x95812,a910)),x95814),x95815))) % 177.41/177.20 [9582]~P68(x95821)+~E(f327(x95823,f376(x95823,x95825,x95824,x95822,x95821)),f2(x95821))+~P1(f327(f35(x95822),x95824))+~P1(f327(f35(x95822),x95825))+E(f327(f327(f80(x95821),f327(f327(f6(x95822,x95821),x95823),x95824)),f327(f327(f6(x95822,x95821),x95823),x95825)),f327(f327(f6(x95822,x95821),x95823),f327(f327(f102(f922(x95822,a910)),x95824),x95825))) % 177.41/177.20 [9583]~P75(x95831)+~E(f327(x95833,f342(x95833,x95835,x95834,x95832,x95831)),f78(x95831))+~P1(f327(f35(x95832),x95834))+~P1(f327(f35(x95832),x95835))+E(f327(f327(f81(x95831),f327(f327(f9(x95832,x95831),x95833),x95834)),f327(f327(f9(x95832,x95831),x95833),x95835)),f327(f327(f9(x95832,x95831),x95833),f327(f327(f102(f922(x95832,a910)),x95834),x95835))) % 177.41/177.20 [9584]~P75(x95841)+~E(f327(x95843,f347(x95843,x95845,x95844,x95842,x95841)),f78(x95841))+~P1(f327(f35(x95842),x95844))+~P1(f327(f35(x95842),x95845))+E(f327(f327(f81(x95841),f327(f327(f9(x95842,x95841),x95843),x95844)),f327(f327(f9(x95842,x95841),x95843),x95845)),f327(f327(f9(x95842,x95841),x95843),f327(f327(f102(f922(x95842,a910)),x95844),x95845))) % 177.41/177.20 [9796]~P75(x97961)+~E(f327(x97963,f343(x97963,x97965,x97964,x97962,x97961)),f78(x97961))+~P1(f327(f35(x97962),x97964))+~P1(f327(f35(x97962),x97965))+E(f327(f327(f81(x97961),f327(f327(f327(f65(x97961,x97962,f81(x97961)),x97963),f78(x97961)),x97964)),f327(f327(f327(f65(x97961,x97962,f81(x97961)),x97963),f78(x97961)),x97965)),f327(f327(f327(f65(x97961,x97962,f81(x97961)),x97963),f78(x97961)),f327(f327(f102(f922(x97962,a910)),x97964),x97965))) % 177.41/177.20 [9907]~P68(x99072)+E(f327(f327(f6(x99071,x99072),x99073),x99074),f327(f327(f6(x99071,x99072),x99073),x99075))+~P1(f327(f35(x99071),x99075))+~P1(f327(f327(f234(f922(x99071,a910)),x99074),x99075))+P1(f327(f327(f329(x99071),f455(x99073,x99074,x99075,x99071,x99072)),f327(f327(f23(f922(x99071,a910)),x99075),x99074))) % 177.41/177.20 [9908]~P68(x99082)+E(f327(f327(f6(x99081,x99082),x99083),x99084),f327(f327(f6(x99081,x99082),x99083),x99085))+~P1(f327(f35(x99081),x99085))+~P1(f327(f327(f234(f922(x99081,a910)),x99084),x99085))+P1(f327(f327(f329(x99081),f456(x99083,x99084,x99085,x99081,x99082)),f327(f327(f23(f922(x99081,a910)),x99085),x99084))) % 177.41/177.20 [9909]~P75(x99092)+E(f327(f327(f9(x99091,x99092),x99093),x99094),f327(f327(f9(x99091,x99092),x99093),x99095))+~P1(f327(f35(x99091),x99095))+~P1(f327(f327(f234(f922(x99091,a910)),x99094),x99095))+P1(f327(f327(f329(x99091),f894(x99093,x99094,x99095,x99091,x99092)),f327(f327(f23(f922(x99091,a910)),x99095),x99094))) % 177.41/177.20 [9910]~P75(x99102)+E(f327(f327(f9(x99101,x99102),x99103),x99104),f327(f327(f9(x99101,x99102),x99103),x99105))+~P1(f327(f35(x99101),x99105))+~P1(f327(f327(f234(f922(x99101,a910)),x99104),x99105))+P1(f327(f327(f329(x99101),f895(x99103,x99104,x99105,x99101,x99102)),f327(f327(f23(f922(x99101,a910)),x99105),x99104))) % 177.41/177.20 [9928]~P68(x99281)+~P1(f327(f35(x99282),x99284))+~P1(f327(f35(x99282),x99285))+E(f327(f327(f80(x99281),f327(f327(f6(x99282,x99281),x99283),x99284)),f327(f327(f6(x99282,x99281),x99283),x99285)),f327(f327(f6(x99282,x99281),x99283),f327(f327(f102(f922(x99282,a910)),x99284),x99285)))+P1(f327(f327(f329(x99282),f374(x99283,x99285,x99284,x99282,x99281)),f327(f327(f103(f922(x99282,a910)),x99284),x99285))) % 177.41/177.20 [9929]~P68(x99291)+~P1(f327(f35(x99292),x99294))+~P1(f327(f35(x99292),x99295))+E(f327(f327(f80(x99291),f327(f327(f6(x99292,x99291),x99293),x99294)),f327(f327(f6(x99292,x99291),x99293),x99295)),f327(f327(f6(x99292,x99291),x99293),f327(f327(f102(f922(x99292,a910)),x99294),x99295)))+P1(f327(f327(f329(x99292),f376(x99293,x99295,x99294,x99292,x99291)),f327(f327(f103(f922(x99292,a910)),x99294),x99295))) % 177.41/177.20 [9930]~P75(x99301)+~P1(f327(f35(x99302),x99304))+~P1(f327(f35(x99302),x99305))+E(f327(f327(f81(x99301),f327(f327(f9(x99302,x99301),x99303),x99304)),f327(f327(f9(x99302,x99301),x99303),x99305)),f327(f327(f9(x99302,x99301),x99303),f327(f327(f102(f922(x99302,a910)),x99304),x99305)))+P1(f327(f327(f329(x99302),f342(x99303,x99305,x99304,x99302,x99301)),f327(f327(f103(f922(x99302,a910)),x99304),x99305))) % 177.41/177.20 [9931]~P75(x99311)+~P1(f327(f35(x99312),x99314))+~P1(f327(f35(x99312),x99315))+E(f327(f327(f81(x99311),f327(f327(f9(x99312,x99311),x99313),x99314)),f327(f327(f9(x99312,x99311),x99313),x99315)),f327(f327(f9(x99312,x99311),x99313),f327(f327(f102(f922(x99312,a910)),x99314),x99315)))+P1(f327(f327(f329(x99312),f347(x99313,x99315,x99314,x99312,x99311)),f327(f327(f103(f922(x99312,a910)),x99314),x99315))) % 177.41/177.20 [9937]~P88(x99375)+~P1(f327(f35(x99371),x99374))+P1(f327(f327(f234(x99375),f327(f327(f6(x99371,x99375),x99372),x99373)),f327(f327(f6(x99371,x99375),x99372),x99374)))+~P1(f327(f327(f234(f922(x99371,a910)),x99373),x99374))+P1(f327(f327(f329(x99371),f375(x99372,x99373,x99374,x99371,x99375)),f327(f327(f23(f922(x99371,a910)),x99374),x99373))) % 177.41/177.20 [9981]~P75(x99811)+~P1(f327(f35(x99812),x99814))+~P1(f327(f35(x99812),x99815))+E(f327(f327(f81(x99811),f327(f327(f327(f65(x99811,x99812,f81(x99811)),x99813),f78(x99811)),x99814)),f327(f327(f327(f65(x99811,x99812,f81(x99811)),x99813),f78(x99811)),x99815)),f327(f327(f327(f65(x99811,x99812,f81(x99811)),x99813),f78(x99811)),f327(f327(f102(f922(x99812,a910)),x99814),x99815)))+P1(f327(f327(f329(x99812),f343(x99813,x99815,x99814,x99812,x99811)),f327(f327(f103(f922(x99812,a910)),x99814),x99815))) % 177.41/177.20 [8941]~P16(x89411,x89414,x89415)+~P1(f327(f35(x89411),x89412))+E(f327(f327(f23(f922(x89411,a910)),x89412),f327(f327(f309(x89411),x89413),f190(f922(x89411,a910)))),f190(f922(x89411,a910)))+~P1(f327(f327(f329(x89411),x89413),x89412))+E(f327(f327(x89414,x89413),f327(x89415,f327(f327(f23(f922(x89411,a910)),x89412),f327(f327(f309(x89411),x89413),f190(f922(x89411,a910)))))),f327(x89415,x89412)) % 177.41/177.20 [9019]~P16(x90191,x90194,x90195)+~P1(f327(f35(x90191),x90193))+~P1(f327(f35(x90191),x90192))+E(f327(f327(f103(f922(x90191,a910)),x90192),x90193),f190(f922(x90191,a910)))+E(f327(f327(x90194,f327(x90195,f327(f327(f102(f922(x90191,a910)),x90192),x90193))),f327(x90195,f327(f327(f103(f922(x90191,a910)),x90192),x90193))),f327(f327(x90194,f327(x90195,x90192)),f327(x90195,x90193))) % 177.41/177.20 [9586]~P1(f327(f327(f234(a1),x95864),f2(a1)))+~P1(f327(f327(f235(a1),x95863),x95865))+P1(f327(f327(f234(a1),x95861),x95862))+~P1(f327(f327(f235(a1),x95863),x95864))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),f327(f327(f81(a1),x95863),x95862)),x95865)),f327(f327(f80(a1),f327(f327(f81(a1),x95863),x95861)),x95864))) % 177.41/177.20 [9588]~P1(f327(f327(f234(a1),f2(a1)),x95885))+P1(f327(f327(f234(a1),x95881),x95882))+~P1(f327(f327(f235(a1),x95883),x95884))+~P1(f327(f327(f235(a1),x95885),x95884))+~P1(f327(f327(f234(a1),f327(f327(f80(a1),f327(f327(f81(a1),x95884),x95881)),x95885)),f327(f327(f80(a1),f327(f327(f81(a1),x95884),x95882)),x95883))) % 177.41/177.20 [9704]~P62(x97045)+E(f327(x97041,f413(x97041,x97042,x97043,x97044,x97045)),f2(x97045))+~P1(f327(f35(x97044),x97043))+~P1(f327(f35(x97044),x97042))+E(f327(f327(f291(x97045),f327(f327(f81(x97045),f327(f327(f9(x97044,x97045),x97041),x97043)),f327(f327(f9(x97044,x97045),x97041),x97042))),f327(f327(f9(x97044,x97045),x97041),f327(f327(f103(f922(x97044,a910)),x97043),x97042))),f327(f327(f9(x97044,x97045),x97041),f327(f327(f102(f922(x97044,a910)),x97043),x97042))) % 177.41/177.20 [9973]~P62(x99731)+~P1(f327(f35(x99732),x99734))+~P1(f327(f35(x99732),x99735))+E(f327(f327(f291(x99731),f327(f327(f81(x99731),f327(f327(f9(x99732,x99731),x99733),x99734)),f327(f327(f9(x99732,x99731),x99733),x99735))),f327(f327(f9(x99732,x99731),x99733),f327(f327(f103(f922(x99732,a910)),x99734),x99735))),f327(f327(f9(x99732,x99731),x99733),f327(f327(f102(f922(x99732,a910)),x99734),x99735)))+P1(f327(f327(f329(x99732),f413(x99733,x99735,x99734,x99732,x99731)),f327(f327(f103(f922(x99732,a910)),x99734),x99735))) % 177.41/177.20 [9296]E(f327(f327(f135(x92961),x92962),x92963),f327(f327(f135(x92961),x92964),x92965))+~E(f327(f327(f176(x92961),f327(f191(f916(x92961)),x92964)),x92962),x92964)+~E(f327(f327(f176(x92961),f327(f191(f916(x92961)),x92962)),x92964),x92962)+~E(x92965,f327(f327(f135(x92961),f327(f327(f139(x92961),f327(f191(f916(x92961)),x92964)),x92962)),x92963))+~E(f327(f327(f135(x92961),f327(f327(f139(x92961),f327(f191(f916(x92961)),x92962)),x92964)),x92965),x92963) % 177.41/177.20 [9702]~P108(x97022)+E(f327(f327(f149(x97021,x97022,x97023),x97024),f171(x97021,x97024,x97025)),x97025)+~P11(x97022,f327(f327(f155(x97021,x97022),x97023),x97025))+~P1(f327(f327(f329(x97021),x97024),f327(f173(x97021),x97025)))+~E(f327(f142(x97021),f327(f137(x97021,f327(f327(f8(x97022,a910,x97021),f327(a324,f327(x97023,x97024))),x97023)),x97025)),x97024) % 177.41/177.20 [10038]~P72(x100381)+~P1(f327(f66(x100381,x100381,f81(x100381),x100382,x100383),x100385))+~P1(f327(f327(f329(x100381),x100384),x100383))+P1(f327(f327(f329(x100381),x100382),x100383))+P1(f327(f66(x100381,x100381,f81(x100381),x100384,f327(f327(f309(x100381),x100382),f327(f327(f23(f922(x100381,a910)),x100383),f327(f327(f309(x100381),x100384),f190(f922(x100381,a910)))))),x100385)) % 177.41/177.20 [7443]E(x74431,x74432)+~P23(x74434,x74435,x74433,x74436)+~E(f327(x74433,x74431),f327(x74433,x74432))+~P1(f327(f327(f329(x74434),x74432),x74436))+~P1(f327(f327(f329(x74434),x74431),x74436)) % 177.41/177.20 [6693]~P144(x66934)+E(x66931,x66932)+~E(x66935,x66936)+E(x66933,f2(x66934))+~E(f327(f327(f80(x66934),x66935),f327(f327(f81(x66934),x66933),x66931)),f327(f327(f80(x66934),x66936),f327(f327(f81(x66934),x66933),x66932))) % 177.41/177.20 [7725]~P108(x77251)+~P3(x77251)+~P1(f327(f327(f235(x77251),x77252),f327(x77255,x77256)))+~P1(f327(f327(f329(x77253),x77256),x77254))+P1(f327(f327(f235(x77251),x77252),f327(f327(f40(x77253,x77251),x77254),x77255))) % 177.41/177.20 [10034]~P23(x100342,x100341,x100343,x100344)+~P23(x100341,x100342,x100346,x100345)+P24(x100341,x100342,f822(x100343,x100344,x100345,x100346,x100342,x100341),x100345,x100344)+~P1(f327(f327(f234(f922(x100342,a910)),f327(f310(x100341,x100342,x100346),x100345)),x100344))+~P1(f327(f327(f234(f922(x100341,a910)),f327(f310(x100342,x100341,x100343),x100344)),x100345)) % 177.41/177.20 [8403]~P108(x84031)+~P3(x84031)+~P1(f327(f327(f235(x84031),f327(x84034,x84036)),x84035))+~P1(f327(f327(f329(x84032),x84036),x84033))+P1(f327(f327(f235(x84031),f327(f327(f41(x84032,x84031),x84033),x84034)),x84035)) % 177.41/177.20 [8655]~P17(x86552,x86555,x86556,x86551)+~P1(f327(f35(x86552),x86554))+~P1(f327(f35(x86552),x86553))+~E(f327(f327(f103(f922(x86552,a910)),x86553),x86554),f190(f922(x86552,a910)))+E(f327(x86551,f327(f327(f102(f922(x86552,a910)),x86553),x86554)),f327(f72(x86555,x86555,x86555,f327(x86551,x86553)),f327(x86551,x86554))) % 177.41/177.20 [10248]~P75(x102481)+~E(f810(x102484,x102485,x102483,x102486,x102482,x102481),f811(x102484,x102485,x102483,x102486,x102482,x102481))+~P1(f327(f35(x102482),x102486))+E(f327(f327(f327(f65(x102481,x102482,f81(x102481)),f327(f327(f8(f922(x102483,a910),x102481,x102482),f327(f327(f65(x102481,x102483,f81(x102481)),x102484),f78(x102481))),x102485)),f78(x102481)),x102486),f327(f327(f327(f65(x102481,x102483,f81(x102481)),x102484),f78(x102481)),f327(f327(f40(x102482,f922(x102483,a910)),x102486),x102485)))+P1(f327(f327(f329(x102482),f809(x102484,x102485,x102483,x102486,x102482,x102481)),x102486)) % 177.41/177.20 [10278]~P75(x102781)+~E(f810(x102784,x102785,x102783,x102786,x102782,x102781),f811(x102784,x102785,x102783,x102786,x102782,x102781))+~P1(f327(f35(x102782),x102786))+E(f327(f327(f327(f65(x102781,x102782,f81(x102781)),f327(f327(f8(f922(x102783,a910),x102781,x102782),f327(f327(f65(x102781,x102783,f81(x102781)),x102784),f78(x102781))),x102785)),f78(x102781)),x102786),f327(f327(f327(f65(x102781,x102783,f81(x102781)),x102784),f78(x102781)),f327(f327(f40(x102782,f922(x102783,a910)),x102786),x102785)))+~P1(f327(f35(x102783),f327(x102785,f809(x102784,x102785,x102783,x102786,x102782,x102781)))) % 177.41/177.20 [10281]~P75(x102811)+~P1(f327(f35(x102812),x102816))+E(f327(f327(f327(f65(x102811,x102812,f81(x102811)),f327(f327(f8(f922(x102813,a910),x102811,x102812),f327(f327(f65(x102811,x102813,f81(x102811)),x102814),f78(x102811))),x102815)),f78(x102811)),x102816),f327(f327(f327(f65(x102811,x102813,f81(x102811)),x102814),f78(x102811)),f327(f327(f40(x102812,f922(x102813,a910)),x102816),x102815)))+P1(f327(f327(f329(x102812),f809(x102814,x102815,x102813,x102816,x102812,x102811)),x102816))+P1(f327(f327(f329(x102812),f811(x102814,x102815,x102813,x102816,x102812,x102811)),x102816)) % 177.41/177.20 [10282]~P75(x102821)+~P1(f327(f35(x102822),x102826))+E(f327(f327(f327(f65(x102821,x102822,f81(x102821)),f327(f327(f8(f922(x102823,a910),x102821,x102822),f327(f327(f65(x102821,x102823,f81(x102821)),x102824),f78(x102821))),x102825)),f78(x102821)),x102826),f327(f327(f327(f65(x102821,x102823,f81(x102821)),x102824),f78(x102821)),f327(f327(f40(x102822,f922(x102823,a910)),x102826),x102825)))+P1(f327(f327(f329(x102822),f809(x102824,x102825,x102823,x102826,x102822,x102821)),x102826))+P1(f327(f327(f329(x102822),f810(x102824,x102825,x102823,x102826,x102822,x102821)),x102826)) % 177.41/177.20 [10302]~P75(x103021)+~P1(f327(f35(x103022),x103026))+E(f327(f327(f327(f65(x103021,x103022,f81(x103021)),f327(f327(f8(f922(x103023,a910),x103021,x103022),f327(f327(f65(x103021,x103023,f81(x103021)),x103024),f78(x103021))),x103025)),f78(x103021)),x103026),f327(f327(f327(f65(x103021,x103023,f81(x103021)),x103024),f78(x103021)),f327(f327(f40(x103022,f922(x103023,a910)),x103026),x103025)))+P1(f327(f327(f329(x103022),f811(x103024,x103025,x103023,x103026,x103022,x103021)),x103026))+~P1(f327(f35(x103023),f327(x103025,f809(x103024,x103025,x103023,x103026,x103022,x103021)))) % 177.41/177.20 [10303]~P75(x103031)+~P1(f327(f35(x103032),x103036))+E(f327(f327(f327(f65(x103031,x103032,f81(x103031)),f327(f327(f8(f922(x103033,a910),x103031,x103032),f327(f327(f65(x103031,x103033,f81(x103031)),x103034),f78(x103031))),x103035)),f78(x103031)),x103036),f327(f327(f327(f65(x103031,x103033,f81(x103031)),x103034),f78(x103031)),f327(f327(f40(x103032,f922(x103033,a910)),x103036),x103035)))+P1(f327(f327(f329(x103032),f810(x103034,x103035,x103033,x103036,x103032,x103031)),x103036))+~P1(f327(f35(x103033),f327(x103035,f809(x103034,x103035,x103033,x103036,x103032,x103031)))) % 177.41/177.20 [10314]~P75(x103141)+~E(f327(f327(f103(f922(x103143,a910)),f327(x103145,f811(x103144,x103145,x103143,x103146,x103142,x103141))),f327(x103145,f810(x103144,x103145,x103143,x103146,x103142,x103141))),f190(f922(x103143,a910)))+~P1(f327(f35(x103142),x103146))+E(f327(f327(f327(f65(x103141,x103142,f81(x103141)),f327(f327(f8(f922(x103143,a910),x103141,x103142),f327(f327(f65(x103141,x103143,f81(x103141)),x103144),f78(x103141))),x103145)),f78(x103141)),x103146),f327(f327(f327(f65(x103141,x103143,f81(x103141)),x103144),f78(x103141)),f327(f327(f40(x103142,f922(x103143,a910)),x103146),x103145)))+P1(f327(f327(f329(x103142),f809(x103144,x103145,x103143,x103146,x103142,x103141)),x103146)) % 177.41/177.20 [10325]~P75(x103251)+~E(f327(f327(f103(f922(x103253,a910)),f327(x103255,f811(x103254,x103255,x103253,x103256,x103252,x103251))),f327(x103255,f810(x103254,x103255,x103253,x103256,x103252,x103251))),f190(f922(x103253,a910)))+~P1(f327(f35(x103252),x103256))+E(f327(f327(f327(f65(x103251,x103252,f81(x103251)),f327(f327(f8(f922(x103253,a910),x103251,x103252),f327(f327(f65(x103251,x103253,f81(x103251)),x103254),f78(x103251))),x103255)),f78(x103251)),x103256),f327(f327(f327(f65(x103251,x103253,f81(x103251)),x103254),f78(x103251)),f327(f327(f40(x103252,f922(x103253,a910)),x103256),x103255)))+~P1(f327(f35(x103253),f327(x103255,f809(x103254,x103255,x103253,x103256,x103252,x103251)))) % 177.41/177.20 [9385]~P121(x93851)+~P118(x93851)+~P1(f327(f327(f287(x93851),x93852),x93855))+~P1(f327(f327(f287(x93851),x93852),f327(f327(f80(x93851),x93853),x93856)))+P1(f327(f327(f287(x93851),x93852),f327(f327(f80(x93851),f327(f327(f23(x93851),x93853),f327(f327(f81(x93851),x93854),x93855))),x93856))) % 177.41/177.20 [9575]~P121(x95751)+~P118(x95751)+~P1(f327(f327(f287(x95751),x95752),x95755))+P1(f327(f327(f287(x95751),x95752),f327(f327(f80(x95751),x95753),x95754)))+~P1(f327(f327(f287(x95751),x95752),f327(f327(f80(x95751),f327(f327(f23(x95751),x95753),f327(f327(f81(x95751),x95756),x95755))),x95754))) % 177.41/177.20 [8989]E(x89891,x89892)+~P54(x89894,x89895,x89896,x89893,x89897)+~E(f327(x89893,x89891),f327(x89893,x89892))+~P1(f327(f327(f329(x89895),x89892),x89897))+~P1(f327(f327(f329(x89895),x89891),x89897)) % 177.41/177.20 [10292]~P1(f327(x102922,x102924))+~E(x102925,f327(f137(x102921,x102922),x102927))+E(f327(f137(x102921,x102922),x102923),f327(f327(f152(x102921),x102924),x102925))+~E(x102923,f327(f327(f135(x102921),x102926),f327(f327(f152(x102921),x102924),x102927)))+P1(f327(x102922,f743(x102925,x102924,x102923,x102922,x102921,x102926,x102927))) % 177.41/177.20 [10293]~P1(f327(x102934,x102932))+~E(x102933,f327(f137(x102931,x102934),x102937))+E(f327(f327(f152(x102931),x102932),x102933),f327(f137(x102931,x102934),x102935))+~E(x102935,f327(f327(f135(x102931),x102936),f327(f327(f152(x102931),x102932),x102937)))+P1(f327(x102934,f742(x102935,x102934,x102933,x102932,x102931,x102936,x102937))) % 177.41/177.20 [10337]~P1(f327(x103372,x103374))+~E(x103375,f327(f137(x103371,x103372),x103377))+E(f327(f137(x103371,x103372),x103373),f327(f327(f152(x103371),x103374),x103375))+~E(x103373,f327(f327(f135(x103371),x103376),f327(f327(f152(x103371),x103374),x103377)))+P1(f327(f327(f329(x103371),f743(x103375,x103374,x103373,x103372,x103371,x103376,x103377)),f327(f173(x103371),x103376))) % 177.41/177.20 [10338]~P1(f327(x103384,x103382))+~E(x103383,f327(f137(x103381,x103384),x103387))+E(f327(f327(f152(x103381),x103382),x103383),f327(f137(x103381,x103384),x103385))+~E(x103385,f327(f327(f135(x103381),x103386),f327(f327(f152(x103381),x103382),x103387)))+P1(f327(f327(f329(x103381),f742(x103385,x103384,x103383,x103382,x103381,x103386,x103387)),f327(f173(x103381),x103386))) % 177.41/177.20 [10342]~P6(x103421,x103427,x103426)+~P9(x103421,f922(x103425,a910),x103426,x103424)+P1(f327(f327(f329(x103421),f511(x103422,x103423,x103424,x103425,x103426,x103427,x103421)),x103427))+~P1(f327(f327(f329(f922(x103421,a910)),x103423),f327(f327(f61(x103421),x103427),x103426)))+P1(f327(f327(f329(f922(x103425,a910)),f327(f327(f40(x103421,f922(x103425,a910)),x103423),x103424)),x103422)) % 177.41/177.20 [10399]~P6(x103992,x103996,x103997)+~P9(x103992,f922(x103991,a910),x103997,x103994)+~P1(f327(f327(f329(f922(x103992,a910)),x103993),f327(f327(f61(x103992),x103996),x103997)))+~P1(f327(f327(f329(f922(x103991,a910)),f327(x103994,f511(x103995,x103993,x103994,x103991,x103997,x103996,x103992))),x103995))+P1(f327(f327(f329(f922(x103991,a910)),f327(f327(f40(x103992,f922(x103991,a910)),x103993),x103994)),x103995)) % 177.41/177.20 [8574]~P75(x85742)+~P23(x85741,x85745,x85748,x85744)+~E(x85743,f327(f72(x85745,x85742,x85741,x85746),x85748))+~E(x85747,f327(f310(x85741,x85745,x85748),x85744))+E(f327(f327(f9(x85741,x85742),x85743),x85744),f327(f327(f9(x85745,x85742),x85746),x85747)) % 177.41/177.20 [10403]~P75(x104032)+~P23(x104035,x104031,x104038,x104037)+~E(f327(x104036,f593(x104033,x104036,x104034,x104037,x104038,x104031,x104035,x104032)),f327(f327(f72(x104031,x104032,x104035,x104033),x104038),f593(x104033,x104036,x104034,x104037,x104038,x104031,x104035,x104032)))+~E(x104034,f327(f310(x104035,x104031,x104038),x104037))+E(f327(f327(f9(x104031,x104032),x104033),x104034),f327(f327(f9(x104035,x104032),x104036),x104037)) % 177.41/177.20 [10406]~P68(x104062)+~P23(x104061,x104065,x104068,x104064)+~E(x104067,f327(f310(x104061,x104065,x104068),x104064))+E(f327(f327(f6(x104061,x104062),x104063),x104064),f327(f327(f6(x104065,x104062),x104066),x104067))+P1(f327(f327(f329(x104061),f626(x104066,x104063,x104067,x104064,x104068,x104065,x104061,x104062)),x104064)) % 177.41/177.20 [10407]~P75(x104072)+~P23(x104071,x104075,x104078,x104074)+~E(x104077,f327(f310(x104071,x104075,x104078),x104074))+E(f327(f327(f9(x104071,x104072),x104073),x104074),f327(f327(f9(x104075,x104072),x104076),x104077))+P1(f327(f327(f329(x104071),f593(x104076,x104073,x104077,x104074,x104078,x104075,x104071,x104072)),x104074)) % 177.41/177.20 [10412]~P68(x104122)+~P23(x104125,x104121,x104128,x104127)+~E(x104124,f327(f310(x104125,x104121,x104128),x104127))+~E(f327(x104126,f626(x104123,x104126,x104124,x104127,x104128,x104121,x104125,x104122)),f327(x104123,f327(x104128,f626(x104123,x104126,x104124,x104127,x104128,x104121,x104125,x104122))))+E(f327(f327(f6(x104121,x104122),x104123),x104124),f327(f327(f6(x104125,x104122),x104126),x104127)) % 177.41/177.20 [9869]~P21(x98696,x98692,x98695,x98697,x98698,x98691)+~P1(f327(f35(x98692),x98694))+~P1(f327(f35(x98692),x98693))+~E(f327(f327(f103(f922(x98692,a910)),x98693),x98694),f190(f922(x98692,a910)))+E(f327(x98691,f327(f327(f102(f922(x98692,a910)),x98693),x98694)),f327(f327(x98695,f327(x98691,x98693)),f327(x98691,x98694))) % 177.41/177.20 [10275]~P21(x102758,x102752,x102755,x102757,x102756,x102751)+~E(f327(x102756,f485(x102754,x102753,x102751,x102756,x102757,x102755,x102752)),x102757)+~P1(f327(f35(x102752),x102753))+~P1(f327(f35(x102752),x102754))+E(f327(x102751,f327(f327(f102(f922(x102752,a910)),x102753),x102754)),f327(f327(x102755,f327(x102751,x102753)),f327(x102751,x102754))) % 177.41/177.20 [10349]~P21(x103498,x103492,x103495,x103497,x103496,x103491)+~P1(f327(f35(x103492),x103493))+~P1(f327(f35(x103492),x103494))+E(f327(x103491,f327(f327(f102(f922(x103492,a910)),x103493),x103494)),f327(f327(x103495,f327(x103491,x103493)),f327(x103491,x103494)))+P1(f327(f327(f329(x103492),f485(x103494,x103493,x103491,x103496,x103497,x103495,x103492)),f327(f327(f103(f922(x103492,a910)),x103493),x103494))) % 177.41/177.20 [10025]~P6(x100254,x100258,x100255)+~P6(x100251,x100259,x100253)+~P10(x100251,x100254,f922(x100252,a910),x100253,x100255,x100257)+P9(x100251,f922(x100252,a910),x100253,f327(f327(f8(f922(x100254,f922(x100252,a910)),f922(x100252,a910),x100251),f327(f40(x100254,f922(x100252,a910)),f327(f285(x100254,x100254,x100255),f327(f327(f309(x100254),x100256),f190(f922(x100254,a910)))))),x100257))+~P1(f327(f327(f329(x100254),x100256),x100258)) % 177.41/177.20 [5590]~P108(x55903)+~P11(x55903,x55901)+E(x55901,f720(x55902,x55903))+~E(f327(f173(x55903),x55901),x55902)+~P1(f327(f35(x55903),x55902))+~P1(f327(f138(x55903),x55901)) % 177.41/177.20 [7434]P13(x74341,x74342)+~E(f327(x74342,f802(x74342)),f327(x74342,f803(x74342)))+~P1(f327(f327(x74342,f802(x74342)),f802(x74342)))+~P1(f327(f327(x74342,f802(x74342)),f803(x74342)))+~P1(f327(f327(x74342,f803(x74342)),f803(x74342)))+~P1(f327(f327(x74342,x74343),x74343)) % 177.41/177.20 [5214]~P116(x52142)+~P129(x52142)+~P134(x52142)+~P145(x52142)+E(x52141,f2(x52142))+~E(f327(f327(f244(x52142),x52141),x52143),f2(x52142)) % 177.41/177.20 [5215]~P116(x52152)+~P129(x52152)+~P134(x52152)+~P145(x52152)+~E(x52151,f2(a915))+~E(f327(f327(f244(x52152),x52153),x52151),f2(x52152)) % 177.41/177.20 [6675]~P88(x66751)+~E(x66753,f2(x66751))+~E(x66752,f2(x66751))+E(f327(f327(f80(x66751),x66752),x66753),f2(x66751))+~P1(f327(f327(f234(x66751),f2(x66751)),x66753))+~P1(f327(f327(f234(x66751),f2(x66751)),x66752)) % 177.41/177.20 [9057]~E(f327(f251(a915,a915),x90573),f2(a915))+~E(x90571,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),x90573)),x90572)),f327(f256(a915,a915),x90573)))+P1(f327(f49(x90571,x90572),x90573))+~P1(f327(f327(f234(a915),f327(f256(a915,a915),x90573)),f2(a915)))+P1(f327(f327(f235(a915),f2(a915)),x90572))+~P1(f327(f327(f235(a915),x90572),f327(f256(a915,a915),x90573))) % 177.41/177.20 [9065]E(x90651,f2(a915))+~E(x90652,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),x90653)),x90651)),f327(f256(a915,a915),x90653)))+P1(f327(f49(x90652,x90651),x90653))+~P1(f327(f327(f235(a915),f2(a915)),x90651))+~P1(f327(f327(f234(a915),f2(a915)),f327(f256(a915,a915),x90653)))+~P1(f327(f327(f235(a915),f327(f256(a915,a915),x90653)),x90651)) % 177.41/177.20 [9083]~E(f327(f251(a915,a915),x90833),f2(a915))+~E(x90831,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),x90833)),x90832)),f327(f256(a915,a915),x90833)))+P1(f327(f49(x90831,x90832),x90833))+~P1(f327(f327(f235(a915),f2(a915)),x90832))+~P1(f327(f327(f234(a915),f2(a915)),f327(f256(a915,a915),x90833)))+~P1(f327(f327(f235(a915),f327(f256(a915,a915),x90833)),x90832)) % 177.41/177.20 [7058]~P108(x70582)+E(x70581,f190(f922(x70582,a910)))+E(x70583,f190(f922(x70582,a910)))+~P1(f327(f35(x70582),x70581))+~P1(f327(f35(x70582),x70583))+E(f14(x70582,f327(f327(f102(f922(x70582,a910)),x70583),x70581)),f327(f327(f189(x70582),f14(x70582,x70583)),f14(x70582,x70581))) % 177.41/177.20 [7059]~P108(x70592)+E(x70591,f190(f922(x70592,a910)))+E(x70593,f190(f922(x70592,a910)))+~P1(f327(f35(x70592),x70591))+~P1(f327(f35(x70592),x70593))+E(f15(x70592,f327(f327(f102(f922(x70592,a910)),x70593),x70591)),f327(f327(f238(x70592),f15(x70592,x70593)),f15(x70592,x70591))) % 177.41/177.20 [7060]~P96(x70602)+E(x70601,f190(f922(x70602,a910)))+E(x70603,f190(f922(x70602,a910)))+~P1(f327(f35(x70602),x70601))+~P1(f327(f35(x70602),x70603))+E(f13(x70602,f327(f327(f102(f922(x70602,a910)),x70603),x70601)),f327(f327(f102(x70602),f13(x70602,x70603)),f13(x70602,x70601))) % 177.41/177.20 [7061]~P96(x70612)+E(x70611,f190(f922(x70612,a910)))+E(x70613,f190(f922(x70612,a910)))+~P1(f327(f35(x70612),x70611))+~P1(f327(f35(x70612),x70613))+E(f10(x70612,f327(f327(f102(f922(x70612,a910)),x70613),x70611)),f327(f327(f103(x70612),f10(x70612,x70613)),f10(x70612,x70611))) % 177.41/177.20 [7700]~P95(x77002)+E(x77001,f190(f922(x77002,a910)))+E(x77003,f190(f922(x77002,a910)))+~P1(f327(f35(x77002),x77001))+~P1(f327(f35(x77002),x77003))+E(f327(f327(f81(x77002),f327(f63(x77002,f81(x77002)),x77003)),f327(f63(x77002,f81(x77002)),x77001)),f327(f63(x77002,f81(x77002)),f327(f327(f102(f922(x77002,a910)),x77003),x77001))) % 177.41/177.20 [7861]~P108(x78612)+E(x78611,f190(f922(x78612,a910)))+E(x78613,f190(f922(x78612,a910)))+~P1(f327(f35(x78612),x78611))+~P1(f327(f35(x78612),x78613))+E(f327(f327(f189(x78612),f11(x78612,f189(x78612),x78613)),f11(x78612,f189(x78612),x78611)),f11(x78612,f189(x78612),f327(f327(f102(f922(x78612,a910)),x78613),x78611))) % 177.41/177.20 [7862]~P108(x78622)+E(x78621,f190(f922(x78622,a910)))+E(x78623,f190(f922(x78622,a910)))+~P1(f327(f35(x78622),x78621))+~P1(f327(f35(x78622),x78623))+E(f327(f327(f238(x78622),f12(x78622,f238(x78622),x78623)),f12(x78622,f238(x78622),x78621)),f12(x78622,f238(x78622),f327(f327(f102(f922(x78622,a910)),x78623),x78621))) % 177.41/177.20 [8890]~P1(f327(x88901,x88903))+P1(f327(x88901,f443(x88901,x88902)))+P1(f327(x88901,f435(x88901,x88902)))+~P1(f327(f327(f235(a1),f2(a1)),x88902))+~P1(f327(f327(f329(a1),x88903),f303(a1,f78(a1),x88902)))+P1(f327(x88901,f327(f327(f23(a1),f435(x88901,x88902)),f327(f327(f81(a1),f442(x88901,x88902)),x88902)))) % 177.41/177.20 [9195]~P1(f327(x91951,x91953))+~P1(f327(x91951,f435(x91951,x91952)))+P1(f327(x91951,f443(x91951,x91952)))+~P1(f327(f327(f235(a1),f2(a1)),x91952))+~P1(f327(f327(f329(a1),x91953),f303(a1,f78(a1),x91952)))+~P1(f327(x91951,f327(f327(f23(a1),f435(x91951,x91952)),f327(f327(f81(a1),f442(x91951,x91952)),x91952)))) % 177.41/177.20 [10439]~P100(x104392)+E(x104391,f190(f922(x104392,a910)))+E(x104393,f190(f922(x104392,a910)))+~P1(f327(f35(x104392),x104391))+~P1(f327(f35(x104392),x104393))+E(f10(x104392,f327(f262(x104392),f327(f327(f8(f922(x104392,a910),a910,x104392),f87(x104392)),f327(f327(f8(f922(x104392,f922(x104392,a910)),f922(x104392,a910),x104392),f327(f8(f922(x104392,a910),a910,x104392),f87(x104392))),f327(f327(f7(x104392,f922(x104392,f922(x104392,a910)),f922(x104392,f922(x104392,a910))),f327(f327(f8(f922(x104392,f922(f922(x104392,a910),f922(x104392,a910))),f922(f922(x104392,f922(x104392,a910)),f922(x104392,f922(x104392,a910))),x104392),f18(x104392,f922(x104392,a910),f922(x104392,a910))),f327(f327(f8(f922(x104392,f922(x104392,f922(a910,a910))),f922(x104392,f922(f922(x104392,a910),f922(x104392,a910))),x104392),f327(f8(f922(x104392,f922(a910,a910)),f922(f922(x104392,a910),f922(x104392,a910)),x104392),f18(x104392,a910,a910))),f327(f327(f8(f922(x104392,f922(x104392,a910)),f922(x104392,f922(x104392,f922(a910,a910))),x104392),f327(f8(f922(x104392,a910),f922(x104392,f922(a910,a910)),x104392),f327(f8(a910,f922(a910,a910),x104392),a325))),f327(f327(f7(x104392,f922(x104392,f922(x104392,x104392)),f922(x104392,f922(x104392,a910))),f327(f327(f8(f922(f922(x104392,x104392),f922(x104392,a910)),f922(f922(x104392,f922(x104392,x104392)),f922(x104392,f922(x104392,a910))),x104392),f8(f922(x104392,x104392),f922(x104392,a910),x104392)),f327(f327(f8(f922(x104392,a910),f922(f922(x104392,x104392),f922(x104392,a910)),x104392),f8(x104392,a910,x104392)),a324))),f102(x104392)))))),f327(f327(f7(x104392,f922(x104392,a910),f922(x104392,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x104392,a910),f922(x104392,a910)),x104392),f8(a910,a910,x104392)),f327(f327(f8(a910,f922(a910,a910),x104392),a325),f327(f327(f7(x104392,f922(x104392,a910),a910),f329(x104392)),x104393)))),f327(f327(f7(x104392,f922(x104392,a910),a910),f329(x104392)),x104391))))))),f327(f327(f102(x104392),f10(x104392,x104393)),f10(x104392,x104391))) % 177.41/177.20 [10440]~P100(x104402)+E(x104401,f190(f922(x104402,a910)))+E(x104403,f190(f922(x104402,a910)))+~P1(f327(f35(x104402),x104401))+~P1(f327(f35(x104402),x104403))+E(f13(x104402,f327(f262(x104402),f327(f327(f8(f922(x104402,a910),a910,x104402),f87(x104402)),f327(f327(f8(f922(x104402,f922(x104402,a910)),f922(x104402,a910),x104402),f327(f8(f922(x104402,a910),a910,x104402),f87(x104402))),f327(f327(f7(x104402,f922(x104402,f922(x104402,a910)),f922(x104402,f922(x104402,a910))),f327(f327(f8(f922(x104402,f922(f922(x104402,a910),f922(x104402,a910))),f922(f922(x104402,f922(x104402,a910)),f922(x104402,f922(x104402,a910))),x104402),f18(x104402,f922(x104402,a910),f922(x104402,a910))),f327(f327(f8(f922(x104402,f922(x104402,f922(a910,a910))),f922(x104402,f922(f922(x104402,a910),f922(x104402,a910))),x104402),f327(f8(f922(x104402,f922(a910,a910)),f922(f922(x104402,a910),f922(x104402,a910)),x104402),f18(x104402,a910,a910))),f327(f327(f8(f922(x104402,f922(x104402,a910)),f922(x104402,f922(x104402,f922(a910,a910))),x104402),f327(f8(f922(x104402,a910),f922(x104402,f922(a910,a910)),x104402),f327(f8(a910,f922(a910,a910),x104402),a325))),f327(f327(f7(x104402,f922(x104402,f922(x104402,x104402)),f922(x104402,f922(x104402,a910))),f327(f327(f8(f922(f922(x104402,x104402),f922(x104402,a910)),f922(f922(x104402,f922(x104402,x104402)),f922(x104402,f922(x104402,a910))),x104402),f8(f922(x104402,x104402),f922(x104402,a910),x104402)),f327(f327(f8(f922(x104402,a910),f922(f922(x104402,x104402),f922(x104402,a910)),x104402),f8(x104402,a910,x104402)),a324))),f103(x104402)))))),f327(f327(f7(x104402,f922(x104402,a910),f922(x104402,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x104402,a910),f922(x104402,a910)),x104402),f8(a910,a910,x104402)),f327(f327(f8(a910,f922(a910,a910),x104402),a325),f327(f327(f7(x104402,f922(x104402,a910),a910),f329(x104402)),x104403)))),f327(f327(f7(x104402,f922(x104402,a910),a910),f329(x104402)),x104401))))))),f327(f327(f103(x104402),f13(x104402,x104403)),f13(x104402,x104401))) % 177.41/177.20 [10441]~P108(x104412)+E(x104411,f190(f922(x104412,a910)))+E(x104413,f190(f922(x104412,a910)))+~P1(f327(f35(x104412),x104411))+~P1(f327(f35(x104412),x104413))+E(f11(x104412,f189(x104412),f327(f262(x104412),f327(f327(f8(f922(x104412,a910),a910,x104412),f87(x104412)),f327(f327(f8(f922(x104412,f922(x104412,a910)),f922(x104412,a910),x104412),f327(f8(f922(x104412,a910),a910,x104412),f87(x104412))),f327(f327(f7(x104412,f922(x104412,f922(x104412,a910)),f922(x104412,f922(x104412,a910))),f327(f327(f8(f922(x104412,f922(f922(x104412,a910),f922(x104412,a910))),f922(f922(x104412,f922(x104412,a910)),f922(x104412,f922(x104412,a910))),x104412),f18(x104412,f922(x104412,a910),f922(x104412,a910))),f327(f327(f8(f922(x104412,f922(x104412,f922(a910,a910))),f922(x104412,f922(f922(x104412,a910),f922(x104412,a910))),x104412),f327(f8(f922(x104412,f922(a910,a910)),f922(f922(x104412,a910),f922(x104412,a910)),x104412),f18(x104412,a910,a910))),f327(f327(f8(f922(x104412,f922(x104412,a910)),f922(x104412,f922(x104412,f922(a910,a910))),x104412),f327(f8(f922(x104412,a910),f922(x104412,f922(a910,a910)),x104412),f327(f8(a910,f922(a910,a910),x104412),a325))),f327(f327(f7(x104412,f922(x104412,f922(x104412,x104412)),f922(x104412,f922(x104412,a910))),f327(f327(f8(f922(f922(x104412,x104412),f922(x104412,a910)),f922(f922(x104412,f922(x104412,x104412)),f922(x104412,f922(x104412,a910))),x104412),f8(f922(x104412,x104412),f922(x104412,a910),x104412)),f327(f327(f8(f922(x104412,a910),f922(f922(x104412,x104412),f922(x104412,a910)),x104412),f8(x104412,a910,x104412)),a324))),f238(x104412)))))),f327(f327(f7(x104412,f922(x104412,a910),f922(x104412,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x104412,a910),f922(x104412,a910)),x104412),f8(a910,a910,x104412)),f327(f327(f8(a910,f922(a910,a910),x104412),a325),f327(f327(f7(x104412,f922(x104412,a910),a910),f329(x104412)),x104413)))),f327(f327(f7(x104412,f922(x104412,a910),a910),f329(x104412)),x104411))))))),f327(f327(f238(x104412),f11(x104412,f189(x104412),x104413)),f11(x104412,f189(x104412),x104411))) % 177.41/177.20 [10442]~P108(x104422)+E(x104421,f190(f922(x104422,a910)))+E(x104423,f190(f922(x104422,a910)))+~P1(f327(f35(x104422),x104421))+~P1(f327(f35(x104422),x104423))+E(f12(x104422,f238(x104422),f327(f262(x104422),f327(f327(f8(f922(x104422,a910),a910,x104422),f87(x104422)),f327(f327(f8(f922(x104422,f922(x104422,a910)),f922(x104422,a910),x104422),f327(f8(f922(x104422,a910),a910,x104422),f87(x104422))),f327(f327(f7(x104422,f922(x104422,f922(x104422,a910)),f922(x104422,f922(x104422,a910))),f327(f327(f8(f922(x104422,f922(f922(x104422,a910),f922(x104422,a910))),f922(f922(x104422,f922(x104422,a910)),f922(x104422,f922(x104422,a910))),x104422),f18(x104422,f922(x104422,a910),f922(x104422,a910))),f327(f327(f8(f922(x104422,f922(x104422,f922(a910,a910))),f922(x104422,f922(f922(x104422,a910),f922(x104422,a910))),x104422),f327(f8(f922(x104422,f922(a910,a910)),f922(f922(x104422,a910),f922(x104422,a910)),x104422),f18(x104422,a910,a910))),f327(f327(f8(f922(x104422,f922(x104422,a910)),f922(x104422,f922(x104422,f922(a910,a910))),x104422),f327(f8(f922(x104422,a910),f922(x104422,f922(a910,a910)),x104422),f327(f8(a910,f922(a910,a910),x104422),a325))),f327(f327(f7(x104422,f922(x104422,f922(x104422,x104422)),f922(x104422,f922(x104422,a910))),f327(f327(f8(f922(f922(x104422,x104422),f922(x104422,a910)),f922(f922(x104422,f922(x104422,x104422)),f922(x104422,f922(x104422,a910))),x104422),f8(f922(x104422,x104422),f922(x104422,a910),x104422)),f327(f327(f8(f922(x104422,a910),f922(f922(x104422,x104422),f922(x104422,a910)),x104422),f8(x104422,a910,x104422)),a324))),f189(x104422)))))),f327(f327(f7(x104422,f922(x104422,a910),f922(x104422,a910)),f327(f327(f8(f922(a910,a910),f922(f922(x104422,a910),f922(x104422,a910)),x104422),f8(a910,a910,x104422)),f327(f327(f8(a910,f922(a910,a910),x104422),a325),f327(f327(f7(x104422,f922(x104422,a910),a910),f329(x104422)),x104423)))),f327(f327(f7(x104422,f922(x104422,a910),a910),f329(x104422)),x104421))))))),f327(f327(f189(x104422),f12(x104422,f238(x104422),x104423)),f12(x104422,f238(x104422),x104421))) % 177.41/177.20 [7390]~P126(x73903)+E(x73901,x73902)+~E(f327(f327(f244(x73903),x73901),x73904),f327(f327(f244(x73903),x73902),x73904))+~P1(f327(f327(f234(x73903),f2(x73903)),x73902))+~P1(f327(f327(f234(x73903),f2(x73903)),x73901))+~P1(f327(f327(f235(a915),f2(a915)),x73904)) % 177.41/177.20 [7661]~P108(x76612)+E(x76611,f190(f922(x76612,a910)))+~P1(f327(f35(x76612),x76611))+~P1(f327(f327(f329(x76612),x76614),x76611))+P1(f327(f327(f234(x76612),x76613),x76614))+~P1(f327(f327(f234(x76612),x76613),f327(f63(x76612,f238(x76612)),x76611))) % 177.41/177.20 [7662]~P102(x76622)+E(x76621,f190(f922(x76622,a910)))+~P1(f327(f35(x76622),x76621))+~P1(f327(f327(f329(x76622),x76624),x76621))+P1(f327(f327(f234(x76622),x76623),x76624))+~P1(f327(f327(f234(x76622),x76623),f327(f63(x76622,f103(x76622)),x76621))) % 177.41/177.20 [7663]~P108(x76632)+E(x76631,f190(f922(x76632,a910)))+~P1(f327(f35(x76632),x76631))+~P1(f327(f327(f329(x76632),x76634),x76631))+P1(f327(f327(f235(x76632),x76633),x76634))+~P1(f327(f327(f235(x76632),x76633),f327(f63(x76632,f238(x76632)),x76631))) % 177.41/177.20 [7568]E(x75681,f2(a1))+E(f327(f327(f37(a1),x75682),x75681),x75683)+~P1(f327(f327(f234(a1),x75684),f2(a1)))+~E(x75682,f327(f327(f80(a1),f327(f327(f81(a1),x75681),x75683)),x75684))+P1(f327(f327(f235(a1),f2(a1)),x75681))+~P1(f327(f327(f235(a1),x75681),x75684)) % 177.41/177.20 [7583]E(f46(a1,x75832,x75831),x75833)+E(x75831,f2(a1))+~P1(f327(f327(f234(a1),x75833),f2(a1)))+~E(x75832,f327(f327(f80(a1),f327(f327(f81(a1),x75831),x75834)),x75833))+P1(f327(f327(f235(a1),f2(a1)),x75831))+~P1(f327(f327(f235(a1),x75831),x75833)) % 177.41/177.20 [7699]E(x76991,f2(a1))+E(f327(f327(f37(a1),x76992),x76991),x76993)+~E(x76992,f327(f327(f80(a1),f327(f327(f81(a1),x76991),x76993)),x76994))+~P1(f327(f327(f234(a1),f2(a1)),x76994))+~P1(f327(f327(f235(a1),f2(a1)),x76991))+~P1(f327(f327(f235(a1),x76994),x76991)) % 177.41/177.20 [7721]E(f46(a1,x77212,x77211),x77213)+E(x77211,f2(a1))+~E(x77212,f327(f327(f80(a1),f327(f327(f81(a1),x77211),x77214)),x77213))+~P1(f327(f327(f234(a1),f2(a1)),x77213))+~P1(f327(f327(f235(a1),f2(a1)),x77211))+~P1(f327(f327(f235(a1),x77213),x77211)) % 177.41/177.20 [7865]~P108(x78652)+E(x78651,f190(f922(x78652,a910)))+~P1(f327(f35(x78652),x78651))+~P1(f327(f327(f234(x78652),x78654),x78653))+~P1(f327(f327(f329(x78652),x78654),x78651))+P1(f327(f327(f234(x78652),f327(f63(x78652,f238(x78652)),x78651)),x78653)) % 177.41/177.20 [7866]~P108(x78662)+E(x78661,f190(f922(x78662,a910)))+~P1(f327(f35(x78662),x78661))+~P1(f327(f327(f235(x78662),x78664),x78663))+~P1(f327(f327(f329(x78662),x78664),x78661))+P1(f327(f327(f235(x78662),f327(f63(x78662,f238(x78662)),x78661)),x78663)) % 177.41/177.20 [8427]~P1(f327(f327(f234(a1),x84274),f2(a1)))+~E(x84271,f327(f327(f80(a1),f327(f327(f81(a1),x84272),x84273)),x84274))+~P1(f327(f327(f234(a1),f2(a1)),x84274))+~P1(f327(f327(f235(a1),x84274),x84272))+~P1(f327(f327(f235(a1),x84272),x84274))+P1(f327(f50(x84271,x84272),f327(f327(f252(a1,a1),x84273),x84274))) % 177.41/177.20 [8594]~P110(x85941)+P1(f327(f327(f235(f922(x85941,a910)),f303(x85941,x85942,x85943)),f303(x85941,x85944,x85945)))+~P1(f327(f327(f234(x85941),x85944),x85942))+~P1(f327(f327(f234(x85941),x85944),x85945))+~P1(f327(f327(f234(x85941),x85943),x85945))+~P1(f327(f327(f235(x85941),x85943),x85945)) % 177.41/177.20 [8595]~P110(x85951)+P1(f327(f327(f235(f922(x85951,a910)),f303(x85951,x85952,x85953)),f303(x85951,x85954,x85955)))+~P1(f327(f327(f234(x85951),x85953),x85955))+~P1(f327(f327(f234(x85951),x85954),x85955))+~P1(f327(f327(f234(x85951),x85954),x85952))+~P1(f327(f327(f235(x85951),x85954),x85952)) % 177.41/177.20 [9454]P56(x94542,x94543,x94544,x94541)+E(x94541,f190(f922(x94542,a910)))+~P1(f327(f35(x94542),x94544))+~P1(f327(f35(x94542),x94541))+~P1(f327(f327(x94543,f538(x94541,x94544,x94543,x94542)),x94545))+~P1(f327(f327(f329(x94542),x94545),x94541)) % 177.41/177.20 [9455]P56(x94552,x94553,x94554,x94551)+E(x94551,f190(f922(x94552,a910)))+~P1(f327(f35(x94552),x94554))+~P1(f327(f35(x94552),x94551))+~P1(f327(f327(x94553,f793(x94553,x94551,x94554,x94552)),x94555))+~P1(f327(f327(f329(x94552),x94555),x94551)) % 177.41/177.20 [9456]P56(x94562,x94563,x94564,x94561)+E(x94561,f190(f922(x94562,a910)))+~P1(f327(f35(x94562),x94564))+~P1(f327(f35(x94562),x94561))+~P1(f327(f327(x94563,f794(x94561,x94564,x94563,x94562)),x94565))+~P1(f327(f327(f329(x94562),x94565),x94561)) % 177.41/177.20 [9604]~E(x96043,x96045)+~P68(x96041)+~P75(x96041)+~P38(x96043)+E(f327(f327(f6(a1,x96041),x96042),x96043),f327(f327(f6(a1,x96041),x96044),x96045))+P1(f327(f327(f234(a1),f2(a1)),f468(x96042,x96044,x96043,x96045,x96041))) % 177.41/177.20 [9605]~E(x96053,x96055)+~P68(x96051)+~P75(x96051)+~P38(x96053)+E(f327(f327(f9(a1,x96051),x96052),x96053),f327(f327(f9(a1,x96051),x96054),x96055))+P1(f327(f327(f234(a1),f2(a1)),f458(x96052,x96054,x96053,x96055,x96051))) % 177.41/177.20 [9779]~E(x97795,x97793)+~P68(x97791)+~P75(x97791)+~P38(x97795)+~E(f327(x97792,f468(x97794,x97792,x97795,x97793,x97791)),f327(x97794,f468(x97794,x97792,x97795,x97793,x97791)))+E(f327(f327(f6(a1,x97791),x97792),x97793),f327(f327(f6(a1,x97791),x97794),x97795)) % 177.41/177.20 [9780]~E(x97805,x97803)+~P68(x97801)+~P75(x97801)+~P38(x97805)+~E(f327(x97802,f458(x97804,x97802,x97805,x97803,x97801)),f327(x97804,f458(x97804,x97802,x97805,x97803,x97801)))+E(f327(f327(f9(a1,x97801),x97802),x97803),f327(f327(f9(a1,x97801),x97804),x97805)) % 177.41/177.20 [9867]~P78(x98673)+E(f327(x98671,x98672),f2(x98673))+~E(f327(f327(f6(x98674,x98673),x98671),x98675),f2(x98673))+~P1(f327(f35(x98674),x98675))+P1(f327(f327(f329(x98674),f401(x98672,x98671,x98675,x98674,x98673)),x98675))+~P1(f327(f327(f329(x98674),x98672),x98675)) % 177.41/177.20 [9996]~P78(x99963)+E(f327(x99961,x99962),f2(x99963))+~E(f327(f327(f6(x99964,x99963),x99961),x99965),f2(x99963))+~P1(f327(f35(x99964),x99965))+~P1(f327(f327(f329(x99964),x99962),x99965))+~P1(f327(f327(f234(x99963),f2(x99963)),f327(x99961,f401(x99962,x99961,x99965,x99964,x99963)))) % 177.41/177.20 [8512]~P137(x85121)+~P1(f327(f327(f234(x85121),x85123),x85125))+~P1(f327(f327(f234(x85121),x85122),x85124))+~P1(f327(f327(f234(x85121),f2(x85121)),x85123))+~P1(f327(f327(f234(x85121),f2(x85121)),x85124))+P1(f327(f327(f234(x85121),f327(f327(f81(x85121),x85122),x85123)),f327(f327(f81(x85121),x85124),x85125))) % 177.41/177.20 [8513]~P137(x85131)+~P1(f327(f327(f234(x85131),x85133),x85135))+~P1(f327(f327(f234(x85131),x85132),x85134))+~P1(f327(f327(f234(x85131),f2(x85131)),x85133))+~P1(f327(f327(f234(x85131),f2(x85131)),x85132))+P1(f327(f327(f234(x85131),f327(f327(f81(x85131),x85132),x85133)),f327(f327(f81(x85131),x85134),x85135))) % 177.41/177.20 [8514]~P64(x85141)+~P1(f327(f327(f235(x85141),f2(x85141)),x85145))+~P1(f327(f327(f234(x85141),x85145),x85143))+~P1(f327(f327(f234(x85141),x85142),x85144))+~P1(f327(f327(f234(x85141),f2(x85141)),x85142))+P1(f327(f327(f234(x85141),f327(f327(f291(x85141),x85142),x85143)),f327(f327(f291(x85141),x85144),x85145))) % 177.41/177.20 [8515]~P130(x85151)+~P1(f327(f327(f234(x85151),x85153),x85155))+~P1(f327(f327(f234(x85151),f2(x85151)),x85152))+~P1(f327(f327(f235(x85151),x85152),x85154))+~P1(f327(f327(f235(x85151),f2(x85151)),x85153))+P1(f327(f327(f235(x85151),f327(f327(f81(x85151),x85152),x85153)),f327(f327(f81(x85151),x85154),x85155))) % 177.41/177.20 [8516]~P130(x85161)+~P1(f327(f327(f234(x85161),x85162),x85164))+~P1(f327(f327(f234(x85161),f2(x85161)),x85163))+~P1(f327(f327(f235(x85161),x85163),x85165))+~P1(f327(f327(f235(x85161),f2(x85161)),x85162))+P1(f327(f327(f235(x85161),f327(f327(f81(x85161),x85162),x85163)),f327(f327(f81(x85161),x85164),x85165))) % 177.41/177.20 [8517]~P130(x85171)+~P1(f327(f327(f234(x85171),f2(x85171)),x85173))+~P1(f327(f327(f234(x85171),f2(x85171)),x85172))+~P1(f327(f327(f235(x85171),x85173),x85175))+~P1(f327(f327(f235(x85171),x85172),x85174))+P1(f327(f327(f235(x85171),f327(f327(f81(x85171),x85172),x85173)),f327(f327(f81(x85171),x85174),x85175))) % 177.41/177.20 [8518]~P130(x85181)+~P1(f327(f327(f234(x85181),f2(x85181)),x85183))+~P1(f327(f327(f235(x85181),x85183),x85185))+~P1(f327(f327(f235(x85181),x85182),x85184))+~P1(f327(f327(f235(x85181),f2(x85181)),x85184))+P1(f327(f327(f235(x85181),f327(f327(f81(x85181),x85182),x85183)),f327(f327(f81(x85181),x85184),x85185))) % 177.41/177.20 [8519]~P64(x85191)+~P1(f327(f327(f234(x85191),x85195),x85193))+~P1(f327(f327(f234(x85191),f2(x85191)),x85192))+~P1(f327(f327(f235(x85191),x85192),x85194))+~P1(f327(f327(f235(x85191),f2(x85191)),x85195))+P1(f327(f327(f235(x85191),f327(f327(f291(x85191),x85192),x85193)),f327(f327(f291(x85191),x85194),x85195))) % 177.41/177.20 [8520]~P64(x85201)+~P1(f327(f327(f234(x85201),x85202),x85204))+~P1(f327(f327(f235(x85201),x85205),x85203))+~P1(f327(f327(f235(x85201),f2(x85201)),x85205))+~P1(f327(f327(f235(x85201),f2(x85201)),x85202))+P1(f327(f327(f235(x85201),f327(f327(f291(x85201),x85202),x85203)),f327(f327(f291(x85201),x85204),x85205))) % 177.41/177.20 [9911]~P68(x99115)+~P85(x99115)+E(x99111,f190(f922(x99112,a910)))+~P1(f327(f35(x99112),x99111))+P1(f327(f327(f329(x99112),f645(x99113,x99114,x99111,x99112,x99115)),x99111))+P1(f327(f327(f235(x99115),f327(f327(f6(x99112,x99115),x99114),x99111)),f327(f327(f6(x99112,x99115),x99113),x99111))) % 177.41/177.20 [10021]~P68(x100211)+~P83(x100211)+~P1(f327(f35(x100212),x100215))+~P1(f327(f327(f234(x100211),f2(x100211)),f327(x100213,f382(x100213,x100214,x100215,x100212,x100211))))+P1(f327(f327(f234(x100211),f327(f327(f6(x100212,x100211),x100213),x100214)),f327(f327(f6(x100212,x100211),x100213),x100215)))+~P1(f327(f327(f234(f922(x100212,a910)),x100214),x100215)) % 177.41/177.20 [10192]~P68(x101923)+~P85(x101923)+E(x101921,f190(f922(x101922,a910)))+~P1(f327(f35(x101922),x101921))+~P1(f327(f327(f235(x101923),f327(x101924,f645(x101925,x101924,x101921,x101922,x101923))),f327(x101925,f645(x101925,x101924,x101921,x101922,x101923))))+P1(f327(f327(f235(x101923),f327(f327(f6(x101922,x101923),x101924),x101921)),f327(f327(f6(x101922,x101923),x101925),x101921))) % 177.41/177.20 [7244]~P15(x72442,x72445,x72444)+E(x72441,f190(f922(x72442,a910)))+E(x72443,f190(f922(x72442,a910)))+~P1(f327(f35(x72442),x72441))+~P1(f327(f35(x72442),x72443))+E(f327(x72444,f327(f327(f102(f922(x72442,a910)),x72443),x72441)),f327(f327(x72445,f327(x72444,x72443)),f327(x72444,x72441))) % 177.41/177.20 [7831]~P148(x78311,x78313,x78314)+P1(f327(x78311,x78312))+~P1(f327(f327(f235(a1),x78314),f2(a1)))+~P1(f327(f327(f234(a1),x78315),f2(a1)))+~E(x78313,f327(f327(f80(a1),f327(f327(f81(a1),x78314),x78312)),x78315))+~P1(f327(f327(f235(a1),x78314),x78315)) % 177.41/177.20 [7832]~P147(x78321,x78323,x78324)+P1(f327(x78321,x78322))+~P1(f327(f327(f235(a1),x78324),f2(a1)))+~P1(f327(f327(f234(a1),x78322),f2(a1)))+~E(x78323,f327(f327(f80(a1),f327(f327(f81(a1),x78324),x78325)),x78322))+~P1(f327(f327(f235(a1),x78324),x78322)) % 177.41/177.20 [7874]~P148(x78741,x78743,x78744)+P1(f327(x78741,x78742))+~E(x78743,f327(f327(f80(a1),f327(f327(f81(a1),x78744),x78742)),x78745))+~P1(f327(f327(f234(a1),f2(a1)),x78745))+~P1(f327(f327(f235(a1),f2(a1)),x78744))+~P1(f327(f327(f235(a1),x78745),x78744)) % 177.41/177.20 [7875]~P147(x78751,x78753,x78754)+P1(f327(x78751,x78752))+~E(x78753,f327(f327(f80(a1),f327(f327(f81(a1),x78754),x78755)),x78752))+~P1(f327(f327(f234(a1),f2(a1)),x78752))+~P1(f327(f327(f235(a1),f2(a1)),x78754))+~P1(f327(f327(f235(a1),x78752),x78754)) % 177.41/177.20 [8803]P1(f327(f327(x88031,x88032),x88033))+~P1(f327(f327(x88031,f327(f327(f37(a1),x88034),x88035)),f46(a1,x88034,x88035)))+~P1(f327(f327(f235(a1),x88035),f2(a1)))+~P1(f327(f327(f234(a1),x88033),f2(a1)))+~E(x88034,f327(f327(f80(a1),f327(f327(f81(a1),x88035),x88032)),x88033))+~P1(f327(f327(f235(a1),x88035),x88033)) % 177.41/177.20 [8812]P1(f327(f327(x88121,x88122),x88123))+~P1(f327(f327(x88121,f327(f327(f37(a1),x88124),x88125)),f46(a1,x88124,x88125)))+~E(x88124,f327(f327(f80(a1),f327(f327(f81(a1),x88125),x88122)),x88123))+~P1(f327(f327(f234(a1),f2(a1)),x88123))+~P1(f327(f327(f235(a1),f2(a1)),x88125))+~P1(f327(f327(f235(a1),x88123),x88125)) % 177.41/177.20 [9073]E(x90731,x90732)+~P53(x90733,x90735,x90734)+~P1(f327(f327(f329(x90733),x90732),x90735))+~P1(f327(f327(f329(x90733),x90731),x90735))+P1(f327(f327(f329(f921(x90733,x90733)),f327(f327(f252(x90733,x90733),x90731),x90732)),x90734))+P1(f327(f327(f329(f921(x90733,x90733)),f327(f327(f252(x90733,x90733),x90732),x90731)),x90734)) % 177.41/177.20 [9938]~P68(x99385)+~P83(x99385)+~P1(f327(f35(x99381),x99384))+P1(f327(f327(f234(x99385),f327(f327(f6(x99381,x99385),x99382),x99383)),f327(f327(f6(x99381,x99385),x99382),x99384)))+~P1(f327(f327(f234(f922(x99381,a910)),x99383),x99384))+P1(f327(f327(f329(x99381),f382(x99382,x99383,x99384,x99381,x99385)),f327(f327(f23(f922(x99381,a910)),x99384),x99383))) % 177.41/177.20 [10029]E(x100291,f190(f922(x100292,a910)))+~P1(f327(f35(x100292),x100293))+~P1(f327(f35(x100292),x100291))+P1(f327(f327(f329(f921(f922(x100292,a910),f922(x100292,a910))),f327(f327(f252(f922(x100292,a910),f922(x100292,a910)),x100293),x100291)),f319(x100292,x100294)))+~P1(f327(f327(f329(x100292),x100295),x100291))+~P1(f327(f327(f329(f921(x100292,x100292)),f327(f327(f252(x100292,x100292),f547(x100294,x100291,x100293,x100292)),x100295)),x100294)) % 177.41/177.20 [10030]E(x100301,f190(f922(x100302,a910)))+~P1(f327(f35(x100302),x100303))+~P1(f327(f35(x100302),x100301))+P1(f327(f327(f329(f921(f922(x100302,a910),f922(x100302,a910))),f327(f327(f252(f922(x100302,a910),f922(x100302,a910)),x100303),x100301)),f319(x100302,x100304)))+~P1(f327(f327(f329(x100302),x100305),x100301))+~P1(f327(f327(f329(f921(x100302,x100302)),f327(f327(f252(x100302,x100302),f596(x100304,x100301,x100303,x100302)),x100305)),x100304)) % 177.41/177.20 [10196]~P78(x101961)+~E(f327(f327(f6(x101965,x101961),x101962),x101966),x101964)+~P1(f327(f35(x101965),x101966))+P1(f327(f327(f329(x101965),f414(x101963,x101964,x101962,x101966,x101965,x101961)),x101966))+P1(f327(f327(f234(x101961),f327(x101962,x101963)),x101964))+~P1(f327(f327(f329(x101965),x101963),x101966)) % 177.41/177.20 [10245]~P78(x102451)+~E(f327(f327(f6(x102455,x102451),x102452),x102456),x102454)+~P1(f327(f35(x102455),x102456))+~P1(f327(f327(f329(x102455),x102453),x102456))+~P1(f327(f327(f234(x102451),f2(x102451)),f327(x102452,f414(x102453,x102454,x102452,x102456,x102455,x102451))))+P1(f327(f327(f234(x102451),f327(x102452,x102453)),x102454)) % 177.41/177.20 [10384]~E(x103845,x103848)+~E(x103844,x103847)+~P109(x103841)+~P68(x103842)+E(f327(f327(f6(x103841,x103842),x103843),f327(f302(x103841,x103844),x103845)),f327(f327(f6(x103841,x103842),x103846),f327(f302(x103841,x103847),x103848)))+P1(f327(f327(f234(x103841),x103844),f600(x103843,x103846,x103845,x103848,x103844,x103847,x103841,x103842))) % 177.41/177.20 [10402]~E(x104027,x104024)+~E(x104028,x104025)+~P109(x104021)+~P68(x104022)+~E(f327(x104023,f600(x104026,x104023,x104028,x104025,x104027,x104024,x104021,x104022)),f327(x104026,f600(x104026,x104023,x104028,x104025,x104027,x104024,x104021,x104022)))+E(f327(f327(f6(x104021,x104022),x104023),f327(f302(x104021,x104024),x104025)),f327(f327(f6(x104021,x104022),x104026),f327(f302(x104021,x104027),x104028))) % 177.41/177.20 [10405]~E(x104054,x104057)+~E(x104055,x104058)+~P109(x104051)+~P68(x104052)+E(f327(f327(f6(x104051,x104052),x104053),f327(f302(x104051,x104054),x104055)),f327(f327(f6(x104051,x104052),x104056),f327(f302(x104051,x104057),x104058)))+P1(f327(f327(f235(x104051),f600(x104053,x104056,x104055,x104058,x104054,x104057,x104051,x104052)),x104055)) % 177.41/177.20 [10036]~P6(x100365,x100369,x100366)+~P6(x100361,x1003610,x100363)+~P10(x100361,x100365,f922(x100362,a910),x100363,x100366,x100368)+~P1(f327(f327(f329(x100365),x100367),x100369))+~P1(f327(f327(f329(x100361),x100364),x1003610))+E(f327(f327(f40(x100361,f922(x100362,a910)),f327(f285(x100361,x100361,x100363),f327(f327(f309(x100361),x100364),f190(f922(x100361,a910))))),f327(f327(f8(f922(x100365,f922(x100362,a910)),f922(x100362,a910),x100361),f327(f40(x100365,f922(x100362,a910)),f327(f285(x100365,x100365,x100366),f327(f327(f309(x100365),x100367),f190(f922(x100365,a910)))))),x100368)),f327(f327(x100368,x100364),x100367)) % 177.41/177.20 [5764]~P108(x57643)+~P11(x57643,x57642)+~P11(x57643,x57641)+E(x57641,x57642)+~E(f327(f173(x57643),x57641),f327(f173(x57643),x57642))+~P1(f327(f138(x57643),x57642))+~P1(f327(f138(x57643),x57641)) % 177.41/177.20 [5093]~P116(x50932)+~P129(x50932)+~P134(x50932)+~P145(x50932)+~E(x50933,f2(x50932))+E(x50931,f2(a915))+E(f327(f327(f244(x50932),x50933),x50931),f2(x50932)) % 177.41/177.20 [9332]E(x93321,f2(a915))+~E(x93322,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),x93323)),x93321)),f327(f256(a915,a915),x93323)))+P1(f327(f49(x93322,x93321),x93323))+~P1(f327(f327(f234(a915),f327(f256(a915,a915),x93323)),f2(a915)))+~P1(f327(f327(f234(a915),f2(a915)),f327(f256(a915,a915),x93323)))+~P1(f327(f327(f235(a915),x93321),f327(f256(a915,a915),x93323)))+~P1(f327(f327(f235(a915),f327(f256(a915,a915),x93323)),x93321)) % 177.41/177.20 [9340]~E(f327(f251(a915,a915),x93403),f2(a915))+~E(x93401,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),x93403)),x93402)),f327(f256(a915,a915),x93403)))+P1(f327(f49(x93401,x93402),x93403))+~P1(f327(f327(f234(a915),f327(f256(a915,a915),x93403)),f2(a915)))+~P1(f327(f327(f234(a915),f2(a915)),f327(f256(a915,a915),x93403)))+~P1(f327(f327(f235(a915),x93402),f327(f256(a915,a915),x93403)))+~P1(f327(f327(f235(a915),f327(f256(a915,a915),x93403)),x93402)) % 177.41/177.20 [8182]~P72(x81822)+E(x81821,f190(f922(x81822,a910)))+E(x81823,f190(f922(x81822,a910)))+~P1(f327(f35(x81822),x81821))+~P1(f327(f35(x81822),x81823))+~E(f327(f327(f103(f922(x81822,a910)),x81823),x81821),f190(f922(x81822,a910)))+E(f327(f327(f81(x81822),f327(f63(x81822,f81(x81822)),x81823)),f327(f63(x81822,f81(x81822)),x81821)),f327(f63(x81822,f81(x81822)),f327(f327(f102(f922(x81822,a910)),x81823),x81821))) % 177.41/177.20 [7968]E(x79681,f2(a1))+E(f327(f327(f37(a1),x79682),x79681),x79683)+~P1(f327(f327(f234(a1),x79684),f2(a1)))+~E(x79682,f327(f327(f80(a1),f327(f327(f81(a1),x79681),x79683)),x79684))+~P1(f327(f327(f234(a1),f2(a1)),x79684))+~P1(f327(f327(f235(a1),x79684),x79681))+~P1(f327(f327(f235(a1),x79681),x79684)) % 177.41/177.20 [7976]E(f46(a1,x79762,x79761),x79763)+E(x79761,f2(a1))+~P1(f327(f327(f234(a1),x79763),f2(a1)))+~E(x79762,f327(f327(f80(a1),f327(f327(f81(a1),x79761),x79764)),x79763))+~P1(f327(f327(f234(a1),f2(a1)),x79763))+~P1(f327(f327(f235(a1),x79763),x79761))+~P1(f327(f327(f235(a1),x79761),x79763)) % 177.41/177.20 [7025]~P58(x70252)+E(x70251,f2(x70252))+E(x70253,f2(x70252))+~E(f327(f327(f37(x70252),x70254),x70253),f327(f327(f37(x70252),x70255),x70251))+E(f327(f327(f81(x70252),x70254),x70251),f327(f327(f81(x70252),x70253),x70255))+~P1(f327(f327(f287(x70252),x70251),x70255))+~P1(f327(f327(f287(x70252),x70253),x70254)) % 177.41/177.20 [7026]~P58(x70262)+E(x70261,f2(x70262))+E(x70263,f2(x70262))+~E(f327(f327(f81(x70262),x70264),x70263),f327(f327(f81(x70262),x70261),x70265))+E(f327(f327(f37(x70262),x70264),x70261),f327(f327(f37(x70262),x70265),x70263))+~P1(f327(f327(f287(x70262),x70261),x70264))+~P1(f327(f327(f287(x70262),x70263),x70265)) % 177.41/177.20 [7883]~P16(x78832,x78835,x78834)+E(x78831,f190(f922(x78832,a910)))+E(x78833,f190(f922(x78832,a910)))+~P1(f327(f35(x78832),x78831))+~P1(f327(f35(x78832),x78833))+~E(f327(f327(f103(f922(x78832,a910)),x78833),x78831),f190(f922(x78832,a910)))+E(f327(x78834,f327(f327(f102(f922(x78832,a910)),x78833),x78831)),f327(f327(x78835,f327(x78834,x78833)),f327(x78834,x78831))) % 177.41/177.20 [9577]~P23(x95773,x95771,x95775,x95774)+~P23(x95771,x95773,x95776,x95772)+E(f327(f36(x95771),x95772),f327(f36(x95773),x95774))+~P1(f327(f35(x95773),x95774))+~P1(f327(f35(x95771),x95772))+~P1(f327(f327(f234(f922(x95773,a910)),f327(f310(x95771,x95773,x95776),x95772)),x95774))+~P1(f327(f327(f234(f922(x95771,a910)),f327(f310(x95773,x95771,x95775),x95774)),x95772)) % 177.41/177.20 [9519]~P1(f327(f327(f235(a1),f327(f327(f80(a1),f327(f327(f81(a1),x95195),x95191)),x95196)),f2(a1)))+~E(f327(f327(f80(a1),f327(f327(f81(a1),x95193),x95192)),x95194),f327(f327(f80(a1),f327(f327(f81(a1),x95195),x95191)),x95196))+~P1(f327(f327(f234(a1),f2(a1)),x95196))+~P1(f327(f327(f235(a1),f2(a1)),x95195))+~P1(f327(f327(f234(a1),x95195),x95193))+~P1(f327(f327(f235(a1),x95194),x95193))+P1(f327(f327(f234(a1),x95191),x95192)) % 177.41/177.20 [9283]~E(f327(f327(f80(a1),f327(f327(f81(a1),x92833),x92831)),x92834),f327(f327(f80(a1),f327(f327(f81(a1),x92835),x92832)),x92836))+~P1(f327(f327(f234(a1),f2(a1)),x92834))+~P1(f327(f327(f235(a1),f2(a1)),x92835))+~P1(f327(f327(f234(a1),x92835),x92833))+~P1(f327(f327(f235(a1),x92836),x92835))+P1(f327(f327(f234(a1),x92831),x92832))+~P1(f327(f327(f234(a1),f2(a1)),f327(f327(f80(a1),f327(f327(f81(a1),x92835),x92832)),x92836))) % 177.41/177.20 [9459]~P132(x94591)+~E(f327(f327(f80(x94591),x94592),x94594),f78(x94591))+~P1(f327(f327(f234(x94591),x94595),x94596))+~P1(f327(f327(f234(x94591),x94593),x94596))+~P1(f327(f327(f234(x94591),f2(x94591)),x94594))+~P1(f327(f327(f234(x94591),f2(x94591)),x94592))+P1(f327(f327(f234(x94591),f327(f327(f80(x94591),f327(f327(f81(x94591),x94592),x94593)),f327(f327(f81(x94591),x94594),x94595))),x94596)) % 177.41/177.20 [9460]~P133(x94601)+~E(f327(f327(f80(x94601),x94602),x94604),f78(x94601))+~P1(f327(f327(f234(x94601),f2(x94601)),x94604))+~P1(f327(f327(f234(x94601),f2(x94601)),x94602))+~P1(f327(f327(f235(x94601),x94605),x94606))+~P1(f327(f327(f235(x94601),x94603),x94606))+P1(f327(f327(f235(x94601),f327(f327(f80(x94601),f327(f327(f81(x94601),x94602),x94603)),f327(f327(f81(x94601),x94604),x94605))),x94606)) % 177.41/177.20 [10295]~P6(x102957,x102956,x102955)+E(x102951,x102952)+~P9(x102957,f922(x102954,a910),x102955,x102953)+E(f327(x102953,f519(x102951,x102952,x102953,x102954,x102955,x102956,x102957)),f327(x102953,f520(x102951,x102952,x102953,x102954,x102955,x102956,x102957)))+~E(f327(f327(f40(x102957,f922(x102954,a910)),x102951),x102953),f327(f327(f40(x102957,f922(x102954,a910)),x102952),x102953))+~P1(f327(f327(f329(f922(x102957,a910)),x102952),f327(f327(f61(x102957),x102956),x102955)))+~P1(f327(f327(f329(f922(x102957,a910)),x102951),f327(f327(f61(x102957),x102956),x102955))) % 177.41/177.20 [10340]~P6(x103403,x103407,x103406)+E(x103401,x103402)+~P9(x103403,f922(x103405,a910),x103406,x103404)+~E(f327(f327(f40(x103403,f922(x103405,a910)),x103401),x103404),f327(f327(f40(x103403,f922(x103405,a910)),x103402),x103404))+P1(f327(f327(f329(x103403),f520(x103401,x103402,x103404,x103405,x103406,x103407,x103403)),x103407))+~P1(f327(f327(f329(f922(x103403,a910)),x103402),f327(f327(f61(x103403),x103407),x103406)))+~P1(f327(f327(f329(f922(x103403,a910)),x103401),f327(f327(f61(x103403),x103407),x103406))) % 177.41/177.20 [10341]~P6(x103413,x103417,x103416)+E(x103411,x103412)+~P9(x103413,f922(x103415,a910),x103416,x103414)+~E(f327(f327(f40(x103413,f922(x103415,a910)),x103411),x103414),f327(f327(f40(x103413,f922(x103415,a910)),x103412),x103414))+P1(f327(f327(f329(x103413),f519(x103411,x103412,x103414,x103415,x103416,x103417,x103413)),x103417))+~P1(f327(f327(f329(f922(x103413,a910)),x103412),f327(f327(f61(x103413),x103417),x103416)))+~P1(f327(f327(f329(f922(x103413,a910)),x103411),f327(f327(f61(x103413),x103417),x103416))) % 177.41/177.20 [10421]E(x104211,x104212)+~P6(x104213,x104216,x104217)+~P9(x104213,f922(x104214,a910),x104217,x104215)+~E(f327(f327(f40(x104213,f922(x104214,a910)),x104211),x104215),f327(f327(f40(x104213,f922(x104214,a910)),x104212),x104215))+~P1(f327(f327(f329(f921(x104213,x104213)),f327(f327(f252(x104213,x104213),f520(x104211,x104212,x104215,x104214,x104217,x104216,x104213)),f519(x104211,x104212,x104215,x104214,x104217,x104216,x104213))),x104217))+~P1(f327(f327(f329(f922(x104213,a910)),x104212),f327(f327(f61(x104213),x104216),x104217)))+~P1(f327(f327(f329(f922(x104213,a910)),x104211),f327(f327(f61(x104213),x104216),x104217))) % 177.41/177.20 [9282]~P6(x92821,x92827,x92824)+~E(x92825,x92826)+~P1(f327(f327(f329(x92821),x92823),x92826))+~P1(f327(f327(f329(x92821),x92822),x92825))+~P1(f327(f327(f329(f922(x92821,a910)),x92826),f327(f327(f61(x92821),x92827),x92824)))+~P1(f327(f327(f329(f922(x92821,a910)),x92825),f327(f327(f61(x92821),x92827),x92824)))+P1(f327(f327(f329(f921(x92821,x92821)),f327(f327(f252(x92821,x92821),x92822),x92823)),x92824)) % 177.41/177.20 [9418]E(x94181,x94182)+~P6(x94183,x94184,x94185)+~P1(f327(f327(f329(x94183),x94186),x94182))+~P1(f327(f327(f329(x94183),x94187),x94181))+~P1(f327(f327(f329(f922(x94183,a910)),x94182),f327(f327(f61(x94183),x94184),x94185)))+~P1(f327(f327(f329(f922(x94183,a910)),x94181),f327(f327(f61(x94183),x94184),x94185)))+~P1(f327(f327(f329(f921(x94183,x94183)),f327(f327(f252(x94183,x94183),x94187),x94186)),x94185)) % 177.41/177.20 [10448]~P6(x104489,x104488,x104487)+~P6(x104481,x1044811,x1044810)+~P10(x104481,x104489,f922(x104486,a910),x1044810,x104487,x104485)+P1(f327(f327(f329(x104481),f512(x104482,x104483,x104484,x104485,x104486,x104487,x104488,x104489,x1044810,x1044811,x104481)),x1044811))+~P1(f327(f327(f329(f922(x104489,a910)),x104483),f327(f327(f61(x104489),x104488),x104487)))+~P1(f327(f327(f329(f922(x104481,a910)),x104484),f327(f327(f61(x104481),x1044811),x1044810)))+P1(f327(f327(f329(f922(x104486,a910)),f327(f327(f40(x104481,f922(x104486,a910)),x104484),f327(f327(f8(f922(x104489,f922(x104486,a910)),f922(x104486,a910),x104481),f327(f40(x104489,f922(x104486,a910)),x104483)),x104485))),x104482)) % 177.41/177.20 [10449]~P6(x1044911,x1044910,x104499)+~P6(x104491,x104498,x104497)+~P10(x1044911,x104491,f922(x104496,a910),x104499,x104497,x104495)+P1(f327(f327(f329(x104491),f513(x104492,x104493,x104494,x104495,x104496,x104497,x104498,x104491,x104499,x1044910,x1044911)),x104498))+~P1(f327(f327(f329(f922(x1044911,a910)),x104494),f327(f327(f61(x1044911),x1044910),x104499)))+~P1(f327(f327(f329(f922(x104491,a910)),x104493),f327(f327(f61(x104491),x104498),x104497)))+P1(f327(f327(f329(f922(x104496,a910)),f327(f327(f40(x1044911,f922(x104496,a910)),x104494),f327(f327(f8(f922(x104491,f922(x104496,a910)),f922(x104496,a910),x1044911),f327(f40(x104491,f922(x104496,a910)),x104493)),x104495))),x104492)) % 177.41/177.20 [10450]~P6(x104502,x104508,x104509)+~P6(x104504,x1045010,x1045011)+~P10(x104502,x104504,f922(x104501,a910),x104509,x1045011,x104506)+~P1(f327(f327(f329(f922(x104502,a910)),x104503),f327(f327(f61(x104502),x104508),x104509)))+~P1(f327(f327(f329(f922(x104504,a910)),x104505),f327(f327(f61(x104504),x1045010),x1045011)))+~P1(f327(f327(f329(f922(x104501,a910)),f327(f327(x104506,f512(x104507,x104505,x104503,x104506,x104501,x1045011,x1045010,x104504,x104509,x104508,x104502)),f513(x104507,x104505,x104503,x104506,x104501,x1045011,x1045010,x104504,x104509,x104508,x104502))),x104507))+P1(f327(f327(f329(f922(x104501,a910)),f327(f327(f40(x104502,f922(x104501,a910)),x104503),f327(f327(f8(f922(x104504,f922(x104501,a910)),f922(x104501,a910),x104502),f327(f40(x104504,f922(x104501,a910)),x104505)),x104506))),x104507)) % 177.41/177.20 [9318]E(x93181,x93182)+~P108(x93184)+~P23(x93183,x93184,x93185,f327(f327(f102(f922(x93183,a910)),f327(f173(x93183),x93181)),f327(f173(x93183),x93182)))+~E(f327(f173(x93183),x93181),f327(f173(x93183),x93182))+~P11(x93184,f327(f327(f155(x93183,x93184),x93185),x93182))+~P11(x93184,f327(f327(f155(x93183,x93184),x93185),x93181))+~P1(f327(f138(x93184),f327(f327(f155(x93183,x93184),x93185),x93182)))+~P1(f327(f138(x93184),f327(f327(f155(x93183,x93184),x93185),x93181))) % 177.41/177.20 %EqnAxiom % 177.41/177.20 [1]E(x11,x11) % 177.41/177.20 [2]E(x22,x21)+~E(x21,x22) % 177.41/177.20 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 177.41/177.20 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 177.41/177.20 [5]~E(x51,x52)+E(f101(x51),f101(x52)) % 177.41/177.20 [6]~E(x61,x62)+E(f23(x61),f23(x62)) % 177.41/177.20 [7]~E(x71,x72)+E(f189(x71),f189(x72)) % 177.41/177.20 [8]~E(x81,x82)+E(f102(x81),f102(x82)) % 177.41/177.20 [9]~E(x91,x92)+E(f238(x91),f238(x92)) % 177.41/177.20 [10]~E(x101,x102)+E(f103(x101),f103(x102)) % 177.41/177.20 [11]~E(x111,x112)+E(f190(x111),f190(x112)) % 177.41/177.20 [12]~E(x121,x122)+E(f327(x121,x123),f327(x122,x123)) % 177.41/177.20 [13]~E(x131,x132)+E(f327(x133,x131),f327(x133,x132)) % 177.41/177.20 [14]~E(x141,x142)+E(f28(x141),f28(x142)) % 177.41/177.20 [15]~E(x151,x152)+E(f918(x151),f918(x152)) % 177.41/177.20 [16]~E(x161,x162)+E(f104(x161),f104(x162)) % 177.41/177.20 [17]~E(x171,x172)+E(f31(x171),f31(x172)) % 177.41/177.20 [18]~E(x181,x182)+E(f84(x181),f84(x182)) % 177.41/177.20 [19]~E(x191,x192)+E(f917(x191),f917(x192)) % 177.41/177.20 [20]~E(x201,x202)+E(f916(x201),f916(x202)) % 177.41/177.20 [21]~E(x211,x212)+E(f513(x211,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112),f513(x212,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112)) % 177.41/177.20 [22]~E(x221,x222)+E(f513(x223,x221,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f513(x223,x222,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212)) % 177.41/177.20 [23]~E(x231,x232)+E(f513(x233,x234,x231,x235,x236,x237,x238,x239,x2310,x2311,x2312),f513(x233,x234,x232,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 177.41/177.20 [24]~E(x241,x242)+E(f513(x243,x244,x245,x241,x246,x247,x248,x249,x2410,x2411,x2412),f513(x243,x244,x245,x242,x246,x247,x248,x249,x2410,x2411,x2412)) % 177.41/177.20 [25]~E(x251,x252)+E(f513(x253,x254,x255,x256,x251,x257,x258,x259,x2510,x2511,x2512),f513(x253,x254,x255,x256,x252,x257,x258,x259,x2510,x2511,x2512)) % 177.41/177.20 [26]~E(x261,x262)+E(f513(x263,x264,x265,x266,x267,x261,x268,x269,x2610,x2611,x2612),f513(x263,x264,x265,x266,x267,x262,x268,x269,x2610,x2611,x2612)) % 177.41/177.20 [27]~E(x271,x272)+E(f513(x273,x274,x275,x276,x277,x278,x271,x279,x2710,x2711,x2712),f513(x273,x274,x275,x276,x277,x278,x272,x279,x2710,x2711,x2712)) % 177.41/177.20 [28]~E(x281,x282)+E(f513(x283,x284,x285,x286,x287,x288,x289,x281,x2810,x2811,x2812),f513(x283,x284,x285,x286,x287,x288,x289,x282,x2810,x2811,x2812)) % 177.41/177.20 [29]~E(x291,x292)+E(f513(x293,x294,x295,x296,x297,x298,x299,x2910,x291,x2911,x2912),f513(x293,x294,x295,x296,x297,x298,x299,x2910,x292,x2911,x2912)) % 177.41/177.20 [30]~E(x301,x302)+E(f513(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x301,x3012),f513(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x302,x3012)) % 177.41/177.20 [31]~E(x311,x312)+E(f513(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x311),f513(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x312)) % 177.41/177.20 [32]~E(x321,x322)+E(f78(x321),f78(x322)) % 177.41/177.20 [33]~E(x331,x332)+E(f921(x331,x333),f921(x332,x333)) % 177.41/177.20 [34]~E(x341,x342)+E(f921(x343,x341),f921(x343,x342)) % 177.41/177.20 [35]~E(x351,x352)+E(f512(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f512(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512)) % 177.41/177.20 [36]~E(x361,x362)+E(f512(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f512(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 177.41/177.20 [37]~E(x371,x372)+E(f512(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f512(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 177.41/177.20 [38]~E(x381,x382)+E(f512(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f512(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812)) % 177.41/177.20 [39]~E(x391,x392)+E(f512(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f512(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912)) % 177.41/177.20 [40]~E(x401,x402)+E(f512(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f512(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012)) % 177.41/177.20 [41]~E(x411,x412)+E(f512(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f512(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112)) % 177.41/177.20 [42]~E(x421,x422)+E(f512(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f512(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212)) % 177.41/177.20 [43]~E(x431,x432)+E(f512(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f512(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312)) % 177.41/177.20 [44]~E(x441,x442)+E(f512(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f512(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412)) % 177.41/177.20 [45]~E(x451,x452)+E(f512(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f512(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452)) % 177.41/177.20 [46]~E(x461,x462)+E(f4(x461),f4(x462)) % 177.41/177.20 [47]~E(x471,x472)+E(f329(x471),f329(x472)) % 177.41/177.20 [48]~E(x481,x482)+E(f922(x481,x483),f922(x482,x483)) % 177.41/177.20 [49]~E(x491,x492)+E(f922(x493,x491),f922(x493,x492)) % 177.41/177.20 [50]~E(x501,x502)+E(f112(x501),f112(x502)) % 177.41/177.20 [51]~E(x511,x512)+E(f81(x511),f81(x512)) % 177.41/177.20 [52]~E(x521,x522)+E(f913(x521),f913(x522)) % 177.41/177.20 [53]~E(x531,x532)+E(f234(x531),f234(x532)) % 177.41/177.20 [54]~E(x541,x542)+E(f65(x541,x543,x544),f65(x542,x543,x544)) % 177.41/177.20 [55]~E(x551,x552)+E(f65(x553,x551,x554),f65(x553,x552,x554)) % 177.41/177.20 [56]~E(x561,x562)+E(f65(x563,x564,x561),f65(x563,x564,x562)) % 177.41/177.20 [57]~E(x571,x572)+E(f309(x571),f309(x572)) % 177.41/177.20 [58]~E(x581,x582)+E(f79(x581),f79(x582)) % 177.41/177.20 [59]~E(x591,x592)+E(f165(x591),f165(x592)) % 177.41/177.20 [60]~E(x601,x602)+E(f191(x601),f191(x602)) % 177.41/177.20 [61]~E(x611,x612)+E(f114(x611),f114(x612)) % 177.41/177.20 [62]~E(x621,x622)+E(f105(x621),f105(x622)) % 177.41/177.20 [63]~E(x631,x632)+E(f571(x631,x633,x634),f571(x632,x633,x634)) % 177.41/177.20 [64]~E(x641,x642)+E(f571(x643,x641,x644),f571(x643,x642,x644)) % 177.41/177.20 [65]~E(x651,x652)+E(f571(x653,x654,x651),f571(x653,x654,x652)) % 177.41/177.20 [66]~E(x661,x662)+E(f80(x661),f80(x662)) % 177.41/177.20 [67]~E(x671,x672)+E(f7(x671,x673,x674),f7(x672,x673,x674)) % 177.41/177.20 [68]~E(x681,x682)+E(f7(x683,x681,x684),f7(x683,x682,x684)) % 177.41/177.20 [69]~E(x691,x692)+E(f7(x693,x694,x691),f7(x693,x694,x692)) % 177.41/177.20 [70]~E(x701,x702)+E(f235(x701),f235(x702)) % 177.41/177.20 [71]~E(x711,x712)+E(f307(x711,x713),f307(x712,x713)) % 177.41/177.20 [72]~E(x721,x722)+E(f307(x723,x721),f307(x723,x722)) % 177.41/177.20 [73]~E(x731,x732)+E(f851(x731,x733,x734),f851(x732,x733,x734)) % 177.41/177.20 [74]~E(x741,x742)+E(f851(x743,x741,x744),f851(x743,x742,x744)) % 177.41/177.20 [75]~E(x751,x752)+E(f851(x753,x754,x751),f851(x753,x754,x752)) % 177.41/177.20 [76]~E(x761,x762)+E(f287(x761),f287(x762)) % 177.41/177.20 [77]~E(x771,x772)+E(f244(x771),f244(x772)) % 177.41/177.20 [78]~E(x781,x782)+E(f416(x781,x783),f416(x782,x783)) % 177.41/177.20 [79]~E(x791,x792)+E(f416(x793,x791),f416(x793,x792)) % 177.41/177.20 [80]~E(x801,x802)+E(f37(x801),f37(x802)) % 177.41/177.20 [81]~E(x811,x812)+E(f257(x811,x813,x814),f257(x812,x813,x814)) % 177.41/177.20 [82]~E(x821,x822)+E(f257(x823,x821,x824),f257(x823,x822,x824)) % 177.41/177.20 [83]~E(x831,x832)+E(f257(x833,x834,x831),f257(x833,x834,x832)) % 177.41/177.20 [84]~E(x841,x842)+E(f160(x841,x843),f160(x842,x843)) % 177.41/177.20 [85]~E(x851,x852)+E(f160(x853,x851),f160(x853,x852)) % 177.41/177.20 [86]~E(x861,x862)+E(f61(x861),f61(x862)) % 177.41/177.20 [87]~E(x871,x872)+E(f8(x871,x873,x874),f8(x872,x873,x874)) % 177.41/177.20 [88]~E(x881,x882)+E(f8(x883,x881,x884),f8(x883,x882,x884)) % 177.41/177.20 [89]~E(x891,x892)+E(f8(x893,x894,x891),f8(x893,x894,x892)) % 177.41/177.20 [90]~E(x901,x902)+E(f178(x901,x903,x904),f178(x902,x903,x904)) % 177.41/177.20 [91]~E(x911,x912)+E(f178(x913,x911,x914),f178(x913,x912,x914)) % 177.41/177.20 [92]~E(x921,x922)+E(f178(x923,x924,x921),f178(x923,x924,x922)) % 177.41/177.20 [93]~E(x931,x932)+E(f16(x931,x933),f16(x932,x933)) % 177.41/177.20 [94]~E(x941,x942)+E(f16(x943,x941),f16(x943,x942)) % 177.41/177.20 [95]~E(x951,x952)+E(f46(x951,x953,x954),f46(x952,x953,x954)) % 177.41/177.20 [96]~E(x961,x962)+E(f46(x963,x961,x964),f46(x963,x962,x964)) % 177.41/177.20 [97]~E(x971,x972)+E(f46(x973,x974,x971),f46(x973,x974,x972)) % 177.41/177.20 [98]~E(x981,x982)+E(f111(x981),f111(x982)) % 177.41/177.20 [99]~E(x991,x992)+E(f252(x991,x993),f252(x992,x993)) % 177.41/177.20 [100]~E(x1001,x1002)+E(f252(x1003,x1001),f252(x1003,x1002)) % 177.41/177.20 [101]~E(x1011,x1012)+E(f729(x1011,x1013),f729(x1012,x1013)) % 177.41/177.20 [102]~E(x1021,x1022)+E(f729(x1023,x1021),f729(x1023,x1022)) % 177.41/177.20 [103]~E(x1031,x1032)+E(f282(x1031),f282(x1032)) % 177.41/177.20 [104]~E(x1041,x1042)+E(f97(x1041),f97(x1042)) % 177.41/177.20 [105]~E(x1051,x1052)+E(f303(x1051,x1053,x1054),f303(x1052,x1053,x1054)) % 177.41/177.20 [106]~E(x1061,x1062)+E(f303(x1063,x1061,x1064),f303(x1063,x1062,x1064)) % 177.41/177.20 [107]~E(x1071,x1072)+E(f303(x1073,x1074,x1071),f303(x1073,x1074,x1072)) % 177.41/177.20 [108]~E(x1081,x1082)+E(f408(x1081,x1083),f408(x1082,x1083)) % 177.41/177.20 [109]~E(x1091,x1092)+E(f408(x1093,x1091),f408(x1093,x1092)) % 177.41/177.20 [110]~E(x1101,x1102)+E(f173(x1101),f173(x1102)) % 177.41/177.20 [111]~E(x1111,x1112)+E(f262(x1111),f262(x1112)) % 177.41/177.20 [112]~E(x1121,x1122)+E(f148(x1121,x1123),f148(x1122,x1123)) % 177.41/177.20 [113]~E(x1131,x1132)+E(f148(x1133,x1131),f148(x1133,x1132)) % 177.41/177.20 [114]~E(x1141,x1142)+E(f9(x1141,x1143),f9(x1142,x1143)) % 177.41/177.20 [115]~E(x1151,x1152)+E(f9(x1153,x1151),f9(x1153,x1152)) % 177.41/177.20 [116]~E(x1161,x1162)+E(f152(x1161),f152(x1162)) % 177.41/177.20 [117]~E(x1171,x1172)+E(f490(x1171,x1173),f490(x1172,x1173)) % 177.41/177.20 [118]~E(x1181,x1182)+E(f490(x1183,x1181),f490(x1183,x1182)) % 177.41/177.20 [119]~E(x1191,x1192)+E(f310(x1191,x1193,x1194),f310(x1192,x1193,x1194)) % 177.41/177.20 [120]~E(x1201,x1202)+E(f310(x1203,x1201,x1204),f310(x1203,x1202,x1204)) % 177.41/177.20 [121]~E(x1211,x1212)+E(f310(x1213,x1214,x1211),f310(x1213,x1214,x1212)) % 177.41/177.20 [122]~E(x1221,x1222)+E(f6(x1221,x1223),f6(x1222,x1223)) % 177.41/177.20 [123]~E(x1231,x1232)+E(f6(x1233,x1231),f6(x1233,x1232)) % 177.41/177.20 [124]~E(x1241,x1242)+E(f289(x1241,x1243,x1244),f289(x1242,x1243,x1244)) % 177.41/177.20 [125]~E(x1251,x1252)+E(f289(x1253,x1251,x1254),f289(x1253,x1252,x1254)) % 177.41/177.20 [126]~E(x1261,x1262)+E(f289(x1263,x1264,x1261),f289(x1263,x1264,x1262)) % 177.41/177.20 [127]~E(x1271,x1272)+E(f285(x1271,x1273,x1274),f285(x1272,x1273,x1274)) % 177.41/177.20 [128]~E(x1281,x1282)+E(f285(x1283,x1281,x1284),f285(x1283,x1282,x1284)) % 177.41/177.20 [129]~E(x1291,x1292)+E(f285(x1293,x1294,x1291),f285(x1293,x1294,x1292)) % 177.41/177.20 [130]~E(x1301,x1302)+E(f72(x1301,x1303,x1304,x1305),f72(x1302,x1303,x1304,x1305)) % 177.41/177.20 [131]~E(x1311,x1312)+E(f72(x1313,x1311,x1314,x1315),f72(x1313,x1312,x1314,x1315)) % 177.41/177.20 [132]~E(x1321,x1322)+E(f72(x1323,x1324,x1321,x1325),f72(x1323,x1324,x1322,x1325)) % 177.41/177.20 [133]~E(x1331,x1332)+E(f72(x1333,x1334,x1335,x1331),f72(x1333,x1334,x1335,x1332)) % 177.41/177.20 [134]~E(x1341,x1342)+E(f570(x1341,x1343,x1344),f570(x1342,x1343,x1344)) % 177.41/177.20 [135]~E(x1351,x1352)+E(f570(x1353,x1351,x1354),f570(x1353,x1352,x1354)) % 177.41/177.20 [136]~E(x1361,x1362)+E(f570(x1363,x1364,x1361),f570(x1363,x1364,x1362)) % 177.41/177.20 [137]~E(x1371,x1372)+E(f306(x1371,x1373,x1374),f306(x1372,x1373,x1374)) % 177.41/177.20 [138]~E(x1381,x1382)+E(f306(x1383,x1381,x1384),f306(x1383,x1382,x1384)) % 177.41/177.20 [139]~E(x1391,x1392)+E(f306(x1393,x1394,x1391),f306(x1393,x1394,x1392)) % 177.41/177.20 [140]~E(x1401,x1402)+E(f57(x1401),f57(x1402)) % 177.41/177.20 [141]~E(x1411,x1412)+E(f139(x1411),f139(x1412)) % 177.41/177.20 [142]~E(x1421,x1422)+E(f12(x1421,x1423,x1424),f12(x1422,x1423,x1424)) % 177.41/177.20 [143]~E(x1431,x1432)+E(f12(x1433,x1431,x1434),f12(x1433,x1432,x1434)) % 177.41/177.20 [144]~E(x1441,x1442)+E(f12(x1443,x1444,x1441),f12(x1443,x1444,x1442)) % 177.41/177.20 [145]~E(x1451,x1452)+E(f107(x1451),f107(x1452)) % 177.41/177.20 [146]~E(x1461,x1462)+E(f109(x1461),f109(x1462)) % 177.41/177.20 [147]~E(x1471,x1472)+E(f328(x1471),f328(x1472)) % 177.41/177.20 [148]~E(x1481,x1482)+E(f790(x1481,x1483,x1484,x1485),f790(x1482,x1483,x1484,x1485)) % 177.41/177.20 [149]~E(x1491,x1492)+E(f790(x1493,x1491,x1494,x1495),f790(x1493,x1492,x1494,x1495)) % 177.41/177.20 [150]~E(x1501,x1502)+E(f790(x1503,x1504,x1501,x1505),f790(x1503,x1504,x1502,x1505)) % 177.41/177.20 [151]~E(x1511,x1512)+E(f790(x1513,x1514,x1515,x1511),f790(x1513,x1514,x1515,x1512)) % 177.41/177.20 [152]~E(x1521,x1522)+E(f572(x1521),f572(x1522)) % 177.41/177.20 [153]~E(x1531,x1532)+E(f472(x1531,x1533,x1534),f472(x1532,x1533,x1534)) % 177.41/177.20 [154]~E(x1541,x1542)+E(f472(x1543,x1541,x1544),f472(x1543,x1542,x1544)) % 177.41/177.20 [155]~E(x1551,x1552)+E(f472(x1553,x1554,x1551),f472(x1553,x1554,x1552)) % 177.41/177.20 [156]~E(x1561,x1562)+E(f40(x1561,x1563),f40(x1562,x1563)) % 177.41/177.20 [157]~E(x1571,x1572)+E(f40(x1573,x1571),f40(x1573,x1572)) % 177.41/177.20 [158]~E(x1581,x1582)+E(f241(x1581,x1583),f241(x1582,x1583)) % 177.41/177.20 [159]~E(x1591,x1592)+E(f241(x1593,x1591),f241(x1593,x1592)) % 177.41/177.20 [160]~E(x1601,x1602)+E(f35(x1601),f35(x1602)) % 177.41/177.20 [161]~E(x1611,x1612)+E(f75(x1611),f75(x1612)) % 177.41/177.20 [162]~E(x1621,x1622)+E(f18(x1621,x1623,x1624),f18(x1622,x1623,x1624)) % 177.41/177.20 [163]~E(x1631,x1632)+E(f18(x1633,x1631,x1634),f18(x1633,x1632,x1634)) % 177.41/177.20 [164]~E(x1641,x1642)+E(f18(x1643,x1644,x1641),f18(x1643,x1644,x1642)) % 177.41/177.20 [165]~E(x1651,x1652)+E(f688(x1651,x1653,x1654),f688(x1652,x1653,x1654)) % 177.41/177.20 [166]~E(x1661,x1662)+E(f688(x1663,x1661,x1664),f688(x1663,x1662,x1664)) % 177.41/177.20 [167]~E(x1671,x1672)+E(f688(x1673,x1674,x1671),f688(x1673,x1674,x1672)) % 177.41/177.20 [168]~E(x1681,x1682)+E(f5(x1681),f5(x1682)) % 177.41/177.20 [169]~E(x1691,x1692)+E(f639(x1691,x1693,x1694,x1695,x1696,x1697),f639(x1692,x1693,x1694,x1695,x1696,x1697)) % 177.41/177.20 [170]~E(x1701,x1702)+E(f639(x1703,x1701,x1704,x1705,x1706,x1707),f639(x1703,x1702,x1704,x1705,x1706,x1707)) % 177.41/177.20 [171]~E(x1711,x1712)+E(f639(x1713,x1714,x1711,x1715,x1716,x1717),f639(x1713,x1714,x1712,x1715,x1716,x1717)) % 177.41/177.20 [172]~E(x1721,x1722)+E(f639(x1723,x1724,x1725,x1721,x1726,x1727),f639(x1723,x1724,x1725,x1722,x1726,x1727)) % 177.41/177.20 [173]~E(x1731,x1732)+E(f639(x1733,x1734,x1735,x1736,x1731,x1737),f639(x1733,x1734,x1735,x1736,x1732,x1737)) % 177.41/177.20 [174]~E(x1741,x1742)+E(f639(x1743,x1744,x1745,x1746,x1747,x1741),f639(x1743,x1744,x1745,x1746,x1747,x1742)) % 177.41/177.20 [175]~E(x1751,x1752)+E(f787(x1751,x1753),f787(x1752,x1753)) % 177.41/177.20 [176]~E(x1761,x1762)+E(f787(x1763,x1761),f787(x1763,x1762)) % 177.41/177.20 [177]~E(x1771,x1772)+E(f242(x1771),f242(x1772)) % 177.41/177.20 [178]~E(x1781,x1782)+E(f291(x1781),f291(x1782)) % 177.41/177.20 [179]~E(x1791,x1792)+E(f870(x1791,x1793,x1794,x1795),f870(x1792,x1793,x1794,x1795)) % 177.41/177.20 [180]~E(x1801,x1802)+E(f870(x1803,x1801,x1804,x1805),f870(x1803,x1802,x1804,x1805)) % 177.41/177.20 [181]~E(x1811,x1812)+E(f870(x1813,x1814,x1811,x1815),f870(x1813,x1814,x1812,x1815)) % 177.41/177.20 [182]~E(x1821,x1822)+E(f870(x1823,x1824,x1825,x1821),f870(x1823,x1824,x1825,x1822)) % 177.41/177.20 [183]~E(x1831,x1832)+E(f184(x1831,x1833),f184(x1832,x1833)) % 177.41/177.20 [184]~E(x1841,x1842)+E(f184(x1843,x1841),f184(x1843,x1842)) % 177.41/177.20 [185]~E(x1851,x1852)+E(f159(x1851,x1853),f159(x1852,x1853)) % 177.41/177.20 [186]~E(x1861,x1862)+E(f159(x1863,x1861),f159(x1863,x1862)) % 177.41/177.20 [187]~E(x1871,x1872)+E(f119(x1871,x1873,x1874),f119(x1872,x1873,x1874)) % 177.41/177.20 [188]~E(x1881,x1882)+E(f119(x1883,x1881,x1884),f119(x1883,x1882,x1884)) % 177.41/177.20 [189]~E(x1891,x1892)+E(f119(x1893,x1894,x1891),f119(x1893,x1894,x1892)) % 177.41/177.20 [190]~E(x1901,x1902)+E(f860(x1901,x1903,x1904),f860(x1902,x1903,x1904)) % 177.41/177.20 [191]~E(x1911,x1912)+E(f860(x1913,x1911,x1914),f860(x1913,x1912,x1914)) % 177.41/177.20 [192]~E(x1921,x1922)+E(f860(x1923,x1924,x1921),f860(x1923,x1924,x1922)) % 177.41/177.20 [193]~E(x1931,x1932)+E(f667(x1931,x1933),f667(x1932,x1933)) % 177.41/177.20 [194]~E(x1941,x1942)+E(f667(x1943,x1941),f667(x1943,x1942)) % 177.41/177.20 [195]~E(x1951,x1952)+E(f250(x1951,x1953,x1954),f250(x1952,x1953,x1954)) % 177.41/177.20 [196]~E(x1961,x1962)+E(f250(x1963,x1961,x1964),f250(x1963,x1962,x1964)) % 177.41/177.20 [197]~E(x1971,x1972)+E(f250(x1973,x1974,x1971),f250(x1973,x1974,x1972)) % 177.41/177.20 [198]~E(x1981,x1982)+E(f491(x1981,x1983),f491(x1982,x1983)) % 177.41/177.20 [199]~E(x1991,x1992)+E(f491(x1993,x1991),f491(x1993,x1992)) % 177.41/177.20 [200]~E(x2001,x2002)+E(f263(x2001,x2003),f263(x2002,x2003)) % 177.41/177.20 [201]~E(x2011,x2012)+E(f263(x2013,x2011),f263(x2013,x2012)) % 177.41/177.20 [202]~E(x2021,x2022)+E(f580(x2021,x2023,x2024),f580(x2022,x2023,x2024)) % 177.41/177.20 [203]~E(x2031,x2032)+E(f580(x2033,x2031,x2034),f580(x2033,x2032,x2034)) % 177.41/177.20 [204]~E(x2041,x2042)+E(f580(x2043,x2044,x2041),f580(x2043,x2044,x2042)) % 177.41/177.20 [205]~E(x2051,x2052)+E(f155(x2051,x2053),f155(x2052,x2053)) % 177.41/177.20 [206]~E(x2061,x2062)+E(f155(x2063,x2061),f155(x2063,x2062)) % 177.41/177.20 [207]~E(x2071,x2072)+E(f175(x2071,x2073,x2074),f175(x2072,x2073,x2074)) % 177.41/177.20 [208]~E(x2081,x2082)+E(f175(x2083,x2081,x2084),f175(x2083,x2082,x2084)) % 177.41/177.20 [209]~E(x2091,x2092)+E(f175(x2093,x2094,x2091),f175(x2093,x2094,x2092)) % 177.41/177.20 [210]~E(x2101,x2102)+E(f135(x2101),f135(x2102)) % 177.41/177.20 [211]~E(x2111,x2112)+E(f87(x2111),f87(x2112)) % 177.41/177.20 [212]~E(x2121,x2122)+E(f231(x2121,x2123,x2124,x2125),f231(x2122,x2123,x2124,x2125)) % 177.41/177.20 [213]~E(x2131,x2132)+E(f231(x2133,x2131,x2134,x2135),f231(x2133,x2132,x2134,x2135)) % 177.41/177.20 [214]~E(x2141,x2142)+E(f231(x2143,x2144,x2141,x2145),f231(x2143,x2144,x2142,x2145)) % 177.41/177.20 [215]~E(x2151,x2152)+E(f231(x2153,x2154,x2155,x2151),f231(x2153,x2154,x2155,x2152)) % 177.41/177.20 [216]~E(x2161,x2162)+E(f153(x2161,x2163),f153(x2162,x2163)) % 177.41/177.20 [217]~E(x2171,x2172)+E(f153(x2173,x2171),f153(x2173,x2172)) % 177.41/177.20 [218]~E(x2181,x2182)+E(f60(x2181,x2183,x2184,x2185),f60(x2182,x2183,x2184,x2185)) % 177.41/177.20 [219]~E(x2191,x2192)+E(f60(x2193,x2191,x2194,x2195),f60(x2193,x2192,x2194,x2195)) % 177.41/177.20 [220]~E(x2201,x2202)+E(f60(x2203,x2204,x2201,x2205),f60(x2203,x2204,x2202,x2205)) % 177.41/177.20 [221]~E(x2211,x2212)+E(f60(x2213,x2214,x2215,x2211),f60(x2213,x2214,x2215,x2212)) % 177.41/177.20 [222]~E(x2221,x2222)+E(f316(x2221,x2223),f316(x2222,x2223)) % 177.41/177.20 [223]~E(x2231,x2232)+E(f316(x2233,x2231),f316(x2233,x2232)) % 177.41/177.20 [224]~E(x2241,x2242)+E(f138(x2241),f138(x2242)) % 177.41/177.20 [225]~E(x2251,x2252)+E(f38(x2251,x2253),f38(x2252,x2253)) % 177.41/177.20 [226]~E(x2261,x2262)+E(f38(x2263,x2261),f38(x2263,x2262)) % 177.41/177.20 [227]~E(x2271,x2272)+E(f91(x2271),f91(x2272)) % 177.41/177.20 [228]~E(x2281,x2282)+E(f281(x2281),f281(x2282)) % 177.41/177.20 [229]~E(x2291,x2292)+E(f49(x2291,x2293),f49(x2292,x2293)) % 177.41/177.20 [230]~E(x2301,x2302)+E(f49(x2303,x2301),f49(x2303,x2302)) % 177.41/177.20 [231]~E(x2311,x2312)+E(f179(x2311,x2313),f179(x2312,x2313)) % 177.41/177.20 [232]~E(x2321,x2322)+E(f179(x2323,x2321),f179(x2323,x2322)) % 177.41/177.20 [233]~E(x2331,x2332)+E(f64(x2331,x2333,x2334),f64(x2332,x2333,x2334)) % 177.41/177.20 [234]~E(x2341,x2342)+E(f64(x2343,x2341,x2344),f64(x2343,x2342,x2344)) % 177.41/177.20 [235]~E(x2351,x2352)+E(f64(x2353,x2354,x2351),f64(x2353,x2354,x2352)) % 177.41/177.20 [236]~E(x2361,x2362)+E(f169(x2361),f169(x2362)) % 177.41/177.20 [237]~E(x2371,x2372)+E(f802(x2371),f802(x2372)) % 177.41/177.20 [238]~E(x2381,x2382)+E(f149(x2381,x2383,x2384),f149(x2382,x2383,x2384)) % 177.41/177.20 [239]~E(x2391,x2392)+E(f149(x2393,x2391,x2394),f149(x2393,x2392,x2394)) % 177.41/177.20 [240]~E(x2401,x2402)+E(f149(x2403,x2404,x2401),f149(x2403,x2404,x2402)) % 177.41/177.20 [241]~E(x2411,x2412)+E(f245(x2411,x2413,x2414),f245(x2412,x2413,x2414)) % 177.41/177.20 [242]~E(x2421,x2422)+E(f245(x2423,x2421,x2424),f245(x2423,x2422,x2424)) % 177.41/177.20 [243]~E(x2431,x2432)+E(f245(x2433,x2434,x2431),f245(x2433,x2434,x2432)) % 177.41/177.20 [244]~E(x2441,x2442)+E(f92(x2441,x2443,x2444,x2445),f92(x2442,x2443,x2444,x2445)) % 177.41/177.20 [245]~E(x2451,x2452)+E(f92(x2453,x2451,x2454,x2455),f92(x2453,x2452,x2454,x2455)) % 177.41/177.20 [246]~E(x2461,x2462)+E(f92(x2463,x2464,x2461,x2465),f92(x2463,x2464,x2462,x2465)) % 177.41/177.20 [247]~E(x2471,x2472)+E(f92(x2473,x2474,x2475,x2471),f92(x2473,x2474,x2475,x2472)) % 177.41/177.20 [248]~E(x2481,x2482)+E(f344(x2481,x2483,x2484,x2485,x2486),f344(x2482,x2483,x2484,x2485,x2486)) % 177.41/177.20 [249]~E(x2491,x2492)+E(f344(x2493,x2491,x2494,x2495,x2496),f344(x2493,x2492,x2494,x2495,x2496)) % 177.41/177.20 [250]~E(x2501,x2502)+E(f344(x2503,x2504,x2501,x2505,x2506),f344(x2503,x2504,x2502,x2505,x2506)) % 177.41/177.20 [251]~E(x2511,x2512)+E(f344(x2513,x2514,x2515,x2511,x2516),f344(x2513,x2514,x2515,x2512,x2516)) % 177.41/177.20 [252]~E(x2521,x2522)+E(f344(x2523,x2524,x2525,x2526,x2521),f344(x2523,x2524,x2525,x2526,x2522)) % 177.41/177.20 [253]~E(x2531,x2532)+E(f36(x2531),f36(x2532)) % 177.41/177.20 [254]~E(x2541,x2542)+E(f115(x2541,x2543),f115(x2542,x2543)) % 177.41/177.20 [255]~E(x2551,x2552)+E(f115(x2553,x2551),f115(x2553,x2552)) % 177.41/177.20 [256]~E(x2561,x2562)+E(f424(x2561,x2563,x2564,x2565),f424(x2562,x2563,x2564,x2565)) % 177.41/177.20 [257]~E(x2571,x2572)+E(f424(x2573,x2571,x2574,x2575),f424(x2573,x2572,x2574,x2575)) % 177.41/177.20 [258]~E(x2581,x2582)+E(f424(x2583,x2584,x2581,x2585),f424(x2583,x2584,x2582,x2585)) % 177.41/177.20 [259]~E(x2591,x2592)+E(f424(x2593,x2594,x2595,x2591),f424(x2593,x2594,x2595,x2592)) % 177.41/177.20 [260]~E(x2601,x2602)+E(f39(x2601,x2603),f39(x2602,x2603)) % 177.41/177.20 [261]~E(x2611,x2612)+E(f39(x2613,x2611),f39(x2613,x2612)) % 177.41/177.20 [262]~E(x2621,x2622)+E(f140(x2621,x2623),f140(x2622,x2623)) % 177.41/177.20 [263]~E(x2631,x2632)+E(f140(x2633,x2631),f140(x2633,x2632)) % 177.41/177.20 [264]~E(x2641,x2642)+E(f315(x2641,x2643),f315(x2642,x2643)) % 177.41/177.20 [265]~E(x2651,x2652)+E(f315(x2653,x2651),f315(x2653,x2652)) % 177.41/177.20 [266]~E(x2661,x2662)+E(f193(x2661),f193(x2662)) % 177.41/177.20 [267]~E(x2671,x2672)+E(f506(x2671,x2673,x2674,x2675),f506(x2672,x2673,x2674,x2675)) % 177.41/177.20 [268]~E(x2681,x2682)+E(f506(x2683,x2681,x2684,x2685),f506(x2683,x2682,x2684,x2685)) % 177.41/177.20 [269]~E(x2691,x2692)+E(f506(x2693,x2694,x2691,x2695),f506(x2693,x2694,x2692,x2695)) % 177.41/177.20 [270]~E(x2701,x2702)+E(f506(x2703,x2704,x2705,x2701),f506(x2703,x2704,x2705,x2702)) % 177.41/177.20 [271]~E(x2711,x2712)+E(f116(x2711),f116(x2712)) % 177.41/177.20 [272]~E(x2721,x2722)+E(f920(x2721,x2723),f920(x2722,x2723)) % 177.41/177.20 [273]~E(x2731,x2732)+E(f920(x2733,x2731),f920(x2733,x2732)) % 177.41/177.20 [274]~E(x2741,x2742)+E(f857(x2741,x2743,x2744),f857(x2742,x2743,x2744)) % 177.41/177.20 [275]~E(x2751,x2752)+E(f857(x2753,x2751,x2754),f857(x2753,x2752,x2754)) % 177.41/177.20 [276]~E(x2761,x2762)+E(f857(x2763,x2764,x2761),f857(x2763,x2764,x2762)) % 177.41/177.20 [277]~E(x2771,x2772)+E(f919(x2771,x2773),f919(x2772,x2773)) % 177.41/177.20 [278]~E(x2781,x2782)+E(f919(x2783,x2781),f919(x2783,x2782)) % 177.41/177.20 [279]~E(x2791,x2792)+E(f168(x2791),f168(x2792)) % 177.41/177.20 [280]~E(x2801,x2802)+E(f176(x2801),f176(x2802)) % 177.41/177.20 [281]~E(x2811,x2812)+E(f62(x2811,x2813,x2814),f62(x2812,x2813,x2814)) % 177.41/177.20 [282]~E(x2821,x2822)+E(f62(x2823,x2821,x2824),f62(x2823,x2822,x2824)) % 177.41/177.20 [283]~E(x2831,x2832)+E(f62(x2833,x2834,x2831),f62(x2833,x2834,x2832)) % 177.41/177.20 [284]~E(x2841,x2842)+E(f799(x2841,x2843),f799(x2842,x2843)) % 177.41/177.20 [285]~E(x2851,x2852)+E(f799(x2853,x2851),f799(x2853,x2852)) % 177.41/177.20 [286]~E(x2861,x2862)+E(f172(x2861),f172(x2862)) % 177.41/177.20 [287]~E(x2871,x2872)+E(f272(x2871,x2873),f272(x2872,x2873)) % 177.41/177.20 [288]~E(x2881,x2882)+E(f272(x2883,x2881),f272(x2883,x2882)) % 177.41/177.20 [289]~E(x2891,x2892)+E(f779(x2891,x2893,x2894,x2895),f779(x2892,x2893,x2894,x2895)) % 177.41/177.20 [290]~E(x2901,x2902)+E(f779(x2903,x2901,x2904,x2905),f779(x2903,x2902,x2904,x2905)) % 177.41/177.20 [291]~E(x2911,x2912)+E(f779(x2913,x2914,x2911,x2915),f779(x2913,x2914,x2912,x2915)) % 177.41/177.20 [292]~E(x2921,x2922)+E(f779(x2923,x2924,x2925,x2921),f779(x2923,x2924,x2925,x2922)) % 177.41/177.20 [293]~E(x2931,x2932)+E(f858(x2931,x2933,x2934),f858(x2932,x2933,x2934)) % 177.41/177.20 [294]~E(x2941,x2942)+E(f858(x2943,x2941,x2944),f858(x2943,x2942,x2944)) % 177.41/177.20 [295]~E(x2951,x2952)+E(f858(x2953,x2954,x2951),f858(x2953,x2954,x2952)) % 177.41/177.20 [296]~E(x2961,x2962)+E(f302(x2961,x2963),f302(x2962,x2963)) % 177.41/177.20 [297]~E(x2971,x2972)+E(f302(x2973,x2971),f302(x2973,x2972)) % 177.41/177.20 [298]~E(x2981,x2982)+E(f530(x2981),f530(x2982)) % 177.41/177.20 [299]~E(x2991,x2992)+E(f158(x2991,x2993),f158(x2992,x2993)) % 177.41/177.20 [300]~E(x3001,x3002)+E(f158(x3003,x3001),f158(x3003,x3002)) % 177.41/177.20 [301]~E(x3011,x3012)+E(f82(x3011,x3013),f82(x3012,x3013)) % 177.41/177.20 [302]~E(x3021,x3022)+E(f82(x3023,x3021),f82(x3023,x3022)) % 177.41/177.20 [303]~E(x3031,x3032)+E(f68(x3031,x3033,x3034),f68(x3032,x3033,x3034)) % 177.41/177.20 [304]~E(x3041,x3042)+E(f68(x3043,x3041,x3044),f68(x3043,x3042,x3044)) % 177.41/177.20 [305]~E(x3051,x3052)+E(f68(x3053,x3054,x3051),f68(x3053,x3054,x3052)) % 177.41/177.20 [306]~E(x3061,x3062)+E(f137(x3061,x3063),f137(x3062,x3063)) % 177.41/177.20 [307]~E(x3071,x3072)+E(f137(x3073,x3071),f137(x3073,x3072)) % 177.41/177.20 [308]~E(x3081,x3082)+E(f468(x3081,x3083,x3084,x3085,x3086),f468(x3082,x3083,x3084,x3085,x3086)) % 177.51/177.20 [309]~E(x3091,x3092)+E(f468(x3093,x3091,x3094,x3095,x3096),f468(x3093,x3092,x3094,x3095,x3096)) % 177.51/177.20 [310]~E(x3101,x3102)+E(f468(x3103,x3104,x3101,x3105,x3106),f468(x3103,x3104,x3102,x3105,x3106)) % 177.51/177.20 [311]~E(x3111,x3112)+E(f468(x3113,x3114,x3115,x3111,x3116),f468(x3113,x3114,x3115,x3112,x3116)) % 177.51/177.20 [312]~E(x3121,x3122)+E(f468(x3123,x3124,x3125,x3126,x3121),f468(x3123,x3124,x3125,x3126,x3122)) % 177.51/177.20 [313]~E(x3131,x3132)+E(f214(x3131),f214(x3132)) % 177.51/177.20 [314]~E(x3141,x3142)+E(f256(x3141,x3143),f256(x3142,x3143)) % 177.51/177.20 [315]~E(x3151,x3152)+E(f256(x3153,x3151),f256(x3153,x3152)) % 177.51/177.20 [316]~E(x3161,x3162)+E(f318(x3161,x3163),f318(x3162,x3163)) % 177.51/177.20 [317]~E(x3171,x3172)+E(f318(x3173,x3171),f318(x3173,x3172)) % 177.51/177.20 [318]~E(x3181,x3182)+E(f410(x3181,x3183),f410(x3182,x3183)) % 177.51/177.20 [319]~E(x3191,x3192)+E(f410(x3193,x3191),f410(x3193,x3192)) % 177.51/177.20 [320]~E(x3201,x3202)+E(f319(x3201,x3203),f319(x3202,x3203)) % 177.51/177.20 [321]~E(x3211,x3212)+E(f319(x3213,x3211),f319(x3213,x3212)) % 177.51/177.20 [322]~E(x3221,x3222)+E(f143(x3221,x3223,x3224,x3225),f143(x3222,x3223,x3224,x3225)) % 177.51/177.20 [323]~E(x3231,x3232)+E(f143(x3233,x3231,x3234,x3235),f143(x3233,x3232,x3234,x3235)) % 177.51/177.20 [324]~E(x3241,x3242)+E(f143(x3243,x3244,x3241,x3245),f143(x3243,x3244,x3242,x3245)) % 177.51/177.20 [325]~E(x3251,x3252)+E(f143(x3253,x3254,x3255,x3251),f143(x3253,x3254,x3255,x3252)) % 177.51/177.20 [326]~E(x3261,x3262)+E(f661(x3261,x3263),f661(x3262,x3263)) % 177.51/177.20 [327]~E(x3271,x3272)+E(f661(x3273,x3271),f661(x3273,x3272)) % 177.51/177.20 [328]~E(x3281,x3282)+E(f610(x3281,x3283),f610(x3282,x3283)) % 177.51/177.20 [329]~E(x3291,x3292)+E(f610(x3293,x3291),f610(x3293,x3292)) % 177.51/177.20 [330]~E(x3301,x3302)+E(f721(x3301,x3303),f721(x3302,x3303)) % 177.51/177.20 [331]~E(x3311,x3312)+E(f721(x3313,x3311),f721(x3313,x3312)) % 177.51/177.20 [332]~E(x3321,x3322)+E(f389(x3321,x3323),f389(x3322,x3323)) % 177.51/177.20 [333]~E(x3331,x3332)+E(f389(x3333,x3331),f389(x3333,x3332)) % 177.51/177.20 [334]~E(x3341,x3342)+E(f526(x3341,x3343,x3344),f526(x3342,x3343,x3344)) % 177.51/177.20 [335]~E(x3351,x3352)+E(f526(x3353,x3351,x3354),f526(x3353,x3352,x3354)) % 177.51/177.20 [336]~E(x3361,x3362)+E(f526(x3363,x3364,x3361),f526(x3363,x3364,x3362)) % 177.51/177.20 [337]~E(x3371,x3372)+E(f284(x3371,x3373),f284(x3372,x3373)) % 177.51/177.20 [338]~E(x3381,x3382)+E(f284(x3383,x3381),f284(x3383,x3382)) % 177.51/177.20 [339]~E(x3391,x3392)+E(f48(x3391,x3393),f48(x3392,x3393)) % 177.51/177.20 [340]~E(x3401,x3402)+E(f48(x3403,x3401),f48(x3403,x3402)) % 177.51/177.20 [341]~E(x3411,x3412)+E(f142(x3411),f142(x3412)) % 177.51/177.20 [342]~E(x3421,x3422)+E(f403(x3421,x3423),f403(x3422,x3423)) % 177.51/177.20 [343]~E(x3431,x3432)+E(f403(x3433,x3431),f403(x3433,x3432)) % 177.51/177.20 [344]~E(x3441,x3442)+E(f446(x3441,x3443),f446(x3442,x3443)) % 177.51/177.20 [345]~E(x3451,x3452)+E(f446(x3453,x3451),f446(x3453,x3452)) % 177.51/177.20 [346]~E(x3461,x3462)+E(f632(x3461,x3463,x3464),f632(x3462,x3463,x3464)) % 177.51/177.20 [347]~E(x3471,x3472)+E(f632(x3473,x3471,x3474),f632(x3473,x3472,x3474)) % 177.51/177.20 [348]~E(x3481,x3482)+E(f632(x3483,x3484,x3481),f632(x3483,x3484,x3482)) % 177.51/177.20 [349]~E(x3491,x3492)+E(f321(x3491,x3493,x3494),f321(x3492,x3493,x3494)) % 177.51/177.20 [350]~E(x3501,x3502)+E(f321(x3503,x3501,x3504),f321(x3503,x3502,x3504)) % 177.51/177.20 [351]~E(x3511,x3512)+E(f321(x3513,x3514,x3511),f321(x3513,x3514,x3512)) % 177.51/177.20 [352]~E(x3521,x3522)+E(f259(x3521,x3523,x3524,x3525),f259(x3522,x3523,x3524,x3525)) % 177.51/177.20 [353]~E(x3531,x3532)+E(f259(x3533,x3531,x3534,x3535),f259(x3533,x3532,x3534,x3535)) % 177.51/177.20 [354]~E(x3541,x3542)+E(f259(x3543,x3544,x3541,x3545),f259(x3543,x3544,x3542,x3545)) % 177.51/177.20 [355]~E(x3551,x3552)+E(f259(x3553,x3554,x3555,x3551),f259(x3553,x3554,x3555,x3552)) % 177.51/177.20 [356]~E(x3561,x3562)+E(f286(x3561,x3563),f286(x3562,x3563)) % 177.51/177.20 [357]~E(x3571,x3572)+E(f286(x3573,x3571),f286(x3573,x3572)) % 177.51/177.20 [358]~E(x3581,x3582)+E(f347(x3581,x3583,x3584,x3585,x3586),f347(x3582,x3583,x3584,x3585,x3586)) % 177.51/177.20 [359]~E(x3591,x3592)+E(f347(x3593,x3591,x3594,x3595,x3596),f347(x3593,x3592,x3594,x3595,x3596)) % 177.51/177.20 [360]~E(x3601,x3602)+E(f347(x3603,x3604,x3601,x3605,x3606),f347(x3603,x3604,x3602,x3605,x3606)) % 177.51/177.20 [361]~E(x3611,x3612)+E(f347(x3613,x3614,x3615,x3611,x3616),f347(x3613,x3614,x3615,x3612,x3616)) % 177.51/177.20 [362]~E(x3621,x3622)+E(f347(x3623,x3624,x3625,x3626,x3621),f347(x3623,x3624,x3625,x3626,x3622)) % 177.51/177.20 [363]~E(x3631,x3632)+E(f120(x3631),f120(x3632)) % 177.51/177.20 [364]~E(x3641,x3642)+E(f121(x3641,x3643),f121(x3642,x3643)) % 177.51/177.20 [365]~E(x3651,x3652)+E(f121(x3653,x3651),f121(x3653,x3652)) % 177.51/177.20 [366]~E(x3661,x3662)+E(f14(x3661,x3663),f14(x3662,x3663)) % 177.51/177.20 [367]~E(x3671,x3672)+E(f14(x3673,x3671),f14(x3673,x3672)) % 177.51/177.20 [368]~E(x3681,x3682)+E(f304(x3681),f304(x3682)) % 177.51/177.20 [369]~E(x3691,x3692)+E(f756(x3691,x3693,x3694),f756(x3692,x3693,x3694)) % 177.51/177.20 [370]~E(x3701,x3702)+E(f756(x3703,x3701,x3704),f756(x3703,x3702,x3704)) % 177.51/177.20 [371]~E(x3711,x3712)+E(f756(x3713,x3714,x3711),f756(x3713,x3714,x3712)) % 177.51/177.20 [372]~E(x3721,x3722)+E(f778(x3721,x3723,x3724,x3725),f778(x3722,x3723,x3724,x3725)) % 177.51/177.20 [373]~E(x3731,x3732)+E(f778(x3733,x3731,x3734,x3735),f778(x3733,x3732,x3734,x3735)) % 177.51/177.20 [374]~E(x3741,x3742)+E(f778(x3743,x3744,x3741,x3745),f778(x3743,x3744,x3742,x3745)) % 177.51/177.20 [375]~E(x3751,x3752)+E(f778(x3753,x3754,x3755,x3751),f778(x3753,x3754,x3755,x3752)) % 177.51/177.20 [376]~E(x3761,x3762)+E(f85(x3761,x3763),f85(x3762,x3763)) % 177.51/177.20 [377]~E(x3771,x3772)+E(f85(x3773,x3771),f85(x3773,x3772)) % 177.51/177.20 [378]~E(x3781,x3782)+E(f850(x3781,x3783,x3784),f850(x3782,x3783,x3784)) % 177.51/177.20 [379]~E(x3791,x3792)+E(f850(x3793,x3791,x3794),f850(x3793,x3792,x3794)) % 177.51/177.20 [380]~E(x3801,x3802)+E(f850(x3803,x3804,x3801),f850(x3803,x3804,x3802)) % 177.51/177.20 [381]~E(x3811,x3812)+E(f90(x3811,x3813),f90(x3812,x3813)) % 177.51/177.20 [382]~E(x3821,x3822)+E(f90(x3823,x3821),f90(x3823,x3822)) % 177.51/177.20 [383]~E(x3831,x3832)+E(f41(x3831,x3833),f41(x3832,x3833)) % 177.51/177.20 [384]~E(x3841,x3842)+E(f41(x3843,x3841),f41(x3843,x3842)) % 177.51/177.20 [385]~E(x3851,x3852)+E(f154(x3851,x3853),f154(x3852,x3853)) % 177.51/177.20 [386]~E(x3861,x3862)+E(f154(x3863,x3861),f154(x3863,x3862)) % 177.51/177.20 [387]~E(x3871,x3872)+E(f457(x3871,x3873,x3874,x3875),f457(x3872,x3873,x3874,x3875)) % 177.51/177.20 [388]~E(x3881,x3882)+E(f457(x3883,x3881,x3884,x3885),f457(x3883,x3882,x3884,x3885)) % 177.51/177.20 [389]~E(x3891,x3892)+E(f457(x3893,x3894,x3891,x3895),f457(x3893,x3894,x3892,x3895)) % 177.51/177.20 [390]~E(x3901,x3902)+E(f457(x3903,x3904,x3905,x3901),f457(x3903,x3904,x3905,x3902)) % 177.51/177.20 [391]~E(x3911,x3912)+E(f248(x3911,x3913),f248(x3912,x3913)) % 177.51/177.20 [392]~E(x3921,x3922)+E(f248(x3923,x3921),f248(x3923,x3922)) % 177.51/177.20 [393]~E(x3931,x3932)+E(f51(x3931,x3933),f51(x3932,x3933)) % 177.51/177.20 [394]~E(x3941,x3942)+E(f51(x3943,x3941),f51(x3943,x3942)) % 177.51/177.20 [395]~E(x3951,x3952)+E(f483(x3951,x3953,x3954),f483(x3952,x3953,x3954)) % 177.51/177.20 [396]~E(x3961,x3962)+E(f483(x3963,x3961,x3964),f483(x3963,x3962,x3964)) % 177.51/177.20 [397]~E(x3971,x3972)+E(f483(x3973,x3974,x3971),f483(x3973,x3974,x3972)) % 177.51/177.20 [398]~E(x3981,x3982)+E(f141(x3981,x3983,x3984),f141(x3982,x3983,x3984)) % 177.51/177.20 [399]~E(x3991,x3992)+E(f141(x3993,x3991,x3994),f141(x3993,x3992,x3994)) % 177.51/177.20 [400]~E(x4001,x4002)+E(f141(x4003,x4004,x4001),f141(x4003,x4004,x4002)) % 177.51/177.20 [401]~E(x4011,x4012)+E(f633(x4011,x4013,x4014),f633(x4012,x4013,x4014)) % 177.51/177.20 [402]~E(x4021,x4022)+E(f633(x4023,x4021,x4024),f633(x4023,x4022,x4024)) % 177.51/177.20 [403]~E(x4031,x4032)+E(f633(x4033,x4034,x4031),f633(x4033,x4034,x4032)) % 177.51/177.20 [404]~E(x4041,x4042)+E(f486(x4041),f486(x4042)) % 177.51/177.20 [405]~E(x4051,x4052)+E(f251(x4051,x4053),f251(x4052,x4053)) % 177.51/177.20 [406]~E(x4061,x4062)+E(f251(x4063,x4061),f251(x4063,x4062)) % 177.51/177.20 [407]~E(x4071,x4072)+E(f311(x4071,x4073,x4074),f311(x4072,x4073,x4074)) % 177.51/177.20 [408]~E(x4081,x4082)+E(f311(x4083,x4081,x4084),f311(x4083,x4082,x4084)) % 177.51/177.20 [409]~E(x4091,x4092)+E(f311(x4093,x4094,x4091),f311(x4093,x4094,x4092)) % 177.51/177.20 [410]~E(x4101,x4102)+E(f171(x4101,x4103,x4104),f171(x4102,x4103,x4104)) % 177.51/177.20 [411]~E(x4111,x4112)+E(f171(x4113,x4111,x4114),f171(x4113,x4112,x4114)) % 177.51/177.20 [412]~E(x4121,x4122)+E(f171(x4123,x4124,x4121),f171(x4123,x4124,x4122)) % 177.51/177.20 [413]~E(x4131,x4132)+E(f151(x4131,x4133,x4134,x4135),f151(x4132,x4133,x4134,x4135)) % 177.51/177.20 [414]~E(x4141,x4142)+E(f151(x4143,x4141,x4144,x4145),f151(x4143,x4142,x4144,x4145)) % 177.51/177.20 [415]~E(x4151,x4152)+E(f151(x4153,x4154,x4151,x4155),f151(x4153,x4154,x4152,x4155)) % 177.51/177.20 [416]~E(x4161,x4162)+E(f151(x4163,x4164,x4165,x4161),f151(x4163,x4164,x4165,x4162)) % 177.51/177.20 [417]~E(x4171,x4172)+E(f745(x4171,x4173),f745(x4172,x4173)) % 177.51/177.20 [418]~E(x4181,x4182)+E(f745(x4183,x4181),f745(x4183,x4182)) % 177.51/177.20 [419]~E(x4191,x4192)+E(f560(x4191,x4193,x4194),f560(x4192,x4193,x4194)) % 177.51/177.20 [420]~E(x4201,x4202)+E(f560(x4203,x4201,x4204),f560(x4203,x4202,x4204)) % 177.51/177.20 [421]~E(x4211,x4212)+E(f560(x4213,x4214,x4211),f560(x4213,x4214,x4212)) % 177.51/177.20 [422]~E(x4221,x4222)+E(f662(x4221,x4223),f662(x4222,x4223)) % 177.51/177.20 [423]~E(x4231,x4232)+E(f662(x4233,x4231),f662(x4233,x4232)) % 177.51/177.20 [424]~E(x4241,x4242)+E(f132(x4241,x4243,x4244,x4245),f132(x4242,x4243,x4244,x4245)) % 177.51/177.20 [425]~E(x4251,x4252)+E(f132(x4253,x4251,x4254,x4255),f132(x4253,x4252,x4254,x4255)) % 177.51/177.20 [426]~E(x4261,x4262)+E(f132(x4263,x4264,x4261,x4265),f132(x4263,x4264,x4262,x4265)) % 177.51/177.20 [427]~E(x4271,x4272)+E(f132(x4273,x4274,x4275,x4271),f132(x4273,x4274,x4275,x4272)) % 177.51/177.20 [428]~E(x4281,x4282)+E(f663(x4281,x4283,x4284),f663(x4282,x4283,x4284)) % 177.51/177.20 [429]~E(x4291,x4292)+E(f663(x4293,x4291,x4294),f663(x4293,x4292,x4294)) % 177.51/177.20 [430]~E(x4301,x4302)+E(f663(x4303,x4304,x4301),f663(x4303,x4304,x4302)) % 177.51/177.20 [431]~E(x4311,x4312)+E(f754(x4311,x4313,x4314),f754(x4312,x4313,x4314)) % 177.51/177.20 [432]~E(x4321,x4322)+E(f754(x4323,x4321,x4324),f754(x4323,x4322,x4324)) % 177.51/177.20 [433]~E(x4331,x4332)+E(f754(x4333,x4334,x4331),f754(x4333,x4334,x4332)) % 177.51/177.20 [434]~E(x4341,x4342)+E(f258(x4341,x4343,x4344,x4345,x4346,x4347),f258(x4342,x4343,x4344,x4345,x4346,x4347)) % 177.51/177.20 [435]~E(x4351,x4352)+E(f258(x4353,x4351,x4354,x4355,x4356,x4357),f258(x4353,x4352,x4354,x4355,x4356,x4357)) % 177.51/177.20 [436]~E(x4361,x4362)+E(f258(x4363,x4364,x4361,x4365,x4366,x4367),f258(x4363,x4364,x4362,x4365,x4366,x4367)) % 177.51/177.20 [437]~E(x4371,x4372)+E(f258(x4373,x4374,x4375,x4371,x4376,x4377),f258(x4373,x4374,x4375,x4372,x4376,x4377)) % 177.51/177.20 [438]~E(x4381,x4382)+E(f258(x4383,x4384,x4385,x4386,x4381,x4387),f258(x4383,x4384,x4385,x4386,x4382,x4387)) % 177.51/177.20 [439]~E(x4391,x4392)+E(f258(x4393,x4394,x4395,x4396,x4397,x4391),f258(x4393,x4394,x4395,x4396,x4397,x4392)) % 177.51/177.20 [440]~E(x4401,x4402)+E(f86(x4401,x4403),f86(x4402,x4403)) % 177.51/177.20 [441]~E(x4411,x4412)+E(f86(x4413,x4411),f86(x4413,x4412)) % 177.51/177.20 [442]~E(x4421,x4422)+E(f10(x4421,x4423),f10(x4422,x4423)) % 177.51/177.20 [443]~E(x4431,x4432)+E(f10(x4433,x4431),f10(x4433,x4432)) % 177.51/177.20 [444]~E(x4441,x4442)+E(f640(x4441,x4443,x4444,x4445,x4446,x4447),f640(x4442,x4443,x4444,x4445,x4446,x4447)) % 177.51/177.20 [445]~E(x4451,x4452)+E(f640(x4453,x4451,x4454,x4455,x4456,x4457),f640(x4453,x4452,x4454,x4455,x4456,x4457)) % 177.51/177.20 [446]~E(x4461,x4462)+E(f640(x4463,x4464,x4461,x4465,x4466,x4467),f640(x4463,x4464,x4462,x4465,x4466,x4467)) % 177.51/177.20 [447]~E(x4471,x4472)+E(f640(x4473,x4474,x4475,x4471,x4476,x4477),f640(x4473,x4474,x4475,x4472,x4476,x4477)) % 177.51/177.20 [448]~E(x4481,x4482)+E(f640(x4483,x4484,x4485,x4486,x4481,x4487),f640(x4483,x4484,x4485,x4486,x4482,x4487)) % 177.51/177.20 [449]~E(x4491,x4492)+E(f640(x4493,x4494,x4495,x4496,x4497,x4491),f640(x4493,x4494,x4495,x4496,x4497,x4492)) % 177.51/177.20 [450]~E(x4501,x4502)+E(f182(x4501,x4503),f182(x4502,x4503)) % 177.51/177.20 [451]~E(x4511,x4512)+E(f182(x4513,x4511),f182(x4513,x4512)) % 177.51/177.20 [452]~E(x4521,x4522)+E(f212(x4521,x4523,x4524,x4525),f212(x4522,x4523,x4524,x4525)) % 177.51/177.20 [453]~E(x4531,x4532)+E(f212(x4533,x4531,x4534,x4535),f212(x4533,x4532,x4534,x4535)) % 177.51/177.20 [454]~E(x4541,x4542)+E(f212(x4543,x4544,x4541,x4545),f212(x4543,x4544,x4542,x4545)) % 177.51/177.20 [455]~E(x4551,x4552)+E(f212(x4553,x4554,x4555,x4551),f212(x4553,x4554,x4555,x4552)) % 177.51/177.20 [456]~E(x4561,x4562)+E(f789(x4561,x4563),f789(x4562,x4563)) % 177.51/177.20 [457]~E(x4571,x4572)+E(f789(x4573,x4571),f789(x4573,x4572)) % 177.51/177.20 [458]~E(x4581,x4582)+E(f781(x4581,x4583,x4584,x4585),f781(x4582,x4583,x4584,x4585)) % 177.51/177.20 [459]~E(x4591,x4592)+E(f781(x4593,x4591,x4594,x4595),f781(x4593,x4592,x4594,x4595)) % 177.51/177.20 [460]~E(x4601,x4602)+E(f781(x4603,x4604,x4601,x4605),f781(x4603,x4604,x4602,x4605)) % 177.51/177.20 [461]~E(x4611,x4612)+E(f781(x4613,x4614,x4615,x4611),f781(x4613,x4614,x4615,x4612)) % 177.51/177.20 [462]~E(x4621,x4622)+E(f180(x4621,x4623),f180(x4622,x4623)) % 177.51/177.20 [463]~E(x4631,x4632)+E(f180(x4633,x4631),f180(x4633,x4632)) % 177.51/177.20 [464]~E(x4641,x4642)+E(f502(x4641,x4643,x4644),f502(x4642,x4643,x4644)) % 177.51/177.20 [465]~E(x4651,x4652)+E(f502(x4653,x4651,x4654),f502(x4653,x4652,x4654)) % 177.51/177.20 [466]~E(x4661,x4662)+E(f502(x4663,x4664,x4661),f502(x4663,x4664,x4662)) % 177.51/177.20 [467]~E(x4671,x4672)+E(f812(x4671,x4673),f812(x4672,x4673)) % 177.51/177.20 [468]~E(x4681,x4682)+E(f812(x4683,x4681),f812(x4683,x4682)) % 177.51/177.20 [469]~E(x4691,x4692)+E(f768(x4691,x4693),f768(x4692,x4693)) % 177.51/177.20 [470]~E(x4701,x4702)+E(f768(x4703,x4701),f768(x4703,x4702)) % 177.51/177.20 [471]~E(x4711,x4712)+E(f314(x4711),f314(x4712)) % 177.51/177.20 [472]~E(x4721,x4722)+E(f651(x4721,x4723,x4724,x4725),f651(x4722,x4723,x4724,x4725)) % 177.51/177.20 [473]~E(x4731,x4732)+E(f651(x4733,x4731,x4734,x4735),f651(x4733,x4732,x4734,x4735)) % 177.51/177.20 [474]~E(x4741,x4742)+E(f651(x4743,x4744,x4741,x4745),f651(x4743,x4744,x4742,x4745)) % 177.51/177.20 [475]~E(x4751,x4752)+E(f651(x4753,x4754,x4755,x4751),f651(x4753,x4754,x4755,x4752)) % 177.51/177.20 [476]~E(x4761,x4762)+E(f166(x4761),f166(x4762)) % 177.51/177.20 [477]~E(x4771,x4772)+E(f15(x4771,x4773),f15(x4772,x4773)) % 177.51/177.20 [478]~E(x4781,x4782)+E(f15(x4783,x4781),f15(x4783,x4782)) % 177.51/177.20 [479]~E(x4791,x4792)+E(f74(x4791,x4793,x4794,x4795,x4796),f74(x4792,x4793,x4794,x4795,x4796)) % 177.51/177.20 [480]~E(x4801,x4802)+E(f74(x4803,x4801,x4804,x4805,x4806),f74(x4803,x4802,x4804,x4805,x4806)) % 177.51/177.20 [481]~E(x4811,x4812)+E(f74(x4813,x4814,x4811,x4815,x4816),f74(x4813,x4814,x4812,x4815,x4816)) % 177.51/177.20 [482]~E(x4821,x4822)+E(f74(x4823,x4824,x4825,x4821,x4826),f74(x4823,x4824,x4825,x4822,x4826)) % 177.51/177.20 [483]~E(x4831,x4832)+E(f74(x4833,x4834,x4835,x4836,x4831),f74(x4833,x4834,x4835,x4836,x4832)) % 177.51/177.20 [484]~E(x4841,x4842)+E(f677(x4841,x4843,x4844,x4845,x4846),f677(x4842,x4843,x4844,x4845,x4846)) % 177.51/177.20 [485]~E(x4851,x4852)+E(f677(x4853,x4851,x4854,x4855,x4856),f677(x4853,x4852,x4854,x4855,x4856)) % 177.51/177.20 [486]~E(x4861,x4862)+E(f677(x4863,x4864,x4861,x4865,x4866),f677(x4863,x4864,x4862,x4865,x4866)) % 177.51/177.20 [487]~E(x4871,x4872)+E(f677(x4873,x4874,x4875,x4871,x4876),f677(x4873,x4874,x4875,x4872,x4876)) % 177.51/177.20 [488]~E(x4881,x4882)+E(f677(x4883,x4884,x4885,x4886,x4881),f677(x4883,x4884,x4885,x4886,x4882)) % 177.51/177.20 [489]~E(x4891,x4892)+E(f569(x4891,x4893,x4894),f569(x4892,x4893,x4894)) % 177.51/177.20 [490]~E(x4901,x4902)+E(f569(x4903,x4901,x4904),f569(x4903,x4902,x4904)) % 177.51/177.20 [491]~E(x4911,x4912)+E(f569(x4913,x4914,x4911),f569(x4913,x4914,x4912)) % 177.51/177.20 [492]~E(x4921,x4922)+E(f170(x4921,x4923,x4924),f170(x4922,x4923,x4924)) % 177.51/177.20 [493]~E(x4931,x4932)+E(f170(x4933,x4931,x4934),f170(x4933,x4932,x4934)) % 177.51/177.20 [494]~E(x4941,x4942)+E(f170(x4943,x4944,x4941),f170(x4943,x4944,x4942)) % 177.51/177.20 [495]~E(x4951,x4952)+E(f283(x4951),f283(x4952)) % 177.51/177.20 [496]~E(x4961,x4962)+E(f254(x4961,x4963),f254(x4962,x4963)) % 177.51/177.20 [497]~E(x4971,x4972)+E(f254(x4973,x4971),f254(x4973,x4972)) % 177.51/177.20 [498]~E(x4981,x4982)+E(f308(x4981),f308(x4982)) % 177.51/177.20 [499]~E(x4991,x4992)+E(f384(x4991,x4993,x4994,x4995,x4996),f384(x4992,x4993,x4994,x4995,x4996)) % 177.51/177.20 [500]~E(x5001,x5002)+E(f384(x5003,x5001,x5004,x5005,x5006),f384(x5003,x5002,x5004,x5005,x5006)) % 177.51/177.20 [501]~E(x5011,x5012)+E(f384(x5013,x5014,x5011,x5015,x5016),f384(x5013,x5014,x5012,x5015,x5016)) % 177.51/177.20 [502]~E(x5021,x5022)+E(f384(x5023,x5024,x5025,x5021,x5026),f384(x5023,x5024,x5025,x5022,x5026)) % 177.51/177.20 [503]~E(x5031,x5032)+E(f384(x5033,x5034,x5035,x5036,x5031),f384(x5033,x5034,x5035,x5036,x5032)) % 177.51/177.20 [504]~E(x5041,x5042)+E(f63(x5041,x5043),f63(x5042,x5043)) % 177.51/177.20 [505]~E(x5051,x5052)+E(f63(x5053,x5051),f63(x5053,x5052)) % 177.51/177.20 [506]~E(x5061,x5062)+E(f856(x5061,x5063,x5064),f856(x5062,x5063,x5064)) % 177.51/177.20 [507]~E(x5071,x5072)+E(f856(x5073,x5071,x5074),f856(x5073,x5072,x5074)) % 177.51/177.20 [508]~E(x5081,x5082)+E(f856(x5083,x5084,x5081),f856(x5083,x5084,x5082)) % 177.51/177.20 [509]~E(x5091,x5092)+E(f480(x5091,x5093,x5094),f480(x5092,x5093,x5094)) % 177.51/177.20 [510]~E(x5101,x5102)+E(f480(x5103,x5101,x5104),f480(x5103,x5102,x5104)) % 177.51/177.20 [511]~E(x5111,x5112)+E(f480(x5113,x5114,x5111),f480(x5113,x5114,x5112)) % 177.51/177.20 [512]~E(x5121,x5122)+E(f523(x5121,x5123,x5124),f523(x5122,x5123,x5124)) % 177.51/177.20 [513]~E(x5131,x5132)+E(f523(x5133,x5131,x5134),f523(x5133,x5132,x5134)) % 177.51/177.20 [514]~E(x5141,x5142)+E(f523(x5143,x5144,x5141),f523(x5143,x5144,x5142)) % 177.51/177.20 [515]~E(x5151,x5152)+E(f563(x5151,x5153,x5154,x5155,x5156),f563(x5152,x5153,x5154,x5155,x5156)) % 177.51/177.20 [516]~E(x5161,x5162)+E(f563(x5163,x5161,x5164,x5165,x5166),f563(x5163,x5162,x5164,x5165,x5166)) % 177.51/177.20 [517]~E(x5171,x5172)+E(f563(x5173,x5174,x5171,x5175,x5176),f563(x5173,x5174,x5172,x5175,x5176)) % 177.51/177.20 [518]~E(x5181,x5182)+E(f563(x5183,x5184,x5185,x5181,x5186),f563(x5183,x5184,x5185,x5182,x5186)) % 177.51/177.20 [519]~E(x5191,x5192)+E(f563(x5193,x5194,x5195,x5196,x5191),f563(x5193,x5194,x5195,x5196,x5192)) % 177.51/177.20 [520]~E(x5201,x5202)+E(f713(x5201,x5203,x5204),f713(x5202,x5203,x5204)) % 177.51/177.20 [521]~E(x5211,x5212)+E(f713(x5213,x5211,x5214),f713(x5213,x5212,x5214)) % 177.51/177.20 [522]~E(x5221,x5222)+E(f713(x5223,x5224,x5221),f713(x5223,x5224,x5222)) % 177.51/177.20 [523]~E(x5231,x5232)+E(f709(x5231,x5233,x5234),f709(x5232,x5233,x5234)) % 177.51/177.20 [524]~E(x5241,x5242)+E(f709(x5243,x5241,x5244),f709(x5243,x5242,x5244)) % 177.51/177.20 [525]~E(x5251,x5252)+E(f709(x5253,x5254,x5251),f709(x5253,x5254,x5252)) % 177.51/177.20 [526]~E(x5261,x5262)+E(f11(x5261,x5263,x5264),f11(x5262,x5263,x5264)) % 177.51/177.20 [527]~E(x5271,x5272)+E(f11(x5273,x5271,x5274),f11(x5273,x5272,x5274)) % 177.51/177.20 [528]~E(x5281,x5282)+E(f11(x5283,x5284,x5281),f11(x5283,x5284,x5282)) % 177.51/177.20 [529]~E(x5291,x5292)+E(f222(x5291,x5293,x5294,x5295),f222(x5292,x5293,x5294,x5295)) % 177.51/177.20 [530]~E(x5301,x5302)+E(f222(x5303,x5301,x5304,x5305),f222(x5303,x5302,x5304,x5305)) % 177.51/177.20 [531]~E(x5311,x5312)+E(f222(x5313,x5314,x5311,x5315),f222(x5313,x5314,x5312,x5315)) % 177.51/177.20 [532]~E(x5321,x5322)+E(f222(x5323,x5324,x5325,x5321),f222(x5323,x5324,x5325,x5322)) % 177.51/177.20 [533]~E(x5331,x5332)+E(f301(x5331),f301(x5332)) % 177.51/177.20 [534]~E(x5341,x5342)+E(f146(x5341,x5343),f146(x5342,x5343)) % 177.51/177.20 [535]~E(x5351,x5352)+E(f146(x5353,x5351),f146(x5353,x5352)) % 177.51/177.20 [536]~E(x5361,x5362)+E(f270(x5361,x5363),f270(x5362,x5363)) % 177.51/177.20 [537]~E(x5371,x5372)+E(f270(x5373,x5371),f270(x5373,x5372)) % 177.51/177.20 [538]~E(x5381,x5382)+E(f249(x5381,x5383,x5384),f249(x5382,x5383,x5384)) % 177.51/177.20 [539]~E(x5391,x5392)+E(f249(x5393,x5391,x5394),f249(x5393,x5392,x5394)) % 177.51/177.20 [540]~E(x5401,x5402)+E(f249(x5403,x5404,x5401),f249(x5403,x5404,x5402)) % 177.51/177.20 [541]~E(x5411,x5412)+E(f196(x5411,x5413),f196(x5412,x5413)) % 177.51/177.20 [542]~E(x5421,x5422)+E(f196(x5423,x5421),f196(x5423,x5422)) % 177.51/177.20 [543]~E(x5431,x5432)+E(f671(x5431,x5433),f671(x5432,x5433)) % 177.51/177.20 [544]~E(x5441,x5442)+E(f671(x5443,x5441),f671(x5443,x5442)) % 177.51/177.20 [545]~E(x5451,x5452)+E(f273(x5451,x5453,x5454,x5455),f273(x5452,x5453,x5454,x5455)) % 177.51/177.20 [546]~E(x5461,x5462)+E(f273(x5463,x5461,x5464,x5465),f273(x5463,x5462,x5464,x5465)) % 177.51/177.20 [547]~E(x5471,x5472)+E(f273(x5473,x5474,x5471,x5475),f273(x5473,x5474,x5472,x5475)) % 177.51/177.20 [548]~E(x5481,x5482)+E(f273(x5483,x5484,x5485,x5481),f273(x5483,x5484,x5485,x5482)) % 177.51/177.20 [549]~E(x5491,x5492)+E(f126(x5491,x5493),f126(x5492,x5493)) % 177.51/177.20 [550]~E(x5501,x5502)+E(f126(x5503,x5501),f126(x5503,x5502)) % 177.51/177.20 [551]~E(x5511,x5512)+E(f162(x5511,x5513),f162(x5512,x5513)) % 177.51/177.20 [552]~E(x5521,x5522)+E(f162(x5523,x5521),f162(x5523,x5522)) % 177.51/177.20 [553]~E(x5531,x5532)+E(f744(x5531,x5533),f744(x5532,x5533)) % 177.51/177.20 [554]~E(x5541,x5542)+E(f744(x5543,x5541),f744(x5543,x5542)) % 177.51/177.20 [555]~E(x5551,x5552)+E(f432(x5551,x5553,x5554),f432(x5552,x5553,x5554)) % 177.51/177.20 [556]~E(x5561,x5562)+E(f432(x5563,x5561,x5564),f432(x5563,x5562,x5564)) % 177.51/177.20 [557]~E(x5571,x5572)+E(f432(x5573,x5574,x5571),f432(x5573,x5574,x5572)) % 177.51/177.20 [558]~E(x5581,x5582)+E(f600(x5581,x5583,x5584,x5585,x5586,x5587,x5588,x5589),f600(x5582,x5583,x5584,x5585,x5586,x5587,x5588,x5589)) % 177.51/177.20 [559]~E(x5591,x5592)+E(f600(x5593,x5591,x5594,x5595,x5596,x5597,x5598,x5599),f600(x5593,x5592,x5594,x5595,x5596,x5597,x5598,x5599)) % 177.51/177.20 [560]~E(x5601,x5602)+E(f600(x5603,x5604,x5601,x5605,x5606,x5607,x5608,x5609),f600(x5603,x5604,x5602,x5605,x5606,x5607,x5608,x5609)) % 177.51/177.20 [561]~E(x5611,x5612)+E(f600(x5613,x5614,x5615,x5611,x5616,x5617,x5618,x5619),f600(x5613,x5614,x5615,x5612,x5616,x5617,x5618,x5619)) % 177.51/177.20 [562]~E(x5621,x5622)+E(f600(x5623,x5624,x5625,x5626,x5621,x5627,x5628,x5629),f600(x5623,x5624,x5625,x5626,x5622,x5627,x5628,x5629)) % 177.51/177.20 [563]~E(x5631,x5632)+E(f600(x5633,x5634,x5635,x5636,x5637,x5631,x5638,x5639),f600(x5633,x5634,x5635,x5636,x5637,x5632,x5638,x5639)) % 177.51/177.20 [564]~E(x5641,x5642)+E(f600(x5643,x5644,x5645,x5646,x5647,x5648,x5641,x5649),f600(x5643,x5644,x5645,x5646,x5647,x5648,x5642,x5649)) % 177.51/177.20 [565]~E(x5651,x5652)+E(f600(x5653,x5654,x5655,x5656,x5657,x5658,x5659,x5651),f600(x5653,x5654,x5655,x5656,x5657,x5658,x5659,x5652)) % 177.51/177.20 [566]~E(x5661,x5662)+E(f715(x5661,x5663,x5664,x5665,x5666),f715(x5662,x5663,x5664,x5665,x5666)) % 177.51/177.20 [567]~E(x5671,x5672)+E(f715(x5673,x5671,x5674,x5675,x5676),f715(x5673,x5672,x5674,x5675,x5676)) % 177.51/177.20 [568]~E(x5681,x5682)+E(f715(x5683,x5684,x5681,x5685,x5686),f715(x5683,x5684,x5682,x5685,x5686)) % 177.51/177.20 [569]~E(x5691,x5692)+E(f715(x5693,x5694,x5695,x5691,x5696),f715(x5693,x5694,x5695,x5692,x5696)) % 177.51/177.20 [570]~E(x5701,x5702)+E(f715(x5703,x5704,x5705,x5706,x5701),f715(x5703,x5704,x5705,x5706,x5702)) % 177.51/177.20 [571]~E(x5711,x5712)+E(f528(x5711,x5713,x5714),f528(x5712,x5713,x5714)) % 177.51/177.20 [572]~E(x5721,x5722)+E(f528(x5723,x5721,x5724),f528(x5723,x5722,x5724)) % 177.51/177.20 [573]~E(x5731,x5732)+E(f528(x5733,x5734,x5731),f528(x5733,x5734,x5732)) % 177.51/177.20 [574]~E(x5741,x5742)+E(f218(x5741,x5743),f218(x5742,x5743)) % 177.51/177.20 [575]~E(x5751,x5752)+E(f218(x5753,x5751),f218(x5753,x5752)) % 177.51/177.20 [576]~E(x5761,x5762)+E(f429(x5761,x5763,x5764,x5765),f429(x5762,x5763,x5764,x5765)) % 177.51/177.20 [577]~E(x5771,x5772)+E(f429(x5773,x5771,x5774,x5775),f429(x5773,x5772,x5774,x5775)) % 177.51/177.20 [578]~E(x5781,x5782)+E(f429(x5783,x5784,x5781,x5785),f429(x5783,x5784,x5782,x5785)) % 177.51/177.20 [579]~E(x5791,x5792)+E(f429(x5793,x5794,x5795,x5791),f429(x5793,x5794,x5795,x5792)) % 177.51/177.20 [580]~E(x5801,x5802)+E(f874(x5801,x5803,x5804,x5805),f874(x5802,x5803,x5804,x5805)) % 177.51/177.20 [581]~E(x5811,x5812)+E(f874(x5813,x5811,x5814,x5815),f874(x5813,x5812,x5814,x5815)) % 177.51/177.20 [582]~E(x5821,x5822)+E(f874(x5823,x5824,x5821,x5825),f874(x5823,x5824,x5822,x5825)) % 177.51/177.20 [583]~E(x5831,x5832)+E(f874(x5833,x5834,x5835,x5831),f874(x5833,x5834,x5835,x5832)) % 177.51/177.20 [584]~E(x5841,x5842)+E(f792(x5841,x5843,x5844),f792(x5842,x5843,x5844)) % 177.51/177.20 [585]~E(x5851,x5852)+E(f792(x5853,x5851,x5854),f792(x5853,x5852,x5854)) % 177.51/177.20 [586]~E(x5861,x5862)+E(f792(x5863,x5864,x5861),f792(x5863,x5864,x5862)) % 177.51/177.20 [587]~E(x5871,x5872)+E(f733(x5871,x5873),f733(x5872,x5873)) % 177.51/177.20 [588]~E(x5881,x5882)+E(f733(x5883,x5881),f733(x5883,x5882)) % 177.51/177.20 [589]~E(x5891,x5892)+E(f343(x5891,x5893,x5894,x5895,x5896),f343(x5892,x5893,x5894,x5895,x5896)) % 177.51/177.20 [590]~E(x5901,x5902)+E(f343(x5903,x5901,x5904,x5905,x5906),f343(x5903,x5902,x5904,x5905,x5906)) % 177.51/177.20 [591]~E(x5911,x5912)+E(f343(x5913,x5914,x5911,x5915,x5916),f343(x5913,x5914,x5912,x5915,x5916)) % 177.51/177.20 [592]~E(x5921,x5922)+E(f343(x5923,x5924,x5925,x5921,x5926),f343(x5923,x5924,x5925,x5922,x5926)) % 177.51/177.20 [593]~E(x5931,x5932)+E(f343(x5933,x5934,x5935,x5936,x5931),f343(x5933,x5934,x5935,x5936,x5932)) % 177.51/177.20 [594]~E(x5941,x5942)+E(f30(x5941,x5943),f30(x5942,x5943)) % 177.51/177.20 [595]~E(x5951,x5952)+E(f30(x5953,x5951),f30(x5953,x5952)) % 177.51/177.20 [596]~E(x5961,x5962)+E(f76(x5961,x5963,x5964,x5965,x5966),f76(x5962,x5963,x5964,x5965,x5966)) % 177.51/177.20 [597]~E(x5971,x5972)+E(f76(x5973,x5971,x5974,x5975,x5976),f76(x5973,x5972,x5974,x5975,x5976)) % 177.51/177.20 [598]~E(x5981,x5982)+E(f76(x5983,x5984,x5981,x5985,x5986),f76(x5983,x5984,x5982,x5985,x5986)) % 177.51/177.20 [599]~E(x5991,x5992)+E(f76(x5993,x5994,x5995,x5991,x5996),f76(x5993,x5994,x5995,x5992,x5996)) % 177.51/177.20 [600]~E(x6001,x6002)+E(f76(x6003,x6004,x6005,x6006,x6001),f76(x6003,x6004,x6005,x6006,x6002)) % 177.51/177.20 [601]~E(x6011,x6012)+E(f145(x6011,x6013),f145(x6012,x6013)) % 177.51/177.20 [602]~E(x6021,x6022)+E(f145(x6023,x6021),f145(x6023,x6022)) % 177.51/177.20 [603]~E(x6031,x6032)+E(f66(x6031,x6033,x6034,x6035,x6036),f66(x6032,x6033,x6034,x6035,x6036)) % 177.51/177.20 [604]~E(x6041,x6042)+E(f66(x6043,x6041,x6044,x6045,x6046),f66(x6043,x6042,x6044,x6045,x6046)) % 177.51/177.20 [605]~E(x6051,x6052)+E(f66(x6053,x6054,x6051,x6055,x6056),f66(x6053,x6054,x6052,x6055,x6056)) % 177.51/177.20 [606]~E(x6061,x6062)+E(f66(x6063,x6064,x6065,x6061,x6066),f66(x6063,x6064,x6065,x6062,x6066)) % 177.51/177.20 [607]~E(x6071,x6072)+E(f66(x6073,x6074,x6075,x6076,x6071),f66(x6073,x6074,x6075,x6076,x6072)) % 177.51/177.20 [608]~E(x6081,x6082)+E(f889(x6081,x6083,x6084),f889(x6082,x6083,x6084)) % 177.51/177.20 [609]~E(x6091,x6092)+E(f889(x6093,x6091,x6094),f889(x6093,x6092,x6094)) % 177.51/177.20 [610]~E(x6101,x6102)+E(f889(x6103,x6104,x6101),f889(x6103,x6104,x6102)) % 177.51/177.20 [611]~E(x6111,x6112)+E(f628(x6111,x6113,x6114,x6115),f628(x6112,x6113,x6114,x6115)) % 177.51/177.20 [612]~E(x6121,x6122)+E(f628(x6123,x6121,x6124,x6125),f628(x6123,x6122,x6124,x6125)) % 177.51/177.20 [613]~E(x6131,x6132)+E(f628(x6133,x6134,x6131,x6135),f628(x6133,x6134,x6132,x6135)) % 177.51/177.20 [614]~E(x6141,x6142)+E(f628(x6143,x6144,x6145,x6141),f628(x6143,x6144,x6145,x6142)) % 177.51/177.20 [615]~E(x6151,x6152)+E(f73(x6151,x6153),f73(x6152,x6153)) % 177.51/177.20 [616]~E(x6161,x6162)+E(f73(x6163,x6161),f73(x6163,x6162)) % 177.51/177.20 [617]~E(x6171,x6172)+E(f724(x6171,x6173,x6174,x6175),f724(x6172,x6173,x6174,x6175)) % 177.51/177.20 [618]~E(x6181,x6182)+E(f724(x6183,x6181,x6184,x6185),f724(x6183,x6182,x6184,x6185)) % 177.51/177.20 [619]~E(x6191,x6192)+E(f724(x6193,x6194,x6191,x6195),f724(x6193,x6194,x6192,x6195)) % 177.51/177.20 [620]~E(x6201,x6202)+E(f724(x6203,x6204,x6205,x6201),f724(x6203,x6204,x6205,x6202)) % 177.51/177.20 [621]~E(x6211,x6212)+E(f907(x6211,x6213,x6214,x6215),f907(x6212,x6213,x6214,x6215)) % 177.51/177.20 [622]~E(x6221,x6222)+E(f907(x6223,x6221,x6224,x6225),f907(x6223,x6222,x6224,x6225)) % 177.51/177.20 [623]~E(x6231,x6232)+E(f907(x6233,x6234,x6231,x6235),f907(x6233,x6234,x6232,x6235)) % 177.51/177.20 [624]~E(x6241,x6242)+E(f907(x6243,x6244,x6245,x6241),f907(x6243,x6244,x6245,x6242)) % 177.51/177.20 [625]~E(x6251,x6252)+E(f805(x6251,x6253,x6254),f805(x6252,x6253,x6254)) % 177.51/177.20 [626]~E(x6261,x6262)+E(f805(x6263,x6261,x6264),f805(x6263,x6262,x6264)) % 177.51/177.20 [627]~E(x6271,x6272)+E(f805(x6273,x6274,x6271),f805(x6273,x6274,x6272)) % 177.51/177.20 [628]~E(x6281,x6282)+E(f397(x6281,x6283,x6284,x6285,x6286),f397(x6282,x6283,x6284,x6285,x6286)) % 177.51/177.20 [629]~E(x6291,x6292)+E(f397(x6293,x6291,x6294,x6295,x6296),f397(x6293,x6292,x6294,x6295,x6296)) % 177.51/177.20 [630]~E(x6301,x6302)+E(f397(x6303,x6304,x6301,x6305,x6306),f397(x6303,x6304,x6302,x6305,x6306)) % 177.51/177.20 [631]~E(x6311,x6312)+E(f397(x6313,x6314,x6315,x6311,x6316),f397(x6313,x6314,x6315,x6312,x6316)) % 177.51/177.20 [632]~E(x6321,x6322)+E(f397(x6323,x6324,x6325,x6326,x6321),f397(x6323,x6324,x6325,x6326,x6322)) % 177.51/177.20 [633]~E(x6331,x6332)+E(f266(x6331,x6333),f266(x6332,x6333)) % 177.51/177.20 [634]~E(x6341,x6342)+E(f266(x6343,x6341),f266(x6343,x6342)) % 177.51/177.20 [635]~E(x6351,x6352)+E(f828(x6351,x6353,x6354,x6355),f828(x6352,x6353,x6354,x6355)) % 177.51/177.20 [636]~E(x6361,x6362)+E(f828(x6363,x6361,x6364,x6365),f828(x6363,x6362,x6364,x6365)) % 177.51/177.20 [637]~E(x6371,x6372)+E(f828(x6373,x6374,x6371,x6375),f828(x6373,x6374,x6372,x6375)) % 177.51/177.20 [638]~E(x6381,x6382)+E(f828(x6383,x6384,x6385,x6381),f828(x6383,x6384,x6385,x6382)) % 177.51/177.20 [639]~E(x6391,x6392)+E(f67(x6391,x6393,x6394),f67(x6392,x6393,x6394)) % 177.51/177.20 [640]~E(x6401,x6402)+E(f67(x6403,x6401,x6404),f67(x6403,x6402,x6404)) % 177.51/177.20 [641]~E(x6411,x6412)+E(f67(x6413,x6414,x6411),f67(x6413,x6414,x6412)) % 177.51/177.20 [642]~E(x6421,x6422)+E(f811(x6421,x6423,x6424,x6425,x6426,x6427),f811(x6422,x6423,x6424,x6425,x6426,x6427)) % 177.51/177.20 [643]~E(x6431,x6432)+E(f811(x6433,x6431,x6434,x6435,x6436,x6437),f811(x6433,x6432,x6434,x6435,x6436,x6437)) % 177.51/177.20 [644]~E(x6441,x6442)+E(f811(x6443,x6444,x6441,x6445,x6446,x6447),f811(x6443,x6444,x6442,x6445,x6446,x6447)) % 177.51/177.20 [645]~E(x6451,x6452)+E(f811(x6453,x6454,x6455,x6451,x6456,x6457),f811(x6453,x6454,x6455,x6452,x6456,x6457)) % 177.51/177.20 [646]~E(x6461,x6462)+E(f811(x6463,x6464,x6465,x6466,x6461,x6467),f811(x6463,x6464,x6465,x6466,x6462,x6467)) % 177.51/177.20 [647]~E(x6471,x6472)+E(f811(x6473,x6474,x6475,x6476,x6477,x6471),f811(x6473,x6474,x6475,x6476,x6477,x6472)) % 177.51/177.20 [648]~E(x6481,x6482)+E(f603(x6481,x6483,x6484),f603(x6482,x6483,x6484)) % 177.51/177.20 [649]~E(x6491,x6492)+E(f603(x6493,x6491,x6494),f603(x6493,x6492,x6494)) % 177.51/177.20 [650]~E(x6501,x6502)+E(f603(x6503,x6504,x6501),f603(x6503,x6504,x6502)) % 177.51/177.20 [651]~E(x6511,x6512)+E(f332(x6511),f332(x6512)) % 177.51/177.20 [652]~E(x6521,x6522)+E(f606(x6521,x6523,x6524),f606(x6522,x6523,x6524)) % 177.51/177.20 [653]~E(x6531,x6532)+E(f606(x6533,x6531,x6534),f606(x6533,x6532,x6534)) % 177.51/177.20 [654]~E(x6541,x6542)+E(f606(x6543,x6544,x6541),f606(x6543,x6544,x6542)) % 177.51/177.20 [655]~E(x6551,x6552)+E(f859(x6551,x6553,x6554),f859(x6552,x6553,x6554)) % 177.51/177.20 [656]~E(x6561,x6562)+E(f859(x6563,x6561,x6564),f859(x6563,x6562,x6564)) % 177.51/177.20 [657]~E(x6571,x6572)+E(f859(x6573,x6574,x6571),f859(x6573,x6574,x6572)) % 177.51/177.20 [658]~E(x6581,x6582)+E(f493(x6581,x6583,x6584,x6585,x6586,x6587),f493(x6582,x6583,x6584,x6585,x6586,x6587)) % 177.51/177.20 [659]~E(x6591,x6592)+E(f493(x6593,x6591,x6594,x6595,x6596,x6597),f493(x6593,x6592,x6594,x6595,x6596,x6597)) % 177.51/177.20 [660]~E(x6601,x6602)+E(f493(x6603,x6604,x6601,x6605,x6606,x6607),f493(x6603,x6604,x6602,x6605,x6606,x6607)) % 177.51/177.20 [661]~E(x6611,x6612)+E(f493(x6613,x6614,x6615,x6611,x6616,x6617),f493(x6613,x6614,x6615,x6612,x6616,x6617)) % 177.51/177.20 [662]~E(x6621,x6622)+E(f493(x6623,x6624,x6625,x6626,x6621,x6627),f493(x6623,x6624,x6625,x6626,x6622,x6627)) % 177.51/177.20 [663]~E(x6631,x6632)+E(f493(x6633,x6634,x6635,x6636,x6637,x6631),f493(x6633,x6634,x6635,x6636,x6637,x6632)) % 177.51/177.20 [664]~E(x6641,x6642)+E(f521(x6641,x6643,x6644),f521(x6642,x6643,x6644)) % 177.51/177.20 [665]~E(x6651,x6652)+E(f521(x6653,x6651,x6654),f521(x6653,x6652,x6654)) % 177.51/177.20 [666]~E(x6661,x6662)+E(f521(x6663,x6664,x6661),f521(x6663,x6664,x6662)) % 177.51/177.20 [667]~E(x6671,x6672)+E(f220(x6671,x6673),f220(x6672,x6673)) % 177.51/177.20 [668]~E(x6681,x6682)+E(f220(x6683,x6681),f220(x6683,x6682)) % 177.51/177.20 [669]~E(x6691,x6692)+E(f836(x6691,x6693,x6694,x6695,x6696,x6697,x6698,x6699),f836(x6692,x6693,x6694,x6695,x6696,x6697,x6698,x6699)) % 177.51/177.20 [670]~E(x6701,x6702)+E(f836(x6703,x6701,x6704,x6705,x6706,x6707,x6708,x6709),f836(x6703,x6702,x6704,x6705,x6706,x6707,x6708,x6709)) % 177.51/177.20 [671]~E(x6711,x6712)+E(f836(x6713,x6714,x6711,x6715,x6716,x6717,x6718,x6719),f836(x6713,x6714,x6712,x6715,x6716,x6717,x6718,x6719)) % 177.51/177.20 [672]~E(x6721,x6722)+E(f836(x6723,x6724,x6725,x6721,x6726,x6727,x6728,x6729),f836(x6723,x6724,x6725,x6722,x6726,x6727,x6728,x6729)) % 177.51/177.20 [673]~E(x6731,x6732)+E(f836(x6733,x6734,x6735,x6736,x6731,x6737,x6738,x6739),f836(x6733,x6734,x6735,x6736,x6732,x6737,x6738,x6739)) % 177.51/177.20 [674]~E(x6741,x6742)+E(f836(x6743,x6744,x6745,x6746,x6747,x6741,x6748,x6749),f836(x6743,x6744,x6745,x6746,x6747,x6742,x6748,x6749)) % 177.51/177.20 [675]~E(x6751,x6752)+E(f836(x6753,x6754,x6755,x6756,x6757,x6758,x6751,x6759),f836(x6753,x6754,x6755,x6756,x6757,x6758,x6752,x6759)) % 177.51/177.20 [676]~E(x6761,x6762)+E(f836(x6763,x6764,x6765,x6766,x6767,x6768,x6769,x6761),f836(x6763,x6764,x6765,x6766,x6767,x6768,x6769,x6762)) % 177.51/177.20 [677]~E(x6771,x6772)+E(f275(x6771,x6773),f275(x6772,x6773)) % 177.51/177.20 [678]~E(x6781,x6782)+E(f275(x6783,x6781),f275(x6783,x6782)) % 177.51/177.20 [679]~E(x6791,x6792)+E(f440(x6791,x6793,x6794,x6795),f440(x6792,x6793,x6794,x6795)) % 177.51/177.20 [680]~E(x6801,x6802)+E(f440(x6803,x6801,x6804,x6805),f440(x6803,x6802,x6804,x6805)) % 177.51/177.20 [681]~E(x6811,x6812)+E(f440(x6813,x6814,x6811,x6815),f440(x6813,x6814,x6812,x6815)) % 177.51/177.20 [682]~E(x6821,x6822)+E(f440(x6823,x6824,x6825,x6821),f440(x6823,x6824,x6825,x6822)) % 177.51/177.20 [683]~E(x6831,x6832)+E(f587(x6831,x6833,x6834),f587(x6832,x6833,x6834)) % 177.51/177.20 [684]~E(x6841,x6842)+E(f587(x6843,x6841,x6844),f587(x6843,x6842,x6844)) % 177.51/177.20 [685]~E(x6851,x6852)+E(f587(x6853,x6854,x6851),f587(x6853,x6854,x6852)) % 177.51/177.20 [686]~E(x6861,x6862)+E(f866(x6861,x6863,x6864,x6865,x6866),f866(x6862,x6863,x6864,x6865,x6866)) % 177.51/177.20 [687]~E(x6871,x6872)+E(f866(x6873,x6871,x6874,x6875,x6876),f866(x6873,x6872,x6874,x6875,x6876)) % 177.51/177.20 [688]~E(x6881,x6882)+E(f866(x6883,x6884,x6881,x6885,x6886),f866(x6883,x6884,x6882,x6885,x6886)) % 177.51/177.20 [689]~E(x6891,x6892)+E(f866(x6893,x6894,x6895,x6891,x6896),f866(x6893,x6894,x6895,x6892,x6896)) % 177.51/177.20 [690]~E(x6901,x6902)+E(f866(x6903,x6904,x6905,x6906,x6901),f866(x6903,x6904,x6905,x6906,x6902)) % 177.51/177.20 [691]~E(x6911,x6912)+E(f355(x6911,x6913,x6914,x6915,x6916),f355(x6912,x6913,x6914,x6915,x6916)) % 177.51/177.20 [692]~E(x6921,x6922)+E(f355(x6923,x6921,x6924,x6925,x6926),f355(x6923,x6922,x6924,x6925,x6926)) % 177.51/177.20 [693]~E(x6931,x6932)+E(f355(x6933,x6934,x6931,x6935,x6936),f355(x6933,x6934,x6932,x6935,x6936)) % 177.51/177.20 [694]~E(x6941,x6942)+E(f355(x6943,x6944,x6945,x6941,x6946),f355(x6943,x6944,x6945,x6942,x6946)) % 177.51/177.20 [695]~E(x6951,x6952)+E(f355(x6953,x6954,x6955,x6956,x6951),f355(x6953,x6954,x6955,x6956,x6952)) % 177.51/177.20 [696]~E(x6961,x6962)+E(f882(x6961,x6963),f882(x6962,x6963)) % 177.51/177.20 [697]~E(x6971,x6972)+E(f882(x6973,x6971),f882(x6973,x6972)) % 177.51/177.20 [698]~E(x6981,x6982)+E(f290(x6981,x6983,x6984,x6985),f290(x6982,x6983,x6984,x6985)) % 177.51/177.20 [699]~E(x6991,x6992)+E(f290(x6993,x6991,x6994,x6995),f290(x6993,x6992,x6994,x6995)) % 177.51/177.20 [700]~E(x7001,x7002)+E(f290(x7003,x7004,x7001,x7005),f290(x7003,x7004,x7002,x7005)) % 177.51/177.20 [701]~E(x7011,x7012)+E(f290(x7013,x7014,x7015,x7011),f290(x7013,x7014,x7015,x7012)) % 177.51/177.20 [702]~E(x7021,x7022)+E(f760(x7021,x7023,x7024),f760(x7022,x7023,x7024)) % 177.51/177.20 [703]~E(x7031,x7032)+E(f760(x7033,x7031,x7034),f760(x7033,x7032,x7034)) % 177.51/177.20 [704]~E(x7041,x7042)+E(f760(x7043,x7044,x7041),f760(x7043,x7044,x7042)) % 177.51/177.20 [705]~E(x7051,x7052)+E(f341(x7051,x7053,x7054,x7055),f341(x7052,x7053,x7054,x7055)) % 177.51/177.20 [706]~E(x7061,x7062)+E(f341(x7063,x7061,x7064,x7065),f341(x7063,x7062,x7064,x7065)) % 177.51/177.20 [707]~E(x7071,x7072)+E(f341(x7073,x7074,x7071,x7075),f341(x7073,x7074,x7072,x7075)) % 177.51/177.20 [708]~E(x7081,x7082)+E(f341(x7083,x7084,x7085,x7081),f341(x7083,x7084,x7085,x7082)) % 177.51/177.20 [709]~E(x7091,x7092)+E(f891(x7091,x7093),f891(x7092,x7093)) % 177.51/177.20 [710]~E(x7101,x7102)+E(f891(x7103,x7101),f891(x7103,x7102)) % 177.51/177.20 [711]~E(x7111,x7112)+E(f706(x7111,x7113,x7114),f706(x7112,x7113,x7114)) % 177.51/177.20 [712]~E(x7121,x7122)+E(f706(x7123,x7121,x7124),f706(x7123,x7122,x7124)) % 177.51/177.20 [713]~E(x7131,x7132)+E(f706(x7133,x7134,x7131),f706(x7133,x7134,x7132)) % 177.51/177.20 [714]~E(x7141,x7142)+E(f796(x7141),f796(x7142)) % 177.51/177.20 [715]~E(x7151,x7152)+E(f288(x7151,x7153),f288(x7152,x7153)) % 177.51/177.20 [716]~E(x7161,x7162)+E(f288(x7163,x7161),f288(x7163,x7162)) % 177.51/177.20 [717]~E(x7171,x7172)+E(f50(x7171,x7173),f50(x7172,x7173)) % 177.51/177.20 [718]~E(x7181,x7182)+E(f50(x7183,x7181),f50(x7183,x7182)) % 177.51/177.20 [719]~E(x7191,x7192)+E(f177(x7191,x7193,x7194),f177(x7192,x7193,x7194)) % 177.51/177.20 [720]~E(x7201,x7202)+E(f177(x7203,x7201,x7204),f177(x7203,x7202,x7204)) % 177.51/177.20 [721]~E(x7211,x7212)+E(f177(x7213,x7214,x7211),f177(x7213,x7214,x7212)) % 177.51/177.20 [722]~E(x7221,x7222)+E(f55(x7221,x7223),f55(x7222,x7223)) % 177.51/177.20 [723]~E(x7231,x7232)+E(f55(x7233,x7231),f55(x7233,x7232)) % 177.51/177.20 [724]~E(x7241,x7242)+E(f367(x7241,x7243,x7244),f367(x7242,x7243,x7244)) % 177.51/177.20 [725]~E(x7251,x7252)+E(f367(x7253,x7251,x7254),f367(x7253,x7252,x7254)) % 177.51/177.20 [726]~E(x7261,x7262)+E(f367(x7263,x7264,x7261),f367(x7263,x7264,x7262)) % 177.51/177.20 [727]~E(x7271,x7272)+E(f894(x7271,x7273,x7274,x7275,x7276),f894(x7272,x7273,x7274,x7275,x7276)) % 177.51/177.20 [728]~E(x7281,x7282)+E(f894(x7283,x7281,x7284,x7285,x7286),f894(x7283,x7282,x7284,x7285,x7286)) % 177.51/177.20 [729]~E(x7291,x7292)+E(f894(x7293,x7294,x7291,x7295,x7296),f894(x7293,x7294,x7292,x7295,x7296)) % 177.51/177.20 [730]~E(x7301,x7302)+E(f894(x7303,x7304,x7305,x7301,x7306),f894(x7303,x7304,x7305,x7302,x7306)) % 177.51/177.20 [731]~E(x7311,x7312)+E(f894(x7313,x7314,x7315,x7316,x7311),f894(x7313,x7314,x7315,x7316,x7312)) % 177.51/177.20 [732]~E(x7321,x7322)+E(f488(x7321,x7323,x7324),f488(x7322,x7323,x7324)) % 177.51/177.20 [733]~E(x7331,x7332)+E(f488(x7333,x7331,x7334),f488(x7333,x7332,x7334)) % 177.51/177.20 [734]~E(x7341,x7342)+E(f488(x7343,x7344,x7341),f488(x7343,x7344,x7342)) % 177.51/177.20 [735]~E(x7351,x7352)+E(f185(x7351,x7353,x7354),f185(x7352,x7353,x7354)) % 177.51/177.20 [736]~E(x7361,x7362)+E(f185(x7363,x7361,x7364),f185(x7363,x7362,x7364)) % 177.51/177.20 [737]~E(x7371,x7372)+E(f185(x7373,x7374,x7371),f185(x7373,x7374,x7372)) % 177.51/177.20 [738]~E(x7381,x7382)+E(f531(x7381,x7383,x7384),f531(x7382,x7383,x7384)) % 177.51/177.20 [739]~E(x7391,x7392)+E(f531(x7393,x7391,x7394),f531(x7393,x7392,x7394)) % 177.51/177.20 [740]~E(x7401,x7402)+E(f531(x7403,x7404,x7401),f531(x7403,x7404,x7402)) % 177.51/177.20 [741]~E(x7411,x7412)+E(f545(x7411,x7413,x7414),f545(x7412,x7413,x7414)) % 177.51/177.20 [742]~E(x7421,x7422)+E(f545(x7423,x7421,x7424),f545(x7423,x7422,x7424)) % 177.51/177.20 [743]~E(x7431,x7432)+E(f545(x7433,x7434,x7431),f545(x7433,x7434,x7432)) % 177.51/177.20 [744]~E(x7441,x7442)+E(f331(x7441,x7443,x7444,x7445),f331(x7442,x7443,x7444,x7445)) % 177.51/177.20 [745]~E(x7451,x7452)+E(f331(x7453,x7451,x7454,x7455),f331(x7453,x7452,x7454,x7455)) % 177.51/177.20 [746]~E(x7461,x7462)+E(f331(x7463,x7464,x7461,x7465),f331(x7463,x7464,x7462,x7465)) % 177.51/177.20 [747]~E(x7471,x7472)+E(f331(x7473,x7474,x7475,x7471),f331(x7473,x7474,x7475,x7472)) % 177.51/177.20 [748]~E(x7481,x7482)+E(f832(x7481,x7483,x7484),f832(x7482,x7483,x7484)) % 177.51/177.20 [749]~E(x7491,x7492)+E(f832(x7493,x7491,x7494),f832(x7493,x7492,x7494)) % 177.51/177.20 [750]~E(x7501,x7502)+E(f832(x7503,x7504,x7501),f832(x7503,x7504,x7502)) % 177.51/177.20 [751]~E(x7511,x7512)+E(f264(x7511,x7513),f264(x7512,x7513)) % 177.51/177.20 [752]~E(x7521,x7522)+E(f264(x7523,x7521),f264(x7523,x7522)) % 177.51/177.20 [753]~E(x7531,x7532)+E(f855(x7531,x7533,x7534),f855(x7532,x7533,x7534)) % 177.51/177.20 [754]~E(x7541,x7542)+E(f855(x7543,x7541,x7544),f855(x7543,x7542,x7544)) % 177.51/177.20 [755]~E(x7551,x7552)+E(f855(x7553,x7554,x7551),f855(x7553,x7554,x7552)) % 177.51/177.20 [756]~E(x7561,x7562)+E(f448(x7561),f448(x7562)) % 177.51/177.20 [757]~E(x7571,x7572)+E(f217(x7571,x7573),f217(x7572,x7573)) % 177.51/177.20 [758]~E(x7581,x7582)+E(f217(x7583,x7581),f217(x7583,x7582)) % 177.51/177.20 [759]~E(x7591,x7592)+E(f664(x7591,x7593,x7594,x7595),f664(x7592,x7593,x7594,x7595)) % 177.51/177.20 [760]~E(x7601,x7602)+E(f664(x7603,x7601,x7604,x7605),f664(x7603,x7602,x7604,x7605)) % 177.51/177.20 [761]~E(x7611,x7612)+E(f664(x7613,x7614,x7611,x7615),f664(x7613,x7614,x7612,x7615)) % 177.51/177.20 [762]~E(x7621,x7622)+E(f664(x7623,x7624,x7625,x7621),f664(x7623,x7624,x7625,x7622)) % 177.51/177.20 [763]~E(x7631,x7632)+E(f590(x7631,x7633,x7634,x7635,x7636,x7637),f590(x7632,x7633,x7634,x7635,x7636,x7637)) % 177.51/177.20 [764]~E(x7641,x7642)+E(f590(x7643,x7641,x7644,x7645,x7646,x7647),f590(x7643,x7642,x7644,x7645,x7646,x7647)) % 177.51/177.20 [765]~E(x7651,x7652)+E(f590(x7653,x7654,x7651,x7655,x7656,x7657),f590(x7653,x7654,x7652,x7655,x7656,x7657)) % 177.51/177.20 [766]~E(x7661,x7662)+E(f590(x7663,x7664,x7665,x7661,x7666,x7667),f590(x7663,x7664,x7665,x7662,x7666,x7667)) % 177.51/177.20 [767]~E(x7671,x7672)+E(f590(x7673,x7674,x7675,x7676,x7671,x7677),f590(x7673,x7674,x7675,x7676,x7672,x7677)) % 177.51/177.20 [768]~E(x7681,x7682)+E(f590(x7683,x7684,x7685,x7686,x7687,x7681),f590(x7683,x7684,x7685,x7686,x7687,x7682)) % 177.51/177.20 [769]~E(x7691,x7692)+E(f243(x7691,x7693,x7694),f243(x7692,x7693,x7694)) % 177.51/177.20 [770]~E(x7701,x7702)+E(f243(x7703,x7701,x7704),f243(x7703,x7702,x7704)) % 177.51/177.20 [771]~E(x7711,x7712)+E(f243(x7713,x7714,x7711),f243(x7713,x7714,x7712)) % 177.51/177.20 [772]~E(x7721,x7722)+E(f638(x7721,x7723,x7724,x7725,x7726,x7727),f638(x7722,x7723,x7724,x7725,x7726,x7727)) % 177.51/177.20 [773]~E(x7731,x7732)+E(f638(x7733,x7731,x7734,x7735,x7736,x7737),f638(x7733,x7732,x7734,x7735,x7736,x7737)) % 177.51/177.20 [774]~E(x7741,x7742)+E(f638(x7743,x7744,x7741,x7745,x7746,x7747),f638(x7743,x7744,x7742,x7745,x7746,x7747)) % 177.51/177.20 [775]~E(x7751,x7752)+E(f638(x7753,x7754,x7755,x7751,x7756,x7757),f638(x7753,x7754,x7755,x7752,x7756,x7757)) % 177.51/177.20 [776]~E(x7761,x7762)+E(f638(x7763,x7764,x7765,x7766,x7761,x7767),f638(x7763,x7764,x7765,x7766,x7762,x7767)) % 177.51/177.20 [777]~E(x7771,x7772)+E(f638(x7773,x7774,x7775,x7776,x7777,x7771),f638(x7773,x7774,x7775,x7776,x7777,x7772)) % 177.51/177.20 [778]~E(x7781,x7782)+E(f510(x7781,x7783,x7784,x7785,x7786,x7787,x7788),f510(x7782,x7783,x7784,x7785,x7786,x7787,x7788)) % 177.51/177.20 [779]~E(x7791,x7792)+E(f510(x7793,x7791,x7794,x7795,x7796,x7797,x7798),f510(x7793,x7792,x7794,x7795,x7796,x7797,x7798)) % 177.51/177.20 [780]~E(x7801,x7802)+E(f510(x7803,x7804,x7801,x7805,x7806,x7807,x7808),f510(x7803,x7804,x7802,x7805,x7806,x7807,x7808)) % 177.51/177.20 [781]~E(x7811,x7812)+E(f510(x7813,x7814,x7815,x7811,x7816,x7817,x7818),f510(x7813,x7814,x7815,x7812,x7816,x7817,x7818)) % 177.51/177.20 [782]~E(x7821,x7822)+E(f510(x7823,x7824,x7825,x7826,x7821,x7827,x7828),f510(x7823,x7824,x7825,x7826,x7822,x7827,x7828)) % 177.51/177.20 [783]~E(x7831,x7832)+E(f510(x7833,x7834,x7835,x7836,x7837,x7831,x7838),f510(x7833,x7834,x7835,x7836,x7837,x7832,x7838)) % 177.51/177.20 [784]~E(x7841,x7842)+E(f510(x7843,x7844,x7845,x7846,x7847,x7848,x7841),f510(x7843,x7844,x7845,x7846,x7847,x7848,x7842)) % 177.51/177.20 [785]~E(x7851,x7852)+E(f865(x7851,x7853,x7854),f865(x7852,x7853,x7854)) % 177.51/177.20 [786]~E(x7861,x7862)+E(f865(x7863,x7861,x7864),f865(x7863,x7862,x7864)) % 177.51/177.20 [787]~E(x7871,x7872)+E(f865(x7873,x7874,x7871),f865(x7873,x7874,x7872)) % 177.51/177.20 [788]~E(x7881,x7882)+E(f255(x7881,x7883,x7884,x7885),f255(x7882,x7883,x7884,x7885)) % 177.51/177.20 [789]~E(x7891,x7892)+E(f255(x7893,x7891,x7894,x7895),f255(x7893,x7892,x7894,x7895)) % 177.51/177.20 [790]~E(x7901,x7902)+E(f255(x7903,x7904,x7901,x7905),f255(x7903,x7904,x7902,x7905)) % 177.51/177.20 [791]~E(x7911,x7912)+E(f255(x7913,x7914,x7915,x7911),f255(x7913,x7914,x7915,x7912)) % 177.51/177.20 [792]~E(x7921,x7922)+E(f88(x7921),f88(x7922)) % 177.51/177.20 [793]~E(x7931,x7932)+E(f814(x7931,x7933),f814(x7932,x7933)) % 177.51/177.20 [794]~E(x7941,x7942)+E(f814(x7943,x7941),f814(x7943,x7942)) % 177.51/177.20 [795]~E(x7951,x7952)+E(f555(x7951,x7953,x7954,x7955),f555(x7952,x7953,x7954,x7955)) % 177.51/177.20 [796]~E(x7961,x7962)+E(f555(x7963,x7961,x7964,x7965),f555(x7963,x7962,x7964,x7965)) % 177.51/177.20 [797]~E(x7971,x7972)+E(f555(x7973,x7974,x7971,x7975),f555(x7973,x7974,x7972,x7975)) % 177.51/177.20 [798]~E(x7981,x7982)+E(f555(x7983,x7984,x7985,x7981),f555(x7983,x7984,x7985,x7982)) % 177.51/177.20 [799]~E(x7991,x7992)+E(f759(x7991,x7993),f759(x7992,x7993)) % 177.51/177.20 [800]~E(x8001,x8002)+E(f759(x8003,x8001),f759(x8003,x8002)) % 177.51/177.20 [801]~E(x8011,x8012)+E(f345(x8011,x8013,x8014,x8015,x8016),f345(x8012,x8013,x8014,x8015,x8016)) % 177.51/177.20 [802]~E(x8021,x8022)+E(f345(x8023,x8021,x8024,x8025,x8026),f345(x8023,x8022,x8024,x8025,x8026)) % 177.51/177.20 [803]~E(x8031,x8032)+E(f345(x8033,x8034,x8031,x8035,x8036),f345(x8033,x8034,x8032,x8035,x8036)) % 177.51/177.20 [804]~E(x8041,x8042)+E(f345(x8043,x8044,x8045,x8041,x8046),f345(x8043,x8044,x8045,x8042,x8046)) % 177.51/177.20 [805]~E(x8051,x8052)+E(f345(x8053,x8054,x8055,x8056,x8051),f345(x8053,x8054,x8055,x8056,x8052)) % 177.51/177.20 [806]~E(x8061,x8062)+E(f849(x8061,x8063,x8064),f849(x8062,x8063,x8064)) % 177.51/177.20 [807]~E(x8071,x8072)+E(f849(x8073,x8071,x8074),f849(x8073,x8072,x8074)) % 177.51/177.20 [808]~E(x8081,x8082)+E(f849(x8083,x8084,x8081),f849(x8083,x8084,x8082)) % 177.51/177.20 [809]~E(x8091,x8092)+E(f228(x8091,x8093,x8094,x8095,x8096),f228(x8092,x8093,x8094,x8095,x8096)) % 177.51/177.20 [810]~E(x8101,x8102)+E(f228(x8103,x8101,x8104,x8105,x8106),f228(x8103,x8102,x8104,x8105,x8106)) % 177.51/177.20 [811]~E(x8111,x8112)+E(f228(x8113,x8114,x8111,x8115,x8116),f228(x8113,x8114,x8112,x8115,x8116)) % 177.51/177.20 [812]~E(x8121,x8122)+E(f228(x8123,x8124,x8125,x8121,x8126),f228(x8123,x8124,x8125,x8122,x8126)) % 177.51/177.20 [813]~E(x8131,x8132)+E(f228(x8133,x8134,x8135,x8136,x8131),f228(x8133,x8134,x8135,x8136,x8132)) % 177.51/177.20 [814]~E(x8141,x8142)+E(f656(x8141,x8143,x8144,x8145),f656(x8142,x8143,x8144,x8145)) % 177.51/177.20 [815]~E(x8151,x8152)+E(f656(x8153,x8151,x8154,x8155),f656(x8153,x8152,x8154,x8155)) % 177.51/177.20 [816]~E(x8161,x8162)+E(f656(x8163,x8164,x8161,x8165),f656(x8163,x8164,x8162,x8165)) % 177.51/177.20 [817]~E(x8171,x8172)+E(f656(x8173,x8174,x8175,x8171),f656(x8173,x8174,x8175,x8172)) % 177.51/177.20 [818]~E(x8181,x8182)+E(f211(x8181,x8183,x8184,x8185),f211(x8182,x8183,x8184,x8185)) % 177.51/177.20 [819]~E(x8191,x8192)+E(f211(x8193,x8191,x8194,x8195),f211(x8193,x8192,x8194,x8195)) % 177.51/177.20 [820]~E(x8201,x8202)+E(f211(x8203,x8204,x8201,x8205),f211(x8203,x8204,x8202,x8205)) % 177.51/177.20 [821]~E(x8211,x8212)+E(f211(x8213,x8214,x8215,x8211),f211(x8213,x8214,x8215,x8212)) % 177.51/177.20 [822]~E(x8221,x8222)+E(f186(x8221,x8223,x8224,x8225),f186(x8222,x8223,x8224,x8225)) % 177.51/177.20 [823]~E(x8231,x8232)+E(f186(x8233,x8231,x8234,x8235),f186(x8233,x8232,x8234,x8235)) % 177.51/177.20 [824]~E(x8241,x8242)+E(f186(x8243,x8244,x8241,x8245),f186(x8243,x8244,x8242,x8245)) % 177.51/177.20 [825]~E(x8251,x8252)+E(f186(x8253,x8254,x8255,x8251),f186(x8253,x8254,x8255,x8252)) % 177.51/177.20 [826]~E(x8261,x8262)+E(f788(x8261,x8263),f788(x8262,x8263)) % 177.51/177.20 [827]~E(x8271,x8272)+E(f788(x8273,x8271),f788(x8273,x8272)) % 177.51/177.20 [828]~E(x8281,x8282)+E(f529(x8281,x8283,x8284),f529(x8282,x8283,x8284)) % 177.51/177.20 [829]~E(x8291,x8292)+E(f529(x8293,x8291,x8294),f529(x8293,x8292,x8294)) % 177.51/177.20 [830]~E(x8301,x8302)+E(f529(x8303,x8304,x8301),f529(x8303,x8304,x8302)) % 177.51/177.20 [831]~E(x8311,x8312)+E(f602(x8311,x8313,x8314,x8315,x8316),f602(x8312,x8313,x8314,x8315,x8316)) % 177.51/177.20 [832]~E(x8321,x8322)+E(f602(x8323,x8321,x8324,x8325,x8326),f602(x8323,x8322,x8324,x8325,x8326)) % 177.51/177.20 [833]~E(x8331,x8332)+E(f602(x8333,x8334,x8331,x8335,x8336),f602(x8333,x8334,x8332,x8335,x8336)) % 177.51/177.20 [834]~E(x8341,x8342)+E(f602(x8343,x8344,x8345,x8341,x8346),f602(x8343,x8344,x8345,x8342,x8346)) % 177.51/177.20 [835]~E(x8351,x8352)+E(f602(x8353,x8354,x8355,x8356,x8351),f602(x8353,x8354,x8355,x8356,x8352)) % 177.51/177.20 [836]~E(x8361,x8362)+E(f551(x8361,x8363,x8364,x8365),f551(x8362,x8363,x8364,x8365)) % 177.51/177.20 [837]~E(x8371,x8372)+E(f551(x8373,x8371,x8374,x8375),f551(x8373,x8372,x8374,x8375)) % 177.51/177.20 [838]~E(x8381,x8382)+E(f551(x8383,x8384,x8381,x8385),f551(x8383,x8384,x8382,x8385)) % 177.51/177.20 [839]~E(x8391,x8392)+E(f551(x8393,x8394,x8395,x8391),f551(x8393,x8394,x8395,x8392)) % 177.51/177.20 [840]~E(x8401,x8402)+E(f562(x8401,x8403,x8404,x8405,x8406),f562(x8402,x8403,x8404,x8405,x8406)) % 177.51/177.20 [841]~E(x8411,x8412)+E(f562(x8413,x8411,x8414,x8415,x8416),f562(x8413,x8412,x8414,x8415,x8416)) % 177.51/177.20 [842]~E(x8421,x8422)+E(f562(x8423,x8424,x8421,x8425,x8426),f562(x8423,x8424,x8422,x8425,x8426)) % 177.51/177.20 [843]~E(x8431,x8432)+E(f562(x8433,x8434,x8435,x8431,x8436),f562(x8433,x8434,x8435,x8432,x8436)) % 177.51/177.20 [844]~E(x8441,x8442)+E(f562(x8443,x8444,x8445,x8446,x8441),f562(x8443,x8444,x8445,x8446,x8442)) % 177.51/177.20 [845]~E(x8451,x8452)+E(f26(x8451,x8453,x8454),f26(x8452,x8453,x8454)) % 177.51/177.20 [846]~E(x8461,x8462)+E(f26(x8463,x8461,x8464),f26(x8463,x8462,x8464)) % 177.51/177.20 [847]~E(x8471,x8472)+E(f26(x8473,x8474,x8471),f26(x8473,x8474,x8472)) % 177.51/177.20 [848]~E(x8481,x8482)+E(f479(x8481,x8483,x8484),f479(x8482,x8483,x8484)) % 177.51/177.20 [849]~E(x8491,x8492)+E(f479(x8493,x8491,x8494),f479(x8493,x8492,x8494)) % 177.51/177.20 [850]~E(x8501,x8502)+E(f479(x8503,x8504,x8501),f479(x8503,x8504,x8502)) % 177.51/177.20 [851]~E(x8511,x8512)+E(f798(x8511,x8513),f798(x8512,x8513)) % 177.51/177.20 [852]~E(x8521,x8522)+E(f798(x8523,x8521),f798(x8523,x8522)) % 177.51/177.20 [853]~E(x8531,x8532)+E(f470(x8531,x8533,x8534),f470(x8532,x8533,x8534)) % 177.51/177.20 [854]~E(x8541,x8542)+E(f470(x8543,x8541,x8544),f470(x8543,x8542,x8544)) % 177.51/177.20 [855]~E(x8551,x8552)+E(f470(x8553,x8554,x8551),f470(x8553,x8554,x8552)) % 177.51/177.20 [856]~E(x8561,x8562)+E(f515(x8561,x8563,x8564),f515(x8562,x8563,x8564)) % 177.51/177.20 [857]~E(x8571,x8572)+E(f515(x8573,x8571,x8574),f515(x8573,x8572,x8574)) % 177.51/177.20 [858]~E(x8581,x8582)+E(f515(x8583,x8584,x8581),f515(x8583,x8584,x8582)) % 177.51/177.20 [859]~E(x8591,x8592)+E(f382(x8591,x8593,x8594,x8595,x8596),f382(x8592,x8593,x8594,x8595,x8596)) % 177.51/177.20 [860]~E(x8601,x8602)+E(f382(x8603,x8601,x8604,x8605,x8606),f382(x8603,x8602,x8604,x8605,x8606)) % 177.51/177.20 [861]~E(x8611,x8612)+E(f382(x8613,x8614,x8611,x8615,x8616),f382(x8613,x8614,x8612,x8615,x8616)) % 177.51/177.20 [862]~E(x8621,x8622)+E(f382(x8623,x8624,x8625,x8621,x8626),f382(x8623,x8624,x8625,x8622,x8626)) % 177.51/177.20 [863]~E(x8631,x8632)+E(f382(x8633,x8634,x8635,x8636,x8631),f382(x8633,x8634,x8635,x8636,x8632)) % 177.51/177.20 [864]~E(x8641,x8642)+E(f612(x8641,x8643,x8644,x8645,x8646),f612(x8642,x8643,x8644,x8645,x8646)) % 177.51/177.20 [865]~E(x8651,x8652)+E(f612(x8653,x8651,x8654,x8655,x8656),f612(x8653,x8652,x8654,x8655,x8656)) % 177.51/177.20 [866]~E(x8661,x8662)+E(f612(x8663,x8664,x8661,x8665,x8666),f612(x8663,x8664,x8662,x8665,x8666)) % 177.51/177.20 [867]~E(x8671,x8672)+E(f612(x8673,x8674,x8675,x8671,x8676),f612(x8673,x8674,x8675,x8672,x8676)) % 177.51/177.20 [868]~E(x8681,x8682)+E(f612(x8683,x8684,x8685,x8686,x8681),f612(x8683,x8684,x8685,x8686,x8682)) % 177.51/177.20 [869]~E(x8691,x8692)+E(f312(x8691,x8693),f312(x8692,x8693)) % 177.51/177.20 [870]~E(x8701,x8702)+E(f312(x8703,x8701),f312(x8703,x8702)) % 177.51/177.20 [871]~E(x8711,x8712)+E(f646(x8711,x8713),f646(x8712,x8713)) % 177.51/177.20 [872]~E(x8721,x8722)+E(f646(x8723,x8721),f646(x8723,x8722)) % 177.51/177.20 [873]~E(x8731,x8732)+E(f467(x8731,x8733,x8734),f467(x8732,x8733,x8734)) % 177.51/177.20 [874]~E(x8741,x8742)+E(f467(x8743,x8741,x8744),f467(x8743,x8742,x8744)) % 177.51/177.20 [875]~E(x8751,x8752)+E(f467(x8753,x8754,x8751),f467(x8753,x8754,x8752)) % 177.51/177.20 [876]~E(x8761,x8762)+E(f246(x8761,x8763,x8764,x8765,x8766,x8767),f246(x8762,x8763,x8764,x8765,x8766,x8767)) % 177.51/177.20 [877]~E(x8771,x8772)+E(f246(x8773,x8771,x8774,x8775,x8776,x8777),f246(x8773,x8772,x8774,x8775,x8776,x8777)) % 177.51/177.20 [878]~E(x8781,x8782)+E(f246(x8783,x8784,x8781,x8785,x8786,x8787),f246(x8783,x8784,x8782,x8785,x8786,x8787)) % 177.51/177.20 [879]~E(x8791,x8792)+E(f246(x8793,x8794,x8795,x8791,x8796,x8797),f246(x8793,x8794,x8795,x8792,x8796,x8797)) % 177.51/177.20 [880]~E(x8801,x8802)+E(f246(x8803,x8804,x8805,x8806,x8801,x8807),f246(x8803,x8804,x8805,x8806,x8802,x8807)) % 177.51/177.20 [881]~E(x8811,x8812)+E(f246(x8813,x8814,x8815,x8816,x8817,x8811),f246(x8813,x8814,x8815,x8816,x8817,x8812)) % 177.51/177.20 [882]~E(x8821,x8822)+E(f505(x8821,x8823,x8824),f505(x8822,x8823,x8824)) % 177.51/177.20 [883]~E(x8831,x8832)+E(f505(x8833,x8831,x8834),f505(x8833,x8832,x8834)) % 177.51/177.20 [884]~E(x8841,x8842)+E(f505(x8843,x8844,x8841),f505(x8843,x8844,x8842)) % 177.51/177.20 [885]~E(x8851,x8852)+E(f194(x8851,x8853),f194(x8852,x8853)) % 177.51/177.20 [886]~E(x8861,x8862)+E(f194(x8863,x8861),f194(x8863,x8862)) % 177.51/177.20 [887]~E(x8871,x8872)+E(f898(x8871,x8873,x8874),f898(x8872,x8873,x8874)) % 177.51/177.20 [888]~E(x8881,x8882)+E(f898(x8883,x8881,x8884),f898(x8883,x8882,x8884)) % 177.51/177.20 [889]~E(x8891,x8892)+E(f898(x8893,x8894,x8891),f898(x8893,x8894,x8892)) % 177.51/177.20 [890]~E(x8901,x8902)+E(f122(x8901,x8903),f122(x8902,x8903)) % 177.51/177.20 [891]~E(x8911,x8912)+E(f122(x8913,x8911),f122(x8913,x8912)) % 177.51/177.20 [892]~E(x8921,x8922)+E(f229(x8921,x8923),f229(x8922,x8923)) % 177.51/177.20 [893]~E(x8931,x8932)+E(f229(x8933,x8931),f229(x8933,x8932)) % 177.51/177.20 [894]~E(x8941,x8942)+E(f623(x8941,x8943,x8944,x8945,x8946),f623(x8942,x8943,x8944,x8945,x8946)) % 177.51/177.20 [895]~E(x8951,x8952)+E(f623(x8953,x8951,x8954,x8955,x8956),f623(x8953,x8952,x8954,x8955,x8956)) % 177.51/177.20 [896]~E(x8961,x8962)+E(f623(x8963,x8964,x8961,x8965,x8966),f623(x8963,x8964,x8962,x8965,x8966)) % 177.51/177.20 [897]~E(x8971,x8972)+E(f623(x8973,x8974,x8975,x8971,x8976),f623(x8973,x8974,x8975,x8972,x8976)) % 177.51/177.20 [898]~E(x8981,x8982)+E(f623(x8983,x8984,x8985,x8986,x8981),f623(x8983,x8984,x8985,x8986,x8982)) % 177.51/177.20 [899]~E(x8991,x8992)+E(f726(x8991,x8993),f726(x8992,x8993)) % 177.51/177.20 [900]~E(x9001,x9002)+E(f726(x9003,x9001),f726(x9003,x9002)) % 177.51/177.20 [901]~E(x9011,x9012)+E(f297(x9011,x9013,x9014,x9015,x9016),f297(x9012,x9013,x9014,x9015,x9016)) % 177.51/177.20 [902]~E(x9021,x9022)+E(f297(x9023,x9021,x9024,x9025,x9026),f297(x9023,x9022,x9024,x9025,x9026)) % 177.51/177.20 [903]~E(x9031,x9032)+E(f297(x9033,x9034,x9031,x9035,x9036),f297(x9033,x9034,x9032,x9035,x9036)) % 177.51/177.20 [904]~E(x9041,x9042)+E(f297(x9043,x9044,x9045,x9041,x9046),f297(x9043,x9044,x9045,x9042,x9046)) % 177.51/177.20 [905]~E(x9051,x9052)+E(f297(x9053,x9054,x9055,x9056,x9051),f297(x9053,x9054,x9055,x9056,x9052)) % 177.51/177.20 [906]~E(x9061,x9062)+E(f676(x9061,x9063,x9064,x9065,x9066),f676(x9062,x9063,x9064,x9065,x9066)) % 177.51/177.20 [907]~E(x9071,x9072)+E(f676(x9073,x9071,x9074,x9075,x9076),f676(x9073,x9072,x9074,x9075,x9076)) % 177.51/177.20 [908]~E(x9081,x9082)+E(f676(x9083,x9084,x9081,x9085,x9086),f676(x9083,x9084,x9082,x9085,x9086)) % 177.51/177.20 [909]~E(x9091,x9092)+E(f676(x9093,x9094,x9095,x9091,x9096),f676(x9093,x9094,x9095,x9092,x9096)) % 177.51/177.20 [910]~E(x9101,x9102)+E(f676(x9103,x9104,x9105,x9106,x9101),f676(x9103,x9104,x9105,x9106,x9102)) % 177.51/177.20 [911]~E(x9111,x9112)+E(f751(x9111,x9113,x9114),f751(x9112,x9113,x9114)) % 177.51/177.20 [912]~E(x9121,x9122)+E(f751(x9123,x9121,x9124),f751(x9123,x9122,x9124)) % 177.51/177.20 [913]~E(x9131,x9132)+E(f751(x9133,x9134,x9131),f751(x9133,x9134,x9132)) % 177.51/177.20 [914]~E(x9141,x9142)+E(f863(x9141,x9143,x9144),f863(x9142,x9143,x9144)) % 177.51/177.20 [915]~E(x9151,x9152)+E(f863(x9153,x9151,x9154),f863(x9153,x9152,x9154)) % 177.51/177.20 [916]~E(x9161,x9162)+E(f863(x9163,x9164,x9161),f863(x9163,x9164,x9162)) % 177.51/177.20 [917]~E(x9171,x9172)+E(f547(x9171,x9173,x9174,x9175),f547(x9172,x9173,x9174,x9175)) % 177.51/177.20 [918]~E(x9181,x9182)+E(f547(x9183,x9181,x9184,x9185),f547(x9183,x9182,x9184,x9185)) % 177.51/177.20 [919]~E(x9191,x9192)+E(f547(x9193,x9194,x9191,x9195),f547(x9193,x9194,x9192,x9195)) % 177.51/177.20 [920]~E(x9201,x9202)+E(f547(x9203,x9204,x9205,x9201),f547(x9203,x9204,x9205,x9202)) % 177.51/177.20 [921]~E(x9211,x9212)+E(f679(x9211,x9213,x9214,x9215,x9216),f679(x9212,x9213,x9214,x9215,x9216)) % 177.51/177.20 [922]~E(x9221,x9222)+E(f679(x9223,x9221,x9224,x9225,x9226),f679(x9223,x9222,x9224,x9225,x9226)) % 177.51/177.20 [923]~E(x9231,x9232)+E(f679(x9233,x9234,x9231,x9235,x9236),f679(x9233,x9234,x9232,x9235,x9236)) % 177.51/177.20 [924]~E(x9241,x9242)+E(f679(x9243,x9244,x9245,x9241,x9246),f679(x9243,x9244,x9245,x9242,x9246)) % 177.51/177.20 [925]~E(x9251,x9252)+E(f679(x9253,x9254,x9255,x9256,x9251),f679(x9253,x9254,x9255,x9256,x9252)) % 177.51/177.20 [926]~E(x9261,x9262)+E(f613(x9261,x9263,x9264,x9265,x9266),f613(x9262,x9263,x9264,x9265,x9266)) % 177.51/177.20 [927]~E(x9271,x9272)+E(f613(x9273,x9271,x9274,x9275,x9276),f613(x9273,x9272,x9274,x9275,x9276)) % 177.51/177.20 [928]~E(x9281,x9282)+E(f613(x9283,x9284,x9281,x9285,x9286),f613(x9283,x9284,x9282,x9285,x9286)) % 177.51/177.20 [929]~E(x9291,x9292)+E(f613(x9293,x9294,x9295,x9291,x9296),f613(x9293,x9294,x9295,x9292,x9296)) % 177.51/177.20 [930]~E(x9301,x9302)+E(f613(x9303,x9304,x9305,x9306,x9301),f613(x9303,x9304,x9305,x9306,x9302)) % 177.51/177.20 [931]~E(x9311,x9312)+E(f54(x9311,x9313),f54(x9312,x9313)) % 177.51/177.20 [932]~E(x9321,x9322)+E(f54(x9323,x9321),f54(x9323,x9322)) % 177.51/177.20 [933]~E(x9331,x9332)+E(f364(x9331,x9333,x9334),f364(x9332,x9333,x9334)) % 177.51/177.20 [934]~E(x9341,x9342)+E(f364(x9343,x9341,x9344),f364(x9343,x9342,x9344)) % 177.51/177.20 [935]~E(x9351,x9352)+E(f364(x9353,x9354,x9351),f364(x9353,x9354,x9352)) % 177.51/177.20 [936]~E(x9361,x9362)+E(f777(x9361,x9363,x9364,x9365),f777(x9362,x9363,x9364,x9365)) % 177.51/177.20 [937]~E(x9371,x9372)+E(f777(x9373,x9371,x9374,x9375),f777(x9373,x9372,x9374,x9375)) % 177.51/177.20 [938]~E(x9381,x9382)+E(f777(x9383,x9384,x9381,x9385),f777(x9383,x9384,x9382,x9385)) % 177.51/177.20 [939]~E(x9391,x9392)+E(f777(x9393,x9394,x9395,x9391),f777(x9393,x9394,x9395,x9392)) % 177.51/177.20 [940]~E(x9401,x9402)+E(f695(x9401,x9403,x9404,x9405,x9406),f695(x9402,x9403,x9404,x9405,x9406)) % 177.51/177.20 [941]~E(x9411,x9412)+E(f695(x9413,x9411,x9414,x9415,x9416),f695(x9413,x9412,x9414,x9415,x9416)) % 177.51/177.20 [942]~E(x9421,x9422)+E(f695(x9423,x9424,x9421,x9425,x9426),f695(x9423,x9424,x9422,x9425,x9426)) % 177.51/177.20 [943]~E(x9431,x9432)+E(f695(x9433,x9434,x9435,x9431,x9436),f695(x9433,x9434,x9435,x9432,x9436)) % 177.51/177.20 [944]~E(x9441,x9442)+E(f695(x9443,x9444,x9445,x9446,x9441),f695(x9443,x9444,x9445,x9446,x9442)) % 177.51/177.20 [945]~E(x9451,x9452)+E(f441(x9451,x9453),f441(x9452,x9453)) % 177.51/177.20 [946]~E(x9461,x9462)+E(f441(x9463,x9461),f441(x9463,x9462)) % 177.51/177.20 [947]~E(x9471,x9472)+E(f698(x9471,x9473,x9474),f698(x9472,x9473,x9474)) % 177.51/177.20 [948]~E(x9481,x9482)+E(f698(x9483,x9481,x9484),f698(x9483,x9482,x9484)) % 177.51/177.20 [949]~E(x9491,x9492)+E(f698(x9493,x9494,x9491),f698(x9493,x9494,x9492)) % 177.51/177.20 [950]~E(x9501,x9502)+E(f576(x9501,x9503,x9504),f576(x9502,x9503,x9504)) % 177.51/177.20 [951]~E(x9511,x9512)+E(f576(x9513,x9511,x9514),f576(x9513,x9512,x9514)) % 177.51/177.20 [952]~E(x9521,x9522)+E(f576(x9523,x9524,x9521),f576(x9523,x9524,x9522)) % 177.51/177.20 [953]~E(x9531,x9532)+E(f418(x9531,x9533,x9534),f418(x9532,x9533,x9534)) % 177.51/177.20 [954]~E(x9541,x9542)+E(f418(x9543,x9541,x9544),f418(x9543,x9542,x9544)) % 177.51/177.20 [955]~E(x9551,x9552)+E(f418(x9553,x9554,x9551),f418(x9553,x9554,x9552)) % 177.51/177.20 [956]~E(x9561,x9562)+E(f207(x9561,x9563,x9564,x9565),f207(x9562,x9563,x9564,x9565)) % 177.51/177.20 [957]~E(x9571,x9572)+E(f207(x9573,x9571,x9574,x9575),f207(x9573,x9572,x9574,x9575)) % 177.51/177.20 [958]~E(x9581,x9582)+E(f207(x9583,x9584,x9581,x9585),f207(x9583,x9584,x9582,x9585)) % 177.51/177.20 [959]~E(x9591,x9592)+E(f207(x9593,x9594,x9595,x9591),f207(x9593,x9594,x9595,x9592)) % 177.51/177.20 [960]~E(x9601,x9602)+E(f476(x9601,x9603,x9604),f476(x9602,x9603,x9604)) % 177.51/177.20 [961]~E(x9611,x9612)+E(f476(x9613,x9611,x9614),f476(x9613,x9612,x9614)) % 177.51/177.20 [962]~E(x9621,x9622)+E(f476(x9623,x9624,x9621),f476(x9623,x9624,x9622)) % 177.51/177.20 [963]~E(x9631,x9632)+E(f13(x9631,x9633),f13(x9632,x9633)) % 177.51/177.20 [964]~E(x9641,x9642)+E(f13(x9643,x9641),f13(x9643,x9642)) % 177.51/177.20 [965]~E(x9651,x9652)+E(f527(x9651,x9653,x9654),f527(x9652,x9653,x9654)) % 177.51/177.20 [966]~E(x9661,x9662)+E(f527(x9663,x9661,x9664),f527(x9663,x9662,x9664)) % 177.51/177.20 [967]~E(x9671,x9672)+E(f527(x9673,x9674,x9671),f527(x9673,x9674,x9672)) % 177.51/177.20 [968]~E(x9681,x9682)+E(f187(x9681),f187(x9682)) % 177.51/177.20 [969]~E(x9691,x9692)+E(f369(x9691,x9693,x9694),f369(x9692,x9693,x9694)) % 177.51/177.20 [970]~E(x9701,x9702)+E(f369(x9703,x9701,x9704),f369(x9703,x9702,x9704)) % 177.51/177.20 [971]~E(x9711,x9712)+E(f369(x9713,x9714,x9711),f369(x9713,x9714,x9712)) % 177.51/177.20 [972]~E(x9721,x9722)+E(f478(x9721,x9723,x9724),f478(x9722,x9723,x9724)) % 177.51/177.20 [973]~E(x9731,x9732)+E(f478(x9733,x9731,x9734),f478(x9733,x9732,x9734)) % 177.51/177.20 [974]~E(x9741,x9742)+E(f478(x9743,x9744,x9741),f478(x9743,x9744,x9742)) % 177.51/177.20 [975]~E(x9751,x9752)+E(f634(x9751,x9753),f634(x9752,x9753)) % 177.51/177.20 [976]~E(x9761,x9762)+E(f634(x9763,x9761),f634(x9763,x9762)) % 177.51/177.20 [977]~E(x9771,x9772)+E(f412(x9771,x9773,x9774),f412(x9772,x9773,x9774)) % 177.51/177.20 [978]~E(x9781,x9782)+E(f412(x9783,x9781,x9784),f412(x9783,x9782,x9784)) % 177.51/177.20 [979]~E(x9791,x9792)+E(f412(x9793,x9794,x9791),f412(x9793,x9794,x9792)) % 177.51/177.20 [980]~E(x9801,x9802)+E(f728(x9801,x9803,x9804,x9805,x9806,x9807,x9808,x9809),f728(x9802,x9803,x9804,x9805,x9806,x9807,x9808,x9809)) % 177.51/177.20 [981]~E(x9811,x9812)+E(f728(x9813,x9811,x9814,x9815,x9816,x9817,x9818,x9819),f728(x9813,x9812,x9814,x9815,x9816,x9817,x9818,x9819)) % 177.51/177.20 [982]~E(x9821,x9822)+E(f728(x9823,x9824,x9821,x9825,x9826,x9827,x9828,x9829),f728(x9823,x9824,x9822,x9825,x9826,x9827,x9828,x9829)) % 177.51/177.20 [983]~E(x9831,x9832)+E(f728(x9833,x9834,x9835,x9831,x9836,x9837,x9838,x9839),f728(x9833,x9834,x9835,x9832,x9836,x9837,x9838,x9839)) % 177.51/177.20 [984]~E(x9841,x9842)+E(f728(x9843,x9844,x9845,x9846,x9841,x9847,x9848,x9849),f728(x9843,x9844,x9845,x9846,x9842,x9847,x9848,x9849)) % 177.51/177.20 [985]~E(x9851,x9852)+E(f728(x9853,x9854,x9855,x9856,x9857,x9851,x9858,x9859),f728(x9853,x9854,x9855,x9856,x9857,x9852,x9858,x9859)) % 177.51/177.20 [986]~E(x9861,x9862)+E(f728(x9863,x9864,x9865,x9866,x9867,x9868,x9861,x9869),f728(x9863,x9864,x9865,x9866,x9867,x9868,x9862,x9869)) % 177.51/177.20 [987]~E(x9871,x9872)+E(f728(x9873,x9874,x9875,x9876,x9877,x9878,x9879,x9871),f728(x9873,x9874,x9875,x9876,x9877,x9878,x9879,x9872)) % 177.51/177.20 [988]~E(x9881,x9882)+E(f44(x9881),f44(x9882)) % 177.51/177.20 [989]~E(x9891,x9892)+E(f839(x9891,x9893,x9894,x9895,x9896,x9897,x9898,x9899),f839(x9892,x9893,x9894,x9895,x9896,x9897,x9898,x9899)) % 177.51/177.20 [990]~E(x9901,x9902)+E(f839(x9903,x9901,x9904,x9905,x9906,x9907,x9908,x9909),f839(x9903,x9902,x9904,x9905,x9906,x9907,x9908,x9909)) % 177.51/177.20 [991]~E(x9911,x9912)+E(f839(x9913,x9914,x9911,x9915,x9916,x9917,x9918,x9919),f839(x9913,x9914,x9912,x9915,x9916,x9917,x9918,x9919)) % 177.51/177.20 [992]~E(x9921,x9922)+E(f839(x9923,x9924,x9925,x9921,x9926,x9927,x9928,x9929),f839(x9923,x9924,x9925,x9922,x9926,x9927,x9928,x9929)) % 177.51/177.20 [993]~E(x9931,x9932)+E(f839(x9933,x9934,x9935,x9936,x9931,x9937,x9938,x9939),f839(x9933,x9934,x9935,x9936,x9932,x9937,x9938,x9939)) % 177.51/177.20 [994]~E(x9941,x9942)+E(f839(x9943,x9944,x9945,x9946,x9947,x9941,x9948,x9949),f839(x9943,x9944,x9945,x9946,x9947,x9942,x9948,x9949)) % 177.51/177.20 [995]~E(x9951,x9952)+E(f839(x9953,x9954,x9955,x9956,x9957,x9958,x9951,x9959),f839(x9953,x9954,x9955,x9956,x9957,x9958,x9952,x9959)) % 177.51/177.20 [996]~E(x9961,x9962)+E(f839(x9963,x9964,x9965,x9966,x9967,x9968,x9969,x9961),f839(x9963,x9964,x9965,x9966,x9967,x9968,x9969,x9962)) % 177.51/177.20 [997]~E(x9971,x9972)+E(f595(x9971,x9973),f595(x9972,x9973)) % 177.51/177.20 [998]~E(x9981,x9982)+E(f595(x9983,x9981),f595(x9983,x9982)) % 177.51/177.20 [999]~E(x9991,x9992)+E(f608(x9991,x9993),f608(x9992,x9993)) % 177.51/177.20 [1000]~E(x10001,x10002)+E(f608(x10003,x10001),f608(x10003,x10002)) % 177.51/177.20 [1001]~E(x10011,x10012)+E(f406(x10011),f406(x10012)) % 177.51/177.20 [1002]~E(x10021,x10022)+E(f436(x10021,x10023,x10024,x10025),f436(x10022,x10023,x10024,x10025)) % 177.51/177.20 [1003]~E(x10031,x10032)+E(f436(x10033,x10031,x10034,x10035),f436(x10033,x10032,x10034,x10035)) % 177.51/177.20 [1004]~E(x10041,x10042)+E(f436(x10043,x10044,x10041,x10045),f436(x10043,x10044,x10042,x10045)) % 177.51/177.20 [1005]~E(x10051,x10052)+E(f436(x10053,x10054,x10055,x10051),f436(x10053,x10054,x10055,x10052)) % 177.51/177.20 [1006]~E(x10061,x10062)+E(f156(x10061,x10063,x10064),f156(x10062,x10063,x10064)) % 177.51/177.20 [1007]~E(x10071,x10072)+E(f156(x10073,x10071,x10074),f156(x10073,x10072,x10074)) % 177.51/177.20 [1008]~E(x10081,x10082)+E(f156(x10083,x10084,x10081),f156(x10083,x10084,x10082)) % 177.51/177.20 [1009]~E(x10091,x10092)+E(f755(x10091,x10093,x10094),f755(x10092,x10093,x10094)) % 177.51/177.20 [1010]~E(x10101,x10102)+E(f755(x10103,x10101,x10104),f755(x10103,x10102,x10104)) % 177.51/177.20 [1011]~E(x10111,x10112)+E(f755(x10113,x10114,x10111),f755(x10113,x10114,x10112)) % 177.51/177.20 [1012]~E(x10121,x10122)+E(f770(x10121,x10123,x10124,x10125,x10126),f770(x10122,x10123,x10124,x10125,x10126)) % 177.51/177.20 [1013]~E(x10131,x10132)+E(f770(x10133,x10131,x10134,x10135,x10136),f770(x10133,x10132,x10134,x10135,x10136)) % 177.51/177.20 [1014]~E(x10141,x10142)+E(f770(x10143,x10144,x10141,x10145,x10146),f770(x10143,x10144,x10142,x10145,x10146)) % 177.51/177.20 [1015]~E(x10151,x10152)+E(f770(x10153,x10154,x10155,x10151,x10156),f770(x10153,x10154,x10155,x10152,x10156)) % 177.51/177.20 [1016]~E(x10161,x10162)+E(f770(x10163,x10164,x10165,x10166,x10161),f770(x10163,x10164,x10165,x10166,x10162)) % 177.51/177.20 [1017]~E(x10171,x10172)+E(f819(x10171,x10173),f819(x10172,x10173)) % 177.51/177.20 [1018]~E(x10181,x10182)+E(f819(x10183,x10181),f819(x10183,x10182)) % 177.51/177.20 [1019]~E(x10191,x10192)+E(f197(x10191,x10193,x10194,x10195),f197(x10192,x10193,x10194,x10195)) % 177.51/177.20 [1020]~E(x10201,x10202)+E(f197(x10203,x10201,x10204,x10205),f197(x10203,x10202,x10204,x10205)) % 177.51/177.20 [1021]~E(x10211,x10212)+E(f197(x10213,x10214,x10211,x10215),f197(x10213,x10214,x10212,x10215)) % 177.51/177.20 [1022]~E(x10221,x10222)+E(f197(x10223,x10224,x10225,x10221),f197(x10223,x10224,x10225,x10222)) % 177.51/177.20 [1023]~E(x10231,x10232)+E(f360(x10231,x10233,x10234,x10235,x10236,x10237),f360(x10232,x10233,x10234,x10235,x10236,x10237)) % 177.51/177.20 [1024]~E(x10241,x10242)+E(f360(x10243,x10241,x10244,x10245,x10246,x10247),f360(x10243,x10242,x10244,x10245,x10246,x10247)) % 177.51/177.20 [1025]~E(x10251,x10252)+E(f360(x10253,x10254,x10251,x10255,x10256,x10257),f360(x10253,x10254,x10252,x10255,x10256,x10257)) % 177.51/177.20 [1026]~E(x10261,x10262)+E(f360(x10263,x10264,x10265,x10261,x10266,x10267),f360(x10263,x10264,x10265,x10262,x10266,x10267)) % 177.51/177.20 [1027]~E(x10271,x10272)+E(f360(x10273,x10274,x10275,x10276,x10271,x10277),f360(x10273,x10274,x10275,x10276,x10272,x10277)) % 177.51/177.20 [1028]~E(x10281,x10282)+E(f360(x10283,x10284,x10285,x10286,x10287,x10281),f360(x10283,x10284,x10285,x10286,x10287,x10282)) % 177.51/177.20 [1029]~E(x10291,x10292)+E(f320(x10291,x10293,x10294,x10295),f320(x10292,x10293,x10294,x10295)) % 177.51/177.20 [1030]~E(x10301,x10302)+E(f320(x10303,x10301,x10304,x10305),f320(x10303,x10302,x10304,x10305)) % 177.51/177.20 [1031]~E(x10311,x10312)+E(f320(x10313,x10314,x10311,x10315),f320(x10313,x10314,x10312,x10315)) % 177.51/177.20 [1032]~E(x10321,x10322)+E(f320(x10323,x10324,x10325,x10321),f320(x10323,x10324,x10325,x10322)) % 177.51/177.20 [1033]~E(x10331,x10332)+E(f425(x10331,x10333,x10334),f425(x10332,x10333,x10334)) % 177.51/177.20 [1034]~E(x10341,x10342)+E(f425(x10343,x10341,x10344),f425(x10343,x10342,x10344)) % 177.51/177.20 [1035]~E(x10351,x10352)+E(f425(x10353,x10354,x10351),f425(x10353,x10354,x10352)) % 177.51/177.20 [1036]~E(x10361,x10362)+E(f647(x10361,x10363,x10364,x10365,x10366),f647(x10362,x10363,x10364,x10365,x10366)) % 177.51/177.20 [1037]~E(x10371,x10372)+E(f647(x10373,x10371,x10374,x10375,x10376),f647(x10373,x10372,x10374,x10375,x10376)) % 177.51/177.20 [1038]~E(x10381,x10382)+E(f647(x10383,x10384,x10381,x10385,x10386),f647(x10383,x10384,x10382,x10385,x10386)) % 177.51/177.20 [1039]~E(x10391,x10392)+E(f647(x10393,x10394,x10395,x10391,x10396),f647(x10393,x10394,x10395,x10392,x10396)) % 177.51/177.20 [1040]~E(x10401,x10402)+E(f647(x10403,x10404,x10405,x10406,x10401),f647(x10403,x10404,x10405,x10406,x10402)) % 177.51/177.20 [1041]~E(x10411,x10412)+E(f426(x10411,x10413,x10414),f426(x10412,x10413,x10414)) % 177.51/177.20 [1042]~E(x10421,x10422)+E(f426(x10423,x10421,x10424),f426(x10423,x10422,x10424)) % 177.51/177.20 [1043]~E(x10431,x10432)+E(f426(x10433,x10434,x10431),f426(x10433,x10434,x10432)) % 177.51/177.20 [1044]~E(x10441,x10442)+E(f503(x10441,x10443,x10444),f503(x10442,x10443,x10444)) % 177.51/177.20 [1045]~E(x10451,x10452)+E(f503(x10453,x10451,x10454),f503(x10453,x10452,x10454)) % 177.51/177.20 [1046]~E(x10461,x10462)+E(f503(x10463,x10464,x10461),f503(x10463,x10464,x10462)) % 177.51/177.20 [1047]~E(x10471,x10472)+E(f459(x10471,x10473,x10474),f459(x10472,x10473,x10474)) % 177.51/177.20 [1048]~E(x10481,x10482)+E(f459(x10483,x10481,x10484),f459(x10483,x10482,x10484)) % 177.51/177.20 [1049]~E(x10491,x10492)+E(f459(x10493,x10494,x10491),f459(x10493,x10494,x10492)) % 177.51/177.20 [1050]~E(x10501,x10502)+E(f442(x10501,x10503),f442(x10502,x10503)) % 177.51/177.20 [1051]~E(x10511,x10512)+E(f442(x10513,x10511),f442(x10513,x10512)) % 177.51/177.20 [1052]~E(x10521,x10522)+E(f77(x10521,x10523,x10524,x10525),f77(x10522,x10523,x10524,x10525)) % 177.51/177.20 [1053]~E(x10531,x10532)+E(f77(x10533,x10531,x10534,x10535),f77(x10533,x10532,x10534,x10535)) % 177.51/177.20 [1054]~E(x10541,x10542)+E(f77(x10543,x10544,x10541,x10545),f77(x10543,x10544,x10542,x10545)) % 177.51/177.20 [1055]~E(x10551,x10552)+E(f77(x10553,x10554,x10555,x10551),f77(x10553,x10554,x10555,x10552)) % 177.51/177.20 [1056]~E(x10561,x10562)+E(f593(x10561,x10563,x10564,x10565,x10566,x10567,x10568,x10569),f593(x10562,x10563,x10564,x10565,x10566,x10567,x10568,x10569)) % 177.51/177.20 [1057]~E(x10571,x10572)+E(f593(x10573,x10571,x10574,x10575,x10576,x10577,x10578,x10579),f593(x10573,x10572,x10574,x10575,x10576,x10577,x10578,x10579)) % 177.51/177.20 [1058]~E(x10581,x10582)+E(f593(x10583,x10584,x10581,x10585,x10586,x10587,x10588,x10589),f593(x10583,x10584,x10582,x10585,x10586,x10587,x10588,x10589)) % 177.51/177.20 [1059]~E(x10591,x10592)+E(f593(x10593,x10594,x10595,x10591,x10596,x10597,x10598,x10599),f593(x10593,x10594,x10595,x10592,x10596,x10597,x10598,x10599)) % 177.51/177.20 [1060]~E(x10601,x10602)+E(f593(x10603,x10604,x10605,x10606,x10601,x10607,x10608,x10609),f593(x10603,x10604,x10605,x10606,x10602,x10607,x10608,x10609)) % 177.51/177.20 [1061]~E(x10611,x10612)+E(f593(x10613,x10614,x10615,x10616,x10617,x10611,x10618,x10619),f593(x10613,x10614,x10615,x10616,x10617,x10612,x10618,x10619)) % 177.51/177.20 [1062]~E(x10621,x10622)+E(f593(x10623,x10624,x10625,x10626,x10627,x10628,x10621,x10629),f593(x10623,x10624,x10625,x10626,x10627,x10628,x10622,x10629)) % 177.51/177.20 [1063]~E(x10631,x10632)+E(f593(x10633,x10634,x10635,x10636,x10637,x10638,x10639,x10631),f593(x10633,x10634,x10635,x10636,x10637,x10638,x10639,x10632)) % 177.51/177.20 [1064]~E(x10641,x10642)+E(f617(x10641,x10643,x10644,x10645),f617(x10642,x10643,x10644,x10645)) % 177.51/177.20 [1065]~E(x10651,x10652)+E(f617(x10653,x10651,x10654,x10655),f617(x10653,x10652,x10654,x10655)) % 177.51/177.20 [1066]~E(x10661,x10662)+E(f617(x10663,x10664,x10661,x10665),f617(x10663,x10664,x10662,x10665)) % 177.51/177.20 [1067]~E(x10671,x10672)+E(f617(x10673,x10674,x10675,x10671),f617(x10673,x10674,x10675,x10672)) % 177.51/177.20 [1068]~E(x10681,x10682)+E(f575(x10681,x10683,x10684),f575(x10682,x10683,x10684)) % 177.51/177.20 [1069]~E(x10691,x10692)+E(f575(x10693,x10691,x10694),f575(x10693,x10692,x10694)) % 177.51/177.20 [1070]~E(x10701,x10702)+E(f575(x10703,x10704,x10701),f575(x10703,x10704,x10702)) % 177.51/177.20 [1071]~E(x10711,x10712)+E(f507(x10711,x10713,x10714,x10715,x10716,x10717),f507(x10712,x10713,x10714,x10715,x10716,x10717)) % 177.51/177.20 [1072]~E(x10721,x10722)+E(f507(x10723,x10721,x10724,x10725,x10726,x10727),f507(x10723,x10722,x10724,x10725,x10726,x10727)) % 177.51/177.20 [1073]~E(x10731,x10732)+E(f507(x10733,x10734,x10731,x10735,x10736,x10737),f507(x10733,x10734,x10732,x10735,x10736,x10737)) % 177.51/177.20 [1074]~E(x10741,x10742)+E(f507(x10743,x10744,x10745,x10741,x10746,x10747),f507(x10743,x10744,x10745,x10742,x10746,x10747)) % 177.51/177.20 [1075]~E(x10751,x10752)+E(f507(x10753,x10754,x10755,x10756,x10751,x10757),f507(x10753,x10754,x10755,x10756,x10752,x10757)) % 177.51/177.20 [1076]~E(x10761,x10762)+E(f507(x10763,x10764,x10765,x10766,x10767,x10761),f507(x10763,x10764,x10765,x10766,x10767,x10762)) % 177.51/177.20 [1077]~E(x10771,x10772)+E(f888(x10771,x10773,x10774),f888(x10772,x10773,x10774)) % 177.51/177.20 [1078]~E(x10781,x10782)+E(f888(x10783,x10781,x10784),f888(x10783,x10782,x10784)) % 177.51/177.20 [1079]~E(x10791,x10792)+E(f888(x10793,x10794,x10791),f888(x10793,x10794,x10792)) % 177.51/177.20 [1080]~E(x10801,x10802)+E(f624(x10801,x10803,x10804,x10805,x10806),f624(x10802,x10803,x10804,x10805,x10806)) % 177.51/177.20 [1081]~E(x10811,x10812)+E(f624(x10813,x10811,x10814,x10815,x10816),f624(x10813,x10812,x10814,x10815,x10816)) % 177.51/177.20 [1082]~E(x10821,x10822)+E(f624(x10823,x10824,x10821,x10825,x10826),f624(x10823,x10824,x10822,x10825,x10826)) % 177.51/177.20 [1083]~E(x10831,x10832)+E(f624(x10833,x10834,x10835,x10831,x10836),f624(x10833,x10834,x10835,x10832,x10836)) % 177.51/177.20 [1084]~E(x10841,x10842)+E(f624(x10843,x10844,x10845,x10846,x10841),f624(x10843,x10844,x10845,x10846,x10842)) % 177.51/177.20 [1085]~E(x10851,x10852)+E(f835(x10851,x10853,x10854,x10855,x10856,x10857,x10858,x10859),f835(x10852,x10853,x10854,x10855,x10856,x10857,x10858,x10859)) % 177.51/177.20 [1086]~E(x10861,x10862)+E(f835(x10863,x10861,x10864,x10865,x10866,x10867,x10868,x10869),f835(x10863,x10862,x10864,x10865,x10866,x10867,x10868,x10869)) % 177.51/177.20 [1087]~E(x10871,x10872)+E(f835(x10873,x10874,x10871,x10875,x10876,x10877,x10878,x10879),f835(x10873,x10874,x10872,x10875,x10876,x10877,x10878,x10879)) % 177.51/177.20 [1088]~E(x10881,x10882)+E(f835(x10883,x10884,x10885,x10881,x10886,x10887,x10888,x10889),f835(x10883,x10884,x10885,x10882,x10886,x10887,x10888,x10889)) % 177.51/177.20 [1089]~E(x10891,x10892)+E(f835(x10893,x10894,x10895,x10896,x10891,x10897,x10898,x10899),f835(x10893,x10894,x10895,x10896,x10892,x10897,x10898,x10899)) % 177.51/177.20 [1090]~E(x10901,x10902)+E(f835(x10903,x10904,x10905,x10906,x10907,x10901,x10908,x10909),f835(x10903,x10904,x10905,x10906,x10907,x10902,x10908,x10909)) % 177.51/177.20 [1091]~E(x10911,x10912)+E(f835(x10913,x10914,x10915,x10916,x10917,x10918,x10911,x10919),f835(x10913,x10914,x10915,x10916,x10917,x10918,x10912,x10919)) % 177.51/177.20 [1092]~E(x10921,x10922)+E(f835(x10923,x10924,x10925,x10926,x10927,x10928,x10929,x10921),f835(x10923,x10924,x10925,x10926,x10927,x10928,x10929,x10922)) % 177.51/177.20 [1093]~E(x10931,x10932)+E(f846(x10931,x10933,x10934,x10935,x10936,x10937,x10938,x10939),f846(x10932,x10933,x10934,x10935,x10936,x10937,x10938,x10939)) % 177.51/177.20 [1094]~E(x10941,x10942)+E(f846(x10943,x10941,x10944,x10945,x10946,x10947,x10948,x10949),f846(x10943,x10942,x10944,x10945,x10946,x10947,x10948,x10949)) % 177.51/177.20 [1095]~E(x10951,x10952)+E(f846(x10953,x10954,x10951,x10955,x10956,x10957,x10958,x10959),f846(x10953,x10954,x10952,x10955,x10956,x10957,x10958,x10959)) % 177.51/177.20 [1096]~E(x10961,x10962)+E(f846(x10963,x10964,x10965,x10961,x10966,x10967,x10968,x10969),f846(x10963,x10964,x10965,x10962,x10966,x10967,x10968,x10969)) % 177.51/177.20 [1097]~E(x10971,x10972)+E(f846(x10973,x10974,x10975,x10976,x10971,x10977,x10978,x10979),f846(x10973,x10974,x10975,x10976,x10972,x10977,x10978,x10979)) % 177.51/177.20 [1098]~E(x10981,x10982)+E(f846(x10983,x10984,x10985,x10986,x10987,x10981,x10988,x10989),f846(x10983,x10984,x10985,x10986,x10987,x10982,x10988,x10989)) % 177.51/177.20 [1099]~E(x10991,x10992)+E(f846(x10993,x10994,x10995,x10996,x10997,x10998,x10991,x10999),f846(x10993,x10994,x10995,x10996,x10997,x10998,x10992,x10999)) % 177.51/177.20 [1100]~E(x11001,x11002)+E(f846(x11003,x11004,x11005,x11006,x11007,x11008,x11009,x11001),f846(x11003,x11004,x11005,x11006,x11007,x11008,x11009,x11002)) % 177.51/177.20 [1101]~E(x11011,x11012)+E(f210(x11011),f210(x11012)) % 177.51/177.20 [1102]~E(x11021,x11022)+E(f719(x11021,x11023,x11024,x11025),f719(x11022,x11023,x11024,x11025)) % 177.51/177.20 [1103]~E(x11031,x11032)+E(f719(x11033,x11031,x11034,x11035),f719(x11033,x11032,x11034,x11035)) % 177.51/177.20 [1104]~E(x11041,x11042)+E(f719(x11043,x11044,x11041,x11045),f719(x11043,x11044,x11042,x11045)) % 177.51/177.20 [1105]~E(x11051,x11052)+E(f719(x11053,x11054,x11055,x11051),f719(x11053,x11054,x11055,x11052)) % 177.51/177.20 [1106]~E(x11061,x11062)+E(f665(x11061,x11063,x11064,x11065),f665(x11062,x11063,x11064,x11065)) % 177.51/177.20 [1107]~E(x11071,x11072)+E(f665(x11073,x11071,x11074,x11075),f665(x11073,x11072,x11074,x11075)) % 177.51/177.20 [1108]~E(x11081,x11082)+E(f665(x11083,x11084,x11081,x11085),f665(x11083,x11084,x11082,x11085)) % 177.51/177.20 [1109]~E(x11091,x11092)+E(f665(x11093,x11094,x11095,x11091),f665(x11093,x11094,x11095,x11092)) % 177.51/177.20 [1110]~E(x11101,x11102)+E(f417(x11101,x11103,x11104),f417(x11102,x11103,x11104)) % 177.51/177.20 [1111]~E(x11111,x11112)+E(f417(x11113,x11111,x11114),f417(x11113,x11112,x11114)) % 177.51/177.20 [1112]~E(x11121,x11122)+E(f417(x11123,x11124,x11121),f417(x11123,x11124,x11122)) % 177.51/177.20 [1113]~E(x11131,x11132)+E(f233(x11131,x11133,x11134,x11135),f233(x11132,x11133,x11134,x11135)) % 177.51/177.20 [1114]~E(x11141,x11142)+E(f233(x11143,x11141,x11144,x11145),f233(x11143,x11142,x11144,x11145)) % 177.51/177.20 [1115]~E(x11151,x11152)+E(f233(x11153,x11154,x11151,x11155),f233(x11153,x11154,x11152,x11155)) % 177.51/177.20 [1116]~E(x11161,x11162)+E(f233(x11163,x11164,x11165,x11161),f233(x11163,x11164,x11165,x11162)) % 177.51/177.20 [1117]~E(x11171,x11172)+E(f599(x11171,x11173,x11174),f599(x11172,x11173,x11174)) % 177.51/177.20 [1118]~E(x11181,x11182)+E(f599(x11183,x11181,x11184),f599(x11183,x11182,x11184)) % 177.51/177.20 [1119]~E(x11191,x11192)+E(f599(x11193,x11194,x11191),f599(x11193,x11194,x11192)) % 177.51/177.20 [1120]~E(x11201,x11202)+E(f447(x11201,x11203),f447(x11202,x11203)) % 177.51/177.20 [1121]~E(x11211,x11212)+E(f447(x11213,x11211),f447(x11213,x11212)) % 177.51/177.20 [1122]~E(x11221,x11222)+E(f129(x11221,x11223),f129(x11222,x11223)) % 177.51/177.20 [1123]~E(x11231,x11232)+E(f129(x11233,x11231),f129(x11233,x11232)) % 177.51/177.20 [1124]~E(x11241,x11242)+E(f133(x11241,x11243),f133(x11242,x11243)) % 177.51/177.20 [1125]~E(x11251,x11252)+E(f133(x11253,x11251),f133(x11253,x11252)) % 177.51/177.20 [1126]~E(x11261,x11262)+E(f415(x11261,x11263,x11264),f415(x11262,x11263,x11264)) % 177.51/177.20 [1127]~E(x11271,x11272)+E(f415(x11273,x11271,x11274),f415(x11273,x11272,x11274)) % 177.51/177.20 [1128]~E(x11281,x11282)+E(f415(x11283,x11284,x11281),f415(x11283,x11284,x11282)) % 177.51/177.20 [1129]~E(x11291,x11292)+E(f340(x11291,x11293,x11294,x11295),f340(x11292,x11293,x11294,x11295)) % 177.51/177.20 [1130]~E(x11301,x11302)+E(f340(x11303,x11301,x11304,x11305),f340(x11303,x11302,x11304,x11305)) % 177.51/177.20 [1131]~E(x11311,x11312)+E(f340(x11313,x11314,x11311,x11315),f340(x11313,x11314,x11312,x11315)) % 177.51/177.20 [1132]~E(x11321,x11322)+E(f340(x11323,x11324,x11325,x11321),f340(x11323,x11324,x11325,x11322)) % 177.51/177.20 [1133]~E(x11331,x11332)+E(f725(x11331,x11333),f725(x11332,x11333)) % 177.51/177.20 [1134]~E(x11341,x11342)+E(f725(x11343,x11341),f725(x11343,x11342)) % 177.51/177.20 [1135]~E(x11351,x11352)+E(f29(x11351,x11353),f29(x11352,x11353)) % 177.51/177.20 [1136]~E(x11361,x11362)+E(f29(x11363,x11361),f29(x11363,x11362)) % 177.51/177.20 [1137]~E(x11371,x11372)+E(f253(x11371,x11373,x11374,x11375,x11376),f253(x11372,x11373,x11374,x11375,x11376)) % 177.51/177.20 [1138]~E(x11381,x11382)+E(f253(x11383,x11381,x11384,x11385,x11386),f253(x11383,x11382,x11384,x11385,x11386)) % 177.51/177.20 [1139]~E(x11391,x11392)+E(f253(x11393,x11394,x11391,x11395,x11396),f253(x11393,x11394,x11392,x11395,x11396)) % 177.51/177.20 [1140]~E(x11401,x11402)+E(f253(x11403,x11404,x11405,x11401,x11406),f253(x11403,x11404,x11405,x11402,x11406)) % 177.51/177.20 [1141]~E(x11411,x11412)+E(f253(x11413,x11414,x11415,x11416,x11411),f253(x11413,x11414,x11415,x11416,x11412)) % 177.51/177.20 [1142]~E(x11421,x11422)+E(f761(x11421,x11423,x11424),f761(x11422,x11423,x11424)) % 177.51/177.20 [1143]~E(x11431,x11432)+E(f761(x11433,x11431,x11434),f761(x11433,x11432,x11434)) % 177.51/177.20 [1144]~E(x11441,x11442)+E(f761(x11443,x11444,x11441),f761(x11443,x11444,x11442)) % 177.51/177.20 [1145]~E(x11451,x11452)+E(f826(x11451,x11453,x11454,x11455),f826(x11452,x11453,x11454,x11455)) % 177.51/177.20 [1146]~E(x11461,x11462)+E(f826(x11463,x11461,x11464,x11465),f826(x11463,x11462,x11464,x11465)) % 177.51/177.20 [1147]~E(x11471,x11472)+E(f826(x11473,x11474,x11471,x11475),f826(x11473,x11474,x11472,x11475)) % 177.51/177.20 [1148]~E(x11481,x11482)+E(f826(x11483,x11484,x11485,x11481),f826(x11483,x11484,x11485,x11482)) % 177.51/177.20 [1149]~E(x11491,x11492)+E(f433(x11491,x11493,x11494),f433(x11492,x11493,x11494)) % 177.51/177.20 [1150]~E(x11501,x11502)+E(f433(x11503,x11501,x11504),f433(x11503,x11502,x11504)) % 177.51/177.20 [1151]~E(x11511,x11512)+E(f433(x11513,x11514,x11511),f433(x11513,x11514,x11512)) % 177.51/177.20 [1152]~E(x11521,x11522)+E(f501(x11521,x11523,x11524,x11525),f501(x11522,x11523,x11524,x11525)) % 177.51/177.20 [1153]~E(x11531,x11532)+E(f501(x11533,x11531,x11534,x11535),f501(x11533,x11532,x11534,x11535)) % 177.51/177.20 [1154]~E(x11541,x11542)+E(f501(x11543,x11544,x11541,x11545),f501(x11543,x11544,x11542,x11545)) % 177.51/177.20 [1155]~E(x11551,x11552)+E(f501(x11553,x11554,x11555,x11551),f501(x11553,x11554,x11555,x11552)) % 177.51/177.20 [1156]~E(x11561,x11562)+E(f305(x11561,x11563,x11564),f305(x11562,x11563,x11564)) % 177.51/177.20 [1157]~E(x11571,x11572)+E(f305(x11573,x11571,x11574),f305(x11573,x11572,x11574)) % 177.51/177.20 [1158]~E(x11581,x11582)+E(f305(x11583,x11584,x11581),f305(x11583,x11584,x11582)) % 177.51/177.20 [1159]~E(x11591,x11592)+E(f498(x11591,x11593,x11594,x11595),f498(x11592,x11593,x11594,x11595)) % 177.51/177.20 [1160]~E(x11601,x11602)+E(f498(x11603,x11601,x11604,x11605),f498(x11603,x11602,x11604,x11605)) % 177.51/177.20 [1161]~E(x11611,x11612)+E(f498(x11613,x11614,x11611,x11615),f498(x11613,x11614,x11612,x11615)) % 177.51/177.20 [1162]~E(x11621,x11622)+E(f498(x11623,x11624,x11625,x11621),f498(x11623,x11624,x11625,x11622)) % 177.51/177.20 [1163]~E(x11631,x11632)+E(f17(x11631,x11633,x11634,x11635),f17(x11632,x11633,x11634,x11635)) % 177.51/177.20 [1164]~E(x11641,x11642)+E(f17(x11643,x11641,x11644,x11645),f17(x11643,x11642,x11644,x11645)) % 177.51/177.20 [1165]~E(x11651,x11652)+E(f17(x11653,x11654,x11651,x11655),f17(x11653,x11654,x11652,x11655)) % 177.51/177.20 [1166]~E(x11661,x11662)+E(f17(x11663,x11664,x11665,x11661),f17(x11663,x11664,x11665,x11662)) % 177.51/177.20 [1167]~E(x11671,x11672)+E(f201(x11671,x11673),f201(x11672,x11673)) % 177.51/177.20 [1168]~E(x11681,x11682)+E(f201(x11683,x11681),f201(x11683,x11682)) % 177.51/177.20 [1169]~E(x11691,x11692)+E(f247(x11691,x11693,x11694),f247(x11692,x11693,x11694)) % 177.51/177.20 [1170]~E(x11701,x11702)+E(f247(x11703,x11701,x11704),f247(x11703,x11702,x11704)) % 177.51/177.20 [1171]~E(x11711,x11712)+E(f247(x11713,x11714,x11711),f247(x11713,x11714,x11712)) % 177.51/177.20 [1172]~E(x11721,x11722)+E(f130(x11721),f130(x11722)) % 177.51/177.20 [1173]~E(x11731,x11732)+E(f837(x11731,x11733,x11734,x11735,x11736,x11737,x11738,x11739),f837(x11732,x11733,x11734,x11735,x11736,x11737,x11738,x11739)) % 177.51/177.20 [1174]~E(x11741,x11742)+E(f837(x11743,x11741,x11744,x11745,x11746,x11747,x11748,x11749),f837(x11743,x11742,x11744,x11745,x11746,x11747,x11748,x11749)) % 177.51/177.20 [1175]~E(x11751,x11752)+E(f837(x11753,x11754,x11751,x11755,x11756,x11757,x11758,x11759),f837(x11753,x11754,x11752,x11755,x11756,x11757,x11758,x11759)) % 177.51/177.20 [1176]~E(x11761,x11762)+E(f837(x11763,x11764,x11765,x11761,x11766,x11767,x11768,x11769),f837(x11763,x11764,x11765,x11762,x11766,x11767,x11768,x11769)) % 177.51/177.20 [1177]~E(x11771,x11772)+E(f837(x11773,x11774,x11775,x11776,x11771,x11777,x11778,x11779),f837(x11773,x11774,x11775,x11776,x11772,x11777,x11778,x11779)) % 177.51/177.20 [1178]~E(x11781,x11782)+E(f837(x11783,x11784,x11785,x11786,x11787,x11781,x11788,x11789),f837(x11783,x11784,x11785,x11786,x11787,x11782,x11788,x11789)) % 177.51/177.20 [1179]~E(x11791,x11792)+E(f837(x11793,x11794,x11795,x11796,x11797,x11798,x11791,x11799),f837(x11793,x11794,x11795,x11796,x11797,x11798,x11792,x11799)) % 177.51/177.20 [1180]~E(x11801,x11802)+E(f837(x11803,x11804,x11805,x11806,x11807,x11808,x11809,x11801),f837(x11803,x11804,x11805,x11806,x11807,x11808,x11809,x11802)) % 177.51/177.20 [1181]~E(x11811,x11812)+E(f481(x11811,x11813,x11814,x11815,x11816),f481(x11812,x11813,x11814,x11815,x11816)) % 177.51/177.20 [1182]~E(x11821,x11822)+E(f481(x11823,x11821,x11824,x11825,x11826),f481(x11823,x11822,x11824,x11825,x11826)) % 177.51/177.20 [1183]~E(x11831,x11832)+E(f481(x11833,x11834,x11831,x11835,x11836),f481(x11833,x11834,x11832,x11835,x11836)) % 177.51/177.20 [1184]~E(x11841,x11842)+E(f481(x11843,x11844,x11845,x11841,x11846),f481(x11843,x11844,x11845,x11842,x11846)) % 177.51/177.20 [1185]~E(x11851,x11852)+E(f481(x11853,x11854,x11855,x11856,x11851),f481(x11853,x11854,x11855,x11856,x11852)) % 177.51/177.20 [1186]~E(x11861,x11862)+E(f482(x11861,x11863,x11864),f482(x11862,x11863,x11864)) % 177.51/177.20 [1187]~E(x11871,x11872)+E(f482(x11873,x11871,x11874),f482(x11873,x11872,x11874)) % 177.51/177.20 [1188]~E(x11881,x11882)+E(f482(x11883,x11884,x11881),f482(x11883,x11884,x11882)) % 177.51/177.20 [1189]~E(x11891,x11892)+E(f56(x11891,x11893,x11894),f56(x11892,x11893,x11894)) % 177.51/177.20 [1190]~E(x11901,x11902)+E(f56(x11903,x11901,x11904),f56(x11903,x11902,x11904)) % 177.51/177.20 [1191]~E(x11911,x11912)+E(f56(x11913,x11914,x11911),f56(x11913,x11914,x11912)) % 177.51/177.20 [1192]~E(x11921,x11922)+E(f666(x11921,x11923,x11924,x11925),f666(x11922,x11923,x11924,x11925)) % 177.51/177.20 [1193]~E(x11931,x11932)+E(f666(x11933,x11931,x11934,x11935),f666(x11933,x11932,x11934,x11935)) % 177.51/177.20 [1194]~E(x11941,x11942)+E(f666(x11943,x11944,x11941,x11945),f666(x11943,x11944,x11942,x11945)) % 177.51/177.20 [1195]~E(x11951,x11952)+E(f666(x11953,x11954,x11955,x11951),f666(x11953,x11954,x11955,x11952)) % 177.51/177.20 [1196]~E(x11961,x11962)+E(f736(x11961,x11963,x11964,x11965),f736(x11962,x11963,x11964,x11965)) % 177.51/177.20 [1197]~E(x11971,x11972)+E(f736(x11973,x11971,x11974,x11975),f736(x11973,x11972,x11974,x11975)) % 177.51/177.20 [1198]~E(x11981,x11982)+E(f736(x11983,x11984,x11981,x11985),f736(x11983,x11984,x11982,x11985)) % 177.51/177.20 [1199]~E(x11991,x11992)+E(f736(x11993,x11994,x11995,x11991),f736(x11993,x11994,x11995,x11992)) % 177.51/177.20 [1200]~E(x12001,x12002)+E(f313(x12001,x12003,x12004,x12005),f313(x12002,x12003,x12004,x12005)) % 177.51/177.20 [1201]~E(x12011,x12012)+E(f313(x12013,x12011,x12014,x12015),f313(x12013,x12012,x12014,x12015)) % 177.51/177.20 [1202]~E(x12021,x12022)+E(f313(x12023,x12024,x12021,x12025),f313(x12023,x12024,x12022,x12025)) % 177.51/177.20 [1203]~E(x12031,x12032)+E(f313(x12033,x12034,x12035,x12031),f313(x12033,x12034,x12035,x12032)) % 177.51/177.20 [1204]~E(x12041,x12042)+E(f626(x12041,x12043,x12044,x12045,x12046,x12047,x12048,x12049),f626(x12042,x12043,x12044,x12045,x12046,x12047,x12048,x12049)) % 177.51/177.20 [1205]~E(x12051,x12052)+E(f626(x12053,x12051,x12054,x12055,x12056,x12057,x12058,x12059),f626(x12053,x12052,x12054,x12055,x12056,x12057,x12058,x12059)) % 177.51/177.20 [1206]~E(x12061,x12062)+E(f626(x12063,x12064,x12061,x12065,x12066,x12067,x12068,x12069),f626(x12063,x12064,x12062,x12065,x12066,x12067,x12068,x12069)) % 177.51/177.20 [1207]~E(x12071,x12072)+E(f626(x12073,x12074,x12075,x12071,x12076,x12077,x12078,x12079),f626(x12073,x12074,x12075,x12072,x12076,x12077,x12078,x12079)) % 177.51/177.20 [1208]~E(x12081,x12082)+E(f626(x12083,x12084,x12085,x12086,x12081,x12087,x12088,x12089),f626(x12083,x12084,x12085,x12086,x12082,x12087,x12088,x12089)) % 177.51/177.20 [1209]~E(x12091,x12092)+E(f626(x12093,x12094,x12095,x12096,x12097,x12091,x12098,x12099),f626(x12093,x12094,x12095,x12096,x12097,x12092,x12098,x12099)) % 177.51/177.20 [1210]~E(x12101,x12102)+E(f626(x12103,x12104,x12105,x12106,x12107,x12108,x12101,x12109),f626(x12103,x12104,x12105,x12106,x12107,x12108,x12102,x12109)) % 177.51/177.20 [1211]~E(x12111,x12112)+E(f626(x12113,x12114,x12115,x12116,x12117,x12118,x12119,x12111),f626(x12113,x12114,x12115,x12116,x12117,x12118,x12119,x12112)) % 177.51/177.20 [1212]~E(x12121,x12122)+E(f354(x12121,x12123),f354(x12122,x12123)) % 177.51/177.20 [1213]~E(x12131,x12132)+E(f354(x12133,x12131),f354(x12133,x12132)) % 177.51/177.20 [1214]~E(x12141,x12142)+E(f477(x12141,x12143,x12144),f477(x12142,x12143,x12144)) % 177.51/177.20 [1215]~E(x12151,x12152)+E(f477(x12153,x12151,x12154),f477(x12153,x12152,x12154)) % 177.51/177.20 [1216]~E(x12161,x12162)+E(f477(x12163,x12164,x12161),f477(x12163,x12164,x12162)) % 177.51/177.20 [1217]~E(x12171,x12172)+E(f161(x12171,x12173),f161(x12172,x12173)) % 177.51/177.20 [1218]~E(x12181,x12182)+E(f161(x12183,x12181),f161(x12183,x12182)) % 177.51/177.20 [1219]~E(x12191,x12192)+E(f540(x12191,x12193,x12194,x12195),f540(x12192,x12193,x12194,x12195)) % 177.51/177.20 [1220]~E(x12201,x12202)+E(f540(x12203,x12201,x12204,x12205),f540(x12203,x12202,x12204,x12205)) % 177.51/177.20 [1221]~E(x12211,x12212)+E(f540(x12213,x12214,x12211,x12215),f540(x12213,x12214,x12212,x12215)) % 177.51/177.20 [1222]~E(x12221,x12222)+E(f540(x12223,x12224,x12225,x12221),f540(x12223,x12224,x12225,x12222)) % 177.51/177.20 [1223]~E(x12231,x12232)+E(f838(x12231,x12233,x12234,x12235,x12236,x12237,x12238,x12239),f838(x12232,x12233,x12234,x12235,x12236,x12237,x12238,x12239)) % 177.51/177.20 [1224]~E(x12241,x12242)+E(f838(x12243,x12241,x12244,x12245,x12246,x12247,x12248,x12249),f838(x12243,x12242,x12244,x12245,x12246,x12247,x12248,x12249)) % 177.51/177.20 [1225]~E(x12251,x12252)+E(f838(x12253,x12254,x12251,x12255,x12256,x12257,x12258,x12259),f838(x12253,x12254,x12252,x12255,x12256,x12257,x12258,x12259)) % 177.51/177.20 [1226]~E(x12261,x12262)+E(f838(x12263,x12264,x12265,x12261,x12266,x12267,x12268,x12269),f838(x12263,x12264,x12265,x12262,x12266,x12267,x12268,x12269)) % 177.51/177.20 [1227]~E(x12271,x12272)+E(f838(x12273,x12274,x12275,x12276,x12271,x12277,x12278,x12279),f838(x12273,x12274,x12275,x12276,x12272,x12277,x12278,x12279)) % 177.51/177.20 [1228]~E(x12281,x12282)+E(f838(x12283,x12284,x12285,x12286,x12287,x12281,x12288,x12289),f838(x12283,x12284,x12285,x12286,x12287,x12282,x12288,x12289)) % 177.51/177.20 [1229]~E(x12291,x12292)+E(f838(x12293,x12294,x12295,x12296,x12297,x12298,x12291,x12299),f838(x12293,x12294,x12295,x12296,x12297,x12298,x12292,x12299)) % 177.51/177.20 [1230]~E(x12301,x12302)+E(f838(x12303,x12304,x12305,x12306,x12307,x12308,x12309,x12301),f838(x12303,x12304,x12305,x12306,x12307,x12308,x12309,x12302)) % 177.51/177.20 [1231]~E(x12311,x12312)+E(f174(x12311,x12313,x12314),f174(x12312,x12313,x12314)) % 177.51/177.20 [1232]~E(x12321,x12322)+E(f174(x12323,x12321,x12324),f174(x12323,x12322,x12324)) % 177.51/177.20 [1233]~E(x12331,x12332)+E(f174(x12333,x12334,x12331),f174(x12333,x12334,x12332)) % 177.51/177.20 [1234]~E(x12341,x12342)+E(f125(x12341),f125(x12342)) % 177.51/177.20 [1235]~E(x12351,x12352)+E(f226(x12351,x12353,x12354,x12355,x12356),f226(x12352,x12353,x12354,x12355,x12356)) % 177.51/177.20 [1236]~E(x12361,x12362)+E(f226(x12363,x12361,x12364,x12365,x12366),f226(x12363,x12362,x12364,x12365,x12366)) % 177.51/177.20 [1237]~E(x12371,x12372)+E(f226(x12373,x12374,x12371,x12375,x12376),f226(x12373,x12374,x12372,x12375,x12376)) % 177.51/177.20 [1238]~E(x12381,x12382)+E(f226(x12383,x12384,x12385,x12381,x12386),f226(x12383,x12384,x12385,x12382,x12386)) % 177.51/177.20 [1239]~E(x12391,x12392)+E(f226(x12393,x12394,x12395,x12396,x12391),f226(x12393,x12394,x12395,x12396,x12392)) % 177.51/177.20 [1240]~E(x12401,x12402)+E(f678(x12401,x12403,x12404,x12405,x12406),f678(x12402,x12403,x12404,x12405,x12406)) % 177.51/177.20 [1241]~E(x12411,x12412)+E(f678(x12413,x12411,x12414,x12415,x12416),f678(x12413,x12412,x12414,x12415,x12416)) % 177.51/177.20 [1242]~E(x12421,x12422)+E(f678(x12423,x12424,x12421,x12425,x12426),f678(x12423,x12424,x12422,x12425,x12426)) % 177.51/177.20 [1243]~E(x12431,x12432)+E(f678(x12433,x12434,x12435,x12431,x12436),f678(x12433,x12434,x12435,x12432,x12436)) % 177.51/177.20 [1244]~E(x12441,x12442)+E(f678(x12443,x12444,x12445,x12446,x12441),f678(x12443,x12444,x12445,x12446,x12442)) % 177.51/177.20 [1245]~E(x12451,x12452)+E(f117(x12451,x12453,x12454),f117(x12452,x12453,x12454)) % 177.51/177.20 [1246]~E(x12461,x12462)+E(f117(x12463,x12461,x12464),f117(x12463,x12462,x12464)) % 177.51/177.20 [1247]~E(x12471,x12472)+E(f117(x12473,x12474,x12471),f117(x12473,x12474,x12472)) % 177.51/177.20 [1248]~E(x12481,x12482)+E(f435(x12481,x12483),f435(x12482,x12483)) % 177.51/177.20 [1249]~E(x12491,x12492)+E(f435(x12493,x12491),f435(x12493,x12492)) % 177.51/177.20 [1250]~E(x12501,x12502)+E(f675(x12501,x12503,x12504),f675(x12502,x12503,x12504)) % 177.51/177.20 [1251]~E(x12511,x12512)+E(f675(x12513,x12511,x12514),f675(x12513,x12512,x12514)) % 177.51/177.20 [1252]~E(x12521,x12522)+E(f675(x12523,x12524,x12521),f675(x12523,x12524,x12522)) % 177.51/177.20 [1253]~E(x12531,x12532)+E(f499(x12531,x12533,x12534,x12535),f499(x12532,x12533,x12534,x12535)) % 177.51/177.20 [1254]~E(x12541,x12542)+E(f499(x12543,x12541,x12544,x12545),f499(x12543,x12542,x12544,x12545)) % 177.51/177.20 [1255]~E(x12551,x12552)+E(f499(x12553,x12554,x12551,x12555),f499(x12553,x12554,x12552,x12555)) % 177.51/177.20 [1256]~E(x12561,x12562)+E(f499(x12563,x12564,x12565,x12561),f499(x12563,x12564,x12565,x12562)) % 177.51/177.20 [1257]~E(x12571,x12572)+E(f868(x12571,x12573,x12574),f868(x12572,x12573,x12574)) % 177.51/177.20 [1258]~E(x12581,x12582)+E(f868(x12583,x12581,x12584),f868(x12583,x12582,x12584)) % 177.51/177.20 [1259]~E(x12591,x12592)+E(f868(x12593,x12594,x12591),f868(x12593,x12594,x12592)) % 177.51/177.20 [1260]~E(x12601,x12602)+E(f431(x12601,x12603,x12604,x12605),f431(x12602,x12603,x12604,x12605)) % 177.51/177.20 [1261]~E(x12611,x12612)+E(f431(x12613,x12611,x12614,x12615),f431(x12613,x12612,x12614,x12615)) % 177.51/177.20 [1262]~E(x12621,x12622)+E(f431(x12623,x12624,x12621,x12625),f431(x12623,x12624,x12622,x12625)) % 177.51/177.20 [1263]~E(x12631,x12632)+E(f431(x12633,x12634,x12635,x12631),f431(x12633,x12634,x12635,x12632)) % 177.51/177.20 [1264]~E(x12641,x12642)+E(f204(x12641,x12643),f204(x12642,x12643)) % 177.51/177.20 [1265]~E(x12651,x12652)+E(f204(x12653,x12651),f204(x12653,x12652)) % 177.51/177.20 [1266]~E(x12661,x12662)+E(f520(x12661,x12663,x12664,x12665,x12666,x12667,x12668),f520(x12662,x12663,x12664,x12665,x12666,x12667,x12668)) % 177.51/177.20 [1267]~E(x12671,x12672)+E(f520(x12673,x12671,x12674,x12675,x12676,x12677,x12678),f520(x12673,x12672,x12674,x12675,x12676,x12677,x12678)) % 177.51/177.20 [1268]~E(x12681,x12682)+E(f520(x12683,x12684,x12681,x12685,x12686,x12687,x12688),f520(x12683,x12684,x12682,x12685,x12686,x12687,x12688)) % 177.51/177.20 [1269]~E(x12691,x12692)+E(f520(x12693,x12694,x12695,x12691,x12696,x12697,x12698),f520(x12693,x12694,x12695,x12692,x12696,x12697,x12698)) % 177.51/177.20 [1270]~E(x12701,x12702)+E(f520(x12703,x12704,x12705,x12706,x12701,x12707,x12708),f520(x12703,x12704,x12705,x12706,x12702,x12707,x12708)) % 177.51/177.20 [1271]~E(x12711,x12712)+E(f520(x12713,x12714,x12715,x12716,x12717,x12711,x12718),f520(x12713,x12714,x12715,x12716,x12717,x12712,x12718)) % 177.51/177.20 [1272]~E(x12721,x12722)+E(f520(x12723,x12724,x12725,x12726,x12727,x12728,x12721),f520(x12723,x12724,x12725,x12726,x12727,x12728,x12722)) % 177.51/177.20 [1273]~E(x12731,x12732)+E(f718(x12731,x12733,x12734,x12735),f718(x12732,x12733,x12734,x12735)) % 177.51/177.20 [1274]~E(x12741,x12742)+E(f718(x12743,x12741,x12744,x12745),f718(x12743,x12742,x12744,x12745)) % 177.51/177.20 [1275]~E(x12751,x12752)+E(f718(x12753,x12754,x12751,x12755),f718(x12753,x12754,x12752,x12755)) % 177.51/177.20 [1276]~E(x12761,x12762)+E(f718(x12763,x12764,x12765,x12761),f718(x12763,x12764,x12765,x12762)) % 177.51/177.20 [1277]~E(x12771,x12772)+E(f834(x12771,x12773,x12774,x12775,x12776,x12777),f834(x12772,x12773,x12774,x12775,x12776,x12777)) % 177.51/177.20 [1278]~E(x12781,x12782)+E(f834(x12783,x12781,x12784,x12785,x12786,x12787),f834(x12783,x12782,x12784,x12785,x12786,x12787)) % 177.51/177.20 [1279]~E(x12791,x12792)+E(f834(x12793,x12794,x12791,x12795,x12796,x12797),f834(x12793,x12794,x12792,x12795,x12796,x12797)) % 177.51/177.20 [1280]~E(x12801,x12802)+E(f834(x12803,x12804,x12805,x12801,x12806,x12807),f834(x12803,x12804,x12805,x12802,x12806,x12807)) % 177.51/177.20 [1281]~E(x12811,x12812)+E(f834(x12813,x12814,x12815,x12816,x12811,x12817),f834(x12813,x12814,x12815,x12816,x12812,x12817)) % 177.51/177.20 [1282]~E(x12821,x12822)+E(f834(x12823,x12824,x12825,x12826,x12827,x12821),f834(x12823,x12824,x12825,x12826,x12827,x12822)) % 177.51/177.20 [1283]~E(x12831,x12832)+E(f500(x12831,x12833,x12834,x12835),f500(x12832,x12833,x12834,x12835)) % 177.51/177.20 [1284]~E(x12841,x12842)+E(f500(x12843,x12841,x12844,x12845),f500(x12843,x12842,x12844,x12845)) % 177.51/177.20 [1285]~E(x12851,x12852)+E(f500(x12853,x12854,x12851,x12855),f500(x12853,x12854,x12852,x12855)) % 177.51/177.20 [1286]~E(x12861,x12862)+E(f500(x12863,x12864,x12865,x12861),f500(x12863,x12864,x12865,x12862)) % 177.51/177.20 [1287]~E(x12871,x12872)+E(f691(x12871,x12873,x12874,x12875,x12876),f691(x12872,x12873,x12874,x12875,x12876)) % 177.51/177.20 [1288]~E(x12881,x12882)+E(f691(x12883,x12881,x12884,x12885,x12886),f691(x12883,x12882,x12884,x12885,x12886)) % 177.51/177.20 [1289]~E(x12891,x12892)+E(f691(x12893,x12894,x12891,x12895,x12896),f691(x12893,x12894,x12892,x12895,x12896)) % 177.51/177.20 [1290]~E(x12901,x12902)+E(f691(x12903,x12904,x12905,x12901,x12906),f691(x12903,x12904,x12905,x12902,x12906)) % 177.51/177.20 [1291]~E(x12911,x12912)+E(f691(x12913,x12914,x12915,x12916,x12911),f691(x12913,x12914,x12915,x12916,x12912)) % 177.51/177.20 [1292]~E(x12921,x12922)+E(f650(x12921,x12923,x12924,x12925,x12926),f650(x12922,x12923,x12924,x12925,x12926)) % 177.51/177.20 [1293]~E(x12931,x12932)+E(f650(x12933,x12931,x12934,x12935,x12936),f650(x12933,x12932,x12934,x12935,x12936)) % 177.51/177.20 [1294]~E(x12941,x12942)+E(f650(x12943,x12944,x12941,x12945,x12946),f650(x12943,x12944,x12942,x12945,x12946)) % 177.51/177.20 [1295]~E(x12951,x12952)+E(f650(x12953,x12954,x12955,x12951,x12956),f650(x12953,x12954,x12955,x12952,x12956)) % 177.51/177.20 [1296]~E(x12961,x12962)+E(f650(x12963,x12964,x12965,x12966,x12961),f650(x12963,x12964,x12965,x12966,x12962)) % 177.51/177.20 [1297]~E(x12971,x12972)+E(f876(x12971,x12973,x12974,x12975),f876(x12972,x12973,x12974,x12975)) % 177.51/177.20 [1298]~E(x12981,x12982)+E(f876(x12983,x12981,x12984,x12985),f876(x12983,x12982,x12984,x12985)) % 177.51/177.20 [1299]~E(x12991,x12992)+E(f876(x12993,x12994,x12991,x12995),f876(x12993,x12994,x12992,x12995)) % 177.51/177.20 [1300]~E(x13001,x13002)+E(f876(x13003,x13004,x13005,x13001),f876(x13003,x13004,x13005,x13002)) % 177.51/177.20 [1301]~E(x13011,x13012)+E(f680(x13011,x13013,x13014,x13015),f680(x13012,x13013,x13014,x13015)) % 177.51/177.20 [1302]~E(x13021,x13022)+E(f680(x13023,x13021,x13024,x13025),f680(x13023,x13022,x13024,x13025)) % 177.51/177.20 [1303]~E(x13031,x13032)+E(f680(x13033,x13034,x13031,x13035),f680(x13033,x13034,x13032,x13035)) % 177.51/177.20 [1304]~E(x13041,x13042)+E(f680(x13043,x13044,x13045,x13041),f680(x13043,x13044,x13045,x13042)) % 177.51/177.20 [1305]~E(x13051,x13052)+E(f58(x13051),f58(x13052)) % 177.51/177.20 [1306]~E(x13061,x13062)+E(f707(x13061,x13063,x13064),f707(x13062,x13063,x13064)) % 177.51/177.20 [1307]~E(x13071,x13072)+E(f707(x13073,x13071,x13074),f707(x13073,x13072,x13074)) % 177.51/177.20 [1308]~E(x13081,x13082)+E(f707(x13083,x13084,x13081),f707(x13083,x13084,x13082)) % 177.51/177.20 [1309]~E(x13091,x13092)+E(f878(x13091,x13093,x13094,x13095),f878(x13092,x13093,x13094,x13095)) % 177.51/177.20 [1310]~E(x13101,x13102)+E(f878(x13103,x13101,x13104,x13105),f878(x13103,x13102,x13104,x13105)) % 177.51/177.20 [1311]~E(x13111,x13112)+E(f878(x13113,x13114,x13111,x13115),f878(x13113,x13114,x13112,x13115)) % 177.51/177.20 [1312]~E(x13121,x13122)+E(f878(x13123,x13124,x13125,x13121),f878(x13123,x13124,x13125,x13122)) % 177.51/177.20 [1313]~E(x13131,x13132)+E(f566(x13131,x13133),f566(x13132,x13133)) % 177.51/177.20 [1314]~E(x13141,x13142)+E(f566(x13143,x13141),f566(x13143,x13142)) % 177.51/177.20 [1315]~E(x13151,x13152)+E(f753(x13151,x13153,x13154),f753(x13152,x13153,x13154)) % 177.51/177.20 [1316]~E(x13161,x13162)+E(f753(x13163,x13161,x13164),f753(x13163,x13162,x13164)) % 177.51/177.20 [1317]~E(x13171,x13172)+E(f753(x13173,x13174,x13171),f753(x13173,x13174,x13172)) % 177.51/177.20 [1318]~E(x13181,x13182)+E(f825(x13181,x13183,x13184,x13185),f825(x13182,x13183,x13184,x13185)) % 177.51/177.20 [1319]~E(x13191,x13192)+E(f825(x13193,x13191,x13194,x13195),f825(x13193,x13192,x13194,x13195)) % 177.51/177.20 [1320]~E(x13201,x13202)+E(f825(x13203,x13204,x13201,x13205),f825(x13203,x13204,x13202,x13205)) % 177.51/177.20 [1321]~E(x13211,x13212)+E(f825(x13213,x13214,x13215,x13211),f825(x13213,x13214,x13215,x13212)) % 177.51/177.20 [1322]~E(x13221,x13222)+E(f776(x13221,x13223,x13224,x13225),f776(x13222,x13223,x13224,x13225)) % 177.51/177.20 [1323]~E(x13231,x13232)+E(f776(x13233,x13231,x13234,x13235),f776(x13233,x13232,x13234,x13235)) % 177.51/177.20 [1324]~E(x13241,x13242)+E(f776(x13243,x13244,x13241,x13245),f776(x13243,x13244,x13242,x13245)) % 177.51/177.20 [1325]~E(x13251,x13252)+E(f776(x13253,x13254,x13255,x13251),f776(x13253,x13254,x13255,x13252)) % 177.51/177.20 [1326]~E(x13261,x13262)+E(f519(x13261,x13263,x13264,x13265,x13266,x13267,x13268),f519(x13262,x13263,x13264,x13265,x13266,x13267,x13268)) % 177.51/177.20 [1327]~E(x13271,x13272)+E(f519(x13273,x13271,x13274,x13275,x13276,x13277,x13278),f519(x13273,x13272,x13274,x13275,x13276,x13277,x13278)) % 177.51/177.20 [1328]~E(x13281,x13282)+E(f519(x13283,x13284,x13281,x13285,x13286,x13287,x13288),f519(x13283,x13284,x13282,x13285,x13286,x13287,x13288)) % 177.51/177.20 [1329]~E(x13291,x13292)+E(f519(x13293,x13294,x13295,x13291,x13296,x13297,x13298),f519(x13293,x13294,x13295,x13292,x13296,x13297,x13298)) % 177.51/177.20 [1330]~E(x13301,x13302)+E(f519(x13303,x13304,x13305,x13306,x13301,x13307,x13308),f519(x13303,x13304,x13305,x13306,x13302,x13307,x13308)) % 177.51/177.20 [1331]~E(x13311,x13312)+E(f519(x13313,x13314,x13315,x13316,x13317,x13311,x13318),f519(x13313,x13314,x13315,x13316,x13317,x13312,x13318)) % 177.51/177.20 [1332]~E(x13321,x13322)+E(f519(x13323,x13324,x13325,x13326,x13327,x13328,x13321),f519(x13323,x13324,x13325,x13326,x13327,x13328,x13322)) % 177.51/177.20 [1333]~E(x13331,x13332)+E(f701(x13331,x13333),f701(x13332,x13333)) % 177.51/177.20 [1334]~E(x13341,x13342)+E(f701(x13343,x13341),f701(x13343,x13342)) % 177.51/177.20 [1335]~E(x13351,x13352)+E(f622(x13351,x13353,x13354,x13355,x13356),f622(x13352,x13353,x13354,x13355,x13356)) % 177.51/177.20 [1336]~E(x13361,x13362)+E(f622(x13363,x13361,x13364,x13365,x13366),f622(x13363,x13362,x13364,x13365,x13366)) % 177.51/177.20 [1337]~E(x13371,x13372)+E(f622(x13373,x13374,x13371,x13375,x13376),f622(x13373,x13374,x13372,x13375,x13376)) % 177.51/177.20 [1338]~E(x13381,x13382)+E(f622(x13383,x13384,x13385,x13381,x13386),f622(x13383,x13384,x13385,x13382,x13386)) % 177.51/177.20 [1339]~E(x13391,x13392)+E(f622(x13393,x13394,x13395,x13396,x13391),f622(x13393,x13394,x13395,x13396,x13392)) % 177.51/177.20 [1340]~E(x13401,x13402)+E(f615(x13401,x13403,x13404,x13405,x13406),f615(x13402,x13403,x13404,x13405,x13406)) % 177.51/177.20 [1341]~E(x13411,x13412)+E(f615(x13413,x13411,x13414,x13415,x13416),f615(x13413,x13412,x13414,x13415,x13416)) % 177.51/177.20 [1342]~E(x13421,x13422)+E(f615(x13423,x13424,x13421,x13425,x13426),f615(x13423,x13424,x13422,x13425,x13426)) % 177.51/177.20 [1343]~E(x13431,x13432)+E(f615(x13433,x13434,x13435,x13431,x13436),f615(x13433,x13434,x13435,x13432,x13436)) % 177.51/177.20 [1344]~E(x13441,x13442)+E(f615(x13443,x13444,x13445,x13446,x13441),f615(x13443,x13444,x13445,x13446,x13442)) % 177.51/177.20 [1345]~E(x13451,x13452)+E(f727(x13451,x13453),f727(x13452,x13453)) % 177.51/177.20 [1346]~E(x13461,x13462)+E(f727(x13463,x13461),f727(x13463,x13462)) % 177.51/177.20 [1347]~E(x13471,x13472)+E(f144(x13471,x13473),f144(x13472,x13473)) % 177.51/177.20 [1348]~E(x13481,x13482)+E(f144(x13483,x13481),f144(x13483,x13482)) % 177.51/177.20 [1349]~E(x13491,x13492)+E(f375(x13491,x13493,x13494,x13495,x13496),f375(x13492,x13493,x13494,x13495,x13496)) % 177.51/177.20 [1350]~E(x13501,x13502)+E(f375(x13503,x13501,x13504,x13505,x13506),f375(x13503,x13502,x13504,x13505,x13506)) % 177.51/177.20 [1351]~E(x13511,x13512)+E(f375(x13513,x13514,x13511,x13515,x13516),f375(x13513,x13514,x13512,x13515,x13516)) % 177.51/177.20 [1352]~E(x13521,x13522)+E(f375(x13523,x13524,x13525,x13521,x13526),f375(x13523,x13524,x13525,x13522,x13526)) % 177.51/177.20 [1353]~E(x13531,x13532)+E(f375(x13533,x13534,x13535,x13536,x13531),f375(x13533,x13534,x13535,x13536,x13532)) % 177.51/177.20 [1354]~E(x13541,x13542)+E(f604(x13541,x13543,x13544),f604(x13542,x13543,x13544)) % 177.51/177.20 [1355]~E(x13551,x13552)+E(f604(x13553,x13551,x13554),f604(x13553,x13552,x13554)) % 177.51/177.20 [1356]~E(x13561,x13562)+E(f604(x13563,x13564,x13561),f604(x13563,x13564,x13562)) % 177.51/177.20 [1357]~E(x13571,x13572)+E(f271(x13571,x13573,x13574,x13575),f271(x13572,x13573,x13574,x13575)) % 177.51/177.20 [1358]~E(x13581,x13582)+E(f271(x13583,x13581,x13584,x13585),f271(x13583,x13582,x13584,x13585)) % 177.51/177.20 [1359]~E(x13591,x13592)+E(f271(x13593,x13594,x13591,x13595),f271(x13593,x13594,x13592,x13595)) % 177.51/177.20 [1360]~E(x13601,x13602)+E(f271(x13603,x13604,x13605,x13601),f271(x13603,x13604,x13605,x13602)) % 177.51/177.20 [1361]~E(x13611,x13612)+E(f809(x13611,x13613,x13614,x13615,x13616,x13617),f809(x13612,x13613,x13614,x13615,x13616,x13617)) % 177.51/177.20 [1362]~E(x13621,x13622)+E(f809(x13623,x13621,x13624,x13625,x13626,x13627),f809(x13623,x13622,x13624,x13625,x13626,x13627)) % 177.51/177.20 [1363]~E(x13631,x13632)+E(f809(x13633,x13634,x13631,x13635,x13636,x13637),f809(x13633,x13634,x13632,x13635,x13636,x13637)) % 177.51/177.20 [1364]~E(x13641,x13642)+E(f809(x13643,x13644,x13645,x13641,x13646,x13647),f809(x13643,x13644,x13645,x13642,x13646,x13647)) % 177.51/177.20 [1365]~E(x13651,x13652)+E(f809(x13653,x13654,x13655,x13656,x13651,x13657),f809(x13653,x13654,x13655,x13656,x13652,x13657)) % 177.51/177.20 [1366]~E(x13661,x13662)+E(f809(x13663,x13664,x13665,x13666,x13667,x13661),f809(x13663,x13664,x13665,x13666,x13667,x13662)) % 177.51/177.20 [1367]~E(x13671,x13672)+E(f629(x13671,x13673,x13674),f629(x13672,x13673,x13674)) % 177.51/177.20 [1368]~E(x13681,x13682)+E(f629(x13683,x13681,x13684),f629(x13683,x13682,x13684)) % 177.51/177.20 [1369]~E(x13691,x13692)+E(f629(x13693,x13694,x13691),f629(x13693,x13694,x13692)) % 177.51/177.20 [1370]~E(x13701,x13702)+E(f443(x13701,x13703),f443(x13702,x13703)) % 177.51/177.20 [1371]~E(x13711,x13712)+E(f443(x13713,x13711),f443(x13713,x13712)) % 177.51/177.20 [1372]~E(x13721,x13722)+E(f420(x13721,x13723,x13724,x13725),f420(x13722,x13723,x13724,x13725)) % 177.51/177.20 [1373]~E(x13731,x13732)+E(f420(x13733,x13731,x13734,x13735),f420(x13733,x13732,x13734,x13735)) % 177.51/177.20 [1374]~E(x13741,x13742)+E(f420(x13743,x13744,x13741,x13745),f420(x13743,x13744,x13742,x13745)) % 177.51/177.20 [1375]~E(x13751,x13752)+E(f420(x13753,x13754,x13755,x13751),f420(x13753,x13754,x13755,x13752)) % 177.51/177.20 [1376]~E(x13761,x13762)+E(f757(x13761,x13763,x13764),f757(x13762,x13763,x13764)) % 177.51/177.20 [1377]~E(x13771,x13772)+E(f757(x13773,x13771,x13774),f757(x13773,x13772,x13774)) % 177.51/177.20 [1378]~E(x13781,x13782)+E(f757(x13783,x13784,x13781),f757(x13783,x13784,x13782)) % 177.51/177.20 [1379]~E(x13791,x13792)+E(f445(x13791,x13793,x13794,x13795),f445(x13792,x13793,x13794,x13795)) % 177.51/177.20 [1380]~E(x13801,x13802)+E(f445(x13803,x13801,x13804,x13805),f445(x13803,x13802,x13804,x13805)) % 177.51/177.20 [1381]~E(x13811,x13812)+E(f445(x13813,x13814,x13811,x13815),f445(x13813,x13814,x13812,x13815)) % 177.51/177.20 [1382]~E(x13821,x13822)+E(f445(x13823,x13824,x13825,x13821),f445(x13823,x13824,x13825,x13822)) % 177.51/177.20 [1383]~E(x13831,x13832)+E(f511(x13831,x13833,x13834,x13835,x13836,x13837,x13838),f511(x13832,x13833,x13834,x13835,x13836,x13837,x13838)) % 177.51/177.20 [1384]~E(x13841,x13842)+E(f511(x13843,x13841,x13844,x13845,x13846,x13847,x13848),f511(x13843,x13842,x13844,x13845,x13846,x13847,x13848)) % 177.51/177.20 [1385]~E(x13851,x13852)+E(f511(x13853,x13854,x13851,x13855,x13856,x13857,x13858),f511(x13853,x13854,x13852,x13855,x13856,x13857,x13858)) % 177.51/177.20 [1386]~E(x13861,x13862)+E(f511(x13863,x13864,x13865,x13861,x13866,x13867,x13868),f511(x13863,x13864,x13865,x13862,x13866,x13867,x13868)) % 177.51/177.20 [1387]~E(x13871,x13872)+E(f511(x13873,x13874,x13875,x13876,x13871,x13877,x13878),f511(x13873,x13874,x13875,x13876,x13872,x13877,x13878)) % 177.51/177.20 [1388]~E(x13881,x13882)+E(f511(x13883,x13884,x13885,x13886,x13887,x13881,x13888),f511(x13883,x13884,x13885,x13886,x13887,x13882,x13888)) % 177.51/177.20 [1389]~E(x13891,x13892)+E(f511(x13893,x13894,x13895,x13896,x13897,x13898,x13891),f511(x13893,x13894,x13895,x13896,x13897,x13898,x13892)) % 177.51/177.20 [1390]~E(x13901,x13902)+E(f645(x13901,x13903,x13904,x13905,x13906),f645(x13902,x13903,x13904,x13905,x13906)) % 177.51/177.20 [1391]~E(x13911,x13912)+E(f645(x13913,x13911,x13914,x13915,x13916),f645(x13913,x13912,x13914,x13915,x13916)) % 177.51/177.20 [1392]~E(x13921,x13922)+E(f645(x13923,x13924,x13921,x13925,x13926),f645(x13923,x13924,x13922,x13925,x13926)) % 177.51/177.20 [1393]~E(x13931,x13932)+E(f645(x13933,x13934,x13935,x13931,x13936),f645(x13933,x13934,x13935,x13932,x13936)) % 177.51/177.20 [1394]~E(x13941,x13942)+E(f645(x13943,x13944,x13945,x13946,x13941),f645(x13943,x13944,x13945,x13946,x13942)) % 177.51/177.20 [1395]~E(x13951,x13952)+E(f346(x13951,x13953,x13954,x13955,x13956),f346(x13952,x13953,x13954,x13955,x13956)) % 177.51/177.20 [1396]~E(x13961,x13962)+E(f346(x13963,x13961,x13964,x13965,x13966),f346(x13963,x13962,x13964,x13965,x13966)) % 177.51/177.20 [1397]~E(x13971,x13972)+E(f346(x13973,x13974,x13971,x13975,x13976),f346(x13973,x13974,x13972,x13975,x13976)) % 177.51/177.20 [1398]~E(x13981,x13982)+E(f346(x13983,x13984,x13985,x13981,x13986),f346(x13983,x13984,x13985,x13982,x13986)) % 177.51/177.20 [1399]~E(x13991,x13992)+E(f346(x13993,x13994,x13995,x13996,x13991),f346(x13993,x13994,x13995,x13996,x13992)) % 177.51/177.20 [1400]~E(x14001,x14002)+E(f806(x14001,x14003),f806(x14002,x14003)) % 177.51/177.20 [1401]~E(x14011,x14012)+E(f806(x14013,x14011),f806(x14013,x14012)) % 177.51/177.20 [1402]~E(x14021,x14022)+E(f769(x14021,x14023,x14024),f769(x14022,x14023,x14024)) % 177.51/177.20 [1403]~E(x14031,x14032)+E(f769(x14033,x14031,x14034),f769(x14033,x14032,x14034)) % 177.51/177.20 [1404]~E(x14041,x14042)+E(f769(x14043,x14044,x14041),f769(x14043,x14044,x14042)) % 177.51/177.20 [1405]~E(x14051,x14052)+E(f579(x14051,x14053,x14054,x14055,x14056),f579(x14052,x14053,x14054,x14055,x14056)) % 177.51/177.20 [1406]~E(x14061,x14062)+E(f579(x14063,x14061,x14064,x14065,x14066),f579(x14063,x14062,x14064,x14065,x14066)) % 177.51/177.20 [1407]~E(x14071,x14072)+E(f579(x14073,x14074,x14071,x14075,x14076),f579(x14073,x14074,x14072,x14075,x14076)) % 177.51/177.20 [1408]~E(x14081,x14082)+E(f579(x14083,x14084,x14085,x14081,x14086),f579(x14083,x14084,x14085,x14082,x14086)) % 177.51/177.20 [1409]~E(x14091,x14092)+E(f579(x14093,x14094,x14095,x14096,x14091),f579(x14093,x14094,x14095,x14096,x14092)) % 177.51/177.20 [1410]~E(x14101,x14102)+E(f685(x14101,x14103,x14104),f685(x14102,x14103,x14104)) % 177.51/177.20 [1411]~E(x14111,x14112)+E(f685(x14113,x14111,x14114),f685(x14113,x14112,x14114)) % 177.51/177.20 [1412]~E(x14121,x14122)+E(f685(x14123,x14124,x14121),f685(x14123,x14124,x14122)) % 177.51/177.20 [1413]~E(x14131,x14132)+E(f280(x14131,x14133,x14134,x14135),f280(x14132,x14133,x14134,x14135)) % 177.51/177.20 [1414]~E(x14141,x14142)+E(f280(x14143,x14141,x14144,x14145),f280(x14143,x14142,x14144,x14145)) % 177.51/177.20 [1415]~E(x14151,x14152)+E(f280(x14153,x14154,x14151,x14155),f280(x14153,x14154,x14152,x14155)) % 177.51/177.20 [1416]~E(x14161,x14162)+E(f280(x14163,x14164,x14165,x14161),f280(x14163,x14164,x14165,x14162)) % 177.51/177.20 [1417]~E(x14171,x14172)+E(f897(x14171,x14173,x14174,x14175,x14176,x14177),f897(x14172,x14173,x14174,x14175,x14176,x14177)) % 177.51/177.20 [1418]~E(x14181,x14182)+E(f897(x14183,x14181,x14184,x14185,x14186,x14187),f897(x14183,x14182,x14184,x14185,x14186,x14187)) % 177.51/177.20 [1419]~E(x14191,x14192)+E(f897(x14193,x14194,x14191,x14195,x14196,x14197),f897(x14193,x14194,x14192,x14195,x14196,x14197)) % 177.51/177.20 [1420]~E(x14201,x14202)+E(f897(x14203,x14204,x14205,x14201,x14206,x14207),f897(x14203,x14204,x14205,x14202,x14206,x14207)) % 177.51/177.20 [1421]~E(x14211,x14212)+E(f897(x14213,x14214,x14215,x14216,x14211,x14217),f897(x14213,x14214,x14215,x14216,x14212,x14217)) % 177.51/177.20 [1422]~E(x14221,x14222)+E(f897(x14223,x14224,x14225,x14226,x14227,x14221),f897(x14223,x14224,x14225,x14226,x14227,x14222)) % 177.51/177.20 [1423]~E(x14231,x14232)+E(f774(x14231,x14233,x14234),f774(x14232,x14233,x14234)) % 177.51/177.20 [1424]~E(x14241,x14242)+E(f774(x14243,x14241,x14244),f774(x14243,x14242,x14244)) % 177.51/177.20 [1425]~E(x14251,x14252)+E(f774(x14253,x14254,x14251),f774(x14253,x14254,x14252)) % 177.51/177.20 [1426]~E(x14261,x14262)+E(f668(x14261,x14263,x14264),f668(x14262,x14263,x14264)) % 177.51/177.20 [1427]~E(x14271,x14272)+E(f668(x14273,x14271,x14274),f668(x14273,x14272,x14274)) % 177.51/177.20 [1428]~E(x14281,x14282)+E(f668(x14283,x14284,x14281),f668(x14283,x14284,x14282)) % 177.51/177.20 [1429]~E(x14291,x14292)+E(f131(x14291,x14293,x14294,x14295),f131(x14292,x14293,x14294,x14295)) % 177.51/177.20 [1430]~E(x14301,x14302)+E(f131(x14303,x14301,x14304,x14305),f131(x14303,x14302,x14304,x14305)) % 177.51/177.20 [1431]~E(x14311,x14312)+E(f131(x14313,x14314,x14311,x14315),f131(x14313,x14314,x14312,x14315)) % 177.51/177.20 [1432]~E(x14321,x14322)+E(f131(x14323,x14324,x14325,x14321),f131(x14323,x14324,x14325,x14322)) % 177.51/177.20 [1433]~E(x14331,x14332)+E(f444(x14331,x14333,x14334,x14335),f444(x14332,x14333,x14334,x14335)) % 177.51/177.20 [1434]~E(x14341,x14342)+E(f444(x14343,x14341,x14344,x14345),f444(x14343,x14342,x14344,x14345)) % 177.51/177.20 [1435]~E(x14351,x14352)+E(f444(x14353,x14354,x14351,x14355),f444(x14353,x14354,x14352,x14355)) % 177.51/177.20 [1436]~E(x14361,x14362)+E(f444(x14363,x14364,x14365,x14361),f444(x14363,x14364,x14365,x14362)) % 177.51/177.20 [1437]~E(x14371,x14372)+E(f594(x14371,x14373,x14374),f594(x14372,x14373,x14374)) % 177.51/177.20 [1438]~E(x14381,x14382)+E(f594(x14383,x14381,x14384),f594(x14383,x14382,x14384)) % 177.51/177.20 [1439]~E(x14391,x14392)+E(f594(x14393,x14394,x14391),f594(x14393,x14394,x14392)) % 177.51/177.20 [1440]~E(x14401,x14402)+E(f581(x14401,x14403,x14404,x14405,x14406,x14407),f581(x14402,x14403,x14404,x14405,x14406,x14407)) % 177.51/177.20 [1441]~E(x14411,x14412)+E(f581(x14413,x14411,x14414,x14415,x14416,x14417),f581(x14413,x14412,x14414,x14415,x14416,x14417)) % 177.51/177.20 [1442]~E(x14421,x14422)+E(f581(x14423,x14424,x14421,x14425,x14426,x14427),f581(x14423,x14424,x14422,x14425,x14426,x14427)) % 177.51/177.20 [1443]~E(x14431,x14432)+E(f581(x14433,x14434,x14435,x14431,x14436,x14437),f581(x14433,x14434,x14435,x14432,x14436,x14437)) % 177.51/177.20 [1444]~E(x14441,x14442)+E(f581(x14443,x14444,x14445,x14446,x14441,x14447),f581(x14443,x14444,x14445,x14446,x14442,x14447)) % 177.51/177.20 [1445]~E(x14451,x14452)+E(f581(x14453,x14454,x14455,x14456,x14457,x14451),f581(x14453,x14454,x14455,x14456,x14457,x14452)) % 177.51/177.20 [1446]~E(x14461,x14462)+E(f402(x14461,x14463,x14464),f402(x14462,x14463,x14464)) % 177.51/177.20 [1447]~E(x14471,x14472)+E(f402(x14473,x14471,x14474),f402(x14473,x14472,x14474)) % 177.51/177.20 [1448]~E(x14481,x14482)+E(f402(x14483,x14484,x14481),f402(x14483,x14484,x14482)) % 177.51/177.20 [1449]~E(x14491,x14492)+E(f810(x14491,x14493,x14494,x14495,x14496,x14497),f810(x14492,x14493,x14494,x14495,x14496,x14497)) % 177.51/177.20 [1450]~E(x14501,x14502)+E(f810(x14503,x14501,x14504,x14505,x14506,x14507),f810(x14503,x14502,x14504,x14505,x14506,x14507)) % 177.51/177.20 [1451]~E(x14511,x14512)+E(f810(x14513,x14514,x14511,x14515,x14516,x14517),f810(x14513,x14514,x14512,x14515,x14516,x14517)) % 177.51/177.20 [1452]~E(x14521,x14522)+E(f810(x14523,x14524,x14525,x14521,x14526,x14527),f810(x14523,x14524,x14525,x14522,x14526,x14527)) % 177.51/177.20 [1453]~E(x14531,x14532)+E(f810(x14533,x14534,x14535,x14536,x14531,x14537),f810(x14533,x14534,x14535,x14536,x14532,x14537)) % 177.51/177.20 [1454]~E(x14541,x14542)+E(f810(x14543,x14544,x14545,x14546,x14547,x14541),f810(x14543,x14544,x14545,x14546,x14547,x14542)) % 177.51/177.20 [1455]~E(x14551,x14552)+E(f419(x14551,x14553,x14554),f419(x14552,x14553,x14554)) % 177.51/177.20 [1456]~E(x14561,x14562)+E(f419(x14563,x14561,x14564),f419(x14563,x14562,x14564)) % 177.51/177.20 [1457]~E(x14571,x14572)+E(f419(x14573,x14574,x14571),f419(x14573,x14574,x14572)) % 177.51/177.20 [1458]~E(x14581,x14582)+E(f842(x14581,x14583,x14584,x14585,x14586,x14587,x14588),f842(x14582,x14583,x14584,x14585,x14586,x14587,x14588)) % 177.51/177.20 [1459]~E(x14591,x14592)+E(f842(x14593,x14591,x14594,x14595,x14596,x14597,x14598),f842(x14593,x14592,x14594,x14595,x14596,x14597,x14598)) % 177.51/177.20 [1460]~E(x14601,x14602)+E(f842(x14603,x14604,x14601,x14605,x14606,x14607,x14608),f842(x14603,x14604,x14602,x14605,x14606,x14607,x14608)) % 177.51/177.20 [1461]~E(x14611,x14612)+E(f842(x14613,x14614,x14615,x14611,x14616,x14617,x14618),f842(x14613,x14614,x14615,x14612,x14616,x14617,x14618)) % 177.51/177.20 [1462]~E(x14621,x14622)+E(f842(x14623,x14624,x14625,x14626,x14621,x14627,x14628),f842(x14623,x14624,x14625,x14626,x14622,x14627,x14628)) % 177.51/177.20 [1463]~E(x14631,x14632)+E(f842(x14633,x14634,x14635,x14636,x14637,x14631,x14638),f842(x14633,x14634,x14635,x14636,x14637,x14632,x14638)) % 177.51/177.20 [1464]~E(x14641,x14642)+E(f842(x14643,x14644,x14645,x14646,x14647,x14648,x14641),f842(x14643,x14644,x14645,x14646,x14647,x14648,x14642)) % 177.51/177.20 [1465]~E(x14651,x14652)+E(f127(x14651,x14653,x14654),f127(x14652,x14653,x14654)) % 177.51/177.20 [1466]~E(x14661,x14662)+E(f127(x14663,x14661,x14664),f127(x14663,x14662,x14664)) % 177.51/177.20 [1467]~E(x14671,x14672)+E(f127(x14673,x14674,x14671),f127(x14673,x14674,x14672)) % 177.51/177.20 [1468]~E(x14681,x14682)+E(f47(x14681,x14683),f47(x14682,x14683)) % 177.51/177.20 [1469]~E(x14691,x14692)+E(f47(x14693,x14691),f47(x14693,x14692)) % 177.51/177.20 [1470]~E(x14701,x14702)+E(f710(x14701,x14703,x14704),f710(x14702,x14703,x14704)) % 177.51/177.20 [1471]~E(x14711,x14712)+E(f710(x14713,x14711,x14714),f710(x14713,x14712,x14714)) % 177.51/177.20 [1472]~E(x14721,x14722)+E(f710(x14723,x14724,x14721),f710(x14723,x14724,x14722)) % 177.51/177.20 [1473]~E(x14731,x14732)+E(f484(x14731,x14733,x14734,x14735,x14736,x14737),f484(x14732,x14733,x14734,x14735,x14736,x14737)) % 177.51/177.20 [1474]~E(x14741,x14742)+E(f484(x14743,x14741,x14744,x14745,x14746,x14747),f484(x14743,x14742,x14744,x14745,x14746,x14747)) % 177.51/177.20 [1475]~E(x14751,x14752)+E(f484(x14753,x14754,x14751,x14755,x14756,x14757),f484(x14753,x14754,x14752,x14755,x14756,x14757)) % 177.51/177.20 [1476]~E(x14761,x14762)+E(f484(x14763,x14764,x14765,x14761,x14766,x14767),f484(x14763,x14764,x14765,x14762,x14766,x14767)) % 177.51/177.20 [1477]~E(x14771,x14772)+E(f484(x14773,x14774,x14775,x14776,x14771,x14777),f484(x14773,x14774,x14775,x14776,x14772,x14777)) % 177.51/177.20 [1478]~E(x14781,x14782)+E(f484(x14783,x14784,x14785,x14786,x14787,x14781),f484(x14783,x14784,x14785,x14786,x14787,x14782)) % 177.51/177.20 [1479]~E(x14791,x14792)+E(f752(x14791,x14793,x14794),f752(x14792,x14793,x14794)) % 177.51/177.20 [1480]~E(x14801,x14802)+E(f752(x14803,x14801,x14804),f752(x14803,x14802,x14804)) % 177.51/177.20 [1481]~E(x14811,x14812)+E(f752(x14813,x14814,x14811),f752(x14813,x14814,x14812)) % 177.51/177.20 [1482]~E(x14821,x14822)+E(f274(x14821,x14823,x14824),f274(x14822,x14823,x14824)) % 177.51/177.20 [1483]~E(x14831,x14832)+E(f274(x14833,x14831,x14834),f274(x14833,x14832,x14834)) % 177.51/177.20 [1484]~E(x14841,x14842)+E(f274(x14843,x14844,x14841),f274(x14843,x14844,x14842)) % 177.51/177.20 [1485]~E(x14851,x14852)+E(f461(x14851,x14853,x14854),f461(x14852,x14853,x14854)) % 177.51/177.20 [1486]~E(x14861,x14862)+E(f461(x14863,x14861,x14864),f461(x14863,x14862,x14864)) % 177.51/177.20 [1487]~E(x14871,x14872)+E(f461(x14873,x14874,x14871),f461(x14873,x14874,x14872)) % 177.51/177.20 [1488]~E(x14881,x14882)+E(f232(x14881,x14883,x14884),f232(x14882,x14883,x14884)) % 177.51/177.20 [1489]~E(x14891,x14892)+E(f232(x14893,x14891,x14894),f232(x14893,x14892,x14894)) % 177.51/177.20 [1490]~E(x14901,x14902)+E(f232(x14903,x14904,x14901),f232(x14903,x14904,x14902)) % 177.51/177.20 [1491]~E(x14911,x14912)+E(f772(x14911,x14913,x14914,x14915),f772(x14912,x14913,x14914,x14915)) % 177.51/177.20 [1492]~E(x14921,x14922)+E(f772(x14923,x14921,x14924,x14925),f772(x14923,x14922,x14924,x14925)) % 177.51/177.20 [1493]~E(x14931,x14932)+E(f772(x14933,x14934,x14931,x14935),f772(x14933,x14934,x14932,x14935)) % 177.51/177.20 [1494]~E(x14941,x14942)+E(f772(x14943,x14944,x14945,x14941),f772(x14943,x14944,x14945,x14942)) % 177.51/177.20 [1495]~E(x14951,x14952)+E(f794(x14951,x14953,x14954,x14955),f794(x14952,x14953,x14954,x14955)) % 177.51/177.20 [1496]~E(x14961,x14962)+E(f794(x14963,x14961,x14964,x14965),f794(x14963,x14962,x14964,x14965)) % 177.51/177.20 [1497]~E(x14971,x14972)+E(f794(x14973,x14974,x14971,x14975),f794(x14973,x14974,x14972,x14975)) % 177.51/177.20 [1498]~E(x14981,x14982)+E(f794(x14983,x14984,x14985,x14981),f794(x14983,x14984,x14985,x14982)) % 177.51/177.20 [1499]~E(x14991,x14992)+E(f398(x14991,x14993,x14994,x14995),f398(x14992,x14993,x14994,x14995)) % 177.51/177.20 [1500]~E(x15001,x15002)+E(f398(x15003,x15001,x15004,x15005),f398(x15003,x15002,x15004,x15005)) % 177.51/177.20 [1501]~E(x15011,x15012)+E(f398(x15013,x15014,x15011,x15015),f398(x15013,x15014,x15012,x15015)) % 177.51/177.20 [1502]~E(x15021,x15022)+E(f398(x15023,x15024,x15025,x15021),f398(x15023,x15024,x15025,x15022)) % 177.51/177.20 [1503]~E(x15031,x15032)+E(f157(x15031,x15033,x15034,x15035),f157(x15032,x15033,x15034,x15035)) % 177.51/177.20 [1504]~E(x15041,x15042)+E(f157(x15043,x15041,x15044,x15045),f157(x15043,x15042,x15044,x15045)) % 177.51/177.20 [1505]~E(x15051,x15052)+E(f157(x15053,x15054,x15051,x15055),f157(x15053,x15054,x15052,x15055)) % 177.51/177.20 [1506]~E(x15061,x15062)+E(f157(x15063,x15064,x15065,x15061),f157(x15063,x15064,x15065,x15062)) % 177.51/177.20 [1507]~E(x15071,x15072)+E(f376(x15071,x15073,x15074,x15075,x15076),f376(x15072,x15073,x15074,x15075,x15076)) % 177.51/177.20 [1508]~E(x15081,x15082)+E(f376(x15083,x15081,x15084,x15085,x15086),f376(x15083,x15082,x15084,x15085,x15086)) % 177.51/177.20 [1509]~E(x15091,x15092)+E(f376(x15093,x15094,x15091,x15095,x15096),f376(x15093,x15094,x15092,x15095,x15096)) % 177.51/177.20 [1510]~E(x15101,x15102)+E(f376(x15103,x15104,x15105,x15101,x15106),f376(x15103,x15104,x15105,x15102,x15106)) % 177.51/177.20 [1511]~E(x15111,x15112)+E(f376(x15113,x15114,x15115,x15116,x15111),f376(x15113,x15114,x15115,x15116,x15112)) % 177.51/177.20 [1512]~E(x15121,x15122)+E(f682(x15121,x15123,x15124,x15125),f682(x15122,x15123,x15124,x15125)) % 177.51/177.20 [1513]~E(x15131,x15132)+E(f682(x15133,x15131,x15134,x15135),f682(x15133,x15132,x15134,x15135)) % 177.51/177.20 [1514]~E(x15141,x15142)+E(f682(x15143,x15144,x15141,x15145),f682(x15143,x15144,x15142,x15145)) % 177.51/177.20 [1515]~E(x15151,x15152)+E(f682(x15153,x15154,x15155,x15151),f682(x15153,x15154,x15155,x15152)) % 177.51/177.20 [1516]~E(x15161,x15162)+E(f829(x15161,x15163,x15164),f829(x15162,x15163,x15164)) % 177.51/177.20 [1517]~E(x15171,x15172)+E(f829(x15173,x15171,x15174),f829(x15173,x15172,x15174)) % 177.51/177.20 [1518]~E(x15181,x15182)+E(f829(x15183,x15184,x15181),f829(x15183,x15184,x15182)) % 177.51/177.20 [1519]~E(x15191,x15192)+E(f265(x15191,x15193,x15194),f265(x15192,x15193,x15194)) % 177.51/177.20 [1520]~E(x15201,x15202)+E(f265(x15203,x15201,x15204),f265(x15203,x15202,x15204)) % 177.51/177.20 [1521]~E(x15211,x15212)+E(f265(x15213,x15214,x15211),f265(x15213,x15214,x15212)) % 177.51/177.20 [1522]~E(x15221,x15222)+E(f573(x15221),f573(x15222)) % 177.51/177.20 [1523]~E(x15231,x15232)+E(f904(x15231,x15233,x15234,x15235,x15236),f904(x15232,x15233,x15234,x15235,x15236)) % 177.51/177.20 [1524]~E(x15241,x15242)+E(f904(x15243,x15241,x15244,x15245,x15246),f904(x15243,x15242,x15244,x15245,x15246)) % 177.51/177.20 [1525]~E(x15251,x15252)+E(f904(x15253,x15254,x15251,x15255,x15256),f904(x15253,x15254,x15252,x15255,x15256)) % 177.51/177.20 [1526]~E(x15261,x15262)+E(f904(x15263,x15264,x15265,x15261,x15266),f904(x15263,x15264,x15265,x15262,x15266)) % 177.51/177.20 [1527]~E(x15271,x15272)+E(f904(x15273,x15274,x15275,x15276,x15271),f904(x15273,x15274,x15275,x15276,x15272)) % 177.51/177.20 [1528]~E(x15281,x15282)+E(f641(x15281,x15283,x15284,x15285),f641(x15282,x15283,x15284,x15285)) % 177.51/177.20 [1529]~E(x15291,x15292)+E(f641(x15293,x15291,x15294,x15295),f641(x15293,x15292,x15294,x15295)) % 177.51/177.20 [1530]~E(x15301,x15302)+E(f641(x15303,x15304,x15301,x15305),f641(x15303,x15304,x15302,x15305)) % 177.51/177.20 [1531]~E(x15311,x15312)+E(f641(x15313,x15314,x15315,x15311),f641(x15313,x15314,x15315,x15312)) % 177.51/177.20 [1532]~E(x15321,x15322)+E(f586(x15321,x15323,x15324),f586(x15322,x15323,x15324)) % 177.51/177.20 [1533]~E(x15331,x15332)+E(f586(x15333,x15331,x15334),f586(x15333,x15332,x15334)) % 177.51/177.20 [1534]~E(x15341,x15342)+E(f586(x15343,x15344,x15341),f586(x15343,x15344,x15342)) % 177.51/177.20 [1535]~E(x15351,x15352)+E(f27(x15351,x15353,x15354),f27(x15352,x15353,x15354)) % 177.51/177.20 [1536]~E(x15361,x15362)+E(f27(x15363,x15361,x15364),f27(x15363,x15362,x15364)) % 177.51/177.20 [1537]~E(x15371,x15372)+E(f27(x15373,x15374,x15371),f27(x15373,x15374,x15372)) % 177.51/177.20 [1538]~E(x15381,x15382)+E(f225(x15381,x15383,x15384,x15385,x15386),f225(x15382,x15383,x15384,x15385,x15386)) % 177.51/177.20 [1539]~E(x15391,x15392)+E(f225(x15393,x15391,x15394,x15395,x15396),f225(x15393,x15392,x15394,x15395,x15396)) % 177.51/177.20 [1540]~E(x15401,x15402)+E(f225(x15403,x15404,x15401,x15405,x15406),f225(x15403,x15404,x15402,x15405,x15406)) % 177.51/177.20 [1541]~E(x15411,x15412)+E(f225(x15413,x15414,x15415,x15411,x15416),f225(x15413,x15414,x15415,x15412,x15416)) % 177.51/177.20 [1542]~E(x15421,x15422)+E(f225(x15423,x15424,x15425,x15426,x15421),f225(x15423,x15424,x15425,x15426,x15422)) % 177.51/177.20 [1543]~E(x15431,x15432)+E(f413(x15431,x15433,x15434,x15435,x15436),f413(x15432,x15433,x15434,x15435,x15436)) % 177.51/177.20 [1544]~E(x15441,x15442)+E(f413(x15443,x15441,x15444,x15445,x15446),f413(x15443,x15442,x15444,x15445,x15446)) % 177.51/177.20 [1545]~E(x15451,x15452)+E(f413(x15453,x15454,x15451,x15455,x15456),f413(x15453,x15454,x15452,x15455,x15456)) % 177.51/177.20 [1546]~E(x15461,x15462)+E(f413(x15463,x15464,x15465,x15461,x15466),f413(x15463,x15464,x15465,x15462,x15466)) % 177.51/177.20 [1547]~E(x15471,x15472)+E(f413(x15473,x15474,x15475,x15476,x15471),f413(x15473,x15474,x15475,x15476,x15472)) % 177.51/177.20 [1548]~E(x15481,x15482)+E(f854(x15481,x15483,x15484),f854(x15482,x15483,x15484)) % 177.51/177.20 [1549]~E(x15491,x15492)+E(f854(x15493,x15491,x15494),f854(x15493,x15492,x15494)) % 177.51/177.20 [1550]~E(x15501,x15502)+E(f854(x15503,x15504,x15501),f854(x15503,x15504,x15502)) % 177.51/177.20 [1551]~E(x15511,x15512)+E(f673(x15511,x15513,x15514),f673(x15512,x15513,x15514)) % 177.51/177.20 [1552]~E(x15521,x15522)+E(f673(x15523,x15521,x15524),f673(x15523,x15522,x15524)) % 177.51/177.20 [1553]~E(x15531,x15532)+E(f673(x15533,x15534,x15531),f673(x15533,x15534,x15532)) % 177.51/177.20 [1554]~E(x15541,x15542)+E(f784(x15541,x15543),f784(x15542,x15543)) % 177.51/177.20 [1555]~E(x15551,x15552)+E(f784(x15553,x15551),f784(x15553,x15552)) % 177.51/177.20 [1556]~E(x15561,x15562)+E(f277(x15561,x15563,x15564,x15565),f277(x15562,x15563,x15564,x15565)) % 177.51/177.20 [1557]~E(x15571,x15572)+E(f277(x15573,x15571,x15574,x15575),f277(x15573,x15572,x15574,x15575)) % 177.51/177.20 [1558]~E(x15581,x15582)+E(f277(x15583,x15584,x15581,x15585),f277(x15583,x15584,x15582,x15585)) % 177.51/177.20 [1559]~E(x15591,x15592)+E(f277(x15593,x15594,x15595,x15591),f277(x15593,x15594,x15595,x15592)) % 177.51/177.20 [1560]~E(x15601,x15602)+E(f399(x15601,x15603,x15604,x15605,x15606,x15607,x15608,x15609),f399(x15602,x15603,x15604,x15605,x15606,x15607,x15608,x15609)) % 177.51/177.20 [1561]~E(x15611,x15612)+E(f399(x15613,x15611,x15614,x15615,x15616,x15617,x15618,x15619),f399(x15613,x15612,x15614,x15615,x15616,x15617,x15618,x15619)) % 177.51/177.20 [1562]~E(x15621,x15622)+E(f399(x15623,x15624,x15621,x15625,x15626,x15627,x15628,x15629),f399(x15623,x15624,x15622,x15625,x15626,x15627,x15628,x15629)) % 177.51/177.20 [1563]~E(x15631,x15632)+E(f399(x15633,x15634,x15635,x15631,x15636,x15637,x15638,x15639),f399(x15633,x15634,x15635,x15632,x15636,x15637,x15638,x15639)) % 177.51/177.20 [1564]~E(x15641,x15642)+E(f399(x15643,x15644,x15645,x15646,x15641,x15647,x15648,x15649),f399(x15643,x15644,x15645,x15646,x15642,x15647,x15648,x15649)) % 177.51/177.20 [1565]~E(x15651,x15652)+E(f399(x15653,x15654,x15655,x15656,x15657,x15651,x15658,x15659),f399(x15653,x15654,x15655,x15656,x15657,x15652,x15658,x15659)) % 177.51/177.20 [1566]~E(x15661,x15662)+E(f399(x15663,x15664,x15665,x15666,x15667,x15668,x15661,x15669),f399(x15663,x15664,x15665,x15666,x15667,x15668,x15662,x15669)) % 177.51/177.20 [1567]~E(x15671,x15672)+E(f399(x15673,x15674,x15675,x15676,x15677,x15678,x15679,x15671),f399(x15673,x15674,x15675,x15676,x15677,x15678,x15679,x15672)) % 177.51/177.20 [1568]~E(x15681,x15682)+E(f198(x15681,x15683,x15684,x15685),f198(x15682,x15683,x15684,x15685)) % 177.51/177.20 [1569]~E(x15691,x15692)+E(f198(x15693,x15691,x15694,x15695),f198(x15693,x15692,x15694,x15695)) % 177.51/177.20 [1570]~E(x15701,x15702)+E(f198(x15703,x15704,x15701,x15705),f198(x15703,x15704,x15702,x15705)) % 177.51/177.20 [1571]~E(x15711,x15712)+E(f198(x15713,x15714,x15715,x15711),f198(x15713,x15714,x15715,x15712)) % 177.51/177.20 [1572]~E(x15721,x15722)+E(f539(x15721,x15723,x15724,x15725,x15726),f539(x15722,x15723,x15724,x15725,x15726)) % 177.51/177.20 [1573]~E(x15731,x15732)+E(f539(x15733,x15731,x15734,x15735,x15736),f539(x15733,x15732,x15734,x15735,x15736)) % 177.51/177.20 [1574]~E(x15741,x15742)+E(f539(x15743,x15744,x15741,x15745,x15746),f539(x15743,x15744,x15742,x15745,x15746)) % 177.51/177.20 [1575]~E(x15751,x15752)+E(f539(x15753,x15754,x15755,x15751,x15756),f539(x15753,x15754,x15755,x15752,x15756)) % 177.51/177.20 [1576]~E(x15761,x15762)+E(f539(x15763,x15764,x15765,x15766,x15761),f539(x15763,x15764,x15765,x15766,x15762)) % 177.51/177.20 [1577]~E(x15771,x15772)+E(f598(x15771,x15773,x15774,x15775,x15776),f598(x15772,x15773,x15774,x15775,x15776)) % 177.51/177.20 [1578]~E(x15781,x15782)+E(f598(x15783,x15781,x15784,x15785,x15786),f598(x15783,x15782,x15784,x15785,x15786)) % 177.51/177.20 [1579]~E(x15791,x15792)+E(f598(x15793,x15794,x15791,x15795,x15796),f598(x15793,x15794,x15792,x15795,x15796)) % 177.51/177.20 [1580]~E(x15801,x15802)+E(f598(x15803,x15804,x15805,x15801,x15806),f598(x15803,x15804,x15805,x15802,x15806)) % 177.51/177.20 [1581]~E(x15811,x15812)+E(f598(x15813,x15814,x15815,x15816,x15811),f598(x15813,x15814,x15815,x15816,x15812)) % 177.51/177.20 [1582]~E(x15821,x15822)+E(f123(x15821,x15823,x15824,x15825),f123(x15822,x15823,x15824,x15825)) % 177.51/177.20 [1583]~E(x15831,x15832)+E(f123(x15833,x15831,x15834,x15835),f123(x15833,x15832,x15834,x15835)) % 177.51/177.20 [1584]~E(x15841,x15842)+E(f123(x15843,x15844,x15841,x15845),f123(x15843,x15844,x15842,x15845)) % 177.51/177.20 [1585]~E(x15851,x15852)+E(f123(x15853,x15854,x15855,x15851),f123(x15853,x15854,x15855,x15852)) % 177.51/177.20 [1586]~E(x15861,x15862)+E(f208(x15861,x15863,x15864,x15865),f208(x15862,x15863,x15864,x15865)) % 177.51/177.20 [1587]~E(x15871,x15872)+E(f208(x15873,x15871,x15874,x15875),f208(x15873,x15872,x15874,x15875)) % 177.51/177.20 [1588]~E(x15881,x15882)+E(f208(x15883,x15884,x15881,x15885),f208(x15883,x15884,x15882,x15885)) % 177.51/177.20 [1589]~E(x15891,x15892)+E(f208(x15893,x15894,x15895,x15891),f208(x15893,x15894,x15895,x15892)) % 177.51/177.20 [1590]~E(x15901,x15902)+E(f473(x15901,x15903,x15904),f473(x15902,x15903,x15904)) % 177.51/177.20 [1591]~E(x15911,x15912)+E(f473(x15913,x15911,x15914),f473(x15913,x15912,x15914)) % 177.51/177.20 [1592]~E(x15921,x15922)+E(f473(x15923,x15924,x15921),f473(x15923,x15924,x15922)) % 177.51/177.20 [1593]~E(x15931,x15932)+E(f150(x15931,x15933,x15934,x15935,x15936),f150(x15932,x15933,x15934,x15935,x15936)) % 177.51/177.20 [1594]~E(x15941,x15942)+E(f150(x15943,x15941,x15944,x15945,x15946),f150(x15943,x15942,x15944,x15945,x15946)) % 177.51/177.20 [1595]~E(x15951,x15952)+E(f150(x15953,x15954,x15951,x15955,x15956),f150(x15953,x15954,x15952,x15955,x15956)) % 177.51/177.20 [1596]~E(x15961,x15962)+E(f150(x15963,x15964,x15965,x15961,x15966),f150(x15963,x15964,x15965,x15962,x15966)) % 177.51/177.20 [1597]~E(x15971,x15972)+E(f150(x15973,x15974,x15975,x15976,x15971),f150(x15973,x15974,x15975,x15976,x15972)) % 177.51/177.20 [1598]~E(x15981,x15982)+E(f683(x15981,x15983,x15984,x15985),f683(x15982,x15983,x15984,x15985)) % 177.51/177.20 [1599]~E(x15991,x15992)+E(f683(x15993,x15991,x15994,x15995),f683(x15993,x15992,x15994,x15995)) % 177.51/177.20 [1600]~E(x16001,x16002)+E(f683(x16003,x16004,x16001,x16005),f683(x16003,x16004,x16002,x16005)) % 177.51/177.20 [1601]~E(x16011,x16012)+E(f683(x16013,x16014,x16015,x16011),f683(x16013,x16014,x16015,x16012)) % 177.51/177.20 [1602]~E(x16021,x16022)+E(f690(x16021,x16023,x16024,x16025,x16026),f690(x16022,x16023,x16024,x16025,x16026)) % 177.51/177.20 [1603]~E(x16031,x16032)+E(f690(x16033,x16031,x16034,x16035,x16036),f690(x16033,x16032,x16034,x16035,x16036)) % 177.51/177.20 [1604]~E(x16041,x16042)+E(f690(x16043,x16044,x16041,x16045,x16046),f690(x16043,x16044,x16042,x16045,x16046)) % 177.51/177.20 [1605]~E(x16051,x16052)+E(f690(x16053,x16054,x16055,x16051,x16056),f690(x16053,x16054,x16055,x16052,x16056)) % 177.51/177.20 [1606]~E(x16061,x16062)+E(f690(x16063,x16064,x16065,x16066,x16061),f690(x16063,x16064,x16065,x16066,x16062)) % 177.51/177.20 [1607]~E(x16071,x16072)+E(f409(x16071,x16073,x16074),f409(x16072,x16073,x16074)) % 177.51/177.20 [1608]~E(x16081,x16082)+E(f409(x16083,x16081,x16084),f409(x16083,x16082,x16084)) % 177.51/177.20 [1609]~E(x16091,x16092)+E(f409(x16093,x16094,x16091),f409(x16093,x16094,x16092)) % 177.51/177.20 [1610]~E(x16101,x16102)+E(f627(x16101,x16103,x16104,x16105),f627(x16102,x16103,x16104,x16105)) % 177.51/177.20 [1611]~E(x16111,x16112)+E(f627(x16113,x16111,x16114,x16115),f627(x16113,x16112,x16114,x16115)) % 177.51/177.20 [1612]~E(x16121,x16122)+E(f627(x16123,x16124,x16121,x16125),f627(x16123,x16124,x16122,x16125)) % 177.51/177.20 [1613]~E(x16131,x16132)+E(f627(x16133,x16134,x16135,x16131),f627(x16133,x16134,x16135,x16132)) % 177.51/177.20 [1614]~E(x16141,x16142)+E(f852(x16141,x16143,x16144),f852(x16142,x16143,x16144)) % 177.51/177.20 [1615]~E(x16151,x16152)+E(f852(x16153,x16151,x16154),f852(x16153,x16152,x16154)) % 177.51/177.20 [1616]~E(x16161,x16162)+E(f852(x16163,x16164,x16161),f852(x16163,x16164,x16162)) % 177.51/177.20 [1617]~E(x16171,x16172)+E(f371(x16171,x16173,x16174,x16175,x16176,x16177),f371(x16172,x16173,x16174,x16175,x16176,x16177)) % 177.51/177.20 [1618]~E(x16181,x16182)+E(f371(x16183,x16181,x16184,x16185,x16186,x16187),f371(x16183,x16182,x16184,x16185,x16186,x16187)) % 177.51/177.20 [1619]~E(x16191,x16192)+E(f371(x16193,x16194,x16191,x16195,x16196,x16197),f371(x16193,x16194,x16192,x16195,x16196,x16197)) % 177.51/177.20 [1620]~E(x16201,x16202)+E(f371(x16203,x16204,x16205,x16201,x16206,x16207),f371(x16203,x16204,x16205,x16202,x16206,x16207)) % 177.51/177.20 [1621]~E(x16211,x16212)+E(f371(x16213,x16214,x16215,x16216,x16211,x16217),f371(x16213,x16214,x16215,x16216,x16212,x16217)) % 177.51/177.20 [1622]~E(x16221,x16222)+E(f371(x16223,x16224,x16225,x16226,x16227,x16221),f371(x16223,x16224,x16225,x16226,x16227,x16222)) % 177.51/177.20 [1623]~E(x16231,x16232)+E(f164(x16231,x16233,x16234,x16235),f164(x16232,x16233,x16234,x16235)) % 177.51/177.20 [1624]~E(x16241,x16242)+E(f164(x16243,x16241,x16244,x16245),f164(x16243,x16242,x16244,x16245)) % 177.51/177.20 [1625]~E(x16251,x16252)+E(f164(x16253,x16254,x16251,x16255),f164(x16253,x16254,x16252,x16255)) % 177.51/177.20 [1626]~E(x16261,x16262)+E(f164(x16263,x16264,x16265,x16261),f164(x16263,x16264,x16265,x16262)) % 177.51/177.20 [1627]~E(x16271,x16272)+E(f497(x16271,x16273,x16274,x16275),f497(x16272,x16273,x16274,x16275)) % 177.51/177.20 [1628]~E(x16281,x16282)+E(f497(x16283,x16281,x16284,x16285),f497(x16283,x16282,x16284,x16285)) % 177.51/177.20 [1629]~E(x16291,x16292)+E(f497(x16293,x16294,x16291,x16295),f497(x16293,x16294,x16292,x16295)) % 177.51/177.20 [1630]~E(x16301,x16302)+E(f497(x16303,x16304,x16305,x16301),f497(x16303,x16304,x16305,x16302)) % 177.51/177.20 [1631]~E(x16311,x16312)+E(f899(x16311,x16313,x16314,x16315),f899(x16312,x16313,x16314,x16315)) % 177.51/177.20 [1632]~E(x16321,x16322)+E(f899(x16323,x16321,x16324,x16325),f899(x16323,x16322,x16324,x16325)) % 177.51/177.20 [1633]~E(x16331,x16332)+E(f899(x16333,x16334,x16331,x16335),f899(x16333,x16334,x16332,x16335)) % 177.51/177.20 [1634]~E(x16341,x16342)+E(f899(x16343,x16344,x16345,x16341),f899(x16343,x16344,x16345,x16342)) % 177.51/177.20 [1635]~E(x16351,x16352)+E(f546(x16351,x16353),f546(x16352,x16353)) % 177.51/177.20 [1636]~E(x16361,x16362)+E(f546(x16363,x16361),f546(x16363,x16362)) % 177.51/177.20 [1637]~E(x16371,x16372)+E(f393(x16371,x16373,x16374),f393(x16372,x16373,x16374)) % 177.51/177.20 [1638]~E(x16381,x16382)+E(f393(x16383,x16381,x16384),f393(x16383,x16382,x16384)) % 177.51/177.20 [1639]~E(x16391,x16392)+E(f393(x16393,x16394,x16391),f393(x16393,x16394,x16392)) % 177.51/177.20 [1640]~E(x16401,x16402)+E(f616(x16401,x16403,x16404,x16405,x16406),f616(x16402,x16403,x16404,x16405,x16406)) % 177.51/177.20 [1641]~E(x16411,x16412)+E(f616(x16413,x16411,x16414,x16415,x16416),f616(x16413,x16412,x16414,x16415,x16416)) % 177.51/177.20 [1642]~E(x16421,x16422)+E(f616(x16423,x16424,x16421,x16425,x16426),f616(x16423,x16424,x16422,x16425,x16426)) % 177.51/177.20 [1643]~E(x16431,x16432)+E(f616(x16433,x16434,x16435,x16431,x16436),f616(x16433,x16434,x16435,x16432,x16436)) % 177.51/177.20 [1644]~E(x16441,x16442)+E(f616(x16443,x16444,x16445,x16446,x16441),f616(x16443,x16444,x16445,x16446,x16442)) % 177.51/177.20 [1645]~E(x16451,x16452)+E(f771(x16451,x16453,x16454,x16455),f771(x16452,x16453,x16454,x16455)) % 177.51/177.20 [1646]~E(x16461,x16462)+E(f771(x16463,x16461,x16464,x16465),f771(x16463,x16462,x16464,x16465)) % 177.51/177.20 [1647]~E(x16471,x16472)+E(f771(x16473,x16474,x16471,x16475),f771(x16473,x16474,x16472,x16475)) % 177.51/177.20 [1648]~E(x16481,x16482)+E(f771(x16483,x16484,x16485,x16481),f771(x16483,x16484,x16485,x16482)) % 177.51/177.20 [1649]~E(x16491,x16492)+E(f631(x16491,x16493,x16494),f631(x16492,x16493,x16494)) % 177.51/177.20 [1650]~E(x16501,x16502)+E(f631(x16503,x16501,x16504),f631(x16503,x16502,x16504)) % 177.51/177.20 [1651]~E(x16511,x16512)+E(f631(x16513,x16514,x16511),f631(x16513,x16514,x16512)) % 177.51/177.20 [1652]~E(x16521,x16522)+E(f747(x16521,x16523,x16524),f747(x16522,x16523,x16524)) % 177.51/177.20 [1653]~E(x16531,x16532)+E(f747(x16533,x16531,x16534),f747(x16533,x16532,x16534)) % 177.51/177.20 [1654]~E(x16541,x16542)+E(f747(x16543,x16544,x16541),f747(x16543,x16544,x16542)) % 177.51/177.20 [1655]~E(x16551,x16552)+E(f582(x16551,x16553,x16554,x16555,x16556,x16557),f582(x16552,x16553,x16554,x16555,x16556,x16557)) % 177.51/177.20 [1656]~E(x16561,x16562)+E(f582(x16563,x16561,x16564,x16565,x16566,x16567),f582(x16563,x16562,x16564,x16565,x16566,x16567)) % 177.51/177.20 [1657]~E(x16571,x16572)+E(f582(x16573,x16574,x16571,x16575,x16576,x16577),f582(x16573,x16574,x16572,x16575,x16576,x16577)) % 177.51/177.20 [1658]~E(x16581,x16582)+E(f582(x16583,x16584,x16585,x16581,x16586,x16587),f582(x16583,x16584,x16585,x16582,x16586,x16587)) % 177.51/177.20 [1659]~E(x16591,x16592)+E(f582(x16593,x16594,x16595,x16596,x16591,x16597),f582(x16593,x16594,x16595,x16596,x16592,x16597)) % 177.51/177.20 [1660]~E(x16601,x16602)+E(f582(x16603,x16604,x16605,x16606,x16607,x16601),f582(x16603,x16604,x16605,x16606,x16607,x16602)) % 177.51/177.20 [1661]~E(x16611,x16612)+E(f118(x16611,x16613,x16614),f118(x16612,x16613,x16614)) % 177.51/177.20 [1662]~E(x16621,x16622)+E(f118(x16623,x16621,x16624),f118(x16623,x16622,x16624)) % 177.51/177.20 [1663]~E(x16631,x16632)+E(f118(x16633,x16634,x16631),f118(x16633,x16634,x16632)) % 177.51/177.20 [1664]~E(x16641,x16642)+E(f299(x16641,x16643,x16644,x16645),f299(x16642,x16643,x16644,x16645)) % 177.51/177.20 [1665]~E(x16651,x16652)+E(f299(x16653,x16651,x16654,x16655),f299(x16653,x16652,x16654,x16655)) % 177.51/177.20 [1666]~E(x16661,x16662)+E(f299(x16663,x16664,x16661,x16665),f299(x16663,x16664,x16662,x16665)) % 177.51/177.20 [1667]~E(x16671,x16672)+E(f299(x16673,x16674,x16675,x16671),f299(x16673,x16674,x16675,x16672)) % 177.51/177.20 [1668]~E(x16681,x16682)+E(f268(x16681,x16683),f268(x16682,x16683)) % 177.51/177.20 [1669]~E(x16691,x16692)+E(f268(x16693,x16691),f268(x16693,x16692)) % 177.51/177.20 [1670]~E(x16701,x16702)+E(f381(x16701,x16703),f381(x16702,x16703)) % 177.51/177.20 [1671]~E(x16711,x16712)+E(f381(x16713,x16711),f381(x16713,x16712)) % 177.51/177.20 [1672]~E(x16721,x16722)+E(f358(x16721,x16723,x16724),f358(x16722,x16723,x16724)) % 177.51/177.20 [1673]~E(x16731,x16732)+E(f358(x16733,x16731,x16734),f358(x16733,x16732,x16734)) % 177.51/177.20 [1674]~E(x16741,x16742)+E(f358(x16743,x16744,x16741),f358(x16743,x16744,x16742)) % 177.51/177.20 [1675]~E(x16751,x16752)+E(f618(x16751,x16753,x16754,x16755),f618(x16752,x16753,x16754,x16755)) % 177.51/177.20 [1676]~E(x16761,x16762)+E(f618(x16763,x16761,x16764,x16765),f618(x16763,x16762,x16764,x16765)) % 177.51/177.20 [1677]~E(x16771,x16772)+E(f618(x16773,x16774,x16771,x16775),f618(x16773,x16774,x16772,x16775)) % 177.51/177.20 [1678]~E(x16781,x16782)+E(f618(x16783,x16784,x16785,x16781),f618(x16783,x16784,x16785,x16782)) % 177.51/177.20 [1679]~E(x16791,x16792)+E(f702(x16791,x16793),f702(x16792,x16793)) % 177.51/177.20 [1680]~E(x16801,x16802)+E(f702(x16803,x16801),f702(x16803,x16802)) % 177.51/177.20 [1681]~E(x16811,x16812)+E(f450(x16811,x16813,x16814),f450(x16812,x16813,x16814)) % 177.51/177.20 [1682]~E(x16821,x16822)+E(f450(x16823,x16821,x16824),f450(x16823,x16822,x16824)) % 177.51/177.20 [1683]~E(x16831,x16832)+E(f450(x16833,x16834,x16831),f450(x16833,x16834,x16832)) % 177.51/177.20 [1684]~E(x16841,x16842)+E(f460(x16841,x16843,x16844),f460(x16842,x16843,x16844)) % 177.51/177.20 [1685]~E(x16851,x16852)+E(f460(x16853,x16851,x16854),f460(x16853,x16852,x16854)) % 177.51/177.20 [1686]~E(x16861,x16862)+E(f460(x16863,x16864,x16861),f460(x16863,x16864,x16862)) % 177.51/177.20 [1687]~E(x16871,x16872)+E(f452(x16871,x16873,x16874,x16875),f452(x16872,x16873,x16874,x16875)) % 177.51/177.20 [1688]~E(x16881,x16882)+E(f452(x16883,x16881,x16884,x16885),f452(x16883,x16882,x16884,x16885)) % 177.51/177.20 [1689]~E(x16891,x16892)+E(f452(x16893,x16894,x16891,x16895),f452(x16893,x16894,x16892,x16895)) % 177.51/177.20 [1690]~E(x16901,x16902)+E(f452(x16903,x16904,x16905,x16901),f452(x16903,x16904,x16905,x16902)) % 177.51/177.20 [1691]~E(x16911,x16912)+E(f655(x16911,x16913,x16914),f655(x16912,x16913,x16914)) % 177.51/177.20 [1692]~E(x16921,x16922)+E(f655(x16923,x16921,x16924),f655(x16923,x16922,x16924)) % 177.51/177.20 [1693]~E(x16931,x16932)+E(f655(x16933,x16934,x16931),f655(x16933,x16934,x16932)) % 177.51/177.20 [1694]~E(x16941,x16942)+E(f427(x16941,x16943,x16944,x16945),f427(x16942,x16943,x16944,x16945)) % 177.51/177.20 [1695]~E(x16951,x16952)+E(f427(x16953,x16951,x16954,x16955),f427(x16953,x16952,x16954,x16955)) % 177.51/177.20 [1696]~E(x16961,x16962)+E(f427(x16963,x16964,x16961,x16965),f427(x16963,x16964,x16962,x16965)) % 177.51/177.20 [1697]~E(x16971,x16972)+E(f427(x16973,x16974,x16975,x16971),f427(x16973,x16974,x16975,x16972)) % 177.51/177.20 [1698]~E(x16981,x16982)+E(f871(x16981,x16983,x16984,x16985),f871(x16982,x16983,x16984,x16985)) % 177.51/177.20 [1699]~E(x16991,x16992)+E(f871(x16993,x16991,x16994,x16995),f871(x16993,x16992,x16994,x16995)) % 177.51/177.20 [1700]~E(x17001,x17002)+E(f871(x17003,x17004,x17001,x17005),f871(x17003,x17004,x17002,x17005)) % 177.51/177.20 [1701]~E(x17011,x17012)+E(f871(x17013,x17014,x17015,x17011),f871(x17013,x17014,x17015,x17012)) % 177.51/177.20 [1702]~E(x17021,x17022)+E(f659(x17021,x17023,x17024,x17025),f659(x17022,x17023,x17024,x17025)) % 177.51/177.20 [1703]~E(x17031,x17032)+E(f659(x17033,x17031,x17034,x17035),f659(x17033,x17032,x17034,x17035)) % 177.51/177.20 [1704]~E(x17041,x17042)+E(f659(x17043,x17044,x17041,x17045),f659(x17043,x17044,x17042,x17045)) % 177.51/177.20 [1705]~E(x17051,x17052)+E(f659(x17053,x17054,x17055,x17051),f659(x17053,x17054,x17055,x17052)) % 177.51/177.20 [1706]~E(x17061,x17062)+E(f394(x17061,x17063,x17064),f394(x17062,x17063,x17064)) % 177.51/177.20 [1707]~E(x17071,x17072)+E(f394(x17073,x17071,x17074),f394(x17073,x17072,x17074)) % 177.51/177.20 [1708]~E(x17081,x17082)+E(f394(x17083,x17084,x17081),f394(x17083,x17084,x17082)) % 177.51/177.20 [1709]~E(x17091,x17092)+E(f485(x17091,x17093,x17094,x17095,x17096,x17097,x17098),f485(x17092,x17093,x17094,x17095,x17096,x17097,x17098)) % 177.51/177.20 [1710]~E(x17101,x17102)+E(f485(x17103,x17101,x17104,x17105,x17106,x17107,x17108),f485(x17103,x17102,x17104,x17105,x17106,x17107,x17108)) % 177.51/177.20 [1711]~E(x17111,x17112)+E(f485(x17113,x17114,x17111,x17115,x17116,x17117,x17118),f485(x17113,x17114,x17112,x17115,x17116,x17117,x17118)) % 177.51/177.20 [1712]~E(x17121,x17122)+E(f485(x17123,x17124,x17125,x17121,x17126,x17127,x17128),f485(x17123,x17124,x17125,x17122,x17126,x17127,x17128)) % 177.51/177.20 [1713]~E(x17131,x17132)+E(f485(x17133,x17134,x17135,x17136,x17131,x17137,x17138),f485(x17133,x17134,x17135,x17136,x17132,x17137,x17138)) % 177.51/177.20 [1714]~E(x17141,x17142)+E(f485(x17143,x17144,x17145,x17146,x17147,x17141,x17148),f485(x17143,x17144,x17145,x17146,x17147,x17142,x17148)) % 177.51/177.20 [1715]~E(x17151,x17152)+E(f485(x17153,x17154,x17155,x17156,x17157,x17158,x17151),f485(x17153,x17154,x17155,x17156,x17157,x17158,x17152)) % 177.51/177.20 [1716]~E(x17161,x17162)+E(f509(x17161,x17163,x17164,x17165,x17166),f509(x17162,x17163,x17164,x17165,x17166)) % 177.51/177.20 [1717]~E(x17171,x17172)+E(f509(x17173,x17171,x17174,x17175,x17176),f509(x17173,x17172,x17174,x17175,x17176)) % 177.51/177.20 [1718]~E(x17181,x17182)+E(f509(x17183,x17184,x17181,x17185,x17186),f509(x17183,x17184,x17182,x17185,x17186)) % 177.51/177.20 [1719]~E(x17191,x17192)+E(f509(x17193,x17194,x17195,x17191,x17196),f509(x17193,x17194,x17195,x17192,x17196)) % 177.51/177.20 [1720]~E(x17201,x17202)+E(f509(x17203,x17204,x17205,x17206,x17201),f509(x17203,x17204,x17205,x17206,x17202)) % 177.51/177.20 [1721]~E(x17211,x17212)+E(f167(x17211,x17213,x17214),f167(x17212,x17213,x17214)) % 177.51/177.20 [1722]~E(x17221,x17222)+E(f167(x17223,x17221,x17224),f167(x17223,x17222,x17224)) % 177.51/177.20 [1723]~E(x17231,x17232)+E(f167(x17233,x17234,x17231),f167(x17233,x17234,x17232)) % 177.51/177.20 [1724]~E(x17241,x17242)+E(f731(x17241,x17243),f731(x17242,x17243)) % 177.51/177.20 [1725]~E(x17251,x17252)+E(f731(x17253,x17251),f731(x17253,x17252)) % 177.51/177.20 [1726]~E(x17261,x17262)+E(f592(x17261,x17263,x17264,x17265,x17266,x17267),f592(x17262,x17263,x17264,x17265,x17266,x17267)) % 177.51/177.20 [1727]~E(x17271,x17272)+E(f592(x17273,x17271,x17274,x17275,x17276,x17277),f592(x17273,x17272,x17274,x17275,x17276,x17277)) % 177.51/177.20 [1728]~E(x17281,x17282)+E(f592(x17283,x17284,x17281,x17285,x17286,x17287),f592(x17283,x17284,x17282,x17285,x17286,x17287)) % 177.51/177.20 [1729]~E(x17291,x17292)+E(f592(x17293,x17294,x17295,x17291,x17296,x17297),f592(x17293,x17294,x17295,x17292,x17296,x17297)) % 177.51/177.20 [1730]~E(x17301,x17302)+E(f592(x17303,x17304,x17305,x17306,x17301,x17307),f592(x17303,x17304,x17305,x17306,x17302,x17307)) % 177.51/177.20 [1731]~E(x17311,x17312)+E(f592(x17313,x17314,x17315,x17316,x17317,x17311),f592(x17313,x17314,x17315,x17316,x17317,x17312)) % 177.51/177.20 [1732]~E(x17321,x17322)+E(f793(x17321,x17323,x17324,x17325),f793(x17322,x17323,x17324,x17325)) % 177.51/177.20 [1733]~E(x17331,x17332)+E(f793(x17333,x17331,x17334,x17335),f793(x17333,x17332,x17334,x17335)) % 177.51/177.20 [1734]~E(x17341,x17342)+E(f793(x17343,x17344,x17341,x17345),f793(x17343,x17344,x17342,x17345)) % 177.51/177.20 [1735]~E(x17351,x17352)+E(f793(x17353,x17354,x17355,x17351),f793(x17353,x17354,x17355,x17352)) % 177.51/177.20 [1736]~E(x17361,x17362)+E(f361(x17361,x17363,x17364,x17365,x17366,x17367,x17368),f361(x17362,x17363,x17364,x17365,x17366,x17367,x17368)) % 177.51/177.20 [1737]~E(x17371,x17372)+E(f361(x17373,x17371,x17374,x17375,x17376,x17377,x17378),f361(x17373,x17372,x17374,x17375,x17376,x17377,x17378)) % 177.51/177.20 [1738]~E(x17381,x17382)+E(f361(x17383,x17384,x17381,x17385,x17386,x17387,x17388),f361(x17383,x17384,x17382,x17385,x17386,x17387,x17388)) % 177.51/177.20 [1739]~E(x17391,x17392)+E(f361(x17393,x17394,x17395,x17391,x17396,x17397,x17398),f361(x17393,x17394,x17395,x17392,x17396,x17397,x17398)) % 177.51/177.20 [1740]~E(x17401,x17402)+E(f361(x17403,x17404,x17405,x17406,x17401,x17407,x17408),f361(x17403,x17404,x17405,x17406,x17402,x17407,x17408)) % 177.51/177.20 [1741]~E(x17411,x17412)+E(f361(x17413,x17414,x17415,x17416,x17417,x17411,x17418),f361(x17413,x17414,x17415,x17416,x17417,x17412,x17418)) % 177.51/177.20 [1742]~E(x17421,x17422)+E(f361(x17423,x17424,x17425,x17426,x17427,x17428,x17421),f361(x17423,x17424,x17425,x17426,x17427,x17428,x17422)) % 177.51/177.20 [1743]~E(x17431,x17432)+E(f365(x17431,x17433,x17434),f365(x17432,x17433,x17434)) % 177.51/177.20 [1744]~E(x17441,x17442)+E(f365(x17443,x17441,x17444),f365(x17443,x17442,x17444)) % 177.51/177.20 [1745]~E(x17451,x17452)+E(f365(x17453,x17454,x17451),f365(x17453,x17454,x17452)) % 177.51/177.20 [1746]~E(x17461,x17462)+E(f147(x17461,x17463),f147(x17462,x17463)) % 177.51/177.20 [1747]~E(x17471,x17472)+E(f147(x17473,x17471),f147(x17473,x17472)) % 177.51/177.20 [1748]~E(x17481,x17482)+E(f514(x17481,x17483),f514(x17482,x17483)) % 177.51/177.20 [1749]~E(x17491,x17492)+E(f514(x17493,x17491),f514(x17493,x17492)) % 177.51/177.20 [1750]~E(x17501,x17502)+E(f128(x17501,x17503,x17504,x17505,x17506),f128(x17502,x17503,x17504,x17505,x17506)) % 177.51/177.20 [1751]~E(x17511,x17512)+E(f128(x17513,x17511,x17514,x17515,x17516),f128(x17513,x17512,x17514,x17515,x17516)) % 177.51/177.20 [1752]~E(x17521,x17522)+E(f128(x17523,x17524,x17521,x17525,x17526),f128(x17523,x17524,x17522,x17525,x17526)) % 177.51/177.20 [1753]~E(x17531,x17532)+E(f128(x17533,x17534,x17535,x17531,x17536),f128(x17533,x17534,x17535,x17532,x17536)) % 177.51/177.20 [1754]~E(x17541,x17542)+E(f128(x17543,x17544,x17545,x17546,x17541),f128(x17543,x17544,x17545,x17546,x17542)) % 177.51/177.20 [1755]~E(x17551,x17552)+E(f738(x17551,x17553,x17554,x17555,x17556),f738(x17552,x17553,x17554,x17555,x17556)) % 177.51/177.20 [1756]~E(x17561,x17562)+E(f738(x17563,x17561,x17564,x17565,x17566),f738(x17563,x17562,x17564,x17565,x17566)) % 177.51/177.20 [1757]~E(x17571,x17572)+E(f738(x17573,x17574,x17571,x17575,x17576),f738(x17573,x17574,x17572,x17575,x17576)) % 177.51/177.20 [1758]~E(x17581,x17582)+E(f738(x17583,x17584,x17585,x17581,x17586),f738(x17583,x17584,x17585,x17582,x17586)) % 177.51/177.20 [1759]~E(x17591,x17592)+E(f738(x17593,x17594,x17595,x17596,x17591),f738(x17593,x17594,x17595,x17596,x17592)) % 177.51/177.20 [1760]~E(x17601,x17602)+E(f714(x17601,x17603,x17604),f714(x17602,x17603,x17604)) % 177.51/177.20 [1761]~E(x17611,x17612)+E(f714(x17613,x17611,x17614),f714(x17613,x17612,x17614)) % 177.51/177.20 [1762]~E(x17621,x17622)+E(f714(x17623,x17624,x17621),f714(x17623,x17624,x17622)) % 177.51/177.20 [1763]~E(x17631,x17632)+E(f896(x17631,x17633,x17634),f896(x17632,x17633,x17634)) % 177.51/177.20 [1764]~E(x17641,x17642)+E(f896(x17643,x17641,x17644),f896(x17643,x17642,x17644)) % 177.51/177.20 [1765]~E(x17651,x17652)+E(f896(x17653,x17654,x17651),f896(x17653,x17654,x17652)) % 177.51/177.20 [1766]~E(x17661,x17662)+E(f762(x17661,x17663,x17664),f762(x17662,x17663,x17664)) % 177.51/177.20 [1767]~E(x17671,x17672)+E(f762(x17673,x17671,x17674),f762(x17673,x17672,x17674)) % 177.51/177.20 [1768]~E(x17681,x17682)+E(f762(x17683,x17684,x17681),f762(x17683,x17684,x17682)) % 177.51/177.20 [1769]~E(x17691,x17692)+E(f808(x17691,x17693,x17694,x17695,x17696),f808(x17692,x17693,x17694,x17695,x17696)) % 177.51/177.20 [1770]~E(x17701,x17702)+E(f808(x17703,x17701,x17704,x17705,x17706),f808(x17703,x17702,x17704,x17705,x17706)) % 177.51/177.20 [1771]~E(x17711,x17712)+E(f808(x17713,x17714,x17711,x17715,x17716),f808(x17713,x17714,x17712,x17715,x17716)) % 177.51/177.20 [1772]~E(x17721,x17722)+E(f808(x17723,x17724,x17725,x17721,x17726),f808(x17723,x17724,x17725,x17722,x17726)) % 177.51/177.20 [1773]~E(x17731,x17732)+E(f808(x17733,x17734,x17735,x17736,x17731),f808(x17733,x17734,x17735,x17736,x17732)) % 177.51/177.20 [1774]~E(x17741,x17742)+E(f163(x17741,x17743),f163(x17742,x17743)) % 177.51/177.20 [1775]~E(x17751,x17752)+E(f163(x17753,x17751),f163(x17753,x17752)) % 177.51/177.20 [1776]~E(x17761,x17762)+E(f267(x17761),f267(x17762)) % 177.51/177.20 [1777]~E(x17771,x17772)+E(f875(x17771,x17773,x17774,x17775),f875(x17772,x17773,x17774,x17775)) % 177.51/177.20 [1778]~E(x17781,x17782)+E(f875(x17783,x17781,x17784,x17785),f875(x17783,x17782,x17784,x17785)) % 177.51/177.20 [1779]~E(x17791,x17792)+E(f875(x17793,x17794,x17791,x17795),f875(x17793,x17794,x17792,x17795)) % 177.51/177.20 [1780]~E(x17801,x17802)+E(f875(x17803,x17804,x17805,x17801),f875(x17803,x17804,x17805,x17802)) % 177.51/177.20 [1781]~E(x17811,x17812)+E(f556(x17811,x17813,x17814,x17815),f556(x17812,x17813,x17814,x17815)) % 177.51/177.20 [1782]~E(x17821,x17822)+E(f556(x17823,x17821,x17824,x17825),f556(x17823,x17822,x17824,x17825)) % 177.51/177.20 [1783]~E(x17831,x17832)+E(f556(x17833,x17834,x17831,x17835),f556(x17833,x17834,x17832,x17835)) % 177.51/177.20 [1784]~E(x17841,x17842)+E(f556(x17843,x17844,x17845,x17841),f556(x17843,x17844,x17845,x17842)) % 177.51/177.20 [1785]~E(x17851,x17852)+E(f124(x17851),f124(x17852)) % 177.51/177.20 [1786]~E(x17861,x17862)+E(f43(x17861),f43(x17862)) % 177.51/177.20 [1787]~E(x17871,x17872)+E(f95(x17871,x17873,x17874,x17875),f95(x17872,x17873,x17874,x17875)) % 177.51/177.20 [1788]~E(x17881,x17882)+E(f95(x17883,x17881,x17884,x17885),f95(x17883,x17882,x17884,x17885)) % 177.51/177.20 [1789]~E(x17891,x17892)+E(f95(x17893,x17894,x17891,x17895),f95(x17893,x17894,x17892,x17895)) % 177.51/177.20 [1790]~E(x17901,x17902)+E(f95(x17903,x17904,x17905,x17901),f95(x17903,x17904,x17905,x17902)) % 177.51/177.20 [1791]~E(x17911,x17912)+E(f362(x17911,x17913),f362(x17912,x17913)) % 177.51/177.20 [1792]~E(x17921,x17922)+E(f362(x17923,x17921),f362(x17923,x17922)) % 177.51/177.20 [1793]~E(x17931,x17932)+E(f723(x17931,x17933),f723(x17932,x17933)) % 177.51/177.20 [1794]~E(x17941,x17942)+E(f723(x17943,x17941),f723(x17943,x17942)) % 177.51/177.20 [1795]~E(x17951,x17952)+E(f620(x17951,x17953,x17954,x17955,x17956),f620(x17952,x17953,x17954,x17955,x17956)) % 177.51/177.20 [1796]~E(x17961,x17962)+E(f620(x17963,x17961,x17964,x17965,x17966),f620(x17963,x17962,x17964,x17965,x17966)) % 177.51/177.20 [1797]~E(x17971,x17972)+E(f620(x17973,x17974,x17971,x17975,x17976),f620(x17973,x17974,x17972,x17975,x17976)) % 177.51/177.20 [1798]~E(x17981,x17982)+E(f620(x17983,x17984,x17985,x17981,x17986),f620(x17983,x17984,x17985,x17982,x17986)) % 177.51/177.20 [1799]~E(x17991,x17992)+E(f620(x17993,x17994,x17995,x17996,x17991),f620(x17993,x17994,x17995,x17996,x17992)) % 177.51/177.20 [1800]~E(x18001,x18002)+E(f681(x18001,x18003,x18004,x18005),f681(x18002,x18003,x18004,x18005)) % 177.51/177.20 [1801]~E(x18011,x18012)+E(f681(x18013,x18011,x18014,x18015),f681(x18013,x18012,x18014,x18015)) % 177.51/177.20 [1802]~E(x18021,x18022)+E(f681(x18023,x18024,x18021,x18025),f681(x18023,x18024,x18022,x18025)) % 177.51/177.20 [1803]~E(x18031,x18032)+E(f681(x18033,x18034,x18035,x18031),f681(x18033,x18034,x18035,x18032)) % 177.51/177.20 [1804]~E(x18041,x18042)+E(f350(x18041,x18043,x18044,x18045),f350(x18042,x18043,x18044,x18045)) % 177.51/177.20 [1805]~E(x18051,x18052)+E(f350(x18053,x18051,x18054,x18055),f350(x18053,x18052,x18054,x18055)) % 177.51/177.20 [1806]~E(x18061,x18062)+E(f350(x18063,x18064,x18061,x18065),f350(x18063,x18064,x18062,x18065)) % 177.51/177.20 [1807]~E(x18071,x18072)+E(f350(x18073,x18074,x18075,x18071),f350(x18073,x18074,x18075,x18072)) % 177.51/177.20 [1808]~E(x18081,x18082)+E(f699(x18081,x18083,x18084),f699(x18082,x18083,x18084)) % 177.51/177.20 [1809]~E(x18091,x18092)+E(f699(x18093,x18091,x18094),f699(x18093,x18092,x18094)) % 177.51/177.20 [1810]~E(x18101,x18102)+E(f699(x18103,x18104,x18101),f699(x18103,x18104,x18102)) % 177.51/177.20 [1811]~E(x18111,x18112)+E(f379(x18111),f379(x18112)) % 177.51/177.20 [1812]~E(x18121,x18122)+E(f827(x18121,x18123,x18124,x18125),f827(x18122,x18123,x18124,x18125)) % 177.51/177.20 [1813]~E(x18131,x18132)+E(f827(x18133,x18131,x18134,x18135),f827(x18133,x18132,x18134,x18135)) % 177.51/177.20 [1814]~E(x18141,x18142)+E(f827(x18143,x18144,x18141,x18145),f827(x18143,x18144,x18142,x18145)) % 177.51/177.20 [1815]~E(x18151,x18152)+E(f827(x18153,x18154,x18155,x18151),f827(x18153,x18154,x18155,x18152)) % 177.51/177.20 [1816]~E(x18161,x18162)+E(f840(x18161,x18163,x18164,x18165,x18166,x18167,x18168,x18169),f840(x18162,x18163,x18164,x18165,x18166,x18167,x18168,x18169)) % 177.51/177.20 [1817]~E(x18171,x18172)+E(f840(x18173,x18171,x18174,x18175,x18176,x18177,x18178,x18179),f840(x18173,x18172,x18174,x18175,x18176,x18177,x18178,x18179)) % 177.51/177.20 [1818]~E(x18181,x18182)+E(f840(x18183,x18184,x18181,x18185,x18186,x18187,x18188,x18189),f840(x18183,x18184,x18182,x18185,x18186,x18187,x18188,x18189)) % 177.51/177.20 [1819]~E(x18191,x18192)+E(f840(x18193,x18194,x18195,x18191,x18196,x18197,x18198,x18199),f840(x18193,x18194,x18195,x18192,x18196,x18197,x18198,x18199)) % 177.51/177.20 [1820]~E(x18201,x18202)+E(f840(x18203,x18204,x18205,x18206,x18201,x18207,x18208,x18209),f840(x18203,x18204,x18205,x18206,x18202,x18207,x18208,x18209)) % 177.51/177.20 [1821]~E(x18211,x18212)+E(f840(x18213,x18214,x18215,x18216,x18217,x18211,x18218,x18219),f840(x18213,x18214,x18215,x18216,x18217,x18212,x18218,x18219)) % 177.51/177.20 [1822]~E(x18221,x18222)+E(f840(x18223,x18224,x18225,x18226,x18227,x18228,x18221,x18229),f840(x18223,x18224,x18225,x18226,x18227,x18228,x18222,x18229)) % 177.51/177.20 [1823]~E(x18231,x18232)+E(f840(x18233,x18234,x18235,x18236,x18237,x18238,x18239,x18231),f840(x18233,x18234,x18235,x18236,x18237,x18238,x18239,x18232)) % 177.51/177.20 [1824]~E(x18241,x18242)+E(f712(x18241,x18243),f712(x18242,x18243)) % 177.51/177.20 [1825]~E(x18251,x18252)+E(f712(x18253,x18251),f712(x18253,x18252)) % 177.51/177.20 [1826]~E(x18261,x18262)+E(f804(x18261),f804(x18262)) % 177.51/177.20 [1827]~E(x18271,x18272)+E(f414(x18271,x18273,x18274,x18275,x18276,x18277),f414(x18272,x18273,x18274,x18275,x18276,x18277)) % 177.51/177.20 [1828]~E(x18281,x18282)+E(f414(x18283,x18281,x18284,x18285,x18286,x18287),f414(x18283,x18282,x18284,x18285,x18286,x18287)) % 177.51/177.20 [1829]~E(x18291,x18292)+E(f414(x18293,x18294,x18291,x18295,x18296,x18297),f414(x18293,x18294,x18292,x18295,x18296,x18297)) % 177.51/177.20 [1830]~E(x18301,x18302)+E(f414(x18303,x18304,x18305,x18301,x18306,x18307),f414(x18303,x18304,x18305,x18302,x18306,x18307)) % 177.51/177.20 [1831]~E(x18311,x18312)+E(f414(x18313,x18314,x18315,x18316,x18311,x18317),f414(x18313,x18314,x18315,x18316,x18312,x18317)) % 177.51/177.20 [1832]~E(x18321,x18322)+E(f414(x18323,x18324,x18325,x18326,x18327,x18321),f414(x18323,x18324,x18325,x18326,x18327,x18322)) % 177.51/177.20 [1833]~E(x18331,x18332)+E(f200(x18331,x18333,x18334,x18335),f200(x18332,x18333,x18334,x18335)) % 177.51/177.20 [1834]~E(x18341,x18342)+E(f200(x18343,x18341,x18344,x18345),f200(x18343,x18342,x18344,x18345)) % 177.51/177.20 [1835]~E(x18351,x18352)+E(f200(x18353,x18354,x18351,x18355),f200(x18353,x18354,x18352,x18355)) % 177.51/177.20 [1836]~E(x18361,x18362)+E(f200(x18363,x18364,x18365,x18361),f200(x18363,x18364,x18365,x18362)) % 177.51/177.20 [1837]~E(x18371,x18372)+E(f336(x18371,x18373,x18374),f336(x18372,x18373,x18374)) % 177.51/177.20 [1838]~E(x18381,x18382)+E(f336(x18383,x18381,x18384),f336(x18383,x18382,x18384)) % 177.51/177.20 [1839]~E(x18391,x18392)+E(f336(x18393,x18394,x18391),f336(x18393,x18394,x18392)) % 177.51/177.20 [1840]~E(x18401,x18402)+E(f853(x18401,x18403,x18404,x18405,x18406,x18407,x18408),f853(x18402,x18403,x18404,x18405,x18406,x18407,x18408)) % 177.51/177.20 [1841]~E(x18411,x18412)+E(f853(x18413,x18411,x18414,x18415,x18416,x18417,x18418),f853(x18413,x18412,x18414,x18415,x18416,x18417,x18418)) % 177.51/177.20 [1842]~E(x18421,x18422)+E(f853(x18423,x18424,x18421,x18425,x18426,x18427,x18428),f853(x18423,x18424,x18422,x18425,x18426,x18427,x18428)) % 177.51/177.20 [1843]~E(x18431,x18432)+E(f853(x18433,x18434,x18435,x18431,x18436,x18437,x18438),f853(x18433,x18434,x18435,x18432,x18436,x18437,x18438)) % 177.51/177.20 [1844]~E(x18441,x18442)+E(f853(x18443,x18444,x18445,x18446,x18441,x18447,x18448),f853(x18443,x18444,x18445,x18446,x18442,x18447,x18448)) % 177.51/177.20 [1845]~E(x18451,x18452)+E(f853(x18453,x18454,x18455,x18456,x18457,x18451,x18458),f853(x18453,x18454,x18455,x18456,x18457,x18452,x18458)) % 177.51/177.20 [1846]~E(x18461,x18462)+E(f853(x18463,x18464,x18465,x18466,x18467,x18468,x18461),f853(x18463,x18464,x18465,x18466,x18467,x18468,x18462)) % 177.51/177.20 [1847]~E(x18471,x18472)+E(f553(x18471,x18473,x18474,x18475,x18476,x18477,x18478),f553(x18472,x18473,x18474,x18475,x18476,x18477,x18478)) % 177.51/177.20 [1848]~E(x18481,x18482)+E(f553(x18483,x18481,x18484,x18485,x18486,x18487,x18488),f553(x18483,x18482,x18484,x18485,x18486,x18487,x18488)) % 177.51/177.20 [1849]~E(x18491,x18492)+E(f553(x18493,x18494,x18491,x18495,x18496,x18497,x18498),f553(x18493,x18494,x18492,x18495,x18496,x18497,x18498)) % 177.51/177.20 [1850]~E(x18501,x18502)+E(f553(x18503,x18504,x18505,x18501,x18506,x18507,x18508),f553(x18503,x18504,x18505,x18502,x18506,x18507,x18508)) % 177.51/177.20 [1851]~E(x18511,x18512)+E(f553(x18513,x18514,x18515,x18516,x18511,x18517,x18518),f553(x18513,x18514,x18515,x18516,x18512,x18517,x18518)) % 177.51/177.20 [1852]~E(x18521,x18522)+E(f553(x18523,x18524,x18525,x18526,x18527,x18521,x18528),f553(x18523,x18524,x18525,x18526,x18527,x18522,x18528)) % 177.51/177.20 [1853]~E(x18531,x18532)+E(f553(x18533,x18534,x18535,x18536,x18537,x18538,x18531),f553(x18533,x18534,x18535,x18536,x18537,x18538,x18532)) % 177.51/177.20 [1854]~E(x18541,x18542)+E(f357(x18541,x18543),f357(x18542,x18543)) % 177.51/177.20 [1855]~E(x18551,x18552)+E(f357(x18553,x18551),f357(x18553,x18552)) % 177.51/177.20 [1856]~E(x18561,x18562)+E(f351(x18561,x18563,x18564),f351(x18562,x18563,x18564)) % 177.51/177.20 [1857]~E(x18571,x18572)+E(f351(x18573,x18571,x18574),f351(x18573,x18572,x18574)) % 177.51/177.20 [1858]~E(x18581,x18582)+E(f351(x18583,x18584,x18581),f351(x18583,x18584,x18582)) % 177.51/177.20 [1859]~E(x18591,x18592)+E(f421(x18591,x18593,x18594,x18595),f421(x18592,x18593,x18594,x18595)) % 177.51/177.20 [1860]~E(x18601,x18602)+E(f421(x18603,x18601,x18604,x18605),f421(x18603,x18602,x18604,x18605)) % 177.51/177.20 [1861]~E(x18611,x18612)+E(f421(x18613,x18614,x18611,x18615),f421(x18613,x18614,x18612,x18615)) % 177.51/177.20 [1862]~E(x18621,x18622)+E(f421(x18623,x18624,x18625,x18621),f421(x18623,x18624,x18625,x18622)) % 177.51/177.20 [1863]~E(x18631,x18632)+E(f821(x18631,x18633),f821(x18632,x18633)) % 177.51/177.20 [1864]~E(x18641,x18642)+E(f821(x18643,x18641),f821(x18643,x18642)) % 177.51/177.20 [1865]~E(x18651,x18652)+E(f462(x18651,x18653,x18654),f462(x18652,x18653,x18654)) % 177.51/177.20 [1866]~E(x18661,x18662)+E(f462(x18663,x18661,x18664),f462(x18663,x18662,x18664)) % 177.51/177.20 [1867]~E(x18671,x18672)+E(f462(x18673,x18674,x18671),f462(x18673,x18674,x18672)) % 177.51/177.20 [1868]~E(x18681,x18682)+E(f824(x18681,x18683,x18684),f824(x18682,x18683,x18684)) % 177.51/177.20 [1869]~E(x18691,x18692)+E(f824(x18693,x18691,x18694),f824(x18693,x18692,x18694)) % 177.51/177.20 [1870]~E(x18701,x18702)+E(f824(x18703,x18704,x18701),f824(x18703,x18704,x18702)) % 177.51/177.20 [1871]~E(x18711,x18712)+E(f342(x18711,x18713,x18714,x18715,x18716),f342(x18712,x18713,x18714,x18715,x18716)) % 177.51/177.20 [1872]~E(x18721,x18722)+E(f342(x18723,x18721,x18724,x18725,x18726),f342(x18723,x18722,x18724,x18725,x18726)) % 177.51/177.20 [1873]~E(x18731,x18732)+E(f342(x18733,x18734,x18731,x18735,x18736),f342(x18733,x18734,x18732,x18735,x18736)) % 177.51/177.20 [1874]~E(x18741,x18742)+E(f342(x18743,x18744,x18745,x18741,x18746),f342(x18743,x18744,x18745,x18742,x18746)) % 177.51/177.20 [1875]~E(x18751,x18752)+E(f342(x18753,x18754,x18755,x18756,x18751),f342(x18753,x18754,x18755,x18756,x18752)) % 177.51/177.20 [1876]~E(x18761,x18762)+E(f637(x18761,x18763,x18764,x18765),f637(x18762,x18763,x18764,x18765)) % 177.51/177.20 [1877]~E(x18771,x18772)+E(f637(x18773,x18771,x18774,x18775),f637(x18773,x18772,x18774,x18775)) % 177.51/177.20 [1878]~E(x18781,x18782)+E(f637(x18783,x18784,x18781,x18785),f637(x18783,x18784,x18782,x18785)) % 177.51/177.20 [1879]~E(x18791,x18792)+E(f637(x18793,x18794,x18795,x18791),f637(x18793,x18794,x18795,x18792)) % 177.51/177.20 [1880]~E(x18801,x18802)+E(f333(x18801),f333(x18802)) % 177.51/177.20 [1881]~E(x18811,x18812)+E(f649(x18811,x18813,x18814,x18815,x18816),f649(x18812,x18813,x18814,x18815,x18816)) % 177.51/177.20 [1882]~E(x18821,x18822)+E(f649(x18823,x18821,x18824,x18825,x18826),f649(x18823,x18822,x18824,x18825,x18826)) % 177.51/177.20 [1883]~E(x18831,x18832)+E(f649(x18833,x18834,x18831,x18835,x18836),f649(x18833,x18834,x18832,x18835,x18836)) % 177.51/177.20 [1884]~E(x18841,x18842)+E(f649(x18843,x18844,x18845,x18841,x18846),f649(x18843,x18844,x18845,x18842,x18846)) % 177.51/177.20 [1885]~E(x18851,x18852)+E(f649(x18853,x18854,x18855,x18856,x18851),f649(x18853,x18854,x18855,x18856,x18852)) % 177.51/177.20 [1886]~E(x18861,x18862)+E(f205(x18861,x18863,x18864),f205(x18862,x18863,x18864)) % 177.51/177.20 [1887]~E(x18871,x18872)+E(f205(x18873,x18871,x18874),f205(x18873,x18872,x18874)) % 177.51/177.20 [1888]~E(x18881,x18882)+E(f205(x18883,x18884,x18881),f205(x18883,x18884,x18882)) % 177.51/177.20 [1889]~E(x18891,x18892)+E(f722(x18891,x18893),f722(x18892,x18893)) % 177.51/177.20 [1890]~E(x18901,x18902)+E(f722(x18903,x18901),f722(x18903,x18902)) % 177.51/177.20 [1891]~E(x18911,x18912)+E(f670(x18911,x18913,x18914),f670(x18912,x18913,x18914)) % 177.51/177.20 [1892]~E(x18921,x18922)+E(f670(x18923,x18921,x18924),f670(x18923,x18922,x18924)) % 177.51/177.20 [1893]~E(x18931,x18932)+E(f670(x18933,x18934,x18931),f670(x18933,x18934,x18932)) % 177.51/177.20 [1894]~E(x18941,x18942)+E(f508(x18941,x18943,x18944,x18945),f508(x18942,x18943,x18944,x18945)) % 177.51/177.20 [1895]~E(x18951,x18952)+E(f508(x18953,x18951,x18954,x18955),f508(x18953,x18952,x18954,x18955)) % 177.51/177.20 [1896]~E(x18961,x18962)+E(f508(x18963,x18964,x18961,x18965),f508(x18963,x18964,x18962,x18965)) % 177.51/177.20 [1897]~E(x18971,x18972)+E(f508(x18973,x18974,x18975,x18971),f508(x18973,x18974,x18975,x18972)) % 177.51/177.20 [1898]~E(x18981,x18982)+E(f380(x18981,x18983),f380(x18982,x18983)) % 177.51/177.20 [1899]~E(x18991,x18992)+E(f380(x18993,x18991),f380(x18993,x18992)) % 177.51/177.20 [1900]~E(x19001,x19002)+E(f293(x19001,x19003),f293(x19002,x19003)) % 177.51/177.20 [1901]~E(x19011,x19012)+E(f293(x19013,x19011),f293(x19013,x19012)) % 177.51/177.20 [1902]~E(x19021,x19022)+E(f300(x19021,x19023,x19024,x19025,x19026),f300(x19022,x19023,x19024,x19025,x19026)) % 177.51/177.20 [1903]~E(x19031,x19032)+E(f300(x19033,x19031,x19034,x19035,x19036),f300(x19033,x19032,x19034,x19035,x19036)) % 177.51/177.20 [1904]~E(x19041,x19042)+E(f300(x19043,x19044,x19041,x19045,x19046),f300(x19043,x19044,x19042,x19045,x19046)) % 177.51/177.20 [1905]~E(x19051,x19052)+E(f300(x19053,x19054,x19055,x19051,x19056),f300(x19053,x19054,x19055,x19052,x19056)) % 177.51/177.20 [1906]~E(x19061,x19062)+E(f300(x19063,x19064,x19065,x19066,x19061),f300(x19063,x19064,x19065,x19066,x19062)) % 177.51/177.20 [1907]~E(x19071,x19072)+E(f880(x19071,x19073,x19074,x19075),f880(x19072,x19073,x19074,x19075)) % 177.51/177.20 [1908]~E(x19081,x19082)+E(f880(x19083,x19081,x19084,x19085),f880(x19083,x19082,x19084,x19085)) % 177.51/177.20 [1909]~E(x19091,x19092)+E(f880(x19093,x19094,x19091,x19095),f880(x19093,x19094,x19092,x19095)) % 177.51/177.20 [1910]~E(x19101,x19102)+E(f880(x19103,x19104,x19105,x19101),f880(x19103,x19104,x19105,x19102)) % 177.51/177.20 [1911]~E(x19111,x19112)+E(f370(x19111,x19113,x19114,x19115),f370(x19112,x19113,x19114,x19115)) % 177.51/177.20 [1912]~E(x19121,x19122)+E(f370(x19123,x19121,x19124,x19125),f370(x19123,x19122,x19124,x19125)) % 177.51/177.20 [1913]~E(x19131,x19132)+E(f370(x19133,x19134,x19131,x19135),f370(x19133,x19134,x19132,x19135)) % 177.51/177.20 [1914]~E(x19141,x19142)+E(f370(x19143,x19144,x19145,x19141),f370(x19143,x19144,x19145,x19142)) % 177.51/177.20 [1915]~E(x19151,x19152)+E(f405(x19151,x19153),f405(x19152,x19153)) % 177.51/177.20 [1916]~E(x19161,x19162)+E(f405(x19163,x19161),f405(x19163,x19162)) % 177.51/177.20 [1917]~E(x19171,x19172)+E(f750(x19171,x19173,x19174),f750(x19172,x19173,x19174)) % 177.51/177.20 [1918]~E(x19181,x19182)+E(f750(x19183,x19181,x19184),f750(x19183,x19182,x19184)) % 177.51/177.20 [1919]~E(x19191,x19192)+E(f750(x19193,x19194,x19191),f750(x19193,x19194,x19192)) % 177.51/177.20 [1920]~E(x19201,x19202)+E(f584(x19201,x19203,x19204,x19205,x19206,x19207),f584(x19202,x19203,x19204,x19205,x19206,x19207)) % 177.51/177.20 [1921]~E(x19211,x19212)+E(f584(x19213,x19211,x19214,x19215,x19216,x19217),f584(x19213,x19212,x19214,x19215,x19216,x19217)) % 177.51/177.20 [1922]~E(x19221,x19222)+E(f584(x19223,x19224,x19221,x19225,x19226,x19227),f584(x19223,x19224,x19222,x19225,x19226,x19227)) % 177.51/177.20 [1923]~E(x19231,x19232)+E(f584(x19233,x19234,x19235,x19231,x19236,x19237),f584(x19233,x19234,x19235,x19232,x19236,x19237)) % 177.51/177.20 [1924]~E(x19241,x19242)+E(f584(x19243,x19244,x19245,x19246,x19241,x19247),f584(x19243,x19244,x19245,x19246,x19242,x19247)) % 177.51/177.20 [1925]~E(x19251,x19252)+E(f584(x19253,x19254,x19255,x19256,x19257,x19251),f584(x19253,x19254,x19255,x19256,x19257,x19252)) % 177.51/177.20 [1926]~E(x19261,x19262)+E(f203(x19261),f203(x19262)) % 177.51/177.20 [1927]~E(x19271,x19272)+E(f583(x19271,x19273,x19274,x19275,x19276,x19277),f583(x19272,x19273,x19274,x19275,x19276,x19277)) % 177.51/177.20 [1928]~E(x19281,x19282)+E(f583(x19283,x19281,x19284,x19285,x19286,x19287),f583(x19283,x19282,x19284,x19285,x19286,x19287)) % 177.51/177.20 [1929]~E(x19291,x19292)+E(f583(x19293,x19294,x19291,x19295,x19296,x19297),f583(x19293,x19294,x19292,x19295,x19296,x19297)) % 177.51/177.20 [1930]~E(x19301,x19302)+E(f583(x19303,x19304,x19305,x19301,x19306,x19307),f583(x19303,x19304,x19305,x19302,x19306,x19307)) % 177.51/177.20 [1931]~E(x19311,x19312)+E(f583(x19313,x19314,x19315,x19316,x19311,x19317),f583(x19313,x19314,x19315,x19316,x19312,x19317)) % 177.51/177.20 [1932]~E(x19321,x19322)+E(f583(x19323,x19324,x19325,x19326,x19327,x19321),f583(x19323,x19324,x19325,x19326,x19327,x19322)) % 177.51/177.20 [1933]~E(x19331,x19332)+E(f93(x19331,x19333,x19334),f93(x19332,x19333,x19334)) % 177.51/177.20 [1934]~E(x19341,x19342)+E(f93(x19343,x19341,x19344),f93(x19343,x19342,x19344)) % 177.51/177.20 [1935]~E(x19351,x19352)+E(f93(x19353,x19354,x19351),f93(x19353,x19354,x19352)) % 177.51/177.20 [1936]~E(x19361,x19362)+E(f822(x19361,x19363,x19364,x19365,x19366,x19367),f822(x19362,x19363,x19364,x19365,x19366,x19367)) % 177.51/177.20 [1937]~E(x19371,x19372)+E(f822(x19373,x19371,x19374,x19375,x19376,x19377),f822(x19373,x19372,x19374,x19375,x19376,x19377)) % 177.51/177.20 [1938]~E(x19381,x19382)+E(f822(x19383,x19384,x19381,x19385,x19386,x19387),f822(x19383,x19384,x19382,x19385,x19386,x19387)) % 177.51/177.20 [1939]~E(x19391,x19392)+E(f822(x19393,x19394,x19395,x19391,x19396,x19397),f822(x19393,x19394,x19395,x19392,x19396,x19397)) % 177.51/177.20 [1940]~E(x19401,x19402)+E(f822(x19403,x19404,x19405,x19406,x19401,x19407),f822(x19403,x19404,x19405,x19406,x19402,x19407)) % 177.51/177.20 [1941]~E(x19411,x19412)+E(f822(x19413,x19414,x19415,x19416,x19417,x19411),f822(x19413,x19414,x19415,x19416,x19417,x19412)) % 177.51/177.20 [1942]~E(x19421,x19422)+E(f635(x19421,x19423,x19424,x19425,x19426),f635(x19422,x19423,x19424,x19425,x19426)) % 177.51/177.20 [1943]~E(x19431,x19432)+E(f635(x19433,x19431,x19434,x19435,x19436),f635(x19433,x19432,x19434,x19435,x19436)) % 177.51/177.20 [1944]~E(x19441,x19442)+E(f635(x19443,x19444,x19441,x19445,x19446),f635(x19443,x19444,x19442,x19445,x19446)) % 177.51/177.20 [1945]~E(x19451,x19452)+E(f635(x19453,x19454,x19455,x19451,x19456),f635(x19453,x19454,x19455,x19452,x19456)) % 177.51/177.20 [1946]~E(x19461,x19462)+E(f635(x19463,x19464,x19465,x19466,x19461),f635(x19463,x19464,x19465,x19466,x19462)) % 177.51/177.20 [1947]~E(x19471,x19472)+E(f42(x19471),f42(x19472)) % 177.51/177.20 [1948]~E(x19481,x19482)+E(f202(x19481),f202(x19482)) % 177.51/177.20 [1949]~E(x19491,x19492)+E(f561(x19491,x19493,x19494,x19495,x19496),f561(x19492,x19493,x19494,x19495,x19496)) % 177.51/177.20 [1950]~E(x19501,x19502)+E(f561(x19503,x19501,x19504,x19505,x19506),f561(x19503,x19502,x19504,x19505,x19506)) % 177.51/177.20 [1951]~E(x19511,x19512)+E(f561(x19513,x19514,x19511,x19515,x19516),f561(x19513,x19514,x19512,x19515,x19516)) % 177.51/177.20 [1952]~E(x19521,x19522)+E(f561(x19523,x19524,x19525,x19521,x19526),f561(x19523,x19524,x19525,x19522,x19526)) % 177.51/177.20 [1953]~E(x19531,x19532)+E(f561(x19533,x19534,x19535,x19536,x19531),f561(x19533,x19534,x19535,x19536,x19532)) % 177.51/177.20 [1954]~E(x19541,x19542)+E(f19(x19541,x19543,x19544,x19545),f19(x19542,x19543,x19544,x19545)) % 177.51/177.20 [1955]~E(x19551,x19552)+E(f19(x19553,x19551,x19554,x19555),f19(x19553,x19552,x19554,x19555)) % 177.51/177.20 [1956]~E(x19561,x19562)+E(f19(x19563,x19564,x19561,x19565),f19(x19563,x19564,x19562,x19565)) % 177.51/177.20 [1957]~E(x19571,x19572)+E(f19(x19573,x19574,x19575,x19571),f19(x19573,x19574,x19575,x19572)) % 177.51/177.20 [1958]~E(x19581,x19582)+E(f216(x19581,x19583),f216(x19582,x19583)) % 177.51/177.20 [1959]~E(x19591,x19592)+E(f216(x19593,x19591),f216(x19593,x19592)) % 177.51/177.20 [1960]~E(x19601,x19602)+E(f717(x19601,x19603,x19604),f717(x19602,x19603,x19604)) % 177.51/177.20 [1961]~E(x19611,x19612)+E(f717(x19613,x19611,x19614),f717(x19613,x19612,x19614)) % 177.51/177.20 [1962]~E(x19621,x19622)+E(f717(x19623,x19624,x19621),f717(x19623,x19624,x19622)) % 177.51/177.20 [1963]~E(x19631,x19632)+E(f861(x19631,x19633,x19634,x19635),f861(x19632,x19633,x19634,x19635)) % 177.51/177.20 [1964]~E(x19641,x19642)+E(f861(x19643,x19641,x19644,x19645),f861(x19643,x19642,x19644,x19645)) % 177.51/177.20 [1965]~E(x19651,x19652)+E(f861(x19653,x19654,x19651,x19655),f861(x19653,x19654,x19652,x19655)) % 177.51/177.20 [1966]~E(x19661,x19662)+E(f861(x19663,x19664,x19665,x19661),f861(x19663,x19664,x19665,x19662)) % 177.51/177.20 [1967]~E(x19671,x19672)+E(f558(x19671,x19673,x19674,x19675,x19676,x19677),f558(x19672,x19673,x19674,x19675,x19676,x19677)) % 177.51/177.20 [1968]~E(x19681,x19682)+E(f558(x19683,x19681,x19684,x19685,x19686,x19687),f558(x19683,x19682,x19684,x19685,x19686,x19687)) % 177.51/177.20 [1969]~E(x19691,x19692)+E(f558(x19693,x19694,x19691,x19695,x19696,x19697),f558(x19693,x19694,x19692,x19695,x19696,x19697)) % 177.51/177.20 [1970]~E(x19701,x19702)+E(f558(x19703,x19704,x19705,x19701,x19706,x19707),f558(x19703,x19704,x19705,x19702,x19706,x19707)) % 177.51/177.20 [1971]~E(x19711,x19712)+E(f558(x19713,x19714,x19715,x19716,x19711,x19717),f558(x19713,x19714,x19715,x19716,x19712,x19717)) % 177.51/177.20 [1972]~E(x19721,x19722)+E(f558(x19723,x19724,x19725,x19726,x19727,x19721),f558(x19723,x19724,x19725,x19726,x19727,x19722)) % 177.51/177.20 [1973]~E(x19731,x19732)+E(f703(x19731,x19733),f703(x19732,x19733)) % 177.51/177.20 [1974]~E(x19741,x19742)+E(f703(x19743,x19741),f703(x19743,x19742)) % 177.51/177.20 [1975]~E(x19751,x19752)+E(f674(x19751,x19753,x19754,x19755),f674(x19752,x19753,x19754,x19755)) % 177.51/177.20 [1976]~E(x19761,x19762)+E(f674(x19763,x19761,x19764,x19765),f674(x19763,x19762,x19764,x19765)) % 177.51/177.20 [1977]~E(x19771,x19772)+E(f674(x19773,x19774,x19771,x19775),f674(x19773,x19774,x19772,x19775)) % 177.51/177.20 [1978]~E(x19781,x19782)+E(f674(x19783,x19784,x19785,x19781),f674(x19783,x19784,x19785,x19782)) % 177.51/177.20 [1979]~E(x19791,x19792)+E(f422(x19791,x19793,x19794,x19795),f422(x19792,x19793,x19794,x19795)) % 177.51/177.20 [1980]~E(x19801,x19802)+E(f422(x19803,x19801,x19804,x19805),f422(x19803,x19802,x19804,x19805)) % 177.51/177.20 [1981]~E(x19811,x19812)+E(f422(x19813,x19814,x19811,x19815),f422(x19813,x19814,x19812,x19815)) % 177.51/177.20 [1982]~E(x19821,x19822)+E(f422(x19823,x19824,x19825,x19821),f422(x19823,x19824,x19825,x19822)) % 177.51/177.20 [1983]~E(x19831,x19832)+E(f554(x19831,x19833),f554(x19832,x19833)) % 177.51/177.20 [1984]~E(x19841,x19842)+E(f554(x19843,x19841),f554(x19843,x19842)) % 177.51/177.20 [1985]~E(x19851,x19852)+E(f535(x19851,x19853),f535(x19852,x19853)) % 177.51/177.20 [1986]~E(x19861,x19862)+E(f535(x19863,x19861),f535(x19863,x19862)) % 177.51/177.20 [1987]~E(x19871,x19872)+E(f786(x19871,x19873,x19874,x19875,x19876,x19877,x19878),f786(x19872,x19873,x19874,x19875,x19876,x19877,x19878)) % 177.51/177.20 [1988]~E(x19881,x19882)+E(f786(x19883,x19881,x19884,x19885,x19886,x19887,x19888),f786(x19883,x19882,x19884,x19885,x19886,x19887,x19888)) % 177.51/177.20 [1989]~E(x19891,x19892)+E(f786(x19893,x19894,x19891,x19895,x19896,x19897,x19898),f786(x19893,x19894,x19892,x19895,x19896,x19897,x19898)) % 177.51/177.20 [1990]~E(x19901,x19902)+E(f786(x19903,x19904,x19905,x19901,x19906,x19907,x19908),f786(x19903,x19904,x19905,x19902,x19906,x19907,x19908)) % 177.51/177.20 [1991]~E(x19911,x19912)+E(f786(x19913,x19914,x19915,x19916,x19911,x19917,x19918),f786(x19913,x19914,x19915,x19916,x19912,x19917,x19918)) % 177.51/177.20 [1992]~E(x19921,x19922)+E(f786(x19923,x19924,x19925,x19926,x19927,x19921,x19928),f786(x19923,x19924,x19925,x19926,x19927,x19922,x19928)) % 177.51/177.20 [1993]~E(x19931,x19932)+E(f786(x19933,x19934,x19935,x19936,x19937,x19938,x19931),f786(x19933,x19934,x19935,x19936,x19937,x19938,x19932)) % 177.51/177.20 [1994]~E(x19941,x19942)+E(f542(x19941,x19943),f542(x19942,x19943)) % 177.51/177.20 [1995]~E(x19951,x19952)+E(f542(x19953,x19951),f542(x19953,x19952)) % 177.51/177.20 [1996]~E(x19961,x19962)+E(f469(x19961,x19963,x19964,x19965),f469(x19962,x19963,x19964,x19965)) % 177.51/177.20 [1997]~E(x19971,x19972)+E(f469(x19973,x19971,x19974,x19975),f469(x19973,x19972,x19974,x19975)) % 177.51/177.20 [1998]~E(x19981,x19982)+E(f469(x19983,x19984,x19981,x19985),f469(x19983,x19984,x19982,x19985)) % 177.51/177.20 [1999]~E(x19991,x19992)+E(f469(x19993,x19994,x19995,x19991),f469(x19993,x19994,x19995,x19992)) % 177.51/177.20 [2000]~E(x20001,x20002)+E(f577(x20001,x20003,x20004),f577(x20002,x20003,x20004)) % 177.51/177.20 [2001]~E(x20011,x20012)+E(f577(x20013,x20011,x20014),f577(x20013,x20012,x20014)) % 177.51/177.20 [2002]~E(x20021,x20022)+E(f577(x20023,x20024,x20021),f577(x20023,x20024,x20022)) % 177.51/177.20 [2003]~E(x20031,x20032)+E(f783(x20031,x20033,x20034,x20035,x20036,x20037,x20038),f783(x20032,x20033,x20034,x20035,x20036,x20037,x20038)) % 177.51/177.20 [2004]~E(x20041,x20042)+E(f783(x20043,x20041,x20044,x20045,x20046,x20047,x20048),f783(x20043,x20042,x20044,x20045,x20046,x20047,x20048)) % 177.51/177.20 [2005]~E(x20051,x20052)+E(f783(x20053,x20054,x20051,x20055,x20056,x20057,x20058),f783(x20053,x20054,x20052,x20055,x20056,x20057,x20058)) % 177.51/177.20 [2006]~E(x20061,x20062)+E(f783(x20063,x20064,x20065,x20061,x20066,x20067,x20068),f783(x20063,x20064,x20065,x20062,x20066,x20067,x20068)) % 177.51/177.20 [2007]~E(x20071,x20072)+E(f783(x20073,x20074,x20075,x20076,x20071,x20077,x20078),f783(x20073,x20074,x20075,x20076,x20072,x20077,x20078)) % 177.51/177.20 [2008]~E(x20081,x20082)+E(f783(x20083,x20084,x20085,x20086,x20087,x20081,x20088),f783(x20083,x20084,x20085,x20086,x20087,x20082,x20088)) % 177.51/177.20 [2009]~E(x20091,x20092)+E(f783(x20093,x20094,x20095,x20096,x20097,x20098,x20091),f783(x20093,x20094,x20095,x20096,x20097,x20098,x20092)) % 177.51/177.20 [2010]~E(x20101,x20102)+E(f378(x20101),f378(x20102)) % 177.51/177.20 [2011]~E(x20111,x20112)+E(f496(x20111,x20113,x20114,x20115),f496(x20112,x20113,x20114,x20115)) % 177.51/177.20 [2012]~E(x20121,x20122)+E(f496(x20123,x20121,x20124,x20125),f496(x20123,x20122,x20124,x20125)) % 177.51/177.20 [2013]~E(x20131,x20132)+E(f496(x20133,x20134,x20131,x20135),f496(x20133,x20134,x20132,x20135)) % 177.51/177.20 [2014]~E(x20141,x20142)+E(f496(x20143,x20144,x20145,x20141),f496(x20143,x20144,x20145,x20142)) % 177.51/177.20 [2015]~E(x20151,x20152)+E(f458(x20151,x20153,x20154,x20155,x20156),f458(x20152,x20153,x20154,x20155,x20156)) % 177.51/177.20 [2016]~E(x20161,x20162)+E(f458(x20163,x20161,x20164,x20165,x20166),f458(x20163,x20162,x20164,x20165,x20166)) % 177.51/177.20 [2017]~E(x20171,x20172)+E(f458(x20173,x20174,x20171,x20175,x20176),f458(x20173,x20174,x20172,x20175,x20176)) % 177.51/177.20 [2018]~E(x20181,x20182)+E(f458(x20183,x20184,x20185,x20181,x20186),f458(x20183,x20184,x20185,x20182,x20186)) % 177.51/177.20 [2019]~E(x20191,x20192)+E(f458(x20193,x20194,x20195,x20196,x20191),f458(x20193,x20194,x20195,x20196,x20192)) % 177.51/177.20 [2020]~E(x20201,x20202)+E(f574(x20201,x20203),f574(x20202,x20203)) % 177.51/177.20 [2021]~E(x20211,x20212)+E(f574(x20213,x20211),f574(x20213,x20212)) % 177.51/177.20 [2022]~E(x20221,x20222)+E(f648(x20221,x20223,x20224,x20225,x20226),f648(x20222,x20223,x20224,x20225,x20226)) % 177.51/177.20 [2023]~E(x20231,x20232)+E(f648(x20233,x20231,x20234,x20235,x20236),f648(x20233,x20232,x20234,x20235,x20236)) % 177.51/177.20 [2024]~E(x20241,x20242)+E(f648(x20243,x20244,x20241,x20245,x20246),f648(x20243,x20244,x20242,x20245,x20246)) % 177.51/177.20 [2025]~E(x20251,x20252)+E(f648(x20253,x20254,x20255,x20251,x20256),f648(x20253,x20254,x20255,x20252,x20256)) % 177.51/177.20 [2026]~E(x20261,x20262)+E(f648(x20263,x20264,x20265,x20266,x20261),f648(x20263,x20264,x20265,x20266,x20262)) % 177.51/177.20 [2027]~E(x20271,x20272)+E(f764(x20271,x20273,x20274,x20275),f764(x20272,x20273,x20274,x20275)) % 177.51/177.20 [2028]~E(x20281,x20282)+E(f764(x20283,x20281,x20284,x20285),f764(x20283,x20282,x20284,x20285)) % 177.51/177.20 [2029]~E(x20291,x20292)+E(f764(x20293,x20294,x20291,x20295),f764(x20293,x20294,x20292,x20295)) % 177.51/177.20 [2030]~E(x20301,x20302)+E(f764(x20303,x20304,x20305,x20301),f764(x20303,x20304,x20305,x20302)) % 177.51/177.20 [2031]~E(x20311,x20312)+E(f516(x20311,x20313),f516(x20312,x20313)) % 177.51/177.20 [2032]~E(x20321,x20322)+E(f516(x20323,x20321),f516(x20323,x20322)) % 177.51/177.20 [2033]~E(x20331,x20332)+E(f525(x20331,x20333,x20334),f525(x20332,x20333,x20334)) % 177.51/177.20 [2034]~E(x20341,x20342)+E(f525(x20343,x20341,x20344),f525(x20343,x20342,x20344)) % 177.51/177.20 [2035]~E(x20351,x20352)+E(f525(x20353,x20354,x20351),f525(x20353,x20354,x20352)) % 177.51/177.20 [2036]~E(x20361,x20362)+E(f543(x20361,x20363,x20364,x20365),f543(x20362,x20363,x20364,x20365)) % 177.51/177.20 [2037]~E(x20371,x20372)+E(f543(x20373,x20371,x20374,x20375),f543(x20373,x20372,x20374,x20375)) % 177.51/177.20 [2038]~E(x20381,x20382)+E(f543(x20383,x20384,x20381,x20385),f543(x20383,x20384,x20382,x20385)) % 177.51/177.20 [2039]~E(x20391,x20392)+E(f543(x20393,x20394,x20395,x20391),f543(x20393,x20394,x20395,x20392)) % 177.51/177.20 [2040]~E(x20401,x20402)+E(f749(x20401,x20403,x20404),f749(x20402,x20403,x20404)) % 177.51/177.20 [2041]~E(x20411,x20412)+E(f749(x20413,x20411,x20414),f749(x20413,x20412,x20414)) % 177.51/177.20 [2042]~E(x20421,x20422)+E(f749(x20423,x20424,x20421),f749(x20423,x20424,x20422)) % 177.51/177.20 [2043]~E(x20431,x20432)+E(f881(x20431,x20433,x20434,x20435,x20436),f881(x20432,x20433,x20434,x20435,x20436)) % 177.51/177.20 [2044]~E(x20441,x20442)+E(f881(x20443,x20441,x20444,x20445,x20446),f881(x20443,x20442,x20444,x20445,x20446)) % 177.51/177.20 [2045]~E(x20451,x20452)+E(f881(x20453,x20454,x20451,x20455,x20456),f881(x20453,x20454,x20452,x20455,x20456)) % 177.51/177.20 [2046]~E(x20461,x20462)+E(f881(x20463,x20464,x20465,x20461,x20466),f881(x20463,x20464,x20465,x20462,x20466)) % 177.51/177.20 [2047]~E(x20471,x20472)+E(f881(x20473,x20474,x20475,x20476,x20471),f881(x20473,x20474,x20475,x20476,x20472)) % 177.51/177.20 [2048]~E(x20481,x20482)+E(f366(x20481,x20483,x20484),f366(x20482,x20483,x20484)) % 177.51/177.20 [2049]~E(x20491,x20492)+E(f366(x20493,x20491,x20494),f366(x20493,x20492,x20494)) % 177.51/177.20 [2050]~E(x20501,x20502)+E(f366(x20503,x20504,x20501),f366(x20503,x20504,x20502)) % 177.51/177.20 [2051]~E(x20511,x20512)+E(f377(x20511),f377(x20512)) % 177.51/177.20 [2052]~E(x20521,x20522)+E(f465(x20521,x20523,x20524),f465(x20522,x20523,x20524)) % 177.51/177.20 [2053]~E(x20531,x20532)+E(f465(x20533,x20531,x20534),f465(x20533,x20532,x20534)) % 177.51/177.20 [2054]~E(x20541,x20542)+E(f465(x20543,x20544,x20541),f465(x20543,x20544,x20542)) % 177.51/177.20 [2055]~E(x20551,x20552)+E(f463(x20551,x20553),f463(x20552,x20553)) % 177.51/177.20 [2056]~E(x20561,x20562)+E(f463(x20563,x20561),f463(x20563,x20562)) % 177.51/177.20 [2057]~E(x20571,x20572)+E(f385(x20571),f385(x20572)) % 177.51/177.20 [2058]~E(x20581,x20582)+E(f818(x20581,x20583),f818(x20582,x20583)) % 177.51/177.20 [2059]~E(x20591,x20592)+E(f818(x20593,x20591),f818(x20593,x20592)) % 177.51/177.20 [2060]~E(x20601,x20602)+E(f230(x20601,x20603,x20604),f230(x20602,x20603,x20604)) % 177.51/177.20 [2061]~E(x20611,x20612)+E(f230(x20613,x20611,x20614),f230(x20613,x20612,x20614)) % 177.51/177.20 [2062]~E(x20621,x20622)+E(f230(x20623,x20624,x20621),f230(x20623,x20624,x20622)) % 177.51/177.20 [2063]~E(x20631,x20632)+E(f372(x20631,x20633,x20634),f372(x20632,x20633,x20634)) % 177.51/177.20 [2064]~E(x20641,x20642)+E(f372(x20643,x20641,x20644),f372(x20643,x20642,x20644)) % 177.51/177.20 [2065]~E(x20651,x20652)+E(f372(x20653,x20654,x20651),f372(x20653,x20654,x20652)) % 177.51/177.20 [2066]~E(x20661,x20662)+E(f743(x20661,x20663,x20664,x20665,x20666,x20667,x20668),f743(x20662,x20663,x20664,x20665,x20666,x20667,x20668)) % 177.51/177.20 [2067]~E(x20671,x20672)+E(f743(x20673,x20671,x20674,x20675,x20676,x20677,x20678),f743(x20673,x20672,x20674,x20675,x20676,x20677,x20678)) % 177.51/177.20 [2068]~E(x20681,x20682)+E(f743(x20683,x20684,x20681,x20685,x20686,x20687,x20688),f743(x20683,x20684,x20682,x20685,x20686,x20687,x20688)) % 177.51/177.20 [2069]~E(x20691,x20692)+E(f743(x20693,x20694,x20695,x20691,x20696,x20697,x20698),f743(x20693,x20694,x20695,x20692,x20696,x20697,x20698)) % 177.51/177.20 [2070]~E(x20701,x20702)+E(f743(x20703,x20704,x20705,x20706,x20701,x20707,x20708),f743(x20703,x20704,x20705,x20706,x20702,x20707,x20708)) % 177.51/177.20 [2071]~E(x20711,x20712)+E(f743(x20713,x20714,x20715,x20716,x20717,x20711,x20718),f743(x20713,x20714,x20715,x20716,x20717,x20712,x20718)) % 177.51/177.20 [2072]~E(x20721,x20722)+E(f743(x20723,x20724,x20725,x20726,x20727,x20728,x20721),f743(x20723,x20724,x20725,x20726,x20727,x20728,x20722)) % 177.51/177.20 [2073]~E(x20731,x20732)+E(f276(x20731,x20733,x20734,x20735),f276(x20732,x20733,x20734,x20735)) % 177.51/177.20 [2074]~E(x20741,x20742)+E(f276(x20743,x20741,x20744,x20745),f276(x20743,x20742,x20744,x20745)) % 177.51/177.20 [2075]~E(x20751,x20752)+E(f276(x20753,x20754,x20751,x20755),f276(x20753,x20754,x20752,x20755)) % 177.51/177.20 [2076]~E(x20761,x20762)+E(f276(x20763,x20764,x20765,x20761),f276(x20763,x20764,x20765,x20762)) % 177.51/177.20 [2077]~E(x20771,x20772)+E(f400(x20771,x20773,x20774),f400(x20772,x20773,x20774)) % 177.51/177.20 [2078]~E(x20781,x20782)+E(f400(x20783,x20781,x20784),f400(x20783,x20782,x20784)) % 177.51/177.20 [2079]~E(x20791,x20792)+E(f400(x20793,x20794,x20791),f400(x20793,x20794,x20792)) % 177.51/177.20 [2080]~E(x20801,x20802)+E(f705(x20801,x20803),f705(x20802,x20803)) % 177.51/177.20 [2081]~E(x20811,x20812)+E(f705(x20813,x20811),f705(x20813,x20812)) % 177.51/177.20 [2082]~E(x20821,x20822)+E(f213(x20821,x20823,x20824,x20825,x20826,x20827,x20828),f213(x20822,x20823,x20824,x20825,x20826,x20827,x20828)) % 177.51/177.20 [2083]~E(x20831,x20832)+E(f213(x20833,x20831,x20834,x20835,x20836,x20837,x20838),f213(x20833,x20832,x20834,x20835,x20836,x20837,x20838)) % 177.51/177.20 [2084]~E(x20841,x20842)+E(f213(x20843,x20844,x20841,x20845,x20846,x20847,x20848),f213(x20843,x20844,x20842,x20845,x20846,x20847,x20848)) % 177.51/177.20 [2085]~E(x20851,x20852)+E(f213(x20853,x20854,x20855,x20851,x20856,x20857,x20858),f213(x20853,x20854,x20855,x20852,x20856,x20857,x20858)) % 177.51/177.20 [2086]~E(x20861,x20862)+E(f213(x20863,x20864,x20865,x20866,x20861,x20867,x20868),f213(x20863,x20864,x20865,x20866,x20862,x20867,x20868)) % 177.51/177.20 [2087]~E(x20871,x20872)+E(f213(x20873,x20874,x20875,x20876,x20877,x20871,x20878),f213(x20873,x20874,x20875,x20876,x20877,x20872,x20878)) % 177.51/177.20 [2088]~E(x20881,x20882)+E(f213(x20883,x20884,x20885,x20886,x20887,x20888,x20881),f213(x20883,x20884,x20885,x20886,x20887,x20888,x20882)) % 177.51/177.20 [2089]~E(x20891,x20892)+E(f536(x20891,x20893),f536(x20892,x20893)) % 177.51/177.20 [2090]~E(x20901,x20902)+E(f536(x20903,x20901),f536(x20903,x20902)) % 177.51/177.20 [2091]~E(x20911,x20912)+E(f732(x20911,x20913,x20914,x20915,x20916),f732(x20912,x20913,x20914,x20915,x20916)) % 177.51/177.20 [2092]~E(x20921,x20922)+E(f732(x20923,x20921,x20924,x20925,x20926),f732(x20923,x20922,x20924,x20925,x20926)) % 177.51/177.20 [2093]~E(x20931,x20932)+E(f732(x20933,x20934,x20931,x20935,x20936),f732(x20933,x20934,x20932,x20935,x20936)) % 177.51/177.20 [2094]~E(x20941,x20942)+E(f732(x20943,x20944,x20945,x20941,x20946),f732(x20943,x20944,x20945,x20942,x20946)) % 177.51/177.20 [2095]~E(x20951,x20952)+E(f732(x20953,x20954,x20955,x20956,x20951),f732(x20953,x20954,x20955,x20956,x20952)) % 177.51/177.20 [2096]~E(x20961,x20962)+E(f720(x20961,x20963),f720(x20962,x20963)) % 177.51/177.20 [2097]~E(x20971,x20972)+E(f720(x20973,x20971),f720(x20973,x20972)) % 177.51/177.20 [2098]~E(x20981,x20982)+E(f348(x20981,x20983,x20984,x20985,x20986),f348(x20982,x20983,x20984,x20985,x20986)) % 177.51/177.20 [2099]~E(x20991,x20992)+E(f348(x20993,x20991,x20994,x20995,x20996),f348(x20993,x20992,x20994,x20995,x20996)) % 177.51/177.20 [2100]~E(x21001,x21002)+E(f348(x21003,x21004,x21001,x21005,x21006),f348(x21003,x21004,x21002,x21005,x21006)) % 177.51/177.20 [2101]~E(x21011,x21012)+E(f348(x21013,x21014,x21015,x21011,x21016),f348(x21013,x21014,x21015,x21012,x21016)) % 177.51/177.20 [2102]~E(x21021,x21022)+E(f348(x21023,x21024,x21025,x21026,x21021),f348(x21023,x21024,x21025,x21026,x21022)) % 177.51/177.20 [2103]~E(x21031,x21032)+E(f693(x21031,x21033),f693(x21032,x21033)) % 177.51/177.20 [2104]~E(x21041,x21042)+E(f693(x21043,x21041),f693(x21043,x21042)) % 177.51/177.20 [2105]~E(x21051,x21052)+E(f843(x21051,x21053,x21054,x21055,x21056,x21057,x21058,x21059),f843(x21052,x21053,x21054,x21055,x21056,x21057,x21058,x21059)) % 177.51/177.20 [2106]~E(x21061,x21062)+E(f843(x21063,x21061,x21064,x21065,x21066,x21067,x21068,x21069),f843(x21063,x21062,x21064,x21065,x21066,x21067,x21068,x21069)) % 177.51/177.20 [2107]~E(x21071,x21072)+E(f843(x21073,x21074,x21071,x21075,x21076,x21077,x21078,x21079),f843(x21073,x21074,x21072,x21075,x21076,x21077,x21078,x21079)) % 177.51/177.20 [2108]~E(x21081,x21082)+E(f843(x21083,x21084,x21085,x21081,x21086,x21087,x21088,x21089),f843(x21083,x21084,x21085,x21082,x21086,x21087,x21088,x21089)) % 177.51/177.20 [2109]~E(x21091,x21092)+E(f843(x21093,x21094,x21095,x21096,x21091,x21097,x21098,x21099),f843(x21093,x21094,x21095,x21096,x21092,x21097,x21098,x21099)) % 177.51/177.20 [2110]~E(x21101,x21102)+E(f843(x21103,x21104,x21105,x21106,x21107,x21101,x21108,x21109),f843(x21103,x21104,x21105,x21106,x21107,x21102,x21108,x21109)) % 177.51/177.20 [2111]~E(x21111,x21112)+E(f843(x21113,x21114,x21115,x21116,x21117,x21118,x21111,x21119),f843(x21113,x21114,x21115,x21116,x21117,x21118,x21112,x21119)) % 177.51/177.20 [2112]~E(x21121,x21122)+E(f843(x21123,x21124,x21125,x21126,x21127,x21128,x21129,x21121),f843(x21123,x21124,x21125,x21126,x21127,x21128,x21129,x21122)) % 177.51/177.20 [2113]~E(x21131,x21132)+E(f643(x21131,x21133,x21134,x21135),f643(x21132,x21133,x21134,x21135)) % 177.51/177.20 [2114]~E(x21141,x21142)+E(f643(x21143,x21141,x21144,x21145),f643(x21143,x21142,x21144,x21145)) % 177.51/177.20 [2115]~E(x21151,x21152)+E(f643(x21153,x21154,x21151,x21155),f643(x21153,x21154,x21152,x21155)) % 177.51/177.20 [2116]~E(x21161,x21162)+E(f643(x21163,x21164,x21165,x21161),f643(x21163,x21164,x21165,x21162)) % 177.51/177.20 [2117]~E(x21171,x21172)+E(f349(x21171,x21173,x21174,x21175,x21176),f349(x21172,x21173,x21174,x21175,x21176)) % 177.51/177.20 [2118]~E(x21181,x21182)+E(f349(x21183,x21181,x21184,x21185,x21186),f349(x21183,x21182,x21184,x21185,x21186)) % 177.51/177.20 [2119]~E(x21191,x21192)+E(f349(x21193,x21194,x21191,x21195,x21196),f349(x21193,x21194,x21192,x21195,x21196)) % 177.51/177.20 [2120]~E(x21201,x21202)+E(f349(x21203,x21204,x21205,x21201,x21206),f349(x21203,x21204,x21205,x21202,x21206)) % 177.51/177.20 [2121]~E(x21211,x21212)+E(f349(x21213,x21214,x21215,x21216,x21211),f349(x21213,x21214,x21215,x21216,x21212)) % 177.51/177.20 [2122]~E(x21221,x21222)+E(f495(x21221,x21223,x21224,x21225,x21226,x21227),f495(x21222,x21223,x21224,x21225,x21226,x21227)) % 177.51/177.20 [2123]~E(x21231,x21232)+E(f495(x21233,x21231,x21234,x21235,x21236,x21237),f495(x21233,x21232,x21234,x21235,x21236,x21237)) % 177.51/177.20 [2124]~E(x21241,x21242)+E(f495(x21243,x21244,x21241,x21245,x21246,x21247),f495(x21243,x21244,x21242,x21245,x21246,x21247)) % 177.51/177.20 [2125]~E(x21251,x21252)+E(f495(x21253,x21254,x21255,x21251,x21256,x21257),f495(x21253,x21254,x21255,x21252,x21256,x21257)) % 177.51/177.20 [2126]~E(x21261,x21262)+E(f495(x21263,x21264,x21265,x21266,x21261,x21267),f495(x21263,x21264,x21265,x21266,x21262,x21267)) % 177.51/177.20 [2127]~E(x21271,x21272)+E(f495(x21273,x21274,x21275,x21276,x21277,x21271),f495(x21273,x21274,x21275,x21276,x21277,x21272)) % 177.51/177.20 [2128]~E(x21281,x21282)+E(f877(x21281,x21283,x21284,x21285,x21286),f877(x21282,x21283,x21284,x21285,x21286)) % 177.51/177.20 [2129]~E(x21291,x21292)+E(f877(x21293,x21291,x21294,x21295,x21296),f877(x21293,x21292,x21294,x21295,x21296)) % 177.51/177.20 [2130]~E(x21301,x21302)+E(f877(x21303,x21304,x21301,x21305,x21306),f877(x21303,x21304,x21302,x21305,x21306)) % 177.51/177.20 [2131]~E(x21311,x21312)+E(f877(x21313,x21314,x21315,x21311,x21316),f877(x21313,x21314,x21315,x21312,x21316)) % 177.51/177.20 [2132]~E(x21321,x21322)+E(f877(x21323,x21324,x21325,x21326,x21321),f877(x21323,x21324,x21325,x21326,x21322)) % 177.51/177.20 [2133]~E(x21331,x21332)+E(f260(x21331,x21333,x21334,x21335,x21336),f260(x21332,x21333,x21334,x21335,x21336)) % 177.51/177.20 [2134]~E(x21341,x21342)+E(f260(x21343,x21341,x21344,x21345,x21346),f260(x21343,x21342,x21344,x21345,x21346)) % 177.51/177.20 [2135]~E(x21351,x21352)+E(f260(x21353,x21354,x21351,x21355,x21356),f260(x21353,x21354,x21352,x21355,x21356)) % 177.51/177.20 [2136]~E(x21361,x21362)+E(f260(x21363,x21364,x21365,x21361,x21366),f260(x21363,x21364,x21365,x21362,x21366)) % 177.51/177.20 [2137]~E(x21371,x21372)+E(f260(x21373,x21374,x21375,x21376,x21371),f260(x21373,x21374,x21375,x21376,x21372)) % 177.51/177.20 [2138]~E(x21381,x21382)+E(f740(x21381,x21383,x21384,x21385,x21386),f740(x21382,x21383,x21384,x21385,x21386)) % 177.51/177.20 [2139]~E(x21391,x21392)+E(f740(x21393,x21391,x21394,x21395,x21396),f740(x21393,x21392,x21394,x21395,x21396)) % 177.51/177.20 [2140]~E(x21401,x21402)+E(f740(x21403,x21404,x21401,x21405,x21406),f740(x21403,x21404,x21402,x21405,x21406)) % 177.51/177.20 [2141]~E(x21411,x21412)+E(f740(x21413,x21414,x21415,x21411,x21416),f740(x21413,x21414,x21415,x21412,x21416)) % 177.51/177.20 [2142]~E(x21421,x21422)+E(f740(x21423,x21424,x21425,x21426,x21421),f740(x21423,x21424,x21425,x21426,x21422)) % 177.51/177.20 [2143]~E(x21431,x21432)+E(f766(x21431,x21433,x21434,x21435),f766(x21432,x21433,x21434,x21435)) % 177.51/177.20 [2144]~E(x21441,x21442)+E(f766(x21443,x21441,x21444,x21445),f766(x21443,x21442,x21444,x21445)) % 177.51/177.20 [2145]~E(x21451,x21452)+E(f766(x21453,x21454,x21451,x21455),f766(x21453,x21454,x21452,x21455)) % 177.51/177.20 [2146]~E(x21461,x21462)+E(f766(x21463,x21464,x21465,x21461),f766(x21463,x21464,x21465,x21462)) % 177.51/177.20 [2147]~E(x21471,x21472)+E(f434(x21471,x21473,x21474,x21475),f434(x21472,x21473,x21474,x21475)) % 177.51/177.20 [2148]~E(x21481,x21482)+E(f434(x21483,x21481,x21484,x21485),f434(x21483,x21482,x21484,x21485)) % 177.51/177.20 [2149]~E(x21491,x21492)+E(f434(x21493,x21494,x21491,x21495),f434(x21493,x21494,x21492,x21495)) % 177.51/177.20 [2150]~E(x21501,x21502)+E(f434(x21503,x21504,x21505,x21501),f434(x21503,x21504,x21505,x21502)) % 177.51/177.20 [2151]~E(x21511,x21512)+E(f588(x21511,x21513,x21514),f588(x21512,x21513,x21514)) % 177.51/177.20 [2152]~E(x21521,x21522)+E(f588(x21523,x21521,x21524),f588(x21523,x21522,x21524)) % 177.51/177.20 [2153]~E(x21531,x21532)+E(f588(x21533,x21534,x21531),f588(x21533,x21534,x21532)) % 177.51/177.20 [2154]~E(x21541,x21542)+E(f660(x21541,x21543),f660(x21542,x21543)) % 177.51/177.20 [2155]~E(x21551,x21552)+E(f660(x21553,x21551),f660(x21553,x21552)) % 177.51/177.20 [2156]~E(x21561,x21562)+E(f368(x21561,x21563,x21564,x21565),f368(x21562,x21563,x21564,x21565)) % 177.51/177.20 [2157]~E(x21571,x21572)+E(f368(x21573,x21571,x21574,x21575),f368(x21573,x21572,x21574,x21575)) % 177.51/177.20 [2158]~E(x21581,x21582)+E(f368(x21583,x21584,x21581,x21585),f368(x21583,x21584,x21582,x21585)) % 177.51/177.20 [2159]~E(x21591,x21592)+E(f368(x21593,x21594,x21595,x21591),f368(x21593,x21594,x21595,x21592)) % 177.51/177.20 [2160]~E(x21601,x21602)+E(f841(x21601,x21603,x21604,x21605,x21606,x21607,x21608),f841(x21602,x21603,x21604,x21605,x21606,x21607,x21608)) % 177.51/177.20 [2161]~E(x21611,x21612)+E(f841(x21613,x21611,x21614,x21615,x21616,x21617,x21618),f841(x21613,x21612,x21614,x21615,x21616,x21617,x21618)) % 177.51/177.20 [2162]~E(x21621,x21622)+E(f841(x21623,x21624,x21621,x21625,x21626,x21627,x21628),f841(x21623,x21624,x21622,x21625,x21626,x21627,x21628)) % 177.51/177.20 [2163]~E(x21631,x21632)+E(f841(x21633,x21634,x21635,x21631,x21636,x21637,x21638),f841(x21633,x21634,x21635,x21632,x21636,x21637,x21638)) % 177.51/177.20 [2164]~E(x21641,x21642)+E(f841(x21643,x21644,x21645,x21646,x21641,x21647,x21648),f841(x21643,x21644,x21645,x21646,x21642,x21647,x21648)) % 177.51/177.20 [2165]~E(x21651,x21652)+E(f841(x21653,x21654,x21655,x21656,x21657,x21651,x21658),f841(x21653,x21654,x21655,x21656,x21657,x21652,x21658)) % 177.51/177.20 [2166]~E(x21661,x21662)+E(f841(x21663,x21664,x21665,x21666,x21667,x21668,x21661),f841(x21663,x21664,x21665,x21666,x21667,x21668,x21662)) % 177.51/177.20 [2167]~E(x21671,x21672)+E(f887(x21671,x21673,x21674,x21675,x21676,x21677),f887(x21672,x21673,x21674,x21675,x21676,x21677)) % 177.51/177.20 [2168]~E(x21681,x21682)+E(f887(x21683,x21681,x21684,x21685,x21686,x21687),f887(x21683,x21682,x21684,x21685,x21686,x21687)) % 177.51/177.20 [2169]~E(x21691,x21692)+E(f887(x21693,x21694,x21691,x21695,x21696,x21697),f887(x21693,x21694,x21692,x21695,x21696,x21697)) % 177.51/177.20 [2170]~E(x21701,x21702)+E(f887(x21703,x21704,x21705,x21701,x21706,x21707),f887(x21703,x21704,x21705,x21702,x21706,x21707)) % 177.51/177.20 [2171]~E(x21711,x21712)+E(f887(x21713,x21714,x21715,x21716,x21711,x21717),f887(x21713,x21714,x21715,x21716,x21712,x21717)) % 177.51/177.20 [2172]~E(x21721,x21722)+E(f887(x21723,x21724,x21725,x21726,x21727,x21721),f887(x21723,x21724,x21725,x21726,x21727,x21722)) % 177.51/177.20 [2173]~E(x21731,x21732)+E(f735(x21731,x21733),f735(x21732,x21733)) % 177.51/177.20 [2174]~E(x21741,x21742)+E(f735(x21743,x21741),f735(x21743,x21742)) % 177.51/177.20 [2175]~E(x21751,x21752)+E(f374(x21751,x21753,x21754,x21755,x21756),f374(x21752,x21753,x21754,x21755,x21756)) % 177.51/177.20 [2176]~E(x21761,x21762)+E(f374(x21763,x21761,x21764,x21765,x21766),f374(x21763,x21762,x21764,x21765,x21766)) % 177.51/177.20 [2177]~E(x21771,x21772)+E(f374(x21773,x21774,x21771,x21775,x21776),f374(x21773,x21774,x21772,x21775,x21776)) % 177.51/177.20 [2178]~E(x21781,x21782)+E(f374(x21783,x21784,x21785,x21781,x21786),f374(x21783,x21784,x21785,x21782,x21786)) % 177.51/177.20 [2179]~E(x21791,x21792)+E(f374(x21793,x21794,x21795,x21796,x21791),f374(x21793,x21794,x21795,x21796,x21792)) % 177.51/177.20 [2180]~E(x21801,x21802)+E(f820(x21801,x21803,x21804,x21805),f820(x21802,x21803,x21804,x21805)) % 177.51/177.20 [2181]~E(x21811,x21812)+E(f820(x21813,x21811,x21814,x21815),f820(x21813,x21812,x21814,x21815)) % 177.51/177.20 [2182]~E(x21821,x21822)+E(f820(x21823,x21824,x21821,x21825),f820(x21823,x21824,x21822,x21825)) % 177.51/177.20 [2183]~E(x21831,x21832)+E(f820(x21833,x21834,x21835,x21831),f820(x21833,x21834,x21835,x21832)) % 177.51/177.20 [2184]~E(x21841,x21842)+E(f872(x21841,x21843,x21844,x21845),f872(x21842,x21843,x21844,x21845)) % 177.51/177.20 [2185]~E(x21851,x21852)+E(f872(x21853,x21851,x21854,x21855),f872(x21853,x21852,x21854,x21855)) % 177.51/177.20 [2186]~E(x21861,x21862)+E(f872(x21863,x21864,x21861,x21865),f872(x21863,x21864,x21862,x21865)) % 177.51/177.20 [2187]~E(x21871,x21872)+E(f872(x21873,x21874,x21875,x21871),f872(x21873,x21874,x21875,x21872)) % 177.51/177.20 [2188]~E(x21881,x21882)+E(f636(x21881,x21883,x21884,x21885),f636(x21882,x21883,x21884,x21885)) % 177.51/177.20 [2189]~E(x21891,x21892)+E(f636(x21893,x21891,x21894,x21895),f636(x21893,x21892,x21894,x21895)) % 177.51/177.20 [2190]~E(x21901,x21902)+E(f636(x21903,x21904,x21901,x21905),f636(x21903,x21904,x21902,x21905)) % 177.51/177.20 [2191]~E(x21911,x21912)+E(f636(x21913,x21914,x21915,x21911),f636(x21913,x21914,x21915,x21912)) % 177.51/177.20 [2192]~E(x21921,x21922)+E(f611(x21921,x21923),f611(x21922,x21923)) % 177.51/177.20 [2193]~E(x21931,x21932)+E(f611(x21933,x21931),f611(x21933,x21932)) % 177.51/177.20 [2194]~E(x21941,x21942)+E(f261(x21941,x21943,x21944,x21945,x21946),f261(x21942,x21943,x21944,x21945,x21946)) % 177.51/177.20 [2195]~E(x21951,x21952)+E(f261(x21953,x21951,x21954,x21955,x21956),f261(x21953,x21952,x21954,x21955,x21956)) % 177.51/177.20 [2196]~E(x21961,x21962)+E(f261(x21963,x21964,x21961,x21965,x21966),f261(x21963,x21964,x21962,x21965,x21966)) % 177.51/177.20 [2197]~E(x21971,x21972)+E(f261(x21973,x21974,x21975,x21971,x21976),f261(x21973,x21974,x21975,x21972,x21976)) % 177.51/177.20 [2198]~E(x21981,x21982)+E(f261(x21983,x21984,x21985,x21986,x21981),f261(x21983,x21984,x21985,x21986,x21982)) % 177.51/177.20 [2199]~E(x21991,x21992)+E(f292(x21991,x21993),f292(x21992,x21993)) % 177.51/177.20 [2200]~E(x22001,x22002)+E(f292(x22003,x22001),f292(x22003,x22002)) % 177.51/177.20 [2201]~E(x22011,x22012)+E(f209(x22011,x22013,x22014,x22015,x22016,x22017,x22018),f209(x22012,x22013,x22014,x22015,x22016,x22017,x22018)) % 177.51/177.20 [2202]~E(x22021,x22022)+E(f209(x22023,x22021,x22024,x22025,x22026,x22027,x22028),f209(x22023,x22022,x22024,x22025,x22026,x22027,x22028)) % 177.51/177.20 [2203]~E(x22031,x22032)+E(f209(x22033,x22034,x22031,x22035,x22036,x22037,x22038),f209(x22033,x22034,x22032,x22035,x22036,x22037,x22038)) % 177.51/177.20 [2204]~E(x22041,x22042)+E(f209(x22043,x22044,x22045,x22041,x22046,x22047,x22048),f209(x22043,x22044,x22045,x22042,x22046,x22047,x22048)) % 177.51/177.20 [2205]~E(x22051,x22052)+E(f209(x22053,x22054,x22055,x22056,x22051,x22057,x22058),f209(x22053,x22054,x22055,x22056,x22052,x22057,x22058)) % 177.51/177.20 [2206]~E(x22061,x22062)+E(f209(x22063,x22064,x22065,x22066,x22067,x22061,x22068),f209(x22063,x22064,x22065,x22066,x22067,x22062,x22068)) % 177.51/177.20 [2207]~E(x22071,x22072)+E(f209(x22073,x22074,x22075,x22076,x22077,x22078,x22071),f209(x22073,x22074,x22075,x22076,x22077,x22078,x22072)) % 177.51/177.20 [2208]~E(x22081,x22082)+E(f537(x22081,x22083,x22084),f537(x22082,x22083,x22084)) % 177.51/177.20 [2209]~E(x22091,x22092)+E(f537(x22093,x22091,x22094),f537(x22093,x22092,x22094)) % 177.51/177.20 [2210]~E(x22101,x22102)+E(f537(x22103,x22104,x22101),f537(x22103,x22104,x22102)) % 177.51/177.20 [2211]~E(x22111,x22112)+E(f823(x22111,x22113,x22114,x22115,x22116),f823(x22112,x22113,x22114,x22115,x22116)) % 177.51/177.20 [2212]~E(x22121,x22122)+E(f823(x22123,x22121,x22124,x22125,x22126),f823(x22123,x22122,x22124,x22125,x22126)) % 177.51/177.20 [2213]~E(x22131,x22132)+E(f823(x22133,x22134,x22131,x22135,x22136),f823(x22133,x22134,x22132,x22135,x22136)) % 177.51/177.20 [2214]~E(x22141,x22142)+E(f823(x22143,x22144,x22145,x22141,x22146),f823(x22143,x22144,x22145,x22142,x22146)) % 177.51/177.20 [2215]~E(x22151,x22152)+E(f823(x22153,x22154,x22155,x22156,x22151),f823(x22153,x22154,x22155,x22156,x22152)) % 177.51/177.20 [2216]~E(x22161,x22162)+E(f136(x22161),f136(x22162)) % 177.51/177.20 [2217]~E(x22171,x22172)+E(f689(x22171,x22173,x22174),f689(x22172,x22173,x22174)) % 177.51/177.20 [2218]~E(x22181,x22182)+E(f689(x22183,x22181,x22184),f689(x22183,x22182,x22184)) % 177.51/177.20 [2219]~E(x22191,x22192)+E(f689(x22193,x22194,x22191),f689(x22193,x22194,x22192)) % 177.51/177.20 [2220]~E(x22201,x22202)+E(f395(x22201,x22203,x22204),f395(x22202,x22203,x22204)) % 177.51/177.20 [2221]~E(x22211,x22212)+E(f395(x22213,x22211,x22214),f395(x22213,x22212,x22214)) % 177.51/177.20 [2222]~E(x22221,x22222)+E(f395(x22223,x22224,x22221),f395(x22223,x22224,x22222)) % 177.51/177.20 [2223]~E(x22231,x22232)+E(f902(x22231,x22233,x22234,x22235,x22236),f902(x22232,x22233,x22234,x22235,x22236)) % 177.51/177.20 [2224]~E(x22241,x22242)+E(f902(x22243,x22241,x22244,x22245,x22246),f902(x22243,x22242,x22244,x22245,x22246)) % 177.51/177.20 [2225]~E(x22251,x22252)+E(f902(x22253,x22254,x22251,x22255,x22256),f902(x22253,x22254,x22252,x22255,x22256)) % 177.51/177.20 [2226]~E(x22261,x22262)+E(f902(x22263,x22264,x22265,x22261,x22266),f902(x22263,x22264,x22265,x22262,x22266)) % 177.51/177.20 [2227]~E(x22271,x22272)+E(f902(x22273,x22274,x22275,x22276,x22271),f902(x22273,x22274,x22275,x22276,x22272)) % 177.51/177.20 [2228]~E(x22281,x22282)+E(f206(x22281),f206(x22282)) % 177.51/177.20 [2229]~E(x22291,x22292)+E(f652(x22291,x22293,x22294,x22295),f652(x22292,x22293,x22294,x22295)) % 177.51/177.20 [2230]~E(x22301,x22302)+E(f652(x22303,x22301,x22304,x22305),f652(x22303,x22302,x22304,x22305)) % 177.51/177.20 [2231]~E(x22311,x22312)+E(f652(x22313,x22314,x22311,x22315),f652(x22313,x22314,x22312,x22315)) % 177.51/177.20 [2232]~E(x22321,x22322)+E(f652(x22323,x22324,x22325,x22321),f652(x22323,x22324,x22325,x22322)) % 177.51/177.20 [2233]~E(x22331,x22332)+E(f591(x22331,x22333,x22334,x22335,x22336,x22337),f591(x22332,x22333,x22334,x22335,x22336,x22337)) % 177.51/177.20 [2234]~E(x22341,x22342)+E(f591(x22343,x22341,x22344,x22345,x22346,x22347),f591(x22343,x22342,x22344,x22345,x22346,x22347)) % 177.51/177.20 [2235]~E(x22351,x22352)+E(f591(x22353,x22354,x22351,x22355,x22356,x22357),f591(x22353,x22354,x22352,x22355,x22356,x22357)) % 177.51/177.20 [2236]~E(x22361,x22362)+E(f591(x22363,x22364,x22365,x22361,x22366,x22367),f591(x22363,x22364,x22365,x22362,x22366,x22367)) % 177.51/177.20 [2237]~E(x22371,x22372)+E(f591(x22373,x22374,x22375,x22376,x22371,x22377),f591(x22373,x22374,x22375,x22376,x22372,x22377)) % 177.51/177.20 [2238]~E(x22381,x22382)+E(f591(x22383,x22384,x22385,x22386,x22387,x22381),f591(x22383,x22384,x22385,x22386,x22387,x22382)) % 177.51/177.20 [2239]~E(x22391,x22392)+E(f451(x22391,x22393,x22394,x22395),f451(x22392,x22393,x22394,x22395)) % 177.51/177.20 [2240]~E(x22401,x22402)+E(f451(x22403,x22401,x22404,x22405),f451(x22403,x22402,x22404,x22405)) % 177.51/177.20 [2241]~E(x22411,x22412)+E(f451(x22413,x22414,x22411,x22415),f451(x22413,x22414,x22412,x22415)) % 177.51/177.20 [2242]~E(x22421,x22422)+E(f451(x22423,x22424,x22425,x22421),f451(x22423,x22424,x22425,x22422)) % 177.51/177.20 [2243]~E(x22431,x22432)+E(f763(x22431,x22433,x22434),f763(x22432,x22433,x22434)) % 177.51/177.20 [2244]~E(x22441,x22442)+E(f763(x22443,x22441,x22444),f763(x22443,x22442,x22444)) % 177.51/177.20 [2245]~E(x22451,x22452)+E(f763(x22453,x22454,x22451),f763(x22453,x22454,x22452)) % 177.51/177.20 [2246]~E(x22461,x22462)+E(f524(x22461,x22463,x22464,x22465,x22466,x22467,x22468),f524(x22462,x22463,x22464,x22465,x22466,x22467,x22468)) % 177.51/177.20 [2247]~E(x22471,x22472)+E(f524(x22473,x22471,x22474,x22475,x22476,x22477,x22478),f524(x22473,x22472,x22474,x22475,x22476,x22477,x22478)) % 177.51/177.20 [2248]~E(x22481,x22482)+E(f524(x22483,x22484,x22481,x22485,x22486,x22487,x22488),f524(x22483,x22484,x22482,x22485,x22486,x22487,x22488)) % 177.51/177.20 [2249]~E(x22491,x22492)+E(f524(x22493,x22494,x22495,x22491,x22496,x22497,x22498),f524(x22493,x22494,x22495,x22492,x22496,x22497,x22498)) % 177.51/177.20 [2250]~E(x22501,x22502)+E(f524(x22503,x22504,x22505,x22506,x22501,x22507,x22508),f524(x22503,x22504,x22505,x22506,x22502,x22507,x22508)) % 177.51/177.20 [2251]~E(x22511,x22512)+E(f524(x22513,x22514,x22515,x22516,x22517,x22511,x22518),f524(x22513,x22514,x22515,x22516,x22517,x22512,x22518)) % 177.51/177.20 [2252]~E(x22521,x22522)+E(f524(x22523,x22524,x22525,x22526,x22527,x22528,x22521),f524(x22523,x22524,x22525,x22526,x22527,x22528,x22522)) % 177.51/177.20 [2253]~E(x22531,x22532)+E(f522(x22531,x22533,x22534),f522(x22532,x22533,x22534)) % 177.51/177.20 [2254]~E(x22541,x22542)+E(f522(x22543,x22541,x22544),f522(x22543,x22542,x22544)) % 177.51/177.20 [2255]~E(x22551,x22552)+E(f522(x22553,x22554,x22551),f522(x22553,x22554,x22552)) % 177.51/177.20 [2256]~E(x22561,x22562)+E(f269(x22561,x22563),f269(x22562,x22563)) % 177.51/177.20 [2257]~E(x22571,x22572)+E(f269(x22573,x22571),f269(x22573,x22572)) % 177.51/177.20 [2258]~E(x22581,x22582)+E(f879(x22581,x22583,x22584,x22585),f879(x22582,x22583,x22584,x22585)) % 177.51/177.20 [2259]~E(x22591,x22592)+E(f879(x22593,x22591,x22594,x22595),f879(x22593,x22592,x22594,x22595)) % 177.51/177.20 [2260]~E(x22601,x22602)+E(f879(x22603,x22604,x22601,x22605),f879(x22603,x22604,x22602,x22605)) % 177.51/177.20 [2261]~E(x22611,x22612)+E(f879(x22613,x22614,x22615,x22611),f879(x22613,x22614,x22615,x22612)) % 177.51/177.20 [2262]~E(x22621,x22622)+E(f96(x22621,x22623,x22624,x22625),f96(x22622,x22623,x22624,x22625)) % 177.51/177.20 [2263]~E(x22631,x22632)+E(f96(x22633,x22631,x22634,x22635),f96(x22633,x22632,x22634,x22635)) % 177.51/177.20 [2264]~E(x22641,x22642)+E(f96(x22643,x22644,x22641,x22645),f96(x22643,x22644,x22642,x22645)) % 177.51/177.20 [2265]~E(x22651,x22652)+E(f96(x22653,x22654,x22655,x22651),f96(x22653,x22654,x22655,x22652)) % 177.51/177.20 [2266]~E(x22661,x22662)+E(f192(x22661,x22663,x22664,x22665),f192(x22662,x22663,x22664,x22665)) % 177.51/177.20 [2267]~E(x22671,x22672)+E(f192(x22673,x22671,x22674,x22675),f192(x22673,x22672,x22674,x22675)) % 177.51/177.20 [2268]~E(x22681,x22682)+E(f192(x22683,x22684,x22681,x22685),f192(x22683,x22684,x22682,x22685)) % 177.51/177.20 [2269]~E(x22691,x22692)+E(f192(x22693,x22694,x22695,x22691),f192(x22693,x22694,x22695,x22692)) % 177.51/177.20 [2270]~E(x22701,x22702)+E(f532(x22701,x22703,x22704,x22705),f532(x22702,x22703,x22704,x22705)) % 177.51/177.20 [2271]~E(x22711,x22712)+E(f532(x22713,x22711,x22714,x22715),f532(x22713,x22712,x22714,x22715)) % 177.51/177.20 [2272]~E(x22721,x22722)+E(f532(x22723,x22724,x22721,x22725),f532(x22723,x22724,x22722,x22725)) % 177.51/177.20 [2273]~E(x22731,x22732)+E(f532(x22733,x22734,x22735,x22731),f532(x22733,x22734,x22735,x22732)) % 177.51/177.20 [2274]~E(x22741,x22742)+E(f791(x22741,x22743,x22744),f791(x22742,x22743,x22744)) % 177.51/177.20 [2275]~E(x22751,x22752)+E(f791(x22753,x22751,x22754),f791(x22753,x22752,x22754)) % 177.51/177.20 [2276]~E(x22761,x22762)+E(f791(x22763,x22764,x22761),f791(x22763,x22764,x22762)) % 177.51/177.20 [2277]~E(x22771,x22772)+E(f895(x22771,x22773,x22774,x22775,x22776),f895(x22772,x22773,x22774,x22775,x22776)) % 177.51/177.20 [2278]~E(x22781,x22782)+E(f895(x22783,x22781,x22784,x22785,x22786),f895(x22783,x22782,x22784,x22785,x22786)) % 177.51/177.20 [2279]~E(x22791,x22792)+E(f895(x22793,x22794,x22791,x22795,x22796),f895(x22793,x22794,x22792,x22795,x22796)) % 177.51/177.20 [2280]~E(x22801,x22802)+E(f895(x22803,x22804,x22805,x22801,x22806),f895(x22803,x22804,x22805,x22802,x22806)) % 177.51/177.20 [2281]~E(x22811,x22812)+E(f895(x22813,x22814,x22815,x22816,x22811),f895(x22813,x22814,x22815,x22816,x22812)) % 177.51/177.20 [2282]~E(x22821,x22822)+E(f411(x22821,x22823,x22824),f411(x22822,x22823,x22824)) % 177.51/177.20 [2283]~E(x22831,x22832)+E(f411(x22833,x22831,x22834),f411(x22833,x22832,x22834)) % 177.51/177.20 [2284]~E(x22841,x22842)+E(f411(x22843,x22844,x22841),f411(x22843,x22844,x22842)) % 177.51/177.20 [2285]~E(x22851,x22852)+E(f614(x22851,x22853,x22854,x22855,x22856,x22857,x22858),f614(x22852,x22853,x22854,x22855,x22856,x22857,x22858)) % 177.51/177.20 [2286]~E(x22861,x22862)+E(f614(x22863,x22861,x22864,x22865,x22866,x22867,x22868),f614(x22863,x22862,x22864,x22865,x22866,x22867,x22868)) % 177.51/177.20 [2287]~E(x22871,x22872)+E(f614(x22873,x22874,x22871,x22875,x22876,x22877,x22878),f614(x22873,x22874,x22872,x22875,x22876,x22877,x22878)) % 177.51/177.20 [2288]~E(x22881,x22882)+E(f614(x22883,x22884,x22885,x22881,x22886,x22887,x22888),f614(x22883,x22884,x22885,x22882,x22886,x22887,x22888)) % 177.51/177.20 [2289]~E(x22891,x22892)+E(f614(x22893,x22894,x22895,x22896,x22891,x22897,x22898),f614(x22893,x22894,x22895,x22896,x22892,x22897,x22898)) % 177.51/177.20 [2290]~E(x22901,x22902)+E(f614(x22903,x22904,x22905,x22906,x22907,x22901,x22908),f614(x22903,x22904,x22905,x22906,x22907,x22902,x22908)) % 177.51/177.20 [2291]~E(x22911,x22912)+E(f614(x22913,x22914,x22915,x22916,x22917,x22918,x22911),f614(x22913,x22914,x22915,x22916,x22917,x22918,x22912)) % 177.51/177.20 [2292]~E(x22921,x22922)+E(f873(x22921,x22923,x22924,x22925,x22926),f873(x22922,x22923,x22924,x22925,x22926)) % 177.51/177.20 [2293]~E(x22931,x22932)+E(f873(x22933,x22931,x22934,x22935,x22936),f873(x22933,x22932,x22934,x22935,x22936)) % 177.51/177.20 [2294]~E(x22941,x22942)+E(f873(x22943,x22944,x22941,x22945,x22946),f873(x22943,x22944,x22942,x22945,x22946)) % 177.51/177.20 [2295]~E(x22951,x22952)+E(f873(x22953,x22954,x22955,x22951,x22956),f873(x22953,x22954,x22955,x22952,x22956)) % 177.51/177.20 [2296]~E(x22961,x22962)+E(f873(x22963,x22964,x22965,x22966,x22961),f873(x22963,x22964,x22965,x22966,x22962)) % 177.51/177.20 [2297]~E(x22971,x22972)+E(f893(x22971,x22973,x22974,x22975),f893(x22972,x22973,x22974,x22975)) % 177.51/177.20 [2298]~E(x22981,x22982)+E(f893(x22983,x22981,x22984,x22985),f893(x22983,x22982,x22984,x22985)) % 177.51/177.20 [2299]~E(x22991,x22992)+E(f893(x22993,x22994,x22991,x22995),f893(x22993,x22994,x22992,x22995)) % 177.51/177.20 [2300]~E(x23001,x23002)+E(f893(x23003,x23004,x23005,x23001),f893(x23003,x23004,x23005,x23002)) % 177.51/177.20 [2301]~E(x23011,x23012)+E(f848(x23011,x23013,x23014,x23015,x23016,x23017),f848(x23012,x23013,x23014,x23015,x23016,x23017)) % 177.51/177.20 [2302]~E(x23021,x23022)+E(f848(x23023,x23021,x23024,x23025,x23026,x23027),f848(x23023,x23022,x23024,x23025,x23026,x23027)) % 177.51/177.20 [2303]~E(x23031,x23032)+E(f848(x23033,x23034,x23031,x23035,x23036,x23037),f848(x23033,x23034,x23032,x23035,x23036,x23037)) % 177.51/177.20 [2304]~E(x23041,x23042)+E(f848(x23043,x23044,x23045,x23041,x23046,x23047),f848(x23043,x23044,x23045,x23042,x23046,x23047)) % 177.51/177.20 [2305]~E(x23051,x23052)+E(f848(x23053,x23054,x23055,x23056,x23051,x23057),f848(x23053,x23054,x23055,x23056,x23052,x23057)) % 177.51/177.20 [2306]~E(x23061,x23062)+E(f848(x23063,x23064,x23065,x23066,x23067,x23061),f848(x23063,x23064,x23065,x23066,x23067,x23062)) % 177.51/177.20 [2307]~E(x23071,x23072)+E(f906(x23071,x23073,x23074,x23075,x23076,x23077,x23078),f906(x23072,x23073,x23074,x23075,x23076,x23077,x23078)) % 177.51/177.20 [2308]~E(x23081,x23082)+E(f906(x23083,x23081,x23084,x23085,x23086,x23087,x23088),f906(x23083,x23082,x23084,x23085,x23086,x23087,x23088)) % 177.51/177.20 [2309]~E(x23091,x23092)+E(f906(x23093,x23094,x23091,x23095,x23096,x23097,x23098),f906(x23093,x23094,x23092,x23095,x23096,x23097,x23098)) % 177.51/177.20 [2310]~E(x23101,x23102)+E(f906(x23103,x23104,x23105,x23101,x23106,x23107,x23108),f906(x23103,x23104,x23105,x23102,x23106,x23107,x23108)) % 177.51/177.20 [2311]~E(x23111,x23112)+E(f906(x23113,x23114,x23115,x23116,x23111,x23117,x23118),f906(x23113,x23114,x23115,x23116,x23112,x23117,x23118)) % 177.51/177.20 [2312]~E(x23121,x23122)+E(f906(x23123,x23124,x23125,x23126,x23127,x23121,x23128),f906(x23123,x23124,x23125,x23126,x23127,x23122,x23128)) % 177.51/177.20 [2313]~E(x23131,x23132)+E(f906(x23133,x23134,x23135,x23136,x23137,x23138,x23131),f906(x23133,x23134,x23135,x23136,x23137,x23138,x23132)) % 177.51/177.20 [2314]~E(x23141,x23142)+E(f296(x23141,x23143,x23144),f296(x23142,x23143,x23144)) % 177.51/177.20 [2315]~E(x23151,x23152)+E(f296(x23153,x23151,x23154),f296(x23153,x23152,x23154)) % 177.51/177.20 [2316]~E(x23161,x23162)+E(f296(x23163,x23164,x23161),f296(x23163,x23164,x23162)) % 177.51/177.20 [2317]~E(x23171,x23172)+E(f533(x23171,x23173,x23174,x23175,x23176),f533(x23172,x23173,x23174,x23175,x23176)) % 177.51/177.20 [2318]~E(x23181,x23182)+E(f533(x23183,x23181,x23184,x23185,x23186),f533(x23183,x23182,x23184,x23185,x23186)) % 177.51/177.20 [2319]~E(x23191,x23192)+E(f533(x23193,x23194,x23191,x23195,x23196),f533(x23193,x23194,x23192,x23195,x23196)) % 177.51/177.20 [2320]~E(x23201,x23202)+E(f533(x23203,x23204,x23205,x23201,x23206),f533(x23203,x23204,x23205,x23202,x23206)) % 177.51/177.20 [2321]~E(x23211,x23212)+E(f533(x23213,x23214,x23215,x23216,x23211),f533(x23213,x23214,x23215,x23216,x23212)) % 177.51/177.20 [2322]~E(x23221,x23222)+E(f589(x23221,x23223,x23224,x23225,x23226),f589(x23222,x23223,x23224,x23225,x23226)) % 177.51/177.20 [2323]~E(x23231,x23232)+E(f589(x23233,x23231,x23234,x23235,x23236),f589(x23233,x23232,x23234,x23235,x23236)) % 177.51/177.20 [2324]~E(x23241,x23242)+E(f589(x23243,x23244,x23241,x23245,x23246),f589(x23243,x23244,x23242,x23245,x23246)) % 177.51/177.20 [2325]~E(x23251,x23252)+E(f589(x23253,x23254,x23255,x23251,x23256),f589(x23253,x23254,x23255,x23252,x23256)) % 177.51/177.20 [2326]~E(x23261,x23262)+E(f589(x23263,x23264,x23265,x23266,x23261),f589(x23263,x23264,x23265,x23266,x23262)) % 177.51/177.20 [2327]~E(x23271,x23272)+E(f741(x23271,x23273,x23274,x23275,x23276),f741(x23272,x23273,x23274,x23275,x23276)) % 177.51/177.20 [2328]~E(x23281,x23282)+E(f741(x23283,x23281,x23284,x23285,x23286),f741(x23283,x23282,x23284,x23285,x23286)) % 177.51/177.20 [2329]~E(x23291,x23292)+E(f741(x23293,x23294,x23291,x23295,x23296),f741(x23293,x23294,x23292,x23295,x23296)) % 177.51/177.20 [2330]~E(x23301,x23302)+E(f741(x23303,x23304,x23305,x23301,x23306),f741(x23303,x23304,x23305,x23302,x23306)) % 177.51/177.20 [2331]~E(x23311,x23312)+E(f741(x23313,x23314,x23315,x23316,x23311),f741(x23313,x23314,x23315,x23316,x23312)) % 177.51/177.20 [2332]~E(x23321,x23322)+E(f568(x23321,x23323),f568(x23322,x23323)) % 177.51/177.20 [2333]~E(x23331,x23332)+E(f568(x23333,x23331),f568(x23333,x23332)) % 177.51/177.20 [2334]~E(x23341,x23342)+E(f383(x23341,x23343,x23344,x23345,x23346),f383(x23342,x23343,x23344,x23345,x23346)) % 177.51/177.20 [2335]~E(x23351,x23352)+E(f383(x23353,x23351,x23354,x23355,x23356),f383(x23353,x23352,x23354,x23355,x23356)) % 177.51/177.20 [2336]~E(x23361,x23362)+E(f383(x23363,x23364,x23361,x23365,x23366),f383(x23363,x23364,x23362,x23365,x23366)) % 177.51/177.20 [2337]~E(x23371,x23372)+E(f383(x23373,x23374,x23375,x23371,x23376),f383(x23373,x23374,x23375,x23372,x23376)) % 177.51/177.20 [2338]~E(x23381,x23382)+E(f383(x23383,x23384,x23385,x23386,x23381),f383(x23383,x23384,x23385,x23386,x23382)) % 177.51/177.20 [2339]~E(x23391,x23392)+E(f803(x23391),f803(x23392)) % 177.51/177.20 [2340]~E(x23401,x23402)+E(f475(x23401,x23403,x23404),f475(x23402,x23403,x23404)) % 177.51/177.20 [2341]~E(x23411,x23412)+E(f475(x23413,x23411,x23414),f475(x23413,x23412,x23414)) % 177.51/177.20 [2342]~E(x23421,x23422)+E(f475(x23423,x23424,x23421),f475(x23423,x23424,x23422)) % 177.51/177.20 [2343]~E(x23431,x23432)+E(f396(x23431,x23433,x23434,x23435),f396(x23432,x23433,x23434,x23435)) % 177.51/177.20 [2344]~E(x23441,x23442)+E(f396(x23443,x23441,x23444,x23445),f396(x23443,x23442,x23444,x23445)) % 177.51/177.20 [2345]~E(x23451,x23452)+E(f396(x23453,x23454,x23451,x23455),f396(x23453,x23454,x23452,x23455)) % 177.51/177.20 [2346]~E(x23461,x23462)+E(f396(x23463,x23464,x23465,x23461),f396(x23463,x23464,x23465,x23462)) % 177.51/177.20 [2347]~E(x23471,x23472)+E(f541(x23471,x23473),f541(x23472,x23473)) % 177.51/177.20 [2348]~E(x23481,x23482)+E(f541(x23483,x23481),f541(x23483,x23482)) % 177.51/177.20 [2349]~E(x23491,x23492)+E(f687(x23491,x23493,x23494),f687(x23492,x23493,x23494)) % 177.51/177.20 [2350]~E(x23501,x23502)+E(f687(x23503,x23501,x23504),f687(x23503,x23502,x23504)) % 177.51/177.20 [2351]~E(x23511,x23512)+E(f687(x23513,x23514,x23511),f687(x23513,x23514,x23512)) % 177.51/177.20 [2352]~E(x23521,x23522)+E(f730(x23521,x23523,x23524,x23525),f730(x23522,x23523,x23524,x23525)) % 177.51/177.20 [2353]~E(x23531,x23532)+E(f730(x23533,x23531,x23534,x23535),f730(x23533,x23532,x23534,x23535)) % 177.51/177.20 [2354]~E(x23541,x23542)+E(f730(x23543,x23544,x23541,x23545),f730(x23543,x23544,x23542,x23545)) % 177.51/177.20 [2355]~E(x23551,x23552)+E(f730(x23553,x23554,x23555,x23551),f730(x23553,x23554,x23555,x23552)) % 177.51/177.20 [2356]~E(x23561,x23562)+E(f337(x23561),f337(x23562)) % 177.51/177.20 [2357]~E(x23571,x23572)+E(f694(x23571,x23573,x23574,x23575),f694(x23572,x23573,x23574,x23575)) % 177.51/177.20 [2358]~E(x23581,x23582)+E(f694(x23583,x23581,x23584,x23585),f694(x23583,x23582,x23584,x23585)) % 177.51/177.20 [2359]~E(x23591,x23592)+E(f694(x23593,x23594,x23591,x23595),f694(x23593,x23594,x23592,x23595)) % 177.51/177.20 [2360]~E(x23601,x23602)+E(f694(x23603,x23604,x23605,x23601),f694(x23603,x23604,x23605,x23602)) % 177.51/177.20 [2361]~E(x23611,x23612)+E(f567(x23611),f567(x23612)) % 177.51/177.20 [2362]~E(x23621,x23622)+E(f227(x23621,x23623,x23624,x23625,x23626),f227(x23622,x23623,x23624,x23625,x23626)) % 177.51/177.20 [2363]~E(x23631,x23632)+E(f227(x23633,x23631,x23634,x23635,x23636),f227(x23633,x23632,x23634,x23635,x23636)) % 177.51/177.20 [2364]~E(x23641,x23642)+E(f227(x23643,x23644,x23641,x23645,x23646),f227(x23643,x23644,x23642,x23645,x23646)) % 177.51/177.20 [2365]~E(x23651,x23652)+E(f227(x23653,x23654,x23655,x23651,x23656),f227(x23653,x23654,x23655,x23652,x23656)) % 177.51/177.20 [2366]~E(x23661,x23662)+E(f227(x23663,x23664,x23665,x23666,x23661),f227(x23663,x23664,x23665,x23666,x23662)) % 177.51/177.20 [2367]~E(x23671,x23672)+E(f746(x23671,x23673,x23674),f746(x23672,x23673,x23674)) % 177.51/177.20 [2368]~E(x23681,x23682)+E(f746(x23683,x23681,x23684),f746(x23683,x23682,x23684)) % 177.51/177.20 [2369]~E(x23691,x23692)+E(f746(x23693,x23694,x23691),f746(x23693,x23694,x23692)) % 177.51/177.20 [2370]~E(x23701,x23702)+E(f601(x23701,x23703,x23704),f601(x23702,x23703,x23704)) % 177.51/177.20 [2371]~E(x23711,x23712)+E(f601(x23713,x23711,x23714),f601(x23713,x23712,x23714)) % 177.51/177.20 [2372]~E(x23721,x23722)+E(f601(x23723,x23724,x23721),f601(x23723,x23724,x23722)) % 177.51/177.20 [2373]~E(x23731,x23732)+E(f862(x23731,x23733,x23734),f862(x23732,x23733,x23734)) % 177.51/177.20 [2374]~E(x23741,x23742)+E(f862(x23743,x23741,x23744),f862(x23743,x23742,x23744)) % 177.51/177.20 [2375]~E(x23751,x23752)+E(f862(x23753,x23754,x23751),f862(x23753,x23754,x23752)) % 177.51/177.20 [2376]~E(x23761,x23762)+E(f692(x23761,x23763),f692(x23762,x23763)) % 177.51/177.20 [2377]~E(x23771,x23772)+E(f692(x23773,x23771),f692(x23773,x23772)) % 177.51/177.20 [2378]~E(x23781,x23782)+E(f453(x23781,x23783,x23784,x23785),f453(x23782,x23783,x23784,x23785)) % 177.51/177.20 [2379]~E(x23791,x23792)+E(f453(x23793,x23791,x23794,x23795),f453(x23793,x23792,x23794,x23795)) % 177.51/177.20 [2380]~E(x23801,x23802)+E(f453(x23803,x23804,x23801,x23805),f453(x23803,x23804,x23802,x23805)) % 177.51/177.20 [2381]~E(x23811,x23812)+E(f453(x23813,x23814,x23815,x23811),f453(x23813,x23814,x23815,x23812)) % 177.51/177.20 [2382]~E(x23821,x23822)+E(f388(x23821,x23823),f388(x23822,x23823)) % 177.51/177.20 [2383]~E(x23831,x23832)+E(f388(x23833,x23831),f388(x23833,x23832)) % 177.51/177.20 [2384]~E(x23841,x23842)+E(f363(x23841,x23843,x23844),f363(x23842,x23843,x23844)) % 177.51/177.20 [2385]~E(x23851,x23852)+E(f363(x23853,x23851,x23854),f363(x23853,x23852,x23854)) % 177.51/177.20 [2386]~E(x23861,x23862)+E(f363(x23863,x23864,x23861),f363(x23863,x23864,x23862)) % 177.51/177.20 [2387]~E(x23871,x23872)+E(f884(x23871,x23873),f884(x23872,x23873)) % 177.51/177.20 [2388]~E(x23881,x23882)+E(f884(x23883,x23881),f884(x23883,x23882)) % 177.51/177.20 [2389]~E(x23891,x23892)+E(f901(x23891,x23893,x23894,x23895,x23896),f901(x23892,x23893,x23894,x23895,x23896)) % 177.51/177.20 [2390]~E(x23901,x23902)+E(f901(x23903,x23901,x23904,x23905,x23906),f901(x23903,x23902,x23904,x23905,x23906)) % 177.51/177.20 [2391]~E(x23911,x23912)+E(f901(x23913,x23914,x23911,x23915,x23916),f901(x23913,x23914,x23912,x23915,x23916)) % 177.51/177.20 [2392]~E(x23921,x23922)+E(f901(x23923,x23924,x23925,x23921,x23926),f901(x23923,x23924,x23925,x23922,x23926)) % 177.51/177.20 [2393]~E(x23931,x23932)+E(f901(x23933,x23934,x23935,x23936,x23931),f901(x23933,x23934,x23935,x23936,x23932)) % 177.51/177.20 [2394]~E(x23941,x23942)+E(f449(x23941,x23943),f449(x23942,x23943)) % 177.51/177.20 [2395]~E(x23951,x23952)+E(f449(x23953,x23951),f449(x23953,x23952)) % 177.51/177.20 [2396]~E(x23961,x23962)+E(f557(x23961,x23963,x23964,x23965,x23966,x23967),f557(x23962,x23963,x23964,x23965,x23966,x23967)) % 177.51/177.20 [2397]~E(x23971,x23972)+E(f557(x23973,x23971,x23974,x23975,x23976,x23977),f557(x23973,x23972,x23974,x23975,x23976,x23977)) % 177.51/177.20 [2398]~E(x23981,x23982)+E(f557(x23983,x23984,x23981,x23985,x23986,x23987),f557(x23983,x23984,x23982,x23985,x23986,x23987)) % 177.51/177.20 [2399]~E(x23991,x23992)+E(f557(x23993,x23994,x23995,x23991,x23996,x23997),f557(x23993,x23994,x23995,x23992,x23996,x23997)) % 177.51/177.20 [2400]~E(x24001,x24002)+E(f557(x24003,x24004,x24005,x24006,x24001,x24007),f557(x24003,x24004,x24005,x24006,x24002,x24007)) % 177.51/177.20 [2401]~E(x24011,x24012)+E(f557(x24013,x24014,x24015,x24016,x24017,x24011),f557(x24013,x24014,x24015,x24016,x24017,x24012)) % 177.51/177.20 [2402]~E(x24021,x24022)+E(f621(x24021,x24023,x24024,x24025,x24026),f621(x24022,x24023,x24024,x24025,x24026)) % 177.51/177.20 [2403]~E(x24031,x24032)+E(f621(x24033,x24031,x24034,x24035,x24036),f621(x24033,x24032,x24034,x24035,x24036)) % 177.51/177.20 [2404]~E(x24041,x24042)+E(f621(x24043,x24044,x24041,x24045,x24046),f621(x24043,x24044,x24042,x24045,x24046)) % 177.51/177.20 [2405]~E(x24051,x24052)+E(f621(x24053,x24054,x24055,x24051,x24056),f621(x24053,x24054,x24055,x24052,x24056)) % 177.51/177.20 [2406]~E(x24061,x24062)+E(f621(x24063,x24064,x24065,x24066,x24061),f621(x24063,x24064,x24065,x24066,x24062)) % 177.51/177.20 [2407]~E(x24071,x24072)+E(f845(x24071,x24073,x24074,x24075,x24076,x24077),f845(x24072,x24073,x24074,x24075,x24076,x24077)) % 177.51/177.20 [2408]~E(x24081,x24082)+E(f845(x24083,x24081,x24084,x24085,x24086,x24087),f845(x24083,x24082,x24084,x24085,x24086,x24087)) % 177.51/177.20 [2409]~E(x24091,x24092)+E(f845(x24093,x24094,x24091,x24095,x24096,x24097),f845(x24093,x24094,x24092,x24095,x24096,x24097)) % 177.51/177.20 [2410]~E(x24101,x24102)+E(f845(x24103,x24104,x24105,x24101,x24106,x24107),f845(x24103,x24104,x24105,x24102,x24106,x24107)) % 177.51/177.20 [2411]~E(x24111,x24112)+E(f845(x24113,x24114,x24115,x24116,x24111,x24117),f845(x24113,x24114,x24115,x24116,x24112,x24117)) % 177.51/177.20 [2412]~E(x24121,x24122)+E(f845(x24123,x24124,x24125,x24126,x24127,x24121),f845(x24123,x24124,x24125,x24126,x24127,x24122)) % 177.51/177.20 [2413]~E(x24131,x24132)+E(f430(x24131,x24133,x24134,x24135),f430(x24132,x24133,x24134,x24135)) % 177.51/177.20 [2414]~E(x24141,x24142)+E(f430(x24143,x24141,x24144,x24145),f430(x24143,x24142,x24144,x24145)) % 177.51/177.20 [2415]~E(x24151,x24152)+E(f430(x24153,x24154,x24151,x24155),f430(x24153,x24154,x24152,x24155)) % 177.51/177.20 [2416]~E(x24161,x24162)+E(f430(x24163,x24164,x24165,x24161),f430(x24163,x24164,x24165,x24162)) % 177.51/177.20 [2417]~E(x24171,x24172)+E(f356(x24171,x24173,x24174,x24175,x24176),f356(x24172,x24173,x24174,x24175,x24176)) % 177.51/177.20 [2418]~E(x24181,x24182)+E(f356(x24183,x24181,x24184,x24185,x24186),f356(x24183,x24182,x24184,x24185,x24186)) % 177.51/177.20 [2419]~E(x24191,x24192)+E(f356(x24193,x24194,x24191,x24195,x24196),f356(x24193,x24194,x24192,x24195,x24196)) % 177.51/177.20 [2420]~E(x24201,x24202)+E(f356(x24203,x24204,x24205,x24201,x24206),f356(x24203,x24204,x24205,x24202,x24206)) % 177.51/177.20 [2421]~E(x24211,x24212)+E(f356(x24213,x24214,x24215,x24216,x24211),f356(x24213,x24214,x24215,x24216,x24212)) % 177.51/177.20 [2422]~E(x24221,x24222)+E(f734(x24221,x24223,x24224),f734(x24222,x24223,x24224)) % 177.51/177.20 [2423]~E(x24231,x24232)+E(f734(x24233,x24231,x24234),f734(x24233,x24232,x24234)) % 177.51/177.20 [2424]~E(x24241,x24242)+E(f734(x24243,x24244,x24241),f734(x24243,x24244,x24242)) % 177.51/177.20 [2425]~E(x24251,x24252)+E(f886(x24251,x24253,x24254),f886(x24252,x24253,x24254)) % 177.51/177.20 [2426]~E(x24261,x24262)+E(f886(x24263,x24261,x24264),f886(x24263,x24262,x24264)) % 177.51/177.20 [2427]~E(x24271,x24272)+E(f886(x24273,x24274,x24271),f886(x24273,x24274,x24272)) % 177.51/177.20 [2428]~E(x24281,x24282)+E(f565(x24281,x24283,x24284,x24285,x24286,x24287,x24288,x24289),f565(x24282,x24283,x24284,x24285,x24286,x24287,x24288,x24289)) % 177.51/177.20 [2429]~E(x24291,x24292)+E(f565(x24293,x24291,x24294,x24295,x24296,x24297,x24298,x24299),f565(x24293,x24292,x24294,x24295,x24296,x24297,x24298,x24299)) % 177.51/177.20 [2430]~E(x24301,x24302)+E(f565(x24303,x24304,x24301,x24305,x24306,x24307,x24308,x24309),f565(x24303,x24304,x24302,x24305,x24306,x24307,x24308,x24309)) % 177.51/177.20 [2431]~E(x24311,x24312)+E(f565(x24313,x24314,x24315,x24311,x24316,x24317,x24318,x24319),f565(x24313,x24314,x24315,x24312,x24316,x24317,x24318,x24319)) % 177.51/177.20 [2432]~E(x24321,x24322)+E(f565(x24323,x24324,x24325,x24326,x24321,x24327,x24328,x24329),f565(x24323,x24324,x24325,x24326,x24322,x24327,x24328,x24329)) % 177.51/177.20 [2433]~E(x24331,x24332)+E(f565(x24333,x24334,x24335,x24336,x24337,x24331,x24338,x24339),f565(x24333,x24334,x24335,x24336,x24337,x24332,x24338,x24339)) % 177.51/177.20 [2434]~E(x24341,x24342)+E(f565(x24343,x24344,x24345,x24346,x24347,x24348,x24341,x24349),f565(x24343,x24344,x24345,x24346,x24347,x24348,x24342,x24349)) % 177.51/177.20 [2435]~E(x24351,x24352)+E(f565(x24353,x24354,x24355,x24356,x24357,x24358,x24359,x24351),f565(x24353,x24354,x24355,x24356,x24357,x24358,x24359,x24352)) % 177.51/177.20 [2436]~E(x24361,x24362)+E(f438(x24361,x24363,x24364,x24365),f438(x24362,x24363,x24364,x24365)) % 177.51/177.20 [2437]~E(x24371,x24372)+E(f438(x24373,x24371,x24374,x24375),f438(x24373,x24372,x24374,x24375)) % 177.51/177.20 [2438]~E(x24381,x24382)+E(f438(x24383,x24384,x24381,x24385),f438(x24383,x24384,x24382,x24385)) % 177.51/177.20 [2439]~E(x24391,x24392)+E(f438(x24393,x24394,x24395,x24391),f438(x24393,x24394,x24395,x24392)) % 177.51/177.20 [2440]~E(x24401,x24402)+E(f797(x24401,x24403),f797(x24402,x24403)) % 177.51/177.20 [2441]~E(x24411,x24412)+E(f797(x24413,x24411),f797(x24413,x24412)) % 177.51/177.20 [2442]~E(x24421,x24422)+E(f844(x24421,x24423,x24424,x24425,x24426,x24427),f844(x24422,x24423,x24424,x24425,x24426,x24427)) % 177.51/177.20 [2443]~E(x24431,x24432)+E(f844(x24433,x24431,x24434,x24435,x24436,x24437),f844(x24433,x24432,x24434,x24435,x24436,x24437)) % 177.51/177.20 [2444]~E(x24441,x24442)+E(f844(x24443,x24444,x24441,x24445,x24446,x24447),f844(x24443,x24444,x24442,x24445,x24446,x24447)) % 177.51/177.20 [2445]~E(x24451,x24452)+E(f844(x24453,x24454,x24455,x24451,x24456,x24457),f844(x24453,x24454,x24455,x24452,x24456,x24457)) % 177.51/177.20 [2446]~E(x24461,x24462)+E(f844(x24463,x24464,x24465,x24466,x24461,x24467),f844(x24463,x24464,x24465,x24466,x24462,x24467)) % 177.51/177.20 [2447]~E(x24471,x24472)+E(f844(x24473,x24474,x24475,x24476,x24477,x24471),f844(x24473,x24474,x24475,x24476,x24477,x24472)) % 177.51/177.20 [2448]~E(x24481,x24482)+E(f767(x24481,x24483,x24484),f767(x24482,x24483,x24484)) % 177.51/177.20 [2449]~E(x24491,x24492)+E(f767(x24493,x24491,x24494),f767(x24493,x24492,x24494)) % 177.51/177.20 [2450]~E(x24501,x24502)+E(f767(x24503,x24504,x24501),f767(x24503,x24504,x24502)) % 177.51/177.20 [2451]~E(x24511,x24512)+E(f492(x24511,x24513,x24514,x24515),f492(x24512,x24513,x24514,x24515)) % 177.51/177.20 [2452]~E(x24521,x24522)+E(f492(x24523,x24521,x24524,x24525),f492(x24523,x24522,x24524,x24525)) % 177.51/177.20 [2453]~E(x24531,x24532)+E(f492(x24533,x24534,x24531,x24535),f492(x24533,x24534,x24532,x24535)) % 177.51/177.20 [2454]~E(x24541,x24542)+E(f492(x24543,x24544,x24545,x24541),f492(x24543,x24544,x24545,x24542)) % 177.51/177.20 [2455]~E(x24551,x24552)+E(f801(x24551,x24553),f801(x24552,x24553)) % 177.51/177.20 [2456]~E(x24561,x24562)+E(f801(x24563,x24561),f801(x24563,x24562)) % 177.51/177.20 [2457]~E(x24571,x24572)+E(f181(x24571),f181(x24572)) % 177.51/177.20 [2458]~E(x24581,x24582)+E(f657(x24581,x24583,x24584),f657(x24582,x24583,x24584)) % 177.51/177.20 [2459]~E(x24591,x24592)+E(f657(x24593,x24591,x24594),f657(x24593,x24592,x24594)) % 177.51/177.20 [2460]~E(x24601,x24602)+E(f657(x24603,x24604,x24601),f657(x24603,x24604,x24602)) % 177.51/177.20 [2461]~E(x24611,x24612)+E(f386(x24611),f386(x24612)) % 177.51/177.20 [2462]~E(x24621,x24622)+E(f338(x24621,x24623),f338(x24622,x24623)) % 177.51/177.20 [2463]~E(x24631,x24632)+E(f338(x24633,x24631),f338(x24633,x24632)) % 177.51/177.20 [2464]~E(x24641,x24642)+E(f471(x24641,x24643,x24644),f471(x24642,x24643,x24644)) % 177.51/177.20 [2465]~E(x24651,x24652)+E(f471(x24653,x24651,x24654),f471(x24653,x24652,x24654)) % 177.51/177.20 [2466]~E(x24661,x24662)+E(f471(x24663,x24664,x24661),f471(x24663,x24664,x24662)) % 177.51/177.20 [2467]~E(x24671,x24672)+E(f437(x24671,x24673,x24674,x24675),f437(x24672,x24673,x24674,x24675)) % 177.51/177.20 [2468]~E(x24681,x24682)+E(f437(x24683,x24681,x24684,x24685),f437(x24683,x24682,x24684,x24685)) % 177.51/177.20 [2469]~E(x24691,x24692)+E(f437(x24693,x24694,x24691,x24695),f437(x24693,x24694,x24692,x24695)) % 177.51/177.20 [2470]~E(x24701,x24702)+E(f437(x24703,x24704,x24705,x24701),f437(x24703,x24704,x24705,x24702)) % 177.51/177.20 [2471]~E(x24711,x24712)+E(f773(x24711),f773(x24712)) % 177.51/177.20 [2472]~E(x24721,x24722)+E(f401(x24721,x24723,x24724,x24725,x24726),f401(x24722,x24723,x24724,x24725,x24726)) % 177.51/177.20 [2473]~E(x24731,x24732)+E(f401(x24733,x24731,x24734,x24735,x24736),f401(x24733,x24732,x24734,x24735,x24736)) % 177.51/177.20 [2474]~E(x24741,x24742)+E(f401(x24743,x24744,x24741,x24745,x24746),f401(x24743,x24744,x24742,x24745,x24746)) % 177.51/177.20 [2475]~E(x24751,x24752)+E(f401(x24753,x24754,x24755,x24751,x24756),f401(x24753,x24754,x24755,x24752,x24756)) % 177.51/177.20 [2476]~E(x24761,x24762)+E(f401(x24763,x24764,x24765,x24766,x24761),f401(x24763,x24764,x24765,x24766,x24762)) % 177.51/177.20 [2477]~E(x24771,x24772)+E(f716(x24771,x24773),f716(x24772,x24773)) % 177.51/177.20 [2478]~E(x24781,x24782)+E(f716(x24783,x24781),f716(x24783,x24782)) % 177.51/177.20 [2479]~E(x24791,x24792)+E(f700(x24791,x24793,x24794),f700(x24792,x24793,x24794)) % 177.51/177.20 [2480]~E(x24801,x24802)+E(f700(x24803,x24801,x24804),f700(x24803,x24802,x24804)) % 177.51/177.20 [2481]~E(x24811,x24812)+E(f700(x24813,x24814,x24811),f700(x24813,x24814,x24812)) % 177.51/177.20 [2482]~E(x24821,x24822)+E(f518(x24821,x24823,x24824),f518(x24822,x24823,x24824)) % 177.51/177.20 [2483]~E(x24831,x24832)+E(f518(x24833,x24831,x24834),f518(x24833,x24832,x24834)) % 177.51/177.20 [2484]~E(x24841,x24842)+E(f518(x24843,x24844,x24841),f518(x24843,x24844,x24842)) % 177.51/177.20 [2485]~E(x24851,x24852)+E(f552(x24851,x24853,x24854,x24855),f552(x24852,x24853,x24854,x24855)) % 177.51/177.20 [2486]~E(x24861,x24862)+E(f552(x24863,x24861,x24864,x24865),f552(x24863,x24862,x24864,x24865)) % 177.51/177.20 [2487]~E(x24871,x24872)+E(f552(x24873,x24874,x24871,x24875),f552(x24873,x24874,x24872,x24875)) % 177.51/177.20 [2488]~E(x24881,x24882)+E(f552(x24883,x24884,x24885,x24881),f552(x24883,x24884,x24885,x24882)) % 177.51/177.20 [2489]~E(x24891,x24892)+E(f407(x24891,x24893),f407(x24892,x24893)) % 177.51/177.20 [2490]~E(x24901,x24902)+E(f407(x24903,x24901),f407(x24903,x24902)) % 177.51/177.20 [2491]~E(x24911,x24912)+E(f339(x24911,x24913,x24914),f339(x24912,x24913,x24914)) % 177.51/177.20 [2492]~E(x24921,x24922)+E(f339(x24923,x24921,x24924),f339(x24923,x24922,x24924)) % 177.51/177.20 [2493]~E(x24931,x24932)+E(f339(x24933,x24934,x24931),f339(x24933,x24934,x24932)) % 177.51/177.20 [2494]~E(x24941,x24942)+E(f423(x24941,x24943,x24944,x24945),f423(x24942,x24943,x24944,x24945)) % 177.51/177.20 [2495]~E(x24951,x24952)+E(f423(x24953,x24951,x24954,x24955),f423(x24953,x24952,x24954,x24955)) % 177.51/177.20 [2496]~E(x24961,x24962)+E(f423(x24963,x24964,x24961,x24965),f423(x24963,x24964,x24962,x24965)) % 177.51/177.20 [2497]~E(x24971,x24972)+E(f423(x24973,x24974,x24975,x24971),f423(x24973,x24974,x24975,x24972)) % 177.51/177.20 [2498]~E(x24981,x24982)+E(f298(x24981,x24983,x24984),f298(x24982,x24983,x24984)) % 177.51/177.20 [2499]~E(x24991,x24992)+E(f298(x24993,x24991,x24994),f298(x24993,x24992,x24994)) % 177.51/177.20 [2500]~E(x25001,x25002)+E(f298(x25003,x25004,x25001),f298(x25003,x25004,x25002)) % 177.51/177.20 [2501]~E(x25011,x25012)+E(f474(x25011,x25013,x25014,x25015),f474(x25012,x25013,x25014,x25015)) % 177.51/177.20 [2502]~E(x25021,x25022)+E(f474(x25023,x25021,x25024,x25025),f474(x25023,x25022,x25024,x25025)) % 177.51/177.20 [2503]~E(x25031,x25032)+E(f474(x25033,x25034,x25031,x25035),f474(x25033,x25034,x25032,x25035)) % 177.51/177.20 [2504]~E(x25041,x25042)+E(f474(x25043,x25044,x25045,x25041),f474(x25043,x25044,x25045,x25042)) % 177.51/177.20 [2505]~E(x25051,x25052)+E(f669(x25051,x25053,x25054),f669(x25052,x25053,x25054)) % 177.51/177.20 [2506]~E(x25061,x25062)+E(f669(x25063,x25061,x25064),f669(x25063,x25062,x25064)) % 177.51/177.20 [2507]~E(x25071,x25072)+E(f669(x25073,x25074,x25071),f669(x25073,x25074,x25072)) % 177.51/177.20 [2508]~E(x25081,x25082)+E(f708(x25081,x25083,x25084),f708(x25082,x25083,x25084)) % 177.51/177.20 [2509]~E(x25091,x25092)+E(f708(x25093,x25091,x25094),f708(x25093,x25092,x25094)) % 177.51/177.20 [2510]~E(x25101,x25102)+E(f708(x25103,x25104,x25101),f708(x25103,x25104,x25102)) % 177.51/177.20 [2511]~E(x25111,x25112)+E(f654(x25111,x25113,x25114),f654(x25112,x25113,x25114)) % 177.51/177.20 [2512]~E(x25121,x25122)+E(f654(x25123,x25121,x25124),f654(x25123,x25122,x25124)) % 177.51/177.20 [2513]~E(x25131,x25132)+E(f654(x25133,x25134,x25131),f654(x25133,x25134,x25132)) % 177.51/177.20 [2514]~E(x25141,x25142)+E(f559(x25141,x25143,x25144,x25145,x25146,x25147),f559(x25142,x25143,x25144,x25145,x25146,x25147)) % 177.51/177.20 [2515]~E(x25151,x25152)+E(f559(x25153,x25151,x25154,x25155,x25156,x25157),f559(x25153,x25152,x25154,x25155,x25156,x25157)) % 177.51/177.20 [2516]~E(x25161,x25162)+E(f559(x25163,x25164,x25161,x25165,x25166,x25167),f559(x25163,x25164,x25162,x25165,x25166,x25167)) % 177.51/177.20 [2517]~E(x25171,x25172)+E(f559(x25173,x25174,x25175,x25171,x25176,x25177),f559(x25173,x25174,x25175,x25172,x25176,x25177)) % 177.51/177.20 [2518]~E(x25181,x25182)+E(f559(x25183,x25184,x25185,x25186,x25181,x25187),f559(x25183,x25184,x25185,x25186,x25182,x25187)) % 177.51/177.20 [2519]~E(x25191,x25192)+E(f559(x25193,x25194,x25195,x25196,x25197,x25191),f559(x25193,x25194,x25195,x25196,x25197,x25192)) % 177.51/177.20 [2520]~E(x25201,x25202)+E(f487(x25201,x25203),f487(x25202,x25203)) % 177.51/177.20 [2521]~E(x25211,x25212)+E(f487(x25213,x25211),f487(x25213,x25212)) % 177.51/177.20 [2522]~E(x25221,x25222)+E(f278(x25221),f278(x25222)) % 177.51/177.20 [2523]~E(x25231,x25232)+E(f765(x25231,x25233,x25234,x25235),f765(x25232,x25233,x25234,x25235)) % 177.51/177.20 [2524]~E(x25241,x25242)+E(f765(x25243,x25241,x25244,x25245),f765(x25243,x25242,x25244,x25245)) % 177.51/177.20 [2525]~E(x25251,x25252)+E(f765(x25253,x25254,x25251,x25255),f765(x25253,x25254,x25252,x25255)) % 177.51/177.20 [2526]~E(x25261,x25262)+E(f765(x25263,x25264,x25265,x25261),f765(x25263,x25264,x25265,x25262)) % 177.51/177.20 [2527]~E(x25271,x25272)+E(f549(x25271,x25273,x25274,x25275),f549(x25272,x25273,x25274,x25275)) % 177.51/177.20 [2528]~E(x25281,x25282)+E(f549(x25283,x25281,x25284,x25285),f549(x25283,x25282,x25284,x25285)) % 177.51/177.20 [2529]~E(x25291,x25292)+E(f549(x25293,x25294,x25291,x25295),f549(x25293,x25294,x25292,x25295)) % 177.51/177.20 [2530]~E(x25301,x25302)+E(f549(x25303,x25304,x25305,x25301),f549(x25303,x25304,x25305,x25302)) % 177.51/177.20 [2531]~E(x25311,x25312)+E(f464(x25311,x25313,x25314),f464(x25312,x25313,x25314)) % 177.51/177.20 [2532]~E(x25321,x25322)+E(f464(x25323,x25321,x25324),f464(x25323,x25322,x25324)) % 177.51/177.20 [2533]~E(x25331,x25332)+E(f464(x25333,x25334,x25331),f464(x25333,x25334,x25332)) % 177.51/177.20 [2534]~E(x25341,x25342)+E(f494(x25341,x25343,x25344,x25345),f494(x25342,x25343,x25344,x25345)) % 177.51/177.20 [2535]~E(x25351,x25352)+E(f494(x25353,x25351,x25354,x25355),f494(x25353,x25352,x25354,x25355)) % 177.51/177.20 [2536]~E(x25361,x25362)+E(f494(x25363,x25364,x25361,x25365),f494(x25363,x25364,x25362,x25365)) % 177.51/177.20 [2537]~E(x25371,x25372)+E(f494(x25373,x25374,x25375,x25371),f494(x25373,x25374,x25375,x25372)) % 177.51/177.20 [2538]~E(x25381,x25382)+E(f903(x25381,x25383,x25384,x25385,x25386),f903(x25382,x25383,x25384,x25385,x25386)) % 177.51/177.20 [2539]~E(x25391,x25392)+E(f903(x25393,x25391,x25394,x25395,x25396),f903(x25393,x25392,x25394,x25395,x25396)) % 177.51/177.20 [2540]~E(x25401,x25402)+E(f903(x25403,x25404,x25401,x25405,x25406),f903(x25403,x25404,x25402,x25405,x25406)) % 177.51/177.20 [2541]~E(x25411,x25412)+E(f903(x25413,x25414,x25415,x25411,x25416),f903(x25413,x25414,x25415,x25412,x25416)) % 177.51/177.20 [2542]~E(x25421,x25422)+E(f903(x25423,x25424,x25425,x25426,x25421),f903(x25423,x25424,x25425,x25426,x25422)) % 177.51/177.20 [2543]~E(x25431,x25432)+E(f704(x25431,x25433),f704(x25432,x25433)) % 177.51/177.20 [2544]~E(x25441,x25442)+E(f704(x25443,x25441),f704(x25443,x25442)) % 177.51/177.20 [2545]~E(x25451,x25452)+E(f742(x25451,x25453,x25454,x25455,x25456,x25457,x25458),f742(x25452,x25453,x25454,x25455,x25456,x25457,x25458)) % 177.51/177.20 [2546]~E(x25461,x25462)+E(f742(x25463,x25461,x25464,x25465,x25466,x25467,x25468),f742(x25463,x25462,x25464,x25465,x25466,x25467,x25468)) % 177.51/177.20 [2547]~E(x25471,x25472)+E(f742(x25473,x25474,x25471,x25475,x25476,x25477,x25478),f742(x25473,x25474,x25472,x25475,x25476,x25477,x25478)) % 177.51/177.20 [2548]~E(x25481,x25482)+E(f742(x25483,x25484,x25485,x25481,x25486,x25487,x25488),f742(x25483,x25484,x25485,x25482,x25486,x25487,x25488)) % 177.51/177.20 [2549]~E(x25491,x25492)+E(f742(x25493,x25494,x25495,x25496,x25491,x25497,x25498),f742(x25493,x25494,x25495,x25496,x25492,x25497,x25498)) % 177.51/177.20 [2550]~E(x25501,x25502)+E(f742(x25503,x25504,x25505,x25506,x25507,x25501,x25508),f742(x25503,x25504,x25505,x25506,x25507,x25502,x25508)) % 177.51/177.20 [2551]~E(x25511,x25512)+E(f742(x25513,x25514,x25515,x25516,x25517,x25518,x25511),f742(x25513,x25514,x25515,x25516,x25517,x25518,x25512)) % 177.51/177.20 [2552]~E(x25521,x25522)+E(f619(x25521,x25523,x25524,x25525,x25526),f619(x25522,x25523,x25524,x25525,x25526)) % 177.51/177.20 [2553]~E(x25531,x25532)+E(f619(x25533,x25531,x25534,x25535,x25536),f619(x25533,x25532,x25534,x25535,x25536)) % 177.51/177.20 [2554]~E(x25541,x25542)+E(f619(x25543,x25544,x25541,x25545,x25546),f619(x25543,x25544,x25542,x25545,x25546)) % 177.51/177.20 [2555]~E(x25551,x25552)+E(f619(x25553,x25554,x25555,x25551,x25556),f619(x25553,x25554,x25555,x25552,x25556)) % 177.51/177.20 [2556]~E(x25561,x25562)+E(f619(x25563,x25564,x25565,x25566,x25561),f619(x25563,x25564,x25565,x25566,x25562)) % 177.51/177.20 [2557]~E(x25571,x25572)+E(f892(x25571,x25573,x25574),f892(x25572,x25573,x25574)) % 177.51/177.20 [2558]~E(x25581,x25582)+E(f892(x25583,x25581,x25584),f892(x25583,x25582,x25584)) % 177.51/177.20 [2559]~E(x25591,x25592)+E(f892(x25593,x25594,x25591),f892(x25593,x25594,x25592)) % 177.51/177.20 [2560]~E(x25601,x25602)+E(f815(x25601,x25603,x25604),f815(x25602,x25603,x25604)) % 177.51/177.20 [2561]~E(x25611,x25612)+E(f815(x25613,x25611,x25614),f815(x25613,x25612,x25614)) % 177.51/177.20 [2562]~E(x25621,x25622)+E(f815(x25623,x25624,x25621),f815(x25623,x25624,x25622)) % 177.51/177.20 [2563]~E(x25631,x25632)+E(f739(x25631,x25633,x25634,x25635,x25636),f739(x25632,x25633,x25634,x25635,x25636)) % 177.51/177.20 [2564]~E(x25641,x25642)+E(f739(x25643,x25641,x25644,x25645,x25646),f739(x25643,x25642,x25644,x25645,x25646)) % 177.51/177.20 [2565]~E(x25651,x25652)+E(f739(x25653,x25654,x25651,x25655,x25656),f739(x25653,x25654,x25652,x25655,x25656)) % 177.51/177.20 [2566]~E(x25661,x25662)+E(f739(x25663,x25664,x25665,x25661,x25666),f739(x25663,x25664,x25665,x25662,x25666)) % 177.51/177.20 [2567]~E(x25671,x25672)+E(f739(x25673,x25674,x25675,x25676,x25671),f739(x25673,x25674,x25675,x25676,x25672)) % 177.51/177.20 [2568]~E(x25681,x25682)+E(f847(x25681,x25683,x25684,x25685,x25686,x25687),f847(x25682,x25683,x25684,x25685,x25686,x25687)) % 177.51/177.20 [2569]~E(x25691,x25692)+E(f847(x25693,x25691,x25694,x25695,x25696,x25697),f847(x25693,x25692,x25694,x25695,x25696,x25697)) % 177.51/177.20 [2570]~E(x25701,x25702)+E(f847(x25703,x25704,x25701,x25705,x25706,x25707),f847(x25703,x25704,x25702,x25705,x25706,x25707)) % 177.51/177.20 [2571]~E(x25711,x25712)+E(f847(x25713,x25714,x25715,x25711,x25716,x25717),f847(x25713,x25714,x25715,x25712,x25716,x25717)) % 177.51/177.20 [2572]~E(x25721,x25722)+E(f847(x25723,x25724,x25725,x25726,x25721,x25727),f847(x25723,x25724,x25725,x25726,x25722,x25727)) % 177.51/177.20 [2573]~E(x25731,x25732)+E(f847(x25733,x25734,x25735,x25736,x25737,x25731),f847(x25733,x25734,x25735,x25736,x25737,x25732)) % 177.51/177.20 [2574]~E(x25741,x25742)+E(f352(x25741,x25743,x25744,x25745),f352(x25742,x25743,x25744,x25745)) % 177.51/177.20 [2575]~E(x25751,x25752)+E(f352(x25753,x25751,x25754,x25755),f352(x25753,x25752,x25754,x25755)) % 177.51/177.20 [2576]~E(x25761,x25762)+E(f352(x25763,x25764,x25761,x25765),f352(x25763,x25764,x25762,x25765)) % 177.51/177.20 [2577]~E(x25771,x25772)+E(f352(x25773,x25774,x25775,x25771),f352(x25773,x25774,x25775,x25772)) % 177.51/177.20 [2578]~E(x25781,x25782)+E(f697(x25781,x25783,x25784,x25785,x25786),f697(x25782,x25783,x25784,x25785,x25786)) % 177.51/177.20 [2579]~E(x25791,x25792)+E(f697(x25793,x25791,x25794,x25795,x25796),f697(x25793,x25792,x25794,x25795,x25796)) % 177.51/177.20 [2580]~E(x25801,x25802)+E(f697(x25803,x25804,x25801,x25805,x25806),f697(x25803,x25804,x25802,x25805,x25806)) % 177.51/177.20 [2581]~E(x25811,x25812)+E(f697(x25813,x25814,x25815,x25811,x25816),f697(x25813,x25814,x25815,x25812,x25816)) % 177.51/177.20 [2582]~E(x25821,x25822)+E(f697(x25823,x25824,x25825,x25826,x25821),f697(x25823,x25824,x25825,x25826,x25822)) % 177.51/177.20 [2583]~E(x25831,x25832)+E(f830(x25831,x25833,x25834,x25835,x25836),f830(x25832,x25833,x25834,x25835,x25836)) % 177.51/177.20 [2584]~E(x25841,x25842)+E(f830(x25843,x25841,x25844,x25845,x25846),f830(x25843,x25842,x25844,x25845,x25846)) % 177.51/177.20 [2585]~E(x25851,x25852)+E(f830(x25853,x25854,x25851,x25855,x25856),f830(x25853,x25854,x25852,x25855,x25856)) % 177.51/177.20 [2586]~E(x25861,x25862)+E(f830(x25863,x25864,x25865,x25861,x25866),f830(x25863,x25864,x25865,x25862,x25866)) % 177.51/177.20 [2587]~E(x25871,x25872)+E(f830(x25873,x25874,x25875,x25876,x25871),f830(x25873,x25874,x25875,x25876,x25872)) % 177.51/177.20 [2588]~E(x25881,x25882)+E(f294(x25881,x25883,x25884),f294(x25882,x25883,x25884)) % 177.51/177.20 [2589]~E(x25891,x25892)+E(f294(x25893,x25891,x25894),f294(x25893,x25892,x25894)) % 177.51/177.20 [2590]~E(x25901,x25902)+E(f294(x25903,x25904,x25901),f294(x25903,x25904,x25902)) % 177.51/177.20 [2591]~E(x25911,x25912)+E(f504(x25911,x25913,x25914),f504(x25912,x25913,x25914)) % 177.51/177.20 [2592]~E(x25921,x25922)+E(f504(x25923,x25921,x25924),f504(x25923,x25922,x25924)) % 177.51/177.20 [2593]~E(x25931,x25932)+E(f504(x25933,x25934,x25931),f504(x25933,x25934,x25932)) % 177.51/177.20 [2594]~E(x25941,x25942)+E(f900(x25941,x25943,x25944,x25945),f900(x25942,x25943,x25944,x25945)) % 177.51/177.20 [2595]~E(x25951,x25952)+E(f900(x25953,x25951,x25954,x25955),f900(x25953,x25952,x25954,x25955)) % 177.51/177.20 [2596]~E(x25961,x25962)+E(f900(x25963,x25964,x25961,x25965),f900(x25963,x25964,x25962,x25965)) % 177.51/177.20 [2597]~E(x25971,x25972)+E(f900(x25973,x25974,x25975,x25971),f900(x25973,x25974,x25975,x25972)) % 177.51/177.20 [2598]~E(x25981,x25982)+E(f609(x25981,x25983,x25984),f609(x25982,x25983,x25984)) % 177.51/177.20 [2599]~E(x25991,x25992)+E(f609(x25993,x25991,x25994),f609(x25993,x25992,x25994)) % 177.51/177.20 [2600]~E(x26001,x26002)+E(f609(x26003,x26004,x26001),f609(x26003,x26004,x26002)) % 177.51/177.20 [2601]~E(x26011,x26012)+E(f390(x26011,x26013),f390(x26012,x26013)) % 177.51/177.20 [2602]~E(x26021,x26022)+E(f390(x26023,x26021),f390(x26023,x26022)) % 177.51/177.20 [2603]~E(x26031,x26032)+E(f224(x26031,x26033,x26034),f224(x26032,x26033,x26034)) % 177.51/177.20 [2604]~E(x26041,x26042)+E(f224(x26043,x26041,x26044),f224(x26043,x26042,x26044)) % 177.51/177.20 [2605]~E(x26051,x26052)+E(f224(x26053,x26054,x26051),f224(x26053,x26054,x26052)) % 177.51/177.20 [2606]~E(x26061,x26062)+E(f439(x26061,x26063,x26064,x26065),f439(x26062,x26063,x26064,x26065)) % 177.51/177.20 [2607]~E(x26071,x26072)+E(f439(x26073,x26071,x26074,x26075),f439(x26073,x26072,x26074,x26075)) % 177.51/177.20 [2608]~E(x26081,x26082)+E(f439(x26083,x26084,x26081,x26085),f439(x26083,x26084,x26082,x26085)) % 177.51/177.20 [2609]~E(x26091,x26092)+E(f439(x26093,x26094,x26095,x26091),f439(x26093,x26094,x26095,x26092)) % 177.51/177.20 [2610]~E(x26101,x26102)+E(f538(x26101,x26103,x26104,x26105),f538(x26102,x26103,x26104,x26105)) % 177.51/177.20 [2611]~E(x26111,x26112)+E(f538(x26113,x26111,x26114,x26115),f538(x26113,x26112,x26114,x26115)) % 177.51/177.20 [2612]~E(x26121,x26122)+E(f538(x26123,x26124,x26121,x26125),f538(x26123,x26124,x26122,x26125)) % 177.51/177.20 [2613]~E(x26131,x26132)+E(f538(x26133,x26134,x26135,x26131),f538(x26133,x26134,x26135,x26132)) % 177.51/177.20 [2614]~E(x26141,x26142)+E(f658(x26141,x26143,x26144),f658(x26142,x26143,x26144)) % 177.51/177.20 [2615]~E(x26151,x26152)+E(f658(x26153,x26151,x26154),f658(x26153,x26152,x26154)) % 177.51/177.20 [2616]~E(x26161,x26162)+E(f658(x26163,x26164,x26161),f658(x26163,x26164,x26162)) % 177.51/177.20 [2617]~E(x26171,x26172)+E(f335(x26171),f335(x26172)) % 177.51/177.20 [2618]~E(x26181,x26182)+E(f758(x26181,x26183,x26184),f758(x26182,x26183,x26184)) % 177.51/177.20 [2619]~E(x26191,x26192)+E(f758(x26193,x26191,x26194),f758(x26193,x26192,x26194)) % 177.51/177.20 [2620]~E(x26201,x26202)+E(f758(x26203,x26204,x26201),f758(x26203,x26204,x26202)) % 177.51/177.20 [2621]~E(x26211,x26212)+E(f454(x26211,x26213,x26214),f454(x26212,x26213,x26214)) % 177.51/177.20 [2622]~E(x26221,x26222)+E(f454(x26223,x26221,x26224),f454(x26223,x26222,x26224)) % 177.51/177.20 [2623]~E(x26231,x26232)+E(f454(x26233,x26234,x26231),f454(x26233,x26234,x26232)) % 177.51/177.20 [2624]~E(x26241,x26242)+E(f630(x26241,x26243,x26244),f630(x26242,x26243,x26244)) % 177.51/177.20 [2625]~E(x26251,x26252)+E(f630(x26253,x26251,x26254),f630(x26253,x26252,x26254)) % 177.51/177.20 [2626]~E(x26261,x26262)+E(f630(x26263,x26264,x26261),f630(x26263,x26264,x26262)) % 177.51/177.20 [2627]~E(x26271,x26272)+E(f748(x26271,x26273,x26274,x26275),f748(x26272,x26273,x26274,x26275)) % 177.51/177.20 [2628]~E(x26281,x26282)+E(f748(x26283,x26281,x26284,x26285),f748(x26283,x26282,x26284,x26285)) % 177.51/177.20 [2629]~E(x26291,x26292)+E(f748(x26293,x26294,x26291,x26295),f748(x26293,x26294,x26292,x26295)) % 177.51/177.20 [2630]~E(x26301,x26302)+E(f748(x26303,x26304,x26305,x26301),f748(x26303,x26304,x26305,x26302)) % 177.51/177.20 [2631]~E(x26311,x26312)+E(f236(x26311,x26313),f236(x26312,x26313)) % 177.51/177.20 [2632]~E(x26321,x26322)+E(f236(x26323,x26321),f236(x26323,x26322)) % 177.51/177.20 [2633]~E(x26331,x26332)+E(f199(x26331,x26333,x26334,x26335),f199(x26332,x26333,x26334,x26335)) % 177.51/177.20 [2634]~E(x26341,x26342)+E(f199(x26343,x26341,x26344,x26345),f199(x26343,x26342,x26344,x26345)) % 177.51/177.20 [2635]~E(x26351,x26352)+E(f199(x26353,x26354,x26351,x26355),f199(x26353,x26354,x26352,x26355)) % 177.51/177.20 [2636]~E(x26361,x26362)+E(f199(x26363,x26364,x26365,x26361),f199(x26363,x26364,x26365,x26362)) % 177.51/177.20 [2637]~E(x26371,x26372)+E(f885(x26371),f885(x26372)) % 177.51/177.20 [2638]~E(x26381,x26382)+E(f359(x26381,x26383,x26384,x26385,x26386),f359(x26382,x26383,x26384,x26385,x26386)) % 177.51/177.20 [2639]~E(x26391,x26392)+E(f359(x26393,x26391,x26394,x26395,x26396),f359(x26393,x26392,x26394,x26395,x26396)) % 177.51/177.20 [2640]~E(x26401,x26402)+E(f359(x26403,x26404,x26401,x26405,x26406),f359(x26403,x26404,x26402,x26405,x26406)) % 177.51/177.20 [2641]~E(x26411,x26412)+E(f359(x26413,x26414,x26415,x26411,x26416),f359(x26413,x26414,x26415,x26412,x26416)) % 177.51/177.20 [2642]~E(x26421,x26422)+E(f359(x26423,x26424,x26425,x26426,x26421),f359(x26423,x26424,x26425,x26426,x26422)) % 177.51/177.20 [2643]~E(x26431,x26432)+E(f831(x26431,x26433,x26434),f831(x26432,x26433,x26434)) % 177.51/177.20 [2644]~E(x26441,x26442)+E(f831(x26443,x26441,x26444),f831(x26443,x26442,x26444)) % 177.51/177.20 [2645]~E(x26451,x26452)+E(f831(x26453,x26454,x26451),f831(x26453,x26454,x26452)) % 177.51/177.20 [2646]~E(x26461,x26462)+E(f672(x26461,x26463,x26464),f672(x26462,x26463,x26464)) % 177.51/177.20 [2647]~E(x26471,x26472)+E(f672(x26473,x26471,x26474),f672(x26473,x26472,x26474)) % 177.51/177.20 [2648]~E(x26481,x26482)+E(f672(x26483,x26484,x26481),f672(x26483,x26484,x26482)) % 177.51/177.20 [2649]~E(x26491,x26492)+E(f684(x26491,x26493,x26494,x26495,x26496),f684(x26492,x26493,x26494,x26495,x26496)) % 177.51/177.20 [2650]~E(x26501,x26502)+E(f684(x26503,x26501,x26504,x26505,x26506),f684(x26503,x26502,x26504,x26505,x26506)) % 177.51/177.20 [2651]~E(x26511,x26512)+E(f684(x26513,x26514,x26511,x26515,x26516),f684(x26513,x26514,x26512,x26515,x26516)) % 177.51/177.20 [2652]~E(x26521,x26522)+E(f684(x26523,x26524,x26525,x26521,x26526),f684(x26523,x26524,x26525,x26522,x26526)) % 177.51/177.20 [2653]~E(x26531,x26532)+E(f684(x26533,x26534,x26535,x26536,x26531),f684(x26533,x26534,x26535,x26536,x26532)) % 177.51/177.20 [2654]~E(x26541,x26542)+E(f785(x26541,x26543,x26544,x26545,x26546,x26547,x26548),f785(x26542,x26543,x26544,x26545,x26546,x26547,x26548)) % 177.51/177.20 [2655]~E(x26551,x26552)+E(f785(x26553,x26551,x26554,x26555,x26556,x26557,x26558),f785(x26553,x26552,x26554,x26555,x26556,x26557,x26558)) % 177.51/177.20 [2656]~E(x26561,x26562)+E(f785(x26563,x26564,x26561,x26565,x26566,x26567,x26568),f785(x26563,x26564,x26562,x26565,x26566,x26567,x26568)) % 177.51/177.20 [2657]~E(x26571,x26572)+E(f785(x26573,x26574,x26575,x26571,x26576,x26577,x26578),f785(x26573,x26574,x26575,x26572,x26576,x26577,x26578)) % 177.51/177.20 [2658]~E(x26581,x26582)+E(f785(x26583,x26584,x26585,x26586,x26581,x26587,x26588),f785(x26583,x26584,x26585,x26586,x26582,x26587,x26588)) % 177.51/177.20 [2659]~E(x26591,x26592)+E(f785(x26593,x26594,x26595,x26596,x26597,x26591,x26598),f785(x26593,x26594,x26595,x26596,x26597,x26592,x26598)) % 177.51/177.20 [2660]~E(x26601,x26602)+E(f785(x26603,x26604,x26605,x26606,x26607,x26608,x26601),f785(x26603,x26604,x26605,x26606,x26607,x26608,x26602)) % 177.51/177.20 [2661]~E(x26611,x26612)+E(f585(x26611,x26613),f585(x26612,x26613)) % 177.51/177.20 [2662]~E(x26621,x26622)+E(f585(x26623,x26621),f585(x26623,x26622)) % 177.51/177.20 [2663]~E(x26631,x26632)+E(f813(x26631,x26633),f813(x26632,x26633)) % 177.51/177.20 [2664]~E(x26641,x26642)+E(f813(x26643,x26641),f813(x26643,x26642)) % 177.51/177.20 [2665]~E(x26651,x26652)+E(f867(x26651,x26653,x26654),f867(x26652,x26653,x26654)) % 177.51/177.20 [2666]~E(x26661,x26662)+E(f867(x26663,x26661,x26664),f867(x26663,x26662,x26664)) % 177.51/177.20 [2667]~E(x26671,x26672)+E(f867(x26673,x26674,x26671),f867(x26673,x26674,x26672)) % 177.51/177.20 [2668]~E(x26681,x26682)+E(f466(x26681,x26683,x26684),f466(x26682,x26683,x26684)) % 177.51/177.20 [2669]~E(x26691,x26692)+E(f466(x26693,x26691,x26694),f466(x26693,x26692,x26694)) % 177.51/177.20 [2670]~E(x26701,x26702)+E(f466(x26703,x26704,x26701),f466(x26703,x26704,x26702)) % 177.51/177.20 [2671]~E(x26711,x26712)+E(f548(x26711,x26713,x26714,x26715),f548(x26712,x26713,x26714,x26715)) % 177.51/177.20 [2672]~E(x26721,x26722)+E(f548(x26723,x26721,x26724,x26725),f548(x26723,x26722,x26724,x26725)) % 177.51/177.20 [2673]~E(x26731,x26732)+E(f548(x26733,x26734,x26731,x26735),f548(x26733,x26734,x26732,x26735)) % 177.51/177.20 [2674]~E(x26741,x26742)+E(f548(x26743,x26744,x26745,x26741),f548(x26743,x26744,x26745,x26742)) % 177.51/177.20 [2675]~E(x26751,x26752)+E(f644(x26751,x26753,x26754),f644(x26752,x26753,x26754)) % 177.51/177.20 [2676]~E(x26761,x26762)+E(f644(x26763,x26761,x26764),f644(x26763,x26762,x26764)) % 177.51/177.20 [2677]~E(x26771,x26772)+E(f644(x26773,x26774,x26771),f644(x26773,x26774,x26772)) % 177.51/177.20 [2678]~E(x26781,x26782)+E(f564(x26781,x26783,x26784,x26785,x26786,x26787,x26788,x26789),f564(x26782,x26783,x26784,x26785,x26786,x26787,x26788,x26789)) % 177.51/177.20 [2679]~E(x26791,x26792)+E(f564(x26793,x26791,x26794,x26795,x26796,x26797,x26798,x26799),f564(x26793,x26792,x26794,x26795,x26796,x26797,x26798,x26799)) % 177.51/177.20 [2680]~E(x26801,x26802)+E(f564(x26803,x26804,x26801,x26805,x26806,x26807,x26808,x26809),f564(x26803,x26804,x26802,x26805,x26806,x26807,x26808,x26809)) % 177.51/177.20 [2681]~E(x26811,x26812)+E(f564(x26813,x26814,x26815,x26811,x26816,x26817,x26818,x26819),f564(x26813,x26814,x26815,x26812,x26816,x26817,x26818,x26819)) % 177.51/177.20 [2682]~E(x26821,x26822)+E(f564(x26823,x26824,x26825,x26826,x26821,x26827,x26828,x26829),f564(x26823,x26824,x26825,x26826,x26822,x26827,x26828,x26829)) % 177.51/177.20 [2683]~E(x26831,x26832)+E(f564(x26833,x26834,x26835,x26836,x26837,x26831,x26838,x26839),f564(x26833,x26834,x26835,x26836,x26837,x26832,x26838,x26839)) % 177.51/177.20 [2684]~E(x26841,x26842)+E(f564(x26843,x26844,x26845,x26846,x26847,x26848,x26841,x26849),f564(x26843,x26844,x26845,x26846,x26847,x26848,x26842,x26849)) % 177.51/177.20 [2685]~E(x26851,x26852)+E(f564(x26853,x26854,x26855,x26856,x26857,x26858,x26859,x26851),f564(x26853,x26854,x26855,x26856,x26857,x26858,x26859,x26852)) % 177.51/177.20 [2686]~E(x26861,x26862)+E(f295(x26861,x26863,x26864),f295(x26862,x26863,x26864)) % 177.51/177.20 [2687]~E(x26871,x26872)+E(f295(x26873,x26871,x26874),f295(x26873,x26872,x26874)) % 177.51/177.20 [2688]~E(x26881,x26882)+E(f295(x26883,x26884,x26881),f295(x26883,x26884,x26882)) % 177.51/177.20 [2689]~E(x26891,x26892)+E(f605(x26891,x26893,x26894),f605(x26892,x26893,x26894)) % 177.51/177.20 [2690]~E(x26901,x26902)+E(f605(x26903,x26901,x26904),f605(x26903,x26902,x26904)) % 177.51/177.20 [2691]~E(x26911,x26912)+E(f605(x26913,x26914,x26911),f605(x26913,x26914,x26912)) % 177.51/177.20 [2692]~E(x26921,x26922)+E(f489(x26921,x26923),f489(x26922,x26923)) % 177.51/177.20 [2693]~E(x26931,x26932)+E(f489(x26933,x26931),f489(x26933,x26932)) % 177.51/177.20 [2694]~E(x26941,x26942)+E(f711(x26941,x26943,x26944),f711(x26942,x26943,x26944)) % 177.51/177.20 [2695]~E(x26951,x26952)+E(f711(x26953,x26951,x26954),f711(x26953,x26952,x26954)) % 177.51/177.20 [2696]~E(x26961,x26962)+E(f711(x26963,x26964,x26961),f711(x26963,x26964,x26962)) % 177.51/177.20 [2697]~E(x26971,x26972)+E(f597(x26971,x26973,x26974,x26975,x26976),f597(x26972,x26973,x26974,x26975,x26976)) % 177.51/177.20 [2698]~E(x26981,x26982)+E(f597(x26983,x26981,x26984,x26985,x26986),f597(x26983,x26982,x26984,x26985,x26986)) % 177.51/177.20 [2699]~E(x26991,x26992)+E(f597(x26993,x26994,x26991,x26995,x26996),f597(x26993,x26994,x26992,x26995,x26996)) % 177.51/177.20 [2700]~E(x27001,x27002)+E(f597(x27003,x27004,x27005,x27001,x27006),f597(x27003,x27004,x27005,x27002,x27006)) % 177.51/177.20 [2701]~E(x27011,x27012)+E(f597(x27013,x27014,x27015,x27016,x27011),f597(x27013,x27014,x27015,x27016,x27012)) % 177.51/177.20 [2702]~E(x27021,x27022)+E(f578(x27021,x27023,x27024,x27025),f578(x27022,x27023,x27024,x27025)) % 177.51/177.20 [2703]~E(x27031,x27032)+E(f578(x27033,x27031,x27034,x27035),f578(x27033,x27032,x27034,x27035)) % 177.51/177.20 [2704]~E(x27041,x27042)+E(f578(x27043,x27044,x27041,x27045),f578(x27043,x27044,x27042,x27045)) % 177.51/177.20 [2705]~E(x27051,x27052)+E(f578(x27053,x27054,x27055,x27051),f578(x27053,x27054,x27055,x27052)) % 177.51/177.20 [2706]~E(x27061,x27062)+E(f456(x27061,x27063,x27064,x27065,x27066),f456(x27062,x27063,x27064,x27065,x27066)) % 177.51/177.20 [2707]~E(x27071,x27072)+E(f456(x27073,x27071,x27074,x27075,x27076),f456(x27073,x27072,x27074,x27075,x27076)) % 177.51/177.20 [2708]~E(x27081,x27082)+E(f456(x27083,x27084,x27081,x27085,x27086),f456(x27083,x27084,x27082,x27085,x27086)) % 177.51/177.20 [2709]~E(x27091,x27092)+E(f456(x27093,x27094,x27095,x27091,x27096),f456(x27093,x27094,x27095,x27092,x27096)) % 177.51/177.20 [2710]~E(x27101,x27102)+E(f456(x27103,x27104,x27105,x27106,x27101),f456(x27103,x27104,x27105,x27106,x27102)) % 177.51/177.20 [2711]~E(x27111,x27112)+E(f807(x27111,x27113),f807(x27112,x27113)) % 177.51/177.20 [2712]~E(x27121,x27122)+E(f807(x27123,x27121),f807(x27123,x27122)) % 177.51/177.20 [2713]~E(x27131,x27132)+E(f864(x27131,x27133,x27134),f864(x27132,x27133,x27134)) % 177.51/177.20 [2714]~E(x27141,x27142)+E(f864(x27143,x27141,x27144),f864(x27143,x27142,x27144)) % 177.51/177.20 [2715]~E(x27151,x27152)+E(f864(x27153,x27154,x27151),f864(x27153,x27154,x27152)) % 177.51/177.20 [2716]~E(x27161,x27162)+E(f353(x27161,x27163,x27164),f353(x27162,x27163,x27164)) % 177.51/177.20 [2717]~E(x27171,x27172)+E(f353(x27173,x27171,x27174),f353(x27173,x27172,x27174)) % 177.51/177.20 [2718]~E(x27181,x27182)+E(f353(x27183,x27184,x27181),f353(x27183,x27184,x27182)) % 177.51/177.20 [2719]~E(x27191,x27192)+E(f782(x27191,x27193,x27194,x27195,x27196,x27197,x27198),f782(x27192,x27193,x27194,x27195,x27196,x27197,x27198)) % 177.51/177.20 [2720]~E(x27201,x27202)+E(f782(x27203,x27201,x27204,x27205,x27206,x27207,x27208),f782(x27203,x27202,x27204,x27205,x27206,x27207,x27208)) % 177.51/177.20 [2721]~E(x27211,x27212)+E(f782(x27213,x27214,x27211,x27215,x27216,x27217,x27218),f782(x27213,x27214,x27212,x27215,x27216,x27217,x27218)) % 177.51/177.20 [2722]~E(x27221,x27222)+E(f782(x27223,x27224,x27225,x27221,x27226,x27227,x27228),f782(x27223,x27224,x27225,x27222,x27226,x27227,x27228)) % 177.51/177.20 [2723]~E(x27231,x27232)+E(f782(x27233,x27234,x27235,x27236,x27231,x27237,x27238),f782(x27233,x27234,x27235,x27236,x27232,x27237,x27238)) % 177.51/177.20 [2724]~E(x27241,x27242)+E(f782(x27243,x27244,x27245,x27246,x27247,x27241,x27248),f782(x27243,x27244,x27245,x27246,x27247,x27242,x27248)) % 177.51/177.20 [2725]~E(x27251,x27252)+E(f782(x27253,x27254,x27255,x27256,x27257,x27258,x27251),f782(x27253,x27254,x27255,x27256,x27257,x27258,x27252)) % 177.51/177.20 [2726]~E(x27261,x27262)+E(f869(x27261,x27263,x27264),f869(x27262,x27263,x27264)) % 177.51/177.20 [2727]~E(x27271,x27272)+E(f869(x27273,x27271,x27274),f869(x27273,x27272,x27274)) % 177.51/177.20 [2728]~E(x27281,x27282)+E(f869(x27283,x27284,x27281),f869(x27283,x27284,x27282)) % 177.51/177.20 [2729]~E(x27291,x27292)+E(f596(x27291,x27293,x27294,x27295),f596(x27292,x27293,x27294,x27295)) % 177.51/177.20 [2730]~E(x27301,x27302)+E(f596(x27303,x27301,x27304,x27305),f596(x27303,x27302,x27304,x27305)) % 177.51/177.20 [2731]~E(x27311,x27312)+E(f596(x27313,x27314,x27311,x27315),f596(x27313,x27314,x27312,x27315)) % 177.51/177.20 [2732]~E(x27321,x27322)+E(f596(x27323,x27324,x27325,x27321),f596(x27323,x27324,x27325,x27322)) % 177.51/177.20 [2733]~E(x27331,x27332)+E(f391(x27331),f391(x27332)) % 177.51/177.20 [2734]~E(x27341,x27342)+E(f696(x27341,x27343,x27344,x27345,x27346),f696(x27342,x27343,x27344,x27345,x27346)) % 177.51/177.20 [2735]~E(x27351,x27352)+E(f696(x27353,x27351,x27354,x27355,x27356),f696(x27353,x27352,x27354,x27355,x27356)) % 177.51/177.20 [2736]~E(x27361,x27362)+E(f696(x27363,x27364,x27361,x27365,x27366),f696(x27363,x27364,x27362,x27365,x27366)) % 177.51/177.20 [2737]~E(x27371,x27372)+E(f696(x27373,x27374,x27375,x27371,x27376),f696(x27373,x27374,x27375,x27372,x27376)) % 177.51/177.20 [2738]~E(x27381,x27382)+E(f696(x27383,x27384,x27385,x27386,x27381),f696(x27383,x27384,x27385,x27386,x27382)) % 177.51/177.20 [2739]~E(x27391,x27392)+E(f428(x27391,x27393,x27394,x27395),f428(x27392,x27393,x27394,x27395)) % 177.51/177.20 [2740]~E(x27401,x27402)+E(f428(x27403,x27401,x27404,x27405),f428(x27403,x27402,x27404,x27405)) % 177.51/177.20 [2741]~E(x27411,x27412)+E(f428(x27413,x27414,x27411,x27415),f428(x27413,x27414,x27412,x27415)) % 177.51/177.20 [2742]~E(x27421,x27422)+E(f428(x27423,x27424,x27425,x27421),f428(x27423,x27424,x27425,x27422)) % 177.51/177.20 [2743]~E(x27431,x27432)+E(f45(x27431),f45(x27432)) % 177.51/177.20 [2744]~E(x27441,x27442)+E(f642(x27441,x27443,x27444,x27445),f642(x27442,x27443,x27444,x27445)) % 177.51/177.20 [2745]~E(x27451,x27452)+E(f642(x27453,x27451,x27454,x27455),f642(x27453,x27452,x27454,x27455)) % 177.51/177.20 [2746]~E(x27461,x27462)+E(f642(x27463,x27464,x27461,x27465),f642(x27463,x27464,x27462,x27465)) % 177.51/177.20 [2747]~E(x27471,x27472)+E(f642(x27473,x27474,x27475,x27471),f642(x27473,x27474,x27475,x27472)) % 177.51/177.20 [2748]~E(x27481,x27482)+E(f279(x27481,x27483,x27484,x27485),f279(x27482,x27483,x27484,x27485)) % 177.51/177.20 [2749]~E(x27491,x27492)+E(f279(x27493,x27491,x27494,x27495),f279(x27493,x27492,x27494,x27495)) % 177.51/177.20 [2750]~E(x27501,x27502)+E(f279(x27503,x27504,x27501,x27505),f279(x27503,x27504,x27502,x27505)) % 177.51/177.20 [2751]~E(x27511,x27512)+E(f279(x27513,x27514,x27515,x27511),f279(x27513,x27514,x27515,x27512)) % 177.51/177.20 [2752]~E(x27521,x27522)+E(f890(x27521,x27523),f890(x27522,x27523)) % 177.51/177.20 [2753]~E(x27531,x27532)+E(f890(x27533,x27531),f890(x27533,x27532)) % 177.51/177.20 [2754]~E(x27541,x27542)+E(f775(x27541,x27543),f775(x27542,x27543)) % 177.51/177.20 [2755]~E(x27551,x27552)+E(f775(x27553,x27551),f775(x27553,x27552)) % 177.51/177.20 [2756]~E(x27561,x27562)+E(f795(x27561,x27563,x27564,x27565,x27566),f795(x27562,x27563,x27564,x27565,x27566)) % 177.51/177.20 [2757]~E(x27571,x27572)+E(f795(x27573,x27571,x27574,x27575,x27576),f795(x27573,x27572,x27574,x27575,x27576)) % 177.51/177.20 [2758]~E(x27581,x27582)+E(f795(x27583,x27584,x27581,x27585,x27586),f795(x27583,x27584,x27582,x27585,x27586)) % 177.51/177.20 [2759]~E(x27591,x27592)+E(f795(x27593,x27594,x27595,x27591,x27596),f795(x27593,x27594,x27595,x27592,x27596)) % 177.51/177.20 [2760]~E(x27601,x27602)+E(f795(x27603,x27604,x27605,x27606,x27601),f795(x27603,x27604,x27605,x27606,x27602)) % 177.51/177.20 [2761]~E(x27611,x27612)+E(f653(x27611,x27613,x27614),f653(x27612,x27613,x27614)) % 177.51/177.20 [2762]~E(x27621,x27622)+E(f653(x27623,x27621,x27624),f653(x27623,x27622,x27624)) % 177.51/177.20 [2763]~E(x27631,x27632)+E(f653(x27633,x27634,x27631),f653(x27633,x27634,x27632)) % 177.51/177.20 [2764]~E(x27641,x27642)+E(f455(x27641,x27643,x27644,x27645,x27646),f455(x27642,x27643,x27644,x27645,x27646)) % 177.51/177.20 [2765]~E(x27651,x27652)+E(f455(x27653,x27651,x27654,x27655,x27656),f455(x27653,x27652,x27654,x27655,x27656)) % 177.51/177.20 [2766]~E(x27661,x27662)+E(f455(x27663,x27664,x27661,x27665,x27666),f455(x27663,x27664,x27662,x27665,x27666)) % 177.51/177.20 [2767]~E(x27671,x27672)+E(f455(x27673,x27674,x27675,x27671,x27676),f455(x27673,x27674,x27675,x27672,x27676)) % 177.51/177.20 [2768]~E(x27681,x27682)+E(f455(x27683,x27684,x27685,x27686,x27681),f455(x27683,x27684,x27685,x27686,x27682)) % 177.51/177.20 [2769]~E(x27691,x27692)+E(f833(x27691,x27693,x27694),f833(x27692,x27693,x27694)) % 177.51/177.20 [2770]~E(x27701,x27702)+E(f833(x27703,x27701,x27704),f833(x27703,x27702,x27704)) % 177.51/177.20 [2771]~E(x27711,x27712)+E(f833(x27713,x27714,x27711),f833(x27713,x27714,x27712)) % 177.51/177.20 [2772]~E(x27721,x27722)+E(f817(x27721,x27723),f817(x27722,x27723)) % 177.51/177.20 [2773]~E(x27731,x27732)+E(f817(x27733,x27731),f817(x27733,x27732)) % 177.51/177.20 [2774]~E(x27741,x27742)+E(f544(x27741,x27743,x27744,x27745),f544(x27742,x27743,x27744,x27745)) % 177.51/177.20 [2775]~E(x27751,x27752)+E(f544(x27753,x27751,x27754,x27755),f544(x27753,x27752,x27754,x27755)) % 177.51/177.20 [2776]~E(x27761,x27762)+E(f544(x27763,x27764,x27761,x27765),f544(x27763,x27764,x27762,x27765)) % 177.51/177.20 [2777]~E(x27771,x27772)+E(f544(x27773,x27774,x27775,x27771),f544(x27773,x27774,x27775,x27772)) % 177.51/177.20 [2778]~E(x27781,x27782)+E(f517(x27781,x27783,x27784),f517(x27782,x27783,x27784)) % 177.51/177.20 [2779]~E(x27791,x27792)+E(f517(x27793,x27791,x27794),f517(x27793,x27792,x27794)) % 177.51/177.20 [2780]~E(x27801,x27802)+E(f517(x27803,x27804,x27801),f517(x27803,x27804,x27802)) % 177.51/177.20 [2781]~E(x27811,x27812)+E(f780(x27811,x27813),f780(x27812,x27813)) % 177.51/177.20 [2782]~E(x27821,x27822)+E(f780(x27823,x27821),f780(x27823,x27822)) % 177.51/177.20 [2783]~E(x27831,x27832)+E(f737(x27831,x27833,x27834,x27835,x27836),f737(x27832,x27833,x27834,x27835,x27836)) % 177.51/177.20 [2784]~E(x27841,x27842)+E(f737(x27843,x27841,x27844,x27845,x27846),f737(x27843,x27842,x27844,x27845,x27846)) % 177.51/177.20 [2785]~E(x27851,x27852)+E(f737(x27853,x27854,x27851,x27855,x27856),f737(x27853,x27854,x27852,x27855,x27856)) % 177.51/177.20 [2786]~E(x27861,x27862)+E(f737(x27863,x27864,x27865,x27861,x27866),f737(x27863,x27864,x27865,x27862,x27866)) % 177.51/177.20 [2787]~E(x27871,x27872)+E(f737(x27873,x27874,x27875,x27876,x27871),f737(x27873,x27874,x27875,x27876,x27872)) % 177.51/177.20 [2788]~E(x27881,x27882)+E(f550(x27881,x27883,x27884,x27885),f550(x27882,x27883,x27884,x27885)) % 177.51/177.20 [2789]~E(x27891,x27892)+E(f550(x27893,x27891,x27894,x27895),f550(x27893,x27892,x27894,x27895)) % 177.51/177.20 [2790]~E(x27901,x27902)+E(f550(x27903,x27904,x27901,x27905),f550(x27903,x27904,x27902,x27905)) % 177.51/177.20 [2791]~E(x27911,x27912)+E(f550(x27913,x27914,x27915,x27911),f550(x27913,x27914,x27915,x27912)) % 177.51/177.20 [2792]~E(x27921,x27922)+E(f387(x27921),f387(x27922)) % 177.51/177.20 [2793]~E(x27931,x27932)+E(f800(x27931,x27933),f800(x27932,x27933)) % 177.51/177.20 [2794]~E(x27941,x27942)+E(f800(x27943,x27941),f800(x27943,x27942)) % 177.51/177.20 [2795]~E(x27951,x27952)+E(f94(x27951,x27953,x27954),f94(x27952,x27953,x27954)) % 177.51/177.20 [2796]~E(x27961,x27962)+E(f94(x27963,x27961,x27964),f94(x27963,x27962,x27964)) % 177.51/177.20 [2797]~E(x27971,x27972)+E(f94(x27973,x27974,x27971),f94(x27973,x27974,x27972)) % 177.51/177.20 [2798]~E(x27981,x27982)+E(f334(x27981),f334(x27982)) % 177.51/177.20 [2799]~E(x27991,x27992)+E(f905(x27991,x27993,x27994,x27995,x27996),f905(x27992,x27993,x27994,x27995,x27996)) % 177.51/177.20 [2800]~E(x28001,x28002)+E(f905(x28003,x28001,x28004,x28005,x28006),f905(x28003,x28002,x28004,x28005,x28006)) % 177.51/177.20 [2801]~E(x28011,x28012)+E(f905(x28013,x28014,x28011,x28015,x28016),f905(x28013,x28014,x28012,x28015,x28016)) % 177.51/177.20 [2802]~E(x28021,x28022)+E(f905(x28023,x28024,x28025,x28021,x28026),f905(x28023,x28024,x28025,x28022,x28026)) % 177.51/177.20 [2803]~E(x28031,x28032)+E(f905(x28033,x28034,x28035,x28036,x28031),f905(x28033,x28034,x28035,x28036,x28032)) % 177.51/177.20 [2804]~E(x28041,x28042)+E(f392(x28041,x28043),f392(x28042,x28043)) % 177.51/177.20 [2805]~E(x28051,x28052)+E(f392(x28053,x28051),f392(x28053,x28052)) % 177.51/177.20 [2806]~E(x28061,x28062)+E(f883(x28061),f883(x28062)) % 177.51/177.20 [2807]~E(x28071,x28072)+E(f237(x28071,x28073),f237(x28072,x28073)) % 177.51/177.20 [2808]~E(x28081,x28082)+E(f237(x28083,x28081),f237(x28083,x28082)) % 177.51/177.20 [2809]~E(x28091,x28092)+E(f607(x28091,x28093),f607(x28092,x28093)) % 177.51/177.20 [2810]~E(x28101,x28102)+E(f607(x28103,x28101),f607(x28103,x28102)) % 177.51/177.20 [2811]~E(x28111,x28112)+E(f625(x28111,x28113,x28114,x28115,x28116),f625(x28112,x28113,x28114,x28115,x28116)) % 177.51/177.20 [2812]~E(x28121,x28122)+E(f625(x28123,x28121,x28124,x28125,x28126),f625(x28123,x28122,x28124,x28125,x28126)) % 177.51/177.20 [2813]~E(x28131,x28132)+E(f625(x28133,x28134,x28131,x28135,x28136),f625(x28133,x28134,x28132,x28135,x28136)) % 177.51/177.20 [2814]~E(x28141,x28142)+E(f625(x28143,x28144,x28145,x28141,x28146),f625(x28143,x28144,x28145,x28142,x28146)) % 177.51/177.20 [2815]~E(x28151,x28152)+E(f625(x28153,x28154,x28155,x28156,x28151),f625(x28153,x28154,x28155,x28156,x28152)) % 177.51/177.20 [2816]~E(x28161,x28162)+E(f534(x28161),f534(x28162)) % 177.51/177.20 [2817]~E(x28171,x28172)+E(f21(x28171,x28173),f21(x28172,x28173)) % 177.51/177.20 [2818]~E(x28181,x28182)+E(f21(x28183,x28181),f21(x28183,x28182)) % 177.51/177.20 [2819]~E(x28191,x28192)+E(f373(x28191,x28193,x28194),f373(x28192,x28193,x28194)) % 177.51/177.20 [2820]~E(x28201,x28202)+E(f373(x28203,x28201,x28204),f373(x28203,x28202,x28204)) % 177.51/177.20 [2821]~E(x28211,x28212)+E(f373(x28213,x28214,x28211),f373(x28213,x28214,x28212)) % 177.51/177.20 [2822]~E(x28221,x28222)+E(f686(x28221,x28223,x28224),f686(x28222,x28223,x28224)) % 177.51/177.20 [2823]~E(x28231,x28232)+E(f686(x28233,x28231,x28234),f686(x28233,x28232,x28234)) % 177.51/177.20 [2824]~E(x28241,x28242)+E(f686(x28243,x28244,x28241),f686(x28243,x28244,x28242)) % 177.51/177.20 [2825]~E(x28251,x28252)+E(f816(x28251,x28253,x28254),f816(x28252,x28253,x28254)) % 177.51/177.20 [2826]~E(x28261,x28262)+E(f816(x28263,x28261,x28264),f816(x28263,x28262,x28264)) % 177.51/177.20 [2827]~E(x28271,x28272)+E(f816(x28273,x28274,x28271),f816(x28273,x28274,x28272)) % 177.51/177.20 [2828]~E(x28281,x28282)+E(f404(x28281),f404(x28282)) % 177.51/177.20 [2829]~P1(x28291)+P1(x28292)+~E(x28291,x28292) % 177.51/177.20 [2830]~P2(x28301)+P2(x28302)+~E(x28301,x28302) % 177.51/177.20 [2831]~P93(x28311)+P93(x28312)+~E(x28311,x28312) % 177.51/177.20 [2832]~P65(x28321)+P65(x28322)+~E(x28321,x28322) % 177.51/177.20 [2833]P11(x28332,x28333)+~E(x28331,x28332)+~P11(x28331,x28333) % 177.51/177.20 [2834]P11(x28343,x28342)+~E(x28341,x28342)+~P11(x28343,x28341) % 177.51/177.20 [2835]~P66(x28351)+P66(x28352)+~E(x28351,x28352) % 177.51/177.20 [2836]~P111(x28361)+P111(x28362)+~E(x28361,x28362) % 177.51/177.20 [2837]~P64(x28371)+P64(x28372)+~E(x28371,x28372) % 177.51/177.20 [2838]~P127(x28381)+P127(x28382)+~E(x28381,x28382) % 177.51/177.20 [2839]~P67(x28391)+P67(x28392)+~E(x28391,x28392) % 177.51/177.20 [2840]~P106(x28401)+P106(x28402)+~E(x28401,x28402) % 177.51/177.20 [2841]~P107(x28411)+P107(x28412)+~E(x28411,x28412) % 177.51/177.20 [2842]P23(x28422,x28423,x28424,x28425)+~E(x28421,x28422)+~P23(x28421,x28423,x28424,x28425) % 177.51/177.20 [2843]P23(x28433,x28432,x28434,x28435)+~E(x28431,x28432)+~P23(x28433,x28431,x28434,x28435) % 177.51/177.20 [2844]P23(x28443,x28444,x28442,x28445)+~E(x28441,x28442)+~P23(x28443,x28444,x28441,x28445) % 177.51/177.20 [2845]P23(x28453,x28454,x28455,x28452)+~E(x28451,x28452)+~P23(x28453,x28454,x28455,x28451) % 177.51/177.20 [2846]~P81(x28461)+P81(x28462)+~E(x28461,x28462) % 177.51/177.20 [2847]P148(x28472,x28473,x28474)+~E(x28471,x28472)+~P148(x28471,x28473,x28474) % 177.51/177.20 [2848]P148(x28483,x28482,x28484)+~E(x28481,x28482)+~P148(x28483,x28481,x28484) % 177.51/177.20 [2849]P148(x28493,x28494,x28492)+~E(x28491,x28492)+~P148(x28493,x28494,x28491) % 177.51/177.20 [2850]~P108(x28501)+P108(x28502)+~E(x28501,x28502) % 177.51/177.20 [2851]~P88(x28511)+P88(x28512)+~E(x28511,x28512) % 177.51/177.20 [2852]~P119(x28521)+P119(x28522)+~E(x28521,x28522) % 177.51/177.20 [2853]~P109(x28531)+P109(x28532)+~E(x28531,x28532) % 177.51/177.20 [2854]~P58(x28541)+P58(x28542)+~E(x28541,x28542) % 177.51/177.20 [2855]~P126(x28551)+P126(x28552)+~E(x28551,x28552) % 177.51/177.20 [2856]~P94(x28561)+P94(x28562)+~E(x28561,x28562) % 177.51/177.20 [2857]~P110(x28571)+P110(x28572)+~E(x28571,x28572) % 177.51/177.20 [2858]~P100(x28581)+P100(x28582)+~E(x28581,x28582) % 177.51/177.20 [2859]P13(x28592,x28593)+~E(x28591,x28592)+~P13(x28591,x28593) % 177.51/177.20 [2860]P13(x28603,x28602)+~E(x28601,x28602)+~P13(x28603,x28601) % 177.51/177.20 [2861]P17(x28612,x28613,x28614,x28615)+~E(x28611,x28612)+~P17(x28611,x28613,x28614,x28615) % 177.51/177.20 [2862]P17(x28623,x28622,x28624,x28625)+~E(x28621,x28622)+~P17(x28623,x28621,x28624,x28625) % 177.51/177.20 [2863]P17(x28633,x28634,x28632,x28635)+~E(x28631,x28632)+~P17(x28633,x28634,x28631,x28635) % 177.51/177.20 [2864]P17(x28643,x28644,x28645,x28642)+~E(x28641,x28642)+~P17(x28643,x28644,x28645,x28641) % 177.51/177.20 [2865]~P68(x28651)+P68(x28652)+~E(x28651,x28652) % 177.51/177.20 [2866]~P63(x28661)+P63(x28662)+~E(x28661,x28662) % 177.51/177.20 [2867]~P62(x28671)+P62(x28672)+~E(x28671,x28672) % 177.51/177.20 [2868]~P78(x28681)+P78(x28682)+~E(x28681,x28682) % 177.51/177.20 [2869]~P69(x28691)+P69(x28692)+~E(x28691,x28692) % 177.51/177.20 [2870]P24(x28702,x28703,x28704,x28705,x28706)+~E(x28701,x28702)+~P24(x28701,x28703,x28704,x28705,x28706) % 177.51/177.20 [2871]P24(x28713,x28712,x28714,x28715,x28716)+~E(x28711,x28712)+~P24(x28713,x28711,x28714,x28715,x28716) % 177.51/177.20 [2872]P24(x28723,x28724,x28722,x28725,x28726)+~E(x28721,x28722)+~P24(x28723,x28724,x28721,x28725,x28726) % 177.51/177.20 [2873]P24(x28733,x28734,x28735,x28732,x28736)+~E(x28731,x28732)+~P24(x28733,x28734,x28735,x28731,x28736) % 177.51/177.20 [2874]P24(x28743,x28744,x28745,x28746,x28742)+~E(x28741,x28742)+~P24(x28743,x28744,x28745,x28746,x28741) % 177.51/177.20 [2875]P6(x28752,x28753,x28754)+~E(x28751,x28752)+~P6(x28751,x28753,x28754) % 177.51/177.20 [2876]P6(x28763,x28762,x28764)+~E(x28761,x28762)+~P6(x28763,x28761,x28764) % 177.51/177.20 [2877]P6(x28773,x28774,x28772)+~E(x28771,x28772)+~P6(x28773,x28774,x28771) % 177.51/177.20 [2878]~P70(x28781)+P70(x28782)+~E(x28781,x28782) % 177.51/177.20 [2879]P29(x28792,x28793,x28794)+~E(x28791,x28792)+~P29(x28791,x28793,x28794) % 177.51/177.20 [2880]P29(x28803,x28802,x28804)+~E(x28801,x28802)+~P29(x28803,x28801,x28804) % 177.51/177.20 [2881]P29(x28813,x28814,x28812)+~E(x28811,x28812)+~P29(x28813,x28814,x28811) % 177.51/177.20 [2882]P147(x28822,x28823,x28824)+~E(x28821,x28822)+~P147(x28821,x28823,x28824) % 177.51/177.20 [2883]P147(x28833,x28832,x28834)+~E(x28831,x28832)+~P147(x28833,x28831,x28834) % 177.51/177.20 [2884]P147(x28843,x28844,x28842)+~E(x28841,x28842)+~P147(x28843,x28844,x28841) % 177.51/177.20 [2885]~P71(x28851)+P71(x28852)+~E(x28851,x28852) % 177.51/177.20 [2886]P22(x28862,x28863,x28864)+~E(x28861,x28862)+~P22(x28861,x28863,x28864) % 177.51/177.20 [2887]P22(x28873,x28872,x28874)+~E(x28871,x28872)+~P22(x28873,x28871,x28874) % 177.51/177.20 [2888]P22(x28883,x28884,x28882)+~E(x28881,x28882)+~P22(x28883,x28884,x28881) % 177.51/177.20 [2889]P14(x28892,x28893,x28894)+~E(x28891,x28892)+~P14(x28891,x28893,x28894) % 177.51/177.20 [2890]P14(x28903,x28902,x28904)+~E(x28901,x28902)+~P14(x28903,x28901,x28904) % 177.51/177.20 [2891]P14(x28913,x28914,x28912)+~E(x28911,x28912)+~P14(x28913,x28914,x28911) % 177.51/177.20 [2892]~P82(x28921)+P82(x28922)+~E(x28921,x28922) % 177.51/177.20 [2893]P37(x28932,x28933)+~E(x28931,x28932)+~P37(x28931,x28933) % 177.51/177.20 [2894]P37(x28943,x28942)+~E(x28941,x28942)+~P37(x28943,x28941) % 177.51/177.20 [2895]~P102(x28951)+P102(x28952)+~E(x28951,x28952) % 177.51/177.20 [2896]~P83(x28961)+P83(x28962)+~E(x28961,x28962) % 177.51/177.20 [2897]P52(x28972,x28973,x28974)+~E(x28971,x28972)+~P52(x28971,x28973,x28974) % 177.51/177.20 [2898]P52(x28983,x28982,x28984)+~E(x28981,x28982)+~P52(x28983,x28981,x28984) % 177.51/177.20 [2899]P52(x28993,x28994,x28992)+~E(x28991,x28992)+~P52(x28993,x28994,x28991) % 177.51/177.20 [2900]~P4(x29001)+P4(x29002)+~E(x29001,x29002) % 177.51/177.20 [2901]~P74(x29011)+P74(x29012)+~E(x29011,x29012) % 177.51/177.20 [2902]~P72(x29021)+P72(x29022)+~E(x29021,x29022) % 177.51/177.20 [2903]~P133(x29031)+P133(x29032)+~E(x29031,x29032) % 177.51/177.20 [2904]P26(x29042,x29043)+~E(x29041,x29042)+~P26(x29041,x29043) % 177.51/177.20 [2905]P26(x29053,x29052)+~E(x29051,x29052)+~P26(x29053,x29051) % 177.51/177.20 [2906]~P85(x29061)+P85(x29062)+~E(x29061,x29062) % 177.51/177.20 [2907]~P3(x29071)+P3(x29072)+~E(x29071,x29072) % 177.51/177.20 [2908]P31(x29082,x29083,x29084)+~E(x29081,x29082)+~P31(x29081,x29083,x29084) % 177.51/177.20 [2909]P31(x29093,x29092,x29094)+~E(x29091,x29092)+~P31(x29093,x29091,x29094) % 177.51/177.20 [2910]P31(x29103,x29104,x29102)+~E(x29101,x29102)+~P31(x29103,x29104,x29101) % 177.51/177.20 [2911]~P139(x29111)+P139(x29112)+~E(x29111,x29112) % 177.51/177.20 [2912]~P38(x29121)+P38(x29122)+~E(x29121,x29122) % 177.51/177.20 [2913]P27(x29132,x29133,x29134)+~E(x29131,x29132)+~P27(x29131,x29133,x29134) % 177.51/177.20 [2914]P27(x29143,x29142,x29144)+~E(x29141,x29142)+~P27(x29143,x29141,x29144) % 177.51/177.20 [2915]P27(x29153,x29154,x29152)+~E(x29151,x29152)+~P27(x29153,x29154,x29151) % 177.51/177.20 [2916]P15(x29162,x29163,x29164)+~E(x29161,x29162)+~P15(x29161,x29163,x29164) % 177.51/177.20 [2917]P15(x29173,x29172,x29174)+~E(x29171,x29172)+~P15(x29173,x29171,x29174) % 177.51/177.20 [2918]P15(x29183,x29184,x29182)+~E(x29181,x29182)+~P15(x29183,x29184,x29181) % 177.51/177.20 [2919]~P112(x29191)+P112(x29192)+~E(x29191,x29192) % 177.51/177.20 [2920]~P76(x29201)+P76(x29202)+~E(x29201,x29202) % 177.51/177.20 [2921]~P142(x29211)+P142(x29212)+~E(x29211,x29212) % 177.51/177.20 [2922]~P144(x29221)+P144(x29222)+~E(x29221,x29222) % 177.51/177.20 [2923]P33(x29232,x29233,x29234)+~E(x29231,x29232)+~P33(x29231,x29233,x29234) % 177.51/177.20 [2924]P33(x29243,x29242,x29244)+~E(x29241,x29242)+~P33(x29243,x29241,x29244) % 177.51/177.20 [2925]P33(x29253,x29254,x29252)+~E(x29251,x29252)+~P33(x29253,x29254,x29251) % 177.51/177.20 [2926]~P113(x29261)+P113(x29262)+~E(x29261,x29262) % 177.51/177.20 [2927]P30(x29272,x29273,x29274,x29275)+~E(x29271,x29272)+~P30(x29271,x29273,x29274,x29275) % 177.51/177.20 [2928]P30(x29283,x29282,x29284,x29285)+~E(x29281,x29282)+~P30(x29283,x29281,x29284,x29285) % 177.51/177.20 [2929]P30(x29293,x29294,x29292,x29295)+~E(x29291,x29292)+~P30(x29293,x29294,x29291,x29295) % 177.51/177.20 [2930]P30(x29303,x29304,x29305,x29302)+~E(x29301,x29302)+~P30(x29303,x29304,x29305,x29301) % 177.51/177.20 [2931]~P130(x29311)+P130(x29312)+~E(x29311,x29312) % 177.51/177.20 [2932]P41(x29322,x29323)+~E(x29321,x29322)+~P41(x29321,x29323) % 177.51/177.20 [2933]P41(x29333,x29332)+~E(x29331,x29332)+~P41(x29333,x29331) % 177.51/177.20 [2934]~P140(x29341)+P140(x29342)+~E(x29341,x29342) % 177.51/177.20 [2935]P5(x29352,x29353)+~E(x29351,x29352)+~P5(x29351,x29353) % 177.51/177.20 [2936]P5(x29363,x29362)+~E(x29361,x29362)+~P5(x29363,x29361) % 177.51/177.20 [2937]~P114(x29371)+P114(x29372)+~E(x29371,x29372) % 177.51/177.20 [2938]~P75(x29381)+P75(x29382)+~E(x29381,x29382) % 177.51/177.20 [2939]P56(x29392,x29393,x29394,x29395)+~E(x29391,x29392)+~P56(x29391,x29393,x29394,x29395) % 177.51/177.20 [2940]P56(x29403,x29402,x29404,x29405)+~E(x29401,x29402)+~P56(x29403,x29401,x29404,x29405) % 177.51/177.20 [2941]P56(x29413,x29414,x29412,x29415)+~E(x29411,x29412)+~P56(x29413,x29414,x29411,x29415) % 177.51/177.20 [2942]P56(x29423,x29424,x29425,x29422)+~E(x29421,x29422)+~P56(x29423,x29424,x29425,x29421) % 177.51/177.20 [2943]P36(x29432,x29433)+~E(x29431,x29432)+~P36(x29431,x29433) % 177.51/177.20 [2944]P36(x29443,x29442)+~E(x29441,x29442)+~P36(x29443,x29441) % 177.51/177.20 [2945]P55(x29452,x29453)+~E(x29451,x29452)+~P55(x29451,x29453) % 177.51/177.20 [2946]P55(x29463,x29462)+~E(x29461,x29462)+~P55(x29463,x29461) % 177.51/177.20 [2947]~P86(x29471)+P86(x29472)+~E(x29471,x29472) % 177.51/177.20 [2948]~P87(x29481)+P87(x29482)+~E(x29481,x29482) % 177.51/177.20 [2949]P57(x29492,x29493)+~E(x29491,x29492)+~P57(x29491,x29493) % 177.51/177.20 [2950]P57(x29503,x29502)+~E(x29501,x29502)+~P57(x29503,x29501) % 177.51/177.20 [2951]~P120(x29511)+P120(x29512)+~E(x29511,x29512) % 177.51/177.20 [2952]~P136(x29521)+P136(x29522)+~E(x29521,x29522) % 177.51/177.20 [2953]~P96(x29531)+P96(x29532)+~E(x29531,x29532) % 177.51/177.20 [2954]P49(x29542,x29543)+~E(x29541,x29542)+~P49(x29541,x29543) % 177.51/177.20 [2955]P49(x29553,x29552)+~E(x29551,x29552)+~P49(x29553,x29551) % 177.51/177.20 [2956]~P61(x29561)+P61(x29562)+~E(x29561,x29562) % 177.51/177.20 [2957]~P115(x29571)+P115(x29572)+~E(x29571,x29572) % 177.51/177.20 [2958]~P97(x29581)+P97(x29582)+~E(x29581,x29582) % 177.51/177.20 [2959]~P101(x29591)+P101(x29592)+~E(x29591,x29592) % 177.51/177.20 [2960]P50(x29602,x29603,x29604)+~E(x29601,x29602)+~P50(x29601,x29603,x29604) % 177.51/177.20 [2961]P50(x29613,x29612,x29614)+~E(x29611,x29612)+~P50(x29613,x29611,x29614) % 177.51/177.20 [2962]P50(x29623,x29624,x29622)+~E(x29621,x29622)+~P50(x29623,x29624,x29621) % 177.51/177.20 [2963]P21(x29632,x29633,x29634,x29635,x29636,x29637)+~E(x29631,x29632)+~P21(x29631,x29633,x29634,x29635,x29636,x29637) % 177.51/177.20 [2964]P21(x29643,x29642,x29644,x29645,x29646,x29647)+~E(x29641,x29642)+~P21(x29643,x29641,x29644,x29645,x29646,x29647) % 177.51/177.20 [2965]P21(x29653,x29654,x29652,x29655,x29656,x29657)+~E(x29651,x29652)+~P21(x29653,x29654,x29651,x29655,x29656,x29657) % 177.51/177.20 [2966]P21(x29663,x29664,x29665,x29662,x29666,x29667)+~E(x29661,x29662)+~P21(x29663,x29664,x29665,x29661,x29666,x29667) % 177.51/177.20 [2967]P21(x29673,x29674,x29675,x29676,x29672,x29677)+~E(x29671,x29672)+~P21(x29673,x29674,x29675,x29676,x29671,x29677) % 177.51/177.20 [2968]P21(x29683,x29684,x29685,x29686,x29687,x29682)+~E(x29681,x29682)+~P21(x29683,x29684,x29685,x29686,x29687,x29681) % 177.51/177.20 [2969]~P98(x29691)+P98(x29692)+~E(x29691,x29692) % 177.51/177.20 [2970]~P79(x29701)+P79(x29702)+~E(x29701,x29702) % 177.51/177.20 [2971]~P60(x29711)+P60(x29712)+~E(x29711,x29712) % 177.51/177.20 [2972]~P146(x29721)+P146(x29722)+~E(x29721,x29722) % 177.51/177.20 [2973]~P80(x29731)+P80(x29732)+~E(x29731,x29732) % 177.51/177.20 [2974]~P116(x29741)+P116(x29742)+~E(x29741,x29742) % 177.51/177.20 [2975]P9(x29752,x29753,x29754,x29755)+~E(x29751,x29752)+~P9(x29751,x29753,x29754,x29755) % 177.51/177.20 [2976]P9(x29763,x29762,x29764,x29765)+~E(x29761,x29762)+~P9(x29763,x29761,x29764,x29765) % 177.51/177.20 [2977]P9(x29773,x29774,x29772,x29775)+~E(x29771,x29772)+~P9(x29773,x29774,x29771,x29775) % 177.51/177.20 [2978]P9(x29783,x29784,x29785,x29782)+~E(x29781,x29782)+~P9(x29783,x29784,x29785,x29781) % 177.51/177.20 [2979]P12(x29792,x29793,x29794)+~E(x29791,x29792)+~P12(x29791,x29793,x29794) % 177.51/177.20 [2980]P12(x29803,x29802,x29804)+~E(x29801,x29802)+~P12(x29803,x29801,x29804) % 177.51/177.20 [2981]P12(x29813,x29814,x29812)+~E(x29811,x29812)+~P12(x29813,x29814,x29811) % 177.51/177.20 [2982]P32(x29822,x29823,x29824,x29825,x29826)+~E(x29821,x29822)+~P32(x29821,x29823,x29824,x29825,x29826) % 177.51/177.20 [2983]P32(x29833,x29832,x29834,x29835,x29836)+~E(x29831,x29832)+~P32(x29833,x29831,x29834,x29835,x29836) % 177.51/177.20 [2984]P32(x29843,x29844,x29842,x29845,x29846)+~E(x29841,x29842)+~P32(x29843,x29844,x29841,x29845,x29846) % 177.51/177.20 [2985]P32(x29853,x29854,x29855,x29852,x29856)+~E(x29851,x29852)+~P32(x29853,x29854,x29855,x29851,x29856) % 177.51/177.20 [2986]P32(x29863,x29864,x29865,x29866,x29862)+~E(x29861,x29862)+~P32(x29863,x29864,x29865,x29866,x29861) % 177.51/177.20 [2987]P53(x29872,x29873,x29874)+~E(x29871,x29872)+~P53(x29871,x29873,x29874) % 177.51/177.20 [2988]P53(x29883,x29882,x29884)+~E(x29881,x29882)+~P53(x29883,x29881,x29884) % 177.51/177.20 [2989]P53(x29893,x29894,x29892)+~E(x29891,x29892)+~P53(x29893,x29894,x29891) % 177.51/177.20 [2990]~P141(x29901)+P141(x29902)+~E(x29901,x29902) % 177.51/177.20 [2991]~P118(x29911)+P118(x29912)+~E(x29911,x29912) % 177.51/177.20 [2992]P35(x29922,x29923)+~E(x29921,x29922)+~P35(x29921,x29923) % 177.51/177.20 [2993]P35(x29933,x29932)+~E(x29931,x29932)+~P35(x29933,x29931) % 177.51/177.20 [2994]~P123(x29941)+P123(x29942)+~E(x29941,x29942) % 177.51/177.20 [2995]~P122(x29951)+P122(x29952)+~E(x29951,x29952) % 177.51/177.20 [2996]~P135(x29961)+P135(x29962)+~E(x29961,x29962) % 177.51/177.20 [2997]~P104(x29971)+P104(x29972)+~E(x29971,x29972) % 177.51/177.20 [2998]~P84(x29981)+P84(x29982)+~E(x29981,x29982) % 177.51/177.20 [2999]~P92(x29991)+P92(x29992)+~E(x29991,x29992) % 177.51/177.20 [3000]~P95(x30001)+P95(x30002)+~E(x30001,x30002) % 177.51/177.20 [3001]P25(x30012,x30013)+~E(x30011,x30012)+~P25(x30011,x30013) % 177.51/177.20 [3002]P25(x30023,x30022)+~E(x30021,x30022)+~P25(x30023,x30021) % 177.51/177.20 [3003]P19(x30032,x30033,x30034,x30035,x30036)+~E(x30031,x30032)+~P19(x30031,x30033,x30034,x30035,x30036) % 177.51/177.20 [3004]P19(x30043,x30042,x30044,x30045,x30046)+~E(x30041,x30042)+~P19(x30043,x30041,x30044,x30045,x30046) % 177.51/177.20 [3005]P19(x30053,x30054,x30052,x30055,x30056)+~E(x30051,x30052)+~P19(x30053,x30054,x30051,x30055,x30056) % 177.51/177.20 [3006]P19(x30063,x30064,x30065,x30062,x30066)+~E(x30061,x30062)+~P19(x30063,x30064,x30065,x30061,x30066) % 177.51/177.20 [3007]P19(x30073,x30074,x30075,x30076,x30072)+~E(x30071,x30072)+~P19(x30073,x30074,x30075,x30076,x30071) % 177.51/177.20 [3008]~P91(x30081)+P91(x30082)+~E(x30081,x30082) % 177.51/177.20 [3009]P8(x30092,x30093,x30094,x30095,x30096)+~E(x30091,x30092)+~P8(x30091,x30093,x30094,x30095,x30096) % 177.51/177.20 [3010]P8(x30103,x30102,x30104,x30105,x30106)+~E(x30101,x30102)+~P8(x30103,x30101,x30104,x30105,x30106) % 177.51/177.20 [3011]P8(x30113,x30114,x30112,x30115,x30116)+~E(x30111,x30112)+~P8(x30113,x30114,x30111,x30115,x30116) % 177.51/177.20 [3012]P8(x30123,x30124,x30125,x30122,x30126)+~E(x30121,x30122)+~P8(x30123,x30124,x30125,x30121,x30126) % 177.51/177.20 [3013]P8(x30133,x30134,x30135,x30136,x30132)+~E(x30131,x30132)+~P8(x30133,x30134,x30135,x30136,x30131) % 177.51/177.20 [3014]P54(x30142,x30143,x30144,x30145,x30146)+~E(x30141,x30142)+~P54(x30141,x30143,x30144,x30145,x30146) % 177.51/177.20 [3015]P54(x30153,x30152,x30154,x30155,x30156)+~E(x30151,x30152)+~P54(x30153,x30151,x30154,x30155,x30156) % 177.51/177.20 [3016]P54(x30163,x30164,x30162,x30165,x30166)+~E(x30161,x30162)+~P54(x30163,x30164,x30161,x30165,x30166) % 177.51/177.20 [3017]P54(x30173,x30174,x30175,x30172,x30176)+~E(x30171,x30172)+~P54(x30173,x30174,x30175,x30171,x30176) % 177.51/177.20 [3018]P54(x30183,x30184,x30185,x30186,x30182)+~E(x30181,x30182)+~P54(x30183,x30184,x30185,x30186,x30181) % 177.51/177.20 [3019]~P129(x30191)+P129(x30192)+~E(x30191,x30192) % 177.51/177.20 [3020]~P89(x30201)+P89(x30202)+~E(x30201,x30202) % 177.51/177.20 [3021]P16(x30212,x30213,x30214)+~E(x30211,x30212)+~P16(x30211,x30213,x30214) % 177.51/177.20 [3022]P16(x30223,x30222,x30224)+~E(x30221,x30222)+~P16(x30223,x30221,x30224) % 177.51/177.20 [3023]P16(x30233,x30234,x30232)+~E(x30231,x30232)+~P16(x30233,x30234,x30231) % 177.51/177.20 [3024]~P134(x30241)+P134(x30242)+~E(x30241,x30242) % 177.51/177.20 [3025]~P121(x30251)+P121(x30252)+~E(x30251,x30252) % 177.51/177.20 [3026]~P138(x30261)+P138(x30262)+~E(x30261,x30262) % 177.51/177.20 [3027]~P145(x30271)+P145(x30272)+~E(x30271,x30272) % 177.51/177.20 [3028]P40(x30282,x30283,x30284,x30285,x30286,x30287)+~E(x30281,x30282)+~P40(x30281,x30283,x30284,x30285,x30286,x30287) % 177.51/177.20 [3029]P40(x30293,x30292,x30294,x30295,x30296,x30297)+~E(x30291,x30292)+~P40(x30293,x30291,x30294,x30295,x30296,x30297) % 177.51/177.20 [3030]P40(x30303,x30304,x30302,x30305,x30306,x30307)+~E(x30301,x30302)+~P40(x30303,x30304,x30301,x30305,x30306,x30307) % 177.51/177.20 [3031]P40(x30313,x30314,x30315,x30312,x30316,x30317)+~E(x30311,x30312)+~P40(x30313,x30314,x30315,x30311,x30316,x30317) % 177.51/177.20 [3032]P40(x30323,x30324,x30325,x30326,x30322,x30327)+~E(x30321,x30322)+~P40(x30323,x30324,x30325,x30326,x30321,x30327) % 177.51/177.20 [3033]P40(x30333,x30334,x30335,x30336,x30337,x30332)+~E(x30331,x30332)+~P40(x30333,x30334,x30335,x30336,x30337,x30331) % 177.51/177.20 [3034]P18(x30342,x30343,x30344,x30345)+~E(x30341,x30342)+~P18(x30341,x30343,x30344,x30345) % 177.51/177.20 [3035]P18(x30353,x30352,x30354,x30355)+~E(x30351,x30352)+~P18(x30353,x30351,x30354,x30355) % 177.51/177.20 [3036]P18(x30363,x30364,x30362,x30365)+~E(x30361,x30362)+~P18(x30363,x30364,x30361,x30365) % 177.51/177.20 [3037]P18(x30373,x30374,x30375,x30372)+~E(x30371,x30372)+~P18(x30373,x30374,x30375,x30371) % 177.51/177.20 [3038]P28(x30382,x30383,x30384)+~E(x30381,x30382)+~P28(x30381,x30383,x30384) % 177.51/177.20 [3039]P28(x30393,x30392,x30394)+~E(x30391,x30392)+~P28(x30393,x30391,x30394) % 177.51/177.20 [3040]P28(x30403,x30404,x30402)+~E(x30401,x30402)+~P28(x30403,x30404,x30401) % 177.51/177.20 [3041]P51(x30412,x30413)+~E(x30411,x30412)+~P51(x30411,x30413) % 177.51/177.20 [3042]P51(x30423,x30422)+~E(x30421,x30422)+~P51(x30423,x30421) % 177.51/177.20 [3043]~P99(x30431)+P99(x30432)+~E(x30431,x30432) % 177.51/177.20 [3044]~P143(x30441)+P143(x30442)+~E(x30441,x30442) % 177.51/177.20 [3045]~P90(x30451)+P90(x30452)+~E(x30451,x30452) % 177.51/177.20 [3046]~P128(x30461)+P128(x30462)+~E(x30461,x30462) % 177.51/177.20 [3047]P48(x30472,x30473)+~E(x30471,x30472)+~P48(x30471,x30473) % 177.51/177.20 [3048]P48(x30483,x30482)+~E(x30481,x30482)+~P48(x30483,x30481) % 177.51/177.20 [3049]~P59(x30491)+P59(x30492)+~E(x30491,x30492) % 177.51/177.20 [3050]P42(x30502,x30503)+~E(x30501,x30502)+~P42(x30501,x30503) % 177.51/177.20 [3051]P42(x30513,x30512)+~E(x30511,x30512)+~P42(x30513,x30511) % 177.51/177.20 [3052]P10(x30522,x30523,x30524,x30525,x30526,x30527)+~E(x30521,x30522)+~P10(x30521,x30523,x30524,x30525,x30526,x30527) % 177.51/177.20 [3053]P10(x30533,x30532,x30534,x30535,x30536,x30537)+~E(x30531,x30532)+~P10(x30533,x30531,x30534,x30535,x30536,x30537) % 177.51/177.20 [3054]P10(x30543,x30544,x30542,x30545,x30546,x30547)+~E(x30541,x30542)+~P10(x30543,x30544,x30541,x30545,x30546,x30547) % 177.51/177.20 [3055]P10(x30553,x30554,x30555,x30552,x30556,x30557)+~E(x30551,x30552)+~P10(x30553,x30554,x30555,x30551,x30556,x30557) % 177.51/177.20 [3056]P10(x30563,x30564,x30565,x30566,x30562,x30567)+~E(x30561,x30562)+~P10(x30563,x30564,x30565,x30566,x30561,x30567) % 177.51/177.20 [3057]P10(x30573,x30574,x30575,x30576,x30577,x30572)+~E(x30571,x30572)+~P10(x30573,x30574,x30575,x30576,x30577,x30571) % 177.51/177.20 [3058]~P43(x30581)+P43(x30582)+~E(x30581,x30582) % 177.51/177.20 [3059]~P131(x30591)+P131(x30592)+~E(x30591,x30592) % 177.51/177.20 [3060]~P137(x30601)+P137(x30602)+~E(x30601,x30602) % 177.51/177.20 [3061]~P77(x30611)+P77(x30612)+~E(x30611,x30612) % 177.51/177.20 [3062]~P105(x30621)+P105(x30622)+~E(x30621,x30622) % 177.51/177.20 [3063]P20(x30632,x30633,x30634,x30635,x30636,x30637)+~E(x30631,x30632)+~P20(x30631,x30633,x30634,x30635,x30636,x30637) % 177.51/177.20 [3064]P20(x30643,x30642,x30644,x30645,x30646,x30647)+~E(x30641,x30642)+~P20(x30643,x30641,x30644,x30645,x30646,x30647) % 177.51/177.20 [3065]P20(x30653,x30654,x30652,x30655,x30656,x30657)+~E(x30651,x30652)+~P20(x30653,x30654,x30651,x30655,x30656,x30657) % 177.51/177.20 [3066]P20(x30663,x30664,x30665,x30662,x30666,x30667)+~E(x30661,x30662)+~P20(x30663,x30664,x30665,x30661,x30666,x30667) % 177.51/177.20 [3067]P20(x30673,x30674,x30675,x30676,x30672,x30677)+~E(x30671,x30672)+~P20(x30673,x30674,x30675,x30676,x30671,x30677) % 177.51/177.20 [3068]P20(x30683,x30684,x30685,x30686,x30687,x30682)+~E(x30681,x30682)+~P20(x30683,x30684,x30685,x30686,x30687,x30681) % 177.51/177.20 [3069]P47(x30692,x30693)+~E(x30691,x30692)+~P47(x30691,x30693) % 177.51/177.20 [3070]P47(x30703,x30702)+~E(x30701,x30702)+~P47(x30703,x30701) % 177.51/177.20 [3071]P46(x30712,x30713,x30714)+~E(x30711,x30712)+~P46(x30711,x30713,x30714) % 177.51/177.20 [3072]P46(x30723,x30722,x30724)+~E(x30721,x30722)+~P46(x30723,x30721,x30724) % 177.51/177.20 [3073]P46(x30733,x30734,x30732)+~E(x30731,x30732)+~P46(x30733,x30734,x30731) % 177.51/177.20 [3074]P39(x30742,x30743,x30744,x30745)+~E(x30741,x30742)+~P39(x30741,x30743,x30744,x30745) % 177.51/177.20 [3075]P39(x30753,x30752,x30754,x30755)+~E(x30751,x30752)+~P39(x30753,x30751,x30754,x30755) % 177.51/177.20 [3076]P39(x30763,x30764,x30762,x30765)+~E(x30761,x30762)+~P39(x30763,x30764,x30761,x30765) % 177.51/177.20 [3077]P39(x30773,x30774,x30775,x30772)+~E(x30771,x30772)+~P39(x30773,x30774,x30775,x30771) % 177.51/177.20 [3078]~P34(x30781)+P34(x30782)+~E(x30781,x30782) % 177.51/177.20 [3079]P45(x30792,x30793,x30794)+~E(x30791,x30792)+~P45(x30791,x30793,x30794) % 177.51/177.20 [3080]P45(x30803,x30802,x30804)+~E(x30801,x30802)+~P45(x30803,x30801,x30804) % 177.51/177.20 [3081]P45(x30813,x30814,x30812)+~E(x30811,x30812)+~P45(x30813,x30814,x30811) % 177.51/177.20 [3082]~P124(x30821)+P124(x30822)+~E(x30821,x30822) % 177.51/177.20 [3083]~P73(x30831)+P73(x30832)+~E(x30831,x30832) % 177.51/177.20 [3084]P44(x30842,x30843)+~E(x30841,x30842)+~P44(x30841,x30843) % 177.51/177.20 [3085]P44(x30853,x30852)+~E(x30851,x30852)+~P44(x30853,x30851) % 177.51/177.20 [3086]~P117(x30861)+P117(x30862)+~E(x30861,x30862) % 177.51/177.20 [3087]P7(x30872,x30873,x30874)+~E(x30871,x30872)+~P7(x30871,x30873,x30874) % 177.51/177.20 [3088]P7(x30883,x30882,x30884)+~E(x30881,x30882)+~P7(x30883,x30881,x30884) % 177.51/177.20 [3089]P7(x30893,x30894,x30892)+~E(x30891,x30892)+~P7(x30893,x30894,x30891) % 177.51/177.20 [3090]~P103(x30901)+P103(x30902)+~E(x30901,x30902) % 177.51/177.20 [3091]~P132(x30911)+P132(x30912)+~E(x30911,x30912) % 177.51/177.20 [3092]~P125(x30921)+P125(x30922)+~E(x30921,x30922) % 177.51/177.20 % 177.51/177.20 %------------------------------------------- % 177.51/177.23 cnf(10454,plain, % 177.51/177.23 (~E(f327(a113,x104541),x104541)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10464,plain, % 177.51/177.23 (~E(f327(a113,x104641),x104641)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10477,plain, % 177.51/177.23 (~E(f327(a113,x104771),x104771)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10482,plain, % 177.51/177.23 (~P1(f327(f327(f173(x104821),f114(x104821)),x104822))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10485,plain, % 177.51/177.23 (~P1(f327(f327(f173(x104851),f114(x104851)),x104852))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10488,plain, % 177.51/177.23 (~E(f327(a113,x104881),x104881)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10491,plain, % 177.51/177.23 (~E(f327(a113,x104911),x104911)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10494,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x104941),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(10497,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x104971),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(10514,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x105141)),x105141))), % 177.51/177.23 inference(rename_variables,[],[4713])). % 177.51/177.23 cnf(10517,plain, % 177.51/177.23 (~E(f327(f327(f152(x105171),x105172),x105173),x105173)), % 177.51/177.23 inference(rename_variables,[],[4670])). % 177.51/177.23 cnf(10523,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x105231),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(10526,plain, % 177.51/177.23 (E(f327(f284(x105261,x105261),f263(x105261,x105262)),x105262)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(10529,plain, % 177.51/177.23 (E(f327(f284(x105291,x105291),f263(x105291,x105292)),x105292)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(10534,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x105341),x105341))), % 177.51/177.23 inference(rename_variables,[],[4703])). % 177.51/177.23 cnf(10539,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x105391),x105392)),x105392))), % 177.51/177.23 inference(rename_variables,[],[4727])). % 177.51/177.23 cnf(10542,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x105421),x105422)),x105422))), % 177.51/177.23 inference(rename_variables,[],[4727])). % 177.51/177.23 cnf(10549,plain, % 177.51/177.23 (~E(x105491,f327(a113,x105491))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,3288,3453,10526,3328,3392,3324,3352,3336,4670,3560,3476,4707,10494,10497,4704,4665,4712,10482,4703,4713,4314,4710,3469,4696,4729,4727,10539,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343])). % 177.51/177.23 cnf(10563,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x105631),x105631))), % 177.51/177.23 inference(rename_variables,[],[4703])). % 177.51/177.23 cnf(10566,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),f46(a915,x105661,x105662)),x105661))), % 177.51/177.23 inference(rename_variables,[],[3949])). % 177.51/177.23 cnf(10587,plain, % 177.51/177.23 (E(f327(f36(a915),f327(f282(a915),x105871)),x105871)), % 177.51/177.23 inference(rename_variables,[],[3388])). % 177.51/177.23 cnf(10595,plain, % 177.51/177.23 (~E(f327(a113,x105951),x105951)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10598,plain, % 177.51/177.23 (~E(f327(a113,x105981),x105981)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10601,plain, % 177.51/177.23 (~E(f327(a113,x106011),x106011)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10603,plain, % 177.51/177.23 (P1(f327(a195,a98))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,3288,3453,10526,3328,3392,3324,3352,3336,3423,4670,3388,4732,3408,3560,3476,4707,10494,10497,4078,3495,4704,4665,4712,10482,4703,10534,10563,3585,4012,3949,4713,10514,4314,4710,4694,3469,4696,4729,4727,10539,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486])). % 177.51/177.23 cnf(10606,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x106061),f327(a113,x106061)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(10615,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x106151),x106151))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(10622,plain, % 177.51/177.23 (E(f327(f284(x106221,x106221),f263(x106221,x106222)),x106222)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(10625,plain, % 177.51/177.23 (E(f327(f284(x106251,x106251),f263(x106251,x106252)),x106252)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(10642,plain, % 177.51/177.23 (P1(f327(f327(f234(a1),x106421),x106421))), % 177.51/177.23 inference(rename_variables,[],[3493])). % 177.51/177.23 cnf(10647,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x106471),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(10650,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x106501,a910)),x106502),f242(f922(x106501,a910))))), % 177.51/177.23 inference(rename_variables,[],[3874])). % 177.51/177.23 cnf(10655,plain, % 177.51/177.23 (~P1(f327(f327(f173(x106551),f114(x106551)),x106552))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10684,plain, % 177.51/177.23 (~E(f327(f327(f152(x106841),x106842),x106843),x106843)), % 177.51/177.23 inference(rename_variables,[],[4670])). % 177.51/177.23 cnf(10687,plain, % 177.51/177.23 (~E(f327(a113,x106871),f2(a915))), % 177.51/177.23 inference(rename_variables,[],[4661])). % 177.51/177.23 cnf(10698,plain, % 177.51/177.23 (P1(f327(f327(f234(a1),x106981),x106981))), % 177.51/177.23 inference(rename_variables,[],[3493])). % 177.51/177.23 cnf(10703,plain, % 177.51/177.23 (~E(f327(a113,x107031),x107031)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10706,plain, % 177.51/177.23 (~P1(f327(f327(f190(f922(x107061,f922(x107062,a910))),x107063),x107064))), % 177.51/177.23 inference(rename_variables,[],[4730])). % 177.51/177.23 cnf(10713,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x107131),x107131))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(10726,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x107261),f327(a113,x107261)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(10747,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x107471,a910)),x107472),f242(f922(x107471,a910))))), % 177.51/177.23 inference(rename_variables,[],[3874])). % 177.51/177.23 cnf(10750,plain, % 177.51/177.23 (~P1(f327(f327(f173(x107501),f114(x107501)),x107502))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10769,plain, % 177.51/177.23 (~P1(f327(f327(f173(x107691),f114(x107691)),x107692))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10776,plain, % 177.51/177.23 (~P1(f327(f327(f173(x107761),f114(x107761)),x107762))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10787,plain, % 177.51/177.23 (~E(f327(a113,x107871),f2(a915))), % 177.51/177.23 inference(rename_variables,[],[4661])). % 177.51/177.23 cnf(10792,plain, % 177.51/177.23 (P1(f327(f327(f329(x107921),x107922),f242(f922(x107921,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(10799,plain, % 177.51/177.23 (~P1(f327(f327(f173(x107991),f114(x107991)),x107992))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10804,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x108041),f327(a113,x108041)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(10807,plain, % 177.51/177.23 (~P1(f327(f327(f173(x108071),f114(x108071)),x108072))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10810,plain, % 177.51/177.23 (~P1(f327(f327(f173(x108101),f114(x108101)),x108102))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10813,plain, % 177.51/177.23 (~P1(f327(f62(x108131,x108132,f190(f922(x108131,a910))),x108133))), % 177.51/177.23 inference(rename_variables,[],[4726])). % 177.51/177.23 cnf(10816,plain, % 177.51/177.23 (~P1(f327(f62(x108161,x108162,f190(f922(x108161,a910))),x108163))), % 177.51/177.23 inference(rename_variables,[],[4726])). % 177.51/177.23 cnf(10819,plain, % 177.51/177.23 (~P1(f327(f327(f190(f922(x108191,f922(x108192,a910))),x108193),x108194))), % 177.51/177.23 inference(rename_variables,[],[4730])). % 177.51/177.23 cnf(10822,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x108221),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(10827,plain, % 177.51/177.23 (~P1(f327(f327(f173(x108271),f114(x108271)),x108272))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(10837,plain, % 177.51/177.23 (~E(f327(f169(x108371),f327(a113,f327(f327(f135(x108371),f327(f169(x108371),x108372)),f327(f327(f152(x108371),x108373),f114(x108371))))),f327(f327(f152(x108371),x108373),x108372))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,4273,4732,3408,3856,3560,10606,10726,10804,3476,4707,10494,10497,10523,10647,4720,3931,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,3493,10642,4703,10534,10563,3645,3585,4012,3949,10566,4713,10514,4314,4710,4694,3469,3473,4697,4696,4726,10813,4729,4730,10706,3972,4727,10539,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189])). % 177.51/177.23 cnf(10838,plain, % 177.51/177.23 (~E(f327(a113,x108381),x108381)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(10856,plain, % 177.51/177.23 (P1(f327(f327(f235(a100),f327(a3,x108561)),f327(a3,f327(a113,x108561))))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,4273,4732,3408,3856,3560,10606,10726,10804,3944,3476,4707,10494,10497,10523,10647,4720,3931,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,3493,10642,4703,10534,10563,3645,3585,4012,3949,10566,4713,10514,4314,4710,4694,3469,3473,4697,4696,4726,10813,4729,4730,10706,3972,4727,10539,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275])). % 177.51/177.23 cnf(10863,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x108631),x108631))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(10866,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x108661),f327(f327(f81(a915),x108661),x108661)))), % 177.51/177.23 inference(rename_variables,[],[3756])). % 177.51/177.23 cnf(10868,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x108681),f327(f327(f81(a915),f327(a113,x108681)),f327(a113,x108681))))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,4273,4732,3408,3856,3560,10606,10726,10804,3944,3476,4707,10494,10497,10523,10647,4720,3931,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,3493,10642,4703,10534,10563,3645,3585,4012,3949,10566,4713,10514,4314,4710,4694,3469,3473,4697,4696,4726,10813,3756,10866,4729,4730,10706,3972,4727,10539,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299])). % 177.51/177.23 cnf(10869,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x108691),f327(f327(f81(a915),x108691),x108691)))), % 177.51/177.23 inference(rename_variables,[],[3756])). % 177.51/177.23 cnf(10872,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x108721),f327(a113,f327(f327(f80(a915),x108722),x108721))))), % 177.51/177.23 inference(rename_variables,[],[3942])). % 177.51/177.23 cnf(10877,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x108771),f327(a113,x108771)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(10880,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x108801),f327(a113,x108801)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(10883,plain, % 177.51/177.23 (P1(f327(f327(f329(x108831),x108832),f242(f922(x108831,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(10902,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x109021)),x109021))), % 177.51/177.23 inference(rename_variables,[],[4713])). % 177.51/177.23 cnf(10905,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x109051)),x109051))), % 177.51/177.23 inference(rename_variables,[],[4713])). % 177.51/177.23 cnf(10908,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x109081),x109082)),x109082))), % 177.51/177.23 inference(rename_variables,[],[4727])). % 177.51/177.23 cnf(10911,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x109111),x109112)),x109112))), % 177.51/177.23 inference(rename_variables,[],[4727])). % 177.51/177.23 cnf(10914,plain, % 177.51/177.23 (P1(f327(f242(f922(x109141,a910)),x109142))), % 177.51/177.23 inference(rename_variables,[],[3553])). % 177.51/177.23 cnf(10917,plain, % 177.51/177.23 (E(f327(f36(a915),f327(f282(a915),x109171)),x109171)), % 177.51/177.23 inference(rename_variables,[],[3388])). % 177.51/177.23 cnf(10920,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x109201),f327(a113,x109201)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(10927,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x109271),x109271))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(10932,plain, % 177.51/177.23 (P1(f327(f327(f234(a1),x109321),x109321))), % 177.51/177.23 inference(rename_variables,[],[3493])). % 177.51/177.23 cnf(10941,plain, % 177.51/177.23 (E(f327(f284(x109411,x109411),f263(x109411,x109412)),x109412)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(10944,plain, % 177.51/177.23 (P1(f327(f242(f922(x109441,a910)),x109442))), % 177.51/177.23 inference(rename_variables,[],[3553])). % 177.51/177.23 cnf(10946,plain, % 177.51/177.23 (P29(x109461,f327(f234(a915),f2(a915)),x109462)), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,10625,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,10587,4273,4732,3408,3856,3792,3560,10606,10726,10804,10877,10880,3944,3476,4707,10494,10497,10523,10647,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,10863,3493,10642,10698,4703,10534,10563,3645,10792,3553,10914,3585,4012,3949,10566,4713,10514,10902,3513,4314,4710,4694,3469,3473,4697,4695,4696,4726,10813,3756,10866,4729,4730,10706,3972,4727,10539,10542,10908,3942,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505])). % 177.51/177.23 cnf(10947,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),f2(a915)),x109471))), % 177.51/177.23 inference(rename_variables,[],[3513])). % 177.51/177.23 cnf(10949,plain, % 177.51/177.23 (P29(x109491,f327(f234(f922(x109492,a910)),f190(f922(x109492,a910))),x109493)), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,10625,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,10587,4273,4732,3408,3856,3792,3560,10606,10726,10804,10877,10880,3944,3476,4707,10494,10497,10523,10647,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,10863,3493,10642,10698,4703,10534,10563,3645,10792,3553,10914,3585,4012,3949,10566,4713,10514,10902,3513,4314,4710,4694,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,4729,4730,10706,3972,4727,10539,10542,10908,3942,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506])). % 177.51/177.23 cnf(10950,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x109501,a910)),f190(f922(x109501,a910))),x109502))), % 177.51/177.23 inference(rename_variables,[],[3941])). % 177.51/177.23 cnf(10953,plain, % 177.51/177.23 (P1(f327(f242(f922(x109531,a910)),x109532))), % 177.51/177.23 inference(rename_variables,[],[3553])). % 177.51/177.23 cnf(10956,plain, % 177.51/177.23 (P1(f327(f242(f922(x109561,a910)),x109562))), % 177.51/177.23 inference(rename_variables,[],[3553])). % 177.51/177.23 cnf(10959,plain, % 177.51/177.23 (P1(f327(f242(f922(x109591,a910)),x109592))), % 177.51/177.23 inference(rename_variables,[],[3553])). % 177.51/177.23 cnf(10961,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(f327(f81(a915),f327(a113,x109611)),f327(a113,x109611))),x109611))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,10625,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,10587,4273,4732,3408,3856,3792,3560,10606,10726,10804,10877,10880,3944,3476,4707,10494,10497,10523,10647,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,10863,3493,10642,10698,4703,10534,10563,3645,10792,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,3513,4314,4710,4694,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,4729,4730,10706,3972,4727,10539,10542,10908,3942,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516])). % 177.51/177.23 cnf(10962,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x109621),f327(f327(f81(a915),x109621),x109621)))), % 177.51/177.23 inference(rename_variables,[],[3756])). % 177.51/177.23 cnf(10966,plain, % 177.51/177.23 (E(f327(f169(x109661),f174(x109662,f327(f327(f135(x109661),f327(f169(x109661),x109663)),f327(f327(f152(x109661),x109664),f114(x109661))),f114(x109662))),f327(f327(f152(x109661),x109664),x109663))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,10587,4273,4732,3408,3856,3792,3560,10606,10726,10804,10877,10880,3944,3476,4707,10494,10497,10523,10647,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,10863,3493,10642,10698,4703,10534,10563,3645,10792,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,3513,4314,4710,4694,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,4729,4730,10706,3972,4727,10539,10542,10908,3942,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555])). % 177.51/177.23 cnf(10971,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,f327(a113,f327(f327(f80(a915),x109711),x109712)))),f327(a113,x109712)))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,10587,4273,4732,3408,3856,3792,3560,10606,10726,10804,10877,10880,10920,3944,3476,4707,10494,10497,10523,10647,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,4223,3874,10650,3492,10615,10713,10863,3493,10642,10698,4703,10534,10563,3645,10792,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,3513,4314,4710,4694,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,4729,4730,10706,3972,4727,10539,10542,10908,3942,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559])). % 177.51/177.23 cnf(11002,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x110021),x110021))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11013,plain, % 177.51/177.23 (~P1(f327(f327(f173(x110131),f114(x110131)),x110132))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(11020,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x110201),f327(a113,x110201)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(11022,plain, % 177.51/177.23 (P1(f327(f327(f235(a1),f327(f327(f23(a1),x110221),f78(a1))),x110221))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3423,4670,10517,3388,10587,4273,4130,4732,3408,3856,3792,3560,10606,10726,10804,10877,10880,10920,3944,3476,4707,10494,10497,10523,10647,10822,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4223,3874,10650,3492,10615,10713,10863,10927,11002,3493,10642,10698,10932,4703,10534,10563,3645,10792,4716,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,4314,4710,4694,4698,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,4729,4730,10706,3972,4727,10539,10542,10908,3942,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823])). % 177.51/177.23 cnf(11023,plain, % 177.51/177.23 (P1(f327(f327(f234(a1),x110231),x110231))), % 177.51/177.23 inference(rename_variables,[],[3493])). % 177.51/177.23 cnf(11028,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x110281),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(11043,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x110431),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(11046,plain, % 177.51/177.23 (~P1(f327(f327(f235(f922(x110461,a910)),x110462),f190(f922(x110461,a910))))), % 177.51/177.23 inference(rename_variables,[],[4724])). % 177.51/177.23 cnf(11049,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x110491),x110491))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11052,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x110521),x110521))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11067,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x110671),x110671))), % 177.51/177.23 inference(rename_variables,[],[4703])). % 177.51/177.23 cnf(11076,plain, % 177.51/177.23 (~P1(f327(f327(f329(x110761),x110762),f190(f922(x110761,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11083,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x110831),x110831))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11086,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x110861,a910)),f327(f310(x110862,x110861,x110863),f327(f311(x110862,x110861,x110863),x110864))),x110864))), % 177.51/177.23 inference(rename_variables,[],[4370])). % 177.51/177.23 cnf(11095,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x110951,a910)),f327(f173(x110951),f327(f137(x110951,x110952),x110953))),f327(f173(x110951),x110953)))), % 177.51/177.23 inference(rename_variables,[],[4139])). % 177.51/177.23 cnf(11098,plain, % 177.51/177.23 (E(f327(f310(x110981,x110981,f5(x110981)),x110982),x110982)), % 177.51/177.23 inference(rename_variables,[],[3549])). % 177.51/177.23 cnf(11103,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),f2(a915)),x111031))), % 177.51/177.23 inference(rename_variables,[],[3513])). % 177.51/177.23 cnf(11106,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x111061),x111061))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11109,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x111091),x111091))), % 177.51/177.23 inference(rename_variables,[],[4703])). % 177.51/177.23 cnf(11118,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x111181),x111181))), % 177.51/177.23 inference(rename_variables,[],[4703])). % 177.51/177.23 cnf(11129,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x111291),f327(f327(f81(a915),x111291),x111291)))), % 177.51/177.23 inference(rename_variables,[],[3756])). % 177.51/177.23 cnf(11135,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x111351),f327(a113,f327(f327(f80(a915),x111352),x111351))))), % 177.51/177.23 inference(rename_variables,[],[3942])). % 177.51/177.23 cnf(11142,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x111421),x111421))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11145,plain, % 177.51/177.23 (P1(f327(f327(f234(a1),x111451),x111451))), % 177.51/177.23 inference(rename_variables,[],[3493])). % 177.51/177.23 cnf(11148,plain, % 177.51/177.23 (~E(f327(a113,x111481),x111481)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11153,plain, % 177.51/177.23 (P1(f327(f327(f329(x111531),x111532),f242(f922(x111531,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(11158,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x111581),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(11160,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x111601,a910)),x111602),f38(f922(x111601,a910),f327(f308(x111601),x111602))))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,4716,11076,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,4314,4710,4694,4698,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695])). % 177.51/177.23 cnf(11173,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),f2(a915)),x111731))), % 177.51/177.23 inference(rename_variables,[],[3513])). % 177.51/177.23 cnf(11180,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x111801),x111801))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11189,plain, % 177.51/177.23 (~P1(f327(f327(f329(x111891),x111892),f190(f922(x111891,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11191,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x111911,a910)),f39(f922(x111911,a910),f327(f308(x111911),x111912))),x111912))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,4716,11076,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969])). % 177.51/177.23 cnf(11193,plain, % 177.51/177.23 (E(f327(f327(f103(f922(x111931,a910)),f327(f327(f103(f922(x111931,a910)),x111932),f327(f79(f922(x111931,a910)),x111933))),x111933),f190(f922(x111931,a910)))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,4716,11076,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971])). % 177.51/177.23 cnf(11196,plain, % 177.51/177.23 (P1(f327(f327(f329(f916(x111961)),x111962),f162(x111961,f242(f922(x111961,a910)))))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,4716,11076,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,3941,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980])). % 177.51/177.23 cnf(11197,plain, % 177.51/177.23 (P1(f327(f327(f329(x111971),x111972),f242(f922(x111971,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(11200,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x112001),f916(x112001))),f327(f327(f252(f916(x112001),f916(x112001)),x112002),f114(x112001))),f146(x112001,x112003)))), % 177.51/177.23 inference(rename_variables,[],[4732])). % 177.51/177.23 cnf(11209,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(x112091,x112091)),x112092),f263(x112091,f190(f922(x112091,a910)))))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,4716,11076,11189,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,3941,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114])). % 177.51/177.23 cnf(11210,plain, % 177.51/177.23 (~P1(f327(f327(f329(x112101),x112102),f190(f922(x112101,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11212,plain, % 177.51/177.23 (~P1(f327(f327(f329(x112121),x112122),f327(f311(x112121,x112123,x112124),f190(f922(x112123,a910)))))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,3288,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,4716,11076,11189,11210,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,3941,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145])). % 177.51/177.23 cnf(11213,plain, % 177.51/177.23 (~P1(f327(f327(f329(x112131),x112132),f190(f922(x112131,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11216,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x112161,a910)),x112162),f327(f327(f309(x112161),x112163),x112162)))), % 177.51/177.23 inference(rename_variables,[],[3939])). % 177.51/177.23 cnf(11219,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),x112191),x112191))), % 177.51/177.23 inference(rename_variables,[],[3492])). % 177.51/177.23 cnf(11222,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x112221,a910)),x112222),f327(f327(f309(x112221),x112223),x112222)))), % 177.51/177.23 inference(rename_variables,[],[3939])). % 177.51/177.23 cnf(11225,plain, % 177.51/177.23 (E(f327(f310(x112251,x112251,f5(x112251)),x112252),x112252)), % 177.51/177.23 inference(rename_variables,[],[3549])). % 177.51/177.23 cnf(11227,plain, % 177.51/177.23 (P32(x112271,x112272,x112273,f115(x112271,f114(x112271)),f114(x112272))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,3288,3338,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,11098,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,4716,11076,11189,11210,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,3939,11216,3941,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251])). % 177.51/177.23 cnf(11240,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x112401,a910)),x112402),f327(f327(f309(x112401),x112403),x112402)))), % 177.51/177.23 inference(rename_variables,[],[3939])). % 177.51/177.23 cnf(11251,plain, % 177.51/177.23 (~E(f327(a113,x112511),f2(a915))), % 177.51/177.23 inference(rename_variables,[],[4661])). % 177.51/177.23 cnf(11254,plain, % 177.51/177.23 (~P1(f327(f327(f173(x112541),f114(x112541)),x112542))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(11258,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),f327(a113,x112581)),x112581)),f307(a915,a317)))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,4661,10687,10787,3288,3338,3453,10526,10529,10622,10625,3430,3328,3392,3324,3352,3336,3963,3549,11098,3423,4670,10517,3388,10587,4273,4130,4732,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,4235,4139,11095,3857,4223,3874,10650,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,4716,11076,11189,11210,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4096,3939,11216,11222,3941,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571])). % 177.51/177.23 cnf(11267,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x112671),f327(a113,x112671)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(11277,plain, % 177.51/177.23 (~E(f327(f310(x112771,f922(x112771,a910),x112772),x112773),f327(f308(x112771),x112773))), % 177.51/177.23 inference(rename_variables,[],[4714])). % 177.51/177.23 cnf(11280,plain, % 177.51/177.23 (~P1(f327(f327(f329(x112801),x112802),f190(f922(x112801,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11283,plain, % 177.51/177.23 (~P1(f327(f327(f329(x112831),x112832),f190(f922(x112831,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11286,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(x112861,x112861)),f327(f327(f252(x112861,x112861),x112862),x112863)),f154(x112861,f114(f922(x112861,a915)))))), % 177.51/177.23 inference(rename_variables,[],[4731])). % 177.51/177.23 cnf(11289,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(x112891,x112891)),f327(f327(f252(x112891,x112891),x112892),x112893)),f154(x112891,f114(f922(x112891,a915)))))), % 177.51/177.23 inference(rename_variables,[],[4731])). % 177.51/177.23 cnf(11294,plain, % 177.51/177.23 (~P1(f327(f327(f329(x112941),x112942),f190(f922(x112941,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11297,plain, % 177.51/177.23 (P1(f327(f327(f329(f921(x112971,x112971)),f327(f327(f252(x112971,x112971),x112972),x112972)),f307(x112971,x112973)))), % 177.51/177.23 inference(rename_variables,[],[4130])). % 177.51/177.23 cnf(11300,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x113001,a910)),f327(f173(x113001),f177(x113001,x113002,x113003))),f327(f173(x113001),x113002)))), % 177.51/177.23 inference(rename_variables,[],[4189])). % 177.51/177.23 cnf(11303,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x113031,a910)),x113032),f242(f922(x113031,a910))))), % 177.51/177.23 inference(rename_variables,[],[3874])). % 177.51/177.23 cnf(11319,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x113191,a910)),f190(f922(x113191,a910))),x113192))), % 177.51/177.23 inference(rename_variables,[],[3941])). % 177.51/177.23 cnf(11330,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x113301),f916(x113301))),f327(f327(f252(f916(x113301),f916(x113301)),x113302),f114(x113301))),f148(x113301,x113303)))), % 177.51/177.23 inference(rename_variables,[],[4733])). % 177.51/177.23 cnf(11341,plain, % 177.51/177.23 (~E(f327(a113,x113411),x113411)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11344,plain, % 177.51/177.23 (~E(f327(a113,x113441),x113441)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11348,plain, % 177.51/177.23 (P1(f327(f327(f329(f921(f916(x113481),f916(x113481))),f327(f327(f252(f916(x113481),f916(x113481)),f114(x113481)),f114(x113481))),f327(f327(f289(f916(x113481),f916(x113481),f916(x113481)),f159(x113481,x113482)),f307(f916(x113481),f159(x113481,x113482)))))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,4661,10687,10787,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,3388,10587,4273,4130,11297,4732,11200,4733,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,4235,4139,11095,4189,3857,4223,3874,10650,10747,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,4716,11076,11189,11210,11213,11280,11283,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,4096,3939,11216,11222,3941,10950,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799])). % 177.51/177.23 cnf(11351,plain, % 177.51/177.23 (~E(f327(a113,x113511),f2(a915))), % 177.51/177.23 inference(rename_variables,[],[4661])). % 177.51/177.23 cnf(11353,plain, % 177.51/177.23 (E(f327(x113531,f327(f92(x113532,x113533,f242(f922(x113532,a910)),x113531),f327(x113531,x113534))),f327(x113531,x113534))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,3388,10587,4273,4130,11297,4732,11200,4733,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,4235,4139,11095,4189,3857,4223,3874,10650,10747,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,4716,11076,11189,11210,11213,11280,11283,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,4096,3939,11216,11222,3941,10950,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813])). % 177.51/177.23 cnf(11356,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x113561,a910)),x113562),x113562))), % 177.51/177.23 inference(rename_variables,[],[3788])). % 177.51/177.23 cnf(11363,plain, % 177.51/177.23 (~E(f327(a113,x113631),x113631)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11366,plain, % 177.51/177.23 (~E(f327(a113,x113661),x113661)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11368,plain, % 177.51/177.23 (~P24(x113681,f922(x113681,a910),x113682,x113683,f327(f308(x113681),x113683))), % 177.51/177.23 inference(scs_inference,[],[4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3388,10587,4273,4130,11297,4732,11200,4733,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,4235,4139,11095,4189,3857,4223,3874,10650,10747,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,4716,11076,11189,11210,11213,11280,11283,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,4096,3939,11216,11222,3788,3941,10950,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852])). % 177.51/177.23 cnf(11371,plain, % 177.51/177.23 (P23(x113711,x113711,f5(x113711),x113712)), % 177.51/177.23 inference(rename_variables,[],[3729])). % 177.51/177.23 cnf(11376,plain, % 177.51/177.23 (~E(f327(f310(x113761,f922(x113761,a910),x113762),x113763),f327(f308(x113761),x113763))), % 177.51/177.23 inference(rename_variables,[],[4714])). % 177.51/177.23 cnf(11381,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x113811,a910)),x113812),f242(f922(x113811,a910))))), % 177.51/177.23 inference(rename_variables,[],[3874])). % 177.51/177.23 cnf(11397,plain, % 177.51/177.23 (~P1(f327(f327(f329(x113971),x113972),f190(f922(x113971,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11400,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x114001)),x114001))), % 177.51/177.23 inference(rename_variables,[],[4713])). % 177.51/177.23 cnf(11405,plain, % 177.51/177.23 (~P1(f327(f327(f329(x114051),x114052),f190(f922(x114051,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11415,plain, % 177.51/177.23 (~P1(f327(f327(f329(a915),f327(a113,f327(f143(a915,a915,f80(a915),f2(a915)),x114151))),f327(f173(a915),x114151)))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,4732,11200,4733,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,4724,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,4716,11076,11189,11210,11213,11280,11283,11294,11397,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,4096,3939,11216,11222,3788,3941,10950,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036])). % 177.51/177.23 cnf(11416,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x114161)),x114161))), % 177.51/177.23 inference(rename_variables,[],[4713])). % 177.51/177.23 cnf(11419,plain, % 177.51/177.23 (~P1(f327(f327(f329(x114191),x114192),f190(f922(x114191,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11432,plain, % 177.51/177.23 (P1(f327(f327(f329(f921(x114321,x114321)),f327(f327(f252(x114321,x114321),x114322),x114322)),f307(x114321,x114323)))), % 177.51/177.23 inference(rename_variables,[],[4130])). % 177.51/177.23 cnf(11435,plain, % 177.51/177.23 (P1(f327(f327(f329(x114351),x114352),f242(f922(x114351,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(11438,plain, % 177.51/177.23 (P1(f327(f327(f329(x114381),x114382),f242(f922(x114381,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(11445,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x114451),f916(x114451))),f327(f327(f252(f916(x114451),f916(x114451)),x114452),f114(x114451))),f146(x114451,x114453)))), % 177.51/177.23 inference(rename_variables,[],[4732])). % 177.51/177.23 cnf(11448,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x114481),f916(x114481))),f327(f327(f252(f916(x114481),f916(x114481)),x114482),f114(x114481))),f148(x114481,x114483)))), % 177.51/177.23 inference(rename_variables,[],[4733])). % 177.51/177.23 cnf(11451,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x114511),f916(x114511))),f327(f327(f252(f916(x114511),f916(x114511)),x114512),f114(x114511))),f158(x114511,x114513)))), % 177.51/177.23 inference(rename_variables,[],[4734])). % 177.51/177.23 cnf(11456,plain, % 177.51/177.23 (~P1(f327(f327(f235(f922(x114561,a910)),x114562),f190(f922(x114561,a910))))), % 177.51/177.23 inference(rename_variables,[],[4724])). % 177.51/177.23 cnf(11458,plain, % 177.51/177.23 (~P1(f327(f327(f329(x114581),x114582),f327(f310(x114583,x114581,x114584),f190(f922(x114583,a910)))))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,4732,11200,11445,4733,11330,4734,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,4724,11046,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,4096,3939,11216,11222,3788,3941,10950,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279])). % 177.51/177.23 cnf(11459,plain, % 177.51/177.23 (~P1(f327(f327(f329(x114591),x114592),f190(f922(x114591,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11463,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x114631,a910)),x114632),f327(f327(f102(f922(x114631,a910)),x114633),f242(f922(x114631,a910)))))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,4732,11200,11445,4733,11330,4734,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,4724,11046,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,4096,3939,11216,11222,3788,3941,10950,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308])). % 177.51/177.23 cnf(11464,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x114641,a910)),x114642),f242(f922(x114641,a910))))), % 177.51/177.23 inference(rename_variables,[],[3874])). % 177.51/177.23 cnf(11470,plain, % 177.51/177.23 (~P1(f327(f327(f255(x114701,x114702,a910,f327(f173(x114703),f114(x114703))),x114704),x114705))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,4732,11200,11445,4733,11330,4734,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,4724,11046,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,4096,3939,11216,11222,3788,3941,10950,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415])). % 177.51/177.23 cnf(11471,plain, % 177.51/177.23 (~P1(f327(f327(f173(x114711),f114(x114711)),x114712))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(11476,plain, % 177.51/177.23 (~P1(f327(f327(f329(x114761),x114762),f190(f922(x114761,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11479,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(x114791,x114791)),f327(f327(f252(x114791,x114791),x114792),x114793)),f154(x114791,f114(f922(x114791,a915)))))), % 177.51/177.23 inference(rename_variables,[],[4731])). % 177.51/177.23 cnf(11482,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x114821,a910)),x114822),x114822))), % 177.51/177.23 inference(rename_variables,[],[3788])). % 177.51/177.23 cnf(11485,plain, % 177.51/177.23 (~P1(f327(f327(f329(x114851),x114852),f190(f922(x114851,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11487,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x114871,a910)),f327(f285(x114872,x114871,f190(f922(f921(x114872,x114871),a910))),x114873)),x114874))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,4732,11200,11445,4733,11330,4734,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,4724,11046,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,11289,4096,3939,11216,11222,3788,11356,3941,10950,11319,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480])). % 177.51/177.23 cnf(11488,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x114881,a910)),f190(f922(x114881,a910))),x114882))), % 177.51/177.23 inference(rename_variables,[],[3941])). % 177.51/177.23 cnf(11491,plain, % 177.51/177.23 (P1(f327(f327(f329(f921(x114911,x114911)),f327(f327(f252(x114911,x114911),x114912),x114912)),f307(x114911,x114913)))), % 177.51/177.23 inference(rename_variables,[],[4130])). % 177.51/177.23 cnf(11502,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x115021),f916(x115021))),f327(f327(f252(f916(x115021),f916(x115021)),x115022),f114(x115021))),f158(x115021,x115023)))), % 177.51/177.23 inference(rename_variables,[],[4734])). % 177.51/177.23 cnf(11509,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x115091),f916(x115091))),f327(f327(f252(f916(x115091),f916(x115091)),f114(x115091)),x115092)),f146(x115091,x115093)))), % 177.51/177.23 inference(rename_variables,[],[4735])). % 177.51/177.23 cnf(11514,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f922(x115141,a910),f922(x115141,a910))),f327(f327(f252(f922(x115141,a910),f922(x115141,a910)),x115142),f190(f922(x115141,a910)))),f314(x115141)))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,11432,4732,11200,11445,4733,11330,4734,11451,4735,4736,3408,3689,3856,3792,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,11289,4096,3939,11216,11222,3788,11356,3941,10950,11319,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644])). % 177.51/177.23 cnf(11517,plain, % 177.51/177.23 (P1(f327(f327(f329(x115171),x115172),f242(f922(x115171,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(11522,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x115221,a910)),f190(f922(x115221,a910))),x115222))), % 177.51/177.23 inference(rename_variables,[],[3941])). % 177.51/177.23 cnf(11527,plain, % 177.51/177.23 (~P1(f327(f327(f329(x115271),x115272),f190(f922(x115271,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11530,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x115301,a910)),x115302),f242(f922(x115301,a910))))), % 177.51/177.23 inference(rename_variables,[],[3874])). % 177.51/177.23 cnf(11534,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x115341,a910)),f327(f285(x115342,x115341,x115343),f190(f922(x115342,a910)))),x115344))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,11432,4732,11200,11445,4733,11330,4734,11451,4735,4736,3408,3689,3856,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,11438,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,11289,4096,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,4277,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751])). % 177.51/177.23 cnf(11535,plain, % 177.51/177.23 (P1(f327(f327(f234(f922(x115351,a910)),f190(f922(x115351,a910))),x115352))), % 177.51/177.23 inference(rename_variables,[],[3941])). % 177.51/177.23 cnf(11537,plain, % 177.51/177.23 (~P1(f327(f66(a915,x115371,x115372,x115373,f242(f922(a915,a910))),x115374))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,4714,11277,3596,3388,10587,4273,4130,11297,11432,4732,11200,11445,4733,11330,4734,11451,4735,4736,3408,3689,3856,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,11438,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,3553,10914,10944,10953,10956,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,11289,4096,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,4277,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772])). % 177.51/177.23 cnf(11548,plain, % 177.51/177.23 (P1(f327(f242(f922(x115481,a910)),x115482))), % 177.51/177.23 inference(rename_variables,[],[3553])). % 177.51/177.23 cnf(11556,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x115561),f916(x115561))),f327(f327(f252(f916(x115561),f916(x115561)),x115562),f114(x115561))),f146(x115561,x115563)))), % 177.51/177.23 inference(rename_variables,[],[4732])). % 177.51/177.23 cnf(11559,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x115591),f916(x115591))),f327(f327(f252(f916(x115591),f916(x115591)),x115592),f114(x115591))),f148(x115591,x115593)))), % 177.51/177.23 inference(rename_variables,[],[4733])). % 177.51/177.23 cnf(11562,plain, % 177.51/177.23 (~E(f327(f327(f152(x115621),x115622),x115623),x115623)), % 177.51/177.23 inference(rename_variables,[],[4670])). % 177.51/177.23 cnf(11565,plain, % 177.51/177.23 (~E(f327(a113,x115651),x115651)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11568,plain, % 177.51/177.23 (~P1(f327(f327(f329(x115681),x115682),f190(f922(x115681,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11573,plain, % 177.51/177.23 (~P1(f327(f327(f329(x115731),x115732),f190(f922(x115731,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11576,plain, % 177.51/177.23 (~P1(f327(f327(f329(x115761),x115762),f190(f922(x115761,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11579,plain, % 177.51/177.23 (P1(f327(f327(f329(f921(f916(x115791),f916(x115791))),f327(f327(f252(f916(x115791),f916(x115791)),x115792),x115792)),f159(x115791,f307(x115791,x115793))))), % 177.51/177.23 inference(rename_variables,[],[4266])). % 177.51/177.23 cnf(11582,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x115821),f916(x115821))),f327(f327(f252(f916(x115821),f916(x115821)),x115822),f114(x115821))),f146(x115821,x115823)))), % 177.51/177.23 inference(rename_variables,[],[4732])). % 177.51/177.23 cnf(11586,plain, % 177.51/177.23 (E(f327(f327(f152(x115861),f649(f307(x115861,x115862),f327(f327(f152(x115861),x115863),x115864),x115864,x115863,x115861)),f650(f307(x115861,x115862),f327(f327(f152(x115861),x115863),x115864),x115864,x115863,x115861)),f327(f327(f152(x115861),x115863),x115864))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,4661,10687,10787,11251,3288,3338,3453,10526,10529,10622,10625,3430,3951,3328,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,10684,4714,11277,3596,3388,10587,4273,4130,11297,11432,4732,11200,11445,11556,4733,11330,11448,4734,11451,4735,11509,4736,3408,3689,3856,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,4707,10494,10497,10523,10647,10822,11028,11043,11158,4720,3931,3698,4078,3519,3521,3495,4704,4665,4266,11579,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,11438,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,3553,10914,10944,10953,10956,10959,3585,4012,3949,10566,4713,10514,10902,10905,11400,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4726,10813,4731,11286,11289,4096,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,4277,3972,4727,10539,10542,10908,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947])). % 177.51/177.23 cnf(11592,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(x115921,x115921)),f327(f327(f252(x115921,x115921),x115922),x115923)),f154(x115921,f114(f922(x115921,a915)))))), % 177.51/177.23 inference(rename_variables,[],[4731])). % 177.51/177.23 cnf(11595,plain, % 177.51/177.23 (~P1(f327(f327(f329(x115951),x115952),f190(f922(x115951,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11598,plain, % 177.51/177.23 (~P1(f327(f327(f329(x115981),x115982),f190(f922(x115981,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11601,plain, % 177.51/177.23 (P1(f327(f327(f329(x116011),x116012),f242(f922(x116011,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(11604,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x116041),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(11609,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(x116091,x116091)),f327(f327(f252(x116091,x116091),x116092),x116093)),f154(x116091,f114(f922(x116091,a915)))))), % 177.51/177.23 inference(rename_variables,[],[4731])). % 177.51/177.23 cnf(11618,plain, % 177.51/177.23 (~E(f327(f310(x116181,f922(x116181,a910),x116182),x116183),f327(f308(x116181),x116183))), % 177.51/177.23 inference(rename_variables,[],[4714])). % 177.51/177.23 cnf(11621,plain, % 177.51/177.23 (~E(f327(f310(x116211,f922(x116211,a910),x116212),x116213),f327(f308(x116211),x116213))), % 177.51/177.23 inference(rename_variables,[],[4714])). % 177.51/177.23 cnf(11626,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x116261),f916(x116261))),f327(f327(f252(f916(x116261),f916(x116261)),x116262),f114(x116261))),f146(x116261,x116263)))), % 177.51/177.23 inference(rename_variables,[],[4732])). % 177.51/177.23 cnf(11632,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(f916(x116321),f916(x116321))),f327(f327(f252(f916(x116321),f916(x116321)),x116322),f114(x116321))),f146(x116321,x116323)))), % 177.51/177.23 inference(rename_variables,[],[4732])). % 177.51/177.23 cnf(11635,plain, % 177.51/177.23 (~P1(f327(f327(f329(x116351),x116352),f190(f922(x116351,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11640,plain, % 177.51/177.23 (~P1(f327(f327(f329(x116401),x116402),f190(f922(x116401,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11643,plain, % 177.51/177.23 (~P1(f327(f327(f329(x116431),x116432),f190(f922(x116431,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11646,plain, % 177.51/177.23 (~P1(f327(f327(f329(x116461),x116462),f190(f922(x116461,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11649,plain, % 177.51/177.23 (~P1(f327(f327(f329(x116491),x116492),f190(f922(x116491,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11652,plain, % 177.51/177.23 (P1(f327(f327(f329(x116521),f327(x116522,x116523)),f327(f310(x116524,x116521,x116522),f242(f922(x116524,a910)))))), % 177.51/177.23 inference(rename_variables,[],[4096])). % 177.51/177.23 cnf(11655,plain, % 177.51/177.23 (~P1(f327(f327(f329(f921(x116551,x116551)),f327(f327(f252(x116551,x116551),x116552),x116553)),f154(x116551,f114(f922(x116551,a915)))))), % 177.51/177.23 inference(rename_variables,[],[4731])). % 177.51/177.23 cnf(11663,plain, % 177.51/177.23 (E(f115(x116631,f114(x116631)),f114(x116631))), % 177.51/177.23 inference(rename_variables,[],[3338])). % 177.51/177.23 cnf(11666,plain, % 177.51/177.23 (~E(f327(a113,x116661),x116661)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11673,plain, % 177.51/177.23 (~E(f327(a113,x116731),x116731)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11678,plain, % 177.51/177.23 (E(f327(f284(x116781,x116781),f263(x116781,x116782)),x116782)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(11681,plain, % 177.51/177.23 (E(f327(f284(x116811,x116811),f263(x116811,x116812)),x116812)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(11687,plain, % 177.51/177.23 (~E(f327(a113,x116871),x116871)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11692,plain, % 177.51/177.23 (~E(f327(f327(f80(a1),x116921),x116921),a98)), % 177.51/177.23 inference(rename_variables,[],[4668])). % 177.51/177.23 cnf(11699,plain, % 177.51/177.23 (E(f327(f327(f23(a915),f2(a915)),x116991),f2(a915))), % 177.51/177.23 inference(rename_variables,[],[3409])). % 177.51/177.23 cnf(11702,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x117021),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(11709,plain, % 177.51/177.23 (E(f327(f327(f80(a1),f327(f327(f81(a1),x117091),f327(f327(f37(a1),x117092),x117091))),f46(a1,x117092,x117091)),x117092)), % 177.51/177.23 inference(rename_variables,[],[4045])). % 177.51/177.23 cnf(11733,plain, % 177.51/177.23 (~E(f327(a113,x117331),x117331)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11736,plain, % 177.51/177.23 (~E(f327(a113,x117361),x117361)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11762,plain, % 177.51/177.23 (~P1(f327(f327(f173(x117621),f114(x117621)),x117622))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(11768,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),f2(a915)),f327(a113,x117681)))), % 177.51/177.23 inference(rename_variables,[],[3572])). % 177.51/177.23 cnf(11769,plain, % 177.51/177.23 (~E(f327(a113,x117691),x117691)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11772,plain, % 177.51/177.23 (P1(f327(f327(f329(x117721),x117722),f242(f922(x117721,a910))))), % 177.51/177.23 inference(rename_variables,[],[3645])). % 177.51/177.23 cnf(11784,plain, % 177.51/177.23 (~E(f327(a113,x117841),x117841)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11787,plain, % 177.51/177.23 (P1(f327(f327(f234(a1),x117871),x117871))), % 177.51/177.23 inference(rename_variables,[],[3493])). % 177.51/177.23 cnf(11794,plain, % 177.51/177.23 (P1(f327(f66(x117941,x117942,x117943,x117944,f190(f922(x117941,a910))),x117944))), % 177.51/177.23 inference(rename_variables,[],[4409])). % 177.51/177.23 cnf(11795,plain, % 177.51/177.23 (E(f327(f284(x117951,x117951),f263(x117951,x117952)),x117952)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(11808,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x118081),x118082)),x118082))), % 177.51/177.23 inference(rename_variables,[],[4727])). % 177.51/177.23 cnf(11811,plain, % 177.51/177.23 (~P1(f327(f327(f235(a1),f327(f101(a1),x118111)),f2(a1)))), % 177.51/177.23 inference(rename_variables,[],[4720])). % 177.51/177.23 cnf(11825,plain, % 177.51/177.23 (~E(f327(f327(f238(a915),f327(a113,x118251)),x118251),f327(a113,x118251))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,3413,4661,10687,10787,11251,3109,3111,3119,3120,3122,3126,3141,3155,3156,3160,3164,3167,3174,3192,3247,3248,3258,3270,3288,4649,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,3430,3951,3328,4045,11709,3392,3324,3352,3336,3963,3549,11098,3423,4128,4670,10517,10684,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,3572,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,4720,3931,3698,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,11145,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,11438,11517,11601,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,3553,10914,10944,10953,10956,10959,3585,4012,3949,10566,4713,10514,10902,10905,11400,11416,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,4277,3972,4727,10539,10542,10908,10911,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533])). % 177.51/177.23 cnf(11834,plain, % 177.51/177.23 (E(f327(f284(x118341,x118341),f263(x118341,x118342)),x118342)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(11839,plain, % 177.51/177.23 (E(f327(f284(x118391,x118391),f263(x118391,x118392)),x118392)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(11842,plain, % 177.51/177.23 (~P1(f327(f327(f235(a1),f327(f101(a1),x118421)),f2(a1)))), % 177.51/177.23 inference(rename_variables,[],[4720])). % 177.51/177.23 cnf(11847,plain, % 177.51/177.23 (~E(f327(a113,x118471),x118471)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11856,plain, % 177.51/177.23 (~P1(f327(f327(f173(x118561),f114(x118561)),x118562))), % 177.51/177.23 inference(rename_variables,[],[4712])). % 177.51/177.23 cnf(11879,plain, % 177.51/177.23 (~P1(f327(f327(f235(a1),f327(f101(a1),x118791)),f2(a1)))), % 177.51/177.23 inference(rename_variables,[],[4720])). % 177.51/177.23 cnf(11882,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x118821),f2(a915)))), % 177.51/177.23 inference(rename_variables,[],[4707])). % 177.51/177.23 cnf(11883,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),x118831),f327(a113,x118831)))), % 177.51/177.23 inference(rename_variables,[],[3560])). % 177.51/177.23 cnf(11886,plain, % 177.51/177.23 (~P1(f327(f327(f235(a1),f327(f101(a1),x118861)),f2(a1)))), % 177.51/177.23 inference(rename_variables,[],[4720])). % 177.51/177.23 cnf(11888,plain, % 177.51/177.23 (~P13(x118881,f329(f922(x118882,a910)))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,3413,4661,10687,10787,11251,3109,3111,3112,3119,3120,3122,3126,3141,3155,3156,3160,3164,3167,3174,3179,3180,3192,3198,3199,3247,3248,3251,3258,3270,3288,4649,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,3430,3951,3328,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,3944,3476,3572,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,4720,11811,11842,11879,3931,3698,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,11145,3494,4703,10534,10563,11067,11109,3645,10792,10883,11153,11197,11435,11438,11517,11601,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,4713,10514,10902,10905,11400,11416,3513,10947,11103,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,4277,3972,4727,10539,10542,10908,10911,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698])). % 177.51/177.23 cnf(11889,plain, % 177.51/177.23 (~P1(f327(f327(f329(x118891),x118892),f190(f922(x118891,a910))))), % 177.51/177.23 inference(rename_variables,[],[4716])). % 177.51/177.23 cnf(11890,plain, % 177.51/177.23 (P1(f327(f327(f329(f922(x118901,a910)),x118902),f327(f308(x118901),x118902)))), % 177.51/177.23 inference(rename_variables,[],[3857])). % 177.51/177.23 cnf(11905,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x119051)),x119051))), % 177.51/177.23 inference(rename_variables,[],[4713])). % 177.51/177.23 cnf(11906,plain, % 177.51/177.23 (~E(f327(a113,x119061),x119061)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11916,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x119161),x119162)),x119161))), % 177.51/177.23 inference(rename_variables,[],[4728])). % 177.51/177.23 cnf(11919,plain, % 177.51/177.23 (~P1(f327(f327(f235(a1),f327(f101(a1),x119191)),f2(a1)))), % 177.51/177.23 inference(rename_variables,[],[4720])). % 177.51/177.23 cnf(11922,plain, % 177.51/177.23 (~E(f327(a113,x119221),x119221)), % 177.51/177.23 inference(rename_variables,[],[4651])). % 177.51/177.23 cnf(11935,plain, % 177.51/177.23 (P1(f327(f327(f329(x119351),x119352),f327(f327(f309(x119351),x119352),x119353)))), % 177.51/177.23 inference(rename_variables,[],[3804])). % 177.51/177.23 cnf(11936,plain, % 177.51/177.23 (~P1(f327(f327(f234(a1),f2(a1)),f327(f79(a1),f327(f101(a1),f327(a113,x119361)))))), % 177.51/177.23 inference(rename_variables,[],[4729])). % 177.51/177.23 cnf(11939,plain, % 177.51/177.23 (P1(f327(f327(f235(a915),f327(f327(f23(a915),x119391),x119392)),f327(a113,x119391)))), % 177.51/177.23 inference(rename_variables,[],[3944])). % 177.51/177.23 cnf(11942,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),f46(a915,x119421,x119422)),x119421))), % 177.51/177.23 inference(rename_variables,[],[3949])). % 177.51/177.23 cnf(11948,plain, % 177.51/177.23 (E(f327(f284(x119481,x119481),f263(x119481,x119482)),x119482)), % 177.51/177.23 inference(rename_variables,[],[3453])). % 177.51/177.23 cnf(11953,plain, % 177.51/177.23 (E(f327(f327(f135(x119531),f170(x119531,x119532,x119533)),f170(x119531,x119534,x119533)),f327(f327(f135(x119531),f170(x119531,x119534,x119533)),f170(x119531,x119532,x119533)))), % 177.51/177.23 inference(rename_variables,[],[4059])). % 177.51/177.23 cnf(11958,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x119581)),x119581))), % 177.51/177.23 inference(rename_variables,[],[4713])). % 177.51/177.23 cnf(11967,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x119671),x119671))), % 177.51/177.23 inference(rename_variables,[],[4703])). % 177.51/177.23 cnf(11970,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),f46(a915,x119701,x119702)),x119701))), % 177.51/177.23 inference(rename_variables,[],[3949])). % 177.51/177.23 cnf(11971,plain, % 177.51/177.23 (P1(f327(f327(f234(a915),f2(a915)),x119711))), % 177.51/177.23 inference(rename_variables,[],[3513])). % 177.51/177.23 cnf(11973,plain, % 177.51/177.23 (~P1(f327(f327(f234(a1),f78(a1)),f2(a1)))), % 177.51/177.23 inference(scs_inference,[],[3729,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,3413,4661,10687,10787,11251,3108,3109,3111,3112,3119,3120,3122,3126,3141,3155,3156,3160,3164,3167,3174,3179,3180,3192,3198,3199,3247,3248,3251,3256,3258,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,3430,3951,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4545,4546,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,3944,3476,3572,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,4720,11811,11842,11879,11886,3931,3698,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,3493,10642,10698,10932,11023,11145,3494,4703,10534,10563,11067,11109,11118,3645,10792,10883,11153,11197,11435,11438,11517,11601,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,4713,10514,10902,10905,11400,11416,11905,3513,10947,11103,11173,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,4730,10706,4370,4277,3972,4727,10539,10542,10908,10911,4728,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982])). % 177.51/177.23 cnf(11988,plain, % 177.51/177.23 (~P1(f327(f327(f235(a915),x119881),x119881))), % 177.51/177.23 inference(rename_variables,[],[4703])). % 177.51/177.23 cnf(11991,plain, % 177.51/177.23 (P1(f327(f327(f329(x119911),f327(x119912,x119913)),f327(f310(x119914,x119911,x119912),f242(f922(x119914,a910)))))), % 177.51/177.23 inference(rename_variables,[],[4096])). % 177.51/177.23 cnf(11992,plain, % 177.51/177.23 (~P1(f327(f327(f234(a915),f327(a113,x119921)),x119921))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(11995,plain, % 177.51/177.24 (P1(f327(f327(f329(x119951),f327(x119952,x119953)),f327(f310(x119954,x119951,x119952),f242(f922(x119954,a910)))))), % 177.51/177.24 inference(rename_variables,[],[4096])). % 177.51/177.24 cnf(11996,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x119961),x119962)),x119962))), % 177.51/177.24 inference(rename_variables,[],[4727])). % 177.51/177.24 cnf(12001,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x120011),x120012)),x120011))), % 177.51/177.24 inference(rename_variables,[],[4728])). % 177.51/177.24 cnf(12004,plain, % 177.51/177.24 (~P1(f327(f327(f173(x120041),f114(x120041)),x120042))), % 177.51/177.24 inference(rename_variables,[],[4712])). % 177.51/177.24 cnf(12007,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x120071),x120071))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12015,plain, % 177.51/177.24 (~P33(x120151,x120152,f114(x120151))), % 177.51/177.24 inference(rename_variables,[],[4681])). % 177.51/177.24 cnf(12018,plain, % 177.51/177.24 (P1(f327(f327(f329(x120181),x120182),f242(f922(x120181,a910))))), % 177.51/177.24 inference(rename_variables,[],[3645])). % 177.51/177.24 cnf(12019,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x120191)),x120191))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(12032,plain, % 177.51/177.24 (~P1(f327(f327(f329(x120321),x120322),f190(f922(x120321,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12035,plain, % 177.51/177.24 (E(f327(f327(f16(x120351,x120352),x120353),x120354),x120353)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(12038,plain, % 177.51/177.24 (E(f327(f327(f16(x120381,x120382),x120383),x120384),x120383)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(12050,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),f2(a915)),f327(a113,x120501)))), % 177.51/177.24 inference(rename_variables,[],[3572])). % 177.51/177.24 cnf(12053,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x120531),x120531))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12056,plain, % 177.51/177.24 (P1(f327(f35(x120561),f327(f173(x120561),x120562)))), % 177.51/177.24 inference(rename_variables,[],[3532])). % 177.51/177.24 cnf(12059,plain, % 177.51/177.24 (P1(f327(f35(x120591),f327(f173(x120591),x120592)))), % 177.51/177.24 inference(rename_variables,[],[3532])). % 177.51/177.24 cnf(12062,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f327(f79(a1),f327(f101(a1),x120621))),f327(f101(a1),x120622)))), % 177.51/177.24 inference(rename_variables,[],[3973])). % 177.51/177.24 cnf(12065,plain, % 177.51/177.24 (~P1(f327(f327(f329(x120651),x120652),f190(f922(x120651,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12083,plain, % 177.51/177.24 (~P1(f327(f327(f329(a915),x120831),f327(f282(a915),f2(a915))))), % 177.51/177.24 inference(scs_inference,[],[3729,4680,4681,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,3413,4661,10687,10787,11251,3108,3109,3111,3112,3115,3119,3120,3122,3126,3141,3155,3156,3160,3164,3167,3174,3179,3180,3192,3196,3198,3199,3247,3248,3251,3256,3258,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,3430,3951,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,3483,12035,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4545,4546,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,3944,11939,3476,3572,11768,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,4720,11811,11842,11879,11886,3931,3698,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,3532,12056,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,3493,10642,10698,10932,11023,11145,3494,3568,4703,10534,10563,11067,11109,11118,11967,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,3513,10947,11103,11173,3973,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,4370,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338])). % 177.51/177.24 cnf(12085,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f46(a915,x120851,f190(a915))),x120851))), % 177.51/177.24 inference(scs_inference,[],[3729,4680,4681,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,3413,4661,10687,10787,11251,3108,3109,3111,3112,3115,3119,3120,3122,3126,3141,3155,3156,3160,3164,3167,3174,3179,3180,3192,3196,3198,3199,3247,3248,3251,3256,3258,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,3430,3951,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,3483,12035,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4545,4546,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,3944,11939,3476,3572,11768,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,4720,11811,11842,11879,11886,3931,3698,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,3532,12056,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,3493,10642,10698,10932,11023,11145,11787,3494,3568,4703,10534,10563,11067,11109,11118,11967,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,3513,10947,11103,11173,3973,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,4370,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369])). % 177.51/177.24 cnf(12086,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x120861),x120861))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12089,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x120891),f327(a113,x120891)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12092,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x120921),x120921))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12103,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x121031),x121031))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12106,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x121061),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(12111,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x121111),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(12120,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f2(a915)),x121201))), % 177.51/177.24 inference(rename_variables,[],[3513])). % 177.51/177.24 cnf(12121,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x121211)),x121211))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(12124,plain, % 177.51/177.24 (~P1(f327(f327(f173(x121241),f114(x121241)),x121242))), % 177.51/177.24 inference(rename_variables,[],[4712])). % 177.51/177.24 cnf(12127,plain, % 177.51/177.24 (~P1(f327(f327(f173(x121271),f114(x121271)),x121272))), % 177.51/177.24 inference(rename_variables,[],[4712])). % 177.51/177.24 cnf(12143,plain, % 177.51/177.24 (P1(f327(f327(f235(a1),f327(f79(a1),f78(a1))),f2(a1)))), % 177.51/177.24 inference(scs_inference,[],[3729,4680,4681,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,3413,4661,10687,10787,11251,3108,3109,3111,3112,3115,3119,3120,3122,3125,3126,3141,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,3430,3951,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,3483,12035,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4545,4546,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,3944,11939,3476,3572,11768,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,4720,11811,11842,11879,11886,11919,3931,3698,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,3532,12056,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,4235,4139,11095,4189,3857,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,3493,10642,10698,10932,11023,11145,11787,12086,12092,3494,3568,4703,10534,10563,11067,11109,11118,11967,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,3513,10947,11103,11173,11971,3973,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,3939,11216,11222,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,4370,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642])). % 177.51/177.24 cnf(12146,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x121461)),x121461))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(12149,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x121491)),x121491))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(12152,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x121521)),x121521))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(12155,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x121551)),x121551))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(12158,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x121581),x121581))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12161,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x121611),x121611))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12164,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x121641),x121641))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12167,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x121671),x121671))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12184,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x121841),x121841))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12187,plain, % 177.51/177.24 (P23(a915,a915,a113,x121871)), % 177.51/177.24 inference(rename_variables,[],[3697])). % 177.51/177.24 cnf(12190,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x121901),x121901))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12201,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x122011),x122011))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12204,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(f921(f916(x122041),f916(x122041)),a910)),f159(x122041,x122042)),f307(f916(x122041),f158(x122041,x122042))))), % 177.51/177.24 inference(rename_variables,[],[4194])). % 177.51/177.24 cnf(12211,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x122111),f327(a113,x122111)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12214,plain, % 177.51/177.24 (P1(f327(f327(f329(f922(x122141,a910)),x122142),f327(f308(x122141),x122142)))), % 177.51/177.24 inference(rename_variables,[],[3857])). % 177.51/177.24 cnf(12215,plain, % 177.51/177.24 (~E(f327(a113,x122151),x122151)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12220,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x122201),x122201))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12225,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x122251),x122251))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12232,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x122321,x122322)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(12239,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x122391,a910)),x122392),f327(f327(f309(x122391),x122393),x122392)))), % 177.51/177.24 inference(rename_variables,[],[3939])). % 177.51/177.24 cnf(12242,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x122421),x122421))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12243,plain, % 177.51/177.24 (~E(f327(a113,x122431),x122431)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12256,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x122561),x122561))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12257,plain, % 177.51/177.24 (~E(f327(a113,x122571),x122571)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12260,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x122601),x122601))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12263,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x122631),x122631))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12266,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x122661),x122661))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12269,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x122691),x122691))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12271,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),f327(a106,f2(a1))),f327(a113,x122711)))), % 177.51/177.24 inference(scs_inference,[],[3729,4680,4681,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,3697,3413,4661,10687,10787,11251,3108,3109,3111,3112,3115,3119,3120,3122,3125,3126,3141,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,3430,3951,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,3483,12035,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4545,4546,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,3944,11939,3476,3572,11768,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,3532,12056,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,4235,4194,4139,11095,4189,3857,11890,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,3494,3568,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,3513,10947,11103,11173,11971,3973,4314,4710,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,3939,11216,11222,11240,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,4370,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,51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% 177.51/177.24 cnf(12272,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x122721),x122721))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12275,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x122751),x122751))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12278,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x122781),x122781))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12279,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x122791),f327(a113,x122791)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12286,plain, % 177.51/177.24 (~E(f327(a113,x122861),x122861)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12291,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x122911),x122911))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12292,plain, % 177.51/177.24 (~E(f327(a113,x122921),x122921)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12295,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x122951),x122951))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12312,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x123121),x123121))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(12317,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f2(a915)),x123171))), % 177.51/177.24 inference(rename_variables,[],[3513])). % 177.51/177.24 cnf(12333,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x123331),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(12336,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x123361),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(12339,plain, % 177.51/177.24 (~P1(f327(f327(f329(x123391),x123392),f190(f922(x123391,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12342,plain, % 177.51/177.24 (~P1(f327(f327(f329(x123421),x123422),f190(f922(x123421,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12345,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x123451),x123451))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12347,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x123471),f327(f327(f238(a915),x123471),x123472)))), % 177.51/177.24 inference(scs_inference,[],[3729,4680,4681,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,3697,3413,4661,10687,10787,11251,3108,3109,3111,3112,3115,3119,3120,3122,3125,3126,3141,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,3430,3439,3951,4259,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,3483,12035,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4545,4546,4668,3792,4317,4008,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,3944,11939,3476,3572,11768,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,3532,12056,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,4235,4194,4139,11095,4189,3857,11890,4223,3874,10650,10747,11303,11381,11464,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,3568,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,3513,10947,11103,11173,11971,12120,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,3939,11216,11222,11240,3788,11356,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,4370,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,47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% 177.51/177.24 cnf(12348,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x123481),x123481))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12351,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x123511),x123511))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12354,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x123541),x123541))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12357,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x123571),f327(a113,x123571)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12364,plain, % 177.51/177.24 (P1(f327(f327(f329(f922(x123641,a910)),x123642),f327(f308(x123641),x123642)))), % 177.51/177.24 inference(rename_variables,[],[3857])). % 177.51/177.24 cnf(12369,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x123691,a910)),x123692),f327(f327(f309(x123691),x123693),x123692)))), % 177.51/177.24 inference(rename_variables,[],[3939])). % 177.51/177.24 cnf(12376,plain, % 177.51/177.24 (~P1(f327(f327(f329(x123761),x123762),f190(f922(x123761,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12385,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x123851,a910)),x123852),f242(f922(x123851,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(12386,plain, % 177.51/177.24 (~E(f327(a113,x123861),x123861)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12389,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x123891,a910)),f327(f173(x123891),f327(f137(x123891,x123892),x123893))),f327(f173(x123891),x123893)))), % 177.51/177.24 inference(rename_variables,[],[4139])). % 177.51/177.24 cnf(12395,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x123951),f327(a113,x123951)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12404,plain, % 177.51/177.24 (E(f327(f284(x124041,x124041),f263(x124041,x124042)),x124042)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12415,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x124151)),x124151))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(12416,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x124161),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(12419,plain, % 177.51/177.24 (P1(f327(f35(x124191),f190(f922(x124191,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(12420,plain, % 177.51/177.24 (~P1(f327(f327(f329(x124201),x124202),f190(f922(x124201,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12427,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x124271,a910)),f327(f173(x124271),f177(x124271,x124272,x124273))),f327(f173(x124271),x124272)))), % 177.51/177.24 inference(rename_variables,[],[4189])). % 177.51/177.24 cnf(12430,plain, % 177.51/177.24 (P23(x124301,x124301,f5(x124301),x124302)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12437,plain, % 177.51/177.24 (P1(f327(f327(f329(f922(x124371,a910)),x124372),f327(f308(x124371),x124372)))), % 177.51/177.24 inference(rename_variables,[],[3857])). % 177.51/177.24 cnf(12444,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x124441),x124441))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12447,plain, % 177.51/177.24 (~P1(f327(f327(f329(x124471),x124472),f190(f922(x124471,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12450,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x124501,a910)),x124502),f327(f327(f309(x124501),x124503),x124502)))), % 177.51/177.24 inference(rename_variables,[],[3939])). % 177.51/177.24 cnf(12451,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x124511,a910)),x124512),f242(f922(x124511,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(12458,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x124581),x124581))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12461,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x124611),x124611))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12464,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x124641),x124641))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12467,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x124671),x124671))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12470,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x124701),f327(a113,x124701)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12473,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x124731),f327(a113,x124731)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12476,plain, % 177.51/177.24 (P1(f327(f327(f287(a915),x124761),x124761))), % 177.51/177.24 inference(rename_variables,[],[3494])). % 177.51/177.24 cnf(12479,plain, % 177.51/177.24 (P1(f327(f327(f287(a915),x124791),x124791))), % 177.51/177.24 inference(rename_variables,[],[3494])). % 177.51/177.24 cnf(12482,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x124821,a910)),x124822),x124822))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(12484,plain, % 177.51/177.24 (~P1(f327(f327(f234(a1),f327(f327(f23(a1),a83),a98)),f2(a1)))), % 177.51/177.24 inference(scs_inference,[],[3729,11371,4680,4681,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,3697,3413,4661,10687,10787,11251,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,3430,3439,3951,4259,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3549,11098,3423,4128,4670,10517,10684,3483,12035,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,3856,4545,4546,4668,3792,4317,4008,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,3532,12056,12059,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,4235,4194,4139,11095,4189,11300,3857,11890,12214,12364,4223,3874,10650,10747,11303,11381,11464,11530,12385,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,3513,10947,11103,11173,11971,12120,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,3939,11216,11222,11240,12239,12369,3788,11356,11482,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,4370,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,984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% 177.51/177.24 cnf(12489,plain, % 177.51/177.24 (P1(f327(f327(f329(f922(x124891,a910)),x124892),f327(f308(x124891),x124892)))), % 177.51/177.24 inference(rename_variables,[],[3857])). % 177.51/177.24 cnf(12498,plain, % 177.51/177.24 (~E(f327(a113,x124981),x124981)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12499,plain, % 177.51/177.24 (E(f327(f310(x124991,x124991,f5(x124991)),x124992),x124992)), % 177.51/177.24 inference(rename_variables,[],[3549])). % 177.51/177.24 cnf(12502,plain, % 177.51/177.24 (P30(x125021,x125022,f114(x125021),f114(x125021))), % 177.51/177.24 inference(rename_variables,[],[3738])). % 177.51/177.24 cnf(12505,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x125051,a910)),f327(f173(x125051),f177(x125051,x125052,x125053))),f327(f173(x125051),x125052)))), % 177.51/177.24 inference(rename_variables,[],[4189])). % 177.51/177.24 cnf(12506,plain, % 177.51/177.24 (P1(f327(f35(x125061),f327(f173(x125061),x125062)))), % 177.51/177.24 inference(rename_variables,[],[3532])). % 177.51/177.24 cnf(12517,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x125171),x125171))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12520,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x125201),x125201))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12525,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f2(a915)),x125251))), % 177.51/177.24 inference(rename_variables,[],[3513])). % 177.51/177.24 cnf(12532,plain, % 177.51/177.24 (P11(a915,f327(f169(a915),f327(f327(f155(f916(x125321),a915),f191(f916(x125321))),f180(x125321,x125322))))), % 177.51/177.24 inference(rename_variables,[],[4055])). % 177.51/177.24 cnf(12535,plain, % 177.51/177.24 (P23(x125351,x125351,f5(x125351),x125352)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12538,plain, % 177.51/177.24 (P23(x125381,x125381,f5(x125381),x125382)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12541,plain, % 177.51/177.24 (P1(f327(f327(f329(f916(x125411)),f114(x125411)),f162(x125411,x125412)))), % 177.51/177.24 inference(rename_variables,[],[3689])). % 177.51/177.24 cnf(12544,plain, % 177.51/177.24 (~P1(f327(f327(f190(f922(x125441,f922(x125442,a910))),x125443),x125444))), % 177.51/177.24 inference(rename_variables,[],[4730])). % 177.51/177.24 cnf(12549,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x125491),x125491))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12550,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f2(a915)),x125501))), % 177.51/177.24 inference(rename_variables,[],[3513])). % 177.51/177.24 cnf(12553,plain, % 177.51/177.24 (~P1(f327(f327(f190(f922(x125531,f922(x125532,a910))),x125533),x125534))), % 177.51/177.24 inference(rename_variables,[],[4730])). % 177.51/177.24 cnf(12556,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(f921(f916(x125561),f916(x125561)),a910)),f159(x125561,x125562)),f307(f916(x125561),f158(x125561,x125562))))), % 177.51/177.24 inference(rename_variables,[],[4194])). % 177.51/177.24 cnf(12562,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x125621,a910)),f327(f310(x125622,x125621,x125623),f327(f311(x125622,x125621,x125623),x125624))),x125624))), % 177.51/177.24 inference(rename_variables,[],[4370])). % 177.51/177.24 cnf(12565,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x125651,a910)),f327(f173(x125651),f177(x125651,x125652,x125653))),f327(f173(x125651),x125652)))), % 177.51/177.24 inference(rename_variables,[],[4189])). % 177.51/177.24 cnf(12566,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x125661,a910)),f327(f173(x125661),f327(f137(x125661,x125662),x125663))),f327(f173(x125661),x125663)))), % 177.51/177.24 inference(rename_variables,[],[4139])). % 177.51/177.24 cnf(12569,plain, % 177.51/177.24 (~P1(f327(f327(f235(f922(x125691,a910)),x125692),f190(f922(x125691,a910))))), % 177.51/177.24 inference(rename_variables,[],[4724])). % 177.51/177.24 cnf(12577,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x125771,a910)),f327(f310(x125772,x125771,x125773),f327(f311(x125772,x125771,x125773),x125774))),x125774))), % 177.51/177.24 inference(rename_variables,[],[4370])). % 177.51/177.24 cnf(12582,plain, % 177.51/177.24 (P1(f327(f327(f329(f916(x125821)),f114(x125821)),f162(x125821,x125822)))), % 177.51/177.24 inference(rename_variables,[],[3689])). % 177.51/177.24 cnf(12585,plain, % 177.51/177.24 (~P1(f327(f327(f329(f921(f916(x125851),f916(x125851))),f327(f327(f252(f916(x125851),f916(x125851)),x125852),f114(x125851))),f146(x125851,x125853)))), % 177.51/177.24 inference(rename_variables,[],[4732])). % 177.51/177.24 cnf(12588,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x125881),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(12590,plain, % 177.51/177.24 (~P1(f327(f35(x125901),f242(f922(x125901,a910))))), % 177.51/177.24 inference(scs_inference,[],[3729,11371,12430,12535,3738,3747,3463,4680,4681,3362,3365,4679,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,3697,3413,4661,10687,10787,11251,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,3430,3439,3951,4259,3328,3691,4045,11709,3392,3324,3352,3347,3336,3337,3963,3372,3549,11098,11225,3423,4128,4670,10517,10684,3483,12035,4714,11277,11376,11618,11621,3596,3387,3388,10587,10917,3650,3305,3409,11699,4273,4130,11297,11432,11491,4732,11200,11445,11556,11582,11626,11632,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,3856,4545,4546,4668,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3682,4721,4266,11579,3814,3532,12056,12059,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,4235,4194,12204,12556,4139,11095,12389,4189,11300,12427,12505,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,3553,10914,10944,10953,10956,10959,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,3939,11216,11222,11240,12239,12369,3788,11356,11482,12482,3941,10950,11319,11488,11522,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,10819,12544,4370,11086,12562,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,93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% 177.51/177.24 cnf(12591,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x125911,a910)),x125912),x125912))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(12594,plain, % 177.51/177.24 (~P1(f327(f327(f329(x125941),x125942),f190(f922(x125941,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12597,plain, % 177.51/177.24 (~P1(f327(f327(f190(f922(x125971,f922(x125972,a910))),x125973),x125974))), % 177.51/177.24 inference(rename_variables,[],[4730])). % 177.51/177.24 cnf(12600,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x126001,a910)),f327(f310(x126002,x126001,x126003),f327(f311(x126002,x126001,x126003),x126004))),x126004))), % 177.51/177.24 inference(rename_variables,[],[4370])). % 177.51/177.24 cnf(12601,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x126011,a910)),x126012),x126012))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(12606,plain, % 177.51/177.24 (E(f327(f284(x126061,x126061),f263(x126061,x126062)),x126062)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12609,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x126091,a910)),f327(f173(x126091),f177(x126091,x126092,x126093))),f327(f173(x126091),x126092)))), % 177.51/177.24 inference(rename_variables,[],[4189])). % 177.51/177.24 cnf(12610,plain, % 177.51/177.24 (P1(f327(f35(x126101),f327(f173(x126101),x126102)))), % 177.51/177.24 inference(rename_variables,[],[3532])). % 177.51/177.24 cnf(12613,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x126131),x126131))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12616,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x126161),x126161))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12619,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x126191),x126191))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12630,plain, % 177.51/177.24 (P23(x126301,x126301,f5(x126301),x126302)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12638,plain, % 177.51/177.24 (~P1(f327(f327(f329(x126381),x126382),f190(f922(x126381,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12641,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(x126411,x126411)),f327(f327(f252(x126411,x126411),x126412),x126412)),f307(x126411,x126413)))), % 177.51/177.24 inference(rename_variables,[],[4130])). % 177.51/177.24 cnf(12644,plain, % 177.51/177.24 (~P1(f327(f327(f329(x126441),x126442),f190(f922(x126441,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12647,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(x126471,x126471)),f327(f327(f252(x126471,x126471),x126472),x126472)),f307(x126471,x126473)))), % 177.51/177.24 inference(rename_variables,[],[4130])). % 177.51/177.24 cnf(12657,plain, % 177.51/177.24 (~E(f327(f327(f152(x126571),x126572),x126573),x126573)), % 177.51/177.24 inference(rename_variables,[],[4670])). % 177.51/177.24 cnf(12664,plain, % 177.51/177.24 (P1(f327(f327(f329(x126641),x126642),f242(f922(x126641,a910))))), % 177.51/177.24 inference(rename_variables,[],[3645])). % 177.51/177.24 cnf(12665,plain, % 177.51/177.24 (~E(f327(a113,x126651),x126651)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12668,plain, % 177.51/177.24 (P1(f327(f327(f329(f916(x126681)),f114(x126681)),f162(x126681,x126682)))), % 177.51/177.24 inference(rename_variables,[],[3689])). % 177.51/177.24 cnf(12669,plain, % 177.51/177.24 (~E(f327(f327(f152(x126691),x126692),x126693),f114(x126691))), % 177.51/177.24 inference(rename_variables,[],[4677])). % 177.51/177.24 cnf(12672,plain, % 177.51/177.24 (P23(x126721,x126721,f5(x126721),x126722)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12675,plain, % 177.51/177.24 (P1(f327(f327(f329(x126751),f327(x126752,x126753)),f327(f310(x126754,x126751,x126752),f242(f922(x126754,a910)))))), % 177.51/177.24 inference(rename_variables,[],[4096])). % 177.51/177.24 cnf(12676,plain, % 177.51/177.24 (P23(x126761,x126761,f5(x126761),x126762)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12679,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x126791,a910)),f190(f922(x126791,a910))),x126792))), % 177.51/177.24 inference(rename_variables,[],[3941])). % 177.51/177.24 cnf(12680,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x126801,a910)),x126802),x126802))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(12683,plain, % 177.51/177.24 (P1(f327(f327(f329(x126831),f327(x126832,x126833)),f327(f310(x126834,x126831,x126832),f242(f922(x126834,a910)))))), % 177.51/177.24 inference(rename_variables,[],[4096])). % 177.51/177.24 cnf(12684,plain, % 177.51/177.24 (P23(x126841,x126841,f5(x126841),x126842)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12687,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(f916(x126871),f916(x126871))),f327(f327(f252(f916(x126871),f916(x126871)),f114(x126871)),f114(x126871))),f159(x126871,x126872)))), % 177.51/177.24 inference(rename_variables,[],[4273])). % 177.51/177.24 cnf(12691,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x126911),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(12697,plain, % 177.51/177.24 (E(f327(f327(f135(x126971),x126972),f114(x126971)),x126972)), % 177.51/177.24 inference(rename_variables,[],[3424])). % 177.51/177.24 cnf(12698,plain, % 177.51/177.24 (~E(f327(f327(f152(x126981),x126982),x126983),x126983)), % 177.51/177.24 inference(rename_variables,[],[4670])). % 177.51/177.24 cnf(12701,plain, % 177.51/177.24 (E(f327(f327(f135(x127011),x127012),f114(x127011)),x127012)), % 177.51/177.24 inference(rename_variables,[],[3424])). % 177.51/177.24 cnf(12702,plain, % 177.51/177.24 (~E(f327(f327(f152(x127021),x127022),x127023),x127023)), % 177.51/177.24 inference(rename_variables,[],[4670])). % 177.51/177.24 cnf(12705,plain, % 177.51/177.24 (E(f327(f327(f135(x127051),x127052),f114(x127051)),x127052)), % 177.51/177.24 inference(rename_variables,[],[3424])). % 177.51/177.24 cnf(12712,plain, % 177.51/177.24 (P49(x127121,f263(x127121,x127122))), % 177.51/177.24 inference(rename_variables,[],[3366])). % 177.51/177.24 cnf(12715,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x127151,a910)),f327(f173(x127151),f327(f137(x127151,x127152),x127153))),f327(f173(x127151),x127153)))), % 177.51/177.24 inference(rename_variables,[],[4139])). % 177.51/177.24 cnf(12716,plain, % 177.51/177.24 (E(f327(f310(x127161,x127161,f5(x127161)),x127162),x127162)), % 177.51/177.24 inference(rename_variables,[],[3549])). % 177.51/177.24 cnf(12721,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x127211,a910)),x127212),f242(f922(x127211,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(12725,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x127251),x127251))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12726,plain, % 177.51/177.24 (~E(f327(a113,x127261),x127261)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12729,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x127291,a910)),f190(f922(x127291,a910))),x127292))), % 177.51/177.24 inference(rename_variables,[],[3941])). % 177.51/177.24 cnf(12732,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x127321),x127321))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12735,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x127351,a910)),x127352),x127352))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(12740,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x127401,a910)),x127402),f327(f327(f309(x127401),x127403),x127402)))), % 177.51/177.24 inference(rename_variables,[],[3939])). % 177.51/177.24 cnf(12743,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x127431,a910)),x127432),x127432))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(12744,plain, % 177.51/177.24 (~P1(f327(f327(f329(x127441),x127442),f190(f922(x127441,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12747,plain, % 177.51/177.24 (~P1(f327(f327(f329(x127471),x127472),f190(f922(x127471,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12756,plain, % 177.51/177.24 (P23(x127561,x127561,f5(x127561),x127562)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12759,plain, % 177.51/177.24 (E(f327(f191(f916(x127591)),f170(x127591,x127592,x127593)),x127592)), % 177.51/177.24 inference(rename_variables,[],[3559])). % 177.51/177.24 cnf(12762,plain, % 177.51/177.24 (P24(x127621,x127621,f31(x127621),x127622,x127622)), % 177.51/177.24 inference(rename_variables,[],[4154])). % 177.51/177.24 cnf(12765,plain, % 177.51/177.24 (P23(x127651,x127651,f5(x127651),x127652)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12768,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x127681),x127681))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12769,plain, % 177.51/177.24 (P1(f327(f242(f922(x127691,a910)),x127692))), % 177.51/177.24 inference(rename_variables,[],[3553])). % 177.51/177.24 cnf(12772,plain, % 177.51/177.24 (~P1(f327(f327(f329(x127721),x127722),f190(f922(x127721,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12775,plain, % 177.51/177.24 (P1(f327(f327(f329(x127751),f327(x127752,x127753)),f327(f310(x127754,x127751,x127752),f242(f922(x127754,a910)))))), % 177.51/177.24 inference(rename_variables,[],[4096])). % 177.51/177.24 cnf(12776,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(x127761,x127761)),f327(f327(f252(x127761,x127761),x127762),x127762)),f307(x127761,x127763)))), % 177.51/177.24 inference(rename_variables,[],[4130])). % 177.51/177.24 cnf(12779,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(x127791,x127791)),f327(f327(f252(x127791,x127791),x127792),x127792)),f307(x127791,x127793)))), % 177.51/177.24 inference(rename_variables,[],[4130])). % 177.51/177.24 cnf(12782,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x127821),x127821))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(12783,plain, % 177.51/177.24 (P1(f327(f242(f922(x127831,a910)),x127832))), % 177.51/177.24 inference(rename_variables,[],[3553])). % 177.51/177.24 cnf(12786,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x127861,a910)),x127862),f242(f922(x127861,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(12787,plain, % 177.51/177.24 (P24(x127871,x127871,f31(x127871),x127872,x127872)), % 177.51/177.24 inference(rename_variables,[],[4154])). % 177.51/177.24 cnf(12790,plain, % 177.51/177.24 (P1(f327(f35(x127901),f327(f173(x127901),x127902)))), % 177.51/177.24 inference(rename_variables,[],[3532])). % 177.51/177.24 cnf(12795,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(f916(x127951),f916(x127951))),f327(f327(f252(f916(x127951),f916(x127951)),f114(x127951)),f114(x127951))),f327(f327(f289(f916(x127951),f916(x127951),f916(x127951)),f159(x127951,x127952)),f159(x127951,x127952))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,3738,3747,3463,4680,4681,3362,3365,3366,4679,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,3548,3697,12187,3413,4661,10687,10787,11251,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,3424,12697,12701,12705,3430,3439,3951,4259,3559,3328,3691,4045,11709,3392,3324,3352,3809,3347,3336,3337,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,4677,12669,3483,12035,4714,11277,11376,11618,11621,3596,4691,3387,3388,10587,10917,3650,3305,3409,11699,4273,12687,4130,11297,11432,11491,12641,12647,12776,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,4668,11692,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3882,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,10819,12544,12553,4370,11086,12562,12577,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638])). % 177.51/177.24 cnf(12797,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(x127971,x127971)),f327(f327(f252(x127971,x127971),x127972),x127972)),f327(f327(f289(x127971,x127971,x127971),f307(x127971,x127973)),f307(x127971,f307(x127971,x127973)))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,3738,3747,3463,4680,4681,3362,3365,3366,4679,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,3548,3697,12187,3413,4661,10687,10787,11251,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,3424,12697,12701,12705,3430,3439,3951,4259,3559,3328,3691,4045,11709,3392,3324,3352,3809,3347,3336,3337,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,4677,12669,3483,12035,4714,11277,11376,11618,11621,3596,4691,3387,3388,10587,10917,3650,3305,3409,11699,4273,12687,4130,11297,11432,11491,12641,12647,12776,12779,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,4668,11692,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3882,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,10819,12544,12553,4370,11086,12562,12577,4277,3972,3917,4727,10539,10542,10908,10911,11808,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648])). % 177.51/177.24 cnf(12800,plain, % 177.51/177.24 (~P1(f327(f327(f190(f922(x128001,f922(x128002,a910))),x128003),x128004))), % 177.51/177.24 inference(rename_variables,[],[4730])). % 177.51/177.24 cnf(12803,plain, % 177.51/177.24 (~P1(f327(f327(f190(f922(x128031,f922(x128032,a910))),x128033),x128034))), % 177.51/177.24 inference(rename_variables,[],[4730])). % 177.51/177.24 cnf(12806,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x128061,a910)),x128062),f242(f922(x128061,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(12809,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(x128091,x128091)),f327(f327(f252(x128091,x128091),x128092),x128092)),f307(x128091,x128093)))), % 177.51/177.24 inference(rename_variables,[],[4130])). % 177.51/177.24 cnf(12812,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),f327(f327(f80(a915),x128121),x128122)),x128122))), % 177.51/177.24 inference(rename_variables,[],[4727])). % 177.51/177.24 cnf(12813,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x128131),f327(a113,x128131)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(12816,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x128161,a910)),x128162),f242(f922(x128161,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(12819,plain, % 177.51/177.24 (E(f327(f284(x128191,x128191),f263(x128191,x128192)),x128192)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12830,plain, % 177.51/177.24 (~P1(f327(f327(f329(x128301),x128302),f190(f922(x128301,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12831,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(f916(x128311),f916(x128311))),f327(f327(f252(f916(x128311),f916(x128311)),f114(x128311)),f114(x128311))),f159(x128311,x128312)))), % 177.51/177.24 inference(rename_variables,[],[4273])). % 177.51/177.24 cnf(12833,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(a915,a915)),f327(f327(f252(a915,a915),f2(a915)),f327(a113,f2(a915)))),f327(f327(f289(a915,a915,a915),f307(a915,a317)),f307(a915,f307(a915,a317)))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,3738,3747,3463,4680,4681,3362,3365,3366,4679,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,3548,3697,12187,3413,4661,10687,10787,11251,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,3829,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,3424,12697,12701,12705,3430,3439,3951,4259,3559,3328,3691,4045,11709,3392,3324,3352,3809,3347,3336,3337,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,4677,12669,3483,12035,4714,11277,11376,11618,11621,3596,4691,3387,3388,10587,10917,3650,3305,3409,11699,4273,12687,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,4668,11692,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3882,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,4726,10813,10816,4731,11286,11289,11479,11592,11609,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,10819,12544,12553,12597,12800,4370,11086,12562,12577,4277,3972,3917,4727,10539,10542,10908,10911,11808,11996,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750])). % 177.51/177.24 cnf(12836,plain, % 177.51/177.24 (~P1(f327(f327(f329(x128361),x128362),f190(f922(x128361,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12841,plain, % 177.51/177.24 (P29(x128411,x128412,f114(x128411))), % 177.51/177.24 inference(rename_variables,[],[3429])). % 177.51/177.24 cnf(12844,plain, % 177.51/177.24 (E(f327(f191(f916(x128441)),f170(x128441,x128442,x128443)),x128442)), % 177.51/177.24 inference(rename_variables,[],[3559])). % 177.51/177.24 cnf(12847,plain, % 177.51/177.24 (~P1(f327(f327(f329(x128471),x128472),f190(f922(x128471,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12852,plain, % 177.51/177.24 (P1(f327(f327(f329(x128521),x128522),f242(f922(x128521,a910))))), % 177.51/177.24 inference(rename_variables,[],[3645])). % 177.51/177.24 cnf(12854,plain, % 177.51/177.24 (~P1(f327(f327(f329(f921(f916(x128541),f916(x128541))),f327(f327(f252(f916(x128541),f916(x128541)),x128542),x128542)),f148(x128541,f154(x128541,f114(f922(x128541,a915))))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,3738,3747,3463,3429,4680,4681,3362,3365,3366,4679,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,3548,3697,12187,3413,4661,10687,10787,11251,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,3829,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,3424,12697,12701,12705,3430,3439,3951,4259,3559,12759,3328,3691,4045,11709,3392,3324,3352,3809,3347,3336,3337,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,4677,12669,3483,12035,4714,11277,11376,11618,11621,3596,4691,3387,3388,10587,10917,3650,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,4668,11692,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3882,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,10819,12544,12553,12597,12800,4370,11086,12562,12577,4277,3972,3917,4727,10539,10542,10908,10911,11808,11996,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108])). % 177.51/177.24 cnf(12856,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x128561),x128561))), % 177.51/177.24 inference(rename_variables,[],[4703])). % 177.51/177.24 cnf(12858,plain, % 177.51/177.24 (P1(f327(f327(f329(f921(f916(x128581),f916(x128581))),f327(f327(f252(f916(x128581),f916(x128581)),f170(x128581,f327(f191(f916(x128581)),x128582),x128583)),x128582)),f159(x128581,f242(f922(f921(x128581,x128581),a910)))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,3738,3747,3463,3429,4680,4681,3362,3365,3366,4679,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,3548,3697,12187,3413,4661,10687,10787,11251,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,3288,4649,3829,4059,11953,3338,11663,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,3424,12697,12701,12705,3430,3439,3951,4259,3559,12759,12844,3328,3691,4045,11709,3392,3324,3352,3809,3347,3336,3337,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,4677,12669,3483,12035,4714,11277,11376,11618,11621,3596,4691,3387,3388,10587,10917,3650,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,4668,11692,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3882,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,3804,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,10819,12544,12553,12597,12800,4370,11086,12562,12577,4277,3972,3917,4727,10539,10542,10908,10911,11808,11996,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175])). % 177.51/177.24 cnf(12859,plain, % 177.51/177.24 (P1(f327(f327(f329(x128591),x128592),f242(f922(x128591,a910))))), % 177.51/177.24 inference(rename_variables,[],[3645])). % 177.51/177.24 cnf(12867,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x128671,a910)),x128672),x128672))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(12870,plain, % 177.51/177.24 (~P1(f327(f327(f329(x128701),x128702),f190(f922(x128701,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(12873,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f2(a1)),f327(f327(f244(a1),f327(f75(a1),x128731)),x128732)))), % 177.51/177.24 inference(rename_variables,[],[3972])). % 177.51/177.24 cnf(12876,plain, % 177.51/177.24 (~E(f327(a113,x128761),x128761)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(12878,plain, % 177.51/177.24 (E(f327(f284(x128781,x128781),f263(x128781,x128782)),x128782)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12880,plain, % 177.51/177.24 (E(f327(f284(x128801,x128801),f263(x128801,x128802)),x128802)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12884,plain, % 177.51/177.24 (E(f327(f284(x128841,x128841),f263(x128841,x128842)),x128842)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12886,plain, % 177.51/177.24 (P23(x128861,x128861,f5(x128861),x128862)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12888,plain, % 177.51/177.24 (P23(x128881,x128881,f5(x128881),x128882)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(12898,plain, % 177.51/177.24 (E(f327(f284(x128981,x128981),f263(x128981,x128982)),x128982)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12900,plain, % 177.51/177.24 (E(f327(f284(x129001,x129001),f263(x129001,x129002)),x129002)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12902,plain, % 177.51/177.24 (P24(x129021,x129021,f31(x129021),x129022,x129022)), % 177.51/177.24 inference(rename_variables,[],[4154])). % 177.51/177.24 cnf(12904,plain, % 177.51/177.24 (P24(x129041,x129041,f31(x129041),x129042,x129042)), % 177.51/177.24 inference(rename_variables,[],[4154])). % 177.51/177.24 cnf(12906,plain, % 177.51/177.24 (P24(x129061,x129061,f31(x129061),x129062,x129062)), % 177.51/177.24 inference(rename_variables,[],[4154])). % 177.51/177.24 cnf(12913,plain, % 177.51/177.24 (E(f190(f922(f921(x129131,x129131),a910)),f263(x129131,f190(f922(x129131,a910))))), % 177.51/177.24 inference(rename_variables,[],[3563])). % 177.51/177.24 cnf(12932,plain, % 177.51/177.24 (P52(x129321,x129321,f263(x129321,x129322))), % 177.51/177.24 inference(rename_variables,[],[3463])). % 177.51/177.24 cnf(12938,plain, % 177.51/177.24 (E(f327(f284(x129381,x129381),f263(x129381,x129382)),x129382)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12940,plain, % 177.51/177.24 (E(f327(f284(x129401,x129401),f263(x129401,x129402)),x129402)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12943,plain, % 177.51/177.24 (E(f327(f284(x129431,x129431),f263(x129431,x129432)),x129432)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12945,plain, % 177.51/177.24 (E(f327(f284(x129451,x129451),f263(x129451,x129452)),x129452)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12951,plain, % 177.51/177.24 (P30(x129511,x129512,f114(x129511),f114(x129511))), % 177.51/177.24 inference(rename_variables,[],[3738])). % 177.51/177.24 cnf(12953,plain, % 177.51/177.24 (P30(x129531,x129532,f114(x129531),f114(x129531))), % 177.51/177.24 inference(rename_variables,[],[3738])). % 177.51/177.24 cnf(12959,plain, % 177.51/177.24 (P36(x129591,f263(x129591,x129592))), % 177.51/177.24 inference(rename_variables,[],[3363])). % 177.51/177.24 cnf(12965,plain, % 177.51/177.24 (P49(x129651,f263(x129651,x129652))), % 177.51/177.24 inference(rename_variables,[],[3366])). % 177.51/177.24 cnf(12970,plain, % 177.51/177.24 (E(f327(f284(x129701,x129701),f263(x129701,x129702)),x129702)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(12972,plain, % 177.51/177.24 (P50(x129721,x129722,f263(x129721,x129722))), % 177.51/177.24 inference(rename_variables,[],[3462])). % 177.51/177.24 cnf(12974,plain, % 177.51/177.24 (P50(x129741,x129742,f263(x129741,x129742))), % 177.51/177.24 inference(rename_variables,[],[3462])). % 177.51/177.24 cnf(12976,plain, % 177.51/177.24 (P50(x129761,x129762,f263(x129761,x129762))), % 177.51/177.24 inference(rename_variables,[],[3462])). % 177.51/177.24 cnf(12980,plain, % 177.51/177.24 (P12(x129801,f922(x129801,a910),f309(x129801))), % 177.51/177.24 inference(rename_variables,[],[3466])). % 177.51/177.24 cnf(12988,plain, % 177.51/177.24 (P53(x129881,f190(f922(x129881,a910)),x129882)), % 177.51/177.24 inference(rename_variables,[],[3511])). % 177.51/177.24 cnf(12992,plain, % 177.51/177.24 (P35(x129921,f154(x129921,x129922))), % 177.51/177.24 inference(rename_variables,[],[3362])). % 177.51/177.24 cnf(12998,plain, % 177.51/177.24 (P40(x129981,x129982,x129983,x129984,f190(f922(x129981,a910)),x129984)), % 177.51/177.24 inference(rename_variables,[],[4431])). % 177.51/177.24 cnf(13010,plain, % 177.51/177.24 (E(f190(f922(f921(x130101,x130101),a910)),f263(x130101,f190(f922(x130101,a910))))), % 177.51/177.24 inference(rename_variables,[],[3563])). % 177.51/177.24 cnf(13024,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x130241),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13026,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),a83),f2(a1)))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3256,3258,3262,3270,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,3424,12697,12701,12705,3430,3439,3951,4259,3559,12759,12844,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,4086,4714,11277,11376,11618,11621,3891,3596,3815,4691,3563,12913,13010,3387,3388,10587,10917,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,4720,11811,11842,11879,11886,11919,3931,3698,3699,4078,3519,3521,3495,4704,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,4314,4710,3984,4020,4694,4698,3469,3473,4697,4695,4696,4438,3804,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,12743,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,4729,11936,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,4277,3972,3917,4727,10539,10542,10908,10911,11808,11996,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642])). % 177.51/177.24 cnf(13033,plain, % 177.51/177.24 (~P1(f327(f327(f235(a1),f327(f101(a1),x130331)),f327(f79(a1),f327(f101(a1),x130332))))), % 177.51/177.24 inference(rename_variables,[],[4725])). % 177.51/177.24 cnf(13043,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x130431),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13046,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x130461),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13049,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x130491,x130492)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13052,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x130521,x130522)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13055,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x130551,x130552)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13058,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x130581,x130582)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13065,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f327(f79(a1),f327(f101(a1),x130651))),f327(f101(a1),x130652)))), % 177.51/177.24 inference(rename_variables,[],[3973])). % 177.51/177.24 cnf(13067,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f2(a1)),f327(f105(a1),f2(a1))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3255,3256,3258,3262,3270,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,3424,12697,12701,12705,3430,3439,3951,4259,3559,12759,12844,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,4086,4714,11277,11376,11618,11621,3891,3596,3815,4691,3563,12913,13010,3387,3388,10587,10917,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,4720,11811,11842,11879,11886,11919,3931,3698,3699,12232,13049,13052,13055,4078,3519,3521,3495,4704,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,12062,4314,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,3804,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,12743,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,4277,3972,3917,3918,4727,10539,10542,10908,10911,11808,11996,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6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% 177.51/177.24 cnf(13070,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x130701),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13071,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x130711),x130711))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13078,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x130781),f327(a113,x130781)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(13080,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f2(a1)),a83))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3152,3155,3156,3160,3164,3167,3174,3179,3180,3188,3192,3196,3198,3199,3247,3248,3251,3255,3256,3258,3262,3270,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,3424,12697,12701,12705,3430,3439,3951,4259,3559,12759,12844,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,4086,4714,11277,11376,11618,11621,3891,3596,3815,4691,3563,12913,13010,3387,3388,10587,10917,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,3835,4317,4008,4055,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,4720,11811,11842,11879,11886,11919,3931,3698,3699,12232,13049,13052,13055,4078,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,3494,12476,3568,12419,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,3553,10914,10944,10953,10956,10959,11548,12769,3592,3585,4012,3949,10566,11942,11970,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,3973,12062,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,3804,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,12743,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,4277,3972,3917,3918,4727,10539,10542,10908,10911,11808,11996,4728,11916,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,650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% 177.51/177.24 cnf(13085,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x130851),x130851))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(13088,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x130881,x130882)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13091,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x130911,x130912)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13094,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x130941),x130941))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13111,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f46(a915,x131111,x131112)),x131111))), % 177.51/177.24 inference(rename_variables,[],[3949])). % 177.51/177.24 cnf(13116,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x131161),f327(a113,x131161)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(13119,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x131191),f327(a113,x131191)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(13120,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x131201),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13129,plain, % 177.51/177.24 (~P1(f327(f327(f235(a1),f327(f101(a1),x131291)),f2(a1)))), % 177.51/177.24 inference(rename_variables,[],[4720])). % 177.51/177.24 cnf(13130,plain, % 177.51/177.24 (P1(f327(f242(f922(x131301,a910)),x131302))), % 177.51/177.24 inference(rename_variables,[],[3553])). % 177.51/177.24 cnf(13133,plain, % 177.51/177.24 (~P1(f327(f327(f235(a1),f327(f101(a1),x131331)),f2(a1)))), % 177.51/177.24 inference(rename_variables,[],[4720])). % 177.51/177.24 cnf(13134,plain, % 177.51/177.24 (P1(f327(f242(f922(x131341,a910)),x131342))), % 177.51/177.24 inference(rename_variables,[],[3553])). % 177.51/177.24 cnf(13137,plain, % 177.51/177.24 (P1(f327(f242(f922(x131371,a910)),x131372))), % 177.51/177.24 inference(rename_variables,[],[3553])). % 177.51/177.24 cnf(13140,plain, % 177.51/177.24 (P1(f327(f242(f922(x131401,a910)),x131402))), % 177.51/177.24 inference(rename_variables,[],[3553])). % 177.51/177.24 cnf(13148,plain, % 177.51/177.24 (~P1(f327(f327(f329(x131481),x131482),f190(f922(x131481,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13149,plain, % 177.51/177.24 (P1(f327(f35(x131491),f190(f922(x131491,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(13152,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x131521),x131521))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13161,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f2(a915)),x131611))), % 177.51/177.24 inference(rename_variables,[],[3513])). % 177.51/177.24 cnf(13164,plain, % 177.51/177.24 (~P1(f327(f327(f329(x131641),x131642),f190(f922(x131641,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13167,plain, % 177.51/177.24 (~P1(f327(f327(f329(x131671),x131672),f190(f922(x131671,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13172,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x131721),x131721))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13180,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x131801),f327(a113,x131801)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(13183,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x131831),x131831))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13188,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x131881),x131881))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13191,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x131911),x131911))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13194,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x131941),x131941))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13197,plain, % 177.51/177.24 (E(f327(f327(f23(f922(x131971,a910)),f190(f922(x131971,a910))),x131972),f190(f922(x131971,a910)))), % 177.51/177.24 inference(rename_variables,[],[3758])). % 177.51/177.24 cnf(13198,plain, % 177.51/177.24 (P1(f327(f35(x131981),f190(f922(x131981,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(13201,plain, % 177.51/177.24 (E(f327(f327(f23(f922(x132011,a910)),f190(f922(x132011,a910))),x132012),f190(f922(x132011,a910)))), % 177.51/177.24 inference(rename_variables,[],[3758])). % 177.51/177.24 cnf(13202,plain, % 177.51/177.24 (P1(f327(f35(x132021),f190(f922(x132021,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(13205,plain, % 177.51/177.24 (E(f327(f327(f23(f922(x132051,a910)),f190(f922(x132051,a910))),x132052),f190(f922(x132051,a910)))), % 177.51/177.24 inference(rename_variables,[],[3758])). % 177.51/177.24 cnf(13206,plain, % 177.51/177.24 (P1(f327(f35(x132061),f190(f922(x132061,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(13209,plain, % 177.51/177.24 (E(f327(f327(f23(f922(x132091,a910)),f190(f922(x132091,a910))),x132092),f190(f922(x132091,a910)))), % 177.51/177.24 inference(rename_variables,[],[3758])). % 177.51/177.24 cnf(13210,plain, % 177.51/177.24 (P1(f327(f35(x132101),f190(f922(x132101,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(13214,plain, % 177.51/177.24 (E(f327(f284(x132141,x132141),f263(x132141,x132142)),x132142)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(13219,plain, % 177.51/177.24 (E(f327(f327(f23(f922(x132191,a910)),f190(f922(x132191,a910))),x132192),f190(f922(x132191,a910)))), % 177.51/177.24 inference(rename_variables,[],[3758])). % 177.51/177.24 cnf(13220,plain, % 177.51/177.24 (P1(f327(f35(x132201),f190(f922(x132201,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(13224,plain, % 177.51/177.24 (P1(f327(f35(x132241),f190(f922(x132241,a910))))), % 177.51/177.24 inference(rename_variables,[],[3568])). % 177.51/177.24 cnf(13227,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x132271),x132271))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13231,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x132311),x132311))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(13238,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x132381),x132381))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13251,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x132511),x132511))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13254,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x132541),x132541))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(13263,plain, % 177.51/177.24 (~P1(f327(f327(f329(x132631),x132632),f190(f922(x132631,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13274,plain, % 177.51/177.24 (P1(f327(f327(f329(x132741),x132742),f242(f922(x132741,a910))))), % 177.51/177.24 inference(rename_variables,[],[3645])). % 177.51/177.24 cnf(13275,plain, % 177.51/177.24 (E(f327(f194(x132751,x132752),x132753),f122(x132751,x132752))), % 177.51/177.24 inference(rename_variables,[],[3407])). % 177.51/177.24 cnf(13278,plain, % 177.51/177.24 (P1(f327(f327(f329(x132781),f327(x132782,x132783)),f327(f310(x132784,x132781,x132782),f242(f922(x132784,a910)))))), % 177.51/177.24 inference(rename_variables,[],[4096])). % 177.51/177.24 cnf(13282,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x132821,a910)),x132822),f242(f922(x132821,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(13285,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x132851,a910)),x132852),x132852))), % 177.51/177.24 inference(rename_variables,[],[3788])). % 177.51/177.24 cnf(13291,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x132911),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13292,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x132921),x132921))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(13296,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x132961),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13297,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x132971),x132971))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(13302,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x133021),x133021))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13309,plain, % 177.51/177.24 (E(f327(f327(f16(x133091,x133092),x133093),x133094),x133093)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(13312,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x133121,a910)),f327(f173(x133121),f177(x133121,x133122,x133123))),f327(f173(x133121),x133122)))), % 177.51/177.24 inference(rename_variables,[],[4189])). % 177.51/177.24 cnf(13319,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x133191),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13320,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x133201),x133201))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(13324,plain, % 177.51/177.24 (~P1(f327(f327(f235(a915),x133241),f2(a915)))), % 177.51/177.24 inference(rename_variables,[],[4707])). % 177.51/177.24 cnf(13325,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),x133251),x133251))), % 177.51/177.24 inference(rename_variables,[],[3493])). % 177.51/177.24 cnf(13329,plain, % 177.51/177.24 (~P1(f327(f327(f234(f922(a915,a910)),f303(a915,f327(a113,x133291),f327(a113,x133291))),f303(a915,x133292,x133291)))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3219,3221,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,4086,4714,11277,11376,11618,11621,3891,3596,3815,4691,3563,12913,13010,3387,3388,10587,10917,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,4078,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,3513,10947,11103,11173,11971,12120,12317,12525,12550,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,3804,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688])). % 177.51/177.24 cnf(13330,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x133301),x133301))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13333,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),x133331),x133331))), % 177.51/177.24 inference(rename_variables,[],[3492])). % 177.51/177.24 cnf(13336,plain, % 177.51/177.24 (~P1(f327(f327(f234(a915),f327(a113,x133361)),x133361))), % 177.51/177.24 inference(rename_variables,[],[4713])). % 177.51/177.24 cnf(13341,plain, % 177.51/177.24 (E(x133411,f878(f327(f5(x133412),f327(f5(x133412),x133411)),f5(x133412),x133412,x133412))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3219,3221,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,4086,4714,11277,11376,11618,11621,3891,3596,3815,4691,3563,12913,13010,3387,3388,10587,10917,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,4078,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,4724,11046,11456,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,3804,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,3939,11216,11222,11240,12239,12369,12450,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,4271,3941,10950,11319,11488,11522,11535,12679,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841])). % 177.51/177.24 cnf(13342,plain, % 177.51/177.24 (P1(f327(f327(f329(x133421),f327(x133422,x133423)),f327(f310(x133424,x133421,x133422),f242(f922(x133424,a910)))))), % 177.51/177.24 inference(rename_variables,[],[4096])). % 177.51/177.24 cnf(13343,plain, % 177.51/177.24 (P23(x133431,x133431,f5(x133431),x133432)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13348,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x133481,a910)),x133482),f242(f922(x133481,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(13349,plain, % 177.51/177.24 (P23(x133491,x133491,f5(x133491),x133492)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13353,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x133531,a910)),x133532),f242(f922(x133531,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(13354,plain, % 177.51/177.24 (P23(x133541,x133541,f5(x133541),x133542)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13358,plain, % 177.51/177.24 (P23(x133581,x133581,f5(x133581),x133582)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13361,plain, % 177.51/177.24 (~P1(f327(f327(f235(f922(x133611,a910)),x133612),f190(f922(x133611,a910))))), % 177.51/177.24 inference(rename_variables,[],[4724])). % 177.51/177.24 cnf(13364,plain, % 177.51/177.24 (P23(x133641,x133641,f5(x133641),x133642)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13367,plain, % 177.51/177.24 (P23(x133671,x133671,f5(x133671),x133672)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13373,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x133731,a910)),x133732),f242(f922(x133731,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(13378,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x133781,a910)),f190(f922(x133781,a910))),x133782))), % 177.51/177.24 inference(rename_variables,[],[3941])). % 177.51/177.24 cnf(13382,plain, % 177.51/177.24 (E(f327(f284(x133821,x133821),f263(x133821,x133822)),x133822)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(13386,plain, % 177.51/177.24 (~P1(f327(f327(f329(x133861),x133862),f190(f922(x133861,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13391,plain, % 177.51/177.24 (P23(x133911,x133911,f5(x133911),x133912)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13394,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x133941,a910)),x133942),f242(f922(x133941,a910))))), % 177.51/177.24 inference(rename_variables,[],[3874])). % 177.51/177.24 cnf(13402,plain, % 177.51/177.24 (E(f327(f327(f16(x134021,x134022),x134023),x134024),x134023)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(13405,plain, % 177.51/177.24 (~P1(f327(f327(f329(x134051),x134052),f190(f922(x134051,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13408,plain, % 177.51/177.24 (~P1(f327(f327(f329(x134081),x134082),f190(f922(x134081,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13413,plain, % 177.51/177.24 (~E(f327(a113,x134131),x134131)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(13416,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x134161),f327(a113,x134161)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(13417,plain, % 177.51/177.24 (~E(f327(a113,x134171),x134171)), % 177.51/177.24 inference(rename_variables,[],[4651])). % 177.51/177.24 cnf(13420,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x134201),f327(a113,f327(f327(f80(a915),x134202),x134201))))), % 177.51/177.24 inference(rename_variables,[],[3942])). % 177.51/177.24 cnf(13421,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),x134211),f327(a113,x134211)))), % 177.51/177.24 inference(rename_variables,[],[3560])). % 177.51/177.24 cnf(13423,plain, % 177.51/177.24 (~E(f327(f327(f81(a915),f327(a113,f2(a915))),f120(x134231)),f327(f327(f81(a915),f327(a113,f2(a915))),f127(x134231,x134232,x134233)))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,12906,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,13343,13349,13354,13358,13364,13367,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,12876,13413,13417,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3219,3221,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,13214,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,13309,4086,4714,11277,11376,11618,11621,3458,3891,3478,3596,3815,4691,3563,12913,13010,3387,3388,10587,10917,4701,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,11502,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,13416,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,4078,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,4189,11300,12427,12505,12565,12609,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,13282,13348,13353,13373,4724,11046,11456,12569,13361,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,13274,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,13263,13386,13405,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,3804,11935,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,13342,3939,11216,11222,11240,12239,12369,12450,12740,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,4271,3941,10950,11319,11488,11522,11535,12679,12729,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,12600,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,11135,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841,9101,9102,9173,9187,9240,9241,9360,9394,9420,9452,9493,9689,9813,9956,10144,10201,10203,6055,6603,6604,6693])). % 177.51/177.24 cnf(13430,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f2(a1)),f327(f101(a1),x134301)))), % 177.51/177.24 inference(rename_variables,[],[3592])). % 177.51/177.24 cnf(13433,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f2(a915)),x134331))), % 177.51/177.24 inference(rename_variables,[],[3513])). % 177.51/177.24 cnf(13437,plain, % 177.51/177.24 (~E(f327(a113,x134371),f2(a915))), % 177.51/177.24 inference(rename_variables,[],[4661])). % 177.51/177.24 cnf(13440,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x134401,a910)),f327(f173(x134401),f177(x134401,x134402,x134403))),f327(f173(x134401),x134402)))), % 177.51/177.24 inference(rename_variables,[],[4189])). % 177.51/177.24 cnf(13445,plain, % 177.51/177.24 (~P1(f327(f327(f329(x134451),x134452),f190(f922(x134451,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13448,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x134481,x134482)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13449,plain, % 177.51/177.24 (E(f327(f327(f189(a915),f327(a113,x134491)),f327(a113,x134492)),f327(a113,f327(f327(f189(a915),x134491),x134492)))), % 177.51/177.24 inference(rename_variables,[],[3664])). % 177.51/177.24 cnf(13452,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x134521,x134522)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13453,plain, % 177.51/177.24 (E(f327(f327(f238(a915),f327(a113,x134531)),f327(a113,x134532)),f327(a113,f327(f327(f238(a915),x134531),x134532)))), % 177.51/177.24 inference(rename_variables,[],[3663])). % 177.51/177.24 cnf(13456,plain, % 177.51/177.24 (P1(f327(f35(a915),f305(a915,x134561,x134562)))), % 177.51/177.24 inference(rename_variables,[],[3699])). % 177.51/177.24 cnf(13465,plain, % 177.51/177.24 (~P1(f327(f327(f329(x134651),x134652),f190(f922(x134651,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13466,plain, % 177.51/177.24 (E(f327(f327(f16(x134661,x134662),x134663),x134664),x134663)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(13469,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x134691,a910)),f327(f173(x134691),f327(f137(x134691,x134692),x134693))),f327(f173(x134691),x134693)))), % 177.51/177.24 inference(rename_variables,[],[4139])). % 177.51/177.24 cnf(13470,plain, % 177.51/177.24 (E(f327(f327(f16(x134701,x134702),x134703),x134704),x134703)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(13473,plain, % 177.51/177.24 (P1(f327(f327(f234(f922(x134731,a910)),f327(f173(x134731),f327(f327(f176(x134731),x134732),x134733))),f327(f173(x134731),x134733)))), % 177.51/177.24 inference(rename_variables,[],[4184])). % 177.51/177.24 cnf(13474,plain, % 177.51/177.24 (E(f327(f327(f16(x134741,x134742),x134743),x134744),x134743)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(13478,plain, % 177.51/177.24 (E(f327(f327(f16(x134781,x134782),x134783),x134784),x134783)), % 177.51/177.24 inference(rename_variables,[],[3483])). % 177.51/177.24 cnf(13491,plain, % 177.51/177.24 (P1(f327(f327(f234(a1),f2(a1)),f327(f101(a1),x134911)))), % 177.51/177.24 inference(rename_variables,[],[3592])). % 177.51/177.24 cnf(13496,plain, % 177.51/177.24 (P23(x134961,x134961,f5(x134961),x134962)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13499,plain, % 177.51/177.24 (~P1(f327(f327(f329(x134991),x134992),f190(f922(x134991,a910))))), % 177.51/177.24 inference(rename_variables,[],[4716])). % 177.51/177.24 cnf(13500,plain, % 177.51/177.24 (E(f327(f284(x135001,x135001),f263(x135001,x135002)),x135002)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(13501,plain, % 177.51/177.24 (P23(x135011,x135011,f5(x135011),x135012)), % 177.51/177.24 inference(rename_variables,[],[3729])). % 177.51/177.24 cnf(13505,plain, % 177.51/177.24 (E(f327(f284(x135051,x135051),f263(x135051,x135052)),x135052)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(13510,plain, % 177.51/177.24 (P1(f327(f327(f235(f922(a1,a910)),f303(a1,f78(a1),f2(a1))),f303(a1,f2(a1),f78(a1))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,12906,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,13343,13349,13354,13358,13364,13367,13391,13496,13501,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,12876,13413,13417,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,11351,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3209,3219,3221,3222,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,13214,13382,13500,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,13309,13402,13466,13470,13474,13478,4086,4714,11277,11376,11618,11621,3458,3891,3478,3596,3815,3588,4691,3563,12913,13010,3387,3388,10587,10917,4701,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,11502,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,13416,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,13091,13448,13452,13456,4078,3663,13453,3664,13449,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,12715,13469,4184,13473,4189,11300,12427,12505,12565,12609,13312,13440,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,13282,13348,13353,13373,13394,4724,11046,11456,12569,13361,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,13274,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,13263,13386,13405,13408,13445,13465,13499,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,13430,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,13161,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,4482,3804,11935,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,13342,3939,11216,11222,11240,12239,12369,12450,12740,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,13285,4271,3941,10950,11319,11488,11522,11535,12679,12729,13378,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,12600,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,11135,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,520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2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841,9101,9102,9173,9187,9240,9241,9360,9394,9420,9452,9493,9689,9813,9956,10144,10201,10203,6055,6603,6604,6693,6713,6714,7133,7354,8683,8762,9009,9196,9197,9267,9268,9447,9541,9542,9543,9544,9753,10020,10034,10406,10407,6675,8594])). % 177.51/177.24 cnf(13512,plain, % 177.51/177.24 (P1(f327(f327(f235(f922(a1,a910)),f303(a1,f2(a1),f2(a1))),f303(a1,f327(f79(a1),f327(f101(a1),f327(a113,x135121))),f2(a1))))), % 177.51/177.24 inference(scs_inference,[],[4154,12762,12787,12902,12904,12906,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,13343,13349,13354,13358,13364,13367,13391,13496,13501,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,12876,13413,13417,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,11351,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3209,3219,3221,3222,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,13214,13382,13500,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,13309,13402,13466,13470,13474,13478,4086,4714,11277,11376,11618,11621,3458,3891,3478,3596,3815,3588,4691,3563,12913,13010,3387,3388,10587,10917,4701,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,11502,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,13416,3944,11939,3476,3572,11768,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,13091,13448,13452,13456,4078,3663,13453,3664,13449,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,12715,13469,4184,13473,4189,11300,12427,12505,12565,12609,13312,13440,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,13282,13348,13353,13373,13394,4724,11046,11456,12569,13361,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,13325,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,13274,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,13263,13386,13405,13408,13445,13465,13499,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,13430,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,13161,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,4482,3804,11935,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,13342,3939,11216,11222,11240,12239,12369,12450,12740,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,13285,4271,3941,10950,11319,11488,11522,11535,12679,12729,13378,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,12600,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,11135,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841,9101,9102,9173,9187,9240,9241,9360,9394,9420,9452,9493,9689,9813,9956,10144,10201,10203,6055,6603,6604,6693,6713,6714,7133,7354,8683,8762,9009,9196,9197,9267,9268,9447,9541,9542,9543,9544,9753,10020,10034,10406,10407,6675,8594,8595])). % 177.51/177.24 cnf(13519,plain, % 177.51/177.24 (P1(f327(f327(f234(a915),f2(a915)),x135191))), % 177.51/177.24 inference(rename_variables,[],[3513])). % 177.51/177.24 cnf(13520,plain, % 177.51/177.24 (P1(f327(f327(f235(a915),f2(a915)),f327(a113,x135201)))), % 177.51/177.24 inference(rename_variables,[],[3572])). % 177.51/177.24 cnf(13521,plain, % 177.51/177.24 (E(f327(f284(x135211,x135211),f263(x135211,x135212)),x135212)), % 177.51/177.24 inference(rename_variables,[],[3453])). % 177.51/177.24 cnf(13524,plain, % 177.51/177.24 (P1(f327(f49(f327(f284(x135241,x135241),f263(x135241,f327(f327(f80(a915),f327(f327(f81(a915),f327(f251(a915,a915),f327(f327(f252(a915,a915),f2(a915)),x135242))),f327(a113,f327(f327(f80(a915),x135243),f327(f256(a915,a915),f327(f327(f252(a915,a915),f2(a915)),x135242)))))),f327(f256(a915,a915),f327(f327(f252(a915,a915),f2(a915)),x135242))))),f327(a113,f327(f327(f80(a915),x135243),f327(f256(a915,a915),f327(f327(f252(a915,a915),f2(a915)),x135242))))),f327(f327(f252(a915,a915),f2(a915)),x135242)))), % 177.51/177.25 inference(scs_inference,[],[4154,12762,12787,12902,12904,12906,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,13343,13349,13354,13358,13364,13367,13391,13496,13501,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,12876,13413,13417,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,11351,13437,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3125,3126,3135,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3209,3219,3221,3222,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,13214,13382,13500,13505,13521,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,13309,13402,13466,13470,13474,13478,4086,4714,11277,11376,11618,11621,3458,3891,3478,3596,3815,3588,4691,3563,12913,13010,3387,3388,10587,10917,4701,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,11502,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3673,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,13416,13421,3944,11939,3476,3572,11768,12050,13520,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,13091,13448,13452,13456,4078,3663,13453,3664,13449,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,12715,13469,4184,13473,4189,11300,12427,12505,12565,12609,13312,13440,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,13282,13348,13353,13373,13394,4724,11046,11456,12569,13361,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,13325,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,13274,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,13263,13386,13405,13408,13445,13465,13499,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,13430,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,13161,13433,13519,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,4482,3804,11935,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,13342,3939,11216,11222,11240,12239,12369,12450,12740,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,13285,4271,3941,10950,11319,11488,11522,11535,12679,12729,13378,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,12600,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,11135,13420,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841,9101,9102,9173,9187,9240,9241,9360,9394,9420,9452,9493,9689,9813,9956,10144,10201,10203,6055,6603,6604,6693,6713,6714,7133,7354,8683,8762,9009,9196,9197,9267,9268,9447,9541,9542,9543,9544,9753,10020,10034,10406,10407,6675,8594,8595,9065,9083])). % 177.51/177.25 cnf(13602,plain, % 177.51/177.25 (P1(f327(f327(f235(a1),f2(a1)),f327(f75(a1),f78(a1))))), % 177.51/177.25 inference(scs_inference,[],[4154,12762,12787,12902,12904,12906,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,13343,13349,13354,13358,13364,13367,13391,13496,13501,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,12876,13413,13417,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,11351,13437,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3123,3125,3126,3135,3139,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3209,3219,3221,3222,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,13214,13382,13500,13505,13521,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,13309,13402,13466,13470,13474,13478,4086,4714,11277,11376,11618,11621,3458,3891,3478,3596,3815,3588,4691,3563,12913,13010,3387,3388,10587,10917,4701,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,11502,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3673,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,13416,13421,3944,11939,3476,3572,11768,12050,13520,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,13324,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,13091,13448,13452,13456,4078,3663,13453,3664,13449,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,12715,13469,4184,13473,4189,11300,12427,12505,12565,12609,13312,13440,4190,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,13282,13348,13353,13373,13394,4724,11046,11456,12569,13361,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,13325,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,13274,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,13263,13386,13405,13408,13445,13465,13499,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,13430,13491,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,13161,13433,13519,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,4482,3804,11935,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,13342,3939,11216,11222,11240,12239,12369,12450,12740,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,13285,4271,3941,10950,11319,11488,11522,11535,12679,12729,13378,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,12600,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,11135,13420,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841,9101,9102,9173,9187,9240,9241,9360,9394,9420,9452,9493,9689,9813,9956,10144,10201,10203,6055,6603,6604,6693,6713,6714,7133,7354,8683,8762,9009,9196,9197,9267,9268,9447,9541,9542,9543,9544,9753,10020,10034,10406,10407,6675,8594,8595,9065,9083,10021,10405,4791,4823,4824,4827,4873,4877,4882,4923,5020,5037,5067,5068,5099,5157,5160,5220,5351,5389,5390,5392,5399,5400,5424,5468,5499,5521,5656,5730,5731,5732,5793,5850,5851])). % 177.51/177.25 cnf(13626,plain, % 177.51/177.25 (~P1(f327(f35(x136261),f38(f922(x136261,a910),f242(f922(f922(x136261,a910),a910)))))), % 177.51/177.25 inference(scs_inference,[],[4154,12762,12787,12902,12904,12906,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,13343,13349,13354,13358,13364,13367,13391,13496,13501,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,12876,13413,13417,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,11351,13437,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3123,3125,3126,3135,3139,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3209,3219,3221,3222,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,13214,13382,13500,13505,13521,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,13309,13402,13466,13470,13474,13478,4086,4714,11277,11376,11618,11621,3458,3891,3478,3596,3815,3588,4691,3563,12913,13010,3387,3388,10587,10917,4701,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,11502,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3673,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,13416,13421,3944,11939,3476,3572,11768,12050,13520,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,13324,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,13091,13448,13452,13456,4078,3663,13453,3664,13449,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,12715,13469,4184,13473,4189,11300,12427,12505,12565,12609,13312,13440,4190,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,13282,13348,13353,13373,13394,4724,11046,11456,12569,13361,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,13325,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,13274,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,13263,13386,13405,13408,13445,13465,13499,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,13430,13491,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,13161,13433,13519,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,4482,3804,11935,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,13342,3939,11216,11222,11240,12239,12369,12450,12740,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,13285,4271,3941,10950,11319,11488,11522,11535,12679,12729,13378,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,12600,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,11135,13420,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841,9101,9102,9173,9187,9240,9241,9360,9394,9420,9452,9493,9689,9813,9956,10144,10201,10203,6055,6603,6604,6693,6713,6714,7133,7354,8683,8762,9009,9196,9197,9267,9268,9447,9541,9542,9543,9544,9753,10020,10034,10406,10407,6675,8594,8595,9065,9083,10021,10405,4791,4823,4824,4827,4873,4877,4882,4923,5020,5037,5067,5068,5099,5157,5160,5220,5351,5389,5390,5392,5399,5400,5424,5468,5499,5521,5656,5730,5731,5732,5793,5850,5851,5877,5881,5940,5942,5951,5957,6036,6121,6227,6274,6331,6442])). % 177.51/177.25 cnf(13652,plain, % 177.51/177.25 (~P23(x136521,x136522,f327(f72(x136523,x136522,x136521,f194(x136524,x136525)),f327(f152(x136526),x136527)),f242(f922(x136521,a910)))), % 177.51/177.25 inference(scs_inference,[],[4154,12762,12787,12902,12904,12906,3729,11371,12430,12535,12538,12630,12672,12676,12684,12756,12765,12886,12888,13343,13349,13354,13358,13364,13367,13391,13496,13501,3738,12502,12951,12953,3747,3462,12972,12974,12976,3463,12932,3429,12841,4680,4681,12015,4431,12998,3466,12980,3304,3362,12992,3363,12959,3364,3365,3366,12712,12965,4679,3790,4651,10454,10464,10477,10488,10491,10595,10598,10601,10703,10838,11148,11341,11344,11363,11366,11565,11666,11673,11687,11733,11736,11769,11784,11847,11906,11922,12215,12243,12257,12286,12292,12386,12498,12665,12726,12876,13413,13417,3548,3511,12988,3697,12187,3413,4661,10687,10787,11251,11351,13437,3105,3106,3108,3109,3111,3112,3114,3115,3118,3119,3120,3122,3123,3125,3126,3135,3139,3141,3142,3145,3148,3152,3155,3156,3160,3164,3167,3173,3174,3179,3180,3188,3192,3196,3198,3199,3209,3219,3221,3222,3224,3225,3234,3247,3248,3251,3255,3256,3257,3258,3262,3263,3270,3281,4648,3288,3361,4649,3829,4059,11953,3338,11663,3474,3450,3453,10526,10529,10622,10625,10941,11678,11681,11795,11834,11839,11948,12404,12606,12819,12878,12880,12884,12898,12900,12938,12940,12943,12945,12970,13214,13382,13500,13505,13521,3424,12697,12701,12705,3430,3439,3951,4259,3407,13275,3559,12759,12844,3327,3328,3691,4045,11709,3547,3392,3324,3352,3809,3347,3545,4163,4053,3872,4634,3336,3337,3314,3963,3372,3549,11098,11225,12499,12716,3423,4128,4670,10517,10684,11562,12657,12698,12702,4677,12669,3483,12035,12038,13309,13402,13466,13470,13474,13478,4086,4714,11277,11376,11618,11621,3458,3891,3478,3596,3815,3588,4691,3563,12913,13010,3387,3388,10587,10917,4701,3650,3380,3305,3409,11699,4273,12687,12831,4130,11297,11432,11491,12641,12647,12776,12779,12809,4732,11200,11445,11556,11582,11626,11632,12585,4733,11330,11448,11559,4734,11451,11502,4735,11509,4736,3408,3689,12541,12582,12668,3856,3638,4545,4546,3673,3710,4668,11692,3833,3792,3835,4317,4008,3758,13197,13201,13205,13209,13219,4055,12532,3675,3934,3560,10606,10726,10804,10877,10880,10920,11020,11267,11883,12089,12211,12279,12357,12395,12470,12473,12813,13078,13116,13119,13180,13416,13421,3944,11939,3476,3572,11768,12050,13520,3753,4707,10494,10497,10523,10647,10822,11028,11043,11158,11604,11702,11882,12106,12111,12333,12336,12416,12588,12691,13024,13043,13046,13070,13120,13291,13296,13319,13324,4720,11811,11842,11879,11886,11919,13129,13133,3931,3698,3699,12232,13049,13052,13055,13058,13088,13091,13448,13452,13456,4078,3663,13453,3664,13449,3519,3521,3495,4704,3386,4665,3882,4195,3682,4721,4266,11579,3814,3532,12056,12059,12506,12610,12790,4712,10482,10485,10655,10750,10769,10776,10799,10807,10810,10827,11013,11254,11471,11762,11856,12004,12124,12127,4235,4194,12204,12556,4139,11095,12389,12566,12715,13469,4184,13473,4189,11300,12427,12505,12565,12609,13312,13440,4190,3857,11890,12214,12364,12437,12489,4223,3874,10650,10747,11303,11381,11464,11530,12385,12451,12721,12786,12806,12816,13282,13348,13353,13373,13394,4724,11046,11456,12569,13361,3492,10615,10713,10863,10927,11002,11049,11052,11083,11106,11142,11180,11219,12007,12053,12184,12242,12260,12263,12266,12269,12444,12458,12461,12464,12467,12549,12613,12732,12782,13071,13094,13152,13172,13183,13188,13191,13194,13227,13238,13251,13302,13330,13333,3493,10642,10698,10932,11023,11145,11787,12086,12092,12103,12190,12201,12220,12225,12272,12295,12312,13085,13231,13254,13292,13297,13320,13325,3494,12476,12479,3568,12419,13149,13198,13202,13206,13210,13220,13224,4703,10534,10563,11067,11109,11118,11967,11988,12158,12161,12164,12167,12256,12275,12278,12291,12345,12348,12351,12354,12517,12520,12616,12619,12725,12768,12856,3645,10792,10883,11153,11197,11435,11438,11517,11601,11772,12018,12664,12852,12859,13274,4716,11076,11189,11210,11213,11280,11283,11294,11397,11405,11419,11459,11476,11485,11527,11568,11573,11576,11595,11598,11635,11640,11643,11646,11649,11889,12032,12065,12339,12342,12376,12420,12447,12594,12638,12644,12744,12747,12772,12830,12836,12847,12870,13148,13164,13167,13263,13386,13405,13408,13445,13465,13499,3553,10914,10944,10953,10956,10959,11548,12769,12783,13130,13134,13137,13140,3592,13430,13491,3585,4012,3949,10566,11942,11970,13111,4713,10514,10902,10905,11400,11416,11905,11958,11992,12019,12121,12146,12149,12152,12155,12415,13336,3513,10947,11103,11173,11971,12120,12317,12525,12550,13161,13433,13519,3973,12062,13065,4314,3704,4710,3984,4020,4694,4698,4699,3469,3473,4697,4695,4696,4438,4482,3804,11935,4409,11794,4726,10813,10816,4731,11286,11289,11479,11592,11609,11655,4096,11652,11991,11995,12675,12683,12775,13278,13342,3939,11216,11222,11240,12239,12369,12450,12740,3788,11356,11482,12482,12591,12601,12680,12735,12743,12867,13285,4271,3941,10950,11319,11488,11522,11535,12679,12729,13378,3646,3756,10866,10869,10962,11129,3755,4729,11936,4725,13033,4730,10706,10819,12544,12553,12597,12800,12803,4370,11086,12562,12577,12600,4277,3972,12873,3917,3918,4727,10539,10542,10908,10911,11808,11996,12812,4728,11916,12001,3942,10872,11135,13420,4209,4744,4770,4825,4829,4857,4872,4879,4881,4917,4922,4951,4957,5043,5069,5070,5085,5107,5135,5136,5158,5159,5173,5177,5202,5208,5224,5228,5229,5230,5235,5236,5259,5283,5285,5286,5296,5301,5307,5343,5344,5352,5360,5364,5366,5380,5382,5388,5393,5394,5407,5413,5416,5417,5421,5454,5469,5478,5480,5481,5484,5485,5486,5496,5498,5504,5505,5506,5512,5516,5517,5518,5526,5530,5531,5537,5550,5558,5571,5573,5581,5583,5584,5587,5591,5618,5632,5633,5648,5660,5682,5688,5712,5713,5716,5735,5743,5744,5749,5750,5760,5762,5775,5779,5788,5789,5791,5792,5808,5813,5822,5823,5834,5841,5855,5859,5862,5868,5869,5870,5873,5878,5914,5915,5918,5920,5922,5924,5925,5926,5928,5930,5932,5937,5944,5959,5973,5979,5980,5983,5994,5995,6002,6006,6008,6013,6021,6059,6074,6083,6086,6095,6099,6100,6101,6102,6103,6108,6113,6123,6129,6147,6151,6160,6189,6204,6233,6250,6251,6254,6269,6271,6273,6275,6290,6291,6294,6296,6299,6300,6316,6324,6325,6326,6328,6330,6366,6367,6373,6376,6382,6386,6420,6422,6424,6426,6435,6437,6440,6446,6448,6453,6456,6464,6472,6474,6475,6482,6504,6505,6506,6507,6508,6510,6516,6521,6555,6556,6559,6560,6561,6563,6564,6565,6566,6573,6605,6606,6615,6636,6637,6659,6661,6673,6674,6680,6710,6712,6727,6766,6768,6769,6823,6846,6889,6903,6911,6920,6921,6922,6923,6941,6942,6949,6961,6964,6966,6968,6969,6970,6972,6986,6997,6998,6999,7012,7067,7078,7080,7103,7104,7138,7145,7152,7182,7213,7269,7298,7355,7376,7385,7388,7448,7458,7520,7522,7536,7545,7546,7547,7563,7567,7569,7615,7625,7628,7643,7690,7692,7695,7738,7739,7757,7827,7845,7869,7892,7904,7918,7929,7940,7941,7967,7969,7971,7980,8018,8029,8054,8081,8114,8145,8178,8217,8233,8235,8251,8252,8319,8330,8395,8419,8438,8465,8504,8505,8522,8561,8563,8565,8571,8587,8591,8606,8627,8635,8637,8647,8652,8656,8657,8658,8659,8660,8661,8680,8695,8696,8714,8715,8720,8721,8722,8723,8724,8742,8743,8744,8754,8767,8770,8781,8786,8788,8790,8791,8792,8799,8805,8813,8816,8833,8834,8843,8844,8852,8871,8884,8888,8909,8931,8932,8935,8936,8942,8951,8952,8975,8986,8996,8997,8998,9001,9024,9025,9036,9085,9091,9097,9099,9115,9118,9129,9130,9131,9142,9206,9237,9238,9239,9254,9271,9279,9307,9308,9376,9409,9415,9425,9426,9427,9436,9464,9480,9484,9488,9510,9511,9538,9602,9607,9610,9642,9643,9644,9668,9669,9686,9707,9708,9714,9726,9751,9772,9781,9782,9783,9784,9799,9801,9806,9836,9837,9843,9844,9888,9889,9900,9901,9926,9944,9946,9947,9955,9960,9967,9991,10026,10028,10032,10082,10117,10127,10129,10133,10134,10136,10145,10146,10166,10171,10267,10356,10357,10358,10359,10420,10438,2,12,13,4757,4758,4776,4818,4819,4821,4844,4850,4851,4861,4906,4908,4956,5086,5087,5100,5124,5180,5181,5187,5188,5190,5192,5201,5204,5205,5213,5226,5227,5233,5254,5255,5272,5277,5278,5279,5280,5284,5292,5295,5302,5357,5362,5363,5368,5374,5404,5414,5419,5435,5452,5453,5460,5461,5463,5474,5492,5494,5495,5502,5509,5510,5522,5523,5524,5525,5527,5528,5533,5534,5535,5536,5567,5568,5569,5577,5578,5579,5580,5624,5629,5631,5667,5669,5670,5672,5673,5675,5676,5678,5687,5692,5694,5695,5696,5698,5700,5701,5702,5703,5704,5705,5714,5724,5727,5738,5754,5755,5758,5768,5771,5772,5773,5800,5810,5825,5826,5835,5836,5838,5840,5845,5880,5885,5887,5946,5981,5982,5987,5993,5996,5997,5998,5999,6018,6022,6023,6032,6054,6087,6106,6107,6111,6112,6114,6137,6141,6144,6145,6146,6162,6173,6174,6206,6207,6211,6235,6238,6241,6263,6264,6292,6295,6304,6313,6315,6323,6327,6335,6336,6337,6338,6369,6370,6387,6439,6476,6478,6479,6501,6502,6509,6513,6514,6517,6531,6547,6568,6569,6574,6583,6598,6618,6624,6626,6641,6642,6646,6648,6649,6650,6652,6654,6655,6656,6660,6666,6667,6669,6670,6676,6678,6720,6726,6741,6744,6745,6746,6779,6784,6786,6791,6792,6802,6806,6818,6841,6842,6844,6845,6856,6860,6862,6881,6884,6904,6924,6935,6936,6937,6943,6957,6976,6978,6980,6982,6987,6993,6995,7009,7014,7015,7052,7053,7054,7069,7070,7072,7073,7093,7095,7110,7136,7160,7171,7173,7175,7177,7178,7210,7211,7212,7216,7217,7225,7227,7228,7229,7251,7260,7261,7272,7282,7322,7332,7338,7345,7356,7361,7363,7370,7379,7392,7409,7430,7432,7451,7506,7507,7508,7510,7512,7516,7521,7582,7611,7626,7631,7642,7673,7676,7698,7722,7740,7743,7744,7754,7774,7776,7778,7780,7781,7782,7783,7784,7809,7835,7836,7868,7870,7871,7872,7877,7898,7915,7920,7926,7928,7936,7948,7949,7951,7972,7978,7999,8067,8068,8069,8117,8123,8124,8147,8148,8165,8166,8167,8224,8225,8254,8284,8293,8307,8322,8351,8355,8361,8373,8391,8396,8418,8463,8492,8506,8525,8528,8554,8580,8638,8639,8642,8643,8712,8746,8747,8748,8749,8776,8808,8837,8845,8846,8887,8908,8953,8969,9015,9018,9033,9040,9082,9125,9126,9144,9145,9159,9276,9281,9285,9305,9316,9339,9341,9344,9350,9352,9353,9363,9364,9383,9391,9401,9408,9419,9450,9468,9523,9524,9530,9569,9594,9599,9638,9648,9651,9652,9654,9655,9667,9691,9706,9716,9717,9719,9721,9750,9870,9871,9921,9922,9961,9997,10090,10108,10175,10243,10330,10348,10353,3,2829,2830,2834,2839,2842,2843,2844,2845,2847,2848,2849,2852,2868,2870,2871,2872,2873,2874,2875,2876,2877,2879,2880,2881,2882,2883,2884,2886,2887,2888,2893,2894,2897,2898,2899,2900,2901,2905,2907,2912,2923,2924,2925,2927,2929,2930,2936,2943,2944,2949,2954,2955,2957,2960,2961,2962,2975,2977,2979,2981,2982,2983,2985,2986,2987,2988,2992,2993,3016,3017,3028,3031,3032,3033,3041,3042,3052,3053,3055,3056,3084,5451,5491,5640,5641,5642,5725,5824,5854,5888,5904,5906,5912,5974,5975,5976,5977,5985,6020,6157,6195,6205,6232,6267,6305,6455,6460,6499,6500,6522,6524,6526,6533,6534,6535,6536,6537,6538,6539,6540,6619,6690,6691,6778,6813,6814,6853,6854,6994,7008,7064,7082,7083,7089,7111,7142,7144,7148,7192,7214,7215,7233,7234,7271,7316,7317,7416,7485,7486,7487,7488,7505,7537,7587,7588,7597,7602,7603,7614,7645,7646,7647,7648,7790,7791,7793,7795,7801,7802,8005,8008,8014,8015,8026,8064,8065,8143,8183,8237,8259,8260,8337,8431,8502,8503,8507,8540,8576,8602,8603,8670,8688,8689,8690,8691,8841,9101,9102,9173,9187,9240,9241,9360,9394,9420,9452,9493,9689,9813,9956,10144,10201,10203,6055,6603,6604,6693,6713,6714,7133,7354,8683,8762,9009,9196,9197,9267,9268,9447,9541,9542,9543,9544,9753,10020,10034,10406,10407,6675,8594,8595,9065,9083,10021,10405,4791,4823,4824,4827,4873,4877,4882,4923,5020,5037,5067,5068,5099,5157,5160,5220,5351,5389,5390,5392,5399,5400,5424,5468,5499,5521,5656,5730,5731,5732,5793,5850,5851,5877,5881,5940,5942,5951,5957,6036,6121,6227,6274,6331,6442,6567,6724,6930,7187,7359,7589,7652,7985,7987,8234,8240,8934,9063])). % 177.51/177.25 cnf(13823,plain, % 177.51/177.25 (~E(f327(f327(f152(x138231),x138232),x138233),x138233)), % 177.51/177.25 inference(rename_variables,[],[4670])). % 177.51/177.25 cnf(13832,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),f2(a915)),x138321))), % 177.51/177.25 inference(rename_variables,[],[3513])). % 177.51/177.25 cnf(13835,plain, % 177.51/177.25 (~P1(f327(f327(f329(a915),x138351),f327(f282(a915),f2(a915))))), % 177.51/177.25 inference(rename_variables,[],[12083])). % 177.51/177.25 cnf(13840,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),x138401),f327(f327(f81(a915),x138401),x138401)))), % 177.51/177.25 inference(rename_variables,[],[3756])). % 177.51/177.25 cnf(13850,plain, % 177.51/177.25 (P1(f327(f327(f234(f922(x138501,a910)),f327(f173(x138501),f177(x138501,x138502,x138503))),f327(f173(x138501),x138502)))), % 177.51/177.25 inference(rename_variables,[],[4189])). % 177.51/177.25 cnf(13868,plain, % 177.51/177.25 (E(f327(f284(x138681,x138681),f263(x138681,x138682)),x138682)), % 177.51/177.25 inference(rename_variables,[],[3453])). % 177.51/177.25 cnf(13875,plain, % 177.51/177.25 (~E(f327(f327(f152(x138751),x138752),x138753),x138753)), % 177.51/177.25 inference(rename_variables,[],[4670])). % 177.51/177.25 cnf(13881,plain, % 177.51/177.25 (E(f327(f327(f135(x138811),x138812),f114(x138811)),x138812)), % 177.51/177.25 inference(rename_variables,[],[3424])). % 177.51/177.25 cnf(13893,plain, % 177.51/177.25 (E(f327(f310(x138931,x138931,f31(x138931)),x138932),x138932)), % 177.51/177.25 inference(rename_variables,[],[3550])). % 177.51/177.25 cnf(13896,plain, % 177.51/177.25 (~P1(f327(f327(f329(x138961),x138962),f190(f922(x138961,a910))))), % 177.51/177.25 inference(rename_variables,[],[4716])). % 177.51/177.25 cnf(13901,plain, % 177.51/177.25 (E(f327(f284(x139011,x139011),f263(x139011,x139012)),x139012)), % 177.51/177.25 inference(rename_variables,[],[3453])). % 177.51/177.25 cnf(13904,plain, % 177.51/177.25 (P1(f327(f327(f235(a915),x139041),f327(a113,f327(f327(f80(a915),x139042),x139041))))), % 177.51/177.25 inference(rename_variables,[],[3942])). % 177.51/177.25 cnf(13907,plain, % 177.51/177.25 (P1(f327(f327(f235(a1),f327(f327(f23(a1),x139071),f78(a1))),x139071))), % 177.51/177.25 inference(rename_variables,[],[11022])). % 177.51/177.25 cnf(13921,plain, % 177.51/177.25 (~P1(f327(f327(f329(x139211),x139212),f327(f311(x139211,x139213,x139214),f190(f922(x139213,a910)))))), % 177.51/177.25 inference(rename_variables,[],[11212])). % 177.51/177.25 cnf(13924,plain, % 177.51/177.25 (P1(f327(f327(f234(f922(x139241,a910)),x139242),x139242))), % 177.51/177.25 inference(rename_variables,[],[3788])). % 177.51/177.25 cnf(13931,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),x139311),f327(f327(f81(a915),x139311),x139311)))), % 177.51/177.25 inference(rename_variables,[],[3756])). % 177.51/177.25 cnf(13959,plain, % 177.51/177.25 (E(f327(x139591,f327(f92(x139592,x139593,f242(f922(x139592,a910)),x139591),f327(x139591,x139594))),f327(x139591,x139594))), % 177.51/177.25 inference(rename_variables,[],[11353])). % 177.51/177.25 cnf(13962,plain, % 177.51/177.25 (~P1(f327(f327(f329(x139621),x139622),f190(f922(x139621,a910))))), % 177.51/177.25 inference(rename_variables,[],[4716])). % 177.51/177.25 cnf(13977,plain, % 177.51/177.25 (~E(f327(f327(f309(x139771),x139772),x139773),f190(f922(x139771,a910)))), % 177.51/177.25 inference(rename_variables,[],[4691])). % 177.51/177.25 cnf(13984,plain, % 177.51/177.25 (~E(f327(f327(f152(x139841),x139842),x139843),f114(x139841))), % 177.51/177.25 inference(rename_variables,[],[4677])). % 177.51/177.25 cnf(13989,plain, % 177.51/177.25 (~E(f327(a113,x139891),f2(a915))), % 177.51/177.25 inference(rename_variables,[],[4661])). % 177.51/177.25 cnf(13994,plain, % 177.51/177.25 (~E(f327(f327(f152(x139941),x139942),x139943),x139943)), % 177.51/177.25 inference(rename_variables,[],[4670])). % 177.51/177.25 cnf(14005,plain, % 177.51/177.25 (~P1(f327(f62(x140051,x140052,f190(f922(x140051,a910))),x140053))), % 177.51/177.25 inference(rename_variables,[],[4726])). % 177.51/177.25 cnf(14042,plain, % 177.51/177.25 (P1(f327(f327(f235(a915),x140421),f327(f327(f81(a915),f327(a113,x140421)),f327(a113,x140421))))), % 177.51/177.25 inference(rename_variables,[],[10868])). % 177.51/177.25 cnf(14047,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),x140471),f327(f327(f81(a915),x140471),x140471)))), % 177.51/177.25 inference(rename_variables,[],[3756])). % 177.51/177.25 cnf(14053,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),x140531),f327(f327(f81(a915),x140531),x140531)))), % 177.51/177.25 inference(rename_variables,[],[3756])). % 177.51/177.25 cnf(14056,plain, % 177.51/177.25 (~P1(f327(f327(f329(a915),x140561),f327(f282(a915),f2(a915))))), % 177.51/177.25 inference(rename_variables,[],[12083])). % 177.51/177.25 cnf(14059,plain, % 177.51/177.25 (~P1(f327(f327(f329(f921(x140591,x140591)),x140592),f263(x140591,f190(f922(x140591,a910)))))), % 177.51/177.25 inference(rename_variables,[],[11209])). % 177.51/177.25 cnf(14080,plain, % 177.51/177.25 (E(f327(f284(x140801,x140801),f263(x140801,x140802)),x140802)), % 177.51/177.25 inference(rename_variables,[],[3453])). % 177.51/177.25 cnf(14095,plain, % 177.51/177.25 (~E(f327(f327(f152(x140951),x140952),x140953),x140953)), % 177.51/177.25 inference(rename_variables,[],[4670])). % 177.51/177.25 cnf(14106,plain, % 177.51/177.25 (~E(f327(f327(f152(x141061),x141062),x141063),x141063)), % 177.51/177.25 inference(rename_variables,[],[4670])). % 177.51/177.25 cnf(14115,plain, % 177.51/177.25 (E(f327(x141151,f327(f92(x141152,x141153,f242(f922(x141152,a910)),x141151),f327(x141151,x141154))),f327(x141151,x141154))), % 177.51/177.25 inference(rename_variables,[],[11353])). % 177.51/177.25 cnf(14129,plain, % 177.51/177.25 (~P1(f327(f327(f329(x141291),x141292),f190(f922(x141291,a910))))), % 177.51/177.25 inference(rename_variables,[],[4716])). % 177.51/177.25 cnf(14134,plain, % 177.51/177.25 (P1(f327(f327(f287(a915),x141341),x141341))), % 177.51/177.25 inference(rename_variables,[],[3494])). % 177.51/177.25 cnf(14141,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),x141411),f327(f327(f81(a915),x141411),x141411)))), % 177.51/177.25 inference(rename_variables,[],[3756])). % 177.51/177.25 cnf(14144,plain, % 177.51/177.25 (P1(f327(f327(f234(f922(x141441,a910)),f327(f173(x141441),f177(x141441,x141442,x141443))),f327(f173(x141441),x141442)))), % 177.51/177.25 inference(rename_variables,[],[4189])). % 177.51/177.25 cnf(14160,plain, % 177.51/177.25 (P1(f327(f327(f329(x141601),f327(x141602,x141603)),f327(f310(x141604,x141601,x141602),f242(f922(x141604,a910)))))), % 177.51/177.25 inference(rename_variables,[],[4096])). % 177.51/177.25 cnf(14170,plain, % 177.51/177.25 (~P1(f327(f327(f234(a915),f327(f327(f81(a915),f327(a113,x141701)),f327(a113,x141701))),x141701))), % 177.51/177.25 inference(rename_variables,[],[10961])). % 177.51/177.25 cnf(14175,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),f46(a915,x141751,x141752)),x141751))), % 177.51/177.25 inference(rename_variables,[],[3949])). % 177.51/177.25 cnf(14178,plain, % 177.51/177.25 (P1(f327(f327(f234(a915),x141781),f327(f327(f80(a915),x141781),x141782)))), % 177.51/177.25 inference(rename_variables,[],[3755])). % 177.51/177.25 cnf(14181,plain, % 177.51/177.25 (~P1(f327(f327(f190(f922(x141811,f922(x141812,a910))),x141813),x141814))), % 177.51/177.25 inference(rename_variables,[],[4730])). % 177.51/177.25 cnf(14186,plain, % 177.51/177.25 (~P1(f327(f327(f329(x141861),x141862),f190(f922(x141861,a910))))), % 177.51/177.25 inference(rename_variables,[],[4716])). % 177.51/177.25 cnf(14189,plain, % 177.51/177.25 (~P1(f327(f327(f329(x141891),x141892),f190(f922(x141891,a910))))), % 177.51/177.25 inference(rename_variables,[],[4716])). % 177.51/177.25 cnf(14195,plain, % 177.51/177.25 (~P1(f327(f327(f329(x141951),x141952),f190(f922(x141951,a910))))), % 177.51/177.25 inference(rename_variables,[],[4716])). % 177.51/177.25 cnf(14209,plain, % 177.51/177.25 (P1(f327(f327(f234(f922(x142091,a910)),f327(f173(x142091),f177(x142091,x142092,x142093))),f327(f173(x142091),x142092)))), % 177.51/177.25 inference(rename_variables,[],[4189])). % 177.51/177.25 cnf(14222,plain, % 177.51/177.25 (P1(f327(f327(f329(x142221),f327(x142222,x142223)),f327(f310(x142224,x142221,x142222),f242(f922(x142224,a910)))))), % 177.51/177.25 inference(rename_variables,[],[4096])). % 177.51/177.25 cnf(14248,plain, % 177.51/177.25 (~P1(f327(f327(f329(a915),x142481),f327(f282(a915),f2(a915))))), % 177.51/177.25 inference(rename_variables,[],[12083])). % 177.51/177.25 cnf(14251,plain, % 177.51/177.25 (P1(f327(f327(f287(a915),x142511),x142511))), % 177.51/177.25 inference(rename_variables,[],[3494])). % 177.51/177.25 cnf(14259,plain, % 177.51/177.25 (P1(f327(f327(f235(a1),f327(f327(f23(a1),x142591),f78(a1))),x142591))), % 177.51/177.25 inference(rename_variables,[],[11022])). % 177.51/177.25 cnf(14268,plain, % 177.51/177.25 (~P1(f327(f327(f329(f921(x142681,x142681)),x142682),f263(x142681,f190(f922(x142681,a910)))))), % 177.51/177.25 inference(rename_variables,[],[11209])). % 177.51/177.25 cnf(14275,plain, % 177.51/177.25 (~P1(f327(f327(f329(a915),x142751),f327(f282(a915),f2(a915))))), % 177.51/177.25 inference(rename_variables,[],[12083])). % 177.51/177.25 cnf(14289,plain, % 177.51/177.25 (~P1(f327(f327(f329(x142891),x142892),f327(f311(x142891,x142893,x142894),f190(f922(x142893,a910)))))), % 177.51/177.25 inference(rename_variables,[],[11212])). % 177.51/177.25 cnf(14298,plain, % 177.51/177.25 (~P1(f327(f327(f329(f921(x142981,x142981)),x142982),f263(x142981,f190(f922(x142981,a910)))))), % 177.51/177.25 inference(rename_variables,[],[11209])). % 177.51/177.25 cnf(14308,plain, % 177.51/177.25 (~P1(f327(f327(f329(f921(x143081,x143081)),x143082),f263(x143081,f190(f922(x143081,a910)))))), % 177.51/177.25 inference(rename_variables,[],[11209])). % 177.51/177.25 cnf(14311,plain, % 177.51/177.25 (P1(f327(f327(f234(f922(x143111,a910)),f327(f173(x143111),f177(x143111,x143112,x143113))),f327(f173(x143111),x143112)))), % 177.51/177.25 inference(rename_variables,[],[4189])). % 177.51/177.25 cnf(14320,plain, % 177.51/177.25 (~E(x143201,f327(a113,x143201))), % 177.51/177.25 inference(rename_variables,[],[10549])). % 177.51/177.25 cnf(14336,plain, % 177.51/177.25 (P1(f327(f327(f329(x143361),f327(x143362,x143363)),f327(f310(x143364,x143361,x143362),f242(f922(x143364,a910)))))), % 177.51/177.25 inference(rename_variables,[],[4096])). % 177.51/177.25 cnf(14354,plain, % 177.51/177.25 (P1(f327(f327(f329(x143541),f327(x143542,x143543)),f327(f310(x143544,x143541,x143542),f242(f922(x143544,a910)))))), % 177.51/177.25 inference(rename_variables,[],[4096])). % 177.51/177.25 cnf(14365,plain, % 177.51/177.25 (P1(f327(f327(f234(f922(x143651,a910)),f327(f173(x143651),f177(x143651,x143652,x143653))),f327(f173(x143651),x143652)))), % 177.51/177.25 inference(rename_variables,[],[4189])). % 177.51/177.25 cnf(14379,plain, % 177.51/177.25 (~P1(f327(f327(f329(a915),x143791),f327(f282(a915),f2(a915))))), % 177.51/177.25 inference(rename_variables,[],[12083])). % 177.51/177.25 cnf(14445,plain, % 177.51/177.25 ($false), % 177.51/177.25 inference(scs_inference,[],[3519,3931,3521,4235,4273,4078,3288,3494,14134,14251,4729,4694,3495,4704,4130,3568,4697,3585,3944,4732,4695,4096,14160,14222,14336,14354,4716,13896,13962,14129,14186,14189,14195,4189,13850,14144,14209,14311,14365,3592,4661,13989,4670,13823,13875,13994,14095,14106,4677,13984,4691,13977,3572,3492,3493,3949,14175,3513,13832,3804,3939,3788,13924,3646,3756,13840,13931,14047,14053,14141,3755,14178,4370,3942,13904,3453,13868,13901,14080,3424,13881,3448,4734,4736,4703,4713,4726,14005,4725,4730,14181,4727,4728,11825,10549,14320,13423,10837,10603,12271,13026,12143,12795,13602,13510,10868,14042,13067,13512,10856,13080,11348,12797,12833,11196,13524,11463,11160,11022,13907,14259,12085,4487,3859,12858,11191,11534,11487,11353,13959,14115,13341,11193,11586,10966,3550,13893,3524,3438,11514,11258,13329,10971,11973,12484,12590,12083,13835,14056,14248,14275,14379,11415,11209,14059,14268,14298,14308,11212,13921,14289,11458,11537,10961,14170,12347,12854,11470,13626,13652,11227,11368,10946,10949,3097,11888,4046,2,12,5107,7138,5937,6275,9799,6930,4951,7080,5478,5979,7448,8565,5296,6328,6474,6563,7536,9001,9946,4917,7520,8723,7625,9464,5236,7104,9714,5980,6846,7182,9836,10127,8251,8627,5994,6382,9270,7941,8659,5928,7967,9480,9510,5573,6961,8054,6151,6108,6147,6968,8591,5400,5633,5730,5869,6659,7145,8647,6941,8235,6521,7971,5504,5550,9843,5743,6567,5750,5660,9844,6922,8843,6099,7845,5834,5069,5688,6680,5208,8722,9307,6274,5480,6448,8792,5499,5862,6823,6386,7563,8934,6074,6300,5618,7918,5228,6949,8975,10357,5043,6573,7269,5468,6331,5417,5648,6555,8935,9118,9783,6036,6002,8742,5481,6273,5498,8951,5583,6189,7522,9376,4791,4827,8786,7980,5571,6999,9130,9237,7738,5506,6290,8029,8217,8833,6330,8996,7940,9751,6564,8799,10032,10136,5486,6422,5220,6673,6516,6942,6969,9643,10028,6101,10166,5352,8419,5530,8233,9668,9024,9669,5159,5413,5762,6710,8637,8909,9505,6376,8438,5868,6326,6442,7892,8635,9900,5822,8395,9837,5926,6123,7546,9991,6970,9784,7012,5099,5881,4881,5235,6998,9426,9602,7298,9708,5944,7904,9926,10356,7152,5424,5855,8587,8852,9607,5158,6324,6661,4823,9782,7643,10082,5343,5915,8561,8081,5469,7695,5584,6637,7757,8145,9025,9099,9409,5389,5394,7569,9901,5136,6233,8952,9538,9239,6366,6712,8888,7359,5496,6420,8791,10267,13,5789,6606,8714,9888,7969,6103,7567,5351,6505,6083,7103,9425,4857]), % 177.51/177.25 ['proof']). % 177.51/177.25 % SZS output end Proof % 177.51/177.25 % Total time :162.200000s %------------------------------------------------------------------------------